id	sid	tid	token	lemma	pos
cord-004615-xfi3p601	1	1	key	key	JJ
cord-004615-xfi3p601	2	1	:	:	:
cord-004615-xfi3p601	2	2	cord-004615-xfi3p601	cord-004615-xfi3p601	LS
cord-004615-xfi3p601	2	3	authors	author	NNS
cord-004615-xfi3p601	2	4	:	:	:
cord-004615-xfi3p601	3	1	Trapman	Trapman	NNP
cord-004615-xfi3p601	3	2	,	,	,
cord-004615-xfi3p601	3	3	Pieter	Pieter	NNP
cord-004615-xfi3p601	3	4	;	;	:
cord-004615-xfi3p601	3	5	Meester	Meester	NNP
cord-004615-xfi3p601	3	6	,	,	,
cord-004615-xfi3p601	3	7	Ronald	Ronald	NNP
cord-004615-xfi3p601	3	8	;	;	:
cord-004615-xfi3p601	3	9	Heesterbeek	Heesterbeek	NNP
cord-004615-xfi3p601	3	10	,	,	,
cord-004615-xfi3p601	4	1	Hans	Hans	NNP
cord-004615-xfi3p601	4	2	title	title	NN
cord-004615-xfi3p601	4	3	:	:	:
cord-004615-xfi3p601	5	1	A	a	DT
cord-004615-xfi3p601	5	2	branching	branching	JJ
cord-004615-xfi3p601	5	3	model	model	NN
cord-004615-xfi3p601	5	4	for	for	IN
cord-004615-xfi3p601	5	5	the	the	DT
cord-004615-xfi3p601	5	6	spread	spread	NN
cord-004615-xfi3p601	5	7	of	of	IN
cord-004615-xfi3p601	5	8	infectious	infectious	JJ
cord-004615-xfi3p601	5	9	animal	animal	NN
cord-004615-xfi3p601	5	10	diseases	disease	NNS
cord-004615-xfi3p601	5	11	in	in	IN
cord-004615-xfi3p601	5	12	varying	vary	VBG
cord-004615-xfi3p601	5	13	environments	environment	NNS
cord-004615-xfi3p601	5	14	date	date	NN
cord-004615-xfi3p601	5	15	:	:	:
cord-004615-xfi3p601	5	16	2004	2004	CD
cord-004615-xfi3p601	5	17	-	-	HYPH
cord-004615-xfi3p601	5	18	03	03	CD
cord-004615-xfi3p601	5	19	-	-	HYPH
cord-004615-xfi3p601	5	20	03	03	CD
cord-004615-xfi3p601	5	21	journal	journal	NN
cord-004615-xfi3p601	5	22	:	:	:
cord-004615-xfi3p601	5	23	J	J	NNP
cord-004615-xfi3p601	5	24	Math	Math	NNP
cord-004615-xfi3p601	5	25	Biol	Biol	NNP
cord-004615-xfi3p601	6	1	DOI	DOI	NNP
cord-004615-xfi3p601	6	2	:	:	:
cord-004615-xfi3p601	6	3	10.1007	10.1007	CD
cord-004615-xfi3p601	6	4	/	/	SYM
cord-004615-xfi3p601	6	5	s00285	s00285	NN
cord-004615-xfi3p601	6	6	-	-	HYPH
cord-004615-xfi3p601	6	7	004	004	CD
cord-004615-xfi3p601	6	8	-	-	HYPH
cord-004615-xfi3p601	6	9	0267	0267	CD
cord-004615-xfi3p601	6	10	-	-	SYM
cord-004615-xfi3p601	6	11	5	5	CD
cord-004615-xfi3p601	6	12	sha	sha	NNP
cord-004615-xfi3p601	6	13	:	:	:
cord-004615-xfi3p601	7	1	6353f50ebc75a4f88524d38c0311250f692e3b7e	6353f50ebc75a4f88524d38c0311250f692e3b7e	CD
cord-004615-xfi3p601	8	1	doc_id	doc_id	CD
cord-004615-xfi3p601	8	2	:	:	:
cord-004615-xfi3p601	8	3	4615	4615	CD
cord-004615-xfi3p601	8	4	cord_uid	cord_uid	NNS
cord-004615-xfi3p601	8	5	:	:	:
cord-004615-xfi3p601	9	1	xfi3p601	xfi3p601	NNP
cord-004615-xfi3p601	10	1	This	this	DT
cord-004615-xfi3p601	10	2	paper	paper	NN
cord-004615-xfi3p601	10	3	is	be	VBZ
cord-004615-xfi3p601	10	4	concerned	concern	VBN
cord-004615-xfi3p601	10	5	with	with	IN
cord-004615-xfi3p601	10	6	a	a	DT
cord-004615-xfi3p601	10	7	stochastic	stochastic	JJ
cord-004615-xfi3p601	10	8	model	model	NN
cord-004615-xfi3p601	10	9	,	,	,
cord-004615-xfi3p601	10	10	describing	describe	VBG
cord-004615-xfi3p601	10	11	outbreaks	outbreak	NNS
cord-004615-xfi3p601	10	12	of	of	IN
cord-004615-xfi3p601	10	13	infectious	infectious	JJ
cord-004615-xfi3p601	10	14	diseases	disease	NNS
cord-004615-xfi3p601	10	15	that	that	WDT
cord-004615-xfi3p601	10	16	have	have	VBP
cord-004615-xfi3p601	10	17	potentially	potentially	RB
cord-004615-xfi3p601	10	18	great	great	JJ
cord-004615-xfi3p601	10	19	animal	animal	NN
cord-004615-xfi3p601	10	20	or	or	CC
cord-004615-xfi3p601	10	21	human	human	JJ
cord-004615-xfi3p601	10	22	health	health	NN
cord-004615-xfi3p601	10	23	consequences	consequence	NNS
cord-004615-xfi3p601	10	24	,	,	,
cord-004615-xfi3p601	10	25	and	and	CC
cord-004615-xfi3p601	10	26	which	which	WDT
cord-004615-xfi3p601	10	27	can	can	MD
cord-004615-xfi3p601	10	28	result	result	VB
cord-004615-xfi3p601	10	29	in	in	IN
cord-004615-xfi3p601	10	30	such	such	JJ
cord-004615-xfi3p601	10	31	severe	severe	JJ
cord-004615-xfi3p601	10	32	economic	economic	JJ
cord-004615-xfi3p601	10	33	losses	loss	NNS
cord-004615-xfi3p601	10	34	that	that	WDT
cord-004615-xfi3p601	10	35	immediate	immediate	JJ
cord-004615-xfi3p601	10	36	sets	set	NNS
cord-004615-xfi3p601	10	37	of	of	IN
cord-004615-xfi3p601	10	38	measures	measure	NNS
cord-004615-xfi3p601	10	39	need	need	VBP
cord-004615-xfi3p601	10	40	to	to	TO
cord-004615-xfi3p601	10	41	be	be	VB
cord-004615-xfi3p601	10	42	taken	take	VBN
cord-004615-xfi3p601	10	43	to	to	TO
cord-004615-xfi3p601	10	44	curb	curb	VB
cord-004615-xfi3p601	10	45	the	the	DT
cord-004615-xfi3p601	10	46	spread	spread	NN
cord-004615-xfi3p601	10	47	.	.	.
cord-004615-xfi3p601	11	1	During	during	IN
cord-004615-xfi3p601	11	2	an	an	DT
cord-004615-xfi3p601	11	3	outbreak	outbreak	NN
cord-004615-xfi3p601	11	4	of	of	IN
cord-004615-xfi3p601	11	5	such	such	PDT
cord-004615-xfi3p601	11	6	a	a	DT
cord-004615-xfi3p601	11	7	disease	disease	NN
cord-004615-xfi3p601	11	8	,	,	,
cord-004615-xfi3p601	11	9	the	the	DT
cord-004615-xfi3p601	11	10	environment	environment	NN
cord-004615-xfi3p601	11	11	that	that	WDT
cord-004615-xfi3p601	11	12	the	the	DT
cord-004615-xfi3p601	11	13	infectious	infectious	JJ
cord-004615-xfi3p601	11	14	agent	agent	NN
cord-004615-xfi3p601	11	15	experiences	experience	NNS
cord-004615-xfi3p601	11	16	is	be	VBZ
cord-004615-xfi3p601	11	17	therefore	therefore	RB
cord-004615-xfi3p601	11	18	changing	change	VBG
cord-004615-xfi3p601	11	19	due	due	IN
cord-004615-xfi3p601	11	20	to	to	IN
cord-004615-xfi3p601	11	21	the	the	DT
cord-004615-xfi3p601	11	22	subsequent	subsequent	JJ
cord-004615-xfi3p601	11	23	control	control	NN
cord-004615-xfi3p601	11	24	measures	measure	NNS
cord-004615-xfi3p601	11	25	taken	take	VBN
cord-004615-xfi3p601	11	26	.	.	.
cord-004615-xfi3p601	12	1	In	in	IN
cord-004615-xfi3p601	12	2	our	-PRON-	PRP$
cord-004615-xfi3p601	12	3	model	model	NN
cord-004615-xfi3p601	12	4	,	,	,
cord-004615-xfi3p601	12	5	we	-PRON-	PRP
cord-004615-xfi3p601	12	6	introduce	introduce	VBP
cord-004615-xfi3p601	12	7	a	a	DT
cord-004615-xfi3p601	12	8	general	general	JJ
cord-004615-xfi3p601	12	9	branching	branching	NN
cord-004615-xfi3p601	12	10	process	process	NN
cord-004615-xfi3p601	12	11	in	in	IN
cord-004615-xfi3p601	12	12	a	a	DT
cord-004615-xfi3p601	12	13	changing	changing	NN
cord-004615-xfi3p601	12	14	(	(	-LRB-
cord-004615-xfi3p601	12	15	but	but	CC
cord-004615-xfi3p601	12	16	not	not	RB
cord-004615-xfi3p601	12	17	random	random	JJ
cord-004615-xfi3p601	12	18	)	)	-RRB-
cord-004615-xfi3p601	12	19	environment	environment	NN
cord-004615-xfi3p601	12	20	.	.	.
cord-004615-xfi3p601	13	1	With	with	IN
cord-004615-xfi3p601	13	2	this	this	DT
cord-004615-xfi3p601	13	3	branching	branching	NN
cord-004615-xfi3p601	13	4	process	process	NN
cord-004615-xfi3p601	13	5	,	,	,
cord-004615-xfi3p601	13	6	we	-PRON-	PRP
cord-004615-xfi3p601	13	7	estimate	estimate	VBP
cord-004615-xfi3p601	13	8	the	the	DT
cord-004615-xfi3p601	13	9	probability	probability	NN
cord-004615-xfi3p601	13	10	of	of	IN
cord-004615-xfi3p601	13	11	extinction	extinction	NN
cord-004615-xfi3p601	13	12	and	and	CC
cord-004615-xfi3p601	13	13	the	the	DT
cord-004615-xfi3p601	13	14	expected	expect	VBN
cord-004615-xfi3p601	13	15	number	number	NN
cord-004615-xfi3p601	13	16	of	of	IN
cord-004615-xfi3p601	13	17	infected	infected	JJ
cord-004615-xfi3p601	13	18	individuals	individual	NNS
cord-004615-xfi3p601	13	19	for	for	IN
cord-004615-xfi3p601	13	20	different	different	JJ
cord-004615-xfi3p601	13	21	control	control	NN
cord-004615-xfi3p601	13	22	measures	measure	NNS
cord-004615-xfi3p601	13	23	.	.	.
cord-004615-xfi3p601	14	1	We	-PRON-	PRP
cord-004615-xfi3p601	14	2	also	also	RB
cord-004615-xfi3p601	14	3	use	use	VBP
cord-004615-xfi3p601	14	4	this	this	DT
cord-004615-xfi3p601	14	5	branching	branch	VBG
cord-004615-xfi3p601	14	6	process	process	NN
cord-004615-xfi3p601	14	7	to	to	TO
cord-004615-xfi3p601	14	8	calculate	calculate	VB
cord-004615-xfi3p601	14	9	the	the	DT
cord-004615-xfi3p601	14	10	generating	generate	VBG
cord-004615-xfi3p601	14	11	function	function	NN
cord-004615-xfi3p601	14	12	of	of	IN
cord-004615-xfi3p601	14	13	the	the	DT
cord-004615-xfi3p601	14	14	number	number	NN
cord-004615-xfi3p601	14	15	of	of	IN
cord-004615-xfi3p601	14	16	infected	infected	JJ
cord-004615-xfi3p601	14	17	individuals	individual	NNS
cord-004615-xfi3p601	14	18	at	at	IN
cord-004615-xfi3p601	14	19	any	any	DT
cord-004615-xfi3p601	14	20	given	give	VBN
cord-004615-xfi3p601	14	21	moment	moment	NN
cord-004615-xfi3p601	14	22	.	.	.
cord-004615-xfi3p601	15	1	The	the	DT
cord-004615-xfi3p601	15	2	model	model	NN
cord-004615-xfi3p601	15	3	and	and	CC
cord-004615-xfi3p601	15	4	methods	method	NNS
cord-004615-xfi3p601	15	5	are	be	VBP
cord-004615-xfi3p601	15	6	designed	design	VBN
cord-004615-xfi3p601	15	7	using	use	VBG
cord-004615-xfi3p601	15	8	important	important	JJ
cord-004615-xfi3p601	15	9	infections	infection	NNS
cord-004615-xfi3p601	15	10	of	of	IN
cord-004615-xfi3p601	15	11	farmed	farm	VBN
cord-004615-xfi3p601	15	12	animals	animal	NNS
cord-004615-xfi3p601	15	13	,	,	,
cord-004615-xfi3p601	15	14	such	such	JJ
cord-004615-xfi3p601	15	15	as	as	IN
cord-004615-xfi3p601	15	16	classical	classical	JJ
cord-004615-xfi3p601	15	17	swine	swine	NN
cord-004615-xfi3p601	15	18	fever	fever	NN
cord-004615-xfi3p601	15	19	,	,	,
cord-004615-xfi3p601	15	20	foot	foot	NN
cord-004615-xfi3p601	15	21	-	-	HYPH
cord-004615-xfi3p601	15	22	and	and	CC
cord-004615-xfi3p601	15	23	-	-	HYPH
cord-004615-xfi3p601	15	24	mouth	mouth	NN
cord-004615-xfi3p601	15	25	disease	disease	NN
cord-004615-xfi3p601	15	26	and	and	CC
cord-004615-xfi3p601	15	27	avian	avian	JJ
cord-004615-xfi3p601	15	28	influenza	influenza	NN
cord-004615-xfi3p601	15	29	as	as	IN
cord-004615-xfi3p601	15	30	motivating	motivate	VBG
cord-004615-xfi3p601	15	31	examples	example	NNS
cord-004615-xfi3p601	15	32	,	,	,
cord-004615-xfi3p601	15	33	but	but	CC
cord-004615-xfi3p601	15	34	have	have	VBP
cord-004615-xfi3p601	15	35	a	a	DT
cord-004615-xfi3p601	15	36	wider	wide	JJR
cord-004615-xfi3p601	15	37	application	application	NN
cord-004615-xfi3p601	15	38	,	,	,
cord-004615-xfi3p601	15	39	for	for	IN
cord-004615-xfi3p601	15	40	example	example	NN
cord-004615-xfi3p601	15	41	to	to	IN
cord-004615-xfi3p601	15	42	emerging	emerge	VBG
cord-004615-xfi3p601	15	43	human	human	JJ
cord-004615-xfi3p601	15	44	infections	infection	NNS
cord-004615-xfi3p601	15	45	that	that	WDT
cord-004615-xfi3p601	15	46	lead	lead	VBP
cord-004615-xfi3p601	15	47	to	to	IN
cord-004615-xfi3p601	15	48	strict	strict	JJ
cord-004615-xfi3p601	15	49	quarantine	quarantine	NN
cord-004615-xfi3p601	15	50	of	of	IN
cord-004615-xfi3p601	15	51	cases	case	NNS
cord-004615-xfi3p601	15	52	and	and	CC
cord-004615-xfi3p601	15	53	suspected	suspect	VBN
cord-004615-xfi3p601	15	54	cases	case	NNS
cord-004615-xfi3p601	15	55	(	(	-LRB-
cord-004615-xfi3p601	15	56	e.g.	e.g.	IN
cord-004615-xfi3p601	15	57	SARS	SARS	NNP
cord-004615-xfi3p601	15	58	)	)	-RRB-
cord-004615-xfi3p601	15	59	and	and	CC
cord-004615-xfi3p601	15	60	contact	contact	NN
cord-004615-xfi3p601	15	61	and	and	CC
cord-004615-xfi3p601	15	62	movement	movement	NN
cord-004615-xfi3p601	15	63	restrictions	restriction	NNS
cord-004615-xfi3p601	15	64	.	.	.
cord-004615-xfi3p601	16	1	Recent	recent	JJ
cord-004615-xfi3p601	16	2	outbreaks	outbreak	NNS
cord-004615-xfi3p601	16	3	of	of	IN
cord-004615-xfi3p601	16	4	infectious	infectious	JJ
cord-004615-xfi3p601	16	5	diseases	disease	NNS
cord-004615-xfi3p601	16	6	of	of	IN
cord-004615-xfi3p601	16	7	animals	animal	NNS
cord-004615-xfi3p601	16	8	(	(	-LRB-
cord-004615-xfi3p601	16	9	e.g.	e.g.	IN
cord-004615-xfi3p601	16	10	classical	classical	JJ
cord-004615-xfi3p601	16	11	swine	swine	NN
cord-004615-xfi3p601	16	12	fever	fever	NN
cord-004615-xfi3p601	16	13	(	(	-LRB-
cord-004615-xfi3p601	16	14	CSF	CSF	NNP
cord-004615-xfi3p601	16	15	)	)	-RRB-
cord-004615-xfi3p601	16	16	,	,	,
cord-004615-xfi3p601	16	17	foot	foot	NN
cord-004615-xfi3p601	16	18	and	and	CC
cord-004615-xfi3p601	16	19	mouth	mouth	NN
cord-004615-xfi3p601	16	20	disease	disease	NN
cord-004615-xfi3p601	16	21	(	(	-LRB-
cord-004615-xfi3p601	16	22	FMD	FMD	NNP
cord-004615-xfi3p601	16	23	)	)	-RRB-
cord-004615-xfi3p601	16	24	and	and	CC
cord-004615-xfi3p601	16	25	avian	avian	JJ
cord-004615-xfi3p601	16	26	influenza	influenza	NN
cord-004615-xfi3p601	16	27	(	(	-LRB-
cord-004615-xfi3p601	16	28	AI	AI	NNP
cord-004615-xfi3p601	16	29	)	)	-RRB-
cord-004615-xfi3p601	16	30	)	)	-RRB-
cord-004615-xfi3p601	16	31	in	in	IN
cord-004615-xfi3p601	16	32	Western	Western	NNP
cord-004615-xfi3p601	16	33	Europe	Europe	NNP
cord-004615-xfi3p601	16	34	have	have	VBP
cord-004615-xfi3p601	16	35	had	have	VBN
cord-004615-xfi3p601	16	36	great	great	JJ
cord-004615-xfi3p601	16	37	impact	impact	NN
cord-004615-xfi3p601	16	38	on	on	IN
cord-004615-xfi3p601	16	39	the	the	DT
cord-004615-xfi3p601	16	40	economy	economy	NN
cord-004615-xfi3p601	16	41	,	,	,
cord-004615-xfi3p601	16	42	public	public	JJ
cord-004615-xfi3p601	16	43	life	life	NN
cord-004615-xfi3p601	16	44	and	and	CC
cord-004615-xfi3p601	16	45	animal	animal	NN
cord-004615-xfi3p601	16	46	health	health	NN
cord-004615-xfi3p601	16	47	and	and	CC
cord-004615-xfi3p601	16	48	welfare	welfare	NN
cord-004615-xfi3p601	16	49	in	in	IN
cord-004615-xfi3p601	16	50	the	the	DT
cord-004615-xfi3p601	16	51	countries	country	NNS
cord-004615-xfi3p601	16	52	involved	involve	VBN
cord-004615-xfi3p601	16	53	.	.	.
cord-004615-xfi3p601	17	1	During	during	IN
cord-004615-xfi3p601	17	2	such	such	PDT
cord-004615-xfi3p601	17	3	an	an	DT
cord-004615-xfi3p601	17	4	outbreak	outbreak	NN
cord-004615-xfi3p601	17	5	one	one	PRP
cord-004615-xfi3p601	17	6	would	would	MD
cord-004615-xfi3p601	17	7	like	like	VB
cord-004615-xfi3p601	17	8	to	to	TO
cord-004615-xfi3p601	17	9	be	be	VB
cord-004615-xfi3p601	17	10	able	able	JJ
cord-004615-xfi3p601	17	11	to	to	TO
cord-004615-xfi3p601	17	12	compare	compare	VB
cord-004615-xfi3p601	17	13	the	the	DT
cord-004615-xfi3p601	17	14	effectiveness	effectiveness	NN
cord-004615-xfi3p601	17	15	of	of	IN
cord-004615-xfi3p601	17	16	proposed	propose	VBN
cord-004615-xfi3p601	17	17	control	control	NN
cord-004615-xfi3p601	17	18	measures	measure	NNS
cord-004615-xfi3p601	17	19	in	in	RP
cord-004615-xfi3p601	17	20	,	,	,
cord-004615-xfi3p601	17	21	for	for	IN
cord-004615-xfi3p601	17	22	example	example	NN
cord-004615-xfi3p601	17	23	,	,	,
cord-004615-xfi3p601	17	24	their	-PRON-	PRP$
cord-004615-xfi3p601	17	25	ability	ability	NN
cord-004615-xfi3p601	17	26	to	to	TO
cord-004615-xfi3p601	17	27	reduce	reduce	VB
cord-004615-xfi3p601	17	28	the	the	DT
cord-004615-xfi3p601	17	29	expected	expect	VBN
cord-004615-xfi3p601	17	30	final	final	JJ
cord-004615-xfi3p601	17	31	size	size	NN
cord-004615-xfi3p601	17	32	and	and	CC
cord-004615-xfi3p601	17	33	the	the	DT
cord-004615-xfi3p601	17	34	expected	expect	VBN
cord-004615-xfi3p601	17	35	duration	duration	NN
cord-004615-xfi3p601	17	36	of	of	IN
cord-004615-xfi3p601	17	37	the	the	DT
cord-004615-xfi3p601	17	38	outbreak	outbreak	NN
cord-004615-xfi3p601	17	39	.	.	.
cord-004615-xfi3p601	18	1	Typical	typical	JJ
cord-004615-xfi3p601	18	2	for	for	IN
cord-004615-xfi3p601	18	3	the	the	DT
cord-004615-xfi3p601	18	4	strategies	strategy	NNS
cord-004615-xfi3p601	18	5	aimed	aim	VBN
cord-004615-xfi3p601	18	6	at	at	IN
cord-004615-xfi3p601	18	7	stopping	stop	VBG
cord-004615-xfi3p601	18	8	outbreaks	outbreak	NNS
cord-004615-xfi3p601	18	9	of	of	IN
cord-004615-xfi3p601	18	10	important	important	JJ
cord-004615-xfi3p601	18	11	diseases	disease	NNS
cord-004615-xfi3p601	18	12	of	of	IN
cord-004615-xfi3p601	18	13	farm	farm	NN
cord-004615-xfi3p601	18	14	animals	animal	NNS
cord-004615-xfi3p601	18	15	,	,	,
cord-004615-xfi3p601	18	16	is	be	VBZ
cord-004615-xfi3p601	18	17	that	that	IN
cord-004615-xfi3p601	18	18	infected	infected	JJ
cord-004615-xfi3p601	18	19	herds	herd	NNS
cord-004615-xfi3p601	18	20	are	be	VBP
cord-004615-xfi3p601	18	21	removed	remove	VBN
cord-004615-xfi3p601	18	22	from	from	IN
cord-004615-xfi3p601	18	23	the	the	DT
cord-004615-xfi3p601	18	24	population	population	NN
cord-004615-xfi3p601	18	25	by	by	IN
cord-004615-xfi3p601	18	26	culling	cull	VBG
cord-004615-xfi3p601	18	27	upon	upon	IN
cord-004615-xfi3p601	18	28	detection	detection	NN
cord-004615-xfi3p601	18	29	.	.	.
cord-004615-xfi3p601	19	1	A	a	DT
cord-004615-xfi3p601	19	2	second	second	JJ
cord-004615-xfi3p601	19	3	characteristic	characteristic	NN
cord-004615-xfi3p601	19	4	is	be	VBZ
cord-004615-xfi3p601	19	5	that	that	IN
cord-004615-xfi3p601	19	6	due	due	IN
cord-004615-xfi3p601	19	7	to	to	IN
cord-004615-xfi3p601	19	8	increasing	increase	VBG
cord-004615-xfi3p601	19	9	quantity	quantity	NN
cord-004615-xfi3p601	19	10	and	and	CC
cord-004615-xfi3p601	19	11	quality	quality	NN
cord-004615-xfi3p601	19	12	of	of	IN
cord-004615-xfi3p601	19	13	the	the	DT
cord-004615-xfi3p601	19	14	imposed	impose	VBN
cord-004615-xfi3p601	19	15	control	control	NN
cord-004615-xfi3p601	19	16	measures	measure	NNS
cord-004615-xfi3p601	19	17	,	,	,
cord-004615-xfi3p601	19	18	the	the	DT
cord-004615-xfi3p601	19	19	environment	environment	NN
cord-004615-xfi3p601	19	20	that	that	WDT
cord-004615-xfi3p601	19	21	the	the	DT
cord-004615-xfi3p601	19	22	infectious	infectious	JJ
cord-004615-xfi3p601	19	23	agent	agent	NN
cord-004615-xfi3p601	19	24	experiences	experience	NNS
cord-004615-xfi3p601	19	25	,	,	,
cord-004615-xfi3p601	19	26	is	be	VBZ
cord-004615-xfi3p601	19	27	changing	change	VBG
cord-004615-xfi3p601	19	28	.	.	.
cord-004615-xfi3p601	20	1	By	by	IN
cord-004615-xfi3p601	20	2	this	this	DT
cord-004615-xfi3p601	20	3	we	-PRON-	PRP
cord-004615-xfi3p601	20	4	mean	mean	VBP
cord-004615-xfi3p601	20	5	that	that	IN
cord-004615-xfi3p601	20	6	consecutive	consecutive	JJ
cord-004615-xfi3p601	20	7	measures	measure	NNS
cord-004615-xfi3p601	20	8	can	can	MD
cord-004615-xfi3p601	20	9	make	make	VB
cord-004615-xfi3p601	20	10	,	,	,
cord-004615-xfi3p601	20	11	for	for	IN
cord-004615-xfi3p601	20	12	example	example	NN
cord-004615-xfi3p601	20	13	,	,	,
cord-004615-xfi3p601	20	14	contact	contact	NN
cord-004615-xfi3p601	20	15	opportunities	opportunity	NNS
cord-004615-xfi3p601	20	16	between	between	IN
cord-004615-xfi3p601	20	17	herds	herd	NNS
cord-004615-xfi3p601	20	18	different	different	JJ
cord-004615-xfi3p601	20	19	in	in	IN
cord-004615-xfi3p601	20	20	different	different	JJ
cord-004615-xfi3p601	20	21	phases	phase	NNS
cord-004615-xfi3p601	20	22	of	of	IN
cord-004615-xfi3p601	20	23	the	the	DT
cord-004615-xfi3p601	20	24	outbreak	outbreak	NN
cord-004615-xfi3p601	20	25	,	,	,
cord-004615-xfi3p601	20	26	or	or	CC
cord-004615-xfi3p601	20	27	can	can	MD
cord-004615-xfi3p601	20	28	make	make	VB
cord-004615-xfi3p601	20	29	the	the	DT
cord-004615-xfi3p601	20	30	infectious	infectious	JJ
cord-004615-xfi3p601	20	31	period	period	NN
cord-004615-xfi3p601	20	32	,	,	,
cord-004615-xfi3p601	20	33	or	or	CC
cord-004615-xfi3p601	20	34	rate	rate	NN
cord-004615-xfi3p601	20	35	with	with	IN
cord-004615-xfi3p601	20	36	which	which	WDT
cord-004615-xfi3p601	20	37	infectivity	infectivity	NN
cord-004615-xfi3p601	20	38	is	be	VBZ
cord-004615-xfi3p601	20	39	produced	produce	VBN
cord-004615-xfi3p601	20	40	,	,	,
cord-004615-xfi3p601	20	41	differ	differ	VBP
cord-004615-xfi3p601	20	42	for	for	IN
cord-004615-xfi3p601	20	43	farms	farm	NNS
cord-004615-xfi3p601	20	44	infected	infect	VBN
cord-004615-xfi3p601	20	45	at	at	IN
cord-004615-xfi3p601	20	46	different	different	JJ
cord-004615-xfi3p601	20	47	times	time	NNS
cord-004615-xfi3p601	20	48	.	.	.
cord-004615-xfi3p601	21	1	In	in	IN
cord-004615-xfi3p601	21	2	most	most	JJS
cord-004615-xfi3p601	21	3	cases	case	NNS
cord-004615-xfi3p601	21	4	,	,	,
cord-004615-xfi3p601	21	5	mathematical	mathematical	JJ
cord-004615-xfi3p601	21	6	methods	method	NNS
cord-004615-xfi3p601	21	7	for	for	IN
cord-004615-xfi3p601	21	8	computing	compute	VBG
cord-004615-xfi3p601	21	9	outbreak	outbreak	NN
cord-004615-xfi3p601	21	10	characteristics	characteristic	NNS
cord-004615-xfi3p601	21	11	such	such	JJ
cord-004615-xfi3p601	21	12	as	as	IN
cord-004615-xfi3p601	21	13	expected	expect	VBN
cord-004615-xfi3p601	21	14	final	final	JJ
cord-004615-xfi3p601	21	15	size	size	NN
cord-004615-xfi3p601	21	16	and	and	CC
cord-004615-xfi3p601	21	17	expected	expect	VBN
cord-004615-xfi3p601	21	18	duration	duration	NN
cord-004615-xfi3p601	21	19	,	,	,
cord-004615-xfi3p601	21	20	assume	assume	VB
cord-004615-xfi3p601	21	21	a	a	DT
cord-004615-xfi3p601	21	22	constant	constant	JJ
cord-004615-xfi3p601	21	23	environment	environment	NN
cord-004615-xfi3p601	21	24	in	in	IN
cord-004615-xfi3p601	21	25	that	that	IN
cord-004615-xfi3p601	21	26	the	the	DT
cord-004615-xfi3p601	21	27	control	control	NN
cord-004615-xfi3p601	21	28	measures	measure	NNS
cord-004615-xfi3p601	21	29	are	be	VBP
cord-004615-xfi3p601	21	30	not	not	RB
cord-004615-xfi3p601	21	31	compounded	compound	VBN
cord-004615-xfi3p601	21	32	in	in	IN
cord-004615-xfi3p601	21	33	time	time	NN
cord-004615-xfi3p601	21	34	and	and	CC
cord-004615-xfi3p601	21	35	do	do	VBP
cord-004615-xfi3p601	21	36	not	not	RB
cord-004615-xfi3p601	21	37	lead	lead	VB
cord-004615-xfi3p601	21	38	to	to	IN
cord-004615-xfi3p601	21	39	changes	change	NNS
cord-004615-xfi3p601	21	40	in	in	IN
cord-004615-xfi3p601	21	41	the	the	DT
cord-004615-xfi3p601	21	42	rates	rate	NNS
cord-004615-xfi3p601	21	43	that	that	WDT
cord-004615-xfi3p601	21	44	govern	govern	VBP
cord-004615-xfi3p601	21	45	epidemic	epidemic	NN
cord-004615-xfi3p601	21	46	spread	spread	NN
cord-004615-xfi3p601	21	47	(	(	-LRB-
cord-004615-xfi3p601	21	48	see	see	VB
cord-004615-xfi3p601	21	49	e.g.	e.g.	JJ
cord-004615-xfi3p601	21	50	[	[	-LRB-
cord-004615-xfi3p601	21	51	2	2	CD
cord-004615-xfi3p601	21	52	]	]	-RRB-
cord-004615-xfi3p601	21	53	)	)	-RRB-
cord-004615-xfi3p601	21	54	.	.	.
cord-004615-xfi3p601	22	1	In	in	IN
cord-004615-xfi3p601	22	2	this	this	DT
cord-004615-xfi3p601	22	3	paper	paper	NN
cord-004615-xfi3p601	22	4	we	-PRON-	PRP
cord-004615-xfi3p601	22	5	aim	aim	VBP
cord-004615-xfi3p601	22	6	to	to	TO
cord-004615-xfi3p601	22	7	develop	develop	VB
cord-004615-xfi3p601	22	8	stochastic	stochastic	JJ
cord-004615-xfi3p601	22	9	methods	method	NNS
cord-004615-xfi3p601	22	10	,	,	,
cord-004615-xfi3p601	22	11	based	base	VBN
cord-004615-xfi3p601	22	12	on	on	IN
cord-004615-xfi3p601	22	13	branching	branch	VBG
cord-004615-xfi3p601	22	14	processes	process	NNS
cord-004615-xfi3p601	22	15	,	,	,
cord-004615-xfi3p601	22	16	which	which	WDT
cord-004615-xfi3p601	22	17	allow	allow	VBP
cord-004615-xfi3p601	22	18	us	-PRON-	PRP
cord-004615-xfi3p601	22	19	to	to	TO
cord-004615-xfi3p601	22	20	compare	compare	VB
cord-004615-xfi3p601	22	21	the	the	DT
cord-004615-xfi3p601	22	22	effectiveness	effectiveness	NN
cord-004615-xfi3p601	22	23	of	of	IN
cord-004615-xfi3p601	22	24	control	control	NN
cord-004615-xfi3p601	22	25	strategies	strategy	NNS
cord-004615-xfi3p601	22	26	during	during	IN
cord-004615-xfi3p601	22	27	such	such	JJ
cord-004615-xfi3p601	22	28	outbreaks	outbreak	NNS
cord-004615-xfi3p601	22	29	in	in	IN
cord-004615-xfi3p601	22	30	situations	situation	NNS
cord-004615-xfi3p601	22	31	where	where	WRB
cord-004615-xfi3p601	22	32	the	the	DT
cord-004615-xfi3p601	22	33	environment	environment	NN
cord-004615-xfi3p601	22	34	is	be	VBZ
cord-004615-xfi3p601	22	35	varying	vary	VBG
cord-004615-xfi3p601	22	36	because	because	IN
cord-004615-xfi3p601	22	37	of	of	IN
cord-004615-xfi3p601	22	38	changes	change	NNS
cord-004615-xfi3p601	22	39	in	in	IN
cord-004615-xfi3p601	22	40	subsequent	subsequent	JJ
cord-004615-xfi3p601	22	41	measures	measure	NNS
cord-004615-xfi3p601	22	42	of	of	IN
cord-004615-xfi3p601	22	43	control	control	NN
cord-004615-xfi3p601	22	44	.	.	.
cord-004615-xfi3p601	23	1	Much	much	JJ
cord-004615-xfi3p601	23	2	work	work	NN
cord-004615-xfi3p601	23	3	has	have	VBZ
cord-004615-xfi3p601	23	4	already	already	RB
cord-004615-xfi3p601	23	5	been	be	VBN
cord-004615-xfi3p601	23	6	done	do	VBN
cord-004615-xfi3p601	23	7	to	to	TO
cord-004615-xfi3p601	23	8	describe	describe	VB
cord-004615-xfi3p601	23	9	the	the	DT
cord-004615-xfi3p601	23	10	spread	spread	NN
cord-004615-xfi3p601	23	11	of	of	IN
cord-004615-xfi3p601	23	12	classical	classical	JJ
cord-004615-xfi3p601	23	13	swine	swine	NN
cord-004615-xfi3p601	23	14	fever	fever	NN
cord-004615-xfi3p601	23	15	(	(	-LRB-
cord-004615-xfi3p601	23	16	see	see	VB
cord-004615-xfi3p601	23	17	e.g.	e.g.	JJ
cord-004615-xfi3p601	23	18	[	[	-LRB-
cord-004615-xfi3p601	23	19	10	10	CD
cord-004615-xfi3p601	23	20	,	,	,
cord-004615-xfi3p601	23	21	11	11	CD
cord-004615-xfi3p601	23	22	,	,	,
cord-004615-xfi3p601	23	23	1	1	CD
cord-004615-xfi3p601	23	24	]	]	-RRB-
cord-004615-xfi3p601	23	25	)	)	-RRB-
cord-004615-xfi3p601	23	26	and	and	CC
cord-004615-xfi3p601	23	27	foot	foot	NN
cord-004615-xfi3p601	23	28	and	and	CC
cord-004615-xfi3p601	23	29	mouth	mouth	NN
cord-004615-xfi3p601	23	30	disease	disease	NN
cord-004615-xfi3p601	23	31	(	(	-LRB-
cord-004615-xfi3p601	23	32	see	see	VB
cord-004615-xfi3p601	23	33	e.g.	e.g.	JJ
cord-004615-xfi3p601	23	34	[	[	-LRB-
cord-004615-xfi3p601	23	35	5	5	CD
cord-004615-xfi3p601	23	36	,	,	,
cord-004615-xfi3p601	23	37	6	6	CD
cord-004615-xfi3p601	23	38	,	,	,
cord-004615-xfi3p601	23	39	9	9	CD
cord-004615-xfi3p601	23	40	,	,	,
cord-004615-xfi3p601	23	41	8	8	CD
cord-004615-xfi3p601	23	42	]	]	-RRB-
cord-004615-xfi3p601	23	43	)	)	-RRB-
cord-004615-xfi3p601	23	44	.	.	.
cord-004615-xfi3p601	24	1	In	in	IN
cord-004615-xfi3p601	24	2	this	this	DT
cord-004615-xfi3p601	24	3	paper	paper	NN
cord-004615-xfi3p601	24	4	,	,	,
cord-004615-xfi3p601	24	5	we	-PRON-	PRP
cord-004615-xfi3p601	24	6	will	will	MD
cord-004615-xfi3p601	24	7	model	model	VB
cord-004615-xfi3p601	24	8	the	the	DT
cord-004615-xfi3p601	24	9	spread	spread	NN
cord-004615-xfi3p601	24	10	of	of	IN
cord-004615-xfi3p601	24	11	infections	infection	NNS
cord-004615-xfi3p601	24	12	in	in	IN
cord-004615-xfi3p601	24	13	a	a	DT
cord-004615-xfi3p601	24	14	much	much	RB
cord-004615-xfi3p601	24	15	more	more	RBR
cord-004615-xfi3p601	24	16	analytic	analytic	JJ
cord-004615-xfi3p601	24	17	way	way	NN
cord-004615-xfi3p601	24	18	than	than	IN
cord-004615-xfi3p601	24	19	is	be	VBZ
cord-004615-xfi3p601	24	20	done	do	VBN
cord-004615-xfi3p601	24	21	in	in	IN
cord-004615-xfi3p601	24	22	earlier	early	JJR
cord-004615-xfi3p601	24	23	models	model	NNS
cord-004615-xfi3p601	24	24	[	[	-LRB-
cord-004615-xfi3p601	24	25	5	5	CD
cord-004615-xfi3p601	24	26	,	,	,
cord-004615-xfi3p601	24	27	6	6	CD
cord-004615-xfi3p601	24	28	,	,	,
cord-004615-xfi3p601	24	29	9	9	CD
cord-004615-xfi3p601	24	30	,	,	,
cord-004615-xfi3p601	24	31	1	1	CD
cord-004615-xfi3p601	24	32	]	]	-RRB-
cord-004615-xfi3p601	24	33	.	.	.
cord-004615-xfi3p601	25	1	We	-PRON-	PRP
cord-004615-xfi3p601	25	2	use	use	VBP
cord-004615-xfi3p601	25	3	an	an	DT
cord-004615-xfi3p601	25	4	iterative	iterative	JJ
cord-004615-xfi3p601	25	5	method	method	NN
cord-004615-xfi3p601	25	6	that	that	WDT
cord-004615-xfi3p601	25	7	computes	compute	VBZ
cord-004615-xfi3p601	25	8	properties	property	NNS
cord-004615-xfi3p601	25	9	of	of	IN
cord-004615-xfi3p601	25	10	the	the	DT
cord-004615-xfi3p601	25	11	spread	spread	NN
cord-004615-xfi3p601	25	12	,	,	,
cord-004615-xfi3p601	25	13	like	like	IN
cord-004615-xfi3p601	25	14	the	the	DT
cord-004615-xfi3p601	25	15	probability	probability	NN
cord-004615-xfi3p601	25	16	of	of	IN
cord-004615-xfi3p601	25	17	a	a	DT
cord-004615-xfi3p601	25	18	major	major	JJ
cord-004615-xfi3p601	25	19	outbreak	outbreak	NN
cord-004615-xfi3p601	25	20	of	of	IN
cord-004615-xfi3p601	25	21	the	the	DT
cord-004615-xfi3p601	25	22	infection	infection	NN
cord-004615-xfi3p601	25	23	and	and	CC
cord-004615-xfi3p601	25	24	the	the	DT
cord-004615-xfi3p601	25	25	final	final	JJ
cord-004615-xfi3p601	25	26	size	size	NN
cord-004615-xfi3p601	25	27	of	of	IN
cord-004615-xfi3p601	25	28	an	an	DT
cord-004615-xfi3p601	25	29	epidemic	epidemic	NN
cord-004615-xfi3p601	25	30	(	(	-LRB-
cord-004615-xfi3p601	25	31	i.e.	i.e.	FW
cord-004615-xfi3p601	25	32	the	the	DT
cord-004615-xfi3p601	25	33	total	total	JJ
cord-004615-xfi3p601	25	34	number	number	NN
cord-004615-xfi3p601	25	35	of	of	IN
cord-004615-xfi3p601	25	36	infected	infected	JJ
cord-004615-xfi3p601	25	37	herds	herd	NNS
cord-004615-xfi3p601	25	38	)	)	-RRB-
cord-004615-xfi3p601	25	39	very	very	RB
cord-004615-xfi3p601	25	40	efficiently	efficiently	RB
cord-004615-xfi3p601	25	41	.	.	.
cord-004615-xfi3p601	26	1	Furthermore	furthermore	RB
cord-004615-xfi3p601	26	2	we	-PRON-	PRP
cord-004615-xfi3p601	26	3	can	can	MD
cord-004615-xfi3p601	26	4	derive	derive	VB
cord-004615-xfi3p601	26	5	some	some	DT
cord-004615-xfi3p601	26	6	properties	property	NNS
cord-004615-xfi3p601	26	7	of	of	IN
cord-004615-xfi3p601	26	8	the	the	DT
cord-004615-xfi3p601	26	9	duration	duration	NN
cord-004615-xfi3p601	26	10	of	of	IN
cord-004615-xfi3p601	26	11	the	the	DT
cord-004615-xfi3p601	26	12	epidemic	epidemic	NN
cord-004615-xfi3p601	26	13	.	.	.
cord-004615-xfi3p601	27	1	We	-PRON-	PRP
cord-004615-xfi3p601	27	2	allow	allow	VBP
cord-004615-xfi3p601	27	3	for	for	IN
cord-004615-xfi3p601	27	4	different	different	JJ
cord-004615-xfi3p601	27	5	types	type	NNS
cord-004615-xfi3p601	27	6	of	of	IN
cord-004615-xfi3p601	27	7	herd	herd	NN
cord-004615-xfi3p601	27	8	.	.	.
cord-004615-xfi3p601	28	1	In	in	IN
cord-004615-xfi3p601	28	2	our	-PRON-	PRP$
cord-004615-xfi3p601	28	3	model	model	NN
cord-004615-xfi3p601	28	4	,	,	,
cord-004615-xfi3p601	28	5	it	-PRON-	PRP
cord-004615-xfi3p601	28	6	is	be	VBZ
cord-004615-xfi3p601	28	7	essential	essential	JJ
cord-004615-xfi3p601	28	8	that	that	IN
cord-004615-xfi3p601	28	9	once	once	IN
cord-004615-xfi3p601	28	10	the	the	DT
cord-004615-xfi3p601	28	11	infection	infection	NN
cord-004615-xfi3p601	28	12	in	in	IN
cord-004615-xfi3p601	28	13	a	a	DT
cord-004615-xfi3p601	28	14	herd	herd	NN
cord-004615-xfi3p601	28	15	is	be	VBZ
cord-004615-xfi3p601	28	16	detected	detect	VBN
cord-004615-xfi3p601	28	17	,	,	,
cord-004615-xfi3p601	28	18	the	the	DT
cord-004615-xfi3p601	28	19	whole	whole	JJ
cord-004615-xfi3p601	28	20	herd	herd	NN
cord-004615-xfi3p601	28	21	will	will	MD
cord-004615-xfi3p601	28	22	be	be	VB
cord-004615-xfi3p601	28	23	culled	cull	VBN
cord-004615-xfi3p601	28	24	.	.	.
cord-004615-xfi3p601	29	1	Therefore	therefore	RB
cord-004615-xfi3p601	29	2	,	,	,
cord-004615-xfi3p601	29	3	our	-PRON-	PRP$
cord-004615-xfi3p601	29	4	main	main	JJ
cord-004615-xfi3p601	29	5	interest	interest	NN
cord-004615-xfi3p601	29	6	is	be	VBZ
cord-004615-xfi3p601	29	7	the	the	DT
cord-004615-xfi3p601	29	8	number	number	NN
cord-004615-xfi3p601	29	9	of	of	IN
cord-004615-xfi3p601	29	10	infected	infected	JJ
cord-004615-xfi3p601	29	11	herds	herd	NNS
cord-004615-xfi3p601	29	12	,	,	,
cord-004615-xfi3p601	29	13	but	but	CC
cord-004615-xfi3p601	29	14	the	the	DT
cord-004615-xfi3p601	29	15	number	number	NN
cord-004615-xfi3p601	29	16	of	of	IN
cord-004615-xfi3p601	29	17	infected	infected	JJ
cord-004615-xfi3p601	29	18	animals	animal	NNS
cord-004615-xfi3p601	29	19	in	in	IN
cord-004615-xfi3p601	29	20	an	an	DT
cord-004615-xfi3p601	29	21	infective	infective	JJ
cord-004615-xfi3p601	29	22	herd	herd	NN
cord-004615-xfi3p601	29	23	is	be	VBZ
cord-004615-xfi3p601	29	24	important	important	JJ
cord-004615-xfi3p601	29	25	for	for	IN
cord-004615-xfi3p601	29	26	determining	determine	VBG
cord-004615-xfi3p601	29	27	the	the	DT
cord-004615-xfi3p601	29	28	infectivity	infectivity	NN
cord-004615-xfi3p601	29	29	of	of	IN
cord-004615-xfi3p601	29	30	a	a	DT
cord-004615-xfi3p601	29	31	herd	herd	NN
cord-004615-xfi3p601	29	32	and	and	CC
cord-004615-xfi3p601	29	33	the	the	DT
cord-004615-xfi3p601	29	34	distribution	distribution	NN
cord-004615-xfi3p601	29	35	of	of	IN
cord-004615-xfi3p601	29	36	the	the	DT
cord-004615-xfi3p601	29	37	detection	detection	NN
cord-004615-xfi3p601	29	38	times	time	NNS
cord-004615-xfi3p601	29	39	.	.	.
cord-004615-xfi3p601	30	1	We	-PRON-	PRP
cord-004615-xfi3p601	30	2	therefore	therefore	RB
cord-004615-xfi3p601	30	3	model	model	VBP
cord-004615-xfi3p601	30	4	the	the	DT
cord-004615-xfi3p601	30	5	spread	spread	NN
cord-004615-xfi3p601	30	6	of	of	IN
cord-004615-xfi3p601	30	7	the	the	DT
cord-004615-xfi3p601	30	8	infection	infection	NN
cord-004615-xfi3p601	30	9	on	on	IN
cord-004615-xfi3p601	30	10	two	two	CD
cord-004615-xfi3p601	30	11	levels	level	NNS
cord-004615-xfi3p601	30	12	,	,	,
cord-004615-xfi3p601	30	13	namely	namely	RB
cord-004615-xfi3p601	30	14	the	the	DT
cord-004615-xfi3p601	30	15	spread	spread	NN
cord-004615-xfi3p601	30	16	of	of	IN
cord-004615-xfi3p601	30	17	the	the	DT
cord-004615-xfi3p601	30	18	infections	infection	NNS
cord-004615-xfi3p601	30	19	within	within	IN
cord-004615-xfi3p601	30	20	a	a	DT
cord-004615-xfi3p601	30	21	herd	herd	NN
cord-004615-xfi3p601	30	22	and	and	CC
cord-004615-xfi3p601	30	23	the	the	DT
cord-004615-xfi3p601	30	24	spread	spread	NN
cord-004615-xfi3p601	30	25	of	of	IN
cord-004615-xfi3p601	30	26	infection	infection	NN
cord-004615-xfi3p601	30	27	between	between	IN
cord-004615-xfi3p601	30	28	herds	herd	NNS
cord-004615-xfi3p601	30	29	;	;	:
cord-004615-xfi3p601	30	30	both	both	DT
cord-004615-xfi3p601	30	31	are	be	VBP
cord-004615-xfi3p601	30	32	described	describe	VBN
cord-004615-xfi3p601	30	33	by	by	IN
cord-004615-xfi3p601	30	34	a	a	DT
cord-004615-xfi3p601	30	35	stochastic	stochastic	JJ
cord-004615-xfi3p601	30	36	process	process	NN
cord-004615-xfi3p601	30	37	.	.	.
cord-004615-xfi3p601	31	1	We	-PRON-	PRP
cord-004615-xfi3p601	31	2	use	use	VBP
cord-004615-xfi3p601	31	3	a	a	DT
cord-004615-xfi3p601	31	4	special	special	JJ
cord-004615-xfi3p601	31	5	branching	branching	NN
cord-004615-xfi3p601	31	6	process	process	NN
cord-004615-xfi3p601	31	7	to	to	TO
cord-004615-xfi3p601	31	8	describe	describe	VB
cord-004615-xfi3p601	31	9	the	the	DT
cord-004615-xfi3p601	31	10	spread	spread	NN
cord-004615-xfi3p601	31	11	of	of	IN
cord-004615-xfi3p601	31	12	the	the	DT
cord-004615-xfi3p601	31	13	infection	infection	NN
cord-004615-xfi3p601	31	14	among	among	IN
cord-004615-xfi3p601	31	15	herds	herd	NNS
cord-004615-xfi3p601	31	16	.	.	.
cord-004615-xfi3p601	32	1	The	the	DT
cord-004615-xfi3p601	32	2	parameters	parameter	NNS
cord-004615-xfi3p601	32	3	of	of	IN
cord-004615-xfi3p601	32	4	this	this	DT
cord-004615-xfi3p601	32	5	branching	branching	NN
cord-004615-xfi3p601	32	6	process	process	NN
cord-004615-xfi3p601	32	7	depend	depend	VBP
cord-004615-xfi3p601	32	8	on	on	IN
cord-004615-xfi3p601	32	9	the	the	DT
cord-004615-xfi3p601	32	10	time	time	NN
cord-004615-xfi3p601	32	11	since	since	IN
cord-004615-xfi3p601	32	12	the	the	DT
cord-004615-xfi3p601	32	13	infection	infection	NN
cord-004615-xfi3p601	32	14	of	of	IN
cord-004615-xfi3p601	32	15	the	the	DT
cord-004615-xfi3p601	32	16	herd	herd	NN
cord-004615-xfi3p601	32	17	and	and	CC
cord-004615-xfi3p601	32	18	on	on	IN
cord-004615-xfi3p601	32	19	the	the	DT
cord-004615-xfi3p601	32	20	environment	environment	NN
cord-004615-xfi3p601	32	21	,	,	,
cord-004615-xfi3p601	32	22	which	which	WDT
cord-004615-xfi3p601	32	23	is	be	VBZ
cord-004615-xfi3p601	32	24	determined	determine	VBN
cord-004615-xfi3p601	32	25	by	by	IN
cord-004615-xfi3p601	32	26	the	the	DT
cord-004615-xfi3p601	32	27	real	real	JJ
cord-004615-xfi3p601	32	28	time	time	NN
cord-004615-xfi3p601	32	29	.	.	.
cord-004615-xfi3p601	33	1	Using	use	VBG
cord-004615-xfi3p601	33	2	branching	branch	VBG
cord-004615-xfi3p601	33	3	processes	process	NNS
cord-004615-xfi3p601	33	4	to	to	TO
cord-004615-xfi3p601	33	5	describe	describe	VB
cord-004615-xfi3p601	33	6	epidemics	epidemic	NNS
cord-004615-xfi3p601	33	7	is	be	VBZ
cord-004615-xfi3p601	33	8	of	of	IN
cord-004615-xfi3p601	33	9	course	course	NN
cord-004615-xfi3p601	33	10	not	not	RB
cord-004615-xfi3p601	33	11	new	new	JJ
cord-004615-xfi3p601	33	12	(	(	-LRB-
cord-004615-xfi3p601	33	13	see	see	VB
cord-004615-xfi3p601	33	14	e.g.	e.g.	JJ
cord-004615-xfi3p601	33	15	[	[	-LRB-
cord-004615-xfi3p601	33	16	4	4	CD
cord-004615-xfi3p601	33	17	]	]	-RRB-
cord-004615-xfi3p601	33	18	)	)	-RRB-
cord-004615-xfi3p601	33	19	,	,	,
cord-004615-xfi3p601	33	20	but	but	CC
cord-004615-xfi3p601	33	21	no	no	DT
cord-004615-xfi3p601	33	22	theory	theory	NN
cord-004615-xfi3p601	33	23	exists	exist	VBZ
cord-004615-xfi3p601	33	24	that	that	WDT
cord-004615-xfi3p601	33	25	gives	give	VBZ
cord-004615-xfi3p601	33	26	short	short	JJ
cord-004615-xfi3p601	33	27	-	-	HYPH
cord-004615-xfi3p601	33	28	term	term	NN
cord-004615-xfi3p601	33	29	predictions	prediction	NNS
cord-004615-xfi3p601	33	30	(	(	-LRB-
cord-004615-xfi3p601	33	31	as	as	IN
cord-004615-xfi3p601	33	32	opposed	oppose	VBN
cord-004615-xfi3p601	33	33	to	to	IN
cord-004615-xfi3p601	33	34	asymptotics	asymptotic	NNS
cord-004615-xfi3p601	33	35	)	)	-RRB-
cord-004615-xfi3p601	33	36	for	for	IN
cord-004615-xfi3p601	33	37	general	general	JJ
cord-004615-xfi3p601	33	38	branching	branch	VBG
cord-004615-xfi3p601	33	39	processes	process	NNS
cord-004615-xfi3p601	33	40	in	in	IN
cord-004615-xfi3p601	33	41	varying	vary	VBG
cord-004615-xfi3p601	33	42	environments	environment	NNS
cord-004615-xfi3p601	33	43	,	,	,
cord-004615-xfi3p601	33	44	with	with	IN
cord-004615-xfi3p601	33	45	an	an	DT
cord-004615-xfi3p601	33	46	age	age	NN
cord-004615-xfi3p601	33	47	-	-	HYPH
cord-004615-xfi3p601	33	48	dependent	dependent	JJ
cord-004615-xfi3p601	33	49	birth	birth	NN
cord-004615-xfi3p601	33	50	rate	rate	NN
cord-004615-xfi3p601	33	51	.	.	.
cord-004615-xfi3p601	34	1	For	for	IN
cord-004615-xfi3p601	34	2	computations	computation	NNS
cord-004615-xfi3p601	34	3	,	,	,
cord-004615-xfi3p601	34	4	it	-PRON-	PRP
cord-004615-xfi3p601	34	5	is	be	VBZ
cord-004615-xfi3p601	34	6	necessary	necessary	JJ
cord-004615-xfi3p601	34	7	that	that	IN
cord-004615-xfi3p601	34	8	after	after	IN
cord-004615-xfi3p601	34	9	a	a	DT
cord-004615-xfi3p601	34	10	certain	certain	JJ
cord-004615-xfi3p601	34	11	moment	moment	NN
cord-004615-xfi3p601	34	12	the	the	DT
cord-004615-xfi3p601	34	13	environment	environment	NN
cord-004615-xfi3p601	34	14	is	be	VBZ
cord-004615-xfi3p601	34	15	constant	constant	JJ
cord-004615-xfi3p601	34	16	.	.	.
cord-004615-xfi3p601	35	1	To	to	TO
cord-004615-xfi3p601	35	2	achieve	achieve	VB
cord-004615-xfi3p601	35	3	this	this	DT
cord-004615-xfi3p601	35	4	we	-PRON-	PRP
cord-004615-xfi3p601	35	5	assume	assume	VBP
cord-004615-xfi3p601	35	6	that	that	IN
cord-004615-xfi3p601	35	7	after	after	IN
cord-004615-xfi3p601	35	8	some	some	DT
cord-004615-xfi3p601	35	9	time	time	NN
cord-004615-xfi3p601	35	10	no	no	DT
cord-004615-xfi3p601	35	11	new	new	JJ
cord-004615-xfi3p601	35	12	measures	measure	NNS
cord-004615-xfi3p601	35	13	will	will	MD
cord-004615-xfi3p601	35	14	be	be	VB
cord-004615-xfi3p601	35	15	taken	take	VBN
cord-004615-xfi3p601	35	16	and	and	CC
cord-004615-xfi3p601	35	17	the	the	DT
cord-004615-xfi3p601	35	18	effects	effect	NNS
cord-004615-xfi3p601	35	19	of	of	IN
cord-004615-xfi3p601	35	20	all	all	DT
cord-004615-xfi3p601	35	21	measures	measure	NNS
cord-004615-xfi3p601	35	22	taken	take	VBN
cord-004615-xfi3p601	35	23	in	in	IN
cord-004615-xfi3p601	35	24	the	the	DT
cord-004615-xfi3p601	35	25	past	past	NN
cord-004615-xfi3p601	35	26	will	will	MD
cord-004615-xfi3p601	35	27	either	either	CC
cord-004615-xfi3p601	35	28	be	be	VB
cord-004615-xfi3p601	35	29	constant	constant	JJ
cord-004615-xfi3p601	35	30	or	or	CC
cord-004615-xfi3p601	35	31	absent	absent	JJ
cord-004615-xfi3p601	35	32	.	.	.
cord-004615-xfi3p601	36	1	In	in	IN
cord-004615-xfi3p601	36	2	other	other	JJ
cord-004615-xfi3p601	36	3	words	word	NNS
cord-004615-xfi3p601	36	4	,	,	,
cord-004615-xfi3p601	36	5	although	although	IN
cord-004615-xfi3p601	36	6	the	the	DT
cord-004615-xfi3p601	36	7	values	value	NNS
cord-004615-xfi3p601	36	8	of	of	IN
cord-004615-xfi3p601	36	9	the	the	DT
cord-004615-xfi3p601	36	10	parameters	parameter	NNS
cord-004615-xfi3p601	36	11	may	may	MD
cord-004615-xfi3p601	36	12	differ	differ	VB
cord-004615-xfi3p601	36	13	from	from	IN
cord-004615-xfi3p601	36	14	those	those	DT
cord-004615-xfi3p601	36	15	before	before	IN
cord-004615-xfi3p601	36	16	certain	certain	JJ
cord-004615-xfi3p601	36	17	measures	measure	NNS
cord-004615-xfi3p601	36	18	were	be	VBD
cord-004615-xfi3p601	36	19	taken	take	VBN
cord-004615-xfi3p601	36	20	,	,	,
cord-004615-xfi3p601	36	21	the	the	DT
cord-004615-xfi3p601	36	22	values	value	NNS
cord-004615-xfi3p601	36	23	are	be	VBP
cord-004615-xfi3p601	36	24	assumed	assume	VBN
cord-004615-xfi3p601	36	25	to	to	TO
cord-004615-xfi3p601	36	26	be	be	VB
cord-004615-xfi3p601	36	27	constant	constant	JJ
cord-004615-xfi3p601	36	28	after	after	IN
cord-004615-xfi3p601	36	29	a	a	DT
cord-004615-xfi3p601	36	30	given	give	VBN
cord-004615-xfi3p601	36	31	moment	moment	NN
cord-004615-xfi3p601	36	32	in	in	IN
cord-004615-xfi3p601	36	33	time	time	NN
cord-004615-xfi3p601	36	34	.	.	.
cord-004615-xfi3p601	37	1	Our	-PRON-	PRP$
cord-004615-xfi3p601	37	2	model	model	NN
cord-004615-xfi3p601	37	3	can	can	MD
cord-004615-xfi3p601	37	4	be	be	VB
cord-004615-xfi3p601	37	5	used	use	VBN
cord-004615-xfi3p601	37	6	to	to	TO
cord-004615-xfi3p601	37	7	predict	predict	VB
cord-004615-xfi3p601	37	8	the	the	DT
cord-004615-xfi3p601	37	9	effects	effect	NNS
cord-004615-xfi3p601	37	10	of	of	IN
cord-004615-xfi3p601	37	11	various	various	JJ
cord-004615-xfi3p601	37	12	control	control	NN
cord-004615-xfi3p601	37	13	measures	measure	NNS
cord-004615-xfi3p601	37	14	and	and	CC
cord-004615-xfi3p601	37	15	strategies	strategy	NNS
cord-004615-xfi3p601	37	16	during	during	IN
cord-004615-xfi3p601	37	17	an	an	DT
cord-004615-xfi3p601	37	18	ongoing	ongoing	JJ
cord-004615-xfi3p601	37	19	outbreak	outbreak	NN
cord-004615-xfi3p601	37	20	.	.	.
cord-004615-xfi3p601	38	1	Meester	Meester	NNP
cord-004615-xfi3p601	38	2	et	et	NNP
cord-004615-xfi3p601	38	3	al	al	NNP
cord-004615-xfi3p601	38	4	.	.	.
cord-004615-xfi3p601	39	1	gave	give	VBD
cord-004615-xfi3p601	39	2	a	a	DT
cord-004615-xfi3p601	39	3	method	method	NN
cord-004615-xfi3p601	39	4	to	to	TO
cord-004615-xfi3p601	39	5	estimate	estimate	VB
cord-004615-xfi3p601	39	6	the	the	DT
cord-004615-xfi3p601	39	7	parameters	parameter	NNS
cord-004615-xfi3p601	39	8	from	from	IN
cord-004615-xfi3p601	39	9	the	the	DT
cord-004615-xfi3p601	39	10	data	datum	NNS
cord-004615-xfi3p601	39	11	available	available	JJ
cord-004615-xfi3p601	39	12	during	during	IN
cord-004615-xfi3p601	39	13	an	an	DT
cord-004615-xfi3p601	39	14	outbreak	outbreak	NN
cord-004615-xfi3p601	39	15	,	,	,
cord-004615-xfi3p601	39	16	[	[	-LRB-
cord-004615-xfi3p601	39	17	10	10	CD
cord-004615-xfi3p601	39	18	]	]	-RRB-
cord-004615-xfi3p601	39	19	.	.	.
cord-004615-xfi3p601	40	1	We	-PRON-	PRP
cord-004615-xfi3p601	40	2	consider	consider	VBP
cord-004615-xfi3p601	40	3	measures	measure	NNS
cord-004615-xfi3p601	40	4	like	like	IN
cord-004615-xfi3p601	40	5	single	single	JJ
cord-004615-xfi3p601	40	6	vaccination	vaccination	NN
cord-004615-xfi3p601	40	7	of	of	IN
cord-004615-xfi3p601	40	8	all	all	DT
cord-004615-xfi3p601	40	9	herds	herd	NNS
cord-004615-xfi3p601	40	10	of	of	IN
cord-004615-xfi3p601	40	11	a	a	DT
cord-004615-xfi3p601	40	12	certain	certain	JJ
cord-004615-xfi3p601	40	13	type	type	NN
cord-004615-xfi3p601	40	14	,	,	,
cord-004615-xfi3p601	40	15	a	a	DT
cord-004615-xfi3p601	40	16	total	total	JJ
cord-004615-xfi3p601	40	17	transport	transport	NN
cord-004615-xfi3p601	40	18	ban	ban	NN
cord-004615-xfi3p601	40	19	or	or	CC
cord-004615-xfi3p601	40	20	killing	killing	NN
cord-004615-xfi3p601	40	21	of	of	IN
cord-004615-xfi3p601	40	22	animals	animal	NNS
cord-004615-xfi3p601	40	23	just	just	RB
cord-004615-xfi3p601	40	24	after	after	IN
cord-004615-xfi3p601	40	25	birth	birth	NN
cord-004615-xfi3p601	40	26	.	.	.
cord-004615-xfi3p601	41	1	Some	some	DT
cord-004615-xfi3p601	41	2	of	of	IN
cord-004615-xfi3p601	41	3	these	these	DT
cord-004615-xfi3p601	41	4	measures	measure	NNS
cord-004615-xfi3p601	41	5	cause	cause	VBP
cord-004615-xfi3p601	41	6	a	a	DT
cord-004615-xfi3p601	41	7	varying	vary	VBG
cord-004615-xfi3p601	41	8	environment	environment	NN
cord-004615-xfi3p601	41	9	.	.	.
cord-004615-xfi3p601	42	1	The	the	DT
cord-004615-xfi3p601	42	2	fraction	fraction	NN
cord-004615-xfi3p601	42	3	susceptible	susceptible	JJ
cord-004615-xfi3p601	42	4	animals	animal	NNS
cord-004615-xfi3p601	42	5	in	in	IN
cord-004615-xfi3p601	42	6	a	a	DT
cord-004615-xfi3p601	42	7	herd	herd	NN
cord-004615-xfi3p601	42	8	or	or	CC
cord-004615-xfi3p601	42	9	the	the	DT
cord-004615-xfi3p601	42	10	fraction	fraction	NN
cord-004615-xfi3p601	42	11	susceptible	susceptible	JJ
cord-004615-xfi3p601	42	12	herds	herd	NNS
cord-004615-xfi3p601	42	13	of	of	IN
cord-004615-xfi3p601	42	14	the	the	DT
cord-004615-xfi3p601	42	15	total	total	JJ
cord-004615-xfi3p601	42	16	number	number	NN
cord-004615-xfi3p601	42	17	of	of	IN
cord-004615-xfi3p601	42	18	herds	herd	NNS
cord-004615-xfi3p601	42	19	may	may	MD
cord-004615-xfi3p601	42	20	be	be	VB
cord-004615-xfi3p601	42	21	varying	vary	VBG
cord-004615-xfi3p601	42	22	and	and	CC
cord-004615-xfi3p601	42	23	so	so	RB
cord-004615-xfi3p601	42	24	the	the	DT
cord-004615-xfi3p601	42	25	infection	infection	NN
cord-004615-xfi3p601	42	26	rate	rate	NN
cord-004615-xfi3p601	42	27	may	may	MD
cord-004615-xfi3p601	42	28	vary	vary	VB
cord-004615-xfi3p601	42	29	in	in	IN
cord-004615-xfi3p601	42	30	time	time	NN
cord-004615-xfi3p601	42	31	as	as	RB
cord-004615-xfi3p601	42	32	well	well	RB
cord-004615-xfi3p601	42	33	.	.	.
cord-004615-xfi3p601	43	1	In	in	IN
cord-004615-xfi3p601	43	2	fighting	fighting	NN
cord-004615-xfi3p601	43	3	outbreaks	outbreak	NNS
cord-004615-xfi3p601	43	4	,	,	,
cord-004615-xfi3p601	43	5	additional	additional	JJ
cord-004615-xfi3p601	43	6	measures	measure	NNS
cord-004615-xfi3p601	43	7	will	will	MD
cord-004615-xfi3p601	43	8	be	be	VB
cord-004615-xfi3p601	43	9	implemented	implement	VBN
cord-004615-xfi3p601	43	10	as	as	RB
cord-004615-xfi3p601	43	11	soon	soon	RB
cord-004615-xfi3p601	43	12	as	as	IN
cord-004615-xfi3p601	43	13	present	present	JJ
cord-004615-xfi3p601	43	14	measures	measure	NNS
cord-004615-xfi3p601	43	15	turn	turn	VBP
cord-004615-xfi3p601	43	16	out	out	RP
cord-004615-xfi3p601	43	17	to	to	TO
cord-004615-xfi3p601	43	18	be	be	VB
cord-004615-xfi3p601	43	19	insufficient	insufficient	JJ
cord-004615-xfi3p601	43	20	.	.	.
cord-004615-xfi3p601	44	1	A	a	DT
cord-004615-xfi3p601	44	2	change	change	NN
cord-004615-xfi3p601	44	3	in	in	IN
cord-004615-xfi3p601	44	4	measure	measure	NN
cord-004615-xfi3p601	44	5	will	will	MD
cord-004615-xfi3p601	44	6	change	change	VB
cord-004615-xfi3p601	44	7	the	the	DT
cord-004615-xfi3p601	44	8	values	value	NNS
cord-004615-xfi3p601	44	9	of	of	IN
cord-004615-xfi3p601	44	10	the	the	DT
cord-004615-xfi3p601	44	11	parameters	parameter	NNS
cord-004615-xfi3p601	44	12	.	.	.
cord-004615-xfi3p601	45	1	We	-PRON-	PRP
cord-004615-xfi3p601	45	2	assume	assume	VBP
cord-004615-xfi3p601	45	3	that	that	IN
cord-004615-xfi3p601	45	4	the	the	DT
cord-004615-xfi3p601	45	5	changes	change	NNS
cord-004615-xfi3p601	45	6	in	in	IN
cord-004615-xfi3p601	45	7	the	the	DT
cord-004615-xfi3p601	45	8	environment	environment	NN
cord-004615-xfi3p601	45	9	are	be	VBP
cord-004615-xfi3p601	45	10	deterministic	deterministic	JJ
cord-004615-xfi3p601	45	11	.	.	.
cord-004615-xfi3p601	46	1	We	-PRON-	PRP
cord-004615-xfi3p601	46	2	develop	develop	VBP
cord-004615-xfi3p601	46	3	the	the	DT
cord-004615-xfi3p601	46	4	theory	theory	NN
cord-004615-xfi3p601	46	5	using	use	VBG
cord-004615-xfi3p601	46	6	a	a	DT
cord-004615-xfi3p601	46	7	classical	classical	JJ
cord-004615-xfi3p601	46	8	swine	swine	NN
cord-004615-xfi3p601	46	9	fever	fever	NN
cord-004615-xfi3p601	46	10	outbreak	outbreak	NN
cord-004615-xfi3p601	46	11	in	in	IN
cord-004615-xfi3p601	46	12	herds	herd	NNS
cord-004615-xfi3p601	46	13	of	of	IN
cord-004615-xfi3p601	46	14	pigs	pig	NNS
cord-004615-xfi3p601	46	15	as	as	IN
cord-004615-xfi3p601	46	16	motivating	motivate	VBG
cord-004615-xfi3p601	46	17	example	example	NN
cord-004615-xfi3p601	46	18	throughout	throughout	IN
cord-004615-xfi3p601	46	19	.	.	.
cord-004615-xfi3p601	47	1	In	in	IN
cord-004615-xfi3p601	47	2	our	-PRON-	PRP$
cord-004615-xfi3p601	47	3	paper	paper	NN
cord-004615-xfi3p601	47	4	we	-PRON-	PRP
cord-004615-xfi3p601	47	5	use	use	VBP
cord-004615-xfi3p601	47	6	the	the	DT
cord-004615-xfi3p601	47	7	same	same	JJ
cord-004615-xfi3p601	47	8	input	input	NN
cord-004615-xfi3p601	47	9	data	datum	NNS
cord-004615-xfi3p601	47	10	as	as	IN
cord-004615-xfi3p601	47	11	Klinkenberg	Klinkenberg	NNP
cord-004615-xfi3p601	47	12	et	et	NNP
cord-004615-xfi3p601	47	13	al	al	NNP
cord-004615-xfi3p601	47	14	.	.	.
cord-004615-xfi3p601	48	1	[	[	-LRB-
cord-004615-xfi3p601	48	2	1	1	CD
cord-004615-xfi3p601	48	3	]	]	-RRB-
cord-004615-xfi3p601	48	4	.	.	.
cord-004615-xfi3p601	49	1	As	as	IN
cord-004615-xfi3p601	49	2	mentioned	mention	VBN
cord-004615-xfi3p601	49	3	in	in	IN
cord-004615-xfi3p601	49	4	the	the	DT
cord-004615-xfi3p601	49	5	introduction	introduction	NN
cord-004615-xfi3p601	49	6	,	,	,
cord-004615-xfi3p601	49	7	we	-PRON-	PRP
cord-004615-xfi3p601	49	8	first	first	RB
cord-004615-xfi3p601	49	9	need	need	VBP
cord-004615-xfi3p601	49	10	to	to	TO
cord-004615-xfi3p601	49	11	model	model	VB
cord-004615-xfi3p601	49	12	the	the	DT
cord-004615-xfi3p601	49	13	spread	spread	NN
cord-004615-xfi3p601	49	14	of	of	IN
cord-004615-xfi3p601	49	15	the	the	DT
cord-004615-xfi3p601	49	16	infection	infection	NN
cord-004615-xfi3p601	49	17	within	within	IN
cord-004615-xfi3p601	49	18	one	one	CD
cord-004615-xfi3p601	49	19	herd	herd	NN
cord-004615-xfi3p601	49	20	,	,	,
cord-004615-xfi3p601	49	21	since	since	IN
cord-004615-xfi3p601	49	22	the	the	DT
cord-004615-xfi3p601	49	23	infectivity	infectivity	NN
cord-004615-xfi3p601	49	24	of	of	IN
cord-004615-xfi3p601	49	25	an	an	DT
cord-004615-xfi3p601	49	26	infective	infective	JJ
cord-004615-xfi3p601	49	27	herd	herd	NN
cord-004615-xfi3p601	49	28	,	,	,
cord-004615-xfi3p601	49	29	and	and	CC
cord-004615-xfi3p601	49	30	also	also	RB
cord-004615-xfi3p601	49	31	the	the	DT
cord-004615-xfi3p601	49	32	time	time	NN
cord-004615-xfi3p601	49	33	at	at	IN
cord-004615-xfi3p601	49	34	which	which	WDT
cord-004615-xfi3p601	49	35	the	the	DT
cord-004615-xfi3p601	49	36	infection	infection	NN
cord-004615-xfi3p601	49	37	is	be	VBZ
cord-004615-xfi3p601	49	38	detected	detect	VBN
cord-004615-xfi3p601	49	39	in	in	IN
cord-004615-xfi3p601	49	40	a	a	DT
cord-004615-xfi3p601	49	41	certain	certain	JJ
cord-004615-xfi3p601	49	42	herd	herd	NN
cord-004615-xfi3p601	49	43	,	,	,
cord-004615-xfi3p601	49	44	depend	depend	VB
cord-004615-xfi3p601	49	45	on	on	IN
cord-004615-xfi3p601	49	46	the	the	DT
cord-004615-xfi3p601	49	47	number	number	NN
cord-004615-xfi3p601	49	48	of	of	IN
cord-004615-xfi3p601	49	49	infected	infected	JJ
cord-004615-xfi3p601	49	50	animals	animal	NNS
cord-004615-xfi3p601	49	51	in	in	IN
cord-004615-xfi3p601	49	52	that	that	DT
cord-004615-xfi3p601	49	53	herd	herd	NN
cord-004615-xfi3p601	49	54	.	.	.
cord-004615-xfi3p601	50	1	We	-PRON-	PRP
cord-004615-xfi3p601	50	2	use	use	VBP
cord-004615-xfi3p601	50	3	t	t	NN
cord-004615-xfi3p601	50	4	for	for	IN
cord-004615-xfi3p601	50	5	the	the	DT
cord-004615-xfi3p601	50	6	time	time	NN
cord-004615-xfi3p601	50	7	elapsed	elapse	VBN
cord-004615-xfi3p601	50	8	since	since	IN
cord-004615-xfi3p601	50	9	the	the	DT
cord-004615-xfi3p601	50	10	first	first	JJ
cord-004615-xfi3p601	50	11	measures	measure	NNS
cord-004615-xfi3p601	50	12	were	be	VBD
cord-004615-xfi3p601	50	13	implemented	implement	VBN
cord-004615-xfi3p601	50	14	.	.	.
cord-004615-xfi3p601	51	1	The	the	DT
cord-004615-xfi3p601	51	2	variable	variable	JJ
cord-004615-xfi3p601	51	3	τ	τ	NN
cord-004615-xfi3p601	51	4	is	be	VBZ
cord-004615-xfi3p601	51	5	used	use	VBN
cord-004615-xfi3p601	51	6	for	for	IN
cord-004615-xfi3p601	51	7	describing	describe	VBG
cord-004615-xfi3p601	51	8	the	the	DT
cord-004615-xfi3p601	51	9	spread	spread	NN
cord-004615-xfi3p601	51	10	of	of	IN
cord-004615-xfi3p601	51	11	the	the	DT
cord-004615-xfi3p601	51	12	infection	infection	NN
cord-004615-xfi3p601	51	13	within	within	IN
cord-004615-xfi3p601	51	14	the	the	DT
cord-004615-xfi3p601	51	15	herds	herd	NNS
cord-004615-xfi3p601	51	16	,	,	,
cord-004615-xfi3p601	51	17	it	-PRON-	PRP
cord-004615-xfi3p601	51	18	is	be	VBZ
cord-004615-xfi3p601	51	19	the	the	DT
cord-004615-xfi3p601	51	20	time	time	NN
cord-004615-xfi3p601	51	21	since	since	IN
cord-004615-xfi3p601	51	22	infection	infection	NN
cord-004615-xfi3p601	51	23	of	of	IN
cord-004615-xfi3p601	51	24	a	a	DT
cord-004615-xfi3p601	51	25	particular	particular	JJ
cord-004615-xfi3p601	51	26	herd	herd	NN
cord-004615-xfi3p601	51	27	and	and	CC
cord-004615-xfi3p601	51	28	therefore	therefore	RB
cord-004615-xfi3p601	51	29	relative	relative	JJ
cord-004615-xfi3p601	51	30	.	.	.
cord-004615-xfi3p601	52	1	The	the	DT
cord-004615-xfi3p601	52	2	τ	τ	NN
cord-004615-xfi3p601	52	3	-clock	-clock	NN
cord-004615-xfi3p601	52	4	starts	start	VBZ
cord-004615-xfi3p601	52	5	ticking	tick	VBG
cord-004615-xfi3p601	52	6	at	at	IN
cord-004615-xfi3p601	52	7	the	the	DT
cord-004615-xfi3p601	52	8	moment	moment	NN
cord-004615-xfi3p601	53	1	the	the	DT
cord-004615-xfi3p601	53	2	first	first	JJ
cord-004615-xfi3p601	53	3	animal	animal	NN
cord-004615-xfi3p601	53	4	in	in	IN
cord-004615-xfi3p601	53	5	the	the	DT
cord-004615-xfi3p601	53	6	herd	herd	NN
cord-004615-xfi3p601	53	7	becomes	become	VBZ
cord-004615-xfi3p601	53	8	infected	infected	JJ
cord-004615-xfi3p601	53	9	.	.	.
cord-004615-xfi3p601	54	1	From	from	IN
cord-004615-xfi3p601	54	2	now	now	RB
cord-004615-xfi3p601	54	3	on	on	RB
cord-004615-xfi3p601	54	4	,	,	,
cord-004615-xfi3p601	54	5	we	-PRON-	PRP
cord-004615-xfi3p601	54	6	will	will	MD
cord-004615-xfi3p601	54	7	call	call	VB
cord-004615-xfi3p601	54	8	τ	τ	NN
cord-004615-xfi3p601	54	9	the	the	DT
cord-004615-xfi3p601	54	10	"	"	``
cord-004615-xfi3p601	54	11	infection	infection	NN
cord-004615-xfi3p601	54	12	-	-	HYPH
cord-004615-xfi3p601	54	13	age	age	NN
cord-004615-xfi3p601	54	14	"	"	''
cord-004615-xfi3p601	54	15	or	or	CC
cord-004615-xfi3p601	54	16	"	"	``
cord-004615-xfi3p601	54	17	age	age	NN
cord-004615-xfi3p601	54	18	"	"	''
cord-004615-xfi3p601	54	19	of	of	IN
cord-004615-xfi3p601	54	20	the	the	DT
cord-004615-xfi3p601	54	21	herd	herd	NN
cord-004615-xfi3p601	54	22	.	.	.
cord-004615-xfi3p601	55	1	We	-PRON-	PRP
cord-004615-xfi3p601	55	2	use	use	VBP
cord-004615-xfi3p601	55	3	only	only	RB
cord-004615-xfi3p601	55	4	four	four	CD
cord-004615-xfi3p601	55	5	types	type	NNS
cord-004615-xfi3p601	55	6	of	of	IN
cord-004615-xfi3p601	55	7	disease	disease	NN
cord-004615-xfi3p601	55	8	-	-	HYPH
cord-004615-xfi3p601	55	9	related	relate	VBN
cord-004615-xfi3p601	55	10	parameters	parameter	NNS
cord-004615-xfi3p601	55	11	:	:	:
cord-004615-xfi3p601	55	12	µ	µ	LS
cord-004615-xfi3p601	55	13	:	:	:
cord-004615-xfi3p601	55	14	The	the	DT
cord-004615-xfi3p601	55	15	recovery	recovery	NN
cord-004615-xfi3p601	55	16	rate	rate	NN
cord-004615-xfi3p601	55	17	of	of	IN
cord-004615-xfi3p601	55	18	individual	individual	JJ
cord-004615-xfi3p601	55	19	animals	animal	NNS
cord-004615-xfi3p601	55	20	in	in	IN
cord-004615-xfi3p601	55	21	a	a	DT
cord-004615-xfi3p601	55	22	herd	herd	NN
cord-004615-xfi3p601	55	23	.	.	.
cord-004615-xfi3p601	56	1	λ	λ	NN
cord-004615-xfi3p601	56	2	:	:	:
cord-004615-xfi3p601	56	3	The	the	DT
cord-004615-xfi3p601	56	4	infection	infection	NN
cord-004615-xfi3p601	56	5	rate	rate	NN
cord-004615-xfi3p601	56	6	of	of	IN
cord-004615-xfi3p601	56	7	individual	individual	JJ
cord-004615-xfi3p601	56	8	animals	animal	NNS
cord-004615-xfi3p601	56	9	within	within	IN
cord-004615-xfi3p601	56	10	a	a	DT
cord-004615-xfi3p601	56	11	herd	herd	NN
cord-004615-xfi3p601	56	12	.	.	.
cord-004615-xfi3p601	57	1	α	α	NN
cord-004615-xfi3p601	57	2	:	:	:
cord-004615-xfi3p601	57	3	The	the	DT
cord-004615-xfi3p601	57	4	per	per	IN
cord-004615-xfi3p601	57	5	capita	capita	FW
cord-004615-xfi3p601	57	6	detection	detection	NN
cord-004615-xfi3p601	57	7	rate	rate	NN
cord-004615-xfi3p601	57	8	of	of	IN
cord-004615-xfi3p601	57	9	infected	infected	JJ
cord-004615-xfi3p601	57	10	animals	animal	NNS
cord-004615-xfi3p601	57	11	within	within	IN
cord-004615-xfi3p601	57	12	a	a	DT
cord-004615-xfi3p601	57	13	herd	herd	NN
cord-004615-xfi3p601	57	14	.	.	.
cord-004615-xfi3p601	58	1	β	β	NN
cord-004615-xfi3p601	58	2	:	:	:
cord-004615-xfi3p601	58	3	The	the	DT
cord-004615-xfi3p601	58	4	rate	rate	NN
cord-004615-xfi3p601	58	5	at	at	IN
cord-004615-xfi3p601	58	6	which	which	WDT
cord-004615-xfi3p601	58	7	one	one	CD
cord-004615-xfi3p601	58	8	infected	infect	VBN
cord-004615-xfi3p601	58	9	animal	animal	NN
cord-004615-xfi3p601	58	10	infects	infect	VBZ
cord-004615-xfi3p601	58	11	susceptible	susceptible	JJ
cord-004615-xfi3p601	58	12	herds	herd	NNS
cord-004615-xfi3p601	58	13	.	.	.
cord-004615-xfi3p601	59	1	We	-PRON-	PRP
cord-004615-xfi3p601	59	2	assume	assume	VBP
cord-004615-xfi3p601	59	3	that	that	IN
cord-004615-xfi3p601	59	4	as	as	RB
cord-004615-xfi3p601	59	5	soon	soon	RB
cord-004615-xfi3p601	59	6	as	as	IN
cord-004615-xfi3p601	59	7	an	an	DT
cord-004615-xfi3p601	59	8	infection	infection	NN
cord-004615-xfi3p601	59	9	at	at	IN
cord-004615-xfi3p601	59	10	a	a	DT
cord-004615-xfi3p601	59	11	particular	particular	JJ
cord-004615-xfi3p601	59	12	herd	herd	NN
cord-004615-xfi3p601	59	13	is	be	VBZ
cord-004615-xfi3p601	59	14	detected	detect	VBN
cord-004615-xfi3p601	59	15	,	,	,
cord-004615-xfi3p601	59	16	the	the	DT
cord-004615-xfi3p601	59	17	whole	whole	JJ
cord-004615-xfi3p601	59	18	herd	herd	NN
cord-004615-xfi3p601	59	19	will	will	MD
cord-004615-xfi3p601	59	20	be	be	VB
cord-004615-xfi3p601	59	21	culled	cull	VBN
cord-004615-xfi3p601	59	22	instantaneously	instantaneously	RB
cord-004615-xfi3p601	59	23	.	.	.
cord-004615-xfi3p601	60	1	Further	further	RB
cord-004615-xfi3p601	60	2	we	-PRON-	PRP
cord-004615-xfi3p601	60	3	assume	assume	VBP
cord-004615-xfi3p601	60	4	that	that	IN
cord-004615-xfi3p601	60	5	the	the	DT
cord-004615-xfi3p601	60	6	rate	rate	NN
cord-004615-xfi3p601	60	7	of	of	IN
cord-004615-xfi3p601	60	8	detection	detection	NN
cord-004615-xfi3p601	60	9	is	be	VBZ
cord-004615-xfi3p601	60	10	proportional	proportional	JJ
cord-004615-xfi3p601	60	11	to	to	IN
cord-004615-xfi3p601	60	12	the	the	DT
cord-004615-xfi3p601	60	13	number	number	NN
cord-004615-xfi3p601	60	14	of	of	IN
cord-004615-xfi3p601	60	15	infected	infected	JJ
cord-004615-xfi3p601	60	16	animals	animal	NNS
cord-004615-xfi3p601	60	17	at	at	IN
cord-004615-xfi3p601	60	18	infection	infection	NN
cord-004615-xfi3p601	60	19	-	-	HYPH
cord-004615-xfi3p601	60	20	age	age	NN
cord-004615-xfi3p601	60	21	τ	τ	NN
cord-004615-xfi3p601	60	22	,	,	,
cord-004615-xfi3p601	60	23	I	-PRON-	PRP
cord-004615-xfi3p601	60	24	(	(	-LRB-
cord-004615-xfi3p601	60	25	τ	τ	NN
cord-004615-xfi3p601	60	26	)	)	-RRB-
cord-004615-xfi3p601	60	27	,	,	,
cord-004615-xfi3p601	60	28	i.e.	i.e.	FW
cord-004615-xfi3p601	60	29	the	the	DT
cord-004615-xfi3p601	60	30	detection	detection	NN
cord-004615-xfi3p601	60	31	rate	rate	NN
cord-004615-xfi3p601	60	32	is	be	VBZ
cord-004615-xfi3p601	60	33	αI	αI	NNP
cord-004615-xfi3p601	60	34	(	(	-LRB-
cord-004615-xfi3p601	60	35	τ	τ	NN
cord-004615-xfi3p601	60	36	)	)	-RRB-
cord-004615-xfi3p601	60	37	,	,	,
cord-004615-xfi3p601	60	38	where	where	WRB
cord-004615-xfi3p601	60	39	α	α	NNP
cord-004615-xfi3p601	60	40	does	do	VBZ
cord-004615-xfi3p601	60	41	not	not	RB
cord-004615-xfi3p601	60	42	depend	depend	VB
cord-004615-xfi3p601	60	43	on	on	IN
cord-004615-xfi3p601	60	44	the	the	DT
cord-004615-xfi3p601	60	45	infection	infection	NN
cord-004615-xfi3p601	60	46	-	-	HYPH
cord-004615-xfi3p601	60	47	age	age	NN
cord-004615-xfi3p601	60	48	.	.	.
cord-004615-xfi3p601	61	1	We	-PRON-	PRP
cord-004615-xfi3p601	61	2	assume	assume	VBP
cord-004615-xfi3p601	61	3	that	that	IN
cord-004615-xfi3p601	61	4	the	the	DT
cord-004615-xfi3p601	61	5	infection	infection	NN
cord-004615-xfi3p601	61	6	in	in	IN
cord-004615-xfi3p601	61	7	a	a	DT
cord-004615-xfi3p601	61	8	herd	herd	NN
cord-004615-xfi3p601	61	9	develops	develop	VBZ
cord-004615-xfi3p601	61	10	as	as	IN
cord-004615-xfi3p601	61	11	an	an	DT
cord-004615-xfi3p601	61	12	autonomous	autonomous	JJ
cord-004615-xfi3p601	61	13	process	process	NN
cord-004615-xfi3p601	61	14	until	until	IN
cord-004615-xfi3p601	61	15	detection	detection	NN
cord-004615-xfi3p601	61	16	.	.	.
cord-004615-xfi3p601	62	1	The	the	DT
cord-004615-xfi3p601	62	2	number	number	NN
cord-004615-xfi3p601	62	3	of	of	IN
cord-004615-xfi3p601	62	4	infected	infected	JJ
cord-004615-xfi3p601	62	5	animals	animal	NNS
cord-004615-xfi3p601	62	6	in	in	IN
cord-004615-xfi3p601	62	7	a	a	DT
cord-004615-xfi3p601	62	8	herd	herd	NN
cord-004615-xfi3p601	62	9	therefore	therefore	RB
cord-004615-xfi3p601	62	10	depends	depend	VBZ
cord-004615-xfi3p601	62	11	only	only	RB
cord-004615-xfi3p601	62	12	on	on	IN
cord-004615-xfi3p601	62	13	the	the	DT
cord-004615-xfi3p601	62	14	infection	infection	NN
cord-004615-xfi3p601	62	15	-	-	HYPH
cord-004615-xfi3p601	62	16	age	age	NN
cord-004615-xfi3p601	62	17	τ	τ	NN
cord-004615-xfi3p601	62	18	,	,	,
cord-004615-xfi3p601	62	19	and	and	CC
cord-004615-xfi3p601	62	20	not	not	RB
cord-004615-xfi3p601	62	21	on	on	IN
cord-004615-xfi3p601	62	22	the	the	DT
cord-004615-xfi3p601	62	23	absolute	absolute	JJ
cord-004615-xfi3p601	62	24	time	time	NN
cord-004615-xfi3p601	63	1	t.	t.	NNP
cord-004615-xfi3p601	64	1	We	-PRON-	PRP
cord-004615-xfi3p601	64	2	describe	describe	VBP
cord-004615-xfi3p601	64	3	the	the	DT
cord-004615-xfi3p601	64	4	number	number	NN
cord-004615-xfi3p601	64	5	of	of	IN
cord-004615-xfi3p601	64	6	infective	infective	JJ
cord-004615-xfi3p601	64	7	animals	animal	NNS
cord-004615-xfi3p601	64	8	by	by	IN
cord-004615-xfi3p601	64	9	an	an	DT
cord-004615-xfi3p601	64	10	ordinary	ordinary	JJ
cord-004615-xfi3p601	64	11	birth	birth	NN
cord-004615-xfi3p601	64	12	and	and	CC
cord-004615-xfi3p601	64	13	death	death	NN
cord-004615-xfi3p601	64	14	process	process	NN
cord-004615-xfi3p601	64	15	,	,	,
cord-004615-xfi3p601	64	16	writing	write	VBG
cord-004615-xfi3p601	64	17	p	p	NN
cord-004615-xfi3p601	64	18	i	i	PRP
cord-004615-xfi3p601	64	19	(	(	-LRB-
cord-004615-xfi3p601	64	20	τ	τ	NN
cord-004615-xfi3p601	64	21	)	)	-RRB-
cord-004615-xfi3p601	64	22	for	for	IN
cord-004615-xfi3p601	64	23	the	the	DT
cord-004615-xfi3p601	64	24	probability	probability	NN
cord-004615-xfi3p601	64	25	of	of	IN
cord-004615-xfi3p601	64	26	i	i	PRP
cord-004615-xfi3p601	64	27	infective	infective	JJ
cord-004615-xfi3p601	64	28	animals	animal	NNS
cord-004615-xfi3p601	64	29	in	in	IN
cord-004615-xfi3p601	64	30	a	a	DT
cord-004615-xfi3p601	64	31	herd	herd	NN
cord-004615-xfi3p601	64	32	at	at	IN
cord-004615-xfi3p601	64	33	infection	infection	NN
cord-004615-xfi3p601	64	34	-	-	HYPH
cord-004615-xfi3p601	64	35	age	age	NN
cord-004615-xfi3p601	64	36	τ	τ	NN
cord-004615-xfi3p601	64	37	and	and	CC
cord-004615-xfi3p601	64	38	δ	δ	NN
cord-004615-xfi3p601	64	39	ij	ij	NNP
cord-004615-xfi3p601	64	40	for	for	IN
cord-004615-xfi3p601	64	41	the	the	DT
cord-004615-xfi3p601	64	42	Kronecker	Kronecker	NNP
cord-004615-xfi3p601	64	43	Delta	Delta	NNP
cord-004615-xfi3p601	64	44	function	function	NN
cord-004615-xfi3p601	64	45	.	.	.
cord-004615-xfi3p601	65	1	We	-PRON-	PRP
cord-004615-xfi3p601	65	2	have	have	VBP
cord-004615-xfi3p601	65	3	,	,	,
cord-004615-xfi3p601	65	4	(	(	-LRB-
cord-004615-xfi3p601	65	5	see	see	VB
cord-004615-xfi3p601	65	6	e.g.	e.g.	JJ
cord-004615-xfi3p601	65	7	[	[	-LRB-
cord-004615-xfi3p601	65	8	3	3	CD
cord-004615-xfi3p601	65	9	]	]	-RRB-
cord-004615-xfi3p601	65	10	):	):	XX
cord-004615-xfi3p601	66	1	Solving	solve	VBG
cord-004615-xfi3p601	66	2	these	these	DT
cord-004615-xfi3p601	66	3	differential	differential	JJ
cord-004615-xfi3p601	66	4	equations	equation	NNS
cord-004615-xfi3p601	66	5	leads	lead	VBZ
cord-004615-xfi3p601	66	6	to	to	IN
cord-004615-xfi3p601	66	7	:	:	:
cord-004615-xfi3p601	66	8	where	where	WRB
cord-004615-xfi3p601	66	9	r	r	NN
cord-004615-xfi3p601	66	10	=	=	SYM
cord-004615-xfi3p601	66	11	λ	λ	NN
cord-004615-xfi3p601	66	12	−	−	NN
cord-004615-xfi3p601	66	13	µ	µ	NN
cord-004615-xfi3p601	66	14	and	and	CC
cord-004615-xfi3p601	66	15	R	r	NN
cord-004615-xfi3p601	66	16	=	=	NN
cord-004615-xfi3p601	67	1	λ	λ	NNP
cord-004615-xfi3p601	67	2	µ	µ	NNP
cord-004615-xfi3p601	67	3	is	be	VBZ
cord-004615-xfi3p601	67	4	the	the	DT
cord-004615-xfi3p601	67	5	reproduction	reproduction	NN
cord-004615-xfi3p601	67	6	ratio	ratio	NN
cord-004615-xfi3p601	67	7	.	.	.
cord-004615-xfi3p601	68	1	We	-PRON-	PRP
cord-004615-xfi3p601	68	2	assume	assume	VBP
cord-004615-xfi3p601	68	3	λ	λ	NN
cord-004615-xfi3p601	68	4	>	>	XX
cord-004615-xfi3p601	68	5	µ	µ	NN
cord-004615-xfi3p601	68	6	,	,	,
cord-004615-xfi3p601	68	7	otherwise	otherwise	RB
cord-004615-xfi3p601	68	8	the	the	DT
cord-004615-xfi3p601	68	9	infection	infection	NN
cord-004615-xfi3p601	68	10	will	will	MD
cord-004615-xfi3p601	68	11	typically	typically	RB
cord-004615-xfi3p601	68	12	only	only	RB
cord-004615-xfi3p601	68	13	cause	cause	VB
cord-004615-xfi3p601	68	14	a	a	DT
cord-004615-xfi3p601	68	15	minor	minor	JJ
cord-004615-xfi3p601	68	16	outbreak	outbreak	NN
cord-004615-xfi3p601	68	17	within	within	IN
cord-004615-xfi3p601	68	18	a	a	DT
cord-004615-xfi3p601	68	19	herd	herd	NN
cord-004615-xfi3p601	68	20	,	,	,
cord-004615-xfi3p601	68	21	and	and	CC
cord-004615-xfi3p601	68	22	will	will	MD
cord-004615-xfi3p601	68	23	therefore	therefore	RB
cord-004615-xfi3p601	68	24	typically	typically	RB
cord-004615-xfi3p601	68	25	not	not	RB
cord-004615-xfi3p601	68	26	infect	infect	VB
cord-004615-xfi3p601	68	27	other	other	JJ
cord-004615-xfi3p601	68	28	herds	herd	NNS
cord-004615-xfi3p601	68	29	.	.	.
cord-004615-xfi3p601	69	1	Hence	hence	RB
cord-004615-xfi3p601	69	2	,	,	,
cord-004615-xfi3p601	69	3	conditioned	condition	VBN
cord-004615-xfi3p601	69	4	on	on	IN
cord-004615-xfi3p601	69	5	the	the	DT
cord-004615-xfi3p601	69	6	event	event	NN
cord-004615-xfi3p601	69	7	that	that	IN
cord-004615-xfi3p601	69	8	the	the	DT
cord-004615-xfi3p601	69	9	epidemic	epidemic	NN
cord-004615-xfi3p601	69	10	in	in	IN
cord-004615-xfi3p601	69	11	a	a	DT
cord-004615-xfi3p601	69	12	herd	herd	NN
cord-004615-xfi3p601	69	13	does	do	VBZ
cord-004615-xfi3p601	69	14	not	not	RB
cord-004615-xfi3p601	69	15	go	go	VB
cord-004615-xfi3p601	69	16	extinct	extinct	JJ
cord-004615-xfi3p601	69	17	before	before	IN
cord-004615-xfi3p601	69	18	age	age	NN
cord-004615-xfi3p601	69	19	τ	τ	NN
cord-004615-xfi3p601	69	20	,	,	,
cord-004615-xfi3p601	69	21	i.e.	i.e.	FW
cord-004615-xfi3p601	69	22	I	i	NN
cord-004615-xfi3p601	69	23	(	(	-LRB-
cord-004615-xfi3p601	69	24	τ	τ	NN
cord-004615-xfi3p601	69	25	)	)	-RRB-
cord-004615-xfi3p601	69	26	>	>	XX
cord-004615-xfi3p601	69	27	0	0	NFP
cord-004615-xfi3p601	69	28	,	,	,
cord-004615-xfi3p601	69	29	I	-PRON-	PRP
cord-004615-xfi3p601	69	30	(	(	-LRB-
cord-004615-xfi3p601	69	31	τ	τ	NN
cord-004615-xfi3p601	69	32	)	)	-RRB-
cord-004615-xfi3p601	69	33	is	be	VBZ
cord-004615-xfi3p601	69	34	geometrically	geometrically	RB
cord-004615-xfi3p601	69	35	distributed	distribute	VBN
cord-004615-xfi3p601	69	36	with	with	IN
cord-004615-xfi3p601	69	37	parameter	parameter	NN
cord-004615-xfi3p601	69	38	(	(	-LRB-
cord-004615-xfi3p601	69	39	1	1	CD
cord-004615-xfi3p601	69	40	−	−	NN
cord-004615-xfi3p601	69	41	Rp	rp	NN
cord-004615-xfi3p601	69	42	0	0	CD
cord-004615-xfi3p601	69	43	(	(	-LRB-
cord-004615-xfi3p601	69	44	τ	τ	NN
cord-004615-xfi3p601	69	45	)	)	-RRB-
cord-004615-xfi3p601	69	46	)	)	-RRB-
cord-004615-xfi3p601	69	47	=	=	NFP
cord-004615-xfi3p601	70	1	R−1	R−1	NFP
cord-004615-xfi3p601	70	2	Re	re	NN
cord-004615-xfi3p601	70	3	rτ	rτ	NNP
cord-004615-xfi3p601	70	4	−1	−1	NNP
cord-004615-xfi3p601	70	5	,	,	,
cord-004615-xfi3p601	70	6	which	which	WDT
cord-004615-xfi3p601	70	7	is	be	VBZ
cord-004615-xfi3p601	70	8	small	small	JJ
cord-004615-xfi3p601	70	9	for	for	IN
cord-004615-xfi3p601	70	10	large	large	JJ
cord-004615-xfi3p601	70	11	τ	τ	NN
cord-004615-xfi3p601	70	12	.	.	.
cord-004615-xfi3p601	71	1	A	a	DT
cord-004615-xfi3p601	71	2	geometric	geometric	JJ
cord-004615-xfi3p601	71	3	random	random	JJ
cord-004615-xfi3p601	71	4	variable	variable	NN
cord-004615-xfi3p601	71	5	with	with	IN
cord-004615-xfi3p601	71	6	small	small	JJ
cord-004615-xfi3p601	71	7	parameter	parameter	NN
cord-004615-xfi3p601	71	8	can	can	MD
cord-004615-xfi3p601	71	9	be	be	VB
cord-004615-xfi3p601	71	10	approximated	approximate	VBN
cord-004615-xfi3p601	71	11	by	by	IN
cord-004615-xfi3p601	71	12	an	an	DT
cord-004615-xfi3p601	71	13	exponential	exponential	JJ
cord-004615-xfi3p601	71	14	random	random	JJ
cord-004615-xfi3p601	71	15	variable	variable	NN
cord-004615-xfi3p601	71	16	with	with	IN
cord-004615-xfi3p601	71	17	the	the	DT
cord-004615-xfi3p601	71	18	same	same	JJ
cord-004615-xfi3p601	71	19	parameter	parameter	NN
cord-004615-xfi3p601	71	20	.	.	.
cord-004615-xfi3p601	72	1	Therefore	therefore	RB
cord-004615-xfi3p601	72	2	,	,	,
cord-004615-xfi3p601	72	3	for	for	IN
cord-004615-xfi3p601	72	4	large	large	JJ
cord-004615-xfi3p601	72	5	τ	τ	NN
cord-004615-xfi3p601	72	6	,	,	,
cord-004615-xfi3p601	72	7	I	-PRON-	PRP
cord-004615-xfi3p601	72	8	(	(	-LRB-
cord-004615-xfi3p601	72	9	τ	τ	NN
cord-004615-xfi3p601	72	10	)	)	-RRB-
cord-004615-xfi3p601	72	11	can	can	MD
cord-004615-xfi3p601	72	12	be	be	VB
cord-004615-xfi3p601	72	13	approximated	approximate	VBN
cord-004615-xfi3p601	72	14	byH	byH	NNS
cord-004615-xfi3p601	72	15	(	(	-LRB-
cord-004615-xfi3p601	72	16	τ	τ	NN
cord-004615-xfi3p601	72	17	)	)	-RRB-
cord-004615-xfi3p601	72	18	,	,	,
cord-004615-xfi3p601	72	19	whereH	whereH	NNP
cord-004615-xfi3p601	72	20	(	(	-LRB-
cord-004615-xfi3p601	72	21	τ	τ	NN
cord-004615-xfi3p601	72	22	)	)	-RRB-
cord-004615-xfi3p601	72	23	is	be	VBZ
cord-004615-xfi3p601	72	24	an	an	DT
cord-004615-xfi3p601	72	25	exponential	exponential	JJ
cord-004615-xfi3p601	72	26	random	random	JJ
cord-004615-xfi3p601	72	27	variable	variable	NN
cord-004615-xfi3p601	72	28	with	with	IN
cord-004615-xfi3p601	72	29	where	where	WRB
cord-004615-xfi3p601	72	30	H	H	NNP
cord-004615-xfi3p601	72	31	is	be	VBZ
cord-004615-xfi3p601	72	32	an	an	DT
cord-004615-xfi3p601	72	33	exponential	exponential	JJ
cord-004615-xfi3p601	72	34	random	random	JJ
cord-004615-xfi3p601	72	35	variable	variable	NN
cord-004615-xfi3p601	72	36	with	with	IN
cord-004615-xfi3p601	72	37	parameter	parameter	NN
cord-004615-xfi3p601	72	38	R−1	r−1	CD
cord-004615-xfi3p601	72	39	R	r	NN
cord-004615-xfi3p601	72	40	.	.	.
cord-004615-xfi3p601	73	1	For	for	IN
cord-004615-xfi3p601	73	2	large	large	JJ
cord-004615-xfi3p601	73	3	τ	τ	NN
cord-004615-xfi3p601	73	4	,	,	,
cord-004615-xfi3p601	73	5	the	the	DT
cord-004615-xfi3p601	73	6	term	term	NN
cord-004615-xfi3p601	73	7	1	1	CD
cord-004615-xfi3p601	73	8	R	r	NN
cord-004615-xfi3p601	73	9	is	be	VBZ
cord-004615-xfi3p601	73	10	negligible	negligible	JJ
cord-004615-xfi3p601	73	11	compared	compare	VBN
cord-004615-xfi3p601	73	12	to	to	IN
cord-004615-xfi3p601	73	13	e	e	NN
cord-004615-xfi3p601	73	14	rτ	rτ	XX
cord-004615-xfi3p601	73	15	.	.	.
cord-004615-xfi3p601	74	1	So	so	RB
cord-004615-xfi3p601	74	2	we	-PRON-	PRP
cord-004615-xfi3p601	74	3	use	use	VBP
cord-004615-xfi3p601	74	4	the	the	DT
cord-004615-xfi3p601	74	5	approximation	approximation	NN
cord-004615-xfi3p601	74	6	where	where	WRB
cord-004615-xfi3p601	74	7	the	the	DT
cord-004615-xfi3p601	74	8	equality	equality	NN
cord-004615-xfi3p601	74	9	is	be	VBZ
cord-004615-xfi3p601	74	10	in	in	IN
cord-004615-xfi3p601	74	11	the	the	DT
cord-004615-xfi3p601	74	12	distributional	distributional	JJ
cord-004615-xfi3p601	74	13	sense	sense	NN
cord-004615-xfi3p601	74	14	.	.	.
cord-004615-xfi3p601	75	1	We	-PRON-	PRP
cord-004615-xfi3p601	75	2	can	can	MD
cord-004615-xfi3p601	75	3	interpret	interpret	VB
cord-004615-xfi3p601	75	4	this	this	DT
cord-004615-xfi3p601	75	5	approximation	approximation	NN
cord-004615-xfi3p601	75	6	as	as	IN
cord-004615-xfi3p601	75	7	follows	follow	VBZ
cord-004615-xfi3p601	75	8	.	.	.
cord-004615-xfi3p601	76	1	The	the	DT
cord-004615-xfi3p601	76	2	random	random	JJ
cord-004615-xfi3p601	76	3	variable	variable	NN
cord-004615-xfi3p601	76	4	H	h	NN
cord-004615-xfi3p601	76	5	represents	represent	VBZ
cord-004615-xfi3p601	76	6	the	the	DT
cord-004615-xfi3p601	76	7	random	random	JJ
cord-004615-xfi3p601	76	8	character	character	NN
cord-004615-xfi3p601	76	9	of	of	IN
cord-004615-xfi3p601	76	10	the	the	DT
cord-004615-xfi3p601	76	11	start	start	NN
cord-004615-xfi3p601	76	12	of	of	IN
cord-004615-xfi3p601	76	13	the	the	DT
cord-004615-xfi3p601	76	14	outbreak	outbreak	NN
cord-004615-xfi3p601	76	15	in	in	IN
cord-004615-xfi3p601	76	16	a	a	DT
cord-004615-xfi3p601	76	17	herd	herd	NN
cord-004615-xfi3p601	76	18	,	,	,
cord-004615-xfi3p601	76	19	when	when	WRB
cord-004615-xfi3p601	76	20	only	only	RB
cord-004615-xfi3p601	76	21	a	a	DT
cord-004615-xfi3p601	76	22	few	few	JJ
cord-004615-xfi3p601	76	23	animals	animal	NNS
cord-004615-xfi3p601	76	24	are	be	VBP
cord-004615-xfi3p601	76	25	infective	infective	JJ
cord-004615-xfi3p601	76	26	.	.	.
cord-004615-xfi3p601	77	1	If	if	IN
cord-004615-xfi3p601	77	2	the	the	DT
cord-004615-xfi3p601	77	3	disease	disease	NN
cord-004615-xfi3p601	77	4	does	do	VBZ
cord-004615-xfi3p601	77	5	not	not	RB
cord-004615-xfi3p601	77	6	go	go	VB
cord-004615-xfi3p601	77	7	extinct	extinct	JJ
cord-004615-xfi3p601	77	8	,	,	,
cord-004615-xfi3p601	77	9	then	then	RB
cord-004615-xfi3p601	77	10	after	after	IN
cord-004615-xfi3p601	77	11	the	the	DT
cord-004615-xfi3p601	77	12	initial	initial	JJ
cord-004615-xfi3p601	77	13	phase	phase	NN
cord-004615-xfi3p601	77	14	,	,	,
cord-004615-xfi3p601	77	15	there	there	EX
cord-004615-xfi3p601	77	16	are	be	VBP
cord-004615-xfi3p601	77	17	many	many	JJ
cord-004615-xfi3p601	77	18	infected	infected	JJ
cord-004615-xfi3p601	77	19	animals	animal	NNS
cord-004615-xfi3p601	77	20	in	in	IN
cord-004615-xfi3p601	77	21	the	the	DT
cord-004615-xfi3p601	77	22	herd	herd	NN
cord-004615-xfi3p601	77	23	,	,	,
cord-004615-xfi3p601	77	24	each	each	DT
cord-004615-xfi3p601	77	25	of	of	IN
cord-004615-xfi3p601	77	26	which	which	WDT
cord-004615-xfi3p601	77	27	causes	cause	VBZ
cord-004615-xfi3p601	77	28	an	an	DT
cord-004615-xfi3p601	77	29	independent	independent	JJ
cord-004615-xfi3p601	77	30	number	number	NN
cord-004615-xfi3p601	77	31	of	of	IN
cord-004615-xfi3p601	77	32	new	new	JJ
cord-004615-xfi3p601	77	33	infections	infection	NNS
cord-004615-xfi3p601	77	34	per	per	IN
cord-004615-xfi3p601	77	35	time	time	NN
cord-004615-xfi3p601	77	36	unit	unit	NN
cord-004615-xfi3p601	77	37	.	.	.
cord-004615-xfi3p601	78	1	According	accord	VBG
cord-004615-xfi3p601	78	2	to	to	IN
cord-004615-xfi3p601	78	3	the	the	DT
cord-004615-xfi3p601	78	4	law	law	NN
cord-004615-xfi3p601	78	5	of	of	IN
cord-004615-xfi3p601	78	6	large	large	JJ
cord-004615-xfi3p601	78	7	numbers	number	NNS
cord-004615-xfi3p601	78	8	,	,	,
cord-004615-xfi3p601	78	9	this	this	DT
cord-004615-xfi3p601	78	10	means	mean	VBZ
cord-004615-xfi3p601	78	11	that	that	IN
cord-004615-xfi3p601	78	12	the	the	DT
cord-004615-xfi3p601	78	13	growth	growth	NN
cord-004615-xfi3p601	78	14	rate	rate	NN
cord-004615-xfi3p601	78	15	is	be	VBZ
cord-004615-xfi3p601	78	16	eventually	eventually	RB
cord-004615-xfi3p601	78	17	almost	almost	RB
cord-004615-xfi3p601	78	18	deterministic	deterministic	JJ
cord-004615-xfi3p601	78	19	.	.	.
cord-004615-xfi3p601	79	1	We	-PRON-	PRP
cord-004615-xfi3p601	79	2	also	also	RB
cord-004615-xfi3p601	79	3	use	use	VBP
cord-004615-xfi3p601	79	4	this	this	DT
cord-004615-xfi3p601	79	5	approximation	approximation	NN
cord-004615-xfi3p601	79	6	for	for	IN
cord-004615-xfi3p601	79	7	small	small	JJ
cord-004615-xfi3p601	79	8	τ	τ	NN
cord-004615-xfi3p601	79	9	.	.	.
cord-004615-xfi3p601	80	1	We	-PRON-	PRP
cord-004615-xfi3p601	80	2	use	use	VBP
cord-004615-xfi3p601	80	3	the	the	DT
cord-004615-xfi3p601	80	4	word	word	NN
cord-004615-xfi3p601	80	5	infective	infective	JJ
cord-004615-xfi3p601	80	6	for	for	IN
cord-004615-xfi3p601	80	7	animals	animal	NNS
cord-004615-xfi3p601	80	8	or	or	CC
cord-004615-xfi3p601	80	9	herds	herd	NNS
cord-004615-xfi3p601	80	10	that	that	WDT
cord-004615-xfi3p601	80	11	are	be	VBP
cord-004615-xfi3p601	80	12	able	able	JJ
cord-004615-xfi3p601	80	13	to	to	TO
cord-004615-xfi3p601	80	14	spread	spread	VB
cord-004615-xfi3p601	80	15	the	the	DT
cord-004615-xfi3p601	80	16	infection	infection	NN
cord-004615-xfi3p601	80	17	.	.	.
cord-004615-xfi3p601	81	1	We	-PRON-	PRP
cord-004615-xfi3p601	81	2	use	use	VBP
cord-004615-xfi3p601	81	3	the	the	DT
cord-004615-xfi3p601	81	4	notation	notation	NN
cord-004615-xfi3p601	81	5	I	-PRON-	PRP
cord-004615-xfi3p601	81	6	(	(	-LRB-
cord-004615-xfi3p601	81	7	τ	τ	NN
cord-004615-xfi3p601	81	8	;	;	:
cord-004615-xfi3p601	81	9	h	h	LS
cord-004615-xfi3p601	81	10	)	)	-RRB-
cord-004615-xfi3p601	81	11	for	for	IN
cord-004615-xfi3p601	81	12	the	the	DT
cord-004615-xfi3p601	81	13	number	number	NN
cord-004615-xfi3p601	81	14	of	of	IN
cord-004615-xfi3p601	81	15	infective	infective	JJ
cord-004615-xfi3p601	81	16	animals	animal	NNS
cord-004615-xfi3p601	81	17	in	in	IN
cord-004615-xfi3p601	81	18	a	a	DT
cord-004615-xfi3p601	81	19	particular	particular	JJ
cord-004615-xfi3p601	81	20	herd	herd	NN
cord-004615-xfi3p601	81	21	,	,	,
cord-004615-xfi3p601	81	22	with	with	IN
cord-004615-xfi3p601	81	23	H	h	NN
cord-004615-xfi3p601	81	24	=	=	SYM
cord-004615-xfi3p601	81	25	h	h	NN
cord-004615-xfi3p601	81	26	given	give	VBN
cord-004615-xfi3p601	81	27	.	.	.
cord-004615-xfi3p601	82	1	1	1	LS
cord-004615-xfi3p601	82	2	.	.	.
cord-004615-xfi3p601	83	1	We	-PRON-	PRP
cord-004615-xfi3p601	83	2	assume	assume	VBP
cord-004615-xfi3p601	83	3	that	that	IN
cord-004615-xfi3p601	83	4	the	the	DT
cord-004615-xfi3p601	83	5	infection	infection	NN
cord-004615-xfi3p601	83	6	and	and	CC
cord-004615-xfi3p601	83	7	recovery	recovery	NN
cord-004615-xfi3p601	83	8	rate	rate	NN
cord-004615-xfi3p601	83	9	of	of	IN
cord-004615-xfi3p601	83	10	individual	individual	JJ
cord-004615-xfi3p601	83	11	infected	infect	VBN
cord-004615-xfi3p601	83	12	animals	animal	NNS
cord-004615-xfi3p601	83	13	are	be	VBP
cord-004615-xfi3p601	83	14	independent	independent	JJ
cord-004615-xfi3p601	83	15	of	of	IN
cord-004615-xfi3p601	83	16	time	time	NN
cord-004615-xfi3p601	83	17	and	and	CC
cord-004615-xfi3p601	83	18	age	age	NN
cord-004615-xfi3p601	83	19	.	.	.
cord-004615-xfi3p601	84	1	2	2	LS
cord-004615-xfi3p601	84	2	.	.	.
cord-004615-xfi3p601	85	1	It	-PRON-	PRP
cord-004615-xfi3p601	85	2	is	be	VBZ
cord-004615-xfi3p601	85	3	possible	possible	JJ
cord-004615-xfi3p601	85	4	to	to	TO
cord-004615-xfi3p601	85	5	use	use	VB
cord-004615-xfi3p601	85	6	alternatives	alternative	NNS
cord-004615-xfi3p601	85	7	for	for	IN
cord-004615-xfi3p601	85	8	the	the	DT
cord-004615-xfi3p601	85	9	birth	birth	NN
cord-004615-xfi3p601	85	10	and	and	CC
cord-004615-xfi3p601	85	11	death	death	NN
cord-004615-xfi3p601	85	12	process	process	NN
cord-004615-xfi3p601	85	13	to	to	TO
cord-004615-xfi3p601	85	14	describe	describe	VB
cord-004615-xfi3p601	85	15	the	the	DT
cord-004615-xfi3p601	85	16	spread	spread	NN
cord-004615-xfi3p601	85	17	within	within	IN
cord-004615-xfi3p601	85	18	a	a	DT
cord-004615-xfi3p601	85	19	herd	herd	NN
cord-004615-xfi3p601	85	20	,	,	,
cord-004615-xfi3p601	85	21	for	for	IN
cord-004615-xfi3p601	85	22	example	example	NN
cord-004615-xfi3p601	85	23	the	the	DT
cord-004615-xfi3p601	85	24	contact	contact	NN
cord-004615-xfi3p601	85	25	process	process	NN
cord-004615-xfi3p601	85	26	.	.	.
cord-004615-xfi3p601	86	1	The	the	DT
cord-004615-xfi3p601	86	2	contact	contact	NN
cord-004615-xfi3p601	86	3	process	process	NN
cord-004615-xfi3p601	86	4	is	be	VBZ
cord-004615-xfi3p601	86	5	appropriate	appropriate	JJ
cord-004615-xfi3p601	86	6	when	when	WRB
cord-004615-xfi3p601	86	7	we	-PRON-	PRP
cord-004615-xfi3p601	86	8	have	have	VBP
cord-004615-xfi3p601	86	9	a	a	DT
cord-004615-xfi3p601	86	10	situation	situation	NN
cord-004615-xfi3p601	86	11	where	where	WRB
cord-004615-xfi3p601	86	12	all	all	DT
cord-004615-xfi3p601	86	13	animals	animal	NNS
cord-004615-xfi3p601	86	14	are	be	VBP
cord-004615-xfi3p601	86	15	positioned	position	VBN
cord-004615-xfi3p601	86	16	in	in	IN
cord-004615-xfi3p601	86	17	a	a	DT
cord-004615-xfi3p601	86	18	row	row	NN
cord-004615-xfi3p601	86	19	and	and	CC
cord-004615-xfi3p601	86	20	do	do	VBP
cord-004615-xfi3p601	86	21	not	not	RB
cord-004615-xfi3p601	86	22	change	change	VB
cord-004615-xfi3p601	86	23	position	position	NN
cord-004615-xfi3p601	86	24	.	.	.
cord-004615-xfi3p601	87	1	Each	each	DT
cord-004615-xfi3p601	87	2	animal	animal	NN
cord-004615-xfi3p601	87	3	can	can	MD
cord-004615-xfi3p601	87	4	only	only	RB
cord-004615-xfi3p601	87	5	infect	infect	VB
cord-004615-xfi3p601	87	6	its	-PRON-	PRP$
cord-004615-xfi3p601	87	7	two	two	CD
cord-004615-xfi3p601	87	8	nearest	near	JJS
cord-004615-xfi3p601	87	9	neighbours	neighbour	NNS
cord-004615-xfi3p601	87	10	.	.	.
cord-004615-xfi3p601	88	1	We	-PRON-	PRP
cord-004615-xfi3p601	88	2	assume	assume	VBP
cord-004615-xfi3p601	88	3	that	that	IN
cord-004615-xfi3p601	88	4	recovered	recover	VBD
cord-004615-xfi3p601	88	5	animals	animal	NNS
cord-004615-xfi3p601	88	6	with	with	IN
cord-004615-xfi3p601	88	7	two	two	CD
cord-004615-xfi3p601	88	8	infective	infective	JJ
cord-004615-xfi3p601	88	9	neighbours	neighbour	NNS
cord-004615-xfi3p601	88	10	are	be	VBP
cord-004615-xfi3p601	88	11	re	re	VBN
cord-004615-xfi3p601	88	12	-	-	VBN
cord-004615-xfi3p601	88	13	infected	infect	VBN
cord-004615-xfi3p601	88	14	immediately	immediately	RB
cord-004615-xfi3p601	88	15	.	.	.
cord-004615-xfi3p601	89	1	Therefore	therefore	RB
cord-004615-xfi3p601	89	2	,	,	,
cord-004615-xfi3p601	89	3	we	-PRON-	PRP
cord-004615-xfi3p601	89	4	only	only	RB
cord-004615-xfi3p601	89	5	consider	consider	VBP
cord-004615-xfi3p601	89	6	the	the	DT
cord-004615-xfi3p601	89	7	animals	animal	NNS
cord-004615-xfi3p601	89	8	at	at	IN
cord-004615-xfi3p601	89	9	the	the	DT
cord-004615-xfi3p601	89	10	edge	edge	NN
cord-004615-xfi3p601	89	11	of	of	IN
cord-004615-xfi3p601	89	12	a	a	DT
cord-004615-xfi3p601	89	13	row	row	NN
cord-004615-xfi3p601	89	14	of	of	IN
cord-004615-xfi3p601	89	15	infective	infective	JJ
cord-004615-xfi3p601	89	16	animals	animal	NNS
cord-004615-xfi3p601	89	17	.	.	.
cord-004615-xfi3p601	90	1	We	-PRON-	PRP
cord-004615-xfi3p601	90	2	still	still	RB
cord-004615-xfi3p601	90	3	assume	assume	VBP
cord-004615-xfi3p601	90	4	that	that	IN
cord-004615-xfi3p601	90	5	the	the	DT
cord-004615-xfi3p601	90	6	recovery	recovery	NN
cord-004615-xfi3p601	90	7	rate	rate	NN
cord-004615-xfi3p601	90	8	is	be	VBZ
cord-004615-xfi3p601	90	9	µ.	µ.	NN
cord-004615-xfi3p601	91	1	An	an	DT
cord-004615-xfi3p601	91	2	infective	infective	JJ
cord-004615-xfi3p601	91	3	animal	animal	NN
cord-004615-xfi3p601	91	4	infects	infect	VBZ
cord-004615-xfi3p601	91	5	each	each	DT
cord-004615-xfi3p601	91	6	of	of	IN
cord-004615-xfi3p601	91	7	its	-PRON-	PRP$
cord-004615-xfi3p601	91	8	susceptible	susceptible	JJ
cord-004615-xfi3p601	91	9	neighbours	neighbour	NNS
cord-004615-xfi3p601	91	10	with	with	IN
cord-004615-xfi3p601	91	11	rate	rate	NN
cord-004615-xfi3p601	91	12	λ	λ	NN
cord-004615-xfi3p601	91	13	.	.	.
cord-004615-xfi3p601	92	1	We	-PRON-	PRP
cord-004615-xfi3p601	92	2	have	have	VBP
cord-004615-xfi3p601	92	3	that	that	WDT
cord-004615-xfi3p601	92	4	Let	let	VB
cord-004615-xfi3p601	92	5	the	the	DT
cord-004615-xfi3p601	92	6	number	number	NN
cord-004615-xfi3p601	92	7	of	of	IN
cord-004615-xfi3p601	92	8	infectives	infective	NNS
cord-004615-xfi3p601	92	9	be	be	VB
cord-004615-xfi3p601	92	10	I	-PRON-	PRP
cord-004615-xfi3p601	92	11	(	(	-LRB-
cord-004615-xfi3p601	92	12	τ	τ	NN
cord-004615-xfi3p601	92	13	)	)	-RRB-
cord-004615-xfi3p601	92	14	.	.	.
cord-004615-xfi3p601	93	1	Then	then	RB
cord-004615-xfi3p601	93	2	E(I	E(I	NNP
cord-004615-xfi3p601	93	3	(	(	-LRB-
cord-004615-xfi3p601	93	4	τ	τ	NN
cord-004615-xfi3p601	93	5	)	)	-RRB-
cord-004615-xfi3p601	93	6	|I	|i	CD
cord-004615-xfi3p601	93	7	(	(	-LRB-
cord-004615-xfi3p601	93	8	τ	τ	NN
cord-004615-xfi3p601	93	9	)	)	-RRB-
cord-004615-xfi3p601	93	10	>	>	NFP
cord-004615-xfi3p601	93	11	0	0	NFP
cord-004615-xfi3p601	93	12	)	)	-RRB-
cord-004615-xfi3p601	93	13	=	=	SYM
cord-004615-xfi3p601	93	14	2rτ	2rτ	NN
cord-004615-xfi3p601	93	15	+	+	CC
cord-004615-xfi3p601	93	16	o(τ	o(τ	CD
cord-004615-xfi3p601	93	17	)	)	-RRB-
cord-004615-xfi3p601	93	18	.	.	.
cord-004615-xfi3p601	94	1	Furthermore	furthermore	RB
cord-004615-xfi3p601	94	2	,	,	,
cord-004615-xfi3p601	94	3	we	-PRON-	PRP
cord-004615-xfi3p601	94	4	can	can	MD
cord-004615-xfi3p601	94	5	show	show	VB
cord-004615-xfi3p601	94	6	that	that	IN
cord-004615-xfi3p601	94	7	Var(I	Var(I	NNP
cord-004615-xfi3p601	94	8	(	(	-LRB-
cord-004615-xfi3p601	94	9	τ	τ	NN
cord-004615-xfi3p601	94	10	)	)	-RRB-
cord-004615-xfi3p601	94	11	|I	|i	CD
cord-004615-xfi3p601	94	12	(	(	-LRB-
cord-004615-xfi3p601	94	13	τ	τ	NN
cord-004615-xfi3p601	94	14	)	)	-RRB-
cord-004615-xfi3p601	94	15	>	>	NFP
cord-004615-xfi3p601	94	16	0	0	NFP
cord-004615-xfi3p601	94	17	)	)	-RRB-
cord-004615-xfi3p601	94	18	=	=	NFP
cord-004615-xfi3p601	94	19	o(τ	o(τ	CD
cord-004615-xfi3p601	94	20	2	2	CD
cord-004615-xfi3p601	94	21	)	)	-RRB-
cord-004615-xfi3p601	94	22	.	.	.
cord-004615-xfi3p601	95	1	This	this	DT
cord-004615-xfi3p601	95	2	implies	imply	VBZ
cord-004615-xfi3p601	95	3	that	that	IN
cord-004615-xfi3p601	95	4	for	for	IN
cord-004615-xfi3p601	95	5	I	-PRON-	PRP
cord-004615-xfi3p601	95	6	(	(	-LRB-
cord-004615-xfi3p601	95	7	τ	τ	NN
cord-004615-xfi3p601	95	8	)	)	-RRB-
cord-004615-xfi3p601	95	9	>	>	NFP
cord-004615-xfi3p601	95	10	0	0	NFP
cord-004615-xfi3p601	95	11	we	-PRON-	PRP
cord-004615-xfi3p601	95	12	have	have	VBP
cord-004615-xfi3p601	95	13	So	so	RB
cord-004615-xfi3p601	95	14	,	,	,
cord-004615-xfi3p601	95	15	in	in	IN
cord-004615-xfi3p601	95	16	contrast	contrast	NN
cord-004615-xfi3p601	95	17	to	to	IN
cord-004615-xfi3p601	95	18	the	the	DT
cord-004615-xfi3p601	95	19	birth	birth	NN
cord-004615-xfi3p601	95	20	and	and	CC
cord-004615-xfi3p601	95	21	death	death	NN
cord-004615-xfi3p601	95	22	model	model	NN
cord-004615-xfi3p601	95	23	,	,	,
cord-004615-xfi3p601	95	24	we	-PRON-	PRP
cord-004615-xfi3p601	95	25	may	may	MD
cord-004615-xfi3p601	95	26	approximate	approximate	VB
cord-004615-xfi3p601	95	27	the	the	DT
cord-004615-xfi3p601	95	28	random	random	JJ
cord-004615-xfi3p601	95	29	variable	variable	NN
cord-004615-xfi3p601	95	30	I	-PRON-	PRP
cord-004615-xfi3p601	95	31	(	(	-LRB-
cord-004615-xfi3p601	95	32	τ	τ	NN
cord-004615-xfi3p601	95	33	)	)	-RRB-
cord-004615-xfi3p601	95	34	for	for	IN
cord-004615-xfi3p601	95	35	large	large	JJ
cord-004615-xfi3p601	95	36	τ	τ	NN
cord-004615-xfi3p601	95	37	by	by	IN
cord-004615-xfi3p601	95	38	a	a	DT
cord-004615-xfi3p601	95	39	deterministic	deterministic	JJ
cord-004615-xfi3p601	95	40	variable	variable	NN
cord-004615-xfi3p601	95	41	2rτ	2rτ	NN
cord-004615-xfi3p601	95	42	.	.	.
cord-004615-xfi3p601	96	1	This	this	DT
cord-004615-xfi3p601	96	2	makes	make	VBZ
cord-004615-xfi3p601	96	3	computations	computation	NNS
cord-004615-xfi3p601	96	4	much	much	RB
cord-004615-xfi3p601	96	5	easier	easy	JJR
cord-004615-xfi3p601	96	6	in	in	IN
cord-004615-xfi3p601	96	7	this	this	DT
cord-004615-xfi3p601	96	8	case	case	NN
cord-004615-xfi3p601	96	9	.	.	.
cord-004615-xfi3p601	97	1	3	3	LS
cord-004615-xfi3p601	97	2	.	.	.
cord-004615-xfi3p601	98	1	In	in	IN
cord-004615-xfi3p601	98	2	the	the	DT
cord-004615-xfi3p601	98	3	original	original	JJ
cord-004615-xfi3p601	98	4	model	model	NN
cord-004615-xfi3p601	98	5	,	,	,
cord-004615-xfi3p601	98	6	the	the	DT
cord-004615-xfi3p601	98	7	number	number	NN
cord-004615-xfi3p601	98	8	of	of	IN
cord-004615-xfi3p601	98	9	animals	animal	NNS
cord-004615-xfi3p601	98	10	in	in	IN
cord-004615-xfi3p601	98	11	one	one	CD
cord-004615-xfi3p601	98	12	herd	herd	NN
cord-004615-xfi3p601	98	13	is	be	VBZ
cord-004615-xfi3p601	98	14	assumed	assume	VBN
cord-004615-xfi3p601	98	15	to	to	TO
cord-004615-xfi3p601	98	16	be	be	VB
cord-004615-xfi3p601	98	17	very	very	RB
cord-004615-xfi3p601	98	18	large	large	JJ
cord-004615-xfi3p601	98	19	compared	compare	VBN
cord-004615-xfi3p601	98	20	to	to	IN
cord-004615-xfi3p601	98	21	the	the	DT
cord-004615-xfi3p601	98	22	number	number	NN
cord-004615-xfi3p601	98	23	of	of	IN
cord-004615-xfi3p601	98	24	infected	infected	JJ
cord-004615-xfi3p601	98	25	animals	animal	NNS
cord-004615-xfi3p601	98	26	.	.	.
cord-004615-xfi3p601	99	1	Therefore	therefore	RB
cord-004615-xfi3p601	99	2	,	,	,
cord-004615-xfi3p601	99	3	we	-PRON-	PRP
cord-004615-xfi3p601	99	4	assume	assume	VBP
cord-004615-xfi3p601	99	5	that	that	IN
cord-004615-xfi3p601	99	6	the	the	DT
cord-004615-xfi3p601	99	7	contact	contact	NN
cord-004615-xfi3p601	99	8	rate	rate	NN
cord-004615-xfi3p601	99	9	between	between	IN
cord-004615-xfi3p601	99	10	infected	infected	JJ
cord-004615-xfi3p601	99	11	and	and	CC
cord-004615-xfi3p601	99	12	susceptible	susceptible	JJ
cord-004615-xfi3p601	99	13	animals	animal	NNS
cord-004615-xfi3p601	99	14	is	be	VBZ
cord-004615-xfi3p601	99	15	constant	constant	JJ
cord-004615-xfi3p601	99	16	,	,	,
cord-004615-xfi3p601	99	17	and	and	CC
cord-004615-xfi3p601	99	18	hence	hence	RB
cord-004615-xfi3p601	99	19	so	so	RB
cord-004615-xfi3p601	99	20	is	be	VBZ
cord-004615-xfi3p601	99	21	the	the	DT
cord-004615-xfi3p601	99	22	birth	birth	NN
cord-004615-xfi3p601	99	23	rate	rate	NN
cord-004615-xfi3p601	99	24	.	.	.
cord-004615-xfi3p601	100	1	From	from	IN
cord-004615-xfi3p601	100	2	data	datum	NNS
cord-004615-xfi3p601	100	3	of	of	IN
cord-004615-xfi3p601	100	4	outbreaks	outbreak	NNS
cord-004615-xfi3p601	100	5	of	of	IN
cord-004615-xfi3p601	100	6	CSF	CSF	NNP
cord-004615-xfi3p601	100	7	in	in	IN
cord-004615-xfi3p601	100	8	the	the	DT
cord-004615-xfi3p601	100	9	past	past	NN
cord-004615-xfi3p601	100	10	,	,	,
cord-004615-xfi3p601	100	11	we	-PRON-	PRP
cord-004615-xfi3p601	100	12	can	can	MD
cord-004615-xfi3p601	100	13	see	see	VB
cord-004615-xfi3p601	100	14	that	that	IN
cord-004615-xfi3p601	100	15	the	the	DT
cord-004615-xfi3p601	100	16	number	number	NN
cord-004615-xfi3p601	100	17	of	of	IN
cord-004615-xfi3p601	100	18	infected	infected	JJ
cord-004615-xfi3p601	100	19	animals	animal	NNS
cord-004615-xfi3p601	100	20	until	until	IN
cord-004615-xfi3p601	100	21	detection	detection	NN
cord-004615-xfi3p601	100	22	of	of	IN
cord-004615-xfi3p601	100	23	the	the	DT
cord-004615-xfi3p601	100	24	infection	infection	NN
cord-004615-xfi3p601	100	25	within	within	IN
cord-004615-xfi3p601	100	26	the	the	DT
cord-004615-xfi3p601	100	27	herd	herd	NN
cord-004615-xfi3p601	100	28	,	,	,
cord-004615-xfi3p601	100	29	is	be	VBZ
cord-004615-xfi3p601	100	30	small	small	JJ
cord-004615-xfi3p601	100	31	compared	compare	VBN
cord-004615-xfi3p601	100	32	to	to	IN
cord-004615-xfi3p601	100	33	the	the	DT
cord-004615-xfi3p601	100	34	total	total	JJ
cord-004615-xfi3p601	100	35	number	number	NN
cord-004615-xfi3p601	100	36	of	of	IN
cord-004615-xfi3p601	100	37	animals	animal	NNS
cord-004615-xfi3p601	100	38	in	in	IN
cord-004615-xfi3p601	100	39	the	the	DT
cord-004615-xfi3p601	100	40	herd	herd	NN
cord-004615-xfi3p601	100	41	,	,	,
cord-004615-xfi3p601	100	42	so	so	IN
cord-004615-xfi3p601	100	43	these	these	DT
cord-004615-xfi3p601	100	44	assumptions	assumption	NNS
cord-004615-xfi3p601	100	45	seem	seem	VBP
cord-004615-xfi3p601	100	46	justified	justified	JJ
cord-004615-xfi3p601	100	47	in	in	IN
cord-004615-xfi3p601	100	48	this	this	DT
cord-004615-xfi3p601	100	49	case	case	NN
cord-004615-xfi3p601	100	50	[	[	-LRB-
cord-004615-xfi3p601	100	51	11	11	CD
cord-004615-xfi3p601	100	52	]	]	-RRB-
cord-004615-xfi3p601	100	53	.	.	.
cord-004615-xfi3p601	101	1	4	4	LS
cord-004615-xfi3p601	101	2	.	.	.
cord-004615-xfi3p601	102	1	The	the	DT
cord-004615-xfi3p601	102	2	within	within	IN
cord-004615-xfi3p601	102	3	-	-	HYPH
cord-004615-xfi3p601	102	4	herd	herd	NN
cord-004615-xfi3p601	102	5	infection	infection	NN
cord-004615-xfi3p601	102	6	and	and	CC
cord-004615-xfi3p601	102	7	recovery	recovery	NN
cord-004615-xfi3p601	102	8	parameters	parameter	NNS
cord-004615-xfi3p601	102	9	λ	λ	NN
cord-004615-xfi3p601	102	10	and	and	CC
cord-004615-xfi3p601	102	11	µ	µ	NN
cord-004615-xfi3p601	102	12	can	can	MD
cord-004615-xfi3p601	102	13	be	be	VB
cord-004615-xfi3p601	102	14	measured	measure	VBN
cord-004615-xfi3p601	102	15	experimentally	experimentally	RB
cord-004615-xfi3p601	102	16	or	or	CC
cord-004615-xfi3p601	102	17	from	from	IN
cord-004615-xfi3p601	102	18	data	datum	NNS
cord-004615-xfi3p601	102	19	of	of	IN
cord-004615-xfi3p601	102	20	past	past	NN
cord-004615-xfi3p601	102	21	or	or	CC
cord-004615-xfi3p601	102	22	on	on	RB
cord-004615-xfi3p601	102	23	-	-	HYPH
cord-004615-xfi3p601	102	24	going	go	VBG
cord-004615-xfi3p601	102	25	outbreaks	outbreak	NNS
cord-004615-xfi3p601	102	26	.	.	.
cord-004615-xfi3p601	103	1	The	the	DT
cord-004615-xfi3p601	103	2	parameter	parameter	NN
cord-004615-xfi3p601	103	3	α	α	NN
cord-004615-xfi3p601	103	4	depends	depend	VBZ
cord-004615-xfi3p601	103	5	on	on	IN
cord-004615-xfi3p601	103	6	the	the	DT
cord-004615-xfi3p601	103	7	development	development	NN
cord-004615-xfi3p601	103	8	of	of	IN
cord-004615-xfi3p601	103	9	symptoms	symptom	NNS
cord-004615-xfi3p601	103	10	of	of	IN
cord-004615-xfi3p601	103	11	infected	infected	JJ
cord-004615-xfi3p601	103	12	animals	animal	NNS
cord-004615-xfi3p601	103	13	and	and	CC
cord-004615-xfi3p601	103	14	how	how	WRB
cord-004615-xfi3p601	103	15	attentive	attentive	JJ
cord-004615-xfi3p601	103	16	the	the	DT
cord-004615-xfi3p601	103	17	farmers	farmer	NNS
cord-004615-xfi3p601	103	18	are	be	VBP
cord-004615-xfi3p601	103	19	.	.	.
cord-004615-xfi3p601	104	1	Therefore	therefore	RB
cord-004615-xfi3p601	104	2	,	,	,
cord-004615-xfi3p601	104	3	in	in	IN
cord-004615-xfi3p601	104	4	reality	reality	NN
cord-004615-xfi3p601	104	5	this	this	DT
cord-004615-xfi3p601	104	6	α	α	NN
cord-004615-xfi3p601	104	7	will	will	MD
cord-004615-xfi3p601	104	8	change	change	VB
cord-004615-xfi3p601	104	9	at	at	IN
cord-004615-xfi3p601	104	10	the	the	DT
cord-004615-xfi3p601	104	11	first	first	JJ
cord-004615-xfi3p601	104	12	detection	detection	NN
cord-004615-xfi3p601	104	13	of	of	IN
cord-004615-xfi3p601	104	14	the	the	DT
cord-004615-xfi3p601	104	15	infection	infection	NN
cord-004615-xfi3p601	104	16	in	in	IN
cord-004615-xfi3p601	104	17	the	the	DT
cord-004615-xfi3p601	104	18	country	country	NN
cord-004615-xfi3p601	104	19	(	(	-LRB-
cord-004615-xfi3p601	104	20	or	or	CC
cord-004615-xfi3p601	104	21	in	in	IN
cord-004615-xfi3p601	104	22	neighbouring	neighbouring	JJ
cord-004615-xfi3p601	104	23	countries	country	NNS
cord-004615-xfi3p601	104	24	)	)	-RRB-
cord-004615-xfi3p601	104	25	,	,	,
cord-004615-xfi3p601	104	26	due	due	IN
cord-004615-xfi3p601	104	27	to	to	IN
cord-004615-xfi3p601	104	28	higher	high	JJR
cord-004615-xfi3p601	104	29	awareness	awareness	NN
cord-004615-xfi3p601	104	30	of	of	IN
cord-004615-xfi3p601	104	31	farmers	farmer	NNS
cord-004615-xfi3p601	104	32	and	and	CC
cord-004615-xfi3p601	104	33	veterinarians	veterinarian	NNS
cord-004615-xfi3p601	104	34	.	.	.
cord-004615-xfi3p601	105	1	It	-PRON-	PRP
cord-004615-xfi3p601	105	2	is	be	VBZ
cord-004615-xfi3p601	105	3	very	very	RB
cord-004615-xfi3p601	105	4	difficult	difficult	JJ
cord-004615-xfi3p601	105	5	to	to	TO
cord-004615-xfi3p601	105	6	estimate	estimate	VB
cord-004615-xfi3p601	105	7	α	α	NN
cord-004615-xfi3p601	105	8	for	for	IN
cord-004615-xfi3p601	105	9	the	the	DT
cord-004615-xfi3p601	105	10	period	period	NN
cord-004615-xfi3p601	105	11	before	before	IN
cord-004615-xfi3p601	105	12	the	the	DT
cord-004615-xfi3p601	105	13	time	time	NN
cord-004615-xfi3p601	105	14	of	of	IN
cord-004615-xfi3p601	105	15	the	the	DT
cord-004615-xfi3p601	105	16	first	first	JJ
cord-004615-xfi3p601	105	17	detection	detection	NN
cord-004615-xfi3p601	105	18	.	.	.
cord-004615-xfi3p601	106	1	For	for	IN
cord-004615-xfi3p601	106	2	the	the	DT
cord-004615-xfi3p601	106	3	time	time	NN
cord-004615-xfi3p601	106	4	after	after	IN
cord-004615-xfi3p601	106	5	the	the	DT
cord-004615-xfi3p601	106	6	first	first	JJ
cord-004615-xfi3p601	106	7	detection	detection	NN
cord-004615-xfi3p601	106	8	,	,	,
cord-004615-xfi3p601	106	9	we	-PRON-	PRP
cord-004615-xfi3p601	106	10	can	can	MD
cord-004615-xfi3p601	106	11	estimate	estimate	VB
cord-004615-xfi3p601	106	12	α	α	NN
cord-004615-xfi3p601	106	13	from	from	IN
cord-004615-xfi3p601	106	14	data	datum	NNS
cord-004615-xfi3p601	106	15	of	of	IN
cord-004615-xfi3p601	106	16	past	past	JJ
cord-004615-xfi3p601	106	17	outbreaks	outbreak	NNS
cord-004615-xfi3p601	106	18	in	in	IN
cord-004615-xfi3p601	106	19	the	the	DT
cord-004615-xfi3p601	106	20	same	same	JJ
cord-004615-xfi3p601	106	21	area	area	NN
cord-004615-xfi3p601	106	22	or	or	CC
cord-004615-xfi3p601	106	23	try	try	VB
cord-004615-xfi3p601	106	24	to	to	TO
cord-004615-xfi3p601	106	25	estimate	estimate	VB
cord-004615-xfi3p601	106	26	this	this	DT
cord-004615-xfi3p601	106	27	parameter	parameter	NN
cord-004615-xfi3p601	106	28	during	during	IN
cord-004615-xfi3p601	106	29	the	the	DT
cord-004615-xfi3p601	106	30	ongoing	ongoing	JJ
cord-004615-xfi3p601	106	31	epidemic	epidemic	NN
cord-004615-xfi3p601	106	32	.	.	.
cord-004615-xfi3p601	107	1	Using	use	VBG
cord-004615-xfi3p601	107	2	data	datum	NNS
cord-004615-xfi3p601	107	3	from	from	IN
cord-004615-xfi3p601	107	4	past	past	JJ
cord-004615-xfi3p601	107	5	outbreaks	outbreak	NNS
cord-004615-xfi3p601	107	6	is	be	VBZ
cord-004615-xfi3p601	107	7	dangerous	dangerous	JJ
cord-004615-xfi3p601	107	8	,	,	,
cord-004615-xfi3p601	107	9	because	because	IN
cord-004615-xfi3p601	107	10	the	the	DT
cord-004615-xfi3p601	107	11	characteristics	characteristic	NNS
cord-004615-xfi3p601	107	12	of	of	IN
cord-004615-xfi3p601	107	13	the	the	DT
cord-004615-xfi3p601	107	14	virus	virus	NN
cord-004615-xfi3p601	107	15	and	and	CC
cord-004615-xfi3p601	107	16	of	of	IN
cord-004615-xfi3p601	107	17	the	the	DT
cord-004615-xfi3p601	107	18	farming	farming	NN
cord-004615-xfi3p601	107	19	practice	practice	NN
cord-004615-xfi3p601	107	20	may	may	MD
cord-004615-xfi3p601	107	21	have	have	VB
cord-004615-xfi3p601	107	22	changed	change	VBN
cord-004615-xfi3p601	107	23	.	.	.
cord-004615-xfi3p601	108	1	Estimation	estimation	NN
cord-004615-xfi3p601	108	2	of	of	IN
cord-004615-xfi3p601	108	3	the	the	DT
cord-004615-xfi3p601	108	4	parameters	parameter	NNS
cord-004615-xfi3p601	108	5	,	,	,
cord-004615-xfi3p601	108	6	during	during	IN
cord-004615-xfi3p601	108	7	an	an	DT
cord-004615-xfi3p601	108	8	on	on	RB
cord-004615-xfi3p601	108	9	-	-	HYPH
cord-004615-xfi3p601	108	10	going	go	VBG
cord-004615-xfi3p601	108	11	outbreak	outbreak	NN
cord-004615-xfi3p601	108	12	is	be	VBZ
cord-004615-xfi3p601	108	13	done	do	VBN
cord-004615-xfi3p601	108	14	by	by	IN
cord-004615-xfi3p601	108	15	Meester	Meester	NNP
cord-004615-xfi3p601	108	16	et	et	NNP
cord-004615-xfi3p601	108	17	al	al	NNP
cord-004615-xfi3p601	108	18	.	.	.
cord-004615-xfi3p601	109	1	[	[	-LRB-
cord-004615-xfi3p601	109	2	10	10	CD
cord-004615-xfi3p601	109	3	]	]	-RRB-
cord-004615-xfi3p601	109	4	.	.	.
cord-004615-xfi3p601	110	1	This	this	DT
cord-004615-xfi3p601	110	2	method	method	NN
cord-004615-xfi3p601	110	3	has	have	VBZ
cord-004615-xfi3p601	110	4	some	some	DT
cord-004615-xfi3p601	110	5	problems	problem	NNS
cord-004615-xfi3p601	110	6	,	,	,
cord-004615-xfi3p601	110	7	e.g.	e.g.	IN
cord-004615-xfi3p601	110	8	the	the	DT
cord-004615-xfi3p601	110	9	time	time	NN
cord-004615-xfi3p601	110	10	necessary	necessary	JJ
cord-004615-xfi3p601	110	11	to	to	TO
cord-004615-xfi3p601	110	12	get	get	VB
cord-004615-xfi3p601	110	13	enough	enough	JJ
cord-004615-xfi3p601	110	14	data	datum	NNS
cord-004615-xfi3p601	110	15	for	for	IN
cord-004615-xfi3p601	110	16	a	a	DT
cord-004615-xfi3p601	110	17	reliable	reliable	JJ
cord-004615-xfi3p601	110	18	estimate	estimate	NN
cord-004615-xfi3p601	110	19	.	.	.
cord-004615-xfi3p601	111	1	Another	another	DT
cord-004615-xfi3p601	111	2	problem	problem	NN
cord-004615-xfi3p601	111	3	is	be	VBZ
cord-004615-xfi3p601	111	4	that	that	IN
cord-004615-xfi3p601	111	5	in	in	IN
cord-004615-xfi3p601	111	6	[	[	-LRB-
cord-004615-xfi3p601	111	7	10	10	CD
cord-004615-xfi3p601	111	8	]	]	-RRB-
cord-004615-xfi3p601	111	9	the	the	DT
cord-004615-xfi3p601	111	10	infectivity	infectivity	NN
cord-004615-xfi3p601	111	11	of	of	IN
cord-004615-xfi3p601	111	12	a	a	DT
cord-004615-xfi3p601	111	13	herd	herd	NN
cord-004615-xfi3p601	111	14	does	do	VBZ
cord-004615-xfi3p601	111	15	not	not	RB
cord-004615-xfi3p601	111	16	depend	depend	VB
cord-004615-xfi3p601	111	17	on	on	IN
cord-004615-xfi3p601	111	18	the	the	DT
cord-004615-xfi3p601	111	19	"	"	``
cord-004615-xfi3p601	111	20	age	age	NN
cord-004615-xfi3p601	111	21	"	"	''
cord-004615-xfi3p601	111	22	of	of	IN
cord-004615-xfi3p601	111	23	the	the	DT
cord-004615-xfi3p601	111	24	herd	herd	NN
cord-004615-xfi3p601	111	25	.	.	.
cord-004615-xfi3p601	112	1	This	this	DT
cord-004615-xfi3p601	112	2	independence	independence	NN
cord-004615-xfi3p601	112	3	of	of	IN
cord-004615-xfi3p601	112	4	age	age	NN
cord-004615-xfi3p601	112	5	is	be	VBZ
cord-004615-xfi3p601	112	6	essential	essential	JJ
cord-004615-xfi3p601	112	7	for	for	IN
cord-004615-xfi3p601	112	8	the	the	DT
cord-004615-xfi3p601	112	9	estimations	estimation	NNS
cord-004615-xfi3p601	112	10	made	make	VBN
cord-004615-xfi3p601	112	11	.	.	.
cord-004615-xfi3p601	113	1	For	for	IN
cord-004615-xfi3p601	113	2	our	-PRON-	PRP$
cord-004615-xfi3p601	113	3	model	model	NN
cord-004615-xfi3p601	113	4	it	-PRON-	PRP
cord-004615-xfi3p601	113	5	is	be	VBZ
cord-004615-xfi3p601	113	6	not	not	RB
cord-004615-xfi3p601	113	7	necessary	necessary	JJ
cord-004615-xfi3p601	113	8	that	that	IN
cord-004615-xfi3p601	113	9	α	α	NN
cord-004615-xfi3p601	113	10	is	be	VBZ
cord-004615-xfi3p601	113	11	constant	constant	JJ
cord-004615-xfi3p601	113	12	in	in	IN
cord-004615-xfi3p601	113	13	time	time	NN
cord-004615-xfi3p601	113	14	.	.	.
cord-004615-xfi3p601	114	1	It	-PRON-	PRP
cord-004615-xfi3p601	114	2	is	be	VBZ
cord-004615-xfi3p601	114	3	possible	possible	JJ
cord-004615-xfi3p601	114	4	to	to	TO
cord-004615-xfi3p601	114	5	extend	extend	VB
cord-004615-xfi3p601	114	6	the	the	DT
cord-004615-xfi3p601	114	7	model	model	NN
cord-004615-xfi3p601	114	8	and	and	CC
cord-004615-xfi3p601	114	9	use	use	VB
cord-004615-xfi3p601	114	10	α(t	α(t	NNP
cord-004615-xfi3p601	114	11	)	)	-RRB-
cord-004615-xfi3p601	114	12	instead	instead	RB
cord-004615-xfi3p601	114	13	of	of	IN
cord-004615-xfi3p601	114	14	α	α	NN
cord-004615-xfi3p601	114	15	.	.	.
cord-004615-xfi3p601	115	1	5	5	LS
cord-004615-xfi3p601	115	2	.	.	.
cord-004615-xfi3p601	116	1	We	-PRON-	PRP
cord-004615-xfi3p601	116	2	assume	assume	VBP
cord-004615-xfi3p601	116	3	that	that	IN
cord-004615-xfi3p601	116	4	culling	culling	NN
cord-004615-xfi3p601	116	5	is	be	VBZ
cord-004615-xfi3p601	116	6	the	the	DT
cord-004615-xfi3p601	116	7	only	only	JJ
cord-004615-xfi3p601	116	8	measure	measure	NN
cord-004615-xfi3p601	116	9	which	which	WDT
cord-004615-xfi3p601	116	10	influences	influence	VBZ
cord-004615-xfi3p601	116	11	the	the	DT
cord-004615-xfi3p601	116	12	within	within	IN
cord-004615-xfi3p601	116	13	-	-	HYPH
cord-004615-xfi3p601	116	14	herd	herd	NN
cord-004615-xfi3p601	116	15	spread	spread	NN
cord-004615-xfi3p601	116	16	of	of	IN
cord-004615-xfi3p601	116	17	the	the	DT
cord-004615-xfi3p601	116	18	infection	infection	NN
cord-004615-xfi3p601	116	19	.	.	.
cord-004615-xfi3p601	117	1	Vaccination	vaccination	NN
cord-004615-xfi3p601	117	2	is	be	VBZ
cord-004615-xfi3p601	117	3	assumed	assume	VBN
cord-004615-xfi3p601	117	4	to	to	TO
cord-004615-xfi3p601	117	5	show	show	VB
cord-004615-xfi3p601	117	6	no	no	DT
cord-004615-xfi3p601	117	7	effect	effect	NN
cord-004615-xfi3p601	117	8	on	on	IN
cord-004615-xfi3p601	117	9	the	the	DT
cord-004615-xfi3p601	117	10	spread	spread	NN
cord-004615-xfi3p601	117	11	in	in	IN
cord-004615-xfi3p601	117	12	the	the	DT
cord-004615-xfi3p601	117	13	herd	herd	NN
cord-004615-xfi3p601	117	14	.	.	.
cord-004615-xfi3p601	118	1	For	for	IN
cord-004615-xfi3p601	118	2	CSF	CSF	NNP
cord-004615-xfi3p601	118	3	this	this	DT
cord-004615-xfi3p601	118	4	assumption	assumption	NN
cord-004615-xfi3p601	118	5	is	be	VBZ
cord-004615-xfi3p601	118	6	justified	justify	VBN
cord-004615-xfi3p601	118	7	by	by	IN
cord-004615-xfi3p601	118	8	the	the	DT
cord-004615-xfi3p601	118	9	fact	fact	NN
cord-004615-xfi3p601	118	10	that	that	IN
cord-004615-xfi3p601	118	11	vaccination	vaccination	NN
cord-004615-xfi3p601	118	12	will	will	MD
cord-004615-xfi3p601	118	13	lead	lead	VB
cord-004615-xfi3p601	118	14	to	to	IN
cord-004615-xfi3p601	118	15	immunity	immunity	NN
cord-004615-xfi3p601	118	16	only	only	RB
cord-004615-xfi3p601	118	17	after	after	IN
cord-004615-xfi3p601	118	18	two	two	CD
cord-004615-xfi3p601	118	19	weeks	week	NNS
cord-004615-xfi3p601	118	20	.	.	.
cord-004615-xfi3p601	119	1	Therefore	therefore	RB
cord-004615-xfi3p601	119	2	,	,	,
cord-004615-xfi3p601	119	3	during	during	IN
cord-004615-xfi3p601	119	4	this	this	DT
cord-004615-xfi3p601	119	5	first	first	JJ
cord-004615-xfi3p601	119	6	two	two	CD
cord-004615-xfi3p601	119	7	weeks	week	NNS
cord-004615-xfi3p601	119	8	the	the	DT
cord-004615-xfi3p601	119	9	spread	spread	NN
cord-004615-xfi3p601	119	10	of	of	IN
cord-004615-xfi3p601	119	11	the	the	DT
cord-004615-xfi3p601	119	12	infection	infection	NN
cord-004615-xfi3p601	119	13	is	be	VBZ
cord-004615-xfi3p601	119	14	not	not	RB
cord-004615-xfi3p601	119	15	affected	affect	VBN
cord-004615-xfi3p601	119	16	by	by	IN
cord-004615-xfi3p601	119	17	this	this	DT
cord-004615-xfi3p601	119	18	measure	measure	NN
cord-004615-xfi3p601	119	19	.	.	.
cord-004615-xfi3p601	120	1	For	for	IN
cord-004615-xfi3p601	120	2	the	the	DT
cord-004615-xfi3p601	120	3	time	time	NN
cord-004615-xfi3p601	120	4	after	after	IN
cord-004615-xfi3p601	120	5	these	these	DT
cord-004615-xfi3p601	120	6	two	two	CD
cord-004615-xfi3p601	120	7	weeks	week	NNS
cord-004615-xfi3p601	120	8	,	,	,
cord-004615-xfi3p601	120	9	we	-PRON-	PRP
cord-004615-xfi3p601	120	10	assume	assume	VBP
cord-004615-xfi3p601	120	11	that	that	IN
cord-004615-xfi3p601	120	12	we	-PRON-	PRP
cord-004615-xfi3p601	120	13	can	can	MD
cord-004615-xfi3p601	120	14	use	use	VB
cord-004615-xfi3p601	120	15	the	the	DT
cord-004615-xfi3p601	120	16	same	same	JJ
cord-004615-xfi3p601	120	17	speed	speed	NN
cord-004615-xfi3p601	120	18	of	of	IN
cord-004615-xfi3p601	120	19	propagation	propagation	NN
cord-004615-xfi3p601	120	20	of	of	IN
cord-004615-xfi3p601	120	21	the	the	DT
cord-004615-xfi3p601	120	22	infection	infection	NN
cord-004615-xfi3p601	120	23	,	,	,
cord-004615-xfi3p601	120	24	for	for	IN
cord-004615-xfi3p601	120	25	computational	computational	JJ
cord-004615-xfi3p601	120	26	reasons	reason	NNS
cord-004615-xfi3p601	120	27	.	.	.
cord-004615-xfi3p601	121	1	The	the	DT
cord-004615-xfi3p601	121	2	approximation	approximation	NN
cord-004615-xfi3p601	121	3	leads	lead	VBZ
cord-004615-xfi3p601	121	4	to	to	IN
cord-004615-xfi3p601	121	5	results	result	NNS
cord-004615-xfi3p601	121	6	that	that	WDT
cord-004615-xfi3p601	121	7	are	be	VBP
cord-004615-xfi3p601	121	8	conservative	conservative	JJ
cord-004615-xfi3p601	121	9	,	,	,
cord-004615-xfi3p601	121	10	that	that	RB
cord-004615-xfi3p601	121	11	is	is	RB
cord-004615-xfi3p601	121	12	,	,	,
cord-004615-xfi3p601	121	13	too	too	RB
cord-004615-xfi3p601	121	14	pessimistic	pessimistic	JJ
cord-004615-xfi3p601	121	15	.	.	.
cord-004615-xfi3p601	122	1	6	6	LS
cord-004615-xfi3p601	122	2	.	.	.
cord-004615-xfi3p601	123	1	We	-PRON-	PRP
cord-004615-xfi3p601	123	2	do	do	VBP
cord-004615-xfi3p601	123	3	not	not	RB
cord-004615-xfi3p601	123	4	take	take	VB
cord-004615-xfi3p601	123	5	characteristics	characteristic	NNS
cord-004615-xfi3p601	123	6	of	of	IN
cord-004615-xfi3p601	123	7	individual	individual	JJ
cord-004615-xfi3p601	123	8	animals	animal	NNS
cord-004615-xfi3p601	123	9	into	into	IN
cord-004615-xfi3p601	123	10	account	account	NN
cord-004615-xfi3p601	123	11	that	that	WDT
cord-004615-xfi3p601	123	12	might	may	MD
cord-004615-xfi3p601	123	13	cause	cause	VB
cord-004615-xfi3p601	123	14	the	the	DT
cord-004615-xfi3p601	123	15	individuals	individual	NNS
cord-004615-xfi3p601	123	16	to	to	TO
cord-004615-xfi3p601	123	17	differ	differ	VB
cord-004615-xfi3p601	123	18	in	in	IN
cord-004615-xfi3p601	123	19	infectivity	infectivity	NN
cord-004615-xfi3p601	123	20	,	,	,
cord-004615-xfi3p601	123	21	susceptibility	susceptibility	NN
cord-004615-xfi3p601	123	22	or	or	CC
cord-004615-xfi3p601	123	23	contact	contact	NN
cord-004615-xfi3p601	123	24	pattern	pattern	NN
cord-004615-xfi3p601	123	25	.	.	.
cord-004615-xfi3p601	124	1	Often	often	RB
cord-004615-xfi3p601	124	2	age	age	NN
cord-004615-xfi3p601	124	3	and	and	CC
cord-004615-xfi3p601	124	4	type	type	NN
cord-004615-xfi3p601	124	5	of	of	IN
cord-004615-xfi3p601	124	6	species	specie	NNS
cord-004615-xfi3p601	124	7	can	can	MD
cord-004615-xfi3p601	124	8	have	have	VB
cord-004615-xfi3p601	124	9	a	a	DT
cord-004615-xfi3p601	124	10	substantial	substantial	JJ
cord-004615-xfi3p601	124	11	influence	influence	NN
cord-004615-xfi3p601	124	12	.	.	.
cord-004615-xfi3p601	125	1	For	for	IN
cord-004615-xfi3p601	125	2	CSF	CSF	NNP
cord-004615-xfi3p601	125	3	this	this	DT
cord-004615-xfi3p601	125	4	implies	imply	VBZ
cord-004615-xfi3p601	125	5	we	-PRON-	PRP
cord-004615-xfi3p601	125	6	do	do	VBP
cord-004615-xfi3p601	125	7	not	not	RB
cord-004615-xfi3p601	125	8	distinguish	distinguish	VB
cord-004615-xfi3p601	125	9	between	between	IN
cord-004615-xfi3p601	125	10	the	the	DT
cord-004615-xfi3p601	125	11	age	age	NN
cord-004615-xfi3p601	125	12	of	of	IN
cord-004615-xfi3p601	125	13	animals	animal	NNS
cord-004615-xfi3p601	125	14	in	in	IN
cord-004615-xfi3p601	125	15	one	one	CD
cord-004615-xfi3p601	125	16	herd	herd	NN
cord-004615-xfi3p601	125	17	.	.	.
cord-004615-xfi3p601	126	1	The	the	DT
cord-004615-xfi3p601	126	2	detection	detection	NN
cord-004615-xfi3p601	126	3	rate	rate	NN
cord-004615-xfi3p601	126	4	and	and	CC
cord-004615-xfi3p601	126	5	infectivity	infectivity	NN
cord-004615-xfi3p601	126	6	of	of	IN
cord-004615-xfi3p601	126	7	herds	herd	NNS
cord-004615-xfi3p601	126	8	with	with	IN
cord-004615-xfi3p601	126	9	many	many	JJ
cord-004615-xfi3p601	126	10	young	young	JJ
cord-004615-xfi3p601	126	11	animals	animal	NNS
cord-004615-xfi3p601	126	12	does	do	VBZ
cord-004615-xfi3p601	126	13	not	not	RB
cord-004615-xfi3p601	126	14	significantly	significantly	RB
cord-004615-xfi3p601	126	15	differ	differ	VB
cord-004615-xfi3p601	126	16	from	from	IN
cord-004615-xfi3p601	126	17	the	the	DT
cord-004615-xfi3p601	126	18	detection	detection	NN
cord-004615-xfi3p601	126	19	rate	rate	NN
cord-004615-xfi3p601	126	20	and	and	CC
cord-004615-xfi3p601	126	21	infectivity	infectivity	NN
cord-004615-xfi3p601	126	22	of	of	IN
cord-004615-xfi3p601	126	23	herds	herd	NNS
cord-004615-xfi3p601	126	24	with	with	IN
cord-004615-xfi3p601	126	25	especially	especially	RB
cord-004615-xfi3p601	126	26	older	old	JJR
cord-004615-xfi3p601	126	27	animals	animal	NNS
cord-004615-xfi3p601	126	28	[	[	-LRB-
cord-004615-xfi3p601	126	29	11	11	CD
cord-004615-xfi3p601	126	30	,	,	,
cord-004615-xfi3p601	126	31	1	1	CD
cord-004615-xfi3p601	126	32	]	]	-RRB-
cord-004615-xfi3p601	126	33	.	.	.
cord-004615-xfi3p601	127	1	7	7	CD
cord-004615-xfi3p601	127	2	.	.	.
cord-004615-xfi3p601	128	1	We	-PRON-	PRP
cord-004615-xfi3p601	128	2	also	also	RB
cord-004615-xfi3p601	128	3	use	use	VBP
cord-004615-xfi3p601	128	4	the	the	DT
cord-004615-xfi3p601	128	5	approximation	approximation	NN
cord-004615-xfi3p601	128	6	I	-PRON-	PRP
cord-004615-xfi3p601	128	7	(	(	-LRB-
cord-004615-xfi3p601	128	8	τ	τ	NN
cord-004615-xfi3p601	128	9	)	)	-RRB-
cord-004615-xfi3p601	128	10	=	=	NFP
cord-004615-xfi3p601	129	1	H	h	NN
cord-004615-xfi3p601	129	2	e	e	NN
cord-004615-xfi3p601	129	3	rτ	rτ	NN
cord-004615-xfi3p601	129	4	for	for	IN
cord-004615-xfi3p601	129	5	small	small	JJ
cord-004615-xfi3p601	129	6	τ	τ	NN
cord-004615-xfi3p601	129	7	.	.	.
cord-004615-xfi3p601	130	1	This	this	DT
cord-004615-xfi3p601	130	2	is	be	VBZ
cord-004615-xfi3p601	130	3	not	not	RB
cord-004615-xfi3p601	130	4	correct	correct	JJ
cord-004615-xfi3p601	130	5	,	,	,
cord-004615-xfi3p601	130	6	but	but	CC
cord-004615-xfi3p601	130	7	due	due	IN
cord-004615-xfi3p601	130	8	to	to	IN
cord-004615-xfi3p601	130	9	the	the	DT
cord-004615-xfi3p601	130	10	small	small	JJ
cord-004615-xfi3p601	130	11	number	number	NN
cord-004615-xfi3p601	130	12	of	of	IN
cord-004615-xfi3p601	130	13	infective	infective	JJ
cord-004615-xfi3p601	130	14	animals	animal	NNS
cord-004615-xfi3p601	130	15	at	at	IN
cord-004615-xfi3p601	130	16	small	small	JJ
cord-004615-xfi3p601	130	17	τ	τ	NN
cord-004615-xfi3p601	130	18	,	,	,
cord-004615-xfi3p601	130	19	the	the	DT
cord-004615-xfi3p601	130	20	probability	probability	NN
cord-004615-xfi3p601	130	21	that	that	IN
cord-004615-xfi3p601	130	22	the	the	DT
cord-004615-xfi3p601	130	23	disease	disease	NN
cord-004615-xfi3p601	130	24	is	be	VBZ
cord-004615-xfi3p601	130	25	detected	detect	VBN
cord-004615-xfi3p601	130	26	at	at	IN
cord-004615-xfi3p601	130	27	small	small	JJ
cord-004615-xfi3p601	130	28	τ	τ	NN
cord-004615-xfi3p601	130	29	is	be	VBZ
cord-004615-xfi3p601	130	30	small	small	JJ
cord-004615-xfi3p601	130	31	too	too	RB
cord-004615-xfi3p601	130	32	.	.	.
cord-004615-xfi3p601	131	1	We	-PRON-	PRP
cord-004615-xfi3p601	131	2	will	will	MD
cord-004615-xfi3p601	131	3	see	see	VB
cord-004615-xfi3p601	131	4	later	later	RB
cord-004615-xfi3p601	131	5	that	that	IN
cord-004615-xfi3p601	131	6	the	the	DT
cord-004615-xfi3p601	131	7	number	number	NN
cord-004615-xfi3p601	131	8	of	of	IN
cord-004615-xfi3p601	131	9	infections	infection	NNS
cord-004615-xfi3p601	131	10	in	in	IN
cord-004615-xfi3p601	131	11	that	that	DT
cord-004615-xfi3p601	131	12	period	period	NN
cord-004615-xfi3p601	131	13	is	be	VBZ
cord-004615-xfi3p601	131	14	as	as	RB
cord-004615-xfi3p601	131	15	well	well	RB
cord-004615-xfi3p601	131	16	,	,	,
cord-004615-xfi3p601	131	17	so	so	CC
cord-004615-xfi3p601	131	18	the	the	DT
cord-004615-xfi3p601	131	19	overall	overall	JJ
cord-004615-xfi3p601	131	20	influence	influence	NN
cord-004615-xfi3p601	131	21	of	of	IN
cord-004615-xfi3p601	131	22	the	the	DT
cord-004615-xfi3p601	131	23	events	event	NNS
cord-004615-xfi3p601	131	24	while	while	IN
cord-004615-xfi3p601	131	25	the	the	DT
cord-004615-xfi3p601	131	26	herd	herd	NN
cord-004615-xfi3p601	131	27	is	be	VBZ
cord-004615-xfi3p601	131	28	'	'	``
cord-004615-xfi3p601	131	29	young	young	JJ
cord-004615-xfi3p601	131	30	'	'	''
cord-004615-xfi3p601	131	31	is	be	VBZ
cord-004615-xfi3p601	131	32	probably	probably	RB
cord-004615-xfi3p601	131	33	not	not	RB
cord-004615-xfi3p601	131	34	so	so	RB
cord-004615-xfi3p601	131	35	large	large	JJ
cord-004615-xfi3p601	131	36	.	.	.
cord-004615-xfi3p601	132	1	In	in	IN
cord-004615-xfi3p601	132	2	this	this	DT
cord-004615-xfi3p601	132	3	section	section	NN
cord-004615-xfi3p601	132	4	,	,	,
cord-004615-xfi3p601	132	5	we	-PRON-	PRP
cord-004615-xfi3p601	132	6	consider	consider	VBP
cord-004615-xfi3p601	132	7	classical	classical	JJ
cord-004615-xfi3p601	132	8	swine	swine	NN
cord-004615-xfi3p601	132	9	fever	fever	NN
cord-004615-xfi3p601	132	10	as	as	IN
cord-004615-xfi3p601	132	11	a	a	DT
cord-004615-xfi3p601	132	12	concrete	concrete	JJ
cord-004615-xfi3p601	132	13	example	example	NN
cord-004615-xfi3p601	132	14	.	.	.
cord-004615-xfi3p601	133	1	We	-PRON-	PRP
cord-004615-xfi3p601	133	2	distinguish	distinguish	VBP
cord-004615-xfi3p601	133	3	between	between	IN
cord-004615-xfi3p601	133	4	two	two	CD
cord-004615-xfi3p601	133	5	types	type	NNS
cord-004615-xfi3p601	133	6	of	of	IN
cord-004615-xfi3p601	133	7	farms	farm	NNS
cord-004615-xfi3p601	133	8	:	:	:
cord-004615-xfi3p601	133	9	multipliers	multiplier	NNS
cord-004615-xfi3p601	133	10	(	(	-LRB-
cord-004615-xfi3p601	133	11	m	m	NNP
cord-004615-xfi3p601	133	12	)	)	-RRB-
cord-004615-xfi3p601	133	13	are	be	VBP
cord-004615-xfi3p601	133	14	,	,	,
cord-004615-xfi3p601	133	15	roughly	roughly	RB
cord-004615-xfi3p601	133	16	speaking	speak	VBG
cord-004615-xfi3p601	133	17	,	,	,
cord-004615-xfi3p601	133	18	farms	farm	NNS
cord-004615-xfi3p601	133	19	where	where	WRB
cord-004615-xfi3p601	133	20	young	young	JJ
cord-004615-xfi3p601	133	21	piglets	piglet	NNS
cord-004615-xfi3p601	133	22	are	be	VBP
cord-004615-xfi3p601	133	23	born	bear	VBN
cord-004615-xfi3p601	133	24	,	,	,
cord-004615-xfi3p601	133	25	and	and	CC
cord-004615-xfi3p601	133	26	finishers	finisher	NNS
cord-004615-xfi3p601	133	27	(	(	-LRB-
cord-004615-xfi3p601	133	28	f	f	NNP
cord-004615-xfi3p601	133	29	)	)	-RRB-
cord-004615-xfi3p601	133	30	are	be	VBP
cord-004615-xfi3p601	133	31	farms	farm	NNS
cord-004615-xfi3p601	133	32	that	that	WDT
cord-004615-xfi3p601	133	33	buy	buy	VBP
cord-004615-xfi3p601	133	34	piglets	piglet	NNS
cord-004615-xfi3p601	133	35	and	and	CC
cord-004615-xfi3p601	133	36	fatten	fatten	VB
cord-004615-xfi3p601	133	37	them	-PRON-	PRP
cord-004615-xfi3p601	133	38	.	.	.
cord-004615-xfi3p601	134	1	p	p	NN
cord-004615-xfi3p601	134	2	m	m	NNP
cord-004615-xfi3p601	134	3	denotes	denote	VBZ
cord-004615-xfi3p601	134	4	the	the	DT
cord-004615-xfi3p601	134	5	fraction	fraction	NN
cord-004615-xfi3p601	134	6	multipliers	multiplier	NNS
cord-004615-xfi3p601	134	7	of	of	IN
cord-004615-xfi3p601	134	8	the	the	DT
cord-004615-xfi3p601	134	9	total	total	JJ
cord-004615-xfi3p601	134	10	number	number	NN
cord-004615-xfi3p601	134	11	of	of	IN
cord-004615-xfi3p601	134	12	herds	herd	NNS
cord-004615-xfi3p601	134	13	and	and	CC
cord-004615-xfi3p601	134	14	p	p	NN
cord-004615-xfi3p601	134	15	f	f	NNP
cord-004615-xfi3p601	134	16	is	be	VBZ
cord-004615-xfi3p601	134	17	the	the	DT
cord-004615-xfi3p601	134	18	fraction	fraction	NN
cord-004615-xfi3p601	134	19	finishers	finisher	NNS
cord-004615-xfi3p601	134	20	.	.	.
cord-004615-xfi3p601	135	1	We	-PRON-	PRP
cord-004615-xfi3p601	135	2	assume	assume	VBP
cord-004615-xfi3p601	135	3	that	that	IN
cord-004615-xfi3p601	135	4	within	within	IN
cord-004615-xfi3p601	135	5	either	either	DT
cord-004615-xfi3p601	135	6	of	of	IN
cord-004615-xfi3p601	135	7	these	these	DT
cord-004615-xfi3p601	135	8	types	type	NNS
cord-004615-xfi3p601	135	9	,	,	,
cord-004615-xfi3p601	135	10	a	a	DT
cord-004615-xfi3p601	135	11	birth	birth	NN
cord-004615-xfi3p601	135	12	and	and	CC
cord-004615-xfi3p601	135	13	death	death	NN
cord-004615-xfi3p601	135	14	model	model	NN
cord-004615-xfi3p601	135	15	(	(	-LRB-
cord-004615-xfi3p601	135	16	with	with	IN
cord-004615-xfi3p601	135	17	the	the	DT
cord-004615-xfi3p601	135	18	same	same	JJ
cord-004615-xfi3p601	135	19	parameters	parameter	NNS
cord-004615-xfi3p601	135	20	for	for	IN
cord-004615-xfi3p601	135	21	both	both	DT
cord-004615-xfi3p601	135	22	types	type	NNS
cord-004615-xfi3p601	135	23	)	)	-RRB-
cord-004615-xfi3p601	135	24	describes	describe	VBZ
cord-004615-xfi3p601	135	25	the	the	DT
cord-004615-xfi3p601	135	26	within	within	IN
cord-004615-xfi3p601	135	27	-	-	HYPH
cord-004615-xfi3p601	135	28	herd	herd	NN
cord-004615-xfi3p601	135	29	spread	spread	NN
cord-004615-xfi3p601	135	30	.	.	.
cord-004615-xfi3p601	136	1	The	the	DT
cord-004615-xfi3p601	136	2	infectivity	infectivity	NN
cord-004615-xfi3p601	136	3	per	per	IN
cord-004615-xfi3p601	136	4	non	non	JJ
cord-004615-xfi3p601	136	5	-	-	JJ
cord-004615-xfi3p601	136	6	transport	transport	JJ
cord-004615-xfi3p601	136	7	contact	contact	NN
cord-004615-xfi3p601	136	8	of	of	IN
cord-004615-xfi3p601	136	9	both	both	DT
cord-004615-xfi3p601	136	10	types	type	NNS
cord-004615-xfi3p601	136	11	of	of	IN
cord-004615-xfi3p601	136	12	herds	herd	NNS
cord-004615-xfi3p601	136	13	develops	develop	VBZ
cord-004615-xfi3p601	136	14	in	in	IN
cord-004615-xfi3p601	136	15	the	the	DT
cord-004615-xfi3p601	136	16	same	same	JJ
cord-004615-xfi3p601	136	17	way	way	NN
cord-004615-xfi3p601	136	18	too	too	RB
cord-004615-xfi3p601	136	19	.	.	.
cord-004615-xfi3p601	137	1	However	however	RB
cord-004615-xfi3p601	137	2	,	,	,
cord-004615-xfi3p601	137	3	transport	transport	NN
cord-004615-xfi3p601	137	4	contacts	contact	NNS
cord-004615-xfi3p601	137	5	are	be	VBP
cord-004615-xfi3p601	137	6	only	only	RB
cord-004615-xfi3p601	137	7	allowed	allow	VBN
cord-004615-xfi3p601	137	8	from	from	IN
cord-004615-xfi3p601	137	9	multipliers	multiplier	NNS
cord-004615-xfi3p601	137	10	to	to	IN
cord-004615-xfi3p601	137	11	finishers	finisher	NNS
cord-004615-xfi3p601	137	12	.	.	.
cord-004615-xfi3p601	138	1	Therefore	therefore	RB
cord-004615-xfi3p601	138	2	,	,	,
cord-004615-xfi3p601	138	3	we	-PRON-	PRP
cord-004615-xfi3p601	138	4	take	take	VBP
cord-004615-xfi3p601	138	5	a	a	DT
cord-004615-xfi3p601	138	6	larger	large	JJR
cord-004615-xfi3p601	138	7	infectivity	infectivity	NN
cord-004615-xfi3p601	138	8	rate	rate	NN
cord-004615-xfi3p601	138	9	for	for	IN
cord-004615-xfi3p601	138	10	contacts	contact	NNS
cord-004615-xfi3p601	138	11	from	from	IN
cord-004615-xfi3p601	138	12	multipliers	multiplier	NNS
cord-004615-xfi3p601	138	13	to	to	IN
cord-004615-xfi3p601	138	14	finishers	finisher	NNS
cord-004615-xfi3p601	138	15	.	.	.
cord-004615-xfi3p601	139	1	We	-PRON-	PRP
cord-004615-xfi3p601	139	2	define	define	VBP
cord-004615-xfi3p601	139	3	A	A	NNP
cord-004615-xfi3p601	139	4	ξ	ξ	NN
cord-004615-xfi3p601	139	5	(	(	-LRB-
cord-004615-xfi3p601	139	6	t	t	NN
cord-004615-xfi3p601	139	7	,	,	,
cord-004615-xfi3p601	139	8	τ	τ	NN
cord-004615-xfi3p601	139	9	;	;	:
cord-004615-xfi3p601	139	10	h	h	LS
cord-004615-xfi3p601	139	11	)	)	-RRB-
cord-004615-xfi3p601	139	12	as	as	IN
cord-004615-xfi3p601	139	13	the	the	DT
cord-004615-xfi3p601	139	14	infectivity	infectivity	NN
cord-004615-xfi3p601	139	15	of	of	IN
cord-004615-xfi3p601	139	16	a	a	DT
cord-004615-xfi3p601	139	17	herd	herd	NN
cord-004615-xfi3p601	139	18	at	at	IN
cord-004615-xfi3p601	139	19	time	time	NN
cord-004615-xfi3p601	139	20	t	t	NNP
cord-004615-xfi3p601	139	21	,	,	,
cord-004615-xfi3p601	139	22	while	while	IN
cord-004615-xfi3p601	139	23	the	the	DT
cord-004615-xfi3p601	139	24	herd	herd	NN
cord-004615-xfi3p601	139	25	was	be	VBD
cord-004615-xfi3p601	139	26	infected	infect	VBN
cord-004615-xfi3p601	139	27	τ	τ	NN
cord-004615-xfi3p601	139	28	time	time	NN
cord-004615-xfi3p601	139	29	units	unit	NNS
cord-004615-xfi3p601	139	30	ago	ago	RB
cord-004615-xfi3p601	139	31	and	and	CC
cord-004615-xfi3p601	139	32	with	with	IN
cord-004615-xfi3p601	139	33	H	h	NN
cord-004615-xfi3p601	139	34	=	=	SYM
cord-004615-xfi3p601	139	35	h	h	NN
cord-004615-xfi3p601	139	36	,	,	,
cord-004615-xfi3p601	139	37	where	where	WRB
cord-004615-xfi3p601	139	38	ξ	ξ	NN
cord-004615-xfi3p601	139	39	is	be	VBZ
cord-004615-xfi3p601	139	40	a	a	DT
cord-004615-xfi3p601	139	41	two	two	CD
cord-004615-xfi3p601	139	42	-	-	HYPH
cord-004615-xfi3p601	139	43	dimensional	dimensional	JJ
cord-004615-xfi3p601	139	44	vector	vector	NN
cord-004615-xfi3p601	139	45	,	,	,
cord-004615-xfi3p601	139	46	denoting	denote	VBG
cord-004615-xfi3p601	139	47	the	the	DT
cord-004615-xfi3p601	139	48	two	two	CD
cord-004615-xfi3p601	139	49	types	type	NNS
cord-004615-xfi3p601	139	50	of	of	IN
cord-004615-xfi3p601	139	51	herds	herd	NNS
cord-004615-xfi3p601	139	52	involved	involve	VBN
cord-004615-xfi3p601	139	53	in	in	IN
cord-004615-xfi3p601	139	54	the	the	DT
cord-004615-xfi3p601	139	55	contact	contact	NN
cord-004615-xfi3p601	139	56	,	,	,
cord-004615-xfi3p601	139	57	so	so	IN
cord-004615-xfi3p601	139	58	that	that	IN
cord-004615-xfi3p601	139	59	ξ	ξ	NN
cord-004615-xfi3p601	139	60	can	can	MD
cord-004615-xfi3p601	139	61	be	be	VB
cord-004615-xfi3p601	139	62	ff	ff	NNP
cord-004615-xfi3p601	139	63	,	,	,
cord-004615-xfi3p601	139	64	f	f	NNP
cord-004615-xfi3p601	139	65	m	m	NNP
cord-004615-xfi3p601	139	66	,	,	,
cord-004615-xfi3p601	139	67	mm	mm	NNP
cord-004615-xfi3p601	139	68	or	or	CC
cord-004615-xfi3p601	139	69	mf	mf	NNP
cord-004615-xfi3p601	139	70	.	.	.
cord-004615-xfi3p601	140	1	When	when	WRB
cord-004615-xfi3p601	140	2	no	no	DT
cord-004615-xfi3p601	140	3	measures	measure	NNS
cord-004615-xfi3p601	140	4	are	be	VBP
cord-004615-xfi3p601	140	5	implemented	implement	VBN
cord-004615-xfi3p601	140	6	,	,	,
cord-004615-xfi3p601	140	7	A	a	DT
cord-004615-xfi3p601	140	8	ξ	ξ	NNP
cord-004615-xfi3p601	140	9	(	(	-LRB-
cord-004615-xfi3p601	140	10	t	t	NN
cord-004615-xfi3p601	140	11	,	,	,
cord-004615-xfi3p601	140	12	τ	τ	NN
cord-004615-xfi3p601	140	13	;	;	:
cord-004615-xfi3p601	140	14	h	h	NNP
cord-004615-xfi3p601	140	15	)	)	-RRB-
cord-004615-xfi3p601	140	16	,	,	,
cord-004615-xfi3p601	140	17	with	with	IN
cord-004615-xfi3p601	140	18	h	h	NNP
cord-004615-xfi3p601	140	19	a	a	DT
cord-004615-xfi3p601	140	20	given	give	VBN
cord-004615-xfi3p601	140	21	realisation	realisation	NN
cord-004615-xfi3p601	140	22	of	of	IN
cord-004615-xfi3p601	140	23	H	H	NNP
cord-004615-xfi3p601	140	24	,	,	,
cord-004615-xfi3p601	140	25	is	be	VBZ
cord-004615-xfi3p601	140	26	proportional	proportional	JJ
cord-004615-xfi3p601	140	27	to	to	IN
cord-004615-xfi3p601	140	28	the	the	DT
cord-004615-xfi3p601	140	29	number	number	NN
cord-004615-xfi3p601	140	30	of	of	IN
cord-004615-xfi3p601	140	31	infected	infected	JJ
cord-004615-xfi3p601	140	32	animals	animal	NNS
cord-004615-xfi3p601	140	33	in	in	IN
cord-004615-xfi3p601	140	34	the	the	DT
cord-004615-xfi3p601	140	35	herd	herd	NN
cord-004615-xfi3p601	140	36	.	.	.
cord-004615-xfi3p601	141	1	Here	here	RB
cord-004615-xfi3p601	141	2	β	β	NN
cord-004615-xfi3p601	141	3	ξ	ξ	NN
cord-004615-xfi3p601	141	4	is	be	VBZ
cord-004615-xfi3p601	141	5	a	a	DT
cord-004615-xfi3p601	141	6	constant	constant	JJ
cord-004615-xfi3p601	141	7	depending	depend	VBG
cord-004615-xfi3p601	141	8	only	only	RB
cord-004615-xfi3p601	141	9	on	on	IN
cord-004615-xfi3p601	141	10	ξ	ξ	NNS
cord-004615-xfi3p601	141	11	.	.	.
cord-004615-xfi3p601	142	1	Because	because	IN
cord-004615-xfi3p601	142	2	the	the	DT
cord-004615-xfi3p601	142	3	non	non	JJ
cord-004615-xfi3p601	142	4	-	-	JJ
cord-004615-xfi3p601	142	5	transport	transport	JJ
cord-004615-xfi3p601	142	6	contacts	contact	NNS
cord-004615-xfi3p601	142	7	all	all	DT
cord-004615-xfi3p601	142	8	happen	happen	VBP
cord-004615-xfi3p601	142	9	at	at	IN
cord-004615-xfi3p601	142	10	the	the	DT
cord-004615-xfi3p601	142	11	same	same	JJ
cord-004615-xfi3p601	142	12	rate	rate	NN
cord-004615-xfi3p601	142	13	we	-PRON-	PRP
cord-004615-xfi3p601	142	14	can	can	MD
cord-004615-xfi3p601	142	15	define	define	VB
cord-004615-xfi3p601	142	16	β	β	NN
cord-004615-xfi3p601	142	17	m	m	NN
cord-004615-xfi3p601	142	18	:	:	:
cord-004615-xfi3p601	142	19	=	=	NFP
cord-004615-xfi3p601	143	1	β	β	NN
cord-004615-xfi3p601	144	1	f	f	NNP
cord-004615-xfi3p601	144	2	m	m	NNP
cord-004615-xfi3p601	144	3	=	=	SYM
cord-004615-xfi3p601	144	4	β	β	NN
cord-004615-xfi3p601	144	5	mm	mm	NN
cord-004615-xfi3p601	144	6	.	.	.
cord-004615-xfi3p601	145	1	Further	further	RB
cord-004615-xfi3p601	145	2	we	-PRON-	PRP
cord-004615-xfi3p601	145	3	write	write	VBP
cord-004615-xfi3p601	145	4	β	β	NN
cord-004615-xfi3p601	145	5	f	f	NN
cord-004615-xfi3p601	145	6	:	:	:
cord-004615-xfi3p601	145	7	=	=	NFP
cord-004615-xfi3p601	146	1	β	β	NNP
cord-004615-xfi3p601	146	2	ff	ff	NNP
cord-004615-xfi3p601	146	3	and	and	CC
cord-004615-xfi3p601	146	4	β	β	NNP
cord-004615-xfi3p601	146	5	mf	mf	NNP
cord-004615-xfi3p601	146	6	is	be	VBZ
cord-004615-xfi3p601	146	7	β	β	NNP
cord-004615-xfi3p601	146	8	f	f	NNP
cord-004615-xfi3p601	146	9	plus	plus	CC
cord-004615-xfi3p601	146	10	some	some	DT
cord-004615-xfi3p601	146	11	additional	additional	JJ
cord-004615-xfi3p601	146	12	term	term	NN
cord-004615-xfi3p601	146	13	for	for	IN
cord-004615-xfi3p601	146	14	infections	infection	NNS
cord-004615-xfi3p601	146	15	caused	cause	VBN
cord-004615-xfi3p601	146	16	by	by	IN
cord-004615-xfi3p601	146	17	transport	transport	NN
cord-004615-xfi3p601	146	18	of	of	IN
cord-004615-xfi3p601	146	19	piglets	piglet	NNS
cord-004615-xfi3p601	146	20	from	from	IN
cord-004615-xfi3p601	146	21	multipliers	multiplier	NNS
cord-004615-xfi3p601	146	22	to	to	IN
cord-004615-xfi3p601	146	23	finishers	finisher	NNS
cord-004615-xfi3p601	146	24	.	.	.
cord-004615-xfi3p601	147	1	Because	because	IN
cord-004615-xfi3p601	147	2	all	all	DT
cord-004615-xfi3p601	147	3	non	non	JJ
cord-004615-xfi3p601	147	4	-	-	JJ
cord-004615-xfi3p601	147	5	transport	transport	JJ
cord-004615-xfi3p601	147	6	infections	infection	NNS
cord-004615-xfi3p601	147	7	happen	happen	VBP
cord-004615-xfi3p601	147	8	at	at	IN
cord-004615-xfi3p601	147	9	the	the	DT
cord-004615-xfi3p601	147	10	same	same	JJ
cord-004615-xfi3p601	147	11	rate	rate	NN
cord-004615-xfi3p601	147	12	the	the	DT
cord-004615-xfi3p601	147	13	ratio	ratio	NN
cord-004615-xfi3p601	147	14	β	β	NN
cord-004615-xfi3p601	147	15	m	m	NN
cord-004615-xfi3p601	147	16	/β	/β	NNP
cord-004615-xfi3p601	148	1	f	f	NNP
cord-004615-xfi3p601	148	2	is	be	VBZ
cord-004615-xfi3p601	148	3	exactly	exactly	RB
cord-004615-xfi3p601	148	4	the	the	DT
cord-004615-xfi3p601	148	5	ratio	ratio	NN
cord-004615-xfi3p601	148	6	of	of	IN
cord-004615-xfi3p601	148	7	the	the	DT
cord-004615-xfi3p601	148	8	multipliers	multiplier	NNS
cord-004615-xfi3p601	148	9	to	to	IN
cord-004615-xfi3p601	148	10	the	the	DT
cord-004615-xfi3p601	148	11	finishers	finisher	NNS
cord-004615-xfi3p601	148	12	.	.	.
cord-004615-xfi3p601	149	1	Note	note	VB
cord-004615-xfi3p601	149	2	that	that	IN
cord-004615-xfi3p601	149	3	the	the	DT
cord-004615-xfi3p601	149	4	infectivity	infectivity	NN
cord-004615-xfi3p601	149	5	does	do	VBZ
cord-004615-xfi3p601	149	6	not	not	RB
cord-004615-xfi3p601	149	7	depend	depend	VB
cord-004615-xfi3p601	149	8	on	on	IN
cord-004615-xfi3p601	149	9	the	the	DT
cord-004615-xfi3p601	149	10	absolute	absolute	JJ
cord-004615-xfi3p601	149	11	time	time	NN
cord-004615-xfi3p601	149	12	t.	t.	NN
cord-004615-xfi3p601	150	1	We	-PRON-	PRP
cord-004615-xfi3p601	150	2	define	define	VBP
cord-004615-xfi3p601	150	3	β	β	NN
cord-004615-xfi3p601	150	4	by	by	IN
cord-004615-xfi3p601	150	5	β	β	NN
cord-004615-xfi3p601	150	6	:	:	:
cord-004615-xfi3p601	150	7	=	=	NFP
cord-004615-xfi3p601	151	1	β	β	NNP
cord-004615-xfi3p601	151	2	m	m	NNP
cord-004615-xfi3p601	151	3	+	+	CC
cord-004615-xfi3p601	151	4	β	β	NN
cord-004615-xfi3p601	151	5	f	f	NNP
cord-004615-xfi3p601	151	6	,	,	,
cord-004615-xfi3p601	151	7	hence	hence	RB
cord-004615-xfi3p601	151	8	β	β	NN
cord-004615-xfi3p601	151	9	m	m	NN
cord-004615-xfi3p601	151	10	=	=	SYM
cord-004615-xfi3p601	151	11	p	p	NN
cord-004615-xfi3p601	151	12	m	m	NNP
cord-004615-xfi3p601	151	13	β	β	NN
cord-004615-xfi3p601	151	14	and	and	CC
cord-004615-xfi3p601	151	15	β	β	NN
cord-004615-xfi3p601	151	16	f	f	NN
cord-004615-xfi3p601	151	17	=	=	SYM
cord-004615-xfi3p601	151	18	p	p	NN
cord-004615-xfi3p601	151	19	f	f	NN
cord-004615-xfi3p601	151	20	β	β	NN
cord-004615-xfi3p601	151	21	.	.	.
cord-004615-xfi3p601	152	1	In	in	IN
cord-004615-xfi3p601	152	2	order	order	NN
cord-004615-xfi3p601	152	3	to	to	TO
cord-004615-xfi3p601	152	4	consider	consider	VB
cord-004615-xfi3p601	152	5	transport	transport	NN
cord-004615-xfi3p601	152	6	contacts	contact	NNS
cord-004615-xfi3p601	152	7	we	-PRON-	PRP
cord-004615-xfi3p601	152	8	also	also	RB
cord-004615-xfi3p601	152	9	define	define	VBP
cord-004615-xfi3p601	152	10	β	β	NN
cord-004615-xfi3p601	152	11	mf	mf	NN
cord-004615-xfi3p601	152	12	=	=	SYM
cord-004615-xfi3p601	152	13	p	p	NN
cord-004615-xfi3p601	152	14	f	f	NNP
cord-004615-xfi3p601	152	15	β	β	NN
cord-004615-xfi3p601	152	16	+	+	CC
cord-004615-xfi3p601	152	17	β	β	NNP
cord-004615-xfi3p601	152	18	tr	tr	FW
cord-004615-xfi3p601	152	19	,	,	,
cord-004615-xfi3p601	152	20	where	where	WRB
cord-004615-xfi3p601	152	21	β	β	NN
cord-004615-xfi3p601	152	22	tr	tr	NNP
cord-004615-xfi3p601	152	23	is	be	VBZ
cord-004615-xfi3p601	152	24	the	the	DT
cord-004615-xfi3p601	152	25	proportionality	proportionality	NN
cord-004615-xfi3p601	152	26	factor	factor	NN
cord-004615-xfi3p601	152	27	of	of	IN
cord-004615-xfi3p601	152	28	the	the	DT
cord-004615-xfi3p601	152	29	part	part	NN
cord-004615-xfi3p601	152	30	of	of	IN
cord-004615-xfi3p601	152	31	the	the	DT
cord-004615-xfi3p601	152	32	infection	infection	NN
cord-004615-xfi3p601	152	33	rate	rate	NN
cord-004615-xfi3p601	152	34	that	that	WDT
cord-004615-xfi3p601	152	35	is	be	VBZ
cord-004615-xfi3p601	152	36	due	due	JJ
cord-004615-xfi3p601	152	37	to	to	IN
cord-004615-xfi3p601	152	38	transport	transport	NN
cord-004615-xfi3p601	152	39	contacts	contact	NNS
cord-004615-xfi3p601	152	40	.	.	.
cord-004615-xfi3p601	153	1	There	there	EX
cord-004615-xfi3p601	153	2	is	be	VBZ
cord-004615-xfi3p601	153	3	no	no	DT
cord-004615-xfi3p601	153	4	term	term	NN
cord-004615-xfi3p601	153	5	p	p	NN
cord-004615-xfi3p601	153	6	f	f	NN
cord-004615-xfi3p601	153	7	in	in	IN
cord-004615-xfi3p601	153	8	front	front	NN
cord-004615-xfi3p601	153	9	of	of	IN
cord-004615-xfi3p601	153	10	β	β	NN
cord-004615-xfi3p601	153	11	tr	tr	FW
cord-004615-xfi3p601	153	12	,	,	,
cord-004615-xfi3p601	153	13	because	because	IN
cord-004615-xfi3p601	153	14	all	all	DT
cord-004615-xfi3p601	153	15	transport	transport	NN
cord-004615-xfi3p601	153	16	contacts	contact	NNS
cord-004615-xfi3p601	153	17	are	be	VBP
cord-004615-xfi3p601	153	18	from	from	IN
cord-004615-xfi3p601	153	19	multipliers	multiplier	NNS
cord-004615-xfi3p601	153	20	to	to	IN
cord-004615-xfi3p601	153	21	finishers	finisher	NNS
cord-004615-xfi3p601	153	22	.	.	.
cord-004615-xfi3p601	154	1	We	-PRON-	PRP
cord-004615-xfi3p601	154	2	assume	assume	VBP
cord-004615-xfi3p601	154	3	that	that	IN
cord-004615-xfi3p601	154	4	the	the	DT
cord-004615-xfi3p601	154	5	total	total	JJ
cord-004615-xfi3p601	154	6	number	number	NN
cord-004615-xfi3p601	154	7	of	of	IN
cord-004615-xfi3p601	154	8	herds	herd	NNS
cord-004615-xfi3p601	154	9	is	be	VBZ
cord-004615-xfi3p601	154	10	very	very	RB
cord-004615-xfi3p601	154	11	large	large	JJ
cord-004615-xfi3p601	154	12	;	;	:
cord-004615-xfi3p601	154	13	in	in	IN
cord-004615-xfi3p601	154	14	our	-PRON-	PRP$
cord-004615-xfi3p601	154	15	computations	computation	NNS
cord-004615-xfi3p601	154	16	,	,	,
cord-004615-xfi3p601	154	17	we	-PRON-	PRP
cord-004615-xfi3p601	154	18	assume	assume	VBP
cord-004615-xfi3p601	154	19	it	-PRON-	PRP
cord-004615-xfi3p601	154	20	to	to	TO
cord-004615-xfi3p601	154	21	be	be	VB
cord-004615-xfi3p601	154	22	infinite	infinite	JJ
cord-004615-xfi3p601	154	23	.	.	.
cord-004615-xfi3p601	155	1	We	-PRON-	PRP
cord-004615-xfi3p601	155	2	already	already	RB
cord-004615-xfi3p601	155	3	know	know	VBP
cord-004615-xfi3p601	155	4	that	that	IN
cord-004615-xfi3p601	155	5	the	the	DT
cord-004615-xfi3p601	155	6	detection	detection	NN
cord-004615-xfi3p601	155	7	-	-	HYPH
cord-004615-xfi3p601	155	8	rate	rate	NN
cord-004615-xfi3p601	155	9	is	be	VBZ
cord-004615-xfi3p601	155	10	given	give	VBN
cord-004615-xfi3p601	155	11	by	by	IN
cord-004615-xfi3p601	156	1	αI	αI	NNP
cord-004615-xfi3p601	156	2	(	(	-LRB-
cord-004615-xfi3p601	156	3	τ	τ	NN
cord-004615-xfi3p601	156	4	;	;	:
cord-004615-xfi3p601	156	5	h	h	LS
cord-004615-xfi3p601	156	6	)	)	-RRB-
cord-004615-xfi3p601	156	7	=	=	NFP
cord-004615-xfi3p601	157	1	αhe	αhe	CC
cord-004615-xfi3p601	157	2	rτ	rτ	XX
cord-004615-xfi3p601	157	3	.	.	.
cord-004615-xfi3p601	158	1	From	from	IN
cord-004615-xfi3p601	158	2	this	this	DT
cord-004615-xfi3p601	158	3	we	-PRON-	PRP
cord-004615-xfi3p601	158	4	can	can	MD
cord-004615-xfi3p601	158	5	deduce	deduce	VB
cord-004615-xfi3p601	158	6	,	,	,
cord-004615-xfi3p601	158	7	for	for	IN
cord-004615-xfi3p601	158	8	given	give	VBN
cord-004615-xfi3p601	158	9	h	h	NN
cord-004615-xfi3p601	158	10	,	,	,
cord-004615-xfi3p601	158	11	the	the	DT
cord-004615-xfi3p601	158	12	probability	probability	NN
cord-004615-xfi3p601	158	13	p	p	NN
cord-004615-xfi3p601	158	14	nd	nd	NNP
cord-004615-xfi3p601	158	15	(	(	-LRB-
cord-004615-xfi3p601	158	16	τ	τ	NN
cord-004615-xfi3p601	158	17	;	;	:
cord-004615-xfi3p601	158	18	h	h	LS
cord-004615-xfi3p601	158	19	)	)	-RRB-
cord-004615-xfi3p601	158	20	that	that	IN
cord-004615-xfi3p601	158	21	an	an	DT
cord-004615-xfi3p601	158	22	infected	infected	JJ
cord-004615-xfi3p601	158	23	herd	herd	NN
cord-004615-xfi3p601	158	24	of	of	IN
cord-004615-xfi3p601	158	25	age	age	NN
cord-004615-xfi3p601	158	26	τ	τ	NN
cord-004615-xfi3p601	158	27	is	be	VBZ
cord-004615-xfi3p601	158	28	not	not	RB
cord-004615-xfi3p601	158	29	yet	yet	RB
cord-004615-xfi3p601	158	30	detected	detect	VBN
cord-004615-xfi3p601	158	31	is	be	VBZ
cord-004615-xfi3p601	158	32	In	in	IN
cord-004615-xfi3p601	158	33	the	the	DT
cord-004615-xfi3p601	158	34	case	case	NN
cord-004615-xfi3p601	158	35	where	where	WRB
cord-004615-xfi3p601	158	36	no	no	DT
cord-004615-xfi3p601	158	37	measures	measure	NNS
cord-004615-xfi3p601	158	38	are	be	VBP
cord-004615-xfi3p601	158	39	implemented	implement	VBN
cord-004615-xfi3p601	158	40	,	,	,
cord-004615-xfi3p601	158	41	the	the	DT
cord-004615-xfi3p601	158	42	expected	expect	VBN
cord-004615-xfi3p601	158	43	number	number	NN
cord-004615-xfi3p601	158	44	of	of	IN
cord-004615-xfi3p601	158	45	infected	infected	JJ
cord-004615-xfi3p601	158	46	multipliers	multiplier	NNS
cord-004615-xfi3p601	158	47	by	by	IN
cord-004615-xfi3p601	158	48	one	one	CD
cord-004615-xfi3p601	158	49	infective	infective	JJ
cord-004615-xfi3p601	158	50	multiplier	multiplier	NN
cord-004615-xfi3p601	158	51	up	up	IN
cord-004615-xfi3p601	158	52	to	to	IN
cord-004615-xfi3p601	158	53	age	age	NN
cord-004615-xfi3p601	158	54	τ	τ	NN
cord-004615-xfi3p601	158	55	,	,	,
cord-004615-xfi3p601	158	56	for	for	IN
cord-004615-xfi3p601	158	57	given	give	VBN
cord-004615-xfi3p601	158	58	h	h	NN
cord-004615-xfi3p601	158	59	,	,	,
cord-004615-xfi3p601	158	60	µ	µ	NN
cord-004615-xfi3p601	158	61	mm	mm	NN
cord-004615-xfi3p601	158	62	(	(	-LRB-
cord-004615-xfi3p601	158	63	τ	τ	NN
cord-004615-xfi3p601	158	64	;	;	:
cord-004615-xfi3p601	158	65	h	h	NNP
cord-004615-xfi3p601	158	66	)	)	-RRB-
cord-004615-xfi3p601	158	67	,	,	,
cord-004615-xfi3p601	158	68	is	be	VBZ
cord-004615-xfi3p601	158	69	given	give	VBN
cord-004615-xfi3p601	158	70	by	by	IN
cord-004615-xfi3p601	158	71	:	:	:
cord-004615-xfi3p601	158	72	To	to	TO
cord-004615-xfi3p601	158	73	see	see	VB
cord-004615-xfi3p601	158	74	this	this	DT
cord-004615-xfi3p601	158	75	,	,	,
cord-004615-xfi3p601	158	76	we	-PRON-	PRP
cord-004615-xfi3p601	158	77	first	first	RB
cord-004615-xfi3p601	158	78	consider	consider	VBP
cord-004615-xfi3p601	158	79	only	only	RB
cord-004615-xfi3p601	158	80	one	one	CD
cord-004615-xfi3p601	158	81	type	type	NN
cord-004615-xfi3p601	158	82	of	of	IN
cord-004615-xfi3p601	158	83	herd	herd	NN
cord-004615-xfi3p601	158	84	.	.	.
cord-004615-xfi3p601	159	1	We	-PRON-	PRP
cord-004615-xfi3p601	159	2	prove	prove	VBP
cord-004615-xfi3p601	159	3	the	the	DT
cord-004615-xfi3p601	159	4	following	follow	VBG
cord-004615-xfi3p601	159	5	proposition	proposition	NN
cord-004615-xfi3p601	159	6	:	:	:
cord-004615-xfi3p601	159	7	Proof	proof	NN
cord-004615-xfi3p601	159	8	.	.	.
cord-004615-xfi3p601	160	1	The	the	DT
cord-004615-xfi3p601	160	2	infection	infection	NN
cord-004615-xfi3p601	160	3	and	and	CC
cord-004615-xfi3p601	160	4	the	the	DT
cord-004615-xfi3p601	160	5	detection	detection	NN
cord-004615-xfi3p601	160	6	rate	rate	NN
cord-004615-xfi3p601	160	7	are	be	VBP
cord-004615-xfi3p601	160	8	proportional	proportional	JJ
cord-004615-xfi3p601	160	9	to	to	IN
cord-004615-xfi3p601	160	10	the	the	DT
cord-004615-xfi3p601	160	11	number	number	NN
cord-004615-xfi3p601	160	12	of	of	IN
cord-004615-xfi3p601	160	13	infective	infective	JJ
cord-004615-xfi3p601	160	14	animals	animal	NNS
cord-004615-xfi3p601	160	15	in	in	IN
cord-004615-xfi3p601	160	16	a	a	DT
cord-004615-xfi3p601	160	17	herd	herd	NN
cord-004615-xfi3p601	160	18	.	.	.
cord-004615-xfi3p601	161	1	The	the	DT
cord-004615-xfi3p601	161	2	ratio	ratio	NN
cord-004615-xfi3p601	161	3	of	of	IN
cord-004615-xfi3p601	161	4	infection	infection	NN
cord-004615-xfi3p601	161	5	rate	rate	NN
cord-004615-xfi3p601	161	6	and	and	CC
cord-004615-xfi3p601	161	7	detection	detection	NN
cord-004615-xfi3p601	161	8	rate	rate	NN
cord-004615-xfi3p601	161	9	is	be	VBZ
cord-004615-xfi3p601	161	10	given	give	VBN
cord-004615-xfi3p601	161	11	by	by	IN
cord-004615-xfi3p601	161	12	β	β	NN
cord-004615-xfi3p601	161	13	/	/	SYM
cord-004615-xfi3p601	161	14	α	α	NN
cord-004615-xfi3p601	161	15	.	.	.
cord-004615-xfi3p601	162	1	We	-PRON-	PRP
cord-004615-xfi3p601	162	2	call	call	VBP
cord-004615-xfi3p601	162	3	the	the	DT
cord-004615-xfi3p601	162	4	detection	detection	NN
cord-004615-xfi3p601	162	5	of	of	IN
cord-004615-xfi3p601	162	6	the	the	DT
cord-004615-xfi3p601	162	7	herd	herd	NN
cord-004615-xfi3p601	162	8	and	and	CC
cord-004615-xfi3p601	162	9	the	the	DT
cord-004615-xfi3p601	162	10	infections	infection	NNS
cord-004615-xfi3p601	162	11	by	by	IN
cord-004615-xfi3p601	162	12	this	this	DT
cord-004615-xfi3p601	162	13	herd	herd	NN
cord-004615-xfi3p601	162	14	events	event	NNS
cord-004615-xfi3p601	162	15	.	.	.
cord-004615-xfi3p601	163	1	The	the	DT
cord-004615-xfi3p601	163	2	probability	probability	NN
cord-004615-xfi3p601	163	3	that	that	IN
cord-004615-xfi3p601	163	4	an	an	DT
cord-004615-xfi3p601	163	5	event	event	NN
cord-004615-xfi3p601	163	6	is	be	VBZ
cord-004615-xfi3p601	163	7	an	an	DT
cord-004615-xfi3p601	163	8	infection	infection	NN
cord-004615-xfi3p601	163	9	is	be	VBZ
cord-004615-xfi3p601	163	10	β	β	NN
cord-004615-xfi3p601	163	11	α+β	α+β	XX
cord-004615-xfi3p601	163	12	and	and	CC
cord-004615-xfi3p601	163	13	a	a	DT
cord-004615-xfi3p601	163	14	detection	detection	NN
cord-004615-xfi3p601	163	15	α	α	NN
cord-004615-xfi3p601	163	16	α+β	α+β	XX
cord-004615-xfi3p601	163	17	.	.	.
cord-004615-xfi3p601	164	1	Therefore	therefore	RB
cord-004615-xfi3p601	164	2	,	,	,
cord-004615-xfi3p601	164	3	the	the	DT
cord-004615-xfi3p601	164	4	number	number	NN
cord-004615-xfi3p601	164	5	of	of	IN
cord-004615-xfi3p601	164	6	events	event	NNS
cord-004615-xfi3p601	164	7	,	,	,
cord-004615-xfi3p601	164	8	including	include	VBG
cord-004615-xfi3p601	164	9	detection	detection	NN
cord-004615-xfi3p601	164	10	,	,	,
cord-004615-xfi3p601	164	11	is	be	VBZ
cord-004615-xfi3p601	164	12	described	describe	VBN
cord-004615-xfi3p601	164	13	by	by	IN
cord-004615-xfi3p601	164	14	a	a	DT
cord-004615-xfi3p601	164	15	geometric	geometric	JJ
cord-004615-xfi3p601	164	16	random	random	JJ
cord-004615-xfi3p601	164	17	variable	variable	NN
cord-004615-xfi3p601	164	18	with	with	IN
cord-004615-xfi3p601	164	19	parameter	parameter	NN
cord-004615-xfi3p601	164	20	α	α	NN
cord-004615-xfi3p601	164	21	α+β	α+β	XX
cord-004615-xfi3p601	164	22	.	.	.
cord-004615-xfi3p601	165	1	Hence	hence	RB
cord-004615-xfi3p601	165	2	the	the	DT
cord-004615-xfi3p601	165	3	direct	direct	JJ
cord-004615-xfi3p601	165	4	offspring	offspring	NN
cord-004615-xfi3p601	165	5	distribution	distribution	NN
cord-004615-xfi3p601	165	6	does	do	VBZ
cord-004615-xfi3p601	165	7	not	not	RB
cord-004615-xfi3p601	165	8	depend	depend	VB
cord-004615-xfi3p601	165	9	on	on	IN
cord-004615-xfi3p601	165	10	the	the	DT
cord-004615-xfi3p601	165	11	size	size	NN
cord-004615-xfi3p601	165	12	at	at	IN
cord-004615-xfi3p601	165	13	the	the	DT
cord-004615-xfi3p601	165	14	start	start	NN
cord-004615-xfi3p601	165	15	of	of	IN
cord-004615-xfi3p601	165	16	the	the	DT
cord-004615-xfi3p601	165	17	process	process	NN
cord-004615-xfi3p601	165	18	.	.	.
cord-004615-xfi3p601	166	1	Moreover	moreover	RB
cord-004615-xfi3p601	166	2	,	,	,
cord-004615-xfi3p601	166	3	the	the	DT
cord-004615-xfi3p601	166	4	same	same	JJ
cord-004615-xfi3p601	166	5	holds	hold	VBZ
cord-004615-xfi3p601	166	6	for	for	IN
cord-004615-xfi3p601	166	7	the	the	DT
cord-004615-xfi3p601	166	8	offspring	offspring	NN
cord-004615-xfi3p601	166	9	of	of	IN
cord-004615-xfi3p601	166	10	this	this	DT
cord-004615-xfi3p601	166	11	direct	direct	JJ
cord-004615-xfi3p601	166	12	offspring	offspring	NN
cord-004615-xfi3p601	166	13	.	.	.
cord-004615-xfi3p601	167	1	In	in	IN
cord-004615-xfi3p601	167	2	the	the	DT
cord-004615-xfi3p601	167	3	same	same	JJ
cord-004615-xfi3p601	167	4	way	way	NN
cord-004615-xfi3p601	167	5	we	-PRON-	PRP
cord-004615-xfi3p601	167	6	can	can	MD
cord-004615-xfi3p601	167	7	prove	prove	VB
cord-004615-xfi3p601	167	8	that	that	IN
cord-004615-xfi3p601	167	9	the	the	DT
cord-004615-xfi3p601	167	10	size	size	NN
cord-004615-xfi3p601	167	11	of	of	IN
cord-004615-xfi3p601	167	12	the	the	DT
cord-004615-xfi3p601	167	13	future	future	JJ
cord-004615-xfi3p601	167	14	offspring	offspring	NN
cord-004615-xfi3p601	167	15	of	of	IN
cord-004615-xfi3p601	167	16	an	an	DT
cord-004615-xfi3p601	167	17	infective	infective	JJ
cord-004615-xfi3p601	167	18	herd	herd	NN
cord-004615-xfi3p601	167	19	is	be	VBZ
cord-004615-xfi3p601	167	20	independent	independent	JJ
cord-004615-xfi3p601	167	21	of	of	IN
cord-004615-xfi3p601	167	22	its	-PRON-	PRP$
cord-004615-xfi3p601	167	23	age	age	NN
cord-004615-xfi3p601	167	24	.	.	.
cord-004615-xfi3p601	168	1	To	to	TO
cord-004615-xfi3p601	168	2	prove	prove	VB
cord-004615-xfi3p601	168	3	(	(	-LRB-
cord-004615-xfi3p601	168	4	3	3	CD
cord-004615-xfi3p601	168	5	)	)	-RRB-
cord-004615-xfi3p601	168	6	,	,	,
cord-004615-xfi3p601	168	7	consider	consider	VB
cord-004615-xfi3p601	168	8	two	two	CD
cord-004615-xfi3p601	168	9	types	type	NNS
cord-004615-xfi3p601	168	10	of	of	IN
cord-004615-xfi3p601	168	11	herds	herd	NNS
cord-004615-xfi3p601	168	12	.	.	.
cord-004615-xfi3p601	169	1	We	-PRON-	PRP
cord-004615-xfi3p601	169	2	note	note	VBP
cord-004615-xfi3p601	169	3	that	that	IN
cord-004615-xfi3p601	169	4	1	1	CD
cord-004615-xfi3p601	169	5	added	add	VBD
cord-004615-xfi3p601	169	6	to	to	IN
cord-004615-xfi3p601	169	7	the	the	DT
cord-004615-xfi3p601	169	8	number	number	NN
cord-004615-xfi3p601	169	9	of	of	IN
cord-004615-xfi3p601	169	10	multipliers	multiplier	NNS
cord-004615-xfi3p601	169	11	infected	infect	VBN
cord-004615-xfi3p601	169	12	by	by	IN
cord-004615-xfi3p601	169	13	one	one	CD
cord-004615-xfi3p601	169	14	infective	infective	JJ
cord-004615-xfi3p601	169	15	multiplier	multiplier	NN
cord-004615-xfi3p601	169	16	is	be	VBZ
cord-004615-xfi3p601	169	17	given	give	VBN
cord-004615-xfi3p601	169	18	by	by	IN
cord-004615-xfi3p601	169	19	a	a	DT
cord-004615-xfi3p601	169	20	geometric	geometric	JJ
cord-004615-xfi3p601	169	21	random	random	JJ
cord-004615-xfi3p601	169	22	variable	variable	NN
cord-004615-xfi3p601	169	23	with	with	IN
cord-004615-xfi3p601	169	24	parameter	parameter	NN
cord-004615-xfi3p601	169	25	α	α	NN
cord-004615-xfi3p601	169	26	α+β	α+β	XX
cord-004615-xfi3p601	169	27	m	m	NN
cord-004615-xfi3p601	169	28	.	.	.
cord-004615-xfi3p601	170	1	(	(	-LRB-
cord-004615-xfi3p601	170	2	1	1	CD
cord-004615-xfi3p601	170	3	is	be	VBZ
cord-004615-xfi3p601	170	4	added	add	VBN
cord-004615-xfi3p601	170	5	because	because	IN
cord-004615-xfi3p601	170	6	the	the	DT
cord-004615-xfi3p601	170	7	final	final	JJ
cord-004615-xfi3p601	170	8	event	event	NN
cord-004615-xfi3p601	170	9	will	will	MD
cord-004615-xfi3p601	170	10	be	be	VB
cord-004615-xfi3p601	170	11	the	the	DT
cord-004615-xfi3p601	170	12	only	only	JJ
cord-004615-xfi3p601	170	13	detection	detection	NN
cord-004615-xfi3p601	170	14	,	,	,
cord-004615-xfi3p601	170	15	and	and	CC
cord-004615-xfi3p601	170	16	the	the	DT
cord-004615-xfi3p601	170	17	number	number	NN
cord-004615-xfi3p601	170	18	of	of	IN
cord-004615-xfi3p601	170	19	events	event	NNS
cord-004615-xfi3p601	170	20	is	be	VBZ
cord-004615-xfi3p601	170	21	described	describe	VBN
cord-004615-xfi3p601	170	22	by	by	IN
cord-004615-xfi3p601	170	23	a	a	DT
cord-004615-xfi3p601	170	24	geometric	geometric	JJ
cord-004615-xfi3p601	170	25	random	random	JJ
cord-004615-xfi3p601	170	26	variable	variable	NN
cord-004615-xfi3p601	170	27	.	.	.
cord-004615-xfi3p601	170	28	)	)	-RRB-
cord-004615-xfi3p601	171	1	So	so	RB
cord-004615-xfi3p601	171	2	the	the	DT
cord-004615-xfi3p601	171	3	expected	expect	VBN
cord-004615-xfi3p601	171	4	number	number	NN
cord-004615-xfi3p601	171	5	of	of	IN
cord-004615-xfi3p601	171	6	future	future	JJ
cord-004615-xfi3p601	171	7	infections	infection	NNS
cord-004615-xfi3p601	171	8	of	of	IN
cord-004615-xfi3p601	171	9	an	an	DT
cord-004615-xfi3p601	171	10	infective	infective	JJ
cord-004615-xfi3p601	171	11	multiplier	multiplier	NN
cord-004615-xfi3p601	171	12	is	be	VBZ
cord-004615-xfi3p601	171	13	β	β	NN
cord-004615-xfi3p601	171	14	m	m	NNP
cord-004615-xfi3p601	171	15	α	α	NNP
cord-004615-xfi3p601	171	16	,	,	,
cord-004615-xfi3p601	171	17	at	at	IN
cord-004615-xfi3p601	171	18	all	all	DT
cord-004615-xfi3p601	171	19	times	time	NNS
cord-004615-xfi3p601	171	20	.	.	.
cord-004615-xfi3p601	172	1	The	the	DT
cord-004615-xfi3p601	172	2	probability	probability	NN
cord-004615-xfi3p601	172	3	that	that	IN
cord-004615-xfi3p601	172	4	an	an	DT
cord-004615-xfi3p601	172	5	infective	infective	JJ
cord-004615-xfi3p601	172	6	herd	herd	NN
cord-004615-xfi3p601	172	7	is	be	VBZ
cord-004615-xfi3p601	172	8	not	not	RB
cord-004615-xfi3p601	172	9	yet	yet	RB
cord-004615-xfi3p601	172	10	detected	detect	VBN
cord-004615-xfi3p601	172	11	at	at	IN
cord-004615-xfi3p601	172	12	age	age	NN
cord-004615-xfi3p601	172	13	τ	τ	NN
cord-004615-xfi3p601	172	14	is	be	VBZ
cord-004615-xfi3p601	172	15	given	give	VBN
cord-004615-xfi3p601	172	16	by	by	IN
cord-004615-xfi3p601	172	17	e	e	NN
cord-004615-xfi3p601	172	18	−	−	NN
cord-004615-xfi3p601	172	19	α	α	NN
cord-004615-xfi3p601	172	20	r	r	NN
cord-004615-xfi3p601	172	21	h(e	h(e	ADD
cord-004615-xfi3p601	172	22	rτ	rτ	.
cord-004615-xfi3p601	172	23	−1	−1	NNP
cord-004615-xfi3p601	172	24	)	)	-RRB-
cord-004615-xfi3p601	172	25	.	.	.
cord-004615-xfi3p601	173	1	From	from	IN
cord-004615-xfi3p601	173	2	this	this	DT
cord-004615-xfi3p601	173	3	and	and	CC
cord-004615-xfi3p601	173	4	Proposition	Proposition	NNP
cord-004615-xfi3p601	173	5	1	1	CD
cord-004615-xfi3p601	173	6	we	-PRON-	PRP
cord-004615-xfi3p601	173	7	deduce	deduce	VBP
cord-004615-xfi3p601	173	8	that	that	IN
cord-004615-xfi3p601	173	9	the	the	DT
cord-004615-xfi3p601	173	10	expected	expect	VBN
cord-004615-xfi3p601	173	11	number	number	NN
cord-004615-xfi3p601	173	12	of	of	IN
cord-004615-xfi3p601	173	13	infections	infection	NNS
cord-004615-xfi3p601	173	14	after	after	IN
cord-004615-xfi3p601	173	15	age	age	NN
cord-004615-xfi3p601	173	16	τ	τ	NN
cord-004615-xfi3p601	173	17	is	be	VBZ
cord-004615-xfi3p601	173	18	given	give	VBN
cord-004615-xfi3p601	173	19	by	by	IN
cord-004615-xfi3p601	173	20	β	β	NN
cord-004615-xfi3p601	173	21	m	m	NN
cord-004615-xfi3p601	173	22	α	α	NN
cord-004615-xfi3p601	173	23	e	e	NN
cord-004615-xfi3p601	173	24	−	−	NN
cord-004615-xfi3p601	173	25	α	α	NN
cord-004615-xfi3p601	173	26	r	r	NN
cord-004615-xfi3p601	173	27	h(e	h(e	ADD
cord-004615-xfi3p601	173	28	rτ	rτ	.
cord-004615-xfi3p601	173	29	−1	−1	NNP
cord-004615-xfi3p601	173	30	)	)	-RRB-
cord-004615-xfi3p601	173	31	.	.	.
cord-004615-xfi3p601	174	1	By	by	IN
cord-004615-xfi3p601	174	2	subtracting	subtract	VBG
cord-004615-xfi3p601	174	3	the	the	DT
cord-004615-xfi3p601	174	4	expected	expect	VBN
cord-004615-xfi3p601	174	5	number	number	NN
cord-004615-xfi3p601	174	6	of	of	IN
cord-004615-xfi3p601	174	7	infections	infection	NNS
cord-004615-xfi3p601	174	8	after	after	IN
cord-004615-xfi3p601	174	9	age	age	NN
cord-004615-xfi3p601	174	10	τ	τ	NN
cord-004615-xfi3p601	174	11	from	from	IN
cord-004615-xfi3p601	174	12	the	the	DT
cord-004615-xfi3p601	174	13	expected	expect	VBN
cord-004615-xfi3p601	174	14	total	total	JJ
cord-004615-xfi3p601	174	15	number	number	NN
cord-004615-xfi3p601	174	16	of	of	IN
cord-004615-xfi3p601	174	17	infections	infection	NNS
cord-004615-xfi3p601	174	18	by	by	IN
cord-004615-xfi3p601	174	19	one	one	CD
cord-004615-xfi3p601	174	20	herd	herd	NN
cord-004615-xfi3p601	174	21	we	-PRON-	PRP
cord-004615-xfi3p601	174	22	get	get	VBP
cord-004615-xfi3p601	174	23	the	the	DT
cord-004615-xfi3p601	174	24	expected	expect	VBN
cord-004615-xfi3p601	174	25	number	number	NN
cord-004615-xfi3p601	174	26	of	of	IN
cord-004615-xfi3p601	174	27	infections	infection	NNS
cord-004615-xfi3p601	174	28	until	until	IN
cord-004615-xfi3p601	174	29	age	age	NN
cord-004615-xfi3p601	174	30	τ	τ	NN
cord-004615-xfi3p601	174	31	.	.	.
cord-004615-xfi3p601	175	1	In	in	IN
cord-004615-xfi3p601	175	2	the	the	DT
cord-004615-xfi3p601	175	3	same	same	JJ
cord-004615-xfi3p601	175	4	way	way	NN
cord-004615-xfi3p601	175	5	we	-PRON-	PRP
cord-004615-xfi3p601	175	6	can	can	MD
cord-004615-xfi3p601	175	7	deduce	deduce	VB
cord-004615-xfi3p601	175	8	µ	µ	NN
cord-004615-xfi3p601	175	9	mf	mf	NN
cord-004615-xfi3p601	175	10	=	=	SYM
cord-004615-xfi3p601	175	11	)	)	-RRB-
cord-004615-xfi3p601	175	12	.	.	.
cord-004615-xfi3p601	176	1	Now	now	RB
cord-004615-xfi3p601	176	2	consider	consider	VB
cord-004615-xfi3p601	176	3	the	the	DT
cord-004615-xfi3p601	176	4	probability	probability	NN
cord-004615-xfi3p601	176	5	p	p	NN
cord-004615-xfi3p601	176	6	f	f	NN
cord-004615-xfi3p601	176	7	kl	kl	NNP
cord-004615-xfi3p601	176	8	that	that	IN
cord-004615-xfi3p601	176	9	a	a	DT
cord-004615-xfi3p601	176	10	finisher	finisher	NN
cord-004615-xfi3p601	176	11	infects	infect	VBZ
cord-004615-xfi3p601	176	12	k	k	NN
cord-004615-xfi3p601	176	13	multipliers	multiplier	NNS
cord-004615-xfi3p601	176	14	and	and	CC
cord-004615-xfi3p601	176	15	l	l	NNP
cord-004615-xfi3p601	176	16	finishers	finisher	NNS
cord-004615-xfi3p601	176	17	.	.	.
cord-004615-xfi3p601	177	1	All	all	DT
cord-004615-xfi3p601	177	2	events	event	NNS
cord-004615-xfi3p601	177	3	(	(	-LRB-
cord-004615-xfi3p601	177	4	infections	infection	NNS
cord-004615-xfi3p601	177	5	of	of	IN
cord-004615-xfi3p601	177	6	multipliers	multiplier	NNS
cord-004615-xfi3p601	177	7	,	,	,
cord-004615-xfi3p601	177	8	infections	infection	NNS
cord-004615-xfi3p601	177	9	of	of	IN
cord-004615-xfi3p601	177	10	finishers	finisher	NNS
cord-004615-xfi3p601	177	11	and	and	CC
cord-004615-xfi3p601	177	12	detection	detection	NN
cord-004615-xfi3p601	177	13	of	of	IN
cord-004615-xfi3p601	177	14	an	an	DT
cord-004615-xfi3p601	177	15	infected	infected	JJ
cord-004615-xfi3p601	177	16	herd	herd	NN
cord-004615-xfi3p601	177	17	)	)	-RRB-
cord-004615-xfi3p601	177	18	happen	happen	VB
cord-004615-xfi3p601	177	19	at	at	IN
cord-004615-xfi3p601	177	20	a	a	DT
cord-004615-xfi3p601	177	21	rate	rate	NN
cord-004615-xfi3p601	177	22	proportional	proportional	JJ
cord-004615-xfi3p601	177	23	to	to	IN
cord-004615-xfi3p601	177	24	the	the	DT
cord-004615-xfi3p601	177	25	number	number	NN
cord-004615-xfi3p601	177	26	of	of	IN
cord-004615-xfi3p601	177	27	infective	infective	JJ
cord-004615-xfi3p601	177	28	animals	animal	NNS
cord-004615-xfi3p601	177	29	in	in	IN
cord-004615-xfi3p601	177	30	the	the	DT
cord-004615-xfi3p601	177	31	infective	infective	JJ
cord-004615-xfi3p601	177	32	herd	herd	NN
cord-004615-xfi3p601	177	33	.	.	.
cord-004615-xfi3p601	178	1	Therefore	therefore	RB
cord-004615-xfi3p601	178	2	,	,	,
cord-004615-xfi3p601	178	3	the	the	DT
cord-004615-xfi3p601	178	4	rates	rate	NNS
cord-004615-xfi3p601	178	5	are	be	VBP
cord-004615-xfi3p601	178	6	all	all	DT
cord-004615-xfi3p601	178	7	proportional	proportional	JJ
cord-004615-xfi3p601	178	8	to	to	IN
cord-004615-xfi3p601	178	9	each	each	DT
cord-004615-xfi3p601	178	10	other	other	JJ
cord-004615-xfi3p601	178	11	.	.	.
cord-004615-xfi3p601	179	1	First	first	RB
cord-004615-xfi3p601	179	2	,	,	,
cord-004615-xfi3p601	179	3	we	-PRON-	PRP
cord-004615-xfi3p601	179	4	only	only	RB
cord-004615-xfi3p601	179	5	consider	consider	VBP
cord-004615-xfi3p601	179	6	infections	infection	NNS
cord-004615-xfi3p601	179	7	and	and	CC
cord-004615-xfi3p601	179	8	detections	detection	NNS
cord-004615-xfi3p601	179	9	,	,	,
cord-004615-xfi3p601	179	10	and	and	CC
cord-004615-xfi3p601	179	11	we	-PRON-	PRP
cord-004615-xfi3p601	179	12	do	do	VBP
cord-004615-xfi3p601	179	13	not	not	RB
cord-004615-xfi3p601	179	14	yet	yet	RB
cord-004615-xfi3p601	179	15	consider	consider	VB
cord-004615-xfi3p601	179	16	the	the	DT
cord-004615-xfi3p601	179	17	different	different	JJ
cord-004615-xfi3p601	179	18	types	type	NNS
cord-004615-xfi3p601	179	19	of	of	IN
cord-004615-xfi3p601	179	20	herds	herd	NNS
cord-004615-xfi3p601	179	21	infected	infect	VBN
cord-004615-xfi3p601	179	22	.	.	.
cord-004615-xfi3p601	180	1	Detection	detection	NN
cord-004615-xfi3p601	180	2	occurs	occur	VBZ
cord-004615-xfi3p601	180	3	with	with	IN
cord-004615-xfi3p601	180	4	rate	rate	NN
cord-004615-xfi3p601	180	5	αhe	αhe	CC
cord-004615-xfi3p601	180	6	rτ	rτ	NNS
cord-004615-xfi3p601	180	7	and	and	CC
cord-004615-xfi3p601	180	8	infection	infection	NN
cord-004615-xfi3p601	180	9	occurs	occur	VBZ
cord-004615-xfi3p601	180	10	with	with	IN
cord-004615-xfi3p601	180	11	rate	rate	NN
cord-004615-xfi3p601	180	12	β	β	NN
cord-004615-xfi3p601	180	13	m	m	NN
cord-004615-xfi3p601	181	1	he	-PRON-	PRP
cord-004615-xfi3p601	181	2	rτ	rτ	.
cord-004615-xfi3p601	182	1	+	+	CC
cord-004615-xfi3p601	183	1	β	β	NN
cord-004615-xfi3p601	184	1	f	f	LS
cord-004615-xfi3p601	184	2	he	-PRON-	PRP
cord-004615-xfi3p601	184	3	rτ	rτ	VBZ
cord-004615-xfi3p601	184	4	=	=	NFP
cord-004615-xfi3p601	185	1	βhe	βhe	NNP
cord-004615-xfi3p601	185	2	rτ	rτ	NNP
cord-004615-xfi3p601	185	3	.	.	.
cord-004615-xfi3p601	186	1	As	as	IN
cord-004615-xfi3p601	186	2	in	in	IN
cord-004615-xfi3p601	186	3	the	the	DT
cord-004615-xfi3p601	186	4	proof	proof	NN
cord-004615-xfi3p601	186	5	of	of	IN
cord-004615-xfi3p601	186	6	Proposition	Proposition	NNP
cord-004615-xfi3p601	186	7	1	1	CD
cord-004615-xfi3p601	186	8	we	-PRON-	PRP
cord-004615-xfi3p601	186	9	can	can	MD
cord-004615-xfi3p601	186	10	describe	describe	VB
cord-004615-xfi3p601	186	11	the	the	DT
cord-004615-xfi3p601	186	12	total	total	JJ
cord-004615-xfi3p601	186	13	number	number	NN
cord-004615-xfi3p601	186	14	of	of	IN
cord-004615-xfi3p601	186	15	events	event	NNS
cord-004615-xfi3p601	186	16	,	,	,
cord-004615-xfi3p601	186	17	D	D	NNS
cord-004615-xfi3p601	186	18	say	say	VBP
cord-004615-xfi3p601	186	19	,	,	,
cord-004615-xfi3p601	186	20	by	by	IN
cord-004615-xfi3p601	186	21	an	an	DT
cord-004615-xfi3p601	186	22	ordinary	ordinary	JJ
cord-004615-xfi3p601	186	23	geometric	geometric	JJ
cord-004615-xfi3p601	186	24	random	random	JJ
cord-004615-xfi3p601	186	25	variable	variable	NN
cord-004615-xfi3p601	186	26	with	with	IN
cord-004615-xfi3p601	186	27	parameter	parameter	NN
cord-004615-xfi3p601	186	28	α	α	NN
cord-004615-xfi3p601	186	29	α+β	α+β	XX
cord-004615-xfi3p601	186	30	.	.	.
cord-004615-xfi3p601	187	1	So	so	RB
cord-004615-xfi3p601	187	2	the	the	DT
cord-004615-xfi3p601	187	3	probability	probability	NN
cord-004615-xfi3p601	187	4	that	that	IN
cord-004615-xfi3p601	187	5	n	n	NN
cord-004615-xfi3p601	187	6	+	+	SYM
cord-004615-xfi3p601	187	7	1	1	CD
cord-004615-xfi3p601	187	8	events	event	NNS
cord-004615-xfi3p601	187	9	occur	occur	VBP
cord-004615-xfi3p601	187	10	,	,	,
cord-004615-xfi3p601	187	11	i.e.	i.e.	FW
cord-004615-xfi3p601	187	12	n	n	NN
cord-004615-xfi3p601	187	13	herds	herd	NNS
cord-004615-xfi3p601	187	14	are	be	VBP
cord-004615-xfi3p601	187	15	infected	infect	VBN
cord-004615-xfi3p601	187	16	by	by	IN
cord-004615-xfi3p601	187	17	one	one	CD
cord-004615-xfi3p601	187	18	finisher	finisher	NN
cord-004615-xfi3p601	187	19	,	,	,
cord-004615-xfi3p601	187	20	is	be	VBZ
cord-004615-xfi3p601	187	21	If	if	IN
cord-004615-xfi3p601	187	22	in	in	IN
cord-004615-xfi3p601	187	23	total	total	JJ
cord-004615-xfi3p601	187	24	n	n	NN
cord-004615-xfi3p601	187	25	herds	herd	NNS
cord-004615-xfi3p601	187	26	are	be	VBP
cord-004615-xfi3p601	187	27	infected	infect	VBN
cord-004615-xfi3p601	187	28	by	by	IN
cord-004615-xfi3p601	187	29	one	one	CD
cord-004615-xfi3p601	187	30	finisher	finisher	NN
cord-004615-xfi3p601	187	31	,	,	,
cord-004615-xfi3p601	187	32	we	-PRON-	PRP
cord-004615-xfi3p601	187	33	know	know	VBP
cord-004615-xfi3p601	187	34	by	by	IN
cord-004615-xfi3p601	187	35	the	the	DT
cord-004615-xfi3p601	187	36	lack	lack	NN
cord-004615-xfi3p601	187	37	of	of	IN
cord-004615-xfi3p601	187	38	memory	memory	NN
cord-004615-xfi3p601	187	39	property	property	NN
cord-004615-xfi3p601	187	40	that	that	WDT
cord-004615-xfi3p601	187	41	the	the	DT
cord-004615-xfi3p601	187	42	number	number	NN
cord-004615-xfi3p601	187	43	of	of	IN
cord-004615-xfi3p601	187	44	infected	infected	JJ
cord-004615-xfi3p601	187	45	multipliers	multiplier	NNS
cord-004615-xfi3p601	187	46	,	,	,
cord-004615-xfi3p601	187	47	N	n	NN
cord-004615-xfi3p601	187	48	f	f	NNP
cord-004615-xfi3p601	187	49	m	m	NNP
cord-004615-xfi3p601	187	50	,	,	,
cord-004615-xfi3p601	187	51	is	be	VBZ
cord-004615-xfi3p601	187	52	binomially	binomially	RB
cord-004615-xfi3p601	187	53	distributed	distribute	VBN
cord-004615-xfi3p601	187	54	with	with	IN
cord-004615-xfi3p601	187	55	parameters	parameter	NNS
cord-004615-xfi3p601	187	56	n	n	NNP
cord-004615-xfi3p601	187	57	and	and	CC
cord-004615-xfi3p601	187	58	β	β	NN
cord-004615-xfi3p601	187	59	m	m	NNP
cord-004615-xfi3p601	187	60	β	β	NNP
cord-004615-xfi3p601	187	61	.	.	.
cord-004615-xfi3p601	188	1	That	that	RB
cord-004615-xfi3p601	188	2	is	is	RB
cord-004615-xfi3p601	188	3	,	,	,
cord-004615-xfi3p601	188	4	We	-PRON-	PRP
cord-004615-xfi3p601	188	5	can	can	MD
cord-004615-xfi3p601	188	6	deduce	deduce	VB
cord-004615-xfi3p601	188	7	in	in	IN
cord-004615-xfi3p601	188	8	the	the	DT
cord-004615-xfi3p601	188	9	same	same	JJ
cord-004615-xfi3p601	188	10	way	way	NN
cord-004615-xfi3p601	188	11	.	.	.
cord-004615-xfi3p601	189	1	Note	note	VB
cord-004615-xfi3p601	189	2	that	that	IN
cord-004615-xfi3p601	189	3	we	-PRON-	PRP
cord-004615-xfi3p601	189	4	did	do	VBD
cord-004615-xfi3p601	189	5	not	not	RB
cord-004615-xfi3p601	189	6	need	need	VB
cord-004615-xfi3p601	189	7	the	the	DT
cord-004615-xfi3p601	189	8	distribution	distribution	NN
cord-004615-xfi3p601	189	9	of	of	IN
cord-004615-xfi3p601	189	10	the	the	DT
cord-004615-xfi3p601	189	11	random	random	JJ
cord-004615-xfi3p601	189	12	variable	variable	NN
cord-004615-xfi3p601	189	13	H	h	NN
cord-004615-xfi3p601	189	14	,	,	,
cord-004615-xfi3p601	189	15	we	-PRON-	PRP
cord-004615-xfi3p601	189	16	only	only	RB
cord-004615-xfi3p601	189	17	needed	need	VBD
cord-004615-xfi3p601	189	18	the	the	DT
cord-004615-xfi3p601	189	19	proportionality	proportionality	NN
cord-004615-xfi3p601	189	20	factors	factor	NNS
cord-004615-xfi3p601	189	21	of	of	IN
cord-004615-xfi3p601	189	22	the	the	DT
cord-004615-xfi3p601	189	23	parameters	parameter	NNS
cord-004615-xfi3p601	189	24	.	.	.
cord-004615-xfi3p601	190	1	In	in	IN
cord-004615-xfi3p601	190	2	the	the	DT
cord-004615-xfi3p601	190	3	special	special	JJ
cord-004615-xfi3p601	190	4	case	case	NN
cord-004615-xfi3p601	190	5	where	where	WRB
cord-004615-xfi3p601	190	6	infection	infection	NN
cord-004615-xfi3p601	190	7	and	and	CC
cord-004615-xfi3p601	190	8	detection	detection	NN
cord-004615-xfi3p601	190	9	rates	rate	NNS
cord-004615-xfi3p601	190	10	are	be	VBP
cord-004615-xfi3p601	190	11	proportional	proportional	JJ
cord-004615-xfi3p601	190	12	and	and	CC
cord-004615-xfi3p601	190	13	these	these	DT
cord-004615-xfi3p601	190	14	rates	rate	NNS
cord-004615-xfi3p601	190	15	are	be	VBP
cord-004615-xfi3p601	190	16	known	know	VBN
cord-004615-xfi3p601	190	17	for	for	IN
cord-004615-xfi3p601	190	18	the	the	DT
cord-004615-xfi3p601	190	19	time	time	NN
cord-004615-xfi3p601	190	20	before	before	IN
cord-004615-xfi3p601	190	21	the	the	DT
cord-004615-xfi3p601	190	22	first	first	JJ
cord-004615-xfi3p601	190	23	detection	detection	NN
cord-004615-xfi3p601	190	24	,	,	,
cord-004615-xfi3p601	190	25	we	-PRON-	PRP
cord-004615-xfi3p601	190	26	can	can	MD
cord-004615-xfi3p601	190	27	also	also	RB
cord-004615-xfi3p601	190	28	give	give	VB
cord-004615-xfi3p601	190	29	the	the	DT
cord-004615-xfi3p601	190	30	distribution	distribution	NN
cord-004615-xfi3p601	190	31	function	function	NN
cord-004615-xfi3p601	190	32	of	of	IN
cord-004615-xfi3p601	190	33	the	the	DT
cord-004615-xfi3p601	190	34	number	number	NN
cord-004615-xfi3p601	190	35	of	of	IN
cord-004615-xfi3p601	190	36	infective	infective	JJ
cord-004615-xfi3p601	190	37	herds	herd	NNS
cord-004615-xfi3p601	190	38	at	at	IN
cord-004615-xfi3p601	190	39	the	the	DT
cord-004615-xfi3p601	190	40	time	time	NN
cord-004615-xfi3p601	190	41	of	of	IN
cord-004615-xfi3p601	190	42	the	the	DT
cord-004615-xfi3p601	190	43	first	first	JJ
cord-004615-xfi3p601	190	44	detection	detection	NN
cord-004615-xfi3p601	190	45	.	.	.
cord-004615-xfi3p601	191	1	This	this	DT
cord-004615-xfi3p601	191	2	distribution	distribution	NN
cord-004615-xfi3p601	191	3	function	function	NN
cord-004615-xfi3p601	191	4	is	be	VBZ
cord-004615-xfi3p601	191	5	the	the	DT
cord-004615-xfi3p601	191	6	same	same	JJ
cord-004615-xfi3p601	191	7	as	as	IN
cord-004615-xfi3p601	191	8	the	the	DT
cord-004615-xfi3p601	191	9	distribution	distribution	NN
cord-004615-xfi3p601	191	10	function	function	NN
cord-004615-xfi3p601	191	11	of	of	IN
cord-004615-xfi3p601	191	12	the	the	DT
cord-004615-xfi3p601	191	13	number	number	NN
cord-004615-xfi3p601	191	14	of	of	IN
cord-004615-xfi3p601	191	15	direct	direct	JJ
cord-004615-xfi3p601	191	16	infections	infection	NNS
cord-004615-xfi3p601	191	17	by	by	IN
cord-004615-xfi3p601	191	18	one	one	CD
cord-004615-xfi3p601	191	19	herd	herd	NN
cord-004615-xfi3p601	191	20	,	,	,
cord-004615-xfi3p601	191	21	because	because	IN
cord-004615-xfi3p601	191	22	it	-PRON-	PRP
cord-004615-xfi3p601	191	23	still	still	RB
cord-004615-xfi3p601	191	24	holds	hold	VBZ
cord-004615-xfi3p601	191	25	that	that	IN
cord-004615-xfi3p601	191	26	an	an	DT
cord-004615-xfi3p601	191	27	event	event	NN
cord-004615-xfi3p601	191	28	is	be	VBZ
cord-004615-xfi3p601	191	29	a	a	DT
cord-004615-xfi3p601	191	30	detection	detection	NN
cord-004615-xfi3p601	191	31	with	with	IN
cord-004615-xfi3p601	191	32	probability	probability	NN
cord-004615-xfi3p601	191	33	α	α	NN
cord-004615-xfi3p601	191	34	α+β	α+β	XX
cord-004615-xfi3p601	191	35	and	and	CC
cord-004615-xfi3p601	191	36	the	the	DT
cord-004615-xfi3p601	191	37	probabilities	probability	NNS
cord-004615-xfi3p601	191	38	of	of	IN
cord-004615-xfi3p601	191	39	infections	infection	NNS
cord-004615-xfi3p601	191	40	of	of	IN
cord-004615-xfi3p601	191	41	finishers	finisher	NNS
cord-004615-xfi3p601	191	42	and	and	CC
cord-004615-xfi3p601	191	43	multipliers	multiplier	NNS
cord-004615-xfi3p601	191	44	are	be	VBP
cord-004615-xfi3p601	191	45	respectively	respectively	RB
cord-004615-xfi3p601	191	46	β	β	FW
cord-004615-xfi3p601	191	47	f	f	NNP
cord-004615-xfi3p601	191	48	α+β	α+β	NNP
cord-004615-xfi3p601	191	49	and	and	CC
cord-004615-xfi3p601	191	50	β	β	NN
cord-004615-xfi3p601	191	51	m	m	NN
cord-004615-xfi3p601	192	1	α+β	α+β	ADD
cord-004615-xfi3p601	192	2	.	.	.
cord-004615-xfi3p601	193	1	We	-PRON-	PRP
cord-004615-xfi3p601	193	2	are	be	VBP
cord-004615-xfi3p601	193	3	also	also	RB
cord-004615-xfi3p601	193	4	interested	interested	JJ
cord-004615-xfi3p601	193	5	in	in	IN
cord-004615-xfi3p601	193	6	the	the	DT
cord-004615-xfi3p601	193	7	probability	probability	NN
cord-004615-xfi3p601	193	8	that	that	IN
cord-004615-xfi3p601	193	9	a	a	DT
cord-004615-xfi3p601	193	10	herd	herd	NN
cord-004615-xfi3p601	193	11	infects	infect	VBZ
cord-004615-xfi3p601	193	12	k	k	NN
cord-004615-xfi3p601	193	13	multipliers	multiplier	NNS
cord-004615-xfi3p601	193	14	and	and	CC
cord-004615-xfi3p601	193	15	l	l	NNP
cord-004615-xfi3p601	193	16	finishers	finisher	NNS
cord-004615-xfi3p601	193	17	,	,	,
cord-004615-xfi3p601	193	18	before	before	IN
cord-004615-xfi3p601	193	19	the	the	DT
cord-004615-xfi3p601	193	20	herd	herd	NN
cord-004615-xfi3p601	193	21	reaches	reach	VBZ
cord-004615-xfi3p601	193	22	age	age	NN
cord-004615-xfi3p601	193	23	τ	τ	NN
cord-004615-xfi3p601	193	24	.	.	.
cord-004615-xfi3p601	194	1	We	-PRON-	PRP
cord-004615-xfi3p601	194	2	consider	consider	VBP
cord-004615-xfi3p601	194	3	a	a	DT
cord-004615-xfi3p601	194	4	finisher	finisher	NN
cord-004615-xfi3p601	194	5	.	.	.
cord-004615-xfi3p601	195	1	We	-PRON-	PRP
cord-004615-xfi3p601	195	2	write	write	VBP
cord-004615-xfi3p601	195	3	P(N	p(n	NN
cord-004615-xfi3p601	195	4	f	f	NN
cord-004615-xfi3p601	195	5	m	m	NN
cord-004615-xfi3p601	195	6	(	(	-LRB-
cord-004615-xfi3p601	195	7	τ	τ	NN
cord-004615-xfi3p601	195	8	;	;	:
cord-004615-xfi3p601	195	9	h	h	LS
cord-004615-xfi3p601	195	10	)	)	-RRB-
cord-004615-xfi3p601	195	11	=	=	NFP
cord-004615-xfi3p601	196	1	k	k	NNP
cord-004615-xfi3p601	197	1	,	,	,
cord-004615-xfi3p601	197	2	N	N	NNP
cord-004615-xfi3p601	197	3	ff	ff	NN
cord-004615-xfi3p601	197	4	(	(	-LRB-
cord-004615-xfi3p601	197	5	τ	τ	NN
cord-004615-xfi3p601	198	1	;	;	:
cord-004615-xfi3p601	198	2	h	h	LS
cord-004615-xfi3p601	198	3	)	)	-RRB-
cord-004615-xfi3p601	198	4	=	=	SYM
cord-004615-xfi3p601	198	5	l	l	NN
cord-004615-xfi3p601	198	6	)	)	-RRB-
cord-004615-xfi3p601	198	7	for	for	IN
cord-004615-xfi3p601	198	8	this	this	DT
cord-004615-xfi3p601	198	9	probability	probability	NN
cord-004615-xfi3p601	199	1	when	when	WRB
cord-004615-xfi3p601	199	2	the	the	DT
cord-004615-xfi3p601	199	3	detection	detection	NN
cord-004615-xfi3p601	199	4	age	age	NN
cord-004615-xfi3p601	199	5	τ	τ	NN
cord-004615-xfi3p601	199	6	d	d	NN
cord-004615-xfi3p601	199	7	and	and	CC
cord-004615-xfi3p601	199	8	H	h	NN
cord-004615-xfi3p601	199	9	=	=	SYM
cord-004615-xfi3p601	199	10	h	h	NN
cord-004615-xfi3p601	199	11	are	be	VBP
cord-004615-xfi3p601	199	12	given	give	VBN
cord-004615-xfi3p601	199	13	.	.	.
cord-004615-xfi3p601	200	1	The	the	DT
cord-004615-xfi3p601	200	2	infections	infection	NNS
cord-004615-xfi3p601	200	3	before	before	IN
cord-004615-xfi3p601	200	4	age	age	NN
cord-004615-xfi3p601	200	5	τ	τ	NN
cord-004615-xfi3p601	200	6	d	d	NN
cord-004615-xfi3p601	200	7	occur	occur	VBP
cord-004615-xfi3p601	200	8	independently	independently	RB
cord-004615-xfi3p601	200	9	of	of	IN
cord-004615-xfi3p601	200	10	each	each	DT
cord-004615-xfi3p601	200	11	other	other	JJ
cord-004615-xfi3p601	200	12	and	and	CC
cord-004615-xfi3p601	200	13	have	have	VBP
cord-004615-xfi3p601	200	14	the	the	DT
cord-004615-xfi3p601	200	15	lack	lack	NN
cord-004615-xfi3p601	200	16	of	of	IN
cord-004615-xfi3p601	200	17	memory	memory	NN
cord-004615-xfi3p601	200	18	property	property	NN
cord-004615-xfi3p601	200	19	.	.	.
cord-004615-xfi3p601	201	1	Therefore	therefore	RB
cord-004615-xfi3p601	201	2	,	,	,
cord-004615-xfi3p601	201	3	for	for	IN
cord-004615-xfi3p601	201	4	τ	τ	NN
cord-004615-xfi3p601	201	5	≤	≤	NN
cord-004615-xfi3p601	201	6	τ	τ	NN
cord-004615-xfi3p601	201	7	d	d	NNP
cord-004615-xfi3p601	201	8	the	the	DT
cord-004615-xfi3p601	201	9	times	time	NNS
cord-004615-xfi3p601	201	10	of	of	IN
cord-004615-xfi3p601	201	11	infections	infection	NNS
cord-004615-xfi3p601	201	12	of	of	IN
cord-004615-xfi3p601	201	13	the	the	DT
cord-004615-xfi3p601	201	14	different	different	JJ
cord-004615-xfi3p601	201	15	types	type	NNS
cord-004615-xfi3p601	201	16	of	of	IN
cord-004615-xfi3p601	201	17	herds	herd	NNS
cord-004615-xfi3p601	201	18	are	be	VBP
cord-004615-xfi3p601	201	19	described	describe	VBN
cord-004615-xfi3p601	201	20	by	by	IN
cord-004615-xfi3p601	201	21	an	an	DT
cord-004615-xfi3p601	201	22	inhomogeneous	inhomogeneous	JJ
cord-004615-xfi3p601	201	23	Poisson	Poisson	NNP
cord-004615-xfi3p601	201	24	-	-	HYPH
cord-004615-xfi3p601	201	25	process	process	NN
cord-004615-xfi3p601	201	26	with	with	IN
cord-004615-xfi3p601	201	27	rate	rate	NN
cord-004615-xfi3p601	201	28	β	β	NN
cord-004615-xfi3p601	201	29	ξ	ξ	NNP
cord-004615-xfi3p601	201	30	he	-PRON-	PRP
cord-004615-xfi3p601	201	31	rτ	rτ	VBZ
cord-004615-xfi3p601	201	32	.	.	.
cord-004615-xfi3p601	202	1	So	so	RB
cord-004615-xfi3p601	202	2	the	the	DT
cord-004615-xfi3p601	202	3	number	number	NN
cord-004615-xfi3p601	202	4	of	of	IN
cord-004615-xfi3p601	202	5	infections	infection	NNS
cord-004615-xfi3p601	202	6	until	until	IN
cord-004615-xfi3p601	202	7	age	age	NN
cord-004615-xfi3p601	202	8	τ	τ	NN
cord-004615-xfi3p601	202	9	is	be	VBZ
cord-004615-xfi3p601	202	10	Poisson	Poisson	NNP
cord-004615-xfi3p601	202	11	distributed	distribute	VBN
cord-004615-xfi3p601	202	12	with	with	IN
cord-004615-xfi3p601	202	13	parameter	parameter	NN
cord-004615-xfi3p601	202	14	hβ	hβ	FW
cord-004615-xfi3p601	202	15	ξ	ξ	NN
cord-004615-xfi3p601	202	16	τ	τ	NN
cord-004615-xfi3p601	202	17	0	0	NFP
cord-004615-xfi3p601	203	1	e	e	LS
cord-004615-xfi3p601	203	2	rs	rs	NNP
cord-004615-xfi3p601	203	3	ds	ds	NNP
cord-004615-xfi3p601	203	4	=	=	SYM
cord-004615-xfi3p601	203	5	hβ	hβ	FW
cord-004615-xfi3p601	203	6	ξ	ξ	NNP
cord-004615-xfi3p601	203	7	(	(	-LRB-
cord-004615-xfi3p601	203	8	e	e	NN
cord-004615-xfi3p601	203	9	rτ	rτ	IN
cord-004615-xfi3p601	203	10	−	−	NNP
cord-004615-xfi3p601	203	11	1	1	CD
cord-004615-xfi3p601	203	12	)	)	-RRB-
cord-004615-xfi3p601	203	13	.	.	.
cord-004615-xfi3p601	204	1	Now	now	RB
cord-004615-xfi3p601	204	2	we	-PRON-	PRP
cord-004615-xfi3p601	204	3	see	see	VBP
cord-004615-xfi3p601	204	4	:	:	:
cord-004615-xfi3p601	205	1	Note	note	VB
cord-004615-xfi3p601	205	2	that	that	IN
cord-004615-xfi3p601	205	3	now	now	RB
cord-004615-xfi3p601	205	4	we	-PRON-	PRP
cord-004615-xfi3p601	205	5	know	know	VBP
cord-004615-xfi3p601	205	6	the	the	DT
cord-004615-xfi3p601	205	7	life	life	NN
cord-004615-xfi3p601	205	8	length	length	NN
cord-004615-xfi3p601	205	9	distribution	distribution	NN
cord-004615-xfi3p601	205	10	,	,	,
cord-004615-xfi3p601	205	11	the	the	DT
cord-004615-xfi3p601	205	12	expected	expect	VBN
cord-004615-xfi3p601	205	13	number	number	NN
cord-004615-xfi3p601	205	14	of	of	IN
cord-004615-xfi3p601	205	15	infections	infection	NNS
cord-004615-xfi3p601	205	16	by	by	IN
cord-004615-xfi3p601	205	17	a	a	DT
cord-004615-xfi3p601	205	18	herd	herd	NN
cord-004615-xfi3p601	205	19	up	up	IN
cord-004615-xfi3p601	205	20	to	to	IN
cord-004615-xfi3p601	205	21	age	age	NN
cord-004615-xfi3p601	205	22	τ	τ	NN
cord-004615-xfi3p601	205	23	and	and	CC
cord-004615-xfi3p601	205	24	the	the	DT
cord-004615-xfi3p601	205	25	underlying	underlie	VBG
cord-004615-xfi3p601	205	26	Galton	Galton	NNP
cord-004615-xfi3p601	205	27	-	-	HYPH
cord-004615-xfi3p601	205	28	Watson	Watson	NNP
cord-004615-xfi3p601	205	29	process	process	NN
cord-004615-xfi3p601	205	30	of	of	IN
cord-004615-xfi3p601	205	31	the	the	DT
cord-004615-xfi3p601	205	32	branching	branching	NN
cord-004615-xfi3p601	205	33	process	process	NN
cord-004615-xfi3p601	205	34	,	,	,
cord-004615-xfi3p601	205	35	we	-PRON-	PRP
cord-004615-xfi3p601	205	36	can	can	MD
cord-004615-xfi3p601	205	37	use	use	VB
cord-004615-xfi3p601	205	38	the	the	DT
cord-004615-xfi3p601	205	39	general	general	JJ
cord-004615-xfi3p601	205	40	theory	theory	NN
cord-004615-xfi3p601	205	41	of	of	IN
cord-004615-xfi3p601	205	42	branching	branch	VBG
cord-004615-xfi3p601	205	43	processes	process	NNS
cord-004615-xfi3p601	205	44	to	to	TO
cord-004615-xfi3p601	205	45	determine	determine	VB
cord-004615-xfi3p601	205	46	some	some	DT
cord-004615-xfi3p601	205	47	other	other	JJ
cord-004615-xfi3p601	205	48	properties	property	NNS
cord-004615-xfi3p601	205	49	,	,	,
cord-004615-xfi3p601	205	50	like	like	IN
cord-004615-xfi3p601	205	51	the	the	DT
cord-004615-xfi3p601	205	52	expected	expect	VBN
cord-004615-xfi3p601	205	53	duration	duration	NN
cord-004615-xfi3p601	205	54	of	of	IN
cord-004615-xfi3p601	205	55	the	the	DT
cord-004615-xfi3p601	205	56	outbreak	outbreak	NN
cord-004615-xfi3p601	205	57	.	.	.
cord-004615-xfi3p601	206	1	(	(	-LRB-
cord-004615-xfi3p601	206	2	[	[	-LRB-
cord-004615-xfi3p601	206	3	4	4	CD
cord-004615-xfi3p601	206	4	]	]	-RRB-
cord-004615-xfi3p601	206	5	,	,	,
cord-004615-xfi3p601	206	6	chapters	chapter	NNS
cord-004615-xfi3p601	206	7	2	2	CD
cord-004615-xfi3p601	206	8	and	and	CC
cord-004615-xfi3p601	206	9	6	6	CD
cord-004615-xfi3p601	206	10	)	)	-RRB-
cord-004615-xfi3p601	206	11	.	.	.
cord-004615-xfi3p601	207	1	1	1	LS
cord-004615-xfi3p601	207	2	.	.	.
cord-004615-xfi3p601	208	1	We	-PRON-	PRP
cord-004615-xfi3p601	208	2	use	use	VBP
cord-004615-xfi3p601	208	3	a	a	DT
cord-004615-xfi3p601	208	4	branching	branch	VBG
cord-004615-xfi3p601	208	5	idea	idea	NN
cord-004615-xfi3p601	208	6	to	to	TO
cord-004615-xfi3p601	208	7	describe	describe	VB
cord-004615-xfi3p601	208	8	the	the	DT
cord-004615-xfi3p601	208	9	spread	spread	NN
cord-004615-xfi3p601	208	10	of	of	IN
cord-004615-xfi3p601	208	11	the	the	DT
cord-004615-xfi3p601	208	12	infection	infection	NN
cord-004615-xfi3p601	208	13	among	among	IN
cord-004615-xfi3p601	208	14	different	different	JJ
cord-004615-xfi3p601	208	15	herds	herd	NNS
cord-004615-xfi3p601	208	16	.	.	.
cord-004615-xfi3p601	209	1	For	for	IN
cord-004615-xfi3p601	209	2	this	this	DT
cord-004615-xfi3p601	209	3	approach	approach	NN
cord-004615-xfi3p601	209	4	,	,	,
cord-004615-xfi3p601	209	5	we	-PRON-	PRP
cord-004615-xfi3p601	209	6	assume	assume	VBP
cord-004615-xfi3p601	209	7	that	that	IN
cord-004615-xfi3p601	209	8	one	one	CD
cord-004615-xfi3p601	209	9	herd	herd	NN
cord-004615-xfi3p601	209	10	has	have	VBZ
cord-004615-xfi3p601	209	11	contacts	contact	NNS
cord-004615-xfi3p601	209	12	with	with	IN
cord-004615-xfi3p601	209	13	many	many	JJ
cord-004615-xfi3p601	209	14	other	other	JJ
cord-004615-xfi3p601	209	15	herds	herd	NNS
cord-004615-xfi3p601	209	16	.	.	.
cord-004615-xfi3p601	210	1	In	in	IN
cord-004615-xfi3p601	210	2	our	-PRON-	PRP$
cord-004615-xfi3p601	210	3	model	model	NN
cord-004615-xfi3p601	210	4	we	-PRON-	PRP
cord-004615-xfi3p601	210	5	do	do	VBP
cord-004615-xfi3p601	210	6	not	not	RB
cord-004615-xfi3p601	210	7	take	take	VB
cord-004615-xfi3p601	210	8	spatial	spatial	JJ
cord-004615-xfi3p601	210	9	distribution	distribution	NN
cord-004615-xfi3p601	210	10	of	of	IN
cord-004615-xfi3p601	210	11	the	the	DT
cord-004615-xfi3p601	210	12	herds	herd	NNS
cord-004615-xfi3p601	210	13	into	into	IN
cord-004615-xfi3p601	210	14	account	account	NN
cord-004615-xfi3p601	210	15	.	.	.
cord-004615-xfi3p601	211	1	As	as	RB
cord-004615-xfi3p601	211	2	long	long	RB
cord-004615-xfi3p601	211	3	as	as	IN
cord-004615-xfi3p601	211	4	there	there	EX
cord-004615-xfi3p601	211	5	are	be	VBP
cord-004615-xfi3p601	211	6	many	many	JJ
cord-004615-xfi3p601	211	7	herds	herd	NNS
cord-004615-xfi3p601	211	8	in	in	IN
cord-004615-xfi3p601	211	9	an	an	DT
cord-004615-xfi3p601	211	10	area	area	NN
cord-004615-xfi3p601	211	11	,	,	,
cord-004615-xfi3p601	211	12	the	the	DT
cord-004615-xfi3p601	211	13	local	local	JJ
cord-004615-xfi3p601	211	14	exhaustion	exhaustion	NN
cord-004615-xfi3p601	211	15	of	of	IN
cord-004615-xfi3p601	211	16	susceptible	susceptible	JJ
cord-004615-xfi3p601	211	17	herds	herd	NNS
cord-004615-xfi3p601	211	18	can	can	MD
cord-004615-xfi3p601	211	19	be	be	VB
cord-004615-xfi3p601	211	20	ignored	ignore	VBN
cord-004615-xfi3p601	211	21	.	.	.
cord-004615-xfi3p601	212	1	If	if	IN
cord-004615-xfi3p601	212	2	the	the	DT
cord-004615-xfi3p601	212	3	outbreak	outbreak	NN
cord-004615-xfi3p601	212	4	is	be	VBZ
cord-004615-xfi3p601	212	5	in	in	IN
cord-004615-xfi3p601	212	6	an	an	DT
cord-004615-xfi3p601	212	7	advanced	advanced	JJ
cord-004615-xfi3p601	212	8	state	state	NN
cord-004615-xfi3p601	212	9	,	,	,
cord-004615-xfi3p601	212	10	however	however	RB
cord-004615-xfi3p601	212	11	,	,	,
cord-004615-xfi3p601	212	12	local	local	JJ
cord-004615-xfi3p601	212	13	depletion	depletion	NN
cord-004615-xfi3p601	212	14	of	of	IN
cord-004615-xfi3p601	212	15	susceptible	susceptible	JJ
cord-004615-xfi3p601	212	16	herds	herd	NNS
cord-004615-xfi3p601	212	17	(	(	-LRB-
cord-004615-xfi3p601	212	18	either	either	CC
cord-004615-xfi3p601	212	19	by	by	IN
cord-004615-xfi3p601	212	20	the	the	DT
cord-004615-xfi3p601	212	21	epidemic	epidemic	NN
cord-004615-xfi3p601	212	22	progression	progression	NN
cord-004615-xfi3p601	212	23	or	or	CC
cord-004615-xfi3p601	212	24	by	by	IN
cord-004615-xfi3p601	212	25	so	so	RB
cord-004615-xfi3p601	212	26	-	-	HYPH
cord-004615-xfi3p601	212	27	called	call	VBN
cord-004615-xfi3p601	212	28	pre	pre	JJ
cord-004615-xfi3p601	212	29	-	-	JJ
cord-004615-xfi3p601	212	30	emptive	emptive	JJ
cord-004615-xfi3p601	212	31	culling	culling	NN
cord-004615-xfi3p601	212	32	)	)	-RRB-
cord-004615-xfi3p601	212	33	will	will	MD
cord-004615-xfi3p601	212	34	certainly	certainly	RB
cord-004615-xfi3p601	212	35	play	play	VB
cord-004615-xfi3p601	212	36	a	a	DT
cord-004615-xfi3p601	212	37	role	role	NN
cord-004615-xfi3p601	212	38	.	.	.
cord-004615-xfi3p601	213	1	As	as	RB
cord-004615-xfi3p601	213	2	long	long	RB
cord-004615-xfi3p601	213	3	as	as	IN
cord-004615-xfi3p601	213	4	there	there	EX
cord-004615-xfi3p601	213	5	are	be	VBP
cord-004615-xfi3p601	213	6	relatively	relatively	RB
cord-004615-xfi3p601	213	7	few	few	JJ
cord-004615-xfi3p601	213	8	infected	infected	JJ
cord-004615-xfi3p601	213	9	herds	herd	NNS
cord-004615-xfi3p601	213	10	in	in	IN
cord-004615-xfi3p601	213	11	a	a	DT
cord-004615-xfi3p601	213	12	neighbourhood	neighbourhood	NN
cord-004615-xfi3p601	213	13	,	,	,
cord-004615-xfi3p601	213	14	(	(	-LRB-
cord-004615-xfi3p601	213	15	i.e.	i.e.	FW
cord-004615-xfi3p601	213	16	a	a	DT
cord-004615-xfi3p601	213	17	group	group	NN
cord-004615-xfi3p601	213	18	of	of	IN
cord-004615-xfi3p601	213	19	herds	herd	NNS
cord-004615-xfi3p601	213	20	that	that	WDT
cord-004615-xfi3p601	213	21	have	have	VBP
cord-004615-xfi3p601	213	22	contacts	contact	NNS
cord-004615-xfi3p601	213	23	with	with	IN
cord-004615-xfi3p601	213	24	each	each	DT
cord-004615-xfi3p601	213	25	other	other	JJ
cord-004615-xfi3p601	213	26	)	)	-RRB-
cord-004615-xfi3p601	213	27	we	-PRON-	PRP
cord-004615-xfi3p601	213	28	assume	assume	VBP
cord-004615-xfi3p601	213	29	that	that	IN
cord-004615-xfi3p601	213	30	the	the	DT
cord-004615-xfi3p601	213	31	infection	infection	NN
cord-004615-xfi3p601	213	32	rate	rate	NN
cord-004615-xfi3p601	213	33	does	do	VBZ
cord-004615-xfi3p601	213	34	not	not	RB
cord-004615-xfi3p601	213	35	directly	directly	RB
cord-004615-xfi3p601	213	36	depend	depend	VB
cord-004615-xfi3p601	213	37	on	on	IN
cord-004615-xfi3p601	213	38	this	this	DT
cord-004615-xfi3p601	213	39	number	number	NN
cord-004615-xfi3p601	213	40	of	of	IN
cord-004615-xfi3p601	213	41	infected	infected	JJ
cord-004615-xfi3p601	213	42	herds	herd	NNS
cord-004615-xfi3p601	213	43	.	.	.
cord-004615-xfi3p601	214	1	Measures	measure	NNS
cord-004615-xfi3p601	214	2	like	like	IN
cord-004615-xfi3p601	214	3	ring	ring	NN
cord-004615-xfi3p601	214	4	-	-	HYPH
cord-004615-xfi3p601	214	5	culling	culling	NN
cord-004615-xfi3p601	214	6	(	(	-LRB-
cord-004615-xfi3p601	214	7	culling	culling	NN
cord-004615-xfi3p601	214	8	of	of	IN
cord-004615-xfi3p601	214	9	all	all	DT
cord-004615-xfi3p601	214	10	herds	herd	NNS
cord-004615-xfi3p601	214	11	within	within	IN
cord-004615-xfi3p601	214	12	a	a	DT
cord-004615-xfi3p601	214	13	certain	certain	JJ
cord-004615-xfi3p601	214	14	distance	distance	NN
cord-004615-xfi3p601	214	15	of	of	IN
cord-004615-xfi3p601	214	16	an	an	DT
cord-004615-xfi3p601	214	17	infected	infected	JJ
cord-004615-xfi3p601	214	18	herd	herd	NN
cord-004615-xfi3p601	214	19	)	)	-RRB-
cord-004615-xfi3p601	214	20	and	and	CC
cord-004615-xfi3p601	214	21	ring	ring	NN
cord-004615-xfi3p601	214	22	vaccination	vaccination	NN
cord-004615-xfi3p601	214	23	can	can	MD
cord-004615-xfi3p601	214	24	not	not	RB
cord-004615-xfi3p601	214	25	be	be	VB
cord-004615-xfi3p601	214	26	considered	consider	VBN
cord-004615-xfi3p601	214	27	in	in	IN
cord-004615-xfi3p601	214	28	our	-PRON-	PRP$
cord-004615-xfi3p601	214	29	model	model	NN
cord-004615-xfi3p601	214	30	.	.	.
cord-004615-xfi3p601	215	1	2	2	LS
cord-004615-xfi3p601	215	2	.	.	.
cord-004615-xfi3p601	216	1	We	-PRON-	PRP
cord-004615-xfi3p601	216	2	distinguish	distinguish	VBP
cord-004615-xfi3p601	216	3	between	between	IN
cord-004615-xfi3p601	216	4	two	two	CD
cord-004615-xfi3p601	216	5	types	type	NNS
cord-004615-xfi3p601	216	6	of	of	IN
cord-004615-xfi3p601	216	7	contacts	contact	NNS
cord-004615-xfi3p601	216	8	,	,	,
cord-004615-xfi3p601	216	9	transport	transport	NN
cord-004615-xfi3p601	216	10	contacts	contact	NNS
cord-004615-xfi3p601	216	11	and	and	CC
cord-004615-xfi3p601	216	12	indirect	indirect	JJ
cord-004615-xfi3p601	216	13	contacts	contact	NNS
cord-004615-xfi3p601	216	14	.	.	.
cord-004615-xfi3p601	217	1	We	-PRON-	PRP
cord-004615-xfi3p601	217	2	have	have	VBP
cord-004615-xfi3p601	217	3	assumed	assume	VBN
cord-004615-xfi3p601	217	4	that	that	IN
cord-004615-xfi3p601	217	5	the	the	DT
cord-004615-xfi3p601	217	6	indirect	indirect	JJ
cord-004615-xfi3p601	217	7	contacts	contact	NNS
cord-004615-xfi3p601	217	8	are	be	VBP
cord-004615-xfi3p601	217	9	the	the	DT
cord-004615-xfi3p601	217	10	same	same	JJ
cord-004615-xfi3p601	217	11	for	for	IN
cord-004615-xfi3p601	217	12	all	all	DT
cord-004615-xfi3p601	217	13	herds	herd	NNS
cord-004615-xfi3p601	217	14	.	.	.
cord-004615-xfi3p601	218	1	Transport	transport	NN
cord-004615-xfi3p601	218	2	contacts	contact	NNS
cord-004615-xfi3p601	218	3	are	be	VBP
cord-004615-xfi3p601	218	4	only	only	RB
cord-004615-xfi3p601	218	5	from	from	IN
cord-004615-xfi3p601	218	6	multipliers	multiplier	NNS
cord-004615-xfi3p601	218	7	to	to	IN
cord-004615-xfi3p601	218	8	finishers	finisher	NNS
cord-004615-xfi3p601	218	9	.	.	.
cord-004615-xfi3p601	219	1	Indirect	indirect	JJ
cord-004615-xfi3p601	219	2	contacts	contact	NNS
cord-004615-xfi3p601	219	3	include	include	VBP
cord-004615-xfi3p601	219	4	transport	transport	NN
cord-004615-xfi3p601	219	5	of	of	IN
cord-004615-xfi3p601	219	6	the	the	DT
cord-004615-xfi3p601	219	7	virus	virus	NN
cord-004615-xfi3p601	219	8	by	by	IN
cord-004615-xfi3p601	219	9	wind	wind	NN
cord-004615-xfi3p601	219	10	,	,	,
cord-004615-xfi3p601	219	11	by	by	IN
cord-004615-xfi3p601	219	12	visits	visit	NNS
cord-004615-xfi3p601	219	13	from	from	IN
cord-004615-xfi3p601	219	14	an	an	DT
cord-004615-xfi3p601	219	15	infective	infective	JJ
cord-004615-xfi3p601	219	16	herd	herd	NN
cord-004615-xfi3p601	219	17	to	to	IN
cord-004615-xfi3p601	219	18	a	a	DT
cord-004615-xfi3p601	219	19	susceptible	susceptible	JJ
cord-004615-xfi3p601	219	20	herd	herd	NN
cord-004615-xfi3p601	219	21	etc	etc	FW
cord-004615-xfi3p601	219	22	.	.	.
cord-004615-xfi3p601	220	1	Transport	transport	NN
cord-004615-xfi3p601	220	2	contacts	contact	NNS
cord-004615-xfi3p601	220	3	are	be	VBP
cord-004615-xfi3p601	220	4	transports	transport	NNS
cord-004615-xfi3p601	220	5	of	of	IN
cord-004615-xfi3p601	220	6	infected	infected	JJ
cord-004615-xfi3p601	220	7	animals	animal	NNS
cord-004615-xfi3p601	220	8	from	from	IN
cord-004615-xfi3p601	220	9	a	a	DT
cord-004615-xfi3p601	220	10	multiplier	multiplier	NN
cord-004615-xfi3p601	220	11	to	to	IN
cord-004615-xfi3p601	220	12	a	a	DT
cord-004615-xfi3p601	220	13	finisher	finisher	NN
cord-004615-xfi3p601	220	14	.	.	.
cord-004615-xfi3p601	221	1	3	3	LS
cord-004615-xfi3p601	221	2	.	.	.
cord-004615-xfi3p601	222	1	We	-PRON-	PRP
cord-004615-xfi3p601	222	2	simplify	simplify	VBP
cord-004615-xfi3p601	222	3	the	the	DT
cord-004615-xfi3p601	222	4	model	model	NN
cord-004615-xfi3p601	222	5	by	by	IN
cord-004615-xfi3p601	222	6	assuming	assume	VBG
cord-004615-xfi3p601	222	7	that	that	IN
cord-004615-xfi3p601	222	8	the	the	DT
cord-004615-xfi3p601	222	9	measures	measure	NNS
cord-004615-xfi3p601	222	10	are	be	VBP
cord-004615-xfi3p601	222	11	implemented	implement	VBN
cord-004615-xfi3p601	222	12	at	at	IN
cord-004615-xfi3p601	222	13	the	the	DT
cord-004615-xfi3p601	222	14	time	time	NN
cord-004615-xfi3p601	222	15	of	of	IN
cord-004615-xfi3p601	222	16	the	the	DT
cord-004615-xfi3p601	222	17	introduction	introduction	NN
cord-004615-xfi3p601	222	18	of	of	IN
cord-004615-xfi3p601	222	19	the	the	DT
cord-004615-xfi3p601	222	20	virus	virus	NN
cord-004615-xfi3p601	222	21	in	in	IN
cord-004615-xfi3p601	222	22	the	the	DT
cord-004615-xfi3p601	222	23	population	population	NN
cord-004615-xfi3p601	222	24	(	(	-LRB-
cord-004615-xfi3p601	222	25	or	or	CC
cord-004615-xfi3p601	222	26	,	,	,
cord-004615-xfi3p601	222	27	in	in	IN
cord-004615-xfi3p601	222	28	other	other	JJ
cord-004615-xfi3p601	222	29	words	word	NNS
cord-004615-xfi3p601	222	30	,	,	,
cord-004615-xfi3p601	222	31	that	that	IN
cord-004615-xfi3p601	222	32	the	the	DT
cord-004615-xfi3p601	222	33	infection	infection	NN
cord-004615-xfi3p601	222	34	is	be	VBZ
cord-004615-xfi3p601	222	35	detected	detect	VBN
cord-004615-xfi3p601	222	36	immediately	immediately	RB
cord-004615-xfi3p601	222	37	)	)	-RRB-
cord-004615-xfi3p601	222	38	.	.	.
cord-004615-xfi3p601	223	1	It	-PRON-	PRP
cord-004615-xfi3p601	223	2	would	would	MD
cord-004615-xfi3p601	223	3	be	be	VB
cord-004615-xfi3p601	223	4	desirable	desirable	JJ
cord-004615-xfi3p601	223	5	to	to	TO
cord-004615-xfi3p601	223	6	implement	implement	VB
cord-004615-xfi3p601	223	7	the	the	DT
cord-004615-xfi3p601	223	8	measures	measure	NNS
cord-004615-xfi3p601	223	9	from	from	IN
cord-004615-xfi3p601	223	10	the	the	DT
cord-004615-xfi3p601	223	11	moment	moment	NN
cord-004615-xfi3p601	223	12	of	of	IN
cord-004615-xfi3p601	223	13	first	first	JJ
cord-004615-xfi3p601	223	14	detection	detection	NN
cord-004615-xfi3p601	223	15	.	.	.
cord-004615-xfi3p601	224	1	It	-PRON-	PRP
cord-004615-xfi3p601	224	2	is	be	VBZ
cord-004615-xfi3p601	224	3	difficult	difficult	JJ
cord-004615-xfi3p601	224	4	,	,	,
cord-004615-xfi3p601	224	5	however	however	RB
cord-004615-xfi3p601	224	6	,	,	,
cord-004615-xfi3p601	224	7	to	to	TO
cord-004615-xfi3p601	224	8	estimate	estimate	VB
cord-004615-xfi3p601	224	9	parameters	parameter	NNS
cord-004615-xfi3p601	224	10	like	like	IN
cord-004615-xfi3p601	224	11	α	α	NN
cord-004615-xfi3p601	224	12	and	and	CC
cord-004615-xfi3p601	224	13	β	β	NN
cord-004615-xfi3p601	224	14	for	for	IN
cord-004615-xfi3p601	224	15	the	the	DT
cord-004615-xfi3p601	224	16	time	time	NN
cord-004615-xfi3p601	224	17	before	before	IN
cord-004615-xfi3p601	224	18	the	the	DT
cord-004615-xfi3p601	224	19	first	first	JJ
cord-004615-xfi3p601	224	20	detection	detection	NN
cord-004615-xfi3p601	224	21	,	,	,
cord-004615-xfi3p601	224	22	when	when	WRB
cord-004615-xfi3p601	224	23	awareness	awareness	NN
cord-004615-xfi3p601	224	24	is	be	VBZ
cord-004615-xfi3p601	224	25	not	not	RB
cord-004615-xfi3p601	224	26	yet	yet	RB
cord-004615-xfi3p601	224	27	heightened	heighten	VBN
cord-004615-xfi3p601	224	28	by	by	IN
cord-004615-xfi3p601	224	29	announcement	announcement	NN
cord-004615-xfi3p601	224	30	of	of	IN
cord-004615-xfi3p601	224	31	the	the	DT
cord-004615-xfi3p601	224	32	outbreak	outbreak	NN
cord-004615-xfi3p601	224	33	,	,	,
cord-004615-xfi3p601	224	34	and	and	CC
cord-004615-xfi3p601	224	35	when	when	WRB
cord-004615-xfi3p601	224	36	increased	increase	VBN
cord-004615-xfi3p601	224	37	hygienic	hygienic	JJ
cord-004615-xfi3p601	224	38	measures	measure	NNS
cord-004615-xfi3p601	224	39	on	on	IN
cord-004615-xfi3p601	224	40	farms	farm	NNS
cord-004615-xfi3p601	224	41	are	be	VBP
cord-004615-xfi3p601	224	42	not	not	RB
cord-004615-xfi3p601	224	43	yet	yet	RB
cord-004615-xfi3p601	224	44	taken	take	VBN
cord-004615-xfi3p601	224	45	.	.	.
cord-004615-xfi3p601	225	1	If	if	IN
cord-004615-xfi3p601	225	2	we	-PRON-	PRP
cord-004615-xfi3p601	225	3	know	know	VBP
cord-004615-xfi3p601	225	4	the	the	DT
cord-004615-xfi3p601	225	5	value	value	NN
cord-004615-xfi3p601	225	6	of	of	IN
cord-004615-xfi3p601	225	7	the	the	DT
cord-004615-xfi3p601	225	8	parameters	parameter	NNS
cord-004615-xfi3p601	225	9	of	of	IN
cord-004615-xfi3p601	225	10	the	the	DT
cord-004615-xfi3p601	225	11	model	model	NN
cord-004615-xfi3p601	225	12	for	for	IN
cord-004615-xfi3p601	225	13	the	the	DT
cord-004615-xfi3p601	225	14	period	period	NN
cord-004615-xfi3p601	225	15	between	between	IN
cord-004615-xfi3p601	225	16	introduction	introduction	NN
cord-004615-xfi3p601	225	17	and	and	CC
cord-004615-xfi3p601	225	18	first	first	JJ
cord-004615-xfi3p601	225	19	detection	detection	NN
cord-004615-xfi3p601	225	20	,	,	,
cord-004615-xfi3p601	225	21	we	-PRON-	PRP
cord-004615-xfi3p601	225	22	are	be	VBP
cord-004615-xfi3p601	225	23	able	able	JJ
cord-004615-xfi3p601	225	24	to	to	TO
cord-004615-xfi3p601	225	25	estimate	estimate	VB
cord-004615-xfi3p601	225	26	the	the	DT
cord-004615-xfi3p601	225	27	probability	probability	NN
cord-004615-xfi3p601	225	28	of	of	IN
cord-004615-xfi3p601	225	29	extinction	extinction	NN
cord-004615-xfi3p601	225	30	and	and	CC
cord-004615-xfi3p601	225	31	the	the	DT
cord-004615-xfi3p601	225	32	expected	expect	VBN
cord-004615-xfi3p601	225	33	final	final	JJ
cord-004615-xfi3p601	225	34	size	size	NN
cord-004615-xfi3p601	225	35	of	of	IN
cord-004615-xfi3p601	225	36	such	such	PDT
cord-004615-xfi3p601	225	37	a	a	DT
cord-004615-xfi3p601	225	38	situation	situation	NN
cord-004615-xfi3p601	225	39	.	.	.
cord-004615-xfi3p601	226	1	However	however	RB
cord-004615-xfi3p601	226	2	,	,	,
cord-004615-xfi3p601	226	3	these	these	DT
cord-004615-xfi3p601	226	4	calculations	calculation	NNS
cord-004615-xfi3p601	226	5	still	still	RB
cord-004615-xfi3p601	226	6	require	require	VBP
cord-004615-xfi3p601	226	7	that	that	IN
cord-004615-xfi3p601	226	8	we	-PRON-	PRP
cord-004615-xfi3p601	226	9	use	use	VBP
cord-004615-xfi3p601	226	10	the	the	DT
cord-004615-xfi3p601	226	11	information	information	NN
cord-004615-xfi3p601	226	12	from	from	IN
cord-004615-xfi3p601	226	13	our	-PRON-	PRP$
cord-004615-xfi3p601	226	14	simplified	simplified	JJ
cord-004615-xfi3p601	226	15	model	model	NN
cord-004615-xfi3p601	226	16	,	,	,
cord-004615-xfi3p601	226	17	where	where	WRB
cord-004615-xfi3p601	226	18	measures	measure	NNS
cord-004615-xfi3p601	226	19	are	be	VBP
cord-004615-xfi3p601	226	20	started	start	VBN
cord-004615-xfi3p601	226	21	directly	directly	RB
cord-004615-xfi3p601	226	22	upon	upon	IN
cord-004615-xfi3p601	226	23	introduction	introduction	NN
cord-004615-xfi3p601	226	24	.	.	.
cord-004615-xfi3p601	227	1	4	4	LS
cord-004615-xfi3p601	227	2	.	.	.
cord-004615-xfi3p601	228	1	The	the	DT
cord-004615-xfi3p601	228	2	function	function	NN
cord-004615-xfi3p601	228	3	µ	µ	NN
cord-004615-xfi3p601	228	4	mm	mm	NN
cord-004615-xfi3p601	228	5	(	(	-LRB-
cord-004615-xfi3p601	228	6	τ	τ	NN
cord-004615-xfi3p601	228	7	;	;	:
cord-004615-xfi3p601	228	8	h	h	LS
cord-004615-xfi3p601	228	9	)	)	-RRB-
cord-004615-xfi3p601	228	10	is	be	VBZ
cord-004615-xfi3p601	228	11	not	not	RB
cord-004615-xfi3p601	228	12	required	require	VBN
cord-004615-xfi3p601	228	13	for	for	IN
cord-004615-xfi3p601	228	14	our	-PRON-	PRP$
cord-004615-xfi3p601	228	15	calculations	calculation	NNS
cord-004615-xfi3p601	228	16	of	of	IN
cord-004615-xfi3p601	228	17	the	the	DT
cord-004615-xfi3p601	228	18	final	final	JJ
cord-004615-xfi3p601	228	19	size	size	NN
cord-004615-xfi3p601	228	20	and	and	CC
cord-004615-xfi3p601	228	21	the	the	DT
cord-004615-xfi3p601	228	22	probability	probability	NN
cord-004615-xfi3p601	228	23	of	of	IN
cord-004615-xfi3p601	228	24	extinction	extinction	NN
cord-004615-xfi3p601	228	25	.	.	.
cord-004615-xfi3p601	229	1	The	the	DT
cord-004615-xfi3p601	229	2	reason	reason	NN
cord-004615-xfi3p601	229	3	why	why	WRB
cord-004615-xfi3p601	229	4	we	-PRON-	PRP
cord-004615-xfi3p601	229	5	include	include	VBP
cord-004615-xfi3p601	229	6	this	this	DT
cord-004615-xfi3p601	229	7	function	function	NN
cord-004615-xfi3p601	229	8	in	in	IN
cord-004615-xfi3p601	229	9	our	-PRON-	PRP$
cord-004615-xfi3p601	229	10	paper	paper	NN
cord-004615-xfi3p601	229	11	is	be	VBZ
cord-004615-xfi3p601	229	12	that	that	IN
cord-004615-xfi3p601	229	13	this	this	DT
cord-004615-xfi3p601	229	14	function	function	NN
cord-004615-xfi3p601	229	15	is	be	VBZ
cord-004615-xfi3p601	229	16	interesting	interesting	JJ
cord-004615-xfi3p601	229	17	in	in	IN
cord-004615-xfi3p601	229	18	its	-PRON-	PRP$
cord-004615-xfi3p601	229	19	own	own	JJ
cord-004615-xfi3p601	229	20	right	right	NN
cord-004615-xfi3p601	229	21	.	.	.
cord-004615-xfi3p601	230	1	It	-PRON-	PRP
cord-004615-xfi3p601	230	2	gives	give	VBZ
cord-004615-xfi3p601	230	3	the	the	DT
cord-004615-xfi3p601	230	4	expected	expect	VBN
cord-004615-xfi3p601	230	5	offspring	offspring	NN
cord-004615-xfi3p601	230	6	τ	τ	NN
cord-004615-xfi3p601	230	7	time	time	NN
cord-004615-xfi3p601	230	8	units	unit	NNS
cord-004615-xfi3p601	230	9	after	after	IN
cord-004615-xfi3p601	230	10	an	an	DT
cord-004615-xfi3p601	230	11	infective	infective	JJ
cord-004615-xfi3p601	230	12	herd	herd	NN
cord-004615-xfi3p601	230	13	is	be	VBZ
cord-004615-xfi3p601	230	14	infected	infect	VBN
cord-004615-xfi3p601	230	15	itself	-PRON-	PRP
cord-004615-xfi3p601	230	16	.	.	.
cord-004615-xfi3p601	231	1	In	in	IN
cord-004615-xfi3p601	231	2	practical	practical	JJ
cord-004615-xfi3p601	231	3	applications	application	NNS
cord-004615-xfi3p601	231	4	,	,	,
cord-004615-xfi3p601	231	5	it	-PRON-	PRP
cord-004615-xfi3p601	231	6	is	be	VBZ
cord-004615-xfi3p601	231	7	possible	possible	JJ
cord-004615-xfi3p601	231	8	that	that	IN
cord-004615-xfi3p601	231	9	by	by	IN
cord-004615-xfi3p601	231	10	contact	contact	NN
cord-004615-xfi3p601	231	11	tracing	trace	VBG
cord-004615-xfi3p601	231	12	some	some	DT
cord-004615-xfi3p601	231	13	herd	herd	NN
cord-004615-xfi3p601	231	14	is	be	VBZ
cord-004615-xfi3p601	231	15	suspected	suspect	VBN
cord-004615-xfi3p601	231	16	of	of	IN
cord-004615-xfi3p601	231	17	being	be	VBG
cord-004615-xfi3p601	231	18	infected	infect	VBN
cord-004615-xfi3p601	231	19	τ	τ	NN
cord-004615-xfi3p601	231	20	time	time	NN
cord-004615-xfi3p601	231	21	-	-	HYPH
cord-004615-xfi3p601	231	22	units	unit	NNS
cord-004615-xfi3p601	231	23	ago	ago	RB
cord-004615-xfi3p601	231	24	.	.	.
cord-004615-xfi3p601	232	1	This	this	DT
cord-004615-xfi3p601	232	2	µ	µ	NN
cord-004615-xfi3p601	232	3	mm	mm	NN
cord-004615-xfi3p601	232	4	(	(	-LRB-
cord-004615-xfi3p601	232	5	τ	τ	NN
cord-004615-xfi3p601	232	6	;	;	:
cord-004615-xfi3p601	232	7	h	h	LS
cord-004615-xfi3p601	232	8	)	)	-RRB-
cord-004615-xfi3p601	232	9	is	be	VBZ
cord-004615-xfi3p601	232	10	then	then	RB
cord-004615-xfi3p601	232	11	the	the	DT
cord-004615-xfi3p601	232	12	expected	expect	VBN
cord-004615-xfi3p601	232	13	number	number	NN
cord-004615-xfi3p601	232	14	of	of	IN
cord-004615-xfi3p601	232	15	infected	infected	JJ
cord-004615-xfi3p601	232	16	multipliers	multiplier	NNS
cord-004615-xfi3p601	232	17	by	by	IN
cord-004615-xfi3p601	232	18	the	the	DT
cord-004615-xfi3p601	232	19	suspected	suspect	VBN
cord-004615-xfi3p601	232	20	herd	herd	NN
cord-004615-xfi3p601	232	21	,	,	,
cord-004615-xfi3p601	232	22	if	if	IN
cord-004615-xfi3p601	232	23	that	that	DT
cord-004615-xfi3p601	232	24	suspected	suspect	VBN
cord-004615-xfi3p601	232	25	herd	herd	NN
cord-004615-xfi3p601	232	26	is	be	VBZ
cord-004615-xfi3p601	232	27	a	a	DT
cord-004615-xfi3p601	232	28	multiplier	multiplier	NN
cord-004615-xfi3p601	232	29	and	and	CC
cord-004615-xfi3p601	232	30	if	if	IN
cord-004615-xfi3p601	232	31	it	-PRON-	PRP
cord-004615-xfi3p601	232	32	is	be	VBZ
cord-004615-xfi3p601	232	33	really	really	RB
cord-004615-xfi3p601	232	34	infected	infected	JJ
cord-004615-xfi3p601	232	35	.	.	.
cord-004615-xfi3p601	233	1	5	5	LS
cord-004615-xfi3p601	233	2	.	.	.
cord-004615-xfi3p601	234	1	The	the	DT
cord-004615-xfi3p601	234	2	proportionality	proportionality	NN
cord-004615-xfi3p601	234	3	of	of	IN
cord-004615-xfi3p601	234	4	the	the	DT
cord-004615-xfi3p601	234	5	infection	infection	NN
cord-004615-xfi3p601	234	6	rate	rate	NN
cord-004615-xfi3p601	234	7	to	to	IN
cord-004615-xfi3p601	234	8	the	the	DT
cord-004615-xfi3p601	234	9	detection	detection	NN
cord-004615-xfi3p601	234	10	rate	rate	NN
cord-004615-xfi3p601	234	11	is	be	VBZ
cord-004615-xfi3p601	234	12	essential	essential	JJ
cord-004615-xfi3p601	234	13	in	in	IN
cord-004615-xfi3p601	234	14	this	this	DT
cord-004615-xfi3p601	234	15	section	section	NN
cord-004615-xfi3p601	234	16	.	.	.
cord-004615-xfi3p601	235	1	Due	due	IN
cord-004615-xfi3p601	235	2	to	to	IN
cord-004615-xfi3p601	235	3	this	this	DT
cord-004615-xfi3p601	235	4	property	property	NN
cord-004615-xfi3p601	235	5	,	,	,
cord-004615-xfi3p601	235	6	we	-PRON-	PRP
cord-004615-xfi3p601	235	7	can	can	MD
cord-004615-xfi3p601	235	8	find	find	VB
cord-004615-xfi3p601	235	9	an	an	DT
cord-004615-xfi3p601	235	10	underlying	underlie	VBG
cord-004615-xfi3p601	235	11	ordinary	ordinary	JJ
cord-004615-xfi3p601	235	12	Galton	Galton	NNP
cord-004615-xfi3p601	235	13	-	-	HYPH
cord-004615-xfi3p601	235	14	Watson	Watson	NNP
cord-004615-xfi3p601	235	15	process	process	NN
cord-004615-xfi3p601	235	16	.	.	.
cord-004615-xfi3p601	236	1	Without	without	IN
cord-004615-xfi3p601	236	2	this	this	DT
cord-004615-xfi3p601	236	3	proportionality	proportionality	NN
cord-004615-xfi3p601	236	4	,	,	,
cord-004615-xfi3p601	236	5	we	-PRON-	PRP
cord-004615-xfi3p601	236	6	may	may	MD
cord-004615-xfi3p601	236	7	ask	ask	VB
cord-004615-xfi3p601	236	8	whether	whether	IN
cord-004615-xfi3p601	236	9	it	-PRON-	PRP
cord-004615-xfi3p601	236	10	is	be	VBZ
cord-004615-xfi3p601	236	11	possible	possible	JJ
cord-004615-xfi3p601	236	12	to	to	TO
cord-004615-xfi3p601	236	13	give	give	VB
cord-004615-xfi3p601	236	14	a	a	DT
cord-004615-xfi3p601	236	15	nice	nice	JJ
cord-004615-xfi3p601	236	16	expression	expression	NN
cord-004615-xfi3p601	236	17	for	for	IN
cord-004615-xfi3p601	236	18	the	the	DT
cord-004615-xfi3p601	236	19	generating	generating	NN
cord-004615-xfi3p601	236	20	function	function	NN
cord-004615-xfi3p601	236	21	.	.	.
cord-004615-xfi3p601	237	1	We	-PRON-	PRP
cord-004615-xfi3p601	237	2	also	also	RB
cord-004615-xfi3p601	237	3	lose	lose	VBP
cord-004615-xfi3p601	237	4	the	the	DT
cord-004615-xfi3p601	237	5	independence	independence	NN
cord-004615-xfi3p601	237	6	of	of	IN
cord-004615-xfi3p601	237	7	h	h	NNP
cord-004615-xfi3p601	237	8	in	in	IN
cord-004615-xfi3p601	237	9	the	the	DT
cord-004615-xfi3p601	237	10	generating	generating	NN
cord-004615-xfi3p601	237	11	function	function	NN
cord-004615-xfi3p601	237	12	,	,	,
cord-004615-xfi3p601	237	13	which	which	WDT
cord-004615-xfi3p601	237	14	gives	give	VBZ
cord-004615-xfi3p601	237	15	some	some	DT
cord-004615-xfi3p601	237	16	computational	computational	JJ
cord-004615-xfi3p601	237	17	problems	problem	NNS
cord-004615-xfi3p601	237	18	.	.	.
cord-004615-xfi3p601	238	1	6	6	LS
cord-004615-xfi3p601	238	2	.	.	.
cord-004615-xfi3p601	239	1	Knowing	know	VBG
cord-004615-xfi3p601	239	2	the	the	DT
cord-004615-xfi3p601	239	3	generating	generate	VBG
cord-004615-xfi3p601	239	4	function	function	NN
cord-004615-xfi3p601	239	5	of	of	IN
cord-004615-xfi3p601	239	6	the	the	DT
cord-004615-xfi3p601	239	7	number	number	NN
cord-004615-xfi3p601	239	8	of	of	IN
cord-004615-xfi3p601	239	9	infected	infected	JJ
cord-004615-xfi3p601	239	10	herds	herd	NNS
cord-004615-xfi3p601	239	11	at	at	IN
cord-004615-xfi3p601	239	12	the	the	DT
cord-004615-xfi3p601	239	13	first	first	JJ
cord-004615-xfi3p601	239	14	detection	detection	NN
cord-004615-xfi3p601	239	15	is	be	VBZ
cord-004615-xfi3p601	239	16	important	important	JJ
cord-004615-xfi3p601	239	17	because	because	IN
cord-004615-xfi3p601	239	18	if	if	IN
cord-004615-xfi3p601	239	19	in	in	IN
cord-004615-xfi3p601	239	20	some	some	DT
cord-004615-xfi3p601	239	21	way	way	NN
cord-004615-xfi3p601	239	22	it	-PRON-	PRP
cord-004615-xfi3p601	239	23	is	be	VBZ
cord-004615-xfi3p601	239	24	possible	possible	JJ
cord-004615-xfi3p601	239	25	to	to	TO
cord-004615-xfi3p601	239	26	estimate	estimate	VB
cord-004615-xfi3p601	239	27	parameters	parameter	NNS
cord-004615-xfi3p601	239	28	for	for	IN
cord-004615-xfi3p601	239	29	the	the	DT
cord-004615-xfi3p601	239	30	time	time	NN
cord-004615-xfi3p601	239	31	before	before	IN
cord-004615-xfi3p601	239	32	the	the	DT
cord-004615-xfi3p601	239	33	first	first	JJ
cord-004615-xfi3p601	239	34	detection	detection	NN
cord-004615-xfi3p601	239	35	,	,	,
cord-004615-xfi3p601	239	36	we	-PRON-	PRP
cord-004615-xfi3p601	239	37	can	can	MD
cord-004615-xfi3p601	239	38	use	use	VB
cord-004615-xfi3p601	239	39	the	the	DT
cord-004615-xfi3p601	239	40	distribution	distribution	NN
cord-004615-xfi3p601	239	41	function	function	NN
cord-004615-xfi3p601	239	42	of	of	IN
cord-004615-xfi3p601	239	43	the	the	DT
cord-004615-xfi3p601	239	44	number	number	NN
cord-004615-xfi3p601	239	45	of	of	IN
cord-004615-xfi3p601	239	46	infective	infective	JJ
cord-004615-xfi3p601	239	47	herds	herd	NNS
cord-004615-xfi3p601	239	48	at	at	IN
cord-004615-xfi3p601	239	49	the	the	DT
cord-004615-xfi3p601	239	50	time	time	NN
cord-004615-xfi3p601	239	51	measures	measure	NNS
cord-004615-xfi3p601	239	52	are	be	VBP
cord-004615-xfi3p601	239	53	implemented	implement	VBN
cord-004615-xfi3p601	239	54	.	.	.
cord-004615-xfi3p601	240	1	We	-PRON-	PRP
cord-004615-xfi3p601	240	2	do	do	VBP
cord-004615-xfi3p601	240	3	not	not	RB
cord-004615-xfi3p601	240	4	have	have	VB
cord-004615-xfi3p601	240	5	the	the	DT
cord-004615-xfi3p601	240	6	'	'	``
cord-004615-xfi3p601	240	7	ages	age	NNS
cord-004615-xfi3p601	240	8	'	'	''
cord-004615-xfi3p601	240	9	of	of	IN
cord-004615-xfi3p601	240	10	the	the	DT
cord-004615-xfi3p601	240	11	infective	infective	JJ
cord-004615-xfi3p601	240	12	herds	herd	NNS
cord-004615-xfi3p601	240	13	at	at	IN
cord-004615-xfi3p601	240	14	the	the	DT
cord-004615-xfi3p601	240	15	first	first	JJ
cord-004615-xfi3p601	240	16	detection	detection	NN
cord-004615-xfi3p601	240	17	,	,	,
cord-004615-xfi3p601	240	18	but	but	CC
cord-004615-xfi3p601	240	19	we	-PRON-	PRP
cord-004615-xfi3p601	240	20	can	can	MD
cord-004615-xfi3p601	240	21	find	find	VB
cord-004615-xfi3p601	240	22	a	a	DT
cord-004615-xfi3p601	240	23	worst	bad	JJS
cord-004615-xfi3p601	240	24	-	-	HYPH
cord-004615-xfi3p601	240	25	case	case	NN
cord-004615-xfi3p601	240	26	-	-	HYPH
cord-004615-xfi3p601	240	27	scenario	scenario	NN
cord-004615-xfi3p601	240	28	,	,	,
cord-004615-xfi3p601	240	29	by	by	IN
cord-004615-xfi3p601	240	30	finding	find	VBG
cord-004615-xfi3p601	240	31	what	what	WDT
cord-004615-xfi3p601	240	32	age	age	NN
cord-004615-xfi3p601	240	33	of	of	IN
cord-004615-xfi3p601	240	34	a	a	DT
cord-004615-xfi3p601	240	35	herd	herd	NN
cord-004615-xfi3p601	240	36	at	at	IN
cord-004615-xfi3p601	240	37	t	t	NN
cord-004615-xfi3p601	240	38	=	=	SYM
cord-004615-xfi3p601	240	39	0	0	NFP
cord-004615-xfi3p601	240	40	leads	lead	VBZ
cord-004615-xfi3p601	240	41	to	to	IN
cord-004615-xfi3p601	240	42	the	the	DT
cord-004615-xfi3p601	240	43	biggest	big	JJS
cord-004615-xfi3p601	240	44	offspring	offspring	NN
cord-004615-xfi3p601	240	45	.	.	.
cord-004615-xfi3p601	241	1	If	if	IN
cord-004615-xfi3p601	241	2	the	the	DT
cord-004615-xfi3p601	241	3	detection	detection	NN
cord-004615-xfi3p601	241	4	and	and	CC
cord-004615-xfi3p601	241	5	infection	infection	NN
cord-004615-xfi3p601	241	6	rate	rate	NN
cord-004615-xfi3p601	241	7	does	do	VBZ
cord-004615-xfi3p601	241	8	not	not	RB
cord-004615-xfi3p601	241	9	depend	depend	VB
cord-004615-xfi3p601	241	10	in	in	IN
cord-004615-xfi3p601	241	11	the	the	DT
cord-004615-xfi3p601	241	12	same	same	JJ
cord-004615-xfi3p601	241	13	way	way	NN
cord-004615-xfi3p601	241	14	on	on	IN
cord-004615-xfi3p601	241	15	the	the	DT
cord-004615-xfi3p601	241	16	number	number	NN
cord-004615-xfi3p601	241	17	of	of	IN
cord-004615-xfi3p601	241	18	infected	infected	JJ
cord-004615-xfi3p601	241	19	animals	animal	NNS
cord-004615-xfi3p601	241	20	,	,	,
cord-004615-xfi3p601	241	21	we	-PRON-	PRP
cord-004615-xfi3p601	241	22	can	can	MD
cord-004615-xfi3p601	241	23	not	not	RB
cord-004615-xfi3p601	241	24	deduce	deduce	VB
cord-004615-xfi3p601	241	25	the	the	DT
cord-004615-xfi3p601	241	26	distribution	distribution	NN
cord-004615-xfi3p601	241	27	function	function	NN
cord-004615-xfi3p601	241	28	at	at	IN
cord-004615-xfi3p601	241	29	the	the	DT
cord-004615-xfi3p601	241	30	time	time	NN
cord-004615-xfi3p601	241	31	of	of	IN
cord-004615-xfi3p601	241	32	the	the	DT
cord-004615-xfi3p601	241	33	first	first	JJ
cord-004615-xfi3p601	241	34	detection	detection	NN
cord-004615-xfi3p601	241	35	in	in	IN
cord-004615-xfi3p601	241	36	this	this	DT
cord-004615-xfi3p601	241	37	way	way	NN
cord-004615-xfi3p601	241	38	.	.	.
cord-004615-xfi3p601	242	1	In	in	IN
cord-004615-xfi3p601	242	2	the	the	DT
cord-004615-xfi3p601	242	3	previous	previous	JJ
cord-004615-xfi3p601	242	4	section	section	NN
cord-004615-xfi3p601	242	5	,	,	,
cord-004615-xfi3p601	242	6	we	-PRON-	PRP
cord-004615-xfi3p601	242	7	considered	consider	VBD
cord-004615-xfi3p601	242	8	the	the	DT
cord-004615-xfi3p601	242	9	model	model	NN
cord-004615-xfi3p601	242	10	for	for	IN
cord-004615-xfi3p601	242	11	the	the	DT
cord-004615-xfi3p601	242	12	spread	spread	NN
cord-004615-xfi3p601	242	13	of	of	IN
cord-004615-xfi3p601	242	14	an	an	DT
cord-004615-xfi3p601	242	15	infectious	infectious	JJ
cord-004615-xfi3p601	242	16	disease	disease	NN
cord-004615-xfi3p601	242	17	in	in	IN
cord-004615-xfi3p601	242	18	non	non	JJ
cord-004615-xfi3p601	242	19	-	-	JJ
cord-004615-xfi3p601	242	20	varying	varying	JJ
cord-004615-xfi3p601	242	21	environments	environment	NNS
cord-004615-xfi3p601	242	22	.	.	.
cord-004615-xfi3p601	243	1	We	-PRON-	PRP
cord-004615-xfi3p601	243	2	heavily	heavily	RB
cord-004615-xfi3p601	243	3	used	use	VBD
cord-004615-xfi3p601	243	4	the	the	DT
cord-004615-xfi3p601	243	5	proportionality	proportionality	NN
cord-004615-xfi3p601	243	6	of	of	IN
cord-004615-xfi3p601	243	7	the	the	DT
cord-004615-xfi3p601	243	8	infection	infection	NN
cord-004615-xfi3p601	243	9	and	and	CC
cord-004615-xfi3p601	243	10	detection	detection	NN
cord-004615-xfi3p601	243	11	rate	rate	NN
cord-004615-xfi3p601	243	12	of	of	IN
cord-004615-xfi3p601	243	13	herds	herd	NNS
cord-004615-xfi3p601	243	14	.	.	.
cord-004615-xfi3p601	244	1	This	this	DT
cord-004615-xfi3p601	244	2	proportionality	proportionality	NN
cord-004615-xfi3p601	244	3	does	do	VBZ
cord-004615-xfi3p601	244	4	not	not	RB
cord-004615-xfi3p601	244	5	hold	hold	VB
cord-004615-xfi3p601	244	6	in	in	IN
cord-004615-xfi3p601	244	7	a	a	DT
cord-004615-xfi3p601	244	8	varying	vary	VBG
cord-004615-xfi3p601	244	9	environment	environment	NN
cord-004615-xfi3p601	244	10	.	.	.
cord-004615-xfi3p601	245	1	Therefore	therefore	RB
cord-004615-xfi3p601	245	2	,	,	,
cord-004615-xfi3p601	245	3	we	-PRON-	PRP
cord-004615-xfi3p601	245	4	need	need	VBP
cord-004615-xfi3p601	245	5	a	a	DT
cord-004615-xfi3p601	245	6	different	different	JJ
cord-004615-xfi3p601	245	7	approach	approach	NN
cord-004615-xfi3p601	245	8	.	.	.
cord-004615-xfi3p601	246	1	We	-PRON-	PRP
cord-004615-xfi3p601	246	2	consider	consider	VBP
cord-004615-xfi3p601	246	3	only	only	RB
cord-004615-xfi3p601	246	4	one	one	CD
cord-004615-xfi3p601	246	5	type	type	NN
cord-004615-xfi3p601	246	6	of	of	IN
cord-004615-xfi3p601	246	7	herd	herd	NN
cord-004615-xfi3p601	246	8	;	;	:
cord-004615-xfi3p601	246	9	the	the	DT
cord-004615-xfi3p601	246	10	multi	multi	JJ
cord-004615-xfi3p601	246	11	-	-	JJ
cord-004615-xfi3p601	246	12	type	type	JJ
cord-004615-xfi3p601	246	13	model	model	NN
cord-004615-xfi3p601	246	14	is	be	VBZ
cord-004615-xfi3p601	246	15	a	a	DT
cord-004615-xfi3p601	246	16	straightforward	straightforward	JJ
cord-004615-xfi3p601	246	17	generalisation	generalisation	NN
cord-004615-xfi3p601	246	18	of	of	IN
cord-004615-xfi3p601	246	19	this	this	DT
cord-004615-xfi3p601	246	20	.	.	.
cord-004615-xfi3p601	247	1	We	-PRON-	PRP
cord-004615-xfi3p601	247	2	assume	assume	VBP
cord-004615-xfi3p601	247	3	that	that	IN
cord-004615-xfi3p601	247	4	the	the	DT
cord-004615-xfi3p601	247	5	spread	spread	NN
cord-004615-xfi3p601	247	6	within	within	IN
cord-004615-xfi3p601	247	7	a	a	DT
cord-004615-xfi3p601	247	8	herd	herd	NN
cord-004615-xfi3p601	247	9	is	be	VBZ
cord-004615-xfi3p601	247	10	not	not	RB
cord-004615-xfi3p601	247	11	influenced	influence	VBN
cord-004615-xfi3p601	247	12	by	by	IN
cord-004615-xfi3p601	247	13	the	the	DT
cord-004615-xfi3p601	247	14	state	state	NN
cord-004615-xfi3p601	247	15	of	of	IN
cord-004615-xfi3p601	247	16	the	the	DT
cord-004615-xfi3p601	247	17	environment	environment	NN
cord-004615-xfi3p601	247	18	.	.	.
cord-004615-xfi3p601	248	1	The	the	DT
cord-004615-xfi3p601	248	2	detection	detection	NN
cord-004615-xfi3p601	248	3	rate	rate	NN
cord-004615-xfi3p601	248	4	only	only	RB
cord-004615-xfi3p601	248	5	depends	depend	VBZ
cord-004615-xfi3p601	248	6	on	on	IN
cord-004615-xfi3p601	248	7	the	the	DT
cord-004615-xfi3p601	248	8	number	number	NN
cord-004615-xfi3p601	248	9	of	of	IN
cord-004615-xfi3p601	248	10	infected	infected	JJ
cord-004615-xfi3p601	248	11	animals	animal	NNS
cord-004615-xfi3p601	248	12	in	in	IN
cord-004615-xfi3p601	248	13	a	a	DT
cord-004615-xfi3p601	248	14	herd	herd	NN
cord-004615-xfi3p601	248	15	and	and	CC
cord-004615-xfi3p601	248	16	is	be	VBZ
cord-004615-xfi3p601	248	17	written	write	VBN
cord-004615-xfi3p601	248	18	as	as	IN
cord-004615-xfi3p601	248	19	αI	αI	NNP
cord-004615-xfi3p601	248	20	(	(	-LRB-
cord-004615-xfi3p601	248	21	τ	τ	NN
cord-004615-xfi3p601	248	22	;	;	:
cord-004615-xfi3p601	248	23	h	h	NNP
cord-004615-xfi3p601	248	24	)	)	-RRB-
cord-004615-xfi3p601	248	25	,	,	,
cord-004615-xfi3p601	248	26	where	where	WRB
cord-004615-xfi3p601	248	27	I	-PRON-	PRP
cord-004615-xfi3p601	248	28	(	(	-LRB-
cord-004615-xfi3p601	248	29	τ	τ	NN
cord-004615-xfi3p601	248	30	;	;	:
cord-004615-xfi3p601	248	31	h	h	LS
cord-004615-xfi3p601	248	32	)	)	-RRB-
cord-004615-xfi3p601	248	33	is	be	VBZ
cord-004615-xfi3p601	248	34	the	the	DT
cord-004615-xfi3p601	248	35	number	number	NN
cord-004615-xfi3p601	248	36	of	of	IN
cord-004615-xfi3p601	248	37	infected	infected	JJ
cord-004615-xfi3p601	248	38	animals	animal	NNS
cord-004615-xfi3p601	248	39	as	as	IN
cord-004615-xfi3p601	248	40	described	describe	VBN
cord-004615-xfi3p601	248	41	in	in	IN
cord-004615-xfi3p601	248	42	Section	section	NN
cord-004615-xfi3p601	248	43	2	2	CD
cord-004615-xfi3p601	248	44	.	.	.
cord-004615-xfi3p601	249	1	In	in	IN
cord-004615-xfi3p601	249	2	this	this	DT
cord-004615-xfi3p601	249	3	section	section	NN
cord-004615-xfi3p601	249	4	,	,	,
cord-004615-xfi3p601	249	5	we	-PRON-	PRP
cord-004615-xfi3p601	249	6	assume	assume	VBP
cord-004615-xfi3p601	249	7	that	that	IN
cord-004615-xfi3p601	249	8	the	the	DT
cord-004615-xfi3p601	249	9	within	within	IN
cord-004615-xfi3p601	249	10	-	-	HYPH
cord-004615-xfi3p601	249	11	herd	herd	NN
cord-004615-xfi3p601	249	12	spread	spread	NN
cord-004615-xfi3p601	249	13	is	be	VBZ
cord-004615-xfi3p601	249	14	described	describe	VBN
cord-004615-xfi3p601	249	15	by	by	IN
cord-004615-xfi3p601	249	16	a	a	DT
cord-004615-xfi3p601	249	17	birth	birth	NN
cord-004615-xfi3p601	249	18	-	-	HYPH
cord-004615-xfi3p601	249	19	and	and	CC
cord-004615-xfi3p601	249	20	-	-	HYPH
cord-004615-xfi3p601	249	21	death	death	NN
cord-004615-xfi3p601	249	22	process	process	NN
cord-004615-xfi3p601	249	23	.	.	.
cord-004615-xfi3p601	250	1	So	so	RB
cord-004615-xfi3p601	250	2	I	-PRON-	PRP
cord-004615-xfi3p601	250	3	(	(	-LRB-
cord-004615-xfi3p601	250	4	τ	τ	NN
cord-004615-xfi3p601	250	5	;	;	:
cord-004615-xfi3p601	250	6	h	h	LS
cord-004615-xfi3p601	250	7	)	)	-RRB-
cord-004615-xfi3p601	250	8	=	=	NFP
cord-004615-xfi3p601	251	1	he	-PRON-	PRP
cord-004615-xfi3p601	251	2	rτ	rτ	VBZ
cord-004615-xfi3p601	251	3	.	.	.
cord-004615-xfi3p601	252	1	We	-PRON-	PRP
cord-004615-xfi3p601	252	2	can	can	MD
cord-004615-xfi3p601	252	3	easily	easily	RB
cord-004615-xfi3p601	252	4	deal	deal	VB
cord-004615-xfi3p601	252	5	with	with	IN
cord-004615-xfi3p601	252	6	other	other	JJ
cord-004615-xfi3p601	252	7	descriptions	description	NNS
cord-004615-xfi3p601	252	8	of	of	IN
cord-004615-xfi3p601	252	9	the	the	DT
cord-004615-xfi3p601	252	10	within	within	JJ
cord-004615-xfi3p601	252	11	-	-	HYPH
cord-004615-xfi3p601	252	12	herd	herd	NN
cord-004615-xfi3p601	252	13	spread	spread	NN
cord-004615-xfi3p601	252	14	.	.	.
cord-004615-xfi3p601	253	1	The	the	DT
cord-004615-xfi3p601	253	2	infection	infection	NN
cord-004615-xfi3p601	253	3	rate	rate	NN
cord-004615-xfi3p601	253	4	may	may	MD
cord-004615-xfi3p601	253	5	change	change	VB
cord-004615-xfi3p601	253	6	due	due	IN
cord-004615-xfi3p601	253	7	to	to	IN
cord-004615-xfi3p601	253	8	control	control	VB
cord-004615-xfi3p601	253	9	measures	measure	NNS
cord-004615-xfi3p601	253	10	.	.	.
cord-004615-xfi3p601	254	1	Some	some	DT
cord-004615-xfi3p601	254	2	measures	measure	NNS
cord-004615-xfi3p601	254	3	lead	lead	VBP
cord-004615-xfi3p601	254	4	to	to	IN
cord-004615-xfi3p601	254	5	an	an	DT
cord-004615-xfi3p601	254	6	infection	infection	NN
cord-004615-xfi3p601	254	7	rate	rate	NN
cord-004615-xfi3p601	254	8	that	that	WDT
cord-004615-xfi3p601	254	9	only	only	RB
cord-004615-xfi3p601	254	10	changes	change	VBZ
cord-004615-xfi3p601	254	11	finitely	finitely	RB
cord-004615-xfi3p601	254	12	many	many	JJ
cord-004615-xfi3p601	254	13	times	time	NNS
cord-004615-xfi3p601	254	14	,	,	,
cord-004615-xfi3p601	254	15	other	other	JJ
cord-004615-xfi3p601	254	16	measures	measure	NNS
cord-004615-xfi3p601	254	17	cause	cause	VBP
cord-004615-xfi3p601	254	18	a	a	DT
cord-004615-xfi3p601	254	19	continuously	continuously	RB
cord-004615-xfi3p601	254	20	varying	vary	VBG
cord-004615-xfi3p601	254	21	infection	infection	NN
cord-004615-xfi3p601	254	22	rate	rate	NN
cord-004615-xfi3p601	254	23	.	.	.
cord-004615-xfi3p601	255	1	We	-PRON-	PRP
cord-004615-xfi3p601	255	2	assume	assume	VBP
cord-004615-xfi3p601	255	3	that	that	IN
cord-004615-xfi3p601	255	4	in	in	IN
cord-004615-xfi3p601	255	5	either	either	DT
cord-004615-xfi3p601	255	6	case	case	NN
cord-004615-xfi3p601	255	7	the	the	DT
cord-004615-xfi3p601	255	8	environment	environment	NN
cord-004615-xfi3p601	255	9	is	be	VBZ
cord-004615-xfi3p601	255	10	constant	constant	JJ
cord-004615-xfi3p601	255	11	after	after	IN
cord-004615-xfi3p601	255	12	some	some	DT
cord-004615-xfi3p601	255	13	given	give	VBN
cord-004615-xfi3p601	255	14	time	time	NN
cord-004615-xfi3p601	255	15	,	,	,
cord-004615-xfi3p601	255	16	t	t	NN
cord-004615-xfi3p601	255	17	=	=	SYM
cord-004615-xfi3p601	255	18	T	t	NN
cord-004615-xfi3p601	255	19	.	.	.
cord-004615-xfi3p601	256	1	That	that	DT
cord-004615-xfi3p601	256	2	is	be	VBZ
cord-004615-xfi3p601	256	3	the	the	DT
cord-004615-xfi3p601	256	4	moment	moment	NN
cord-004615-xfi3p601	256	5	that	that	IN
cord-004615-xfi3p601	256	6	measures	measure	NNS
cord-004615-xfi3p601	256	7	have	have	VBP
cord-004615-xfi3p601	256	8	no	no	DT
cord-004615-xfi3p601	256	9	more	more	RBR
cord-004615-xfi3p601	256	10	added	add	VBN
cord-004615-xfi3p601	256	11	value	value	NN
cord-004615-xfi3p601	256	12	and	and	CC
cord-004615-xfi3p601	256	13	therefore	therefore	RB
cord-004615-xfi3p601	256	14	do	do	VBP
cord-004615-xfi3p601	256	15	not	not	RB
cord-004615-xfi3p601	256	16	lead	lead	VB
cord-004615-xfi3p601	256	17	to	to	IN
cord-004615-xfi3p601	256	18	new	new	JJ
cord-004615-xfi3p601	256	19	changes	change	NNS
cord-004615-xfi3p601	256	20	in	in	IN
cord-004615-xfi3p601	256	21	the	the	DT
cord-004615-xfi3p601	256	22	values	value	NNS
cord-004615-xfi3p601	256	23	of	of	IN
cord-004615-xfi3p601	256	24	the	the	DT
cord-004615-xfi3p601	256	25	model	model	NN
cord-004615-xfi3p601	256	26	parameters	parameter	NNS
cord-004615-xfi3p601	256	27	.	.	.
cord-004615-xfi3p601	257	1	The	the	DT
cord-004615-xfi3p601	257	2	infection	infection	NN
cord-004615-xfi3p601	257	3	rate	rate	NN
cord-004615-xfi3p601	257	4	is	be	VBZ
cord-004615-xfi3p601	257	5	given	give	VBN
cord-004615-xfi3p601	257	6	by	by	IN
cord-004615-xfi3p601	257	7	where	where	WRB
cord-004615-xfi3p601	257	8	φ(t	φ(t	NNP
cord-004615-xfi3p601	257	9	)	)	-RRB-
cord-004615-xfi3p601	257	10	describes	describe	VBZ
cord-004615-xfi3p601	257	11	the	the	DT
cord-004615-xfi3p601	257	12	effects	effect	NNS
cord-004615-xfi3p601	257	13	of	of	IN
cord-004615-xfi3p601	257	14	the	the	DT
cord-004615-xfi3p601	257	15	measures	measure	NNS
cord-004615-xfi3p601	257	16	implemented	implement	VBN
cord-004615-xfi3p601	257	17	.	.	.
cord-004615-xfi3p601	258	1	We	-PRON-	PRP
cord-004615-xfi3p601	258	2	assume	assume	VBP
cord-004615-xfi3p601	258	3	that	that	IN
cord-004615-xfi3p601	258	4	φ(t	φ(t	NNP
cord-004615-xfi3p601	258	5	)	)	-RRB-
cord-004615-xfi3p601	258	6	is	be	VBZ
cord-004615-xfi3p601	258	7	deterministic	deterministic	JJ
cord-004615-xfi3p601	258	8	.	.	.
cord-004615-xfi3p601	259	1	Because	because	IN
cord-004615-xfi3p601	259	2	the	the	DT
cord-004615-xfi3p601	259	3	environment	environment	NN
cord-004615-xfi3p601	259	4	does	do	VBZ
cord-004615-xfi3p601	259	5	not	not	RB
cord-004615-xfi3p601	259	6	influence	influence	VB
cord-004615-xfi3p601	259	7	the	the	DT
cord-004615-xfi3p601	259	8	within	within	IN
cord-004615-xfi3p601	259	9	-	-	HYPH
cord-004615-xfi3p601	259	10	herd	herd	NN
cord-004615-xfi3p601	259	11	spread	spread	NN
cord-004615-xfi3p601	259	12	,	,	,
cord-004615-xfi3p601	259	13	φ(t	φ(t	NNP
cord-004615-xfi3p601	259	14	)	)	-RRB-
cord-004615-xfi3p601	259	15	does	do	VBZ
cord-004615-xfi3p601	259	16	not	not	RB
cord-004615-xfi3p601	259	17	depend	depend	VB
cord-004615-xfi3p601	259	18	on	on	IN
cord-004615-xfi3p601	259	19	the	the	DT
cord-004615-xfi3p601	259	20	age	age	NN
cord-004615-xfi3p601	259	21	τ	τ	NN
cord-004615-xfi3p601	259	22	.	.	.
cord-004615-xfi3p601	260	1	For	for	IN
cord-004615-xfi3p601	260	2	the	the	DT
cord-004615-xfi3p601	260	3	rest	rest	NN
cord-004615-xfi3p601	260	4	of	of	IN
cord-004615-xfi3p601	260	5	this	this	DT
cord-004615-xfi3p601	260	6	section	section	NN
cord-004615-xfi3p601	260	7	it	-PRON-	PRP
cord-004615-xfi3p601	260	8	is	be	VBZ
cord-004615-xfi3p601	260	9	assumed	assume	VBN
cord-004615-xfi3p601	260	10	that	that	IN
cord-004615-xfi3p601	260	11	φ(t	φ(t	NN
cord-004615-xfi3p601	260	12	)	)	-RRB-
cord-004615-xfi3p601	260	13	=	=	SYM
cord-004615-xfi3p601	260	14	1	1	CD
cord-004615-xfi3p601	260	15	for	for	IN
cord-004615-xfi3p601	260	16	t	t	NN
cord-004615-xfi3p601	260	17	≥	≥	NNP
cord-004615-xfi3p601	260	18	T	T	NNP
cord-004615-xfi3p601	260	19	.	.	.
cord-004615-xfi3p601	261	1	The	the	DT
cord-004615-xfi3p601	261	2	assumption	assumption	NN
cord-004615-xfi3p601	261	3	of	of	IN
cord-004615-xfi3p601	261	4	constant	constant	JJ
cord-004615-xfi3p601	261	5	environment	environment	NN
cord-004615-xfi3p601	261	6	after	after	IN
cord-004615-xfi3p601	261	7	some	some	DT
cord-004615-xfi3p601	261	8	given	give	VBN
cord-004615-xfi3p601	261	9	time	time	NN
cord-004615-xfi3p601	261	10	is	be	VBZ
cord-004615-xfi3p601	261	11	often	often	RB
cord-004615-xfi3p601	261	12	realistic	realistic	JJ
cord-004615-xfi3p601	261	13	.	.	.
cord-004615-xfi3p601	262	1	With	with	IN
cord-004615-xfi3p601	262	2	a	a	DT
cord-004615-xfi3p601	262	3	vaccination	vaccination	NN
cord-004615-xfi3p601	262	4	for	for	IN
cord-004615-xfi3p601	262	5	instance	instance	NN
cord-004615-xfi3p601	262	6	,	,	,
cord-004615-xfi3p601	262	7	we	-PRON-	PRP
cord-004615-xfi3p601	262	8	know	know	VBP
cord-004615-xfi3p601	262	9	the	the	DT
cord-004615-xfi3p601	262	10	moment	moment	NN
cord-004615-xfi3p601	262	11	that	that	IN
cord-004615-xfi3p601	262	12	all	all	DT
cord-004615-xfi3p601	262	13	vaccinated	vaccinate	VBN
cord-004615-xfi3p601	262	14	animals	animal	NNS
cord-004615-xfi3p601	262	15	no	no	RB
cord-004615-xfi3p601	262	16	longer	longer	RB
cord-004615-xfi3p601	262	17	live	live	VBP
cord-004615-xfi3p601	262	18	.	.	.
cord-004615-xfi3p601	263	1	In	in	IN
cord-004615-xfi3p601	263	2	other	other	JJ
cord-004615-xfi3p601	263	3	control	control	NN
cord-004615-xfi3p601	263	4	measures	measure	NNS
cord-004615-xfi3p601	263	5	,	,	,
cord-004615-xfi3p601	263	6	like	like	IN
cord-004615-xfi3p601	263	7	a	a	DT
cord-004615-xfi3p601	263	8	transport	transport	NN
cord-004615-xfi3p601	263	9	ban	ban	NN
cord-004615-xfi3p601	263	10	,	,	,
cord-004615-xfi3p601	263	11	we	-PRON-	PRP
cord-004615-xfi3p601	263	12	can	can	MD
cord-004615-xfi3p601	263	13	vary	vary	VB
cord-004615-xfi3p601	263	14	the	the	DT
cord-004615-xfi3p601	263	15	time	time	NN
cord-004615-xfi3p601	263	16	T	T	NNP
cord-004615-xfi3p601	263	17	and	and	CC
cord-004615-xfi3p601	263	18	compute	compute	VB
cord-004615-xfi3p601	263	19	the	the	DT
cord-004615-xfi3p601	263	20	effects	effect	NNS
cord-004615-xfi3p601	263	21	.	.	.
cord-004615-xfi3p601	264	1	We	-PRON-	PRP
cord-004615-xfi3p601	264	2	are	be	VBP
cord-004615-xfi3p601	264	3	looking	look	VBG
cord-004615-xfi3p601	264	4	for	for	IN
cord-004615-xfi3p601	264	5	the	the	DT
cord-004615-xfi3p601	264	6	probability	probability	NN
cord-004615-xfi3p601	264	7	of	of	IN
cord-004615-xfi3p601	264	8	extinction	extinction	NN
cord-004615-xfi3p601	264	9	of	of	IN
cord-004615-xfi3p601	264	10	the	the	DT
cord-004615-xfi3p601	264	11	infection	infection	NN
cord-004615-xfi3p601	264	12	,	,	,
cord-004615-xfi3p601	264	13	the	the	DT
cord-004615-xfi3p601	264	14	expected	expect	VBN
cord-004615-xfi3p601	264	15	final	final	JJ
cord-004615-xfi3p601	264	16	size	size	NN
cord-004615-xfi3p601	264	17	and	and	CC
cord-004615-xfi3p601	264	18	a	a	DT
cord-004615-xfi3p601	264	19	generating	generating	NN
cord-004615-xfi3p601	264	20	function	function	NN
cord-004615-xfi3p601	264	21	for	for	IN
cord-004615-xfi3p601	264	22	the	the	DT
cord-004615-xfi3p601	264	23	number	number	NN
cord-004615-xfi3p601	264	24	of	of	IN
cord-004615-xfi3p601	264	25	infected	infected	JJ
cord-004615-xfi3p601	264	26	herds	herd	NNS
cord-004615-xfi3p601	264	27	at	at	IN
cord-004615-xfi3p601	264	28	a	a	DT
cord-004615-xfi3p601	264	29	certain	certain	JJ
cord-004615-xfi3p601	264	30	moment	moment	NN
cord-004615-xfi3p601	264	31	.	.	.
cord-004615-xfi3p601	265	1	To	to	TO
cord-004615-xfi3p601	265	2	do	do	VB
cord-004615-xfi3p601	265	3	this	this	DT
cord-004615-xfi3p601	265	4	we	-PRON-	PRP
cord-004615-xfi3p601	265	5	use	use	VBP
cord-004615-xfi3p601	265	6	a	a	DT
cord-004615-xfi3p601	265	7	discrete	discrete	JJ
cord-004615-xfi3p601	265	8	approximation	approximation	NN
cord-004615-xfi3p601	265	9	of	of	IN
cord-004615-xfi3p601	265	10	φ(t	φ(t	NNP
cord-004615-xfi3p601	265	11	)	)	-RRB-
cord-004615-xfi3p601	265	12	,	,	,
cord-004615-xfi3p601	265	13	so	so	IN
cord-004615-xfi3p601	265	14	we	-PRON-	PRP
cord-004615-xfi3p601	265	15	have	have	VBP
cord-004615-xfi3p601	265	16	only	only	RB
cord-004615-xfi3p601	265	17	a	a	DT
cord-004615-xfi3p601	265	18	finite	finite	JJ
cord-004615-xfi3p601	265	19	number	number	NN
cord-004615-xfi3p601	265	20	of	of	IN
cord-004615-xfi3p601	265	21	changes	change	NNS
cord-004615-xfi3p601	265	22	.	.	.
cord-004615-xfi3p601	266	1	Because	because	IN
cord-004615-xfi3p601	266	2	the	the	DT
cord-004615-xfi3p601	266	3	environment	environment	NN
cord-004615-xfi3p601	266	4	is	be	VBZ
cord-004615-xfi3p601	266	5	non	non	JJ
cord-004615-xfi3p601	266	6	-	-	JJ
cord-004615-xfi3p601	266	7	varying	varying	JJ
cord-004615-xfi3p601	266	8	after	after	IN
cord-004615-xfi3p601	266	9	a	a	DT
cord-004615-xfi3p601	266	10	certain	certain	JJ
cord-004615-xfi3p601	266	11	moment	moment	NN
cord-004615-xfi3p601	266	12	,	,	,
cord-004615-xfi3p601	266	13	we	-PRON-	PRP
cord-004615-xfi3p601	266	14	can	can	MD
cord-004615-xfi3p601	266	15	use	use	VB
cord-004615-xfi3p601	266	16	the	the	DT
cord-004615-xfi3p601	266	17	ordinary	ordinary	JJ
cord-004615-xfi3p601	266	18	theory	theory	NN
cord-004615-xfi3p601	266	19	of	of	IN
cord-004615-xfi3p601	266	20	branching	branch	VBG
cord-004615-xfi3p601	266	21	processes	process	NNS
cord-004615-xfi3p601	266	22	to	to	TO
cord-004615-xfi3p601	266	23	get	get	VB
cord-004615-xfi3p601	266	24	all	all	DT
cord-004615-xfi3p601	266	25	interesting	interesting	JJ
cord-004615-xfi3p601	266	26	properties	property	NNS
cord-004615-xfi3p601	266	27	for	for	IN
cord-004615-xfi3p601	266	28	herds	herd	NNS
cord-004615-xfi3p601	266	29	infected	infect	VBN
cord-004615-xfi3p601	266	30	after	after	IN
cord-004615-xfi3p601	266	31	t	t	NN
cord-004615-xfi3p601	266	32	=	=	SYM
cord-004615-xfi3p601	266	33	T	T	NNP
cord-004615-xfi3p601	266	34	.	.	.
cord-004615-xfi3p601	267	1	By	by	IN
cord-004615-xfi3p601	267	2	using	use	VBG
cord-004615-xfi3p601	267	3	backward	backward	JJ
cord-004615-xfi3p601	267	4	iteration	iteration	NN
cord-004615-xfi3p601	267	5	we	-PRON-	PRP
cord-004615-xfi3p601	267	6	will	will	MD
cord-004615-xfi3p601	267	7	find	find	VB
cord-004615-xfi3p601	267	8	the	the	DT
cord-004615-xfi3p601	267	9	relevant	relevant	JJ
cord-004615-xfi3p601	267	10	properties	property	NNS
cord-004615-xfi3p601	267	11	of	of	IN
cord-004615-xfi3p601	267	12	the	the	DT
cord-004615-xfi3p601	267	13	epidemic	epidemic	NN
cord-004615-xfi3p601	267	14	for	for	IN
cord-004615-xfi3p601	267	15	a	a	DT
cord-004615-xfi3p601	267	16	herd	herd	NN
cord-004615-xfi3p601	267	17	infected	infect	VBN
cord-004615-xfi3p601	267	18	in	in	IN
cord-004615-xfi3p601	267	19	another	another	DT
cord-004615-xfi3p601	267	20	interval	interval	NN
cord-004615-xfi3p601	267	21	,	,	,
cord-004615-xfi3p601	267	22	because	because	IN
cord-004615-xfi3p601	267	23	these	these	DT
cord-004615-xfi3p601	267	24	properties	property	NNS
cord-004615-xfi3p601	267	25	only	only	RB
cord-004615-xfi3p601	267	26	depend	depend	VBP
cord-004615-xfi3p601	267	27	on	on	IN
cord-004615-xfi3p601	267	28	what	what	WP
cord-004615-xfi3p601	267	29	happens	happen	VBZ
cord-004615-xfi3p601	267	30	in	in	IN
cord-004615-xfi3p601	267	31	the	the	DT
cord-004615-xfi3p601	267	32	intervals	interval	NNS
cord-004615-xfi3p601	267	33	after	after	IN
cord-004615-xfi3p601	267	34	the	the	DT
cord-004615-xfi3p601	267	35	interval	interval	NN
cord-004615-xfi3p601	267	36	of	of	IN
cord-004615-xfi3p601	267	37	infection	infection	NN
cord-004615-xfi3p601	267	38	.	.	.
cord-004615-xfi3p601	268	1	We	-PRON-	PRP
cord-004615-xfi3p601	268	2	can	can	MD
cord-004615-xfi3p601	268	3	compute	compute	VB
cord-004615-xfi3p601	268	4	these	these	DT
cord-004615-xfi3p601	268	5	properties	property	NNS
cord-004615-xfi3p601	268	6	for	for	IN
cord-004615-xfi3p601	268	7	the	the	DT
cord-004615-xfi3p601	268	8	herd	herd	NN
cord-004615-xfi3p601	268	9	infected	infect	VBN
cord-004615-xfi3p601	268	10	at	at	IN
cord-004615-xfi3p601	268	11	t	t	NN
cord-004615-xfi3p601	268	12	=	=	SYM
cord-004615-xfi3p601	268	13	0	0	CD
cord-004615-xfi3p601	268	14	.	.	.
cord-004615-xfi3p601	269	1	Because	because	IN
cord-004615-xfi3p601	269	2	an	an	DT
cord-004615-xfi3p601	269	3	infected	infected	JJ
cord-004615-xfi3p601	269	4	herd	herd	NN
cord-004615-xfi3p601	269	5	will	will	MD
cord-004615-xfi3p601	269	6	almost	almost	RB
cord-004615-xfi3p601	269	7	surely	surely	RB
cord-004615-xfi3p601	269	8	be	be	VB
cord-004615-xfi3p601	269	9	detected	detect	VBN
cord-004615-xfi3p601	269	10	in	in	IN
cord-004615-xfi3p601	269	11	finite	finite	JJ
cord-004615-xfi3p601	269	12	time	time	NN
cord-004615-xfi3p601	269	13	,	,	,
cord-004615-xfi3p601	269	14	the	the	DT
cord-004615-xfi3p601	269	15	probability	probability	NN
cord-004615-xfi3p601	269	16	of	of	IN
cord-004615-xfi3p601	269	17	extinction	extinction	NN
cord-004615-xfi3p601	269	18	of	of	IN
cord-004615-xfi3p601	269	19	the	the	DT
cord-004615-xfi3p601	269	20	'	'	``
cord-004615-xfi3p601	269	21	progeny	progeny	NN
cord-004615-xfi3p601	269	22	'	'	''
cord-004615-xfi3p601	269	23	of	of	IN
cord-004615-xfi3p601	269	24	an	an	DT
cord-004615-xfi3p601	269	25	infected	infected	JJ
cord-004615-xfi3p601	269	26	herd	herd	NN
cord-004615-xfi3p601	270	1	x	x	LS
cord-004615-xfi3p601	270	2	,	,	,
cord-004615-xfi3p601	270	3	is	be	VBZ
cord-004615-xfi3p601	270	4	equal	equal	JJ
cord-004615-xfi3p601	270	5	to	to	IN
cord-004615-xfi3p601	270	6	the	the	DT
cord-004615-xfi3p601	270	7	probability	probability	NN
cord-004615-xfi3p601	270	8	of	of	IN
cord-004615-xfi3p601	270	9	extinction	extinction	NN
cord-004615-xfi3p601	270	10	of	of	IN
cord-004615-xfi3p601	270	11	the	the	DT
cord-004615-xfi3p601	270	12	progeny	progeny	NN
cord-004615-xfi3p601	270	13	of	of	IN
cord-004615-xfi3p601	270	14	all	all	PDT
cord-004615-xfi3p601	270	15	the	the	DT
cord-004615-xfi3p601	270	16	herds	herd	NNS
cord-004615-xfi3p601	270	17	infected	infect	VBN
cord-004615-xfi3p601	270	18	by	by	IN
cord-004615-xfi3p601	270	19	x.	x.	NNP
cord-004615-xfi3p601	271	1	The	the	DT
cord-004615-xfi3p601	271	2	probability	probability	NN
cord-004615-xfi3p601	271	3	of	of	IN
cord-004615-xfi3p601	271	4	extinction	extinction	NN
cord-004615-xfi3p601	271	5	of	of	IN
cord-004615-xfi3p601	271	6	the	the	DT
cord-004615-xfi3p601	271	7	"	"	``
cord-004615-xfi3p601	271	8	progeny	progeny	NN
cord-004615-xfi3p601	271	9	"	"	''
cord-004615-xfi3p601	271	10	of	of	IN
cord-004615-xfi3p601	271	11	a	a	DT
cord-004615-xfi3p601	271	12	herd	herd	NN
cord-004615-xfi3p601	271	13	infected	infect	VBN
cord-004615-xfi3p601	271	14	at	at	IN
cord-004615-xfi3p601	271	15	time	time	NN
cord-004615-xfi3p601	271	16	t	t	NN
cord-004615-xfi3p601	271	17	,	,	,
cord-004615-xfi3p601	271	18	is	be	VBZ
cord-004615-xfi3p601	271	19	denoted	denote	VBN
cord-004615-xfi3p601	271	20	by	by	IN
cord-004615-xfi3p601	271	21	q(t	q(t	CD
cord-004615-xfi3p601	271	22	)	)	-RRB-
cord-004615-xfi3p601	271	23	.	.	.
cord-004615-xfi3p601	272	1	So	so	RB
cord-004615-xfi3p601	272	2	:	:	:
cord-004615-xfi3p601	272	3	Here	here	RB
cord-004615-xfi3p601	272	4	,	,	,
cord-004615-xfi3p601	272	5	the	the	DT
cord-004615-xfi3p601	272	6	times	times	NNP
cord-004615-xfi3p601	272	7	t	t	NNP
cord-004615-xfi3p601	272	8	i	i	PRP
cord-004615-xfi3p601	272	9	are	be	VBP
cord-004615-xfi3p601	272	10	the	the	DT
cord-004615-xfi3p601	272	11	times	time	NNS
cord-004615-xfi3p601	272	12	that	that	IN
cord-004615-xfi3p601	272	13	herds	herd	NNS
cord-004615-xfi3p601	272	14	are	be	VBP
cord-004615-xfi3p601	272	15	infected	infect	VBN
cord-004615-xfi3p601	272	16	by	by	IN
cord-004615-xfi3p601	272	17	the	the	DT
cord-004615-xfi3p601	272	18	herd	herd	NN
cord-004615-xfi3p601	272	19	infected	infect	VBN
cord-004615-xfi3p601	272	20	at	at	IN
cord-004615-xfi3p601	272	21	time	time	NN
cord-004615-xfi3p601	272	22	t	t	NN
cord-004615-xfi3p601	272	23	;	;	:
cord-004615-xfi3p601	272	24	the	the	DT
cord-004615-xfi3p601	272	25	expectation	expectation	NN
cord-004615-xfi3p601	272	26	is	be	VBZ
cord-004615-xfi3p601	272	27	over	over	IN
cord-004615-xfi3p601	272	28	these	these	DT
cord-004615-xfi3p601	272	29	random	random	JJ
cord-004615-xfi3p601	272	30	times	time	NNS
cord-004615-xfi3p601	272	31	of	of	IN
cord-004615-xfi3p601	272	32	infection	infection	NN
cord-004615-xfi3p601	272	33	.	.	.
cord-004615-xfi3p601	273	1	The	the	DT
cord-004615-xfi3p601	273	2	empty	empty	JJ
cord-004615-xfi3p601	273	3	product	product	NN
cord-004615-xfi3p601	273	4	is	be	VBZ
cord-004615-xfi3p601	273	5	defined	define	VBN
cord-004615-xfi3p601	273	6	as	as	IN
cord-004615-xfi3p601	273	7	1	1	CD
cord-004615-xfi3p601	273	8	.	.	.
cord-004615-xfi3p601	274	1	In	in	IN
cord-004615-xfi3p601	274	2	order	order	NN
cord-004615-xfi3p601	274	3	to	to	TO
cord-004615-xfi3p601	274	4	make	make	VB
cord-004615-xfi3p601	274	5	computations	computation	NNS
cord-004615-xfi3p601	274	6	possible	possible	JJ
cord-004615-xfi3p601	274	7	we	-PRON-	PRP
cord-004615-xfi3p601	274	8	use	use	VBP
cord-004615-xfi3p601	274	9	a	a	DT
cord-004615-xfi3p601	274	10	discrete	discrete	JJ
cord-004615-xfi3p601	274	11	time	time	NN
cord-004615-xfi3p601	274	12	approximation	approximation	NN
cord-004615-xfi3p601	274	13	.	.	.
cord-004615-xfi3p601	275	1	We	-PRON-	PRP
cord-004615-xfi3p601	275	2	divide	divide	VBP
cord-004615-xfi3p601	275	3	the	the	DT
cord-004615-xfi3p601	275	4	positive	positive	JJ
cord-004615-xfi3p601	275	5	real	real	JJ
cord-004615-xfi3p601	275	6	line	line	NN
cord-004615-xfi3p601	275	7	into	into	IN
cord-004615-xfi3p601	275	8	N	n	CD
cord-004615-xfi3p601	275	9	+	+	SYM
cord-004615-xfi3p601	275	10	1	1	CD
cord-004615-xfi3p601	275	11	intervals	interval	NNS
cord-004615-xfi3p601	275	12	,	,	,
cord-004615-xfi3p601	275	13	labeled	label	VBN
cord-004615-xfi3p601	275	14	1	1	CD
cord-004615-xfi3p601	275	15	,	,	,
cord-004615-xfi3p601	275	16	2	2	CD
cord-004615-xfi3p601	275	17	,	,	,
cord-004615-xfi3p601	275	18	.	.	.
cord-004615-xfi3p601	275	19	.	.	.
cord-004615-xfi3p601	275	20	.	.	.
cord-004615-xfi3p601	276	1	,	,	,
cord-004615-xfi3p601	276	2	N	n	CD
cord-004615-xfi3p601	276	3	+	+	SYM
cord-004615-xfi3p601	276	4	1	1	CD
cord-004615-xfi3p601	276	5	.	.	.
cord-004615-xfi3p601	277	1	The	the	DT
cord-004615-xfi3p601	277	2	The	the	DT
cord-004615-xfi3p601	277	3	final	final	JJ
cord-004615-xfi3p601	277	4	interval	interval	NN
cord-004615-xfi3p601	278	1	N	n	NN
cord-004615-xfi3p601	278	2	+	+	SYM
cord-004615-xfi3p601	278	3	1	1	CD
cord-004615-xfi3p601	278	4	is	be	VBZ
cord-004615-xfi3p601	278	5	(	(	-LRB-
cord-004615-xfi3p601	278	6	T	T	NNP
cord-004615-xfi3p601	278	7	,	,	,
cord-004615-xfi3p601	278	8	∞	∞	NNP
cord-004615-xfi3p601	278	9	)	)	-RRB-
cord-004615-xfi3p601	278	10	;	;	:
cord-004615-xfi3p601	278	11	in	in	IN
cord-004615-xfi3p601	278	12	this	this	DT
cord-004615-xfi3p601	278	13	final	final	JJ
cord-004615-xfi3p601	278	14	interval	interval	NN
cord-004615-xfi3p601	278	15	all	all	PDT
cord-004615-xfi3p601	278	16	the	the	DT
cord-004615-xfi3p601	278	17	model	model	NN
cord-004615-xfi3p601	278	18	parameters	parameter	NNS
cord-004615-xfi3p601	278	19	are	be	VBP
cord-004615-xfi3p601	278	20	constant	constant	JJ
cord-004615-xfi3p601	278	21	.	.	.
cord-004615-xfi3p601	279	1	The	the	DT
cord-004615-xfi3p601	279	2	time	time	NN
cord-004615-xfi3p601	279	3	t	t	NN
cord-004615-xfi3p601	279	4	=	=	SYM
cord-004615-xfi3p601	279	5	0	0	NFP
cord-004615-xfi3p601	279	6	,	,	,
cord-004615-xfi3p601	279	7	the	the	DT
cord-004615-xfi3p601	279	8	moment	moment	NN
cord-004615-xfi3p601	279	9	of	of	IN
cord-004615-xfi3p601	279	10	the	the	DT
cord-004615-xfi3p601	279	11	first	first	JJ
cord-004615-xfi3p601	279	12	infection	infection	NN
cord-004615-xfi3p601	279	13	,	,	,
cord-004615-xfi3p601	279	14	is	be	VBZ
cord-004615-xfi3p601	279	15	not	not	RB
cord-004615-xfi3p601	279	16	included	include	VBN
cord-004615-xfi3p601	279	17	in	in	IN
cord-004615-xfi3p601	279	18	one	one	CD
cord-004615-xfi3p601	279	19	of	of	IN
cord-004615-xfi3p601	279	20	the	the	DT
cord-004615-xfi3p601	279	21	intervals	interval	NNS
cord-004615-xfi3p601	279	22	,	,	,
cord-004615-xfi3p601	279	23	we	-PRON-	PRP
cord-004615-xfi3p601	279	24	treat	treat	VBP
cord-004615-xfi3p601	279	25	this	this	DT
cord-004615-xfi3p601	279	26	point	point	NN
cord-004615-xfi3p601	279	27	in	in	IN
cord-004615-xfi3p601	279	28	our	-PRON-	PRP$
cord-004615-xfi3p601	279	29	notation	notation	NN
cord-004615-xfi3p601	279	30	as	as	IN
cord-004615-xfi3p601	279	31	interval	interval	NN
cord-004615-xfi3p601	279	32	0	0	CD
cord-004615-xfi3p601	279	33	.	.	.
cord-004615-xfi3p601	280	1	If	if	IN
cord-004615-xfi3p601	280	2	the	the	DT
cord-004615-xfi3p601	280	3	function	function	NN
cord-004615-xfi3p601	280	4	φ(t	φ(t	NNP
cord-004615-xfi3p601	280	5	)	)	-RRB-
cord-004615-xfi3p601	280	6	is	be	VBZ
cord-004615-xfi3p601	280	7	discontinuous	discontinuous	JJ
cord-004615-xfi3p601	280	8	we	-PRON-	PRP
cord-004615-xfi3p601	280	9	may	may	MD
cord-004615-xfi3p601	280	10	choose	choose	VB
cord-004615-xfi3p601	280	11	another	another	DT
cord-004615-xfi3p601	280	12	discretisation	discretisation	NN
cord-004615-xfi3p601	280	13	,	,	,
cord-004615-xfi3p601	280	14	so	so	IN
cord-004615-xfi3p601	280	15	that	that	IN
cord-004615-xfi3p601	280	16	the	the	DT
cord-004615-xfi3p601	280	17	discontinuities	discontinuity	NNS
cord-004615-xfi3p601	280	18	are	be	VBP
cord-004615-xfi3p601	280	19	on	on	IN
cord-004615-xfi3p601	280	20	the	the	DT
cord-004615-xfi3p601	280	21	boundaries	boundary	NNS
cord-004615-xfi3p601	280	22	of	of	IN
cord-004615-xfi3p601	280	23	intervals	interval	NNS
cord-004615-xfi3p601	280	24	.	.	.
cord-004615-xfi3p601	281	1	It	-PRON-	PRP
cord-004615-xfi3p601	281	2	is	be	VBZ
cord-004615-xfi3p601	281	3	not	not	RB
cord-004615-xfi3p601	281	4	essential	essential	JJ
cord-004615-xfi3p601	281	5	that	that	IN
cord-004615-xfi3p601	281	6	all	all	DT
cord-004615-xfi3p601	281	7	intervals	interval	NNS
cord-004615-xfi3p601	281	8	have	have	VBP
cord-004615-xfi3p601	281	9	the	the	DT
cord-004615-xfi3p601	281	10	same	same	JJ
cord-004615-xfi3p601	281	11	length	length	NN
cord-004615-xfi3p601	281	12	.	.	.
cord-004615-xfi3p601	282	1	For	for	IN
cord-004615-xfi3p601	282	2	t	t	NN
cord-004615-xfi3p601	282	3	in	in	IN
cord-004615-xfi3p601	282	4	interval	interval	NN
cord-004615-xfi3p601	282	5	i	i	PRP
cord-004615-xfi3p601	282	6	,	,	,
cord-004615-xfi3p601	282	7	1	1	CD
cord-004615-xfi3p601	282	8	≤	≤	NNPS
cord-004615-xfi3p601	282	9	i	i	NNP
cord-004615-xfi3p601	282	10	≤	≤	NNP
cord-004615-xfi3p601	282	11	N	N	NNP
cord-004615-xfi3p601	282	12	,	,	,
cord-004615-xfi3p601	282	13	q(t	q(t	NNP
cord-004615-xfi3p601	282	14	)	)	-RRB-
cord-004615-xfi3p601	282	15	and	and	CC
cord-004615-xfi3p601	282	16	φ(t	φ(t	NNP
cord-004615-xfi3p601	282	17	)	)	-RRB-
cord-004615-xfi3p601	282	18	are	be	VBP
cord-004615-xfi3p601	282	19	approximately	approximately	RB
cord-004615-xfi3p601	282	20	constant	constant	JJ
cord-004615-xfi3p601	282	21	.	.	.
cord-004615-xfi3p601	283	1	In	in	IN
cord-004615-xfi3p601	283	2	our	-PRON-	PRP$
cord-004615-xfi3p601	283	3	"	"	``
cord-004615-xfi3p601	283	4	discrete	discrete	JJ
cord-004615-xfi3p601	283	5	time	time	NN
cord-004615-xfi3p601	283	6	model	model	NN
cord-004615-xfi3p601	283	7	"	"	''
cord-004615-xfi3p601	283	8	we	-PRON-	PRP
cord-004615-xfi3p601	283	9	will	will	MD
cord-004615-xfi3p601	283	10	write	write	VB
cord-004615-xfi3p601	283	11	q(i	q(i	NNP
cord-004615-xfi3p601	283	12	)	)	-RRB-
cord-004615-xfi3p601	283	13	and	and	CC
cord-004615-xfi3p601	283	14	φ(i	φ(i	NNP
cord-004615-xfi3p601	283	15	)	)	-RRB-
cord-004615-xfi3p601	283	16	for	for	IN
cord-004615-xfi3p601	283	17	the	the	DT
cord-004615-xfi3p601	283	18	value	value	NN
cord-004615-xfi3p601	283	19	of	of	IN
cord-004615-xfi3p601	283	20	q	q	NN
cord-004615-xfi3p601	283	21	and	and	CC
cord-004615-xfi3p601	283	22	φ	φ	NN
cord-004615-xfi3p601	283	23	in	in	IN
cord-004615-xfi3p601	283	24	interval	interval	NN
cord-004615-xfi3p601	283	25	i.	i.	NN
cord-004615-xfi3p601	284	1	For	for	IN
cord-004615-xfi3p601	284	2	instance	instance	NN
cord-004615-xfi3p601	284	3	,	,	,
cord-004615-xfi3p601	284	4	we	-PRON-	PRP
cord-004615-xfi3p601	284	5	can	can	MD
cord-004615-xfi3p601	284	6	take	take	VB
cord-004615-xfi3p601	284	7	φ(i	φ(i	NNP
cord-004615-xfi3p601	284	8	)	)	-RRB-
cord-004615-xfi3p601	284	9	to	to	TO
cord-004615-xfi3p601	284	10	be	be	VB
cord-004615-xfi3p601	284	11	the	the	DT
cord-004615-xfi3p601	284	12	value	value	NN
cord-004615-xfi3p601	284	13	of	of	IN
cord-004615-xfi3p601	284	14	φ(t	φ(t	NNP
cord-004615-xfi3p601	284	15	)	)	-RRB-
cord-004615-xfi3p601	284	16	at	at	IN
cord-004615-xfi3p601	284	17	the	the	DT
cord-004615-xfi3p601	284	18	midpoint	midpoint	NN
cord-004615-xfi3p601	284	19	of	of	IN
cord-004615-xfi3p601	284	20	interval	interval	NN
cord-004615-xfi3p601	284	21	i.	i.	NN
cord-004615-xfi3p601	284	22	Because	because	IN
cord-004615-xfi3p601	284	23	we	-PRON-	PRP
cord-004615-xfi3p601	284	24	accept	accept	VBP
cord-004615-xfi3p601	284	25	discontinuities	discontinuity	NNS
cord-004615-xfi3p601	284	26	in	in	IN
cord-004615-xfi3p601	284	27	φ(t	φ(t	NNP
cord-004615-xfi3p601	284	28	)	)	-RRB-
cord-004615-xfi3p601	284	29	,	,	,
cord-004615-xfi3p601	284	30	this	this	DT
cord-004615-xfi3p601	284	31	function	function	NN
cord-004615-xfi3p601	284	32	may	may	MD
cord-004615-xfi3p601	284	33	differ	differ	VB
cord-004615-xfi3p601	284	34	significantly	significantly	RB
cord-004615-xfi3p601	284	35	for	for	IN
cord-004615-xfi3p601	284	36	neighbouring	neighbour	VBG
cord-004615-xfi3p601	284	37	intervals	interval	NNS
cord-004615-xfi3p601	284	38	.	.	.
cord-004615-xfi3p601	285	1	Now	now	RB
cord-004615-xfi3p601	285	2	,	,	,
cord-004615-xfi3p601	285	3	with	with	IN
cord-004615-xfi3p601	285	4	n(i	n(i	NNP
cord-004615-xfi3p601	285	5	,	,	,
cord-004615-xfi3p601	285	6	j	j	NNP
cord-004615-xfi3p601	285	7	)	)	-RRB-
cord-004615-xfi3p601	285	8	,	,	,
cord-004615-xfi3p601	285	9	the	the	DT
cord-004615-xfi3p601	285	10	number	number	NN
cord-004615-xfi3p601	285	11	of	of	IN
cord-004615-xfi3p601	285	12	infections	infection	NNS
cord-004615-xfi3p601	285	13	in	in	IN
cord-004615-xfi3p601	285	14	interval	interval	NN
cord-004615-xfi3p601	285	15	j	j	NNP
cord-004615-xfi3p601	285	16	,	,	,
cord-004615-xfi3p601	285	17	due	due	IN
cord-004615-xfi3p601	285	18	to	to	IN
cord-004615-xfi3p601	285	19	one	one	CD
cord-004615-xfi3p601	285	20	herd	herd	NN
cord-004615-xfi3p601	285	21	infected	infect	VBN
cord-004615-xfi3p601	285	22	in	in	IN
cord-004615-xfi3p601	285	23	interval	interval	NN
cord-004615-xfi3p601	285	24	i	i	PRP
cord-004615-xfi3p601	285	25	,	,	,
cord-004615-xfi3p601	285	26	we	-PRON-	PRP
cord-004615-xfi3p601	285	27	can	can	MD
cord-004615-xfi3p601	285	28	write	write	VB
cord-004615-xfi3p601	285	29	(	(	-LRB-
cord-004615-xfi3p601	285	30	4	4	LS
cord-004615-xfi3p601	285	31	)	)	-RRB-
cord-004615-xfi3p601	285	32	as	as	IN
cord-004615-xfi3p601	285	33	:	:	:
cord-004615-xfi3p601	285	34	where	where	WRB
cord-004615-xfi3p601	285	35	the	the	DT
cord-004615-xfi3p601	285	36	expectation	expectation	NN
cord-004615-xfi3p601	285	37	is	be	VBZ
cord-004615-xfi3p601	285	38	over	over	IN
cord-004615-xfi3p601	285	39	the	the	DT
cord-004615-xfi3p601	285	40	numbers	number	NNS
cord-004615-xfi3p601	285	41	of	of	IN
cord-004615-xfi3p601	285	42	infections	infection	NNS
cord-004615-xfi3p601	285	43	in	in	IN
cord-004615-xfi3p601	285	44	each	each	DT
cord-004615-xfi3p601	285	45	interval	interval	NN
cord-004615-xfi3p601	285	46	.	.	.
cord-004615-xfi3p601	286	1	q(0	q(0	LS
cord-004615-xfi3p601	286	2	)	)	-RRB-
cord-004615-xfi3p601	286	3	is	be	VBZ
cord-004615-xfi3p601	286	4	the	the	DT
cord-004615-xfi3p601	286	5	probability	probability	NN
cord-004615-xfi3p601	286	6	of	of	IN
cord-004615-xfi3p601	286	7	extinction	extinction	NN
cord-004615-xfi3p601	286	8	of	of	IN
cord-004615-xfi3p601	286	9	the	the	DT
cord-004615-xfi3p601	286	10	progeny	progeny	NN
cord-004615-xfi3p601	286	11	of	of	IN
cord-004615-xfi3p601	286	12	the	the	DT
cord-004615-xfi3p601	286	13	herd	herd	NN
cord-004615-xfi3p601	286	14	infected	infect	VBN
cord-004615-xfi3p601	286	15	at	at	IN
cord-004615-xfi3p601	286	16	time	time	NN
cord-004615-xfi3p601	286	17	t	t	NN
cord-004615-xfi3p601	286	18	=	=	SYM
cord-004615-xfi3p601	286	19	0	0	CD
cord-004615-xfi3p601	286	20	.	.	.
cord-004615-xfi3p601	287	1	We	-PRON-	PRP
cord-004615-xfi3p601	287	2	assume	assume	VBP
cord-004615-xfi3p601	287	3	that	that	IN
cord-004615-xfi3p601	287	4	all	all	DT
cord-004615-xfi3p601	287	5	infections	infection	NNS
cord-004615-xfi3p601	287	6	and	and	CC
cord-004615-xfi3p601	287	7	detections	detection	NNS
cord-004615-xfi3p601	287	8	take	take	VBP
cord-004615-xfi3p601	287	9	place	place	NN
cord-004615-xfi3p601	287	10	on	on	IN
cord-004615-xfi3p601	287	11	the	the	DT
cord-004615-xfi3p601	287	12	midpoint	midpoint	NN
cord-004615-xfi3p601	287	13	of	of	IN
cord-004615-xfi3p601	287	14	the	the	DT
cord-004615-xfi3p601	287	15	interval	interval	NN
cord-004615-xfi3p601	287	16	,	,	,
cord-004615-xfi3p601	287	17	except	except	IN
cord-004615-xfi3p601	287	18	of	of	IN
cord-004615-xfi3p601	287	19	course	course	NN
cord-004615-xfi3p601	287	20	for	for	IN
cord-004615-xfi3p601	287	21	the	the	DT
cord-004615-xfi3p601	287	22	events	event	NNS
cord-004615-xfi3p601	287	23	in	in	IN
cord-004615-xfi3p601	287	24	the	the	DT
cord-004615-xfi3p601	287	25	final	final	JJ
cord-004615-xfi3p601	287	26	interval	interval	NN
cord-004615-xfi3p601	287	27	,	,	,
cord-004615-xfi3p601	287	28	because	because	IN
cord-004615-xfi3p601	287	29	there	there	RB
cord-004615-xfi3p601	287	30	we	-PRON-	PRP
cord-004615-xfi3p601	287	31	can	can	MD
cord-004615-xfi3p601	287	32	compute	compute	VB
cord-004615-xfi3p601	287	33	everything	everything	NN
cord-004615-xfi3p601	287	34	explicitly	explicitly	RB
cord-004615-xfi3p601	287	35	.	.	.
cord-004615-xfi3p601	288	1	Given	give	VBN
cord-004615-xfi3p601	288	2	that	that	IN
cord-004615-xfi3p601	288	3	a	a	DT
cord-004615-xfi3p601	288	4	herd	herd	NN
cord-004615-xfi3p601	288	5	is	be	VBZ
cord-004615-xfi3p601	288	6	not	not	RB
cord-004615-xfi3p601	288	7	yet	yet	RB
cord-004615-xfi3p601	288	8	detected	detect	VBN
cord-004615-xfi3p601	288	9	and	and	CC
cord-004615-xfi3p601	288	10	H	h	NN
cord-004615-xfi3p601	288	11	=	=	SYM
cord-004615-xfi3p601	288	12	h	h	NN
cord-004615-xfi3p601	288	13	,	,	,
cord-004615-xfi3p601	288	14	the	the	DT
cord-004615-xfi3p601	288	15	probability	probability	NN
cord-004615-xfi3p601	288	16	of	of	IN
cord-004615-xfi3p601	288	17	infection	infection	NN
cord-004615-xfi3p601	288	18	in	in	IN
cord-004615-xfi3p601	288	19	a	a	DT
cord-004615-xfi3p601	288	20	certain	certain	JJ
cord-004615-xfi3p601	288	21	interval	interval	NN
cord-004615-xfi3p601	288	22	by	by	IN
cord-004615-xfi3p601	288	23	that	that	DT
cord-004615-xfi3p601	288	24	herd	herd	NN
cord-004615-xfi3p601	288	25	does	do	VBZ
cord-004615-xfi3p601	288	26	not	not	RB
cord-004615-xfi3p601	288	27	depend	depend	VB
cord-004615-xfi3p601	288	28	on	on	IN
cord-004615-xfi3p601	288	29	the	the	DT
cord-004615-xfi3p601	288	30	number	number	NN
cord-004615-xfi3p601	288	31	of	of	IN
cord-004615-xfi3p601	288	32	infections	infection	NNS
cord-004615-xfi3p601	288	33	in	in	IN
cord-004615-xfi3p601	288	34	previous	previous	JJ
cord-004615-xfi3p601	288	35	intervals	interval	NNS
cord-004615-xfi3p601	288	36	.	.	.
cord-004615-xfi3p601	289	1	Consider	consider	VB
cord-004615-xfi3p601	289	2	a	a	DT
cord-004615-xfi3p601	289	3	herd	herd	NN
cord-004615-xfi3p601	289	4	infected	infect	VBN
cord-004615-xfi3p601	289	5	in	in	IN
cord-004615-xfi3p601	289	6	interval	interval	NN
cord-004615-xfi3p601	289	7	i	i	PRP
cord-004615-xfi3p601	289	8	,	,	,
cord-004615-xfi3p601	289	9	denote	denote	VBN
cord-004615-xfi3p601	289	10	by	by	IN
cord-004615-xfi3p601	289	11	D(i	D(i	NNP
cord-004615-xfi3p601	289	12	;	;	:
cord-004615-xfi3p601	289	13	h	h	NN
cord-004615-xfi3p601	289	14	)	)	-RRB-
cord-004615-xfi3p601	289	15	=	=	NFP
cord-004615-xfi3p601	290	1	k	k	NNP
cord-004615-xfi3p601	291	1	the	the	DT
cord-004615-xfi3p601	291	2	event	event	NN
cord-004615-xfi3p601	291	3	that	that	IN
cord-004615-xfi3p601	291	4	this	this	DT
cord-004615-xfi3p601	291	5	particular	particular	JJ
cord-004615-xfi3p601	291	6	herd	herd	NN
cord-004615-xfi3p601	291	7	is	be	VBZ
cord-004615-xfi3p601	291	8	detected	detect	VBN
cord-004615-xfi3p601	291	9	in	in	IN
cord-004615-xfi3p601	291	10	interval	interval	NN
cord-004615-xfi3p601	291	11	k	k	NNP
cord-004615-xfi3p601	291	12	,	,	,
cord-004615-xfi3p601	291	13	given	give	VBN
cord-004615-xfi3p601	291	14	H	h	NN
cord-004615-xfi3p601	291	15	=	=	NN
cord-004615-xfi3p601	291	16	h.	h.	NN
cord-004615-xfi3p601	292	1	After	after	IN
cord-004615-xfi3p601	292	2	detection	detection	NN
cord-004615-xfi3p601	292	3	no	no	DT
cord-004615-xfi3p601	292	4	further	further	JJ
cord-004615-xfi3p601	292	5	infections	infection	NNS
cord-004615-xfi3p601	292	6	occur	occur	VBP
cord-004615-xfi3p601	292	7	.	.	.
cord-004615-xfi3p601	293	1	Define	define	VB
cord-004615-xfi3p601	293	2	n(i	n(i	NNP
cord-004615-xfi3p601	293	3	,	,	,
cord-004615-xfi3p601	293	4	l	l	NNP
cord-004615-xfi3p601	293	5	,	,	,
cord-004615-xfi3p601	293	6	k	k	NNP
cord-004615-xfi3p601	293	7	;	;	:
cord-004615-xfi3p601	293	8	h	h	NNP
cord-004615-xfi3p601	293	9	)	)	-RRB-
cord-004615-xfi3p601	293	10	as	as	IN
cord-004615-xfi3p601	293	11	the	the	DT
cord-004615-xfi3p601	293	12	number	number	NN
cord-004615-xfi3p601	293	13	of	of	IN
cord-004615-xfi3p601	293	14	infections	infection	NNS
cord-004615-xfi3p601	293	15	in	in	IN
cord-004615-xfi3p601	293	16	interval	interval	NN
cord-004615-xfi3p601	293	17	l	l	NN
cord-004615-xfi3p601	293	18	due	due	IN
cord-004615-xfi3p601	293	19	to	to	IN
cord-004615-xfi3p601	293	20	a	a	DT
cord-004615-xfi3p601	293	21	particular	particular	JJ
cord-004615-xfi3p601	293	22	herd	herd	NN
cord-004615-xfi3p601	293	23	infected	infect	VBN
cord-004615-xfi3p601	293	24	in	in	IN
cord-004615-xfi3p601	293	25	interval	interval	NN
cord-004615-xfi3p601	293	26	i	i	PRP
cord-004615-xfi3p601	293	27	,	,	,
cord-004615-xfi3p601	293	28	while	while	IN
cord-004615-xfi3p601	293	29	H	h	NN
cord-004615-xfi3p601	293	30	=	=	SYM
cord-004615-xfi3p601	293	31	h	h	NN
cord-004615-xfi3p601	293	32	and	and	CC
cord-004615-xfi3p601	293	33	the	the	DT
cord-004615-xfi3p601	293	34	interval	interval	NN
cord-004615-xfi3p601	293	35	of	of	IN
cord-004615-xfi3p601	293	36	detection	detection	NN
cord-004615-xfi3p601	293	37	k	k	NN
cord-004615-xfi3p601	293	38	,	,	,
cord-004615-xfi3p601	293	39	are	be	VBP
cord-004615-xfi3p601	293	40	given	give	VBN
cord-004615-xfi3p601	293	41	.	.	.
cord-004615-xfi3p601	294	1	Now	now	RB
cord-004615-xfi3p601	294	2	,	,	,
cord-004615-xfi3p601	294	3	by	by	IN
cord-004615-xfi3p601	294	4	using	use	VBG
cord-004615-xfi3p601	294	5	independence	independence	NN
cord-004615-xfi3p601	294	6	we	-PRON-	PRP
cord-004615-xfi3p601	294	7	have	have	VBP
cord-004615-xfi3p601	294	8	(	(	-LRB-
cord-004615-xfi3p601	294	9	writing	write	VBG
cord-004615-xfi3p601	294	10	P	p	NN
cord-004615-xfi3p601	294	11	H	h	NN
cord-004615-xfi3p601	294	12	for	for	IN
cord-004615-xfi3p601	294	13	the	the	DT
cord-004615-xfi3p601	294	14	distribution	distribution	NN
cord-004615-xfi3p601	294	15	function	function	NN
cord-004615-xfi3p601	294	16	of	of	IN
cord-004615-xfi3p601	294	17	H	h	NN
cord-004615-xfi3p601	294	18	)	)	-RRB-
cord-004615-xfi3p601	295	1	Here	here	RB
cord-004615-xfi3p601	295	2	the	the	DT
cord-004615-xfi3p601	295	3	expectation	expectation	NN
cord-004615-xfi3p601	295	4	inside	inside	IN
cord-004615-xfi3p601	295	5	the	the	DT
cord-004615-xfi3p601	295	6	integral	integral	JJ
cord-004615-xfi3p601	295	7	depends	depend	VBZ
cord-004615-xfi3p601	295	8	on	on	IN
cord-004615-xfi3p601	295	9	h	h	NNP
cord-004615-xfi3p601	295	10	,	,	,
cord-004615-xfi3p601	295	11	contrary	contrary	JJ
cord-004615-xfi3p601	295	12	to	to	IN
cord-004615-xfi3p601	295	13	the	the	DT
cord-004615-xfi3p601	295	14	non	non	JJ
cord-004615-xfi3p601	295	15	-	-	JJ
cord-004615-xfi3p601	295	16	varying	varying	JJ
cord-004615-xfi3p601	295	17	environment	environment	NN
cord-004615-xfi3p601	295	18	case	case	NN
cord-004615-xfi3p601	295	19	.	.	.
cord-004615-xfi3p601	296	1	Note	note	VB
cord-004615-xfi3p601	296	2	that	that	IN
cord-004615-xfi3p601	296	3	the	the	DT
cord-004615-xfi3p601	296	4	number	number	NN
cord-004615-xfi3p601	296	5	of	of	IN
cord-004615-xfi3p601	296	6	infections	infection	NNS
cord-004615-xfi3p601	296	7	in	in	IN
cord-004615-xfi3p601	296	8	a	a	DT
cord-004615-xfi3p601	296	9	certain	certain	JJ
cord-004615-xfi3p601	296	10	interval	interval	NN
cord-004615-xfi3p601	296	11	is	be	VBZ
cord-004615-xfi3p601	296	12	not	not	RB
cord-004615-xfi3p601	296	13	independent	independent	JJ
cord-004615-xfi3p601	296	14	of	of	IN
cord-004615-xfi3p601	296	15	the	the	DT
cord-004615-xfi3p601	296	16	interval	interval	NN
cord-004615-xfi3p601	296	17	of	of	IN
cord-004615-xfi3p601	296	18	detection	detection	NN
cord-004615-xfi3p601	296	19	.	.	.
cord-004615-xfi3p601	297	1	It	-PRON-	PRP
cord-004615-xfi3p601	297	2	does	do	VBZ
cord-004615-xfi3p601	297	3	not	not	RB
cord-004615-xfi3p601	297	4	make	make	VB
cord-004615-xfi3p601	297	5	any	any	DT
cord-004615-xfi3p601	297	6	difference	difference	NN
cord-004615-xfi3p601	297	7	for	for	IN
cord-004615-xfi3p601	297	8	the	the	DT
cord-004615-xfi3p601	297	9	number	number	NN
cord-004615-xfi3p601	297	10	of	of	IN
cord-004615-xfi3p601	297	11	infections	infection	NNS
cord-004615-xfi3p601	297	12	whether	whether	IN
cord-004615-xfi3p601	297	13	a	a	DT
cord-004615-xfi3p601	297	14	herd	herd	NN
cord-004615-xfi3p601	297	15	is	be	VBZ
cord-004615-xfi3p601	297	16	detected	detect	VBN
cord-004615-xfi3p601	297	17	shortly	shortly	RB
cord-004615-xfi3p601	297	18	after	after	IN
cord-004615-xfi3p601	297	19	the	the	DT
cord-004615-xfi3p601	297	20	considered	consider	VBN
cord-004615-xfi3p601	297	21	interval	interval	NN
cord-004615-xfi3p601	297	22	or	or	CC
cord-004615-xfi3p601	297	23	very	very	RB
cord-004615-xfi3p601	297	24	long	long	RB
cord-004615-xfi3p601	297	25	after	after	IN
cord-004615-xfi3p601	297	26	that	that	DT
cord-004615-xfi3p601	297	27	,	,	,
cord-004615-xfi3p601	297	28	but	but	CC
cord-004615-xfi3p601	297	29	it	-PRON-	PRP
cord-004615-xfi3p601	297	30	does	do	VBZ
cord-004615-xfi3p601	297	31	make	make	VB
cord-004615-xfi3p601	297	32	a	a	DT
cord-004615-xfi3p601	297	33	difference	difference	NN
cord-004615-xfi3p601	297	34	whether	whether	IN
cord-004615-xfi3p601	297	35	the	the	DT
cord-004615-xfi3p601	297	36	detection	detection	NN
cord-004615-xfi3p601	297	37	is	be	VBZ
cord-004615-xfi3p601	297	38	in	in	IN
cord-004615-xfi3p601	297	39	the	the	DT
cord-004615-xfi3p601	297	40	considered	consider	VBN
cord-004615-xfi3p601	297	41	interval	interval	NN
cord-004615-xfi3p601	297	42	itself	-PRON-	PRP
cord-004615-xfi3p601	297	43	.	.	.
cord-004615-xfi3p601	298	1	So	so	RB
cord-004615-xfi3p601	298	2	p(n	p(n	NNP
cord-004615-xfi3p601	298	3	;	;	:
cord-004615-xfi3p601	298	4	i	i	PRP
cord-004615-xfi3p601	298	5	,	,	,
cord-004615-xfi3p601	298	6	l	l	NNP
cord-004615-xfi3p601	298	7	,	,	,
cord-004615-xfi3p601	298	8	k	k	NNP
cord-004615-xfi3p601	298	9	;	;	:
cord-004615-xfi3p601	298	10	h	h	NNP
cord-004615-xfi3p601	298	11	)	)	-RRB-
cord-004615-xfi3p601	298	12	:	:	:
cord-004615-xfi3p601	298	13	=	=	SYM
cord-004615-xfi3p601	298	14	P(n(i	P(n(i	NNP
cord-004615-xfi3p601	298	15	,	,	,
cord-004615-xfi3p601	298	16	l	l	NNP
cord-004615-xfi3p601	298	17	,	,	,
cord-004615-xfi3p601	298	18	k	k	NNP
cord-004615-xfi3p601	298	19	;	;	:
cord-004615-xfi3p601	298	20	h	h	NNP
cord-004615-xfi3p601	298	21	)	)	-RRB-
cord-004615-xfi3p601	298	22	=	=	SYM
cord-004615-xfi3p601	298	23	n	n	NN
cord-004615-xfi3p601	298	24	)	)	-RRB-
cord-004615-xfi3p601	298	25	depends	depend	VBZ
cord-004615-xfi3p601	298	26	on	on	IN
cord-004615-xfi3p601	298	27	the	the	DT
cord-004615-xfi3p601	298	28	detection	detection	NN
cord-004615-xfi3p601	298	29	interval	interval	NN
cord-004615-xfi3p601	298	30	k.	k.	NNP
cord-004615-xfi3p601	299	1	For	for	IN
cord-004615-xfi3p601	299	2	computational	computational	JJ
cord-004615-xfi3p601	299	3	reasons	reason	NNS
cord-004615-xfi3p601	299	4	we	-PRON-	PRP
cord-004615-xfi3p601	299	5	suppose	suppose	VBP
cord-004615-xfi3p601	299	6	in	in	IN
cord-004615-xfi3p601	299	7	this	this	DT
cord-004615-xfi3p601	299	8	discrete	discrete	JJ
cord-004615-xfi3p601	299	9	model	model	NN
cord-004615-xfi3p601	299	10	that	that	WDT
cord-004615-xfi3p601	299	11	for	for	IN
cord-004615-xfi3p601	299	12	i	i	PRP
cord-004615-xfi3p601	299	13	≤	≤	NNP
cord-004615-xfi3p601	299	14	N	N	NNP
cord-004615-xfi3p601	299	15	,	,	,
cord-004615-xfi3p601	299	16	p(0	p(0	UH
cord-004615-xfi3p601	299	17	;	;	:
cord-004615-xfi3p601	299	18	i	i	PRP
cord-004615-xfi3p601	299	19	,	,	,
cord-004615-xfi3p601	299	20	i	i	PRP
cord-004615-xfi3p601	299	21	,	,	,
cord-004615-xfi3p601	299	22	k	k	NNP
cord-004615-xfi3p601	299	23	;	;	:
cord-004615-xfi3p601	299	24	h	h	NNP
cord-004615-xfi3p601	299	25	)	)	-RRB-
cord-004615-xfi3p601	299	26	=	=	SYM
cord-004615-xfi3p601	299	27	1	1	CD
cord-004615-xfi3p601	299	28	.	.	.
cord-004615-xfi3p601	300	1	We	-PRON-	PRP
cord-004615-xfi3p601	300	2	write	write	VBP
cord-004615-xfi3p601	300	3	p	p	NN
cord-004615-xfi3p601	300	4	det	det	NNP
cord-004615-xfi3p601	300	5	(	(	-LRB-
cord-004615-xfi3p601	300	6	i	i	PRP
cord-004615-xfi3p601	300	7	,	,	,
cord-004615-xfi3p601	300	8	k	k	NNP
cord-004615-xfi3p601	300	9	;	;	:
cord-004615-xfi3p601	300	10	h	h	NNP
cord-004615-xfi3p601	300	11	)	)	-RRB-
cord-004615-xfi3p601	300	12	for	for	IN
cord-004615-xfi3p601	300	13	P(D(i	P(D(i	NNP
cord-004615-xfi3p601	300	14	;	;	:
cord-004615-xfi3p601	300	15	h	h	NNP
cord-004615-xfi3p601	300	16	)	)	-RRB-
cord-004615-xfi3p601	300	17	=	=	NFP
cord-004615-xfi3p601	301	1	k	k	NNP
cord-004615-xfi3p601	301	2	)	)	-RRB-
cord-004615-xfi3p601	301	3	.	.	.
cord-004615-xfi3p601	302	1	We	-PRON-	PRP
cord-004615-xfi3p601	302	2	are	be	VBP
cord-004615-xfi3p601	302	3	interested	interested	JJ
cord-004615-xfi3p601	302	4	in	in	IN
cord-004615-xfi3p601	302	5	q	q	NN
cord-004615-xfi3p601	302	6	:	:	:
cord-004615-xfi3p601	302	7	=	=	NFP
cord-004615-xfi3p601	302	8	q(0	q(0	NNP
cord-004615-xfi3p601	302	9	)	)	-RRB-
cord-004615-xfi3p601	302	10	.	.	.
cord-004615-xfi3p601	303	1	We	-PRON-	PRP
cord-004615-xfi3p601	303	2	can	can	MD
cord-004615-xfi3p601	303	3	easily	easily	RB
cord-004615-xfi3p601	303	4	compute	compute	VB
cord-004615-xfi3p601	303	5	all	all	PDT
cord-004615-xfi3p601	303	6	these	these	DT
cord-004615-xfi3p601	303	7	probabilities	probability	NNS
cord-004615-xfi3p601	303	8	in	in	IN
cord-004615-xfi3p601	303	9	our	-PRON-	PRP$
cord-004615-xfi3p601	303	10	model	model	NN
cord-004615-xfi3p601	303	11	.	.	.
cord-004615-xfi3p601	304	1	Because	because	IN
cord-004615-xfi3p601	304	2	we	-PRON-	PRP
cord-004615-xfi3p601	304	3	assume	assume	VBP
cord-004615-xfi3p601	304	4	a	a	DT
cord-004615-xfi3p601	304	5	birth	birth	NN
cord-004615-xfi3p601	304	6	-	-	HYPH
cord-004615-xfi3p601	304	7	and	and	CC
cord-004615-xfi3p601	304	8	-	-	HYPH
cord-004615-xfi3p601	304	9	death	death	NN
cord-004615-xfi3p601	304	10	process	process	NN
cord-004615-xfi3p601	304	11	for	for	IN
cord-004615-xfi3p601	304	12	the	the	DT
cord-004615-xfi3p601	304	13	within	within	JJ
cord-004615-xfi3p601	304	14	-	-	HYPH
cord-004615-xfi3p601	304	15	herd	herd	NN
cord-004615-xfi3p601	304	16	spread	spread	NN
cord-004615-xfi3p601	304	17	,	,	,
cord-004615-xfi3p601	304	18	we	-PRON-	PRP
cord-004615-xfi3p601	304	19	have	have	VBP
cord-004615-xfi3p601	304	20	to	to	TO
cord-004615-xfi3p601	304	21	take	take	VB
cord-004615-xfi3p601	304	22	the	the	DT
cord-004615-xfi3p601	304	23	random	random	JJ
cord-004615-xfi3p601	304	24	character	character	NN
cord-004615-xfi3p601	304	25	of	of	IN
cord-004615-xfi3p601	304	26	H	H	NNP
cord-004615-xfi3p601	304	27	into	into	IN
cord-004615-xfi3p601	304	28	account	account	NN
cord-004615-xfi3p601	304	29	.	.	.
cord-004615-xfi3p601	305	1	Doing	do	VBG
cord-004615-xfi3p601	305	2	this	this	DT
cord-004615-xfi3p601	305	3	leads	lead	VBZ
cord-004615-xfi3p601	305	4	to	to	IN
cord-004615-xfi3p601	305	5	the	the	DT
cord-004615-xfi3p601	305	6	following	follow	VBG
cord-004615-xfi3p601	305	7	formulae	formula	NNS
cord-004615-xfi3p601	305	8	:	:	:
cord-004615-xfi3p601	305	9	·	·	NFP
cord-004615-xfi3p601	305	10	·	·	NFP
cord-004615-xfi3p601	305	11	·	·	NFP
cord-004615-xfi3p601	305	12	E(q(k	E(q(k	NNP
cord-004615-xfi3p601	305	13	)	)	-RRB-
cord-004615-xfi3p601	305	14	n(i	n(i	NNP
cord-004615-xfi3p601	305	15	,	,	,
cord-004615-xfi3p601	305	16	k	k	NNP
cord-004615-xfi3p601	305	17	,	,	,
cord-004615-xfi3p601	305	18	k;h	k;h	NNP
cord-004615-xfi3p601	305	19	)	)	-RRB-
cord-004615-xfi3p601	305	20	)	)	-RRB-
cord-004615-xfi3p601	306	1	p	p	NNP
cord-004615-xfi3p601	306	2	det	det	NNP
cord-004615-xfi3p601	306	3	(	(	-LRB-
cord-004615-xfi3p601	306	4	i	i	PRP
cord-004615-xfi3p601	306	5	,	,	,
cord-004615-xfi3p601	306	6	k	k	NNP
cord-004615-xfi3p601	306	7	,	,	,
cord-004615-xfi3p601	306	8	h)dh	h)dh	NNP
cord-004615-xfi3p601	306	9	.	.	.
cord-004615-xfi3p601	307	1	Here	here	RB
cord-004615-xfi3p601	307	2	we	-PRON-	PRP
cord-004615-xfi3p601	307	3	have	have	VBP
cord-004615-xfi3p601	307	4	conditioned	condition	VBN
cord-004615-xfi3p601	307	5	on	on	IN
cord-004615-xfi3p601	307	6	the	the	DT
cord-004615-xfi3p601	307	7	time	time	NN
cord-004615-xfi3p601	307	8	of	of	IN
cord-004615-xfi3p601	307	9	detection	detection	NN
cord-004615-xfi3p601	307	10	and	and	CC
cord-004615-xfi3p601	307	11	on	on	IN
cord-004615-xfi3p601	307	12	h.	h.	NNP
cord-004615-xfi3p601	308	1	We	-PRON-	PRP
cord-004615-xfi3p601	308	2	can	can	MD
cord-004615-xfi3p601	308	3	rewrite	rewrite	VB
cord-004615-xfi3p601	308	4	this	this	DT
cord-004615-xfi3p601	308	5	formula	formula	NN
cord-004615-xfi3p601	308	6	as	as	IN
cord-004615-xfi3p601	308	7	:	:	:
cord-004615-xfi3p601	308	8	Here	here	RB
cord-004615-xfi3p601	308	9	q(i	q(i	NNP
cord-004615-xfi3p601	308	10	)	)	-RRB-
cord-004615-xfi3p601	308	11	depends	depend	VBZ
cord-004615-xfi3p601	308	12	on	on	IN
cord-004615-xfi3p601	308	13	q(l	q(l	NNP
cord-004615-xfi3p601	308	14	)	)	-RRB-
cord-004615-xfi3p601	308	15	for	for	IN
cord-004615-xfi3p601	308	16	l	l	NN
cord-004615-xfi3p601	308	17	>	>	XX
cord-004615-xfi3p601	308	18	i.	i.	NN
cord-004615-xfi3p601	309	1	As	as	IN
cord-004615-xfi3p601	309	2	mentioned	mention	VBN
cord-004615-xfi3p601	309	3	before	before	RB
cord-004615-xfi3p601	309	4	,	,	,
cord-004615-xfi3p601	309	5	we	-PRON-	PRP
cord-004615-xfi3p601	309	6	can	can	MD
cord-004615-xfi3p601	309	7	compute	compute	VB
cord-004615-xfi3p601	309	8	q(N	q(N	NNP
cord-004615-xfi3p601	309	9	+	+	SYM
cord-004615-xfi3p601	309	10	1	1	CD
cord-004615-xfi3p601	309	11	)	)	-RRB-
cord-004615-xfi3p601	309	12	by	by	IN
cord-004615-xfi3p601	309	13	the	the	DT
cord-004615-xfi3p601	309	14	ordinary	ordinary	JJ
cord-004615-xfi3p601	309	15	theory	theory	NN
cord-004615-xfi3p601	309	16	of	of	IN
cord-004615-xfi3p601	309	17	branching	branch	VBG
cord-004615-xfi3p601	309	18	processes	process	NNS
cord-004615-xfi3p601	309	19	.	.	.
cord-004615-xfi3p601	310	1	We	-PRON-	PRP
cord-004615-xfi3p601	310	2	use	use	VBP
cord-004615-xfi3p601	310	3	backward	backward	JJ
cord-004615-xfi3p601	310	4	iteration	iteration	NN
cord-004615-xfi3p601	310	5	to	to	TO
cord-004615-xfi3p601	310	6	compute	compute	VB
cord-004615-xfi3p601	310	7	q(0	q(0	NNP
cord-004615-xfi3p601	310	8	)	)	-RRB-
cord-004615-xfi3p601	310	9	.	.	.
cord-004615-xfi3p601	311	1	Note	note	VB
cord-004615-xfi3p601	311	2	that	that	IN
cord-004615-xfi3p601	311	3	we	-PRON-	PRP
cord-004615-xfi3p601	311	4	also	also	RB
cord-004615-xfi3p601	311	5	know	know	VBP
cord-004615-xfi3p601	311	6	the	the	DT
cord-004615-xfi3p601	311	7	probability	probability	NN
cord-004615-xfi3p601	311	8	of	of	IN
cord-004615-xfi3p601	311	9	extinction	extinction	NN
cord-004615-xfi3p601	311	10	for	for	IN
cord-004615-xfi3p601	311	11	herds	herd	NNS
cord-004615-xfi3p601	311	12	infected	infect	VBN
cord-004615-xfi3p601	311	13	after	after	IN
cord-004615-xfi3p601	311	14	time	time	NN
cord-004615-xfi3p601	311	15	t	t	NN
cord-004615-xfi3p601	311	16	=	=	SYM
cord-004615-xfi3p601	311	17	0	0	CD
cord-004615-xfi3p601	311	18	.	.	.
cord-004615-xfi3p601	312	1	If	if	IN
cord-004615-xfi3p601	312	2	we	-PRON-	PRP
cord-004615-xfi3p601	312	3	estimate	estimate	VBP
cord-004615-xfi3p601	312	4	(	(	-LRB-
cord-004615-xfi3p601	312	5	for	for	IN
cord-004615-xfi3p601	312	6	example	example	NN
cord-004615-xfi3p601	312	7	by	by	IN
cord-004615-xfi3p601	312	8	contact	contact	NN
cord-004615-xfi3p601	312	9	tracing	trace	VBG
cord-004615-xfi3p601	312	10	)	)	-RRB-
cord-004615-xfi3p601	312	11	the	the	DT
cord-004615-xfi3p601	312	12	moment	moment	NN
cord-004615-xfi3p601	312	13	of	of	IN
cord-004615-xfi3p601	312	14	infection	infection	NN
cord-004615-xfi3p601	312	15	of	of	IN
cord-004615-xfi3p601	312	16	a	a	DT
cord-004615-xfi3p601	312	17	certain	certain	JJ
cord-004615-xfi3p601	312	18	herd	herd	NN
cord-004615-xfi3p601	312	19	,	,	,
cord-004615-xfi3p601	312	20	we	-PRON-	PRP
cord-004615-xfi3p601	312	21	can	can	MD
cord-004615-xfi3p601	312	22	use	use	VB
cord-004615-xfi3p601	312	23	this	this	DT
cord-004615-xfi3p601	312	24	information	information	NN
cord-004615-xfi3p601	312	25	to	to	TO
cord-004615-xfi3p601	312	26	improve	improve	VB
cord-004615-xfi3p601	312	27	predictions	prediction	NNS
cord-004615-xfi3p601	312	28	.	.	.
cord-004615-xfi3p601	313	1	In	in	IN
cord-004615-xfi3p601	313	2	almost	almost	RB
cord-004615-xfi3p601	313	3	the	the	DT
cord-004615-xfi3p601	313	4	same	same	JJ
cord-004615-xfi3p601	313	5	way	way	NN
cord-004615-xfi3p601	313	6	we	-PRON-	PRP
cord-004615-xfi3p601	313	7	can	can	MD
cord-004615-xfi3p601	313	8	calculate	calculate	VB
cord-004615-xfi3p601	313	9	the	the	DT
cord-004615-xfi3p601	313	10	expected	expect	VBN
cord-004615-xfi3p601	313	11	final	final	JJ
cord-004615-xfi3p601	313	12	size	size	NN
cord-004615-xfi3p601	313	13	of	of	IN
cord-004615-xfi3p601	313	14	the	the	DT
cord-004615-xfi3p601	313	15	epidemic	epidemic	NN
cord-004615-xfi3p601	313	16	i.e.	i.e.	FW
cord-004615-xfi3p601	313	17	the	the	DT
cord-004615-xfi3p601	313	18	expected	expect	VBN
cord-004615-xfi3p601	313	19	total	total	JJ
cord-004615-xfi3p601	313	20	number	number	NN
cord-004615-xfi3p601	313	21	G	g	NN
cord-004615-xfi3p601	313	22	of	of	IN
cord-004615-xfi3p601	313	23	infected	infected	JJ
cord-004615-xfi3p601	313	24	herds	herd	NNS
cord-004615-xfi3p601	313	25	.	.	.
cord-004615-xfi3p601	314	1	This	this	DT
cord-004615-xfi3p601	314	2	will	will	MD
cord-004615-xfi3p601	314	3	also	also	RB
cord-004615-xfi3p601	314	4	be	be	VB
cord-004615-xfi3p601	314	5	done	do	VBN
cord-004615-xfi3p601	314	6	for	for	IN
cord-004615-xfi3p601	314	7	only	only	RB
cord-004615-xfi3p601	314	8	one	one	CD
cord-004615-xfi3p601	314	9	type	type	NN
cord-004615-xfi3p601	314	10	of	of	IN
cord-004615-xfi3p601	314	11	herd	herd	NN
cord-004615-xfi3p601	314	12	.	.	.
cord-004615-xfi3p601	315	1	If	if	IN
cord-004615-xfi3p601	315	2	q	q	NNP
cord-004615-xfi3p601	315	3	<	<	XX
cord-004615-xfi3p601	315	4	1	1	CD
cord-004615-xfi3p601	315	5	,	,	,
cord-004615-xfi3p601	315	6	there	there	EX
cord-004615-xfi3p601	315	7	is	be	VBZ
cord-004615-xfi3p601	315	8	a	a	DT
cord-004615-xfi3p601	315	9	positive	positive	JJ
cord-004615-xfi3p601	315	10	probability	probability	NN
cord-004615-xfi3p601	315	11	for	for	IN
cord-004615-xfi3p601	315	12	the	the	DT
cord-004615-xfi3p601	315	13	final	final	JJ
cord-004615-xfi3p601	315	14	size	size	NN
cord-004615-xfi3p601	315	15	to	to	TO
cord-004615-xfi3p601	315	16	be	be	VB
cord-004615-xfi3p601	315	17	infinite	infinite	JJ
cord-004615-xfi3p601	315	18	and	and	CC
cord-004615-xfi3p601	315	19	therefore	therefore	RB
cord-004615-xfi3p601	315	20	the	the	DT
cord-004615-xfi3p601	315	21	expected	expect	VBN
cord-004615-xfi3p601	315	22	final	final	JJ
cord-004615-xfi3p601	315	23	size	size	NN
cord-004615-xfi3p601	315	24	will	will	MD
cord-004615-xfi3p601	315	25	always	always	RB
cord-004615-xfi3p601	315	26	be	be	VB
cord-004615-xfi3p601	315	27	infinite	infinite	JJ
cord-004615-xfi3p601	315	28	;	;	:
cord-004615-xfi3p601	315	29	so	so	RB
cord-004615-xfi3p601	315	30	to	to	TO
cord-004615-xfi3p601	315	31	have	have	VB
cord-004615-xfi3p601	315	32	the	the	DT
cord-004615-xfi3p601	315	33	possibility	possibility	NN
cord-004615-xfi3p601	315	34	of	of	IN
cord-004615-xfi3p601	315	35	a	a	DT
cord-004615-xfi3p601	315	36	finite	finite	JJ
cord-004615-xfi3p601	315	37	expected	expect	VBN
cord-004615-xfi3p601	315	38	final	final	JJ
cord-004615-xfi3p601	315	39	size	size	NN
cord-004615-xfi3p601	315	40	we	-PRON-	PRP
cord-004615-xfi3p601	315	41	assume	assume	VBP
cord-004615-xfi3p601	315	42	q	q	NNP
cord-004615-xfi3p601	315	43	=	=	SYM
cord-004615-xfi3p601	315	44	1	1	CD
cord-004615-xfi3p601	315	45	.	.	.
cord-004615-xfi3p601	316	1	We	-PRON-	PRP
cord-004615-xfi3p601	316	2	denote	denote	VBP
cord-004615-xfi3p601	316	3	by	by	IN
cord-004615-xfi3p601	316	4	G(t	g(t	CD
cord-004615-xfi3p601	316	5	)	)	-RRB-
cord-004615-xfi3p601	317	1	the	the	DT
cord-004615-xfi3p601	317	2	size	size	NN
cord-004615-xfi3p601	317	3	of	of	IN
cord-004615-xfi3p601	317	4	the	the	DT
cord-004615-xfi3p601	317	5	progeny	progeny	NN
cord-004615-xfi3p601	317	6	of	of	IN
cord-004615-xfi3p601	317	7	a	a	DT
cord-004615-xfi3p601	317	8	particular	particular	JJ
cord-004615-xfi3p601	317	9	herd	herd	NN
cord-004615-xfi3p601	317	10	,	,	,
cord-004615-xfi3p601	317	11	infected	infect	VBN
cord-004615-xfi3p601	317	12	at	at	IN
cord-004615-xfi3p601	317	13	time	time	NN
cord-004615-xfi3p601	317	14	t	t	NNP
cord-004615-xfi3p601	317	15	(	(	-LRB-
cord-004615-xfi3p601	317	16	including	include	VBG
cord-004615-xfi3p601	317	17	this	this	DT
cord-004615-xfi3p601	317	18	ancestor	ancestor	NN
cord-004615-xfi3p601	317	19	)	)	-RRB-
cord-004615-xfi3p601	317	20	and	and	CC
cord-004615-xfi3p601	317	21	write	write	VB
cord-004615-xfi3p601	317	22	G(0	g(0	NN
cord-004615-xfi3p601	317	23	)	)	-RRB-
cord-004615-xfi3p601	317	24	=	=	NFP
cord-004615-xfi3p601	318	1	G.	G.	NNP
cord-004615-xfi3p601	319	1	The	the	DT
cord-004615-xfi3p601	319	2	expected	expect	VBN
cord-004615-xfi3p601	319	3	number	number	NN
cord-004615-xfi3p601	319	4	of	of	IN
cord-004615-xfi3p601	319	5	herds	herd	NNS
cord-004615-xfi3p601	319	6	in	in	IN
cord-004615-xfi3p601	319	7	the	the	DT
cord-004615-xfi3p601	319	8	progeny	progeny	NN
cord-004615-xfi3p601	319	9	of	of	IN
cord-004615-xfi3p601	319	10	herd	herd	NN
cord-004615-xfi3p601	319	11	X	x	NN
cord-004615-xfi3p601	319	12	,	,	,
cord-004615-xfi3p601	319	13	including	include	VBG
cord-004615-xfi3p601	319	14	X	x	NN
cord-004615-xfi3p601	319	15	itself	-PRON-	PRP
cord-004615-xfi3p601	319	16	,	,	,
cord-004615-xfi3p601	319	17	is	be	VBZ
cord-004615-xfi3p601	319	18	1	1	CD
cord-004615-xfi3p601	319	19	plus	plus	CC
cord-004615-xfi3p601	319	20	the	the	DT
cord-004615-xfi3p601	319	21	sum	sum	NN
cord-004615-xfi3p601	319	22	of	of	IN
cord-004615-xfi3p601	319	23	the	the	DT
cord-004615-xfi3p601	319	24	expected	expect	VBN
cord-004615-xfi3p601	319	25	size	size	NN
cord-004615-xfi3p601	319	26	of	of	IN
cord-004615-xfi3p601	319	27	the	the	DT
cord-004615-xfi3p601	319	28	progenies	progeny	NNS
cord-004615-xfi3p601	319	29	of	of	IN
cord-004615-xfi3p601	319	30	all	all	DT
cord-004615-xfi3p601	319	31	herds	herd	NNS
cord-004615-xfi3p601	319	32	infected	infect	VBN
cord-004615-xfi3p601	319	33	by	by	IN
cord-004615-xfi3p601	319	34	this	this	DT
cord-004615-xfi3p601	319	35	X	x	NN
cord-004615-xfi3p601	319	36	,	,	,
cord-004615-xfi3p601	320	1	i.e.	i.e.	FW
cord-004615-xfi3p601	320	2	Where	where	WRB
cord-004615-xfi3p601	320	3	the	the	DT
cord-004615-xfi3p601	320	4	t	t	NN
cord-004615-xfi3p601	321	1	i	i	PRP
cord-004615-xfi3p601	321	2	's	's	POS
cord-004615-xfi3p601	321	3	are	be	VBP
cord-004615-xfi3p601	321	4	again	again	RB
cord-004615-xfi3p601	321	5	the	the	DT
cord-004615-xfi3p601	321	6	random	random	JJ
cord-004615-xfi3p601	321	7	times	time	NNS
cord-004615-xfi3p601	321	8	at	at	IN
cord-004615-xfi3p601	321	9	which	which	WDT
cord-004615-xfi3p601	321	10	infections	infection	NNS
cord-004615-xfi3p601	321	11	by	by	IN
cord-004615-xfi3p601	321	12	the	the	DT
cord-004615-xfi3p601	321	13	element	element	NN
cord-004615-xfi3p601	321	14	,	,	,
cord-004615-xfi3p601	321	15	infected	infect	VBN
cord-004615-xfi3p601	321	16	on	on	IN
cord-004615-xfi3p601	321	17	time	time	NN
cord-004615-xfi3p601	321	18	t	t	NN
cord-004615-xfi3p601	321	19	,	,	,
cord-004615-xfi3p601	321	20	occur	occur	VBP
cord-004615-xfi3p601	321	21	.	.	.
cord-004615-xfi3p601	322	1	The	the	DT
cord-004615-xfi3p601	322	2	empty	empty	JJ
cord-004615-xfi3p601	322	3	sum	sum	NN
cord-004615-xfi3p601	322	4	is	be	VBZ
cord-004615-xfi3p601	322	5	defined	define	VBN
cord-004615-xfi3p601	322	6	to	to	TO
cord-004615-xfi3p601	322	7	be	be	VB
cord-004615-xfi3p601	322	8	equal	equal	JJ
cord-004615-xfi3p601	322	9	to	to	IN
cord-004615-xfi3p601	322	10	0	0	CD
cord-004615-xfi3p601	322	11	.	.	.
cord-004615-xfi3p601	323	1	In	in	IN
cord-004615-xfi3p601	323	2	the	the	DT
cord-004615-xfi3p601	323	3	same	same	JJ
cord-004615-xfi3p601	323	4	way	way	NN
cord-004615-xfi3p601	323	5	as	as	IN
cord-004615-xfi3p601	323	6	we	-PRON-	PRP
cord-004615-xfi3p601	323	7	deduced	deduce	VBD
cord-004615-xfi3p601	323	8	the	the	DT
cord-004615-xfi3p601	323	9	formulae	formula	NNS
cord-004615-xfi3p601	323	10	for	for	IN
cord-004615-xfi3p601	323	11	q(i	q(i	NNP
cord-004615-xfi3p601	323	12	)	)	-RRB-
cord-004615-xfi3p601	323	13	we	-PRON-	PRP
cord-004615-xfi3p601	323	14	deduce	deduce	VBP
cord-004615-xfi3p601	323	15	the	the	DT
cord-004615-xfi3p601	323	16	formulae	formula	NNS
cord-004615-xfi3p601	323	17	for	for	IN
cord-004615-xfi3p601	323	18	E(G(i	E(G(i	NNP
cord-004615-xfi3p601	323	19	)	)	-RRB-
cord-004615-xfi3p601	323	20	)	)	-RRB-
cord-004615-xfi3p601	323	21	in	in	IN
cord-004615-xfi3p601	323	22	the	the	DT
cord-004615-xfi3p601	323	23	discrete	discrete	JJ
cord-004615-xfi3p601	323	24	approximation	approximation	NN
cord-004615-xfi3p601	323	25	.	.	.
cord-004615-xfi3p601	324	1	We	-PRON-	PRP
cord-004615-xfi3p601	324	2	writeḠ(i	writeḡ(i	RB
cord-004615-xfi3p601	324	3	)	)	-RRB-
cord-004615-xfi3p601	324	4	for	for	IN
cord-004615-xfi3p601	324	5	E(G(i	E(G(i	NNP
cord-004615-xfi3p601	324	6	)	)	-RRB-
cord-004615-xfi3p601	324	7	)	)	-RRB-
cord-004615-xfi3p601	324	8	:	:	:
cord-004615-xfi3p601	324	9	For	for	IN
cord-004615-xfi3p601	324	10	α	α	NN
cord-004615-xfi3p601	324	11	>	>	XX
cord-004615-xfi3p601	324	12	β	β	XX
cord-004615-xfi3p601	324	13	,	,	,
cord-004615-xfi3p601	324	14	Ḡ(N	ḡ(n	JJ
cord-004615-xfi3p601	324	15	+	+	SYM
cord-004615-xfi3p601	324	16	1	1	CD
cord-004615-xfi3p601	324	17	)	)	-RRB-
cord-004615-xfi3p601	324	18	is	be	VBZ
cord-004615-xfi3p601	324	19	known	know	VBN
cord-004615-xfi3p601	324	20	from	from	IN
cord-004615-xfi3p601	324	21	the	the	DT
cord-004615-xfi3p601	324	22	ordinary	ordinary	JJ
cord-004615-xfi3p601	324	23	theory	theory	NN
cord-004615-xfi3p601	324	24	of	of	IN
cord-004615-xfi3p601	324	25	branching	branch	VBG
cord-004615-xfi3p601	324	26	processes	process	NNS
cord-004615-xfi3p601	324	27	(	(	-LRB-
cord-004615-xfi3p601	324	28	see	see	VB
cord-004615-xfi3p601	324	29	e.g.	e.g.	JJ
cord-004615-xfi3p601	324	30	[	[	-LRB-
cord-004615-xfi3p601	324	31	4	4	CD
cord-004615-xfi3p601	324	32	]	]	-RRB-
cord-004615-xfi3p601	324	33	):	):	XX
cord-004615-xfi3p601	324	34	for	for	IN
cord-004615-xfi3p601	324	35	φ(N	φ(n	NN
cord-004615-xfi3p601	324	36	+	+	SYM
cord-004615-xfi3p601	324	37	1	1	CD
cord-004615-xfi3p601	324	38	)	)	-RRB-
cord-004615-xfi3p601	324	39	=	=	NFP
cord-004615-xfi3p601	325	1	1,Ḡ(N	1,Ḡ(N	NNP
cord-004615-xfi3p601	325	2	+	+	SYM
cord-004615-xfi3p601	325	3	1	1	CD
cord-004615-xfi3p601	325	4	)	)	-RRB-
cord-004615-xfi3p601	325	5	=	=	NFP
cord-004615-xfi3p601	326	1	α	α	NNP
cord-004615-xfi3p601	326	2	α−β	α−β	NNS
cord-004615-xfi3p601	326	3	.	.	.
cord-004615-xfi3p601	327	1	We	-PRON-	PRP
cord-004615-xfi3p601	327	2	will	will	MD
cord-004615-xfi3p601	327	3	give	give	VB
cord-004615-xfi3p601	327	4	the	the	DT
cord-004615-xfi3p601	327	5	generating	generating	NN
cord-004615-xfi3p601	327	6	function	function	NN
cord-004615-xfi3p601	327	7	for	for	IN
cord-004615-xfi3p601	327	8	the	the	DT
cord-004615-xfi3p601	327	9	number	number	NN
cord-004615-xfi3p601	327	10	of	of	IN
cord-004615-xfi3p601	327	11	infective	infective	JJ
cord-004615-xfi3p601	327	12	and	and	CC
cord-004615-xfi3p601	327	13	infected	infected	JJ
cord-004615-xfi3p601	327	14	herds	herd	NNS
cord-004615-xfi3p601	327	15	at	at	IN
cord-004615-xfi3p601	327	16	any	any	DT
cord-004615-xfi3p601	327	17	given	give	VBN
cord-004615-xfi3p601	327	18	moment	moment	NN
cord-004615-xfi3p601	327	19	.	.	.
cord-004615-xfi3p601	328	1	Here	here	RB
cord-004615-xfi3p601	328	2	we	-PRON-	PRP
cord-004615-xfi3p601	328	3	will	will	MD
cord-004615-xfi3p601	328	4	consider	consider	VB
cord-004615-xfi3p601	328	5	the	the	DT
cord-004615-xfi3p601	328	6	generating	generate	VBG
cord-004615-xfi3p601	328	7	function	function	NN
cord-004615-xfi3p601	328	8	for	for	IN
cord-004615-xfi3p601	328	9	the	the	DT
cord-004615-xfi3p601	328	10	infective	infective	JJ
cord-004615-xfi3p601	328	11	and	and	CC
cord-004615-xfi3p601	328	12	infected	infected	JJ
cord-004615-xfi3p601	328	13	herds	herd	NNS
cord-004615-xfi3p601	328	14	at	at	IN
cord-004615-xfi3p601	328	15	time	time	NN
cord-004615-xfi3p601	328	16	t	t	NN
cord-004615-xfi3p601	328	17	=	=	SYM
cord-004615-xfi3p601	328	18	T	T	NNP
cord-004615-xfi3p601	328	19	,	,	,
cord-004615-xfi3p601	328	20	the	the	DT
cord-004615-xfi3p601	328	21	time	time	NN
cord-004615-xfi3p601	328	22	after	after	IN
cord-004615-xfi3p601	328	23	which	which	WDT
cord-004615-xfi3p601	328	24	the	the	DT
cord-004615-xfi3p601	328	25	parameter	parameter	NN
cord-004615-xfi3p601	328	26	values	value	NNS
cord-004615-xfi3p601	328	27	are	be	VBP
cord-004615-xfi3p601	328	28	considered	consider	VBN
cord-004615-xfi3p601	328	29	to	to	TO
cord-004615-xfi3p601	328	30	be	be	VB
cord-004615-xfi3p601	328	31	constant	constant	JJ
cord-004615-xfi3p601	328	32	.	.	.
cord-004615-xfi3p601	329	1	Remember	remember	VB
cord-004615-xfi3p601	329	2	that	that	IN
cord-004615-xfi3p601	329	3	the	the	DT
cord-004615-xfi3p601	329	4	age	age	NN
cord-004615-xfi3p601	329	5	of	of	IN
cord-004615-xfi3p601	329	6	an	an	DT
cord-004615-xfi3p601	329	7	infective	infective	JJ
cord-004615-xfi3p601	329	8	herd	herd	NN
cord-004615-xfi3p601	329	9	only	only	RB
cord-004615-xfi3p601	329	10	influences	influence	VBZ
cord-004615-xfi3p601	329	11	the	the	DT
cord-004615-xfi3p601	329	12	number	number	NN
cord-004615-xfi3p601	329	13	of	of	IN
cord-004615-xfi3p601	329	14	infective	infective	JJ
cord-004615-xfi3p601	329	15	animals	animal	NNS
cord-004615-xfi3p601	329	16	in	in	IN
cord-004615-xfi3p601	329	17	that	that	DT
cord-004615-xfi3p601	329	18	herd	herd	NN
cord-004615-xfi3p601	329	19	.	.	.
cord-004615-xfi3p601	330	1	From	from	IN
cord-004615-xfi3p601	330	2	Proposition	Proposition	NNP
cord-004615-xfi3p601	330	3	1	1	CD
cord-004615-xfi3p601	330	4	in	in	IN
cord-004615-xfi3p601	330	5	Section	section	NN
cord-004615-xfi3p601	330	6	3.1	3.1	CD
cord-004615-xfi3p601	330	7	,	,	,
cord-004615-xfi3p601	330	8	we	-PRON-	PRP
cord-004615-xfi3p601	330	9	know	know	VBP
cord-004615-xfi3p601	330	10	that	that	IN
cord-004615-xfi3p601	330	11	the	the	DT
cord-004615-xfi3p601	330	12	expected	expect	VBN
cord-004615-xfi3p601	330	13	direct	direct	JJ
cord-004615-xfi3p601	330	14	offspring	offspring	NN
cord-004615-xfi3p601	330	15	of	of	IN
cord-004615-xfi3p601	330	16	a	a	DT
cord-004615-xfi3p601	330	17	herd	herd	NN
cord-004615-xfi3p601	330	18	,	,	,
cord-004615-xfi3p601	330	19	born	bear	VBN
cord-004615-xfi3p601	330	20	after	after	IN
cord-004615-xfi3p601	330	21	t	t	NN
cord-004615-xfi3p601	330	22	=	=	SYM
cord-004615-xfi3p601	330	23	T	T	NNP
cord-004615-xfi3p601	330	24	,	,	,
cord-004615-xfi3p601	330	25	is	be	VBZ
cord-004615-xfi3p601	330	26	independent	independent	JJ
cord-004615-xfi3p601	330	27	of	of	IN
cord-004615-xfi3p601	330	28	the	the	DT
cord-004615-xfi3p601	330	29	age	age	NN
cord-004615-xfi3p601	330	30	of	of	IN
cord-004615-xfi3p601	330	31	that	that	DT
cord-004615-xfi3p601	330	32	herd	herd	NN
cord-004615-xfi3p601	330	33	,	,	,
cord-004615-xfi3p601	330	34	given	give	VBN
cord-004615-xfi3p601	330	35	that	that	IN
cord-004615-xfi3p601	330	36	the	the	DT
cord-004615-xfi3p601	330	37	herd	herd	NN
cord-004615-xfi3p601	330	38	is	be	VBZ
cord-004615-xfi3p601	330	39	not	not	RB
cord-004615-xfi3p601	330	40	yet	yet	RB
cord-004615-xfi3p601	330	41	detected	detect	VBN
cord-004615-xfi3p601	330	42	at	at	IN
cord-004615-xfi3p601	330	43	that	that	DT
cord-004615-xfi3p601	330	44	time	time	NN
cord-004615-xfi3p601	330	45	.	.	.
cord-004615-xfi3p601	331	1	Furthermore	furthermore	RB
cord-004615-xfi3p601	331	2	we	-PRON-	PRP
cord-004615-xfi3p601	331	3	know	know	VBP
cord-004615-xfi3p601	331	4	that	that	IN
cord-004615-xfi3p601	331	5	the	the	DT
cord-004615-xfi3p601	331	6	size	size	NN
cord-004615-xfi3p601	331	7	of	of	IN
cord-004615-xfi3p601	331	8	the	the	DT
cord-004615-xfi3p601	331	9	offspring	offspring	NN
cord-004615-xfi3p601	331	10	(	(	-LRB-
cord-004615-xfi3p601	331	11	infected	infect	VBN
cord-004615-xfi3p601	331	12	after	after	IN
cord-004615-xfi3p601	331	13	time	time	NN
cord-004615-xfi3p601	331	14	t	t	NN
cord-004615-xfi3p601	331	15	=	=	SYM
cord-004615-xfi3p601	331	16	T	T	NNP
cord-004615-xfi3p601	331	17	)	)	-RRB-
cord-004615-xfi3p601	331	18	of	of	IN
cord-004615-xfi3p601	331	19	a	a	DT
cord-004615-xfi3p601	331	20	herd	herd	NN
cord-004615-xfi3p601	331	21	,	,	,
cord-004615-xfi3p601	331	22	infective	infective	JJ
cord-004615-xfi3p601	331	23	at	at	IN
cord-004615-xfi3p601	331	24	that	that	DT
cord-004615-xfi3p601	331	25	time	time	NN
cord-004615-xfi3p601	331	26	,	,	,
cord-004615-xfi3p601	331	27	does	do	VBZ
cord-004615-xfi3p601	331	28	not	not	RB
cord-004615-xfi3p601	331	29	depend	depend	VB
cord-004615-xfi3p601	331	30	on	on	IN
cord-004615-xfi3p601	331	31	the	the	DT
cord-004615-xfi3p601	331	32	offspring	offspring	NN
cord-004615-xfi3p601	331	33	of	of	IN
cord-004615-xfi3p601	331	34	other	other	JJ
cord-004615-xfi3p601	331	35	herds	herd	NNS
cord-004615-xfi3p601	331	36	that	that	WDT
cord-004615-xfi3p601	331	37	are	be	VBP
cord-004615-xfi3p601	331	38	infective	infective	JJ
cord-004615-xfi3p601	331	39	at	at	IN
cord-004615-xfi3p601	331	40	time	time	NN
cord-004615-xfi3p601	331	41	t	t	NN
cord-004615-xfi3p601	331	42	=	=	SYM
cord-004615-xfi3p601	331	43	T	T	NNP
cord-004615-xfi3p601	331	44	.	.	.
cord-004615-xfi3p601	332	1	So	so	RB
cord-004615-xfi3p601	332	2	for	for	IN
cord-004615-xfi3p601	332	3	the	the	DT
cord-004615-xfi3p601	332	4	distribution	distribution	NN
cord-004615-xfi3p601	332	5	of	of	IN
cord-004615-xfi3p601	332	6	the	the	DT
cord-004615-xfi3p601	332	7	number	number	NN
cord-004615-xfi3p601	332	8	of	of	IN
cord-004615-xfi3p601	332	9	infections	infection	NNS
cord-004615-xfi3p601	332	10	after	after	IN
cord-004615-xfi3p601	332	11	time	time	NN
cord-004615-xfi3p601	332	12	t	t	NN
cord-004615-xfi3p601	332	13	=	=	SYM
cord-004615-xfi3p601	332	14	T	T	NNP
cord-004615-xfi3p601	332	15	,	,	,
cord-004615-xfi3p601	332	16	only	only	RB
cord-004615-xfi3p601	332	17	the	the	DT
cord-004615-xfi3p601	332	18	distribution	distribution	NN
cord-004615-xfi3p601	332	19	of	of	IN
cord-004615-xfi3p601	332	20	the	the	DT
cord-004615-xfi3p601	332	21	number	number	NN
cord-004615-xfi3p601	332	22	of	of	IN
cord-004615-xfi3p601	332	23	infective	infective	JJ
cord-004615-xfi3p601	332	24	herds	herd	NNS
cord-004615-xfi3p601	332	25	at	at	IN
cord-004615-xfi3p601	332	26	that	that	DT
cord-004615-xfi3p601	332	27	time	time	NN
cord-004615-xfi3p601	332	28	is	be	VBZ
cord-004615-xfi3p601	332	29	important	important	JJ
cord-004615-xfi3p601	332	30	.	.	.
cord-004615-xfi3p601	333	1	By	by	IN
cord-004615-xfi3p601	333	2	using	use	VBG
cord-004615-xfi3p601	333	3	Proposition	Proposition	NNP
cord-004615-xfi3p601	333	4	1	1	CD
cord-004615-xfi3p601	333	5	and	and	CC
cord-004615-xfi3p601	333	6	the	the	DT
cord-004615-xfi3p601	333	7	theory	theory	NN
cord-004615-xfi3p601	333	8	for	for	IN
cord-004615-xfi3p601	333	9	ordinary	ordinary	JJ
cord-004615-xfi3p601	333	10	branching	branching	NN
cord-004615-xfi3p601	333	11	processes	process	NNS
cord-004615-xfi3p601	333	12	,	,	,
cord-004615-xfi3p601	333	13	we	-PRON-	PRP
cord-004615-xfi3p601	333	14	can	can	MD
cord-004615-xfi3p601	333	15	compute	compute	VB
cord-004615-xfi3p601	333	16	everything	everything	NN
cord-004615-xfi3p601	333	17	we	-PRON-	PRP
cord-004615-xfi3p601	333	18	want	want	VBP
cord-004615-xfi3p601	333	19	to	to	TO
cord-004615-xfi3p601	333	20	know	know	VB
cord-004615-xfi3p601	333	21	.	.	.
cord-004615-xfi3p601	334	1	We	-PRON-	PRP
cord-004615-xfi3p601	334	2	will	will	MD
cord-004615-xfi3p601	334	3	determine	determine	VB
cord-004615-xfi3p601	334	4	the	the	DT
cord-004615-xfi3p601	334	5	distribution	distribution	NN
cord-004615-xfi3p601	334	6	of	of	IN
cord-004615-xfi3p601	334	7	X	x	NN
cord-004615-xfi3p601	334	8	,	,	,
cord-004615-xfi3p601	334	9	the	the	DT
cord-004615-xfi3p601	334	10	number	number	NN
cord-004615-xfi3p601	334	11	of	of	IN
cord-004615-xfi3p601	334	12	infective	infective	JJ
cord-004615-xfi3p601	334	13	herds	herd	NNS
cord-004615-xfi3p601	334	14	at	at	IN
cord-004615-xfi3p601	334	15	time	time	NN
cord-004615-xfi3p601	334	16	t	t	NN
cord-004615-xfi3p601	334	17	=	=	SYM
cord-004615-xfi3p601	334	18	T	T	NNP
cord-004615-xfi3p601	334	19	.	.	.
cord-004615-xfi3p601	335	1	X	X	NNP
cord-004615-xfi3p601	335	2	i	i	PRP
cord-004615-xfi3p601	335	3	is	be	VBZ
cord-004615-xfi3p601	335	4	the	the	DT
cord-004615-xfi3p601	335	5	number	number	NN
cord-004615-xfi3p601	335	6	of	of	IN
cord-004615-xfi3p601	335	7	infective	infective	JJ
cord-004615-xfi3p601	335	8	herds	herd	NNS
cord-004615-xfi3p601	335	9	at	at	IN
cord-004615-xfi3p601	335	10	time	time	NN
cord-004615-xfi3p601	335	11	T	T	NNP
cord-004615-xfi3p601	335	12	,	,	,
cord-004615-xfi3p601	335	13	from	from	IN
cord-004615-xfi3p601	335	14	the	the	DT
cord-004615-xfi3p601	335	15	progeny	progeny	NN
cord-004615-xfi3p601	335	16	of	of	IN
cord-004615-xfi3p601	335	17	one	one	CD
cord-004615-xfi3p601	335	18	particular	particular	JJ
cord-004615-xfi3p601	335	19	herd	herd	NN
cord-004615-xfi3p601	335	20	infected	infect	VBN
cord-004615-xfi3p601	335	21	in	in	IN
cord-004615-xfi3p601	335	22	interval	interval	NN
cord-004615-xfi3p601	335	23	i.	i.	NN
cord-004615-xfi3p601	336	1	(	(	-LRB-
cord-004615-xfi3p601	336	2	Here	here	RB
cord-004615-xfi3p601	336	3	the	the	DT
cord-004615-xfi3p601	336	4	herd	herd	NN
cord-004615-xfi3p601	336	5	itself	-PRON-	PRP
cord-004615-xfi3p601	336	6	is	be	VBZ
cord-004615-xfi3p601	336	7	a	a	DT
cord-004615-xfi3p601	336	8	part	part	NN
cord-004615-xfi3p601	336	9	of	of	IN
cord-004615-xfi3p601	336	10	its	-PRON-	PRP$
cord-004615-xfi3p601	336	11	own	own	JJ
cord-004615-xfi3p601	336	12	progeny	progeny	NN
cord-004615-xfi3p601	336	13	.	.	.
cord-004615-xfi3p601	336	14	)	)	-RRB-
cord-004615-xfi3p601	337	1	We	-PRON-	PRP
cord-004615-xfi3p601	337	2	denote	denote	VBP
cord-004615-xfi3p601	337	3	X	x	NN
cord-004615-xfi3p601	337	4	0	0	CD
cord-004615-xfi3p601	337	5	by	by	IN
cord-004615-xfi3p601	337	6	X.	X.	NNP
cord-004615-xfi3p601	338	1	We	-PRON-	PRP
cord-004615-xfi3p601	338	2	also	also	RB
cord-004615-xfi3p601	338	3	use	use	VBP
cord-004615-xfi3p601	338	4	Y	Y	NNP
cord-004615-xfi3p601	338	5	i	i	PRP
cord-004615-xfi3p601	338	6	for	for	IN
cord-004615-xfi3p601	338	7	the	the	DT
cord-004615-xfi3p601	338	8	number	number	NN
cord-004615-xfi3p601	338	9	of	of	IN
cord-004615-xfi3p601	338	10	infected	infected	JJ
cord-004615-xfi3p601	338	11	herds	herd	NNS
cord-004615-xfi3p601	338	12	in	in	IN
cord-004615-xfi3p601	338	13	the	the	DT
cord-004615-xfi3p601	338	14	progeny	progeny	NN
cord-004615-xfi3p601	338	15	of	of	IN
cord-004615-xfi3p601	338	16	a	a	DT
cord-004615-xfi3p601	338	17	particular	particular	JJ
cord-004615-xfi3p601	338	18	herd	herd	NN
cord-004615-xfi3p601	338	19	infected	infect	VBN
cord-004615-xfi3p601	338	20	in	in	IN
cord-004615-xfi3p601	338	21	interval	interval	NN
cord-004615-xfi3p601	338	22	i	i	PRP
cord-004615-xfi3p601	338	23	,	,	,
cord-004615-xfi3p601	338	24	that	that	DT
cord-004615-xfi3p601	338	25	is	be	VBZ
cord-004615-xfi3p601	338	26	detected	detect	VBN
cord-004615-xfi3p601	338	27	before	before	IN
cord-004615-xfi3p601	338	28	time	time	NN
cord-004615-xfi3p601	338	29	t	t	NN
cord-004615-xfi3p601	338	30	=	=	SYM
cord-004615-xfi3p601	338	31	T	T	NNP
cord-004615-xfi3p601	338	32	.	.	.
cord-004615-xfi3p601	339	1	The	the	DT
cord-004615-xfi3p601	339	2	generating	generate	VBG
cord-004615-xfi3p601	339	3	function	function	NN
cord-004615-xfi3p601	339	4	of	of	IN
cord-004615-xfi3p601	339	5	the	the	DT
cord-004615-xfi3p601	339	6	distribution	distribution	NN
cord-004615-xfi3p601	339	7	of	of	IN
cord-004615-xfi3p601	339	8	X	x	NN
cord-004615-xfi3p601	339	9	i	i	NNP
cord-004615-xfi3p601	339	10	and	and	CC
cord-004615-xfi3p601	339	11	Y	Y	NNP
cord-004615-xfi3p601	340	1	i	i	PRP
cord-004615-xfi3p601	340	2	is	be	VBZ
cord-004615-xfi3p601	341	1	We	-PRON-	PRP
cord-004615-xfi3p601	341	2	writeg	writeg	MD
cord-004615-xfi3p601	341	3	i	i	PRP
cord-004615-xfi3p601	341	4	(	(	-LRB-
cord-004615-xfi3p601	341	5	s	s	NNP
cord-004615-xfi3p601	341	6	1	1	CD
cord-004615-xfi3p601	341	7	,	,	,
cord-004615-xfi3p601	341	8	s	s	NN
cord-004615-xfi3p601	341	9	2	2	CD
cord-004615-xfi3p601	341	10	;	;	:
cord-004615-xfi3p601	341	11	h	h	NN
cord-004615-xfi3p601	341	12	)	)	-RRB-
cord-004615-xfi3p601	342	1	=	=	NFP
cord-004615-xfi3p601	343	1	E(s	E(s	NNP
cord-004615-xfi3p601	344	1	X	X	NNS
cord-004615-xfi3p601	344	2	i	i	NN
cord-004615-xfi3p601	344	3	1	1	CD
cord-004615-xfi3p601	345	1	s	s	NNP
cord-004615-xfi3p601	346	1	Y	Y	NNP
cord-004615-xfi3p601	347	1	i	i	PRP
cord-004615-xfi3p601	347	2	2	2	CD
cord-004615-xfi3p601	347	3	|h	|h	NN
cord-004615-xfi3p601	347	4	)	)	-RRB-
cord-004615-xfi3p601	347	5	.	.	.
cord-004615-xfi3p601	348	1	We	-PRON-	PRP
cord-004615-xfi3p601	348	2	again	again	RB
cord-004615-xfi3p601	348	3	assume	assume	VBP
cord-004615-xfi3p601	348	4	that	that	IN
cord-004615-xfi3p601	348	5	a	a	DT
cord-004615-xfi3p601	348	6	herd	herd	NN
cord-004615-xfi3p601	348	7	does	do	VBZ
cord-004615-xfi3p601	348	8	not	not	RB
cord-004615-xfi3p601	348	9	infect	infect	VB
cord-004615-xfi3p601	348	10	other	other	JJ
cord-004615-xfi3p601	348	11	herds	herd	NNS
cord-004615-xfi3p601	348	12	in	in	IN
cord-004615-xfi3p601	348	13	the	the	DT
cord-004615-xfi3p601	348	14	interval	interval	NN
cord-004615-xfi3p601	348	15	wherein	wherein	WRB
cord-004615-xfi3p601	348	16	it	-PRON-	PRP
cord-004615-xfi3p601	348	17	becomes	become	VBZ
cord-004615-xfi3p601	348	18	infected	infected	JJ
cord-004615-xfi3p601	348	19	itself	-PRON-	PRP
cord-004615-xfi3p601	348	20	.	.	.
cord-004615-xfi3p601	349	1	So	so	RB
cord-004615-xfi3p601	349	2	:	:	:
cord-004615-xfi3p601	349	3	For	for	IN
cord-004615-xfi3p601	349	4	interval	interval	NN
cord-004615-xfi3p601	349	5	N	n	NN
cord-004615-xfi3p601	349	6	we	-PRON-	PRP
cord-004615-xfi3p601	349	7	have	have	VBP
cord-004615-xfi3p601	350	1	:	:	:
cord-004615-xfi3p601	350	2	Now	now	RB
cord-004615-xfi3p601	350	3	we	-PRON-	PRP
cord-004615-xfi3p601	350	4	can	can	MD
cord-004615-xfi3p601	350	5	determineg	determineg	VB
cord-004615-xfi3p601	350	6	0	0	CD
cord-004615-xfi3p601	350	7	(	(	-LRB-
cord-004615-xfi3p601	350	8	s	s	NN
cord-004615-xfi3p601	350	9	1	1	CD
cord-004615-xfi3p601	350	10	,	,	,
cord-004615-xfi3p601	350	11	s	s	NN
cord-004615-xfi3p601	350	12	2	2	CD
cord-004615-xfi3p601	350	13	)	)	-RRB-
cord-004615-xfi3p601	350	14	point	point	NN
cord-004615-xfi3p601	350	15	wise	wise	JJ
cord-004615-xfi3p601	350	16	.	.	.
cord-004615-xfi3p601	351	1	Note	note	VB
cord-004615-xfi3p601	351	2	that	that	IN
cord-004615-xfi3p601	351	3	we	-PRON-	PRP
cord-004615-xfi3p601	351	4	only	only	RB
cord-004615-xfi3p601	351	5	need	need	VBP
cord-004615-xfi3p601	351	6	to	to	TO
cord-004615-xfi3p601	351	7	computẽ	computẽ	VB
cord-004615-xfi3p601	351	8	g	g	NNP
cord-004615-xfi3p601	351	9	0	0	CD
cord-004615-xfi3p601	351	10	(	(	-LRB-
cord-004615-xfi3p601	351	11	s	s	NNP
cord-004615-xfi3p601	351	12	1	1	CD
cord-004615-xfi3p601	351	13	,	,	,
cord-004615-xfi3p601	351	14	s	s	NN
cord-004615-xfi3p601	351	15	2	2	CD
cord-004615-xfi3p601	351	16	)	)	-RRB-
cord-004615-xfi3p601	351	17	in	in	IN
cord-004615-xfi3p601	351	18	m	m	CD
cord-004615-xfi3p601	351	19	+	+	SYM
cord-004615-xfi3p601	351	20	1	1	CD
cord-004615-xfi3p601	351	21	points	point	NNS
cord-004615-xfi3p601	351	22	to	to	TO
cord-004615-xfi3p601	351	23	give	give	VB
cord-004615-xfi3p601	351	24	a	a	DT
cord-004615-xfi3p601	351	25	good	good	JJ
cord-004615-xfi3p601	351	26	approximation	approximation	NN
cord-004615-xfi3p601	351	27	of	of	IN
cord-004615-xfi3p601	351	28	the	the	DT
cord-004615-xfi3p601	351	29	first	first	JJ
cord-004615-xfi3p601	351	30	m	m	CD
cord-004615-xfi3p601	351	31	derivatives	derivative	NNS
cord-004615-xfi3p601	351	32	of	of	IN
cord-004615-xfi3p601	351	33	this	this	DT
cord-004615-xfi3p601	351	34	function	function	NN
cord-004615-xfi3p601	351	35	for	for	IN
cord-004615-xfi3p601	351	36	a	a	DT
cord-004615-xfi3p601	351	37	certain	certain	JJ
cord-004615-xfi3p601	351	38	point	point	NN
cord-004615-xfi3p601	351	39	.	.	.
cord-004615-xfi3p601	352	1	With	with	IN
cord-004615-xfi3p601	352	2	this	this	DT
cord-004615-xfi3p601	352	3	derivatives	derivative	NNS
cord-004615-xfi3p601	352	4	we	-PRON-	PRP
cord-004615-xfi3p601	352	5	are	be	VBP
cord-004615-xfi3p601	352	6	able	able	JJ
cord-004615-xfi3p601	352	7	to	to	TO
cord-004615-xfi3p601	352	8	compute	compute	VB
cord-004615-xfi3p601	352	9	the	the	DT
cord-004615-xfi3p601	352	10	first	first	JJ
cord-004615-xfi3p601	352	11	m	m	NNP
cord-004615-xfi3p601	352	12	moments	moment	NNS
cord-004615-xfi3p601	352	13	of	of	IN
cord-004615-xfi3p601	352	14	the	the	DT
cord-004615-xfi3p601	352	15	size	size	NN
cord-004615-xfi3p601	352	16	at	at	IN
cord-004615-xfi3p601	352	17	time	time	NN
cord-004615-xfi3p601	352	18	t	t	NN
cord-004615-xfi3p601	352	19	=	=	SYM
cord-004615-xfi3p601	352	20	T	T	NNP
cord-004615-xfi3p601	352	21	or	or	CC
cord-004615-xfi3p601	352	22	to	to	TO
cord-004615-xfi3p601	352	23	approximate	approximate	VB
cord-004615-xfi3p601	352	24	P(X	P(X	NNP
cord-004615-xfi3p601	352	25	=	=	SYM
cord-004615-xfi3p601	352	26	n	n	NN
cord-004615-xfi3p601	352	27	)	)	-RRB-
cord-004615-xfi3p601	352	28	for	for	IN
cord-004615-xfi3p601	352	29	all	all	DT
cord-004615-xfi3p601	352	30	n	n	NNP
cord-004615-xfi3p601	352	31	≤	≤	NN
cord-004615-xfi3p601	352	32	m.	m.	NN
cord-004615-xfi3p601	353	1	With	with	IN
cord-004615-xfi3p601	353	2	this	this	DT
cord-004615-xfi3p601	353	3	generating	generating	NN
cord-004615-xfi3p601	353	4	function	function	NN
cord-004615-xfi3p601	353	5	we	-PRON-	PRP
cord-004615-xfi3p601	353	6	can	can	MD
cord-004615-xfi3p601	353	7	also	also	RB
cord-004615-xfi3p601	353	8	compute	compute	VB
cord-004615-xfi3p601	353	9	the	the	DT
cord-004615-xfi3p601	353	10	probability	probability	NN
cord-004615-xfi3p601	353	11	of	of	IN
cord-004615-xfi3p601	353	12	extinction	extinction	NN
cord-004615-xfi3p601	353	13	and	and	CC
cord-004615-xfi3p601	353	14	the	the	DT
cord-004615-xfi3p601	353	15	expected	expect	VBN
cord-004615-xfi3p601	353	16	final	final	JJ
cord-004615-xfi3p601	353	17	size	size	NN
cord-004615-xfi3p601	353	18	of	of	IN
cord-004615-xfi3p601	353	19	the	the	DT
cord-004615-xfi3p601	353	20	epidemic	epidemic	NN
cord-004615-xfi3p601	353	21	.	.	.
cord-004615-xfi3p601	354	1	We	-PRON-	PRP
cord-004615-xfi3p601	354	2	can	can	MD
cord-004615-xfi3p601	354	3	use	use	VB
cord-004615-xfi3p601	354	4	the	the	DT
cord-004615-xfi3p601	354	5	same	same	JJ
cord-004615-xfi3p601	354	6	reasoning	reasoning	NN
cord-004615-xfi3p601	354	7	as	as	IN
cord-004615-xfi3p601	354	8	before	before	RB
cord-004615-xfi3p601	354	9	.	.	.
cord-004615-xfi3p601	355	1	The	the	DT
cord-004615-xfi3p601	355	2	progenies	progeny	NNS
cord-004615-xfi3p601	355	3	of	of	IN
cord-004615-xfi3p601	355	4	all	all	DT
cord-004615-xfi3p601	355	5	herds	herd	NNS
cord-004615-xfi3p601	355	6	,	,	,
cord-004615-xfi3p601	355	7	infective	infective	JJ
cord-004615-xfi3p601	355	8	at	at	IN
cord-004615-xfi3p601	355	9	time	time	NN
cord-004615-xfi3p601	355	10	t	t	NN
cord-004615-xfi3p601	355	11	=	=	SYM
cord-004615-xfi3p601	355	12	T	T	NNP
cord-004615-xfi3p601	355	13	have	have	VBP
cord-004615-xfi3p601	355	14	to	to	TO
cord-004615-xfi3p601	355	15	go	go	VB
cord-004615-xfi3p601	355	16	extinct	extinct	JJ
cord-004615-xfi3p601	355	17	.	.	.
cord-004615-xfi3p601	356	1	This	this	DT
cord-004615-xfi3p601	356	2	occurs	occur	VBZ
cord-004615-xfi3p601	356	3	with	with	IN
cord-004615-xfi3p601	356	4	probability	probability	NN
cord-004615-xfi3p601	356	5	q	q	NN
cord-004615-xfi3p601	356	6	X	x	NN
cord-004615-xfi3p601	356	7	0	0	CD
cord-004615-xfi3p601	356	8	.	.	.
cord-004615-xfi3p601	357	1	So	so	RB
cord-004615-xfi3p601	357	2	the	the	DT
cord-004615-xfi3p601	357	3	probability	probability	NN
cord-004615-xfi3p601	357	4	of	of	IN
cord-004615-xfi3p601	357	5	extinction	extinction	NN
cord-004615-xfi3p601	357	6	is	be	VBZ
cord-004615-xfi3p601	357	7	∞	∞	NNP
cord-004615-xfi3p601	357	8	k=0	k=0	RB
cord-004615-xfi3p601	357	9	P(X	p(x	NN
cord-004615-xfi3p601	357	10	0	0	NFP
cord-004615-xfi3p601	357	11	=	=	NFP
cord-004615-xfi3p601	357	12	k)(q(N	k)(q(n	NN
cord-004615-xfi3p601	358	1	+	+	CC
cord-004615-xfi3p601	358	2	1	1	CD
cord-004615-xfi3p601	358	3	)	)	-RRB-
cord-004615-xfi3p601	358	4	)	)	-RRB-
cord-004615-xfi3p601	359	1	k	k	NNP
cord-004615-xfi3p601	360	1	=	=	SYM
cord-004615-xfi3p601	360	2	g	g	NN
cord-004615-xfi3p601	360	3	0	0	NFP
cord-004615-xfi3p601	360	4	(	(	-LRB-
cord-004615-xfi3p601	360	5	q(N	q(N	NNP
cord-004615-xfi3p601	360	6	+	+	SYM
cord-004615-xfi3p601	360	7	1	1	CD
cord-004615-xfi3p601	360	8	)	)	-RRB-
cord-004615-xfi3p601	360	9	,	,	,
cord-004615-xfi3p601	360	10	1	1	CD
cord-004615-xfi3p601	360	11	)	)	-RRB-
cord-004615-xfi3p601	360	12	.	.	.
cord-004615-xfi3p601	361	1	Note	note	VB
cord-004615-xfi3p601	361	2	that	that	IN
cord-004615-xfi3p601	361	3	with	with	IN
cord-004615-xfi3p601	361	4	these	these	DT
cord-004615-xfi3p601	361	5	s	s	NN
cord-004615-xfi3p601	361	6	1	1	CD
cord-004615-xfi3p601	361	7	and	and	CC
cord-004615-xfi3p601	361	8	s	s	NN
cord-004615-xfi3p601	361	9	2	2	CD
cord-004615-xfi3p601	361	10	the	the	DT
cord-004615-xfi3p601	361	11	model	model	NN
cord-004615-xfi3p601	361	12	is	be	VBZ
cord-004615-xfi3p601	361	13	exactly	exactly	RB
cord-004615-xfi3p601	361	14	the	the	DT
cord-004615-xfi3p601	361	15	same	same	JJ
cord-004615-xfi3p601	361	16	as	as	IN
cord-004615-xfi3p601	361	17	the	the	DT
cord-004615-xfi3p601	361	18	model	model	NN
cord-004615-xfi3p601	361	19	in	in	IN
cord-004615-xfi3p601	361	20	Section	section	NN
cord-004615-xfi3p601	361	21	4.2	4.2	CD
cord-004615-xfi3p601	361	22	.	.	.
cord-004615-xfi3p601	362	1	For	for	IN
cord-004615-xfi3p601	362	2	the	the	DT
cord-004615-xfi3p601	362	3	expected	expect	VBN
cord-004615-xfi3p601	362	4	final	final	JJ
cord-004615-xfi3p601	362	5	size	size	NN
cord-004615-xfi3p601	362	6	we	-PRON-	PRP
cord-004615-xfi3p601	362	7	add	add	VBP
cord-004615-xfi3p601	362	8	the	the	DT
cord-004615-xfi3p601	362	9	expected	expect	VBN
cord-004615-xfi3p601	362	10	number	number	NN
cord-004615-xfi3p601	362	11	of	of	IN
cord-004615-xfi3p601	362	12	infected	infected	JJ
cord-004615-xfi3p601	362	13	herds	herd	NNS
cord-004615-xfi3p601	362	14	,	,	,
cord-004615-xfi3p601	362	15	already	already	RB
cord-004615-xfi3p601	362	16	detected	detect	VBN
cord-004615-xfi3p601	362	17	,	,	,
cord-004615-xfi3p601	362	18	to	to	IN
cord-004615-xfi3p601	362	19	the	the	DT
cord-004615-xfi3p601	362	20	expected	expect	VBN
cord-004615-xfi3p601	362	21	size	size	NN
cord-004615-xfi3p601	362	22	of	of	IN
cord-004615-xfi3p601	362	23	the	the	DT
cord-004615-xfi3p601	362	24	progeny	progeny	NN
cord-004615-xfi3p601	362	25	of	of	IN
cord-004615-xfi3p601	362	26	all	all	PDT
cord-004615-xfi3p601	362	27	the	the	DT
cord-004615-xfi3p601	362	28	infective	infective	JJ
cord-004615-xfi3p601	362	29	herds	herd	NNS
cord-004615-xfi3p601	362	30	at	at	IN
cord-004615-xfi3p601	362	31	time	time	NN
cord-004615-xfi3p601	362	32	t	t	NN
cord-004615-xfi3p601	362	33	=	=	SYM
cord-004615-xfi3p601	362	34	T	T	NNP
cord-004615-xfi3p601	362	35	(	(	-LRB-
cord-004615-xfi3p601	362	36	again	again	RB
cord-004615-xfi3p601	362	37	including	include	VBG
cord-004615-xfi3p601	362	38	the	the	DT
cord-004615-xfi3p601	362	39	herds	herd	NNS
cord-004615-xfi3p601	362	40	infective	infective	JJ
cord-004615-xfi3p601	362	41	at	at	IN
cord-004615-xfi3p601	362	42	that	that	DT
cord-004615-xfi3p601	362	43	time	time	NN
cord-004615-xfi3p601	362	44	)	)	-RRB-
cord-004615-xfi3p601	362	45	.	.	.
cord-004615-xfi3p601	363	1	This	this	DT
cord-004615-xfi3p601	363	2	is	be	VBZ
cord-004615-xfi3p601	363	3	d	d	XX
cord-004615-xfi3p601	363	4	.	.	.
cord-004615-xfi3p601	364	1	We	-PRON-	PRP
cord-004615-xfi3p601	364	2	can	can	MD
cord-004615-xfi3p601	364	3	only	only	RB
cord-004615-xfi3p601	364	4	use	use	VB
cord-004615-xfi3p601	364	5	this	this	DT
cord-004615-xfi3p601	364	6	property	property	NN
cord-004615-xfi3p601	364	7	if	if	IN
cord-004615-xfi3p601	364	8	after	after	IN
cord-004615-xfi3p601	364	9	time	time	NN
cord-004615-xfi3p601	364	10	t	t	NN
cord-004615-xfi3p601	364	11	=	=	SYM
cord-004615-xfi3p601	364	12	T	T	NNP
cord-004615-xfi3p601	364	13	the	the	DT
cord-004615-xfi3p601	364	14	infection	infection	NN
cord-004615-xfi3p601	364	15	and	and	CC
cord-004615-xfi3p601	364	16	detection	detection	NN
cord-004615-xfi3p601	364	17	rate	rate	NN
cord-004615-xfi3p601	364	18	are	be	VBP
cord-004615-xfi3p601	364	19	proportional	proportional	JJ
cord-004615-xfi3p601	364	20	to	to	IN
cord-004615-xfi3p601	364	21	each	each	DT
cord-004615-xfi3p601	364	22	other	other	JJ
cord-004615-xfi3p601	364	23	,	,	,
cord-004615-xfi3p601	364	24	because	because	IN
cord-004615-xfi3p601	364	25	otherwise	otherwise	RB
cord-004615-xfi3p601	364	26	we	-PRON-	PRP
cord-004615-xfi3p601	364	27	need	need	VBP
cord-004615-xfi3p601	364	28	to	to	TO
cord-004615-xfi3p601	364	29	know	know	VB
cord-004615-xfi3p601	364	30	the	the	DT
cord-004615-xfi3p601	364	31	ages	age	NNS
cord-004615-xfi3p601	364	32	of	of	IN
cord-004615-xfi3p601	364	33	the	the	DT
cord-004615-xfi3p601	364	34	infective	infective	JJ
cord-004615-xfi3p601	364	35	herds	herd	NNS
cord-004615-xfi3p601	364	36	at	at	IN
cord-004615-xfi3p601	364	37	time	time	NN
cord-004615-xfi3p601	364	38	t	t	NN
cord-004615-xfi3p601	364	39	=	=	SYM
cord-004615-xfi3p601	364	40	T	T	NNP
cord-004615-xfi3p601	364	41	.	.	.
cord-004615-xfi3p601	365	1	In	in	IN
cord-004615-xfi3p601	365	2	a	a	DT
cord-004615-xfi3p601	365	3	non	non	JJ
cord-004615-xfi3p601	365	4	-	-	JJ
cord-004615-xfi3p601	365	5	varying	varying	JJ
cord-004615-xfi3p601	365	6	environment	environment	NN
cord-004615-xfi3p601	365	7	,	,	,
cord-004615-xfi3p601	365	8	we	-PRON-	PRP
cord-004615-xfi3p601	365	9	know	know	VBP
cord-004615-xfi3p601	365	10	for	for	IN
cord-004615-xfi3p601	365	11	q	q	NN
cord-004615-xfi3p601	365	12	=	=	SYM
cord-004615-xfi3p601	365	13	1	1	CD
cord-004615-xfi3p601	365	14	the	the	DT
cord-004615-xfi3p601	365	15	"	"	``
cord-004615-xfi3p601	365	16	speed	speed	NN
cord-004615-xfi3p601	365	17	"	"	''
cord-004615-xfi3p601	365	18	at	at	IN
cord-004615-xfi3p601	365	19	which	which	WDT
cord-004615-xfi3p601	365	20	P(Z(t	P(Z(t	NNP
cord-004615-xfi3p601	365	21	)	)	-RRB-
cord-004615-xfi3p601	365	22	>	>	NFP
cord-004615-xfi3p601	365	23	0	0	NFP
cord-004615-xfi3p601	365	24	)	)	-RRB-
cord-004615-xfi3p601	365	25	decreases	decrease	VBZ
cord-004615-xfi3p601	365	26	,	,	,
cord-004615-xfi3p601	365	27	for	for	IN
cord-004615-xfi3p601	365	28	t	t	NN
cord-004615-xfi3p601	366	1	→	→	IN
cord-004615-xfi3p601	366	2	∞	∞	NNP
cord-004615-xfi3p601	366	3	,	,	,
cord-004615-xfi3p601	366	4	where	where	WRB
cord-004615-xfi3p601	366	5	Z(t	Z(t	NNP
cord-004615-xfi3p601	366	6	)	)	-RRB-
cord-004615-xfi3p601	366	7	is	be	VBZ
cord-004615-xfi3p601	366	8	the	the	DT
cord-004615-xfi3p601	366	9	number	number	NN
cord-004615-xfi3p601	366	10	of	of	IN
cord-004615-xfi3p601	366	11	infective	infective	JJ
cord-004615-xfi3p601	366	12	individuals	individual	NNS
cord-004615-xfi3p601	366	13	at	at	IN
cord-004615-xfi3p601	366	14	time	time	NN
cord-004615-xfi3p601	366	15	t	t	NN
cord-004615-xfi3p601	366	16	,	,	,
cord-004615-xfi3p601	366	17	descending	descend	VBG
cord-004615-xfi3p601	366	18	from	from	IN
cord-004615-xfi3p601	366	19	one	one	CD
cord-004615-xfi3p601	366	20	individual	individual	NN
cord-004615-xfi3p601	366	21	infected	infect	VBN
cord-004615-xfi3p601	366	22	at	at	IN
cord-004615-xfi3p601	366	23	time	time	NN
cord-004615-xfi3p601	366	24	t	t	NN
cord-004615-xfi3p601	367	1	=	=	SYM
cord-004615-xfi3p601	367	2	0	0	NFP
cord-004615-xfi3p601	367	3	[	[	-LRB-
cord-004615-xfi3p601	367	4	4	4	CD
cord-004615-xfi3p601	367	5	]	]	-RRB-
cord-004615-xfi3p601	367	6	.	.	.
cord-004615-xfi3p601	368	1	So	so	RB
cord-004615-xfi3p601	368	2	we	-PRON-	PRP
cord-004615-xfi3p601	368	3	can	can	MD
cord-004615-xfi3p601	368	4	give	give	VB
cord-004615-xfi3p601	368	5	an	an	DT
cord-004615-xfi3p601	368	6	upper	upper	JJ
cord-004615-xfi3p601	368	7	bound	bind	VBN
cord-004615-xfi3p601	368	8	for	for	IN
cord-004615-xfi3p601	368	9	the	the	DT
cord-004615-xfi3p601	368	10	probability	probability	NN
cord-004615-xfi3p601	368	11	the	the	DT
cord-004615-xfi3p601	368	12	disease	disease	NN
cord-004615-xfi3p601	368	13	is	be	VBZ
cord-004615-xfi3p601	368	14	already	already	RB
cord-004615-xfi3p601	368	15	extinct	extinct	VBN
cord-004615-xfi3p601	368	16	at	at	IN
cord-004615-xfi3p601	368	17	a	a	DT
cord-004615-xfi3p601	368	18	certain	certain	JJ
cord-004615-xfi3p601	368	19	time	time	NN
cord-004615-xfi3p601	368	20	.	.	.
cord-004615-xfi3p601	369	1	We	-PRON-	PRP
cord-004615-xfi3p601	369	2	do	do	VBP
cord-004615-xfi3p601	369	3	this	this	DT
cord-004615-xfi3p601	369	4	by	by	IN
cord-004615-xfi3p601	369	5	assuming	assume	VBG
cord-004615-xfi3p601	369	6	that	that	IN
cord-004615-xfi3p601	369	7	all	all	DT
cord-004615-xfi3p601	369	8	infective	infective	JJ
cord-004615-xfi3p601	369	9	herds	herd	NNS
cord-004615-xfi3p601	369	10	at	at	IN
cord-004615-xfi3p601	369	11	time	time	NN
cord-004615-xfi3p601	370	1	t	t	NNP
cord-004615-xfi3p601	370	2	=	=	SYM
cord-004615-xfi3p601	370	3	T	T	NNP
cord-004615-xfi3p601	370	4	are	be	VBP
cord-004615-xfi3p601	370	5	infected	infect	VBN
cord-004615-xfi3p601	370	6	at	at	IN
cord-004615-xfi3p601	370	7	that	that	DT
cord-004615-xfi3p601	370	8	time	time	NN
cord-004615-xfi3p601	370	9	.	.	.
cord-004615-xfi3p601	371	1	So	so	RB
cord-004615-xfi3p601	371	2	all	all	DT
cord-004615-xfi3p601	371	3	herd	herd	VBP
cord-004615-xfi3p601	371	4	at	at	IN
cord-004615-xfi3p601	371	5	time	time	NN
cord-004615-xfi3p601	371	6	T	T	NNP
cord-004615-xfi3p601	371	7	have	have	VBP
cord-004615-xfi3p601	371	8	age	age	NN
cord-004615-xfi3p601	371	9	τ	τ	NN
cord-004615-xfi3p601	371	10	=	=	SYM
cord-004615-xfi3p601	371	11	0	0	NFP
cord-004615-xfi3p601	371	12	.	.	.
cord-004615-xfi3p601	372	1	Now	now	RB
cord-004615-xfi3p601	372	2	with	with	IN
cord-004615-xfi3p601	372	3	the	the	DT
cord-004615-xfi3p601	372	4	notation	notation	NN
cord-004615-xfi3p601	372	5	S	s	NN
cord-004615-xfi3p601	372	6	t	t	NN
cord-004615-xfi3p601	372	7	for	for	IN
cord-004615-xfi3p601	372	8	the	the	DT
cord-004615-xfi3p601	372	9	probability	probability	NN
cord-004615-xfi3p601	372	10	that	that	IN
cord-004615-xfi3p601	372	11	the	the	DT
cord-004615-xfi3p601	372	12	progeny	progeny	NN
cord-004615-xfi3p601	372	13	of	of	IN
cord-004615-xfi3p601	372	14	a	a	DT
cord-004615-xfi3p601	372	15	herd	herd	NN
cord-004615-xfi3p601	372	16	infected	infect	VBN
cord-004615-xfi3p601	372	17	at	at	IN
cord-004615-xfi3p601	372	18	time	time	NN
cord-004615-xfi3p601	372	19	T	T	NNP
cord-004615-xfi3p601	372	20	,	,	,
cord-004615-xfi3p601	372	21	will	will	MD
cord-004615-xfi3p601	372	22	not	not	RB
cord-004615-xfi3p601	372	23	survive	survive	VB
cord-004615-xfi3p601	372	24	until	until	IN
cord-004615-xfi3p601	372	25	time	time	NN
cord-004615-xfi3p601	372	26	T	T	NNP
cord-004615-xfi3p601	372	27	+	+	CC
cord-004615-xfi3p601	372	28	t	t	NN
cord-004615-xfi3p601	372	29	and	and	CC
cord-004615-xfi3p601	372	30	with	with	IN
cord-004615-xfi3p601	372	31	Z(t	Z(t	NNP
cord-004615-xfi3p601	372	32	)	)	-RRB-
cord-004615-xfi3p601	372	33	for	for	IN
cord-004615-xfi3p601	372	34	the	the	DT
cord-004615-xfi3p601	372	35	number	number	NN
cord-004615-xfi3p601	372	36	of	of	IN
cord-004615-xfi3p601	372	37	infected	infected	JJ
cord-004615-xfi3p601	372	38	herds	herd	NNS
cord-004615-xfi3p601	372	39	at	at	IN
cord-004615-xfi3p601	372	40	time	time	NN
cord-004615-xfi3p601	372	41	t	t	NNP
cord-004615-xfi3p601	372	42	,	,	,
cord-004615-xfi3p601	372	43	we	-PRON-	PRP
cord-004615-xfi3p601	372	44	have	have	VBP
cord-004615-xfi3p601	372	45	that	that	DT
cord-004615-xfi3p601	372	46	:	:	:
cord-004615-xfi3p601	372	47	1	1	CD
cord-004615-xfi3p601	372	48	.	.	.
cord-004615-xfi3p601	373	1	By	by	IN
cord-004615-xfi3p601	373	2	using	use	VBG
cord-004615-xfi3p601	373	3	this	this	DT
cord-004615-xfi3p601	373	4	iterative	iterative	JJ
cord-004615-xfi3p601	373	5	method	method	NN
cord-004615-xfi3p601	373	6	,	,	,
cord-004615-xfi3p601	373	7	we	-PRON-	PRP
cord-004615-xfi3p601	373	8	can	can	MD
cord-004615-xfi3p601	373	9	compute	compute	VB
cord-004615-xfi3p601	373	10	the	the	DT
cord-004615-xfi3p601	373	11	expected	expect	VBN
cord-004615-xfi3p601	373	12	final	final	JJ
cord-004615-xfi3p601	373	13	size	size	NN
cord-004615-xfi3p601	373	14	of	of	IN
cord-004615-xfi3p601	373	15	an	an	DT
cord-004615-xfi3p601	373	16	outbreak	outbreak	NN
cord-004615-xfi3p601	373	17	very	very	RB
cord-004615-xfi3p601	373	18	fast	fast	RB
cord-004615-xfi3p601	373	19	,	,	,
cord-004615-xfi3p601	373	20	but	but	CC
cord-004615-xfi3p601	373	21	for	for	IN
cord-004615-xfi3p601	373	22	computing	compute	VBG
cord-004615-xfi3p601	373	23	any	any	DT
cord-004615-xfi3p601	373	24	higher	high	JJR
cord-004615-xfi3p601	373	25	moments	moment	NNS
cord-004615-xfi3p601	373	26	of	of	IN
cord-004615-xfi3p601	373	27	this	this	DT
cord-004615-xfi3p601	373	28	final	final	JJ
cord-004615-xfi3p601	373	29	size	size	NN
cord-004615-xfi3p601	373	30	,	,	,
cord-004615-xfi3p601	373	31	we	-PRON-	PRP
cord-004615-xfi3p601	373	32	need	need	VBP
cord-004615-xfi3p601	373	33	substantially	substantially	RB
cord-004615-xfi3p601	373	34	more	more	JJR
cord-004615-xfi3p601	373	35	computational	computational	JJ
cord-004615-xfi3p601	373	36	effort	effort	NN
cord-004615-xfi3p601	373	37	.	.	.
cord-004615-xfi3p601	374	1	By	by	IN
cord-004615-xfi3p601	374	2	using	use	VBG
cord-004615-xfi3p601	374	3	simulations	simulation	NNS
cord-004615-xfi3p601	374	4	,	,	,
cord-004615-xfi3p601	374	5	it	-PRON-	PRP
cord-004615-xfi3p601	374	6	is	be	VBZ
cord-004615-xfi3p601	374	7	possible	possible	JJ
cord-004615-xfi3p601	374	8	to	to	TO
cord-004615-xfi3p601	374	9	estimate	estimate	VB
cord-004615-xfi3p601	374	10	these	these	DT
cord-004615-xfi3p601	374	11	higher	high	JJR
cord-004615-xfi3p601	374	12	moments	moment	NNS
cord-004615-xfi3p601	374	13	too	too	RB
cord-004615-xfi3p601	374	14	.	.	.
cord-004615-xfi3p601	375	1	(	(	-LRB-
cord-004615-xfi3p601	375	2	see	see	VB
cord-004615-xfi3p601	375	3	[	[	-LRB-
cord-004615-xfi3p601	375	4	1	1	CD
cord-004615-xfi3p601	375	5	]	]	-RRB-
cord-004615-xfi3p601	375	6	)	)	-RRB-
cord-004615-xfi3p601	375	7	2	2	CD
cord-004615-xfi3p601	375	8	.	.	.
cord-004615-xfi3p601	376	1	The	the	DT
cord-004615-xfi3p601	376	2	lack	lack	NN
cord-004615-xfi3p601	376	3	of	of	IN
cord-004615-xfi3p601	376	4	memory	memory	NN
cord-004615-xfi3p601	376	5	property	property	NN
cord-004615-xfi3p601	376	6	is	be	VBZ
cord-004615-xfi3p601	376	7	very	very	RB
cord-004615-xfi3p601	376	8	important	important	JJ
cord-004615-xfi3p601	376	9	for	for	IN
cord-004615-xfi3p601	376	10	our	-PRON-	PRP$
cord-004615-xfi3p601	376	11	computations	computation	NNS
cord-004615-xfi3p601	376	12	.	.	.
cord-004615-xfi3p601	377	1	We	-PRON-	PRP
cord-004615-xfi3p601	377	2	used	use	VBD
cord-004615-xfi3p601	377	3	it	-PRON-	PRP
cord-004615-xfi3p601	377	4	to	to	TO
cord-004615-xfi3p601	377	5	write	write	VB
cord-004615-xfi3p601	377	6	the	the	DT
cord-004615-xfi3p601	377	7	formula	formula	NN
cord-004615-xfi3p601	377	8	of	of	IN
cord-004615-xfi3p601	377	9	q(i	q(i	NNP
cord-004615-xfi3p601	377	10	)	)	-RRB-
cord-004615-xfi3p601	377	11	in	in	IN
cord-004615-xfi3p601	377	12	a	a	DT
cord-004615-xfi3p601	377	13	'	'	``
cord-004615-xfi3p601	377	14	convenient	convenient	JJ
cord-004615-xfi3p601	377	15	'	'	''
cord-004615-xfi3p601	377	16	form	form	NN
cord-004615-xfi3p601	377	17	,	,	,
cord-004615-xfi3p601	377	18	with	with	IN
cord-004615-xfi3p601	377	19	expectations	expectation	NNS
cord-004615-xfi3p601	377	20	in	in	IN
cord-004615-xfi3p601	377	21	front	front	NN
cord-004615-xfi3p601	377	22	of	of	IN
cord-004615-xfi3p601	377	23	every	every	DT
cord-004615-xfi3p601	377	24	q(l	q(l	NNP
cord-004615-xfi3p601	377	25	)	)	-RRB-
cord-004615-xfi3p601	377	26	n	n	NN
cord-004615-xfi3p601	377	27	.	.	.
cord-004615-xfi3p601	378	1	The	the	DT
cord-004615-xfi3p601	378	2	speed	speed	NN
cord-004615-xfi3p601	378	3	of	of	IN
cord-004615-xfi3p601	378	4	computations	computation	NNS
cord-004615-xfi3p601	378	5	also	also	RB
cord-004615-xfi3p601	378	6	heavily	heavily	RB
cord-004615-xfi3p601	378	7	depends	depend	VBZ
cord-004615-xfi3p601	378	8	on	on	IN
cord-004615-xfi3p601	378	9	the	the	DT
cord-004615-xfi3p601	378	10	lack	lack	NN
cord-004615-xfi3p601	378	11	of	of	IN
cord-004615-xfi3p601	378	12	memory	memory	NN
cord-004615-xfi3p601	378	13	property	property	NN
cord-004615-xfi3p601	378	14	of	of	IN
cord-004615-xfi3p601	378	15	the	the	DT
cord-004615-xfi3p601	378	16	infection	infection	NN
cord-004615-xfi3p601	378	17	rate	rate	NN
cord-004615-xfi3p601	378	18	.	.	.
cord-004615-xfi3p601	379	1	In	in	IN
cord-004615-xfi3p601	379	2	each	each	DT
cord-004615-xfi3p601	379	3	interval	interval	NN
cord-004615-xfi3p601	379	4	the	the	DT
cord-004615-xfi3p601	379	5	number	number	NN
cord-004615-xfi3p601	379	6	of	of	IN
cord-004615-xfi3p601	379	7	infections	infection	NNS
cord-004615-xfi3p601	379	8	by	by	IN
cord-004615-xfi3p601	379	9	one	one	CD
cord-004615-xfi3p601	379	10	herd	herd	NN
cord-004615-xfi3p601	379	11	is	be	VBZ
cord-004615-xfi3p601	379	12	Poisson	Poisson	NNP
cord-004615-xfi3p601	379	13	distributed	distribute	VBN
cord-004615-xfi3p601	379	14	.	.	.
cord-004615-xfi3p601	380	1	We	-PRON-	PRP
cord-004615-xfi3p601	380	2	can	can	MD
cord-004615-xfi3p601	380	3	easily	easily	RB
cord-004615-xfi3p601	380	4	integrate	integrate	VB
cord-004615-xfi3p601	380	5	h	h	NN
cord-004615-xfi3p601	380	6	out	out	IN
cord-004615-xfi3p601	380	7	of	of	IN
cord-004615-xfi3p601	380	8	the	the	DT
cord-004615-xfi3p601	380	9	formula	formula	NN
cord-004615-xfi3p601	380	10	for	for	IN
cord-004615-xfi3p601	380	11	q(i	q(i	NNP
cord-004615-xfi3p601	380	12	)	)	-RRB-
cord-004615-xfi3p601	380	13	,	,	,
cord-004615-xfi3p601	380	14	for	for	IN
cord-004615-xfi3p601	380	15	Poisson	Poisson	NNP
cord-004615-xfi3p601	380	16	distributed	distribute	VBD
cord-004615-xfi3p601	380	17	numbers	number	NNS
cord-004615-xfi3p601	380	18	of	of	IN
cord-004615-xfi3p601	380	19	infections	infection	NNS
cord-004615-xfi3p601	380	20	.	.	.
cord-004615-xfi3p601	381	1	(	(	-LRB-
cord-004615-xfi3p601	381	2	With	with	IN
cord-004615-xfi3p601	381	3	the	the	DT
cord-004615-xfi3p601	381	4	given	give	VBN
cord-004615-xfi3p601	381	5	distribution	distribution	NN
cord-004615-xfi3p601	381	6	of	of	IN
cord-004615-xfi3p601	381	7	H	h	NN
cord-004615-xfi3p601	381	8	)	)	-RRB-
cord-004615-xfi3p601	381	9	.	.	.
cord-004615-xfi3p601	382	1	In	in	IN
cord-004615-xfi3p601	382	2	this	this	DT
cord-004615-xfi3p601	382	3	section	section	NN
cord-004615-xfi3p601	382	4	we	-PRON-	PRP
cord-004615-xfi3p601	382	5	use	use	VBP
cord-004615-xfi3p601	382	6	the	the	DT
cord-004615-xfi3p601	382	7	Dutch	dutch	JJ
cord-004615-xfi3p601	382	8	classical	classical	JJ
cord-004615-xfi3p601	382	9	swine	swine	NN
cord-004615-xfi3p601	382	10	fever	fever	NN
cord-004615-xfi3p601	382	11	epidemic	epidemic	NN
cord-004615-xfi3p601	382	12	of	of	IN
cord-004615-xfi3p601	382	13	1997	1997	CD
cord-004615-xfi3p601	382	14	as	as	IN
cord-004615-xfi3p601	382	15	example	example	NN
cord-004615-xfi3p601	382	16	.	.	.
cord-004615-xfi3p601	383	1	We	-PRON-	PRP
cord-004615-xfi3p601	383	2	use	use	VBP
cord-004615-xfi3p601	383	3	the	the	DT
cord-004615-xfi3p601	383	4	same	same	JJ
cord-004615-xfi3p601	383	5	data	datum	NNS
cord-004615-xfi3p601	383	6	as	as	IN
cord-004615-xfi3p601	383	7	Klinkenberg	Klinkenberg	NNP
cord-004615-xfi3p601	383	8	et	et	NNP
cord-004615-xfi3p601	383	9	al	al	NNP
cord-004615-xfi3p601	383	10	.	.	.
cord-004615-xfi3p601	384	1	in	in	IN
cord-004615-xfi3p601	384	2	[	[	-LRB-
cord-004615-xfi3p601	384	3	1	1	CD
cord-004615-xfi3p601	384	4	]	]	-RRB-
cord-004615-xfi3p601	384	5	.	.	.
cord-004615-xfi3p601	385	1	However	however	RB
cord-004615-xfi3p601	385	2	,	,	,
cord-004615-xfi3p601	385	3	Klinkenberg	Klinkenberg	NNP
cord-004615-xfi3p601	385	4	et	et	NNP
cord-004615-xfi3p601	385	5	al	al	NNP
cord-004615-xfi3p601	385	6	.	.	.
cord-004615-xfi3p601	386	1	used	use	VBN
cord-004615-xfi3p601	386	2	simulations	simulation	NNS
cord-004615-xfi3p601	386	3	and	and	CC
cord-004615-xfi3p601	386	4	for	for	IN
cord-004615-xfi3p601	386	5	every	every	DT
cord-004615-xfi3p601	386	6	simulation	simulation	NN
cord-004615-xfi3p601	386	7	the	the	DT
cord-004615-xfi3p601	386	8	parameters	parameter	NNS
cord-004615-xfi3p601	386	9	were	be	VBD
cord-004615-xfi3p601	386	10	(	(	-LRB-
cord-004615-xfi3p601	386	11	pseudo-)randomly	pseudo-)randomly	NNP
cord-004615-xfi3p601	386	12	chosen	choose	VBN
cord-004615-xfi3p601	386	13	from	from	IN
cord-004615-xfi3p601	386	14	the	the	DT
cord-004615-xfi3p601	386	15	distributions	distribution	NNS
cord-004615-xfi3p601	386	16	of	of	IN
cord-004615-xfi3p601	386	17	the	the	DT
cord-004615-xfi3p601	386	18	parameters	parameter	NNS
cord-004615-xfi3p601	386	19	,	,	,
cord-004615-xfi3p601	386	20	while	while	IN
cord-004615-xfi3p601	386	21	we	-PRON-	PRP
cord-004615-xfi3p601	386	22	used	use	VBD
cord-004615-xfi3p601	386	23	only	only	RB
cord-004615-xfi3p601	386	24	estimations	estimation	NNS
cord-004615-xfi3p601	386	25	of	of	IN
cord-004615-xfi3p601	386	26	parameters	parameter	NNS
cord-004615-xfi3p601	386	27	for	for	IN
cord-004615-xfi3p601	386	28	our	-PRON-	PRP$
cord-004615-xfi3p601	386	29	computations	computation	NNS
cord-004615-xfi3p601	386	30	.	.	.
cord-004615-xfi3p601	387	1	We	-PRON-	PRP
cord-004615-xfi3p601	387	2	consider	consider	VBP
cord-004615-xfi3p601	387	3	the	the	DT
cord-004615-xfi3p601	387	4	following	following	JJ
cord-004615-xfi3p601	387	5	set	set	NN
cord-004615-xfi3p601	387	6	of	of	IN
cord-004615-xfi3p601	387	7	control	control	NN
cord-004615-xfi3p601	387	8	measures	measure	NNS
cord-004615-xfi3p601	387	9	:	:	:
cord-004615-xfi3p601	387	10	A	a	DT
cord-004615-xfi3p601	387	11	Total	total	JJ
cord-004615-xfi3p601	387	12	transport	transport	NN
cord-004615-xfi3p601	387	13	prohibition	prohibition	NN
cord-004615-xfi3p601	387	14	,	,	,
cord-004615-xfi3p601	387	15	B	B	NNP
cord-004615-xfi3p601	387	16	Killing	killing	NN
cord-004615-xfi3p601	387	17	of	of	IN
cord-004615-xfi3p601	387	18	young	young	JJ
cord-004615-xfi3p601	387	19	piglets	piglet	NNS
cord-004615-xfi3p601	387	20	,	,	,
cord-004615-xfi3p601	387	21	in	in	IN
cord-004615-xfi3p601	387	22	combination	combination	NN
cord-004615-xfi3p601	387	23	with	with	IN
cord-004615-xfi3p601	387	24	a	a	DT
cord-004615-xfi3p601	387	25	breeding	breeding	NN
cord-004615-xfi3p601	387	26	ban	ban	NN
cord-004615-xfi3p601	387	27	,	,	,
cord-004615-xfi3p601	387	28	C	C	NNP
cord-004615-xfi3p601	387	29	Vaccination	vaccination	NN
cord-004615-xfi3p601	387	30	of	of	IN
cord-004615-xfi3p601	387	31	all	all	DT
cord-004615-xfi3p601	387	32	piglets	piglet	NNS
cord-004615-xfi3p601	387	33	(	(	-LRB-
cord-004615-xfi3p601	387	34	not	not	RB
cord-004615-xfi3p601	387	35	sows	sow	VBZ
cord-004615-xfi3p601	387	36	)	)	-RRB-
cord-004615-xfi3p601	387	37	at	at	IN
cord-004615-xfi3p601	387	38	multiplier	multiplier	NN
cord-004615-xfi3p601	387	39	herds	herd	NNS
cord-004615-xfi3p601	387	40	,	,	,
cord-004615-xfi3p601	387	41	followed	follow	VBN
cord-004615-xfi3p601	387	42	by	by	IN
cord-004615-xfi3p601	387	43	recurrent	recurrent	JJ
cord-004615-xfi3p601	387	44	vaccination	vaccination	NN
cord-004615-xfi3p601	387	45	of	of	IN
cord-004615-xfi3p601	387	46	newborn	newborn	JJ
cord-004615-xfi3p601	387	47	piglets	piglet	NNS
cord-004615-xfi3p601	387	48	,	,	,
cord-004615-xfi3p601	387	49	D	D	NNP
cord-004615-xfi3p601	387	50	Single	single	JJ
cord-004615-xfi3p601	387	51	vaccination	vaccination	NN
cord-004615-xfi3p601	387	52	of	of	IN
cord-004615-xfi3p601	387	53	all	all	DT
cord-004615-xfi3p601	387	54	pigs	pig	NNS
cord-004615-xfi3p601	387	55	at	at	IN
cord-004615-xfi3p601	387	56	finishing	finish	VBG
cord-004615-xfi3p601	387	57	herds	herd	NNS
cord-004615-xfi3p601	387	58	,	,	,
cord-004615-xfi3p601	387	59	E	E	NNP
cord-004615-xfi3p601	387	60	Vaccination	vaccination	NN
cord-004615-xfi3p601	387	61	of	of	IN
cord-004615-xfi3p601	387	62	piglets	piglet	NNS
cord-004615-xfi3p601	387	63	on	on	IN
cord-004615-xfi3p601	387	64	arrival	arrival	NN
cord-004615-xfi3p601	387	65	at	at	IN
cord-004615-xfi3p601	387	66	finishing	finish	VBG
cord-004615-xfi3p601	387	67	herds	herd	NNS
cord-004615-xfi3p601	387	68	.	.	.
cord-004615-xfi3p601	388	1	Choosing	choose	VBG
cord-004615-xfi3p601	388	2	a	a	DT
cord-004615-xfi3p601	388	3	(	(	-LRB-
cord-004615-xfi3p601	388	4	combination	combination	NN
cord-004615-xfi3p601	388	5	of	of	IN
cord-004615-xfi3p601	388	6	)	)	-RRB-
cord-004615-xfi3p601	388	7	measure(s	measure(s	NN
cord-004615-xfi3p601	388	8	)	)	-RRB-
cord-004615-xfi3p601	388	9	is	be	VBZ
cord-004615-xfi3p601	388	10	called	call	VBN
cord-004615-xfi3p601	388	11	a	a	DT
cord-004615-xfi3p601	388	12	control	control	NN
cord-004615-xfi3p601	388	13	strategy	strategy	NN
cord-004615-xfi3p601	388	14	or	or	CC
cord-004615-xfi3p601	388	15	scenario	scenario	NN
cord-004615-xfi3p601	388	16	.	.	.
cord-004615-xfi3p601	389	1	The	the	DT
cord-004615-xfi3p601	389	2	effects	effect	NNS
cord-004615-xfi3p601	389	3	of	of	IN
cord-004615-xfi3p601	389	4	different	different	JJ
cord-004615-xfi3p601	389	5	scenarios	scenario	NNS
cord-004615-xfi3p601	389	6	on	on	IN
cord-004615-xfi3p601	389	7	the	the	DT
cord-004615-xfi3p601	389	8	fraction	fraction	NN
cord-004615-xfi3p601	389	9	of	of	IN
cord-004615-xfi3p601	389	10	infective	infective	JJ
cord-004615-xfi3p601	389	11	animals	animal	NNS
cord-004615-xfi3p601	389	12	in	in	IN
cord-004615-xfi3p601	389	13	a	a	DT
cord-004615-xfi3p601	389	14	multiplier	multiplier	NN
cord-004615-xfi3p601	389	15	,	,	,
cord-004615-xfi3p601	389	16	in	in	IN
cord-004615-xfi3p601	389	17	a	a	DT
cord-004615-xfi3p601	389	18	finisher	finisher	NN
cord-004615-xfi3p601	389	19	and	and	CC
cord-004615-xfi3p601	389	20	the	the	DT
cord-004615-xfi3p601	389	21	possibility	possibility	NN
cord-004615-xfi3p601	389	22	of	of	IN
cord-004615-xfi3p601	389	23	transport	transport	NN
cord-004615-xfi3p601	389	24	-	-	HYPH
cord-004615-xfi3p601	389	25	infections	infection	NNS
cord-004615-xfi3p601	389	26	(	(	-LRB-
cord-004615-xfi3p601	389	27	φ	φ	NNP
cord-004615-xfi3p601	389	28	m	m	NN
cord-004615-xfi3p601	389	29	(	(	-LRB-
cord-004615-xfi3p601	389	30	t	t	NN
cord-004615-xfi3p601	389	31	)	)	-RRB-
cord-004615-xfi3p601	389	32	,	,	,
cord-004615-xfi3p601	389	33	φ	φ	NNP
cord-004615-xfi3p601	389	34	f	f	NNP
cord-004615-xfi3p601	389	35	(	(	-LRB-
cord-004615-xfi3p601	389	36	t	t	NN
cord-004615-xfi3p601	389	37	)	)	-RRB-
cord-004615-xfi3p601	389	38	and	and	CC
cord-004615-xfi3p601	389	39	φ	φ	NNP
cord-004615-xfi3p601	389	40	tr	tr	NN
cord-004615-xfi3p601	389	41	(	(	-LRB-
cord-004615-xfi3p601	389	42	t	t	NN
cord-004615-xfi3p601	389	43	)	)	-RRB-
cord-004615-xfi3p601	389	44	respectively	respectively	RB
cord-004615-xfi3p601	389	45	)	)	-RRB-
cord-004615-xfi3p601	389	46	are	be	VBP
cord-004615-xfi3p601	389	47	given	give	VBN
cord-004615-xfi3p601	389	48	in	in	IN
cord-004615-xfi3p601	389	49	Table	Table	NNP
cord-004615-xfi3p601	389	50	1	1	CD
cord-004615-xfi3p601	389	51	(	(	-LRB-
cord-004615-xfi3p601	389	52	This	this	DT
cord-004615-xfi3p601	389	53	table	table	NN
cord-004615-xfi3p601	389	54	is	be	VBZ
cord-004615-xfi3p601	389	55	adapted	adapt	VBN
cord-004615-xfi3p601	389	56	from	from	IN
cord-004615-xfi3p601	389	57	[	[	-LRB-
cord-004615-xfi3p601	389	58	1	1	CD
cord-004615-xfi3p601	389	59	]	]	-RRB-
cord-004615-xfi3p601	389	60	)	)	-RRB-
cord-004615-xfi3p601	389	61	.	.	.
cord-004615-xfi3p601	390	1	For	for	IN
cord-004615-xfi3p601	390	2	example	example	NN
cord-004615-xfi3p601	390	3	,	,	,
cord-004615-xfi3p601	390	4	the	the	DT
cord-004615-xfi3p601	390	5	0	0	CD
cord-004615-xfi3p601	390	6	for	for	IN
cord-004615-xfi3p601	390	7	φ	φ	NNP
cord-004615-xfi3p601	390	8	tr	tr	NNP
cord-004615-xfi3p601	390	9	in	in	IN
cord-004615-xfi3p601	390	10	strategy	strategy	NN
cord-004615-xfi3p601	391	1	A	a	DT
cord-004615-xfi3p601	391	2	means	mean	VBZ
cord-004615-xfi3p601	391	3	that	that	IN
cord-004615-xfi3p601	391	4	infection	infection	NN
cord-004615-xfi3p601	391	5	is	be	VBZ
cord-004615-xfi3p601	391	6	not	not	RB
cord-004615-xfi3p601	391	7	possible	possible	JJ
cord-004615-xfi3p601	391	8	by	by	IN
cord-004615-xfi3p601	391	9	transport	transport	NN
cord-004615-xfi3p601	391	10	contacts	contact	NNS
cord-004615-xfi3p601	391	11	.	.	.
cord-004615-xfi3p601	392	1	As	as	IN
cord-004615-xfi3p601	392	2	another	another	DT
cord-004615-xfi3p601	392	3	example	example	NN
cord-004615-xfi3p601	392	4	,	,	,
cord-004615-xfi3p601	392	5	φ	φ	NNP
cord-004615-xfi3p601	392	6	f	f	NNP
cord-004615-xfi3p601	392	7	(	(	-LRB-
cord-004615-xfi3p601	392	8	t	t	NN
cord-004615-xfi3p601	392	9	)	)	-RRB-
cord-004615-xfi3p601	392	10	=	=	NFP
cord-004615-xfi3p601	393	1	t/100	t/100	NNP
cord-004615-xfi3p601	393	2	for	for	IN
cord-004615-xfi3p601	393	3	t	t	NNP
cord-004615-xfi3p601	393	4	≤	≤	NNP
cord-004615-xfi3p601	393	5	100	100	CD
cord-004615-xfi3p601	393	6	in	in	IN
cord-004615-xfi3p601	393	7	strategy	strategy	NN
cord-004615-xfi3p601	393	8	D	d	NN
cord-004615-xfi3p601	393	9	means	mean	VBZ
cord-004615-xfi3p601	393	10	that	that	IN
cord-004615-xfi3p601	393	11	at	at	IN
cord-004615-xfi3p601	393	12	time	time	NN
cord-004615-xfi3p601	393	13	t	t	NNP
cord-004615-xfi3p601	393	14	a	a	DT
cord-004615-xfi3p601	393	15	fraction	fraction	NN
cord-004615-xfi3p601	393	16	t/100	t/100	NN
cord-004615-xfi3p601	393	17	of	of	IN
cord-004615-xfi3p601	393	18	the	the	DT
cord-004615-xfi3p601	393	19	animals	animal	NNS
cord-004615-xfi3p601	393	20	in	in	IN
cord-004615-xfi3p601	393	21	a	a	DT
cord-004615-xfi3p601	393	22	finisher	finisher	NN
cord-004615-xfi3p601	393	23	is	be	VBZ
cord-004615-xfi3p601	393	24	infective	infective	JJ
cord-004615-xfi3p601	393	25	.	.	.
cord-004615-xfi3p601	394	1	Note	note	VB
cord-004615-xfi3p601	394	2	that	that	IN
cord-004615-xfi3p601	394	3	the	the	DT
cord-004615-xfi3p601	394	4	first	first	JJ
cord-004615-xfi3p601	394	5	12	12	CD
cord-004615-xfi3p601	394	6	strategies	strategy	NNS
cord-004615-xfi3p601	394	7	are	be	VBP
cord-004615-xfi3p601	394	8	in	in	IN
cord-004615-xfi3p601	394	9	a	a	DT
cord-004615-xfi3p601	394	10	constant	constant	JJ
cord-004615-xfi3p601	394	11	environment	environment	NN
cord-004615-xfi3p601	394	12	.	.	.
cord-004615-xfi3p601	395	1	Therefore	therefore	RB
cord-004615-xfi3p601	395	2	,	,	,
cord-004615-xfi3p601	395	3	for	for	IN
cord-004615-xfi3p601	395	4	those	those	DT
cord-004615-xfi3p601	395	5	strategies	strategy	NNS
cord-004615-xfi3p601	395	6	we	-PRON-	PRP
cord-004615-xfi3p601	395	7	can	can	MD
cord-004615-xfi3p601	395	8	compute	compute	VB
cord-004615-xfi3p601	395	9	properties	property	NNS
cord-004615-xfi3p601	395	10	of	of	IN
cord-004615-xfi3p601	395	11	the	the	DT
cord-004615-xfi3p601	395	12	spread	spread	NN
cord-004615-xfi3p601	395	13	of	of	IN
cord-004615-xfi3p601	395	14	the	the	DT
cord-004615-xfi3p601	395	15	disease	disease	NN
cord-004615-xfi3p601	395	16	directly	directly	RB
cord-004615-xfi3p601	395	17	.	.	.
cord-004615-xfi3p601	396	1	The	the	DT
cord-004615-xfi3p601	396	2	probability	probability	NN
cord-004615-xfi3p601	396	3	of	of	IN
cord-004615-xfi3p601	396	4	extinction	extinction	NN
cord-004615-xfi3p601	396	5	is	be	VBZ
cord-004615-xfi3p601	396	6	given	give	VBN
cord-004615-xfi3p601	396	7	in	in	IN
cord-004615-xfi3p601	396	8	Table	Table	NNP
cord-004615-xfi3p601	396	9	2	2	CD
cord-004615-xfi3p601	396	10	.	.	.
cord-004615-xfi3p601	397	1	We	-PRON-	PRP
cord-004615-xfi3p601	397	2	also	also	RB
cord-004615-xfi3p601	397	3	compute	compute	VBP
cord-004615-xfi3p601	397	4	the	the	DT
cord-004615-xfi3p601	397	5	expected	expect	VBN
cord-004615-xfi3p601	397	6	final	final	JJ
cord-004615-xfi3p601	397	7	size	size	NN
cord-004615-xfi3p601	397	8	of	of	IN
cord-004615-xfi3p601	397	9	an	an	DT
cord-004615-xfi3p601	397	10	epidemic	epidemic	NN
cord-004615-xfi3p601	397	11	;	;	:
cord-004615-xfi3p601	397	12	see	see	VB
cord-004615-xfi3p601	397	13	Table	Table	NNP
cord-004615-xfi3p601	397	14	3	3	CD
cord-004615-xfi3p601	397	15	.	.	.
cord-004615-xfi3p601	398	1	We	-PRON-	PRP
cord-004615-xfi3p601	398	2	only	only	RB
cord-004615-xfi3p601	398	3	need	need	VBP
cord-004615-xfi3p601	398	4	to	to	TO
cord-004615-xfi3p601	398	5	compute	compute	VB
cord-004615-xfi3p601	398	6	this	this	DT
cord-004615-xfi3p601	398	7	for	for	IN
cord-004615-xfi3p601	398	8	the	the	DT
cord-004615-xfi3p601	398	9	strategies	strategy	NNS
cord-004615-xfi3p601	398	10	with	with	IN
cord-004615-xfi3p601	398	11	almost	almost	RB
cord-004615-xfi3p601	398	12	sure	sure	JJ
cord-004615-xfi3p601	398	13	extinction	extinction	NN
cord-004615-xfi3p601	398	14	.	.	.
cord-004615-xfi3p601	399	1	The	the	DT
cord-004615-xfi3p601	399	2	expected	expect	VBN
cord-004615-xfi3p601	399	3	number	number	NN
cord-004615-xfi3p601	399	4	of	of	IN
cord-004615-xfi3p601	399	5	infected	infected	JJ
cord-004615-xfi3p601	399	6	multipliers	multiplier	NNS
cord-004615-xfi3p601	399	7	,	,	,
cord-004615-xfi3p601	399	8	while	while	IN
cord-004615-xfi3p601	399	9	the	the	DT
cord-004615-xfi3p601	399	10	initially	initially	RB
cord-004615-xfi3p601	399	11	infected	infected	JJ
cord-004615-xfi3p601	399	12	herd	herd	NN
cord-004615-xfi3p601	399	13	was	be	VBD
cord-004615-xfi3p601	399	14	a	a	DT
cord-004615-xfi3p601	399	15	finisher	finisher	NN
cord-004615-xfi3p601	399	16	is	be	VBZ
cord-004615-xfi3p601	399	17	denoted	denote	VBN
cord-004615-xfi3p601	399	18	by	by	IN
cord-004615-xfi3p601	399	19	G	g	NN
cord-004615-xfi3p601	399	20	f	f	NN
cord-004615-xfi3p601	399	21	m	m	NN
cord-004615-xfi3p601	399	22	.	.	.
cord-004615-xfi3p601	400	1	In	in	IN
cord-004615-xfi3p601	400	2	a	a	DT
cord-004615-xfi3p601	400	3	similar	similar	JJ
cord-004615-xfi3p601	400	4	way	way	NN
cord-004615-xfi3p601	400	5	we	-PRON-	PRP
cord-004615-xfi3p601	400	6	define	define	VBP
cord-004615-xfi3p601	400	7	G	G	NNP
cord-004615-xfi3p601	400	8	mm	mm	NN
cord-004615-xfi3p601	400	9	,	,	,
cord-004615-xfi3p601	400	10	G	G	NNP
cord-004615-xfi3p601	400	11	mf	mf	NN
cord-004615-xfi3p601	400	12	,	,	,
cord-004615-xfi3p601	400	13	G	g	NN
cord-004615-xfi3p601	400	14	ff	ff	NN
cord-004615-xfi3p601	400	15	.	.	.
cord-004615-xfi3p601	401	1	The	the	DT
cord-004615-xfi3p601	401	2	last	last	JJ
cord-004615-xfi3p601	401	3	column	column	NN
cord-004615-xfi3p601	401	4	of	of	IN
cord-004615-xfi3p601	401	5	Table	Table	NNP
cord-004615-xfi3p601	401	6	3	3	CD
cord-004615-xfi3p601	401	7	is	be	VBZ
cord-004615-xfi3p601	401	8	the	the	DT
cord-004615-xfi3p601	401	9	expected	expect	VBN
cord-004615-xfi3p601	401	10	number	number	NN
cord-004615-xfi3p601	401	11	of	of	IN
cord-004615-xfi3p601	401	12	infected	infected	JJ
cord-004615-xfi3p601	401	13	herds	herd	NNS
cord-004615-xfi3p601	401	14	,	,	,
cord-004615-xfi3p601	401	15	when	when	WRB
cord-004615-xfi3p601	401	16	initially	initially	RB
cord-004615-xfi3p601	401	17	five	five	CD
cord-004615-xfi3p601	401	18	multipliers	multiplier	NNS
cord-004615-xfi3p601	401	19	and	and	CC
cord-004615-xfi3p601	401	20	five	five	CD
cord-004615-xfi3p601	401	21	finishers	finisher	NNS
cord-004615-xfi3p601	401	22	were	be	VBD
cord-004615-xfi3p601	401	23	infected	infect	VBN
cord-004615-xfi3p601	401	24	.	.	.
cord-004615-xfi3p601	402	1	Note	note	VB
cord-004615-xfi3p601	402	2	that	that	IN
cord-004615-xfi3p601	402	3	we	-PRON-	PRP
cord-004615-xfi3p601	402	4	can	can	MD
cord-004615-xfi3p601	402	5	not	not	RB
cord-004615-xfi3p601	402	6	compare	compare	VB
cord-004615-xfi3p601	402	7	the	the	DT
cord-004615-xfi3p601	402	8	expected	expect	VBN
cord-004615-xfi3p601	402	9	final	final	JJ
cord-004615-xfi3p601	402	10	size	size	NN
cord-004615-xfi3p601	402	11	with	with	IN
cord-004615-xfi3p601	402	12	the	the	DT
cord-004615-xfi3p601	402	13	results	result	NNS
cord-004615-xfi3p601	402	14	of	of	IN
cord-004615-xfi3p601	402	15	Klinkenberg	Klinkenberg	NNP
cord-004615-xfi3p601	402	16	et	et	FW
cord-004615-xfi3p601	402	17	al	al	NNP
cord-004615-xfi3p601	402	18	.	.	.
cord-004615-xfi3p601	403	1	(	(	-LRB-
cord-004615-xfi3p601	403	2	Table	table	NN
cord-004615-xfi3p601	403	3	6	6	CD
cord-004615-xfi3p601	403	4	in	in	IN
cord-004615-xfi3p601	403	5	[	[	-LRB-
cord-004615-xfi3p601	403	6	1	1	CD
cord-004615-xfi3p601	403	7	]	]	-RRB-
cord-004615-xfi3p601	403	8	)	)	-RRB-
cord-004615-xfi3p601	403	9	,	,	,
cord-004615-xfi3p601	403	10	because	because	IN
cord-004615-xfi3p601	403	11	they	-PRON-	PRP
cord-004615-xfi3p601	403	12	use	use	VBP
cord-004615-xfi3p601	403	13	the	the	DT
cord-004615-xfi3p601	403	14	median	median	NN
cord-004615-xfi3p601	403	15	of	of	IN
cord-004615-xfi3p601	403	16	1000	1000	CD
cord-004615-xfi3p601	403	17	simulations	simulation	NNS
cord-004615-xfi3p601	403	18	,	,	,
cord-004615-xfi3p601	403	19	not	not	RB
cord-004615-xfi3p601	403	20	the	the	DT
cord-004615-xfi3p601	403	21	mean	mean	NN
cord-004615-xfi3p601	403	22	.	.	.
cord-004615-xfi3p601	404	1	The	the	DT
cord-004615-xfi3p601	404	2	results	result	NNS
cord-004615-xfi3p601	404	3	of	of	IN
cord-004615-xfi3p601	404	4	Klinkenberg	Klinkenberg	NNP
cord-004615-xfi3p601	404	5	et	et	NNP
cord-004615-xfi3p601	404	6	al	al	NNP
cord-004615-xfi3p601	404	7	.	.	NNP
cord-004615-xfi3p601	404	8	are	be	VBP
cord-004615-xfi3p601	404	9	given	give	VBN
cord-004615-xfi3p601	404	10	in	in	IN
cord-004615-xfi3p601	404	11	Table	Table	NNP
cord-004615-xfi3p601	404	12	4	4	CD
cord-004615-xfi3p601	404	13	.	.	.
cord-004615-xfi3p601	405	1	The	the	DT
cord-004615-xfi3p601	405	2	95	95	CD
cord-004615-xfi3p601	405	3	%	%	NN
cord-004615-xfi3p601	405	4	confidence	confidence	NN
cord-004615-xfi3p601	405	5	intervals	interval	NNS
cord-004615-xfi3p601	405	6	of	of	IN
cord-004615-xfi3p601	405	7	the	the	DT
cord-004615-xfi3p601	405	8	final	final	JJ
cord-004615-xfi3p601	405	9	size	size	NN
cord-004615-xfi3p601	405	10	are	be	VBP
cord-004615-xfi3p601	405	11	also	also	RB
cord-004615-xfi3p601	405	12	taken	take	VBN
cord-004615-xfi3p601	405	13	from	from	IN
cord-004615-xfi3p601	405	14	[	[	-LRB-
cord-004615-xfi3p601	405	15	1	1	CD
cord-004615-xfi3p601	405	16	]	]	-RRB-
cord-004615-xfi3p601	405	17	and	and	CC
cord-004615-xfi3p601	405	18	were	be	VBD
cord-004615-xfi3p601	405	19	estimated	estimate	VBN
cord-004615-xfi3p601	405	20	by	by	IN
cord-004615-xfi3p601	405	21	simulation	simulation	NN
cord-004615-xfi3p601	405	22	.	.	.
cord-004615-xfi3p601	406	1	We	-PRON-	PRP
cord-004615-xfi3p601	406	2	used	use	VBD
cord-004615-xfi3p601	406	3	the	the	DT
cord-004615-xfi3p601	406	4	generating	generating	NN
cord-004615-xfi3p601	406	5	function	function	NN
cord-004615-xfi3p601	406	6	for	for	IN
cord-004615-xfi3p601	406	7	the	the	DT
cord-004615-xfi3p601	406	8	number	number	NN
cord-004615-xfi3p601	406	9	of	of	IN
cord-004615-xfi3p601	406	10	infected	infected	JJ
cord-004615-xfi3p601	406	11	and	and	CC
cord-004615-xfi3p601	406	12	infective	infective	JJ
cord-004615-xfi3p601	406	13	herds	herd	NNS
cord-004615-xfi3p601	406	14	at	at	IN
cord-004615-xfi3p601	406	15	time	time	NN
cord-004615-xfi3p601	406	16	t	t	NN
cord-004615-xfi3p601	406	17	=	=	SYM
cord-004615-xfi3p601	406	18	T	T	NNP
cord-004615-xfi3p601	406	19	,	,	,
cord-004615-xfi3p601	406	20	the	the	DT
cord-004615-xfi3p601	406	21	point	point	NN
cord-004615-xfi3p601	406	22	in	in	IN
cord-004615-xfi3p601	406	23	time	time	NN
cord-004615-xfi3p601	406	24	after	after	IN
cord-004615-xfi3p601	406	25	which	which	WDT
cord-004615-xfi3p601	406	26	the	the	DT
cord-004615-xfi3p601	406	27	parameter	parameter	NN
cord-004615-xfi3p601	406	28	values	value	NNS
cord-004615-xfi3p601	406	29	are	be	VBP
cord-004615-xfi3p601	406	30	assumed	assume	VBN
cord-004615-xfi3p601	406	31	to	to	TO
cord-004615-xfi3p601	406	32	be	be	VB
cord-004615-xfi3p601	406	33	constant	constant	JJ
cord-004615-xfi3p601	406	34	,	,	,
cord-004615-xfi3p601	406	35	to	to	TO
cord-004615-xfi3p601	406	36	estimate	estimate	VB
cord-004615-xfi3p601	406	37	the	the	DT
cord-004615-xfi3p601	406	38	size	size	NN
cord-004615-xfi3p601	406	39	at	at	IN
cord-004615-xfi3p601	406	40	time	time	NN
cord-004615-xfi3p601	406	41	T	T	NNP
cord-004615-xfi3p601	406	42	(	(	-LRB-
cord-004615-xfi3p601	406	43	which	which	WDT
cord-004615-xfi3p601	406	44	varies	vary	VBZ
cord-004615-xfi3p601	406	45	for	for	IN
cord-004615-xfi3p601	406	46	different	different	JJ
cord-004615-xfi3p601	406	47	strategies	strategy	NNS
cord-004615-xfi3p601	406	48	)	)	-RRB-
cord-004615-xfi3p601	406	49	.	.	.
cord-004615-xfi3p601	407	1	Table	table	NN
cord-004615-xfi3p601	407	2	1	1	CD
cord-004615-xfi3p601	407	3	.	.	.
cord-004615-xfi3p601	408	1	The	the	DT
cord-004615-xfi3p601	408	2	effect	effect	NN
cord-004615-xfi3p601	408	3	of	of	IN
cord-004615-xfi3p601	408	4	different	different	JJ
cord-004615-xfi3p601	408	5	strategies	strategy	NNS
cord-004615-xfi3p601	408	6	on	on	IN
cord-004615-xfi3p601	408	7	φ	φ	NNP
cord-004615-xfi3p601	408	8	f	f	NN
cord-004615-xfi3p601	408	9	(	(	-LRB-
cord-004615-xfi3p601	408	10	t	t	NNP
cord-004615-xfi3p601	408	11	)	)	-RRB-
cord-004615-xfi3p601	408	12	,	,	,
cord-004615-xfi3p601	408	13	φ	φ	NNP
cord-004615-xfi3p601	408	14	m	m	NN
cord-004615-xfi3p601	408	15	(	(	-LRB-
cord-004615-xfi3p601	408	16	t	t	NN
cord-004615-xfi3p601	408	17	)	)	-RRB-
cord-004615-xfi3p601	408	18	and	and	CC
cord-004615-xfi3p601	408	19	φ	φ	NNP
cord-004615-xfi3p601	408	20	tr	tr	NN
cord-004615-xfi3p601	408	21	(	(	-LRB-
cord-004615-xfi3p601	408	22	t	t	NN
cord-004615-xfi3p601	408	23	)	)	-RRB-
cord-004615-xfi3p601	408	24	1	1	CD
cord-004615-xfi3p601	408	25	.	.	.
cord-004615-xfi3p601	409	1	We	-PRON-	PRP
cord-004615-xfi3p601	409	2	estimate	estimate	VBP
cord-004615-xfi3p601	409	3	the	the	DT
cord-004615-xfi3p601	409	4	first	first	JJ
cord-004615-xfi3p601	409	5	two	two	CD
cord-004615-xfi3p601	409	6	moments	moment	NNS
cord-004615-xfi3p601	409	7	of	of	IN
cord-004615-xfi3p601	409	8	the	the	DT
cord-004615-xfi3p601	409	9	size	size	NN
cord-004615-xfi3p601	409	10	at	at	IN
cord-004615-xfi3p601	409	11	time	time	NN
cord-004615-xfi3p601	409	12	T	T	NNP
cord-004615-xfi3p601	409	13	for	for	IN
cord-004615-xfi3p601	409	14	the	the	DT
cord-004615-xfi3p601	409	15	four	four	CD
cord-004615-xfi3p601	409	16	pure	pure	JJ
cord-004615-xfi3p601	409	17	strategies	strategy	NNS
cord-004615-xfi3p601	409	18	in	in	IN
cord-004615-xfi3p601	409	19	a	a	DT
cord-004615-xfi3p601	409	20	varying	vary	VBG
cord-004615-xfi3p601	409	21	environment	environment	NN
cord-004615-xfi3p601	409	22	B	b	NN
cord-004615-xfi3p601	409	23	,	,	,
cord-004615-xfi3p601	409	24	C	C	NNP
cord-004615-xfi3p601	409	25	,	,	,
cord-004615-xfi3p601	409	26	D	D	NNP
cord-004615-xfi3p601	409	27	,	,	,
cord-004615-xfi3p601	409	28	E.	E.	NNP
cord-004615-xfi3p601	409	29	(	(	-LRB-
cord-004615-xfi3p601	409	30	Table	Table	NNP
cord-004615-xfi3p601	409	31	5	5	CD
cord-004615-xfi3p601	409	32	)	)	-RRB-
cord-004615-xfi3p601	410	1	Especially	especially	RB
cord-004615-xfi3p601	410	2	the	the	DT
cord-004615-xfi3p601	410	3	results	result	NNS
cord-004615-xfi3p601	410	4	of	of	IN
cord-004615-xfi3p601	410	5	B	b	NN
cord-004615-xfi3p601	410	6	and	and	CC
cord-004615-xfi3p601	410	7	C	C	NNP
cord-004615-xfi3p601	410	8	are	be	VBP
cord-004615-xfi3p601	410	9	of	of	IN
cord-004615-xfi3p601	410	10	interest	interest	NN
cord-004615-xfi3p601	410	11	because	because	IN
cord-004615-xfi3p601	410	12	they	-PRON-	PRP
cord-004615-xfi3p601	410	13	will	will	MD
cord-004615-xfi3p601	410	14	give	give	VB
cord-004615-xfi3p601	410	15	an	an	DT
cord-004615-xfi3p601	410	16	idea	idea	NN
cord-004615-xfi3p601	410	17	of	of	IN
cord-004615-xfi3p601	410	18	the	the	DT
cord-004615-xfi3p601	410	19	variance	variance	NN
cord-004615-xfi3p601	410	20	of	of	IN
cord-004615-xfi3p601	410	21	the	the	DT
cord-004615-xfi3p601	410	22	final	final	JJ
cord-004615-xfi3p601	410	23	size	size	NN
cord-004615-xfi3p601	410	24	of	of	IN
cord-004615-xfi3p601	410	25	a	a	DT
cord-004615-xfi3p601	410	26	herd	herd	NN
cord-004615-xfi3p601	410	27	.	.	.
cord-004615-xfi3p601	411	1	Next	next	RB
cord-004615-xfi3p601	411	2	we	-PRON-	PRP
cord-004615-xfi3p601	411	3	give	give	VBP
cord-004615-xfi3p601	411	4	covariance	covariance	NN
cord-004615-xfi3p601	411	5	matrices	matrix	NNS
cord-004615-xfi3p601	411	6	(	(	-LRB-
cord-004615-xfi3p601	411	7	for	for	IN
cord-004615-xfi3p601	411	8	different	different	JJ
cord-004615-xfi3p601	411	9	strategies	strategy	NNS
cord-004615-xfi3p601	411	10	and	and	CC
cord-004615-xfi3p601	411	11	different	different	JJ
cord-004615-xfi3p601	411	12	initially	initially	RB
cord-004615-xfi3p601	411	13	infected	infected	JJ
cord-004615-xfi3p601	411	14	herds	herd	NNS
cord-004615-xfi3p601	411	15	)	)	-RRB-
cord-004615-xfi3p601	411	16	of	of	IN
cord-004615-xfi3p601	411	17	the	the	DT
cord-004615-xfi3p601	411	18	number	number	NN
cord-004615-xfi3p601	411	19	of	of	IN
cord-004615-xfi3p601	411	20	infected	infected	JJ
cord-004615-xfi3p601	411	21	multipliers	multiplier	NNS
cord-004615-xfi3p601	411	22	not	not	RB
cord-004615-xfi3p601	411	23	yet	yet	RB
cord-004615-xfi3p601	411	24	detected	detect	VBN
cord-004615-xfi3p601	411	25	,	,	,
cord-004615-xfi3p601	411	26	the	the	DT
cord-004615-xfi3p601	411	27	number	number	NN
cord-004615-xfi3p601	411	28	of	of	IN
cord-004615-xfi3p601	411	29	infected	infected	JJ
cord-004615-xfi3p601	411	30	multipliers	multiplier	NNS
cord-004615-xfi3p601	411	31	already	already	RB
cord-004615-xfi3p601	411	32	detected	detect	VBN
cord-004615-xfi3p601	411	33	,	,	,
cord-004615-xfi3p601	411	34	the	the	DT
cord-004615-xfi3p601	411	35	number	number	NN
cord-004615-xfi3p601	411	36	of	of	IN
cord-004615-xfi3p601	411	37	infected	infected	JJ
cord-004615-xfi3p601	411	38	finishers	finisher	NNS
cord-004615-xfi3p601	411	39	not	not	RB
cord-004615-xfi3p601	411	40	yet	yet	RB
cord-004615-xfi3p601	411	41	detected	detect	VBN
cord-004615-xfi3p601	411	42	and	and	CC
cord-004615-xfi3p601	411	43	the	the	DT
cord-004615-xfi3p601	411	44	number	number	NN
cord-004615-xfi3p601	411	45	of	of	IN
cord-004615-xfi3p601	411	46	finishers	finisher	NNS
cord-004615-xfi3p601	411	47	already	already	RB
cord-004615-xfi3p601	411	48	detected	detect	VBN
cord-004615-xfi3p601	411	49	,	,	,
cord-004615-xfi3p601	411	50	respectively	respectively	RB
cord-004615-xfi3p601	411	51	.	.	.
cord-004615-xfi3p601	412	1	We	-PRON-	PRP
cord-004615-xfi3p601	412	2	denote	denote	VBP
cord-004615-xfi3p601	412	3	by	by	IN
cord-004615-xfi3p601	412	4	V	V	NNP
cord-004615-xfi3p601	412	5	ar	ar	NNP
cord-004615-xfi3p601	413	1	i	i	PRP
cord-004615-xfi3p601	413	2	(	(	-LRB-
cord-004615-xfi3p601	413	3	J	J	NNP
cord-004615-xfi3p601	413	4	)	)	-RRB-
cord-004615-xfi3p601	413	5	the	the	DT
cord-004615-xfi3p601	413	6	covariance	covariance	NN
cord-004615-xfi3p601	413	7	matrix	matrix	NN
cord-004615-xfi3p601	413	8	for	for	IN
cord-004615-xfi3p601	413	9	an	an	DT
cord-004615-xfi3p601	413	10	initially	initially	RB
cord-004615-xfi3p601	413	11	infected	infected	JJ
cord-004615-xfi3p601	413	12	herd	herd	NN
cord-004615-xfi3p601	413	13	of	of	IN
cord-004615-xfi3p601	413	14	type	type	NN
cord-004615-xfi3p601	413	15	i	i	PRP
cord-004615-xfi3p601	413	16	,	,	,
cord-004615-xfi3p601	413	17	while	while	IN
cord-004615-xfi3p601	413	18	the	the	DT
cord-004615-xfi3p601	413	19	strategy	strategy	NN
cord-004615-xfi3p601	413	20	is	be	VBZ
cord-004615-xfi3p601	413	21	J	J	NNP
cord-004615-xfi3p601	413	22	.	.	.
cord-004615-xfi3p601	414	1	By	by	IN
cord-004615-xfi3p601	414	2	comparing	compare	VBG
cord-004615-xfi3p601	414	3	the	the	DT
cord-004615-xfi3p601	414	4	values	value	NNS
cord-004615-xfi3p601	414	5	in	in	IN
cord-004615-xfi3p601	414	6	these	these	DT
cord-004615-xfi3p601	414	7	matrices	matrix	NNS
cord-004615-xfi3p601	414	8	to	to	IN
cord-004615-xfi3p601	414	9	the	the	DT
cord-004615-xfi3p601	414	10	results	result	NNS
cord-004615-xfi3p601	414	11	in	in	IN
cord-004615-xfi3p601	414	12	Table	Table	NNP
cord-004615-xfi3p601	414	13	5	5	CD
cord-004615-xfi3p601	414	14	,	,	,
cord-004615-xfi3p601	414	15	we	-PRON-	PRP
cord-004615-xfi3p601	414	16	know	know	VBP
cord-004615-xfi3p601	414	17	how	how	WRB
cord-004615-xfi3p601	414	18	much	much	JJ
cord-004615-xfi3p601	414	19	trust	trust	NN
cord-004615-xfi3p601	414	20	we	-PRON-	PRP
cord-004615-xfi3p601	414	21	may	may	MD
cord-004615-xfi3p601	414	22	put	put	VB
cord-004615-xfi3p601	414	23	in	in	IN
cord-004615-xfi3p601	414	24	the	the	DT
cord-004615-xfi3p601	414	25	expected	expect	VBN
cord-004615-xfi3p601	414	26	sizes	size	NNS
cord-004615-xfi3p601	414	27	.	.	.
cord-004615-xfi3p601	415	1	Up	up	IN
cord-004615-xfi3p601	415	2	to	to	IN
cord-004615-xfi3p601	415	3	now	now	RB
cord-004615-xfi3p601	415	4	we	-PRON-	PRP
cord-004615-xfi3p601	415	5	used	use	VBD
cord-004615-xfi3p601	415	6	exact	exact	JJ
cord-004615-xfi3p601	415	7	parameters	parameter	NNS
cord-004615-xfi3p601	415	8	.	.	.
cord-004615-xfi3p601	416	1	In	in	IN
cord-004615-xfi3p601	416	2	reality	reality	NN
cord-004615-xfi3p601	416	3	we	-PRON-	PRP
cord-004615-xfi3p601	416	4	can	can	MD
cord-004615-xfi3p601	416	5	not	not	RB
cord-004615-xfi3p601	416	6	estimate	estimate	VB
cord-004615-xfi3p601	416	7	the	the	DT
cord-004615-xfi3p601	416	8	parameters	parameter	NNS
cord-004615-xfi3p601	416	9	exactly	exactly	RB
cord-004615-xfi3p601	416	10	.	.	.
cord-004615-xfi3p601	417	1	In	in	IN
cord-004615-xfi3p601	417	2	order	order	NN
cord-004615-xfi3p601	417	3	to	to	TO
cord-004615-xfi3p601	417	4	get	get	VB
cord-004615-xfi3p601	417	5	some	some	DT
cord-004615-xfi3p601	417	6	insight	insight	NN
cord-004615-xfi3p601	417	7	into	into	IN
cord-004615-xfi3p601	417	8	how	how	WRB
cord-004615-xfi3p601	417	9	the	the	DT
cord-004615-xfi3p601	417	10	computed	compute	VBN
cord-004615-xfi3p601	417	11	properties	property	NNS
cord-004615-xfi3p601	417	12	depend	depend	VBP
cord-004615-xfi3p601	417	13	on	on	IN
cord-004615-xfi3p601	417	14	the	the	DT
cord-004615-xfi3p601	417	15	values	value	NNS
cord-004615-xfi3p601	417	16	of	of	IN
cord-004615-xfi3p601	417	17	the	the	DT
cord-004615-xfi3p601	417	18	different	different	JJ
cord-004615-xfi3p601	417	19	parameters	parameter	NNS
cord-004615-xfi3p601	417	20	,	,	,
cord-004615-xfi3p601	417	21	we	-PRON-	PRP
cord-004615-xfi3p601	417	22	varied	vary	VBD
cord-004615-xfi3p601	417	23	one	one	CD
cord-004615-xfi3p601	417	24	parameter	parameter	NN
cord-004615-xfi3p601	417	25	while	while	IN
cord-004615-xfi3p601	417	26	keeping	keep	VBG
cord-004615-xfi3p601	417	27	the	the	DT
cord-004615-xfi3p601	417	28	other	other	JJ
cord-004615-xfi3p601	417	29	parameters	parameter	NNS
cord-004615-xfi3p601	417	30	constant	constant	JJ
cord-004615-xfi3p601	417	31	.	.	.
cord-004615-xfi3p601	418	1	The	the	DT
cord-004615-xfi3p601	418	2	results	result	NNS
cord-004615-xfi3p601	418	3	for	for	IN
cord-004615-xfi3p601	418	4	the	the	DT
cord-004615-xfi3p601	418	5	strategies	strategy	NNS
cord-004615-xfi3p601	418	6	B	B	NNP
cord-004615-xfi3p601	418	7	and	and	CC
cord-004615-xfi3p601	418	8	D	d	NN
cord-004615-xfi3p601	418	9	are	be	VBP
cord-004615-xfi3p601	418	10	given	give	VBN
cord-004615-xfi3p601	418	11	in	in	IN
cord-004615-xfi3p601	418	12	Figures	figure	NNS
cord-004615-xfi3p601	418	13	1	1	CD
cord-004615-xfi3p601	418	14	and	and	CC
cord-004615-xfi3p601	418	15	2	2	CD
cord-004615-xfi3p601	418	16	.	.	.
cord-004615-xfi3p601	419	1	Note	note	VB
cord-004615-xfi3p601	419	2	that	that	IN
cord-004615-xfi3p601	419	3	the	the	DT
cord-004615-xfi3p601	419	4	scales	scale	NNS
cord-004615-xfi3p601	419	5	on	on	IN
cord-004615-xfi3p601	419	6	the	the	DT
cord-004615-xfi3p601	419	7	axes	axis	NNS
cord-004615-xfi3p601	419	8	differ	differ	VBP
cord-004615-xfi3p601	419	9	for	for	IN
cord-004615-xfi3p601	419	10	the	the	DT
cord-004615-xfi3p601	419	11	different	different	JJ
cord-004615-xfi3p601	419	12	varying	varying	NN
cord-004615-xfi3p601	419	13	parameters	parameter	NNS
cord-004615-xfi3p601	419	14	.	.	.
cord-004615-xfi3p601	420	1	On	on	IN
cord-004615-xfi3p601	420	2	the	the	DT
cord-004615-xfi3p601	420	3	x	x	NN
cord-004615-xfi3p601	420	4	-	-	NNS
cord-004615-xfi3p601	420	5	axes	axis	NNS
cord-004615-xfi3p601	420	6	we	-PRON-	PRP
cord-004615-xfi3p601	420	7	put	put	VBP
cord-004615-xfi3p601	420	8	the	the	DT
cord-004615-xfi3p601	420	9	ratio	ratio	NN
cord-004615-xfi3p601	420	10	between	between	IN
cord-004615-xfi3p601	420	11	the	the	DT
cord-004615-xfi3p601	420	12	value	value	NN
cord-004615-xfi3p601	420	13	of	of	IN
cord-004615-xfi3p601	420	14	the	the	DT
cord-004615-xfi3p601	420	15	parameter	parameter	NN
cord-004615-xfi3p601	420	16	and	and	CC
cord-004615-xfi3p601	420	17	the	the	DT
cord-004615-xfi3p601	420	18	point	point	NN
cord-004615-xfi3p601	420	19	estimator	estimator	NN
cord-004615-xfi3p601	420	20	of	of	IN
cord-004615-xfi3p601	420	21	that	that	DT
cord-004615-xfi3p601	420	22	parameter	parameter	NN
cord-004615-xfi3p601	420	23	.	.	.
cord-004615-xfi3p601	421	1	We	-PRON-	PRP
cord-004615-xfi3p601	421	2	see	see	VBP
cord-004615-xfi3p601	421	3	that	that	IN
cord-004615-xfi3p601	421	4	for	for	IN
cord-004615-xfi3p601	421	5	these	these	DT
cord-004615-xfi3p601	421	6	strategies	strategy	NNS
cord-004615-xfi3p601	421	7	,	,	,
cord-004615-xfi3p601	421	8	the	the	DT
cord-004615-xfi3p601	421	9	parameters	parameter	NNS
cord-004615-xfi3p601	421	10	r	r	NN
cord-004615-xfi3p601	421	11	and	and	CC
cord-004615-xfi3p601	421	12	R	r	NN
cord-004615-xfi3p601	421	13	have	have	VBP
cord-004615-xfi3p601	421	14	relatively	relatively	RB
cord-004615-xfi3p601	421	15	little	little	JJ
cord-004615-xfi3p601	421	16	influence	influence	NN
cord-004615-xfi3p601	421	17	on	on	IN
cord-004615-xfi3p601	421	18	the	the	DT
cord-004615-xfi3p601	421	19	computed	compute	VBN
cord-004615-xfi3p601	421	20	quantities	quantity	NNS
cord-004615-xfi3p601	421	21	,	,	,
cord-004615-xfi3p601	421	22	while	while	IN
cord-004615-xfi3p601	421	23	α	α	NNP
cord-004615-xfi3p601	421	24	and	and	CC
cord-004615-xfi3p601	421	25	β	β	NN
cord-004615-xfi3p601	421	26	do	do	VBP
cord-004615-xfi3p601	421	27	have	have	VB
cord-004615-xfi3p601	421	28	significant	significant	JJ
cord-004615-xfi3p601	421	29	influence	influence	NN
cord-004615-xfi3p601	421	30	.	.	.
cord-004615-xfi3p601	422	1	In	in	IN
cord-004615-xfi3p601	422	2	a	a	DT
cord-004615-xfi3p601	422	3	constant	constant	JJ
cord-004615-xfi3p601	422	4	environment	environment	NN
cord-004615-xfi3p601	422	5	the	the	DT
cord-004615-xfi3p601	422	6	only	only	JJ
cord-004615-xfi3p601	422	7	thing	thing	NN
cord-004615-xfi3p601	422	8	that	that	WDT
cord-004615-xfi3p601	422	9	matters	matter	VBZ
cord-004615-xfi3p601	422	10	is	be	VBZ
cord-004615-xfi3p601	422	11	the	the	DT
cord-004615-xfi3p601	422	12	ratio	ratio	NN
cord-004615-xfi3p601	422	13	β	β	NN
cord-004615-xfi3p601	422	14	α	α	NN
cord-004615-xfi3p601	422	15	.	.	.
cord-004615-xfi3p601	423	1	For	for	IN
cord-004615-xfi3p601	423	2	varying	vary	VBG
cord-004615-xfi3p601	423	3	environments	environment	NNS
cord-004615-xfi3p601	423	4	we	-PRON-	PRP
cord-004615-xfi3p601	423	5	varied	vary	VBD
cord-004615-xfi3p601	423	6	α	α	NN
cord-004615-xfi3p601	423	7	,	,	,
cord-004615-xfi3p601	423	8	while	while	IN
cord-004615-xfi3p601	423	9	keeping	keep	VBG
cord-004615-xfi3p601	423	10	β	β	NN
cord-004615-xfi3p601	423	11	α	α	NNP
cord-004615-xfi3p601	423	12	and	and	CC
cord-004615-xfi3p601	423	13	β	β	NN
cord-004615-xfi3p601	423	14	tr	tr	NNP
cord-004615-xfi3p601	423	15	α	α	NNP
cord-004615-xfi3p601	423	16	constant	constant	JJ
cord-004615-xfi3p601	423	17	.	.	.
cord-004615-xfi3p601	424	1	The	the	DT
cord-004615-xfi3p601	424	2	results	result	NNS
cord-004615-xfi3p601	424	3	are	be	VBP
cord-004615-xfi3p601	424	4	varying	vary	VBG
cord-004615-xfi3p601	424	5	,	,	,
cord-004615-xfi3p601	424	6	but	but	CC
cord-004615-xfi3p601	424	7	not	not	RB
cord-004615-xfi3p601	424	8	very	very	RB
cord-004615-xfi3p601	424	9	much	much	RB
cord-004615-xfi3p601	424	10	.	.	.
cord-004615-xfi3p601	425	1	1	1	LS
cord-004615-xfi3p601	425	2	.	.	.
cord-004615-xfi3p601	426	1	We	-PRON-	PRP
cord-004615-xfi3p601	426	2	can	can	MD
cord-004615-xfi3p601	426	3	not	not	RB
cord-004615-xfi3p601	426	4	estimate	estimate	VB
cord-004615-xfi3p601	426	5	the	the	DT
cord-004615-xfi3p601	426	6	parameters	parameter	NNS
cord-004615-xfi3p601	426	7	exactly	exactly	RB
cord-004615-xfi3p601	426	8	.	.	.
cord-004615-xfi3p601	427	1	Because	because	IN
cord-004615-xfi3p601	427	2	the	the	DT
cord-004615-xfi3p601	427	3	expected	expect	VBN
cord-004615-xfi3p601	427	4	final	final	JJ
cord-004615-xfi3p601	427	5	size	size	NN
cord-004615-xfi3p601	427	6	,	,	,
cord-004615-xfi3p601	427	7	the	the	DT
cord-004615-xfi3p601	427	8	probability	probability	NN
cord-004615-xfi3p601	427	9	of	of	IN
cord-004615-xfi3p601	427	10	extinction	extinction	NN
cord-004615-xfi3p601	427	11	and	and	CC
cord-004615-xfi3p601	427	12	the	the	DT
cord-004615-xfi3p601	427	13	generating	generating	NN
cord-004615-xfi3p601	427	14	function	function	NN
cord-004615-xfi3p601	427	15	for	for	IN
cord-004615-xfi3p601	427	16	the	the	DT
cord-004615-xfi3p601	427	17	number	number	NN
cord-004615-xfi3p601	427	18	of	of	IN
cord-004615-xfi3p601	427	19	infective	infective	JJ
cord-004615-xfi3p601	427	20	herds	herd	NNS
cord-004615-xfi3p601	427	21	at	at	IN
cord-004615-xfi3p601	427	22	a	a	DT
cord-004615-xfi3p601	427	23	certain	certain	JJ
cord-004615-xfi3p601	427	24	moment	moment	NN
cord-004615-xfi3p601	427	25	heavily	heavily	RB
cord-004615-xfi3p601	427	26	depend	depend	VBP
cord-004615-xfi3p601	427	27	on	on	IN
cord-004615-xfi3p601	427	28	some	some	DT
cord-004615-xfi3p601	427	29	of	of	IN
cord-004615-xfi3p601	427	30	the	the	DT
cord-004615-xfi3p601	427	31	parameters	parameter	NNS
cord-004615-xfi3p601	427	32	,	,	,
cord-004615-xfi3p601	427	33	we	-PRON-	PRP
cord-004615-xfi3p601	427	34	can	can	MD
cord-004615-xfi3p601	427	35	not	not	RB
cord-004615-xfi3p601	427	36	really	really	RB
cord-004615-xfi3p601	427	37	use	use	VB
cord-004615-xfi3p601	427	38	the	the	DT
cord-004615-xfi3p601	427	39	computed	compute	VBN
cord-004615-xfi3p601	427	40	values	value	NNS
cord-004615-xfi3p601	427	41	in	in	IN
cord-004615-xfi3p601	427	42	a	a	DT
cord-004615-xfi3p601	427	43	quantitative	quantitative	JJ
cord-004615-xfi3p601	427	44	way	way	NN
cord-004615-xfi3p601	427	45	.	.	.
cord-004615-xfi3p601	428	1	But	but	CC
cord-004615-xfi3p601	428	2	we	-PRON-	PRP
cord-004615-xfi3p601	428	3	can	can	MD
cord-004615-xfi3p601	428	4	use	use	VB
cord-004615-xfi3p601	428	5	them	-PRON-	PRP
cord-004615-xfi3p601	428	6	to	to	TO
cord-004615-xfi3p601	428	7	compare	compare	VB
cord-004615-xfi3p601	428	8	different	different	JJ
cord-004615-xfi3p601	428	9	scenarios	scenario	NNS
cord-004615-xfi3p601	428	10	,	,	,
cord-004615-xfi3p601	428	11	while	while	IN
cord-004615-xfi3p601	428	12	using	use	VBG
cord-004615-xfi3p601	428	13	the	the	DT
cord-004615-xfi3p601	428	14	same	same	JJ
cord-004615-xfi3p601	428	15	parameter	parameter	NN
cord-004615-xfi3p601	428	16	values	value	NNS
cord-004615-xfi3p601	428	17	.	.	.
cord-004615-xfi3p601	429	1	2	2	LS
cord-004615-xfi3p601	429	2	.	.	.
cord-004615-xfi3p601	430	1	We	-PRON-	PRP
cord-004615-xfi3p601	430	2	computed	compute	VBD
cord-004615-xfi3p601	430	3	the	the	DT
cord-004615-xfi3p601	430	4	probability	probability	NN
cord-004615-xfi3p601	430	5	of	of	IN
cord-004615-xfi3p601	430	6	extinction	extinction	NN
cord-004615-xfi3p601	430	7	for	for	IN
cord-004615-xfi3p601	430	8	the	the	DT
cord-004615-xfi3p601	430	9	progeny	progeny	NN
cord-004615-xfi3p601	430	10	of	of	IN
cord-004615-xfi3p601	430	11	one	one	CD
cord-004615-xfi3p601	430	12	infective	infective	JJ
cord-004615-xfi3p601	430	13	herd	herd	NN
cord-004615-xfi3p601	430	14	,	,	,
cord-004615-xfi3p601	430	15	but	but	CC
cord-004615-xfi3p601	430	16	in	in	IN
cord-004615-xfi3p601	430	17	reality	reality	NN
cord-004615-xfi3p601	430	18	we	-PRON-	PRP
cord-004615-xfi3p601	430	19	may	may	MD
cord-004615-xfi3p601	430	20	have	have	VB
cord-004615-xfi3p601	430	21	more	more	JJR
cord-004615-xfi3p601	430	22	than	than	IN
cord-004615-xfi3p601	430	23	one	one	CD
cord-004615-xfi3p601	430	24	infected	infected	JJ
cord-004615-xfi3p601	430	25	herd	herd	NN
cord-004615-xfi3p601	430	26	at	at	IN
cord-004615-xfi3p601	430	27	the	the	DT
cord-004615-xfi3p601	430	28	moment	moment	NN
cord-004615-xfi3p601	430	29	the	the	DT
cord-004615-xfi3p601	430	30	first	first	JJ
cord-004615-xfi3p601	430	31	measures	measure	NNS
cord-004615-xfi3p601	430	32	are	be	VBP
cord-004615-xfi3p601	430	33	implemented	implement	VBN
cord-004615-xfi3p601	430	34	,	,	,
cord-004615-xfi3p601	430	35	so	so	CC
cord-004615-xfi3p601	430	36	the	the	DT
cord-004615-xfi3p601	430	37	probability	probability	NN
cord-004615-xfi3p601	430	38	of	of	IN
cord-004615-xfi3p601	430	39	extinction	extinction	NN
cord-004615-xfi3p601	430	40	may	may	MD
cord-004615-xfi3p601	430	41	be	be	VB
cord-004615-xfi3p601	430	42	much	much	RB
cord-004615-xfi3p601	430	43	less	less	JJR
cord-004615-xfi3p601	430	44	than	than	IN
cord-004615-xfi3p601	430	45	the	the	DT
cord-004615-xfi3p601	430	46	computed	compute	VBN
cord-004615-xfi3p601	430	47	q.	q.	NN
cord-004615-xfi3p601	431	1	We	-PRON-	PRP
cord-004615-xfi3p601	431	2	assumed	assume	VBD
cord-004615-xfi3p601	431	3	that	that	IN
cord-004615-xfi3p601	431	4	different	different	JJ
cord-004615-xfi3p601	431	5	infected	infected	JJ
cord-004615-xfi3p601	431	6	herds	herd	NNS
cord-004615-xfi3p601	431	7	infect	infect	VBP
cord-004615-xfi3p601	431	8	other	other	JJ
cord-004615-xfi3p601	431	9	herds	herd	NNS
cord-004615-xfi3p601	431	10	independently	independently	RB
cord-004615-xfi3p601	431	11	of	of	IN
cord-004615-xfi3p601	431	12	each	each	DT
cord-004615-xfi3p601	431	13	other	other	JJ
cord-004615-xfi3p601	431	14	.	.	.
cord-004615-xfi3p601	432	1	If	if	IN
cord-004615-xfi3p601	432	2	we	-PRON-	PRP
cord-004615-xfi3p601	432	3	simplify	simplify	VBP
cord-004615-xfi3p601	432	4	the	the	DT
cord-004615-xfi3p601	432	5	model	model	NN
cord-004615-xfi3p601	432	6	by	by	IN
cord-004615-xfi3p601	432	7	assuming	assume	VBG
cord-004615-xfi3p601	432	8	that	that	IN
cord-004615-xfi3p601	432	9	all	all	DT
cord-004615-xfi3p601	432	10	herds	herd	NNS
cord-004615-xfi3p601	432	11	at	at	IN
cord-004615-xfi3p601	432	12	time	time	NN
cord-004615-xfi3p601	432	13	t	t	NN
cord-004615-xfi3p601	432	14	=	=	SYM
cord-004615-xfi3p601	432	15	0	0	CD
cord-004615-xfi3p601	432	16	have	have	VBP
cord-004615-xfi3p601	432	17	age	age	NN
cord-004615-xfi3p601	432	18	0	0	NFP
cord-004615-xfi3p601	432	19	,	,	,
cord-004615-xfi3p601	432	20	we	-PRON-	PRP
cord-004615-xfi3p601	432	21	can	can	MD
cord-004615-xfi3p601	432	22	estimate	estimate	VB
cord-004615-xfi3p601	432	23	the	the	DT
cord-004615-xfi3p601	432	24	expected	expect	VBN
cord-004615-xfi3p601	432	25	final	final	JJ
cord-004615-xfi3p601	432	26	size	size	NN
cord-004615-xfi3p601	432	27	by	by	IN
cord-004615-xfi3p601	432	28	the	the	DT
cord-004615-xfi3p601	432	29	number	number	NN
cord-004615-xfi3p601	432	30	of	of	IN
cord-004615-xfi3p601	432	31	initially	initially	RB
cord-004615-xfi3p601	432	32	infected	infect	VBN
cord-004615-xfi3p601	432	33	herds	herd	NNS
cord-004615-xfi3p601	432	34	times	times	IN
cord-004615-xfi3p601	432	35	the	the	DT
cord-004615-xfi3p601	432	36	estimated	estimate	VBN
cord-004615-xfi3p601	432	37	final	final	JJ
cord-004615-xfi3p601	432	38	size	size	NN
cord-004615-xfi3p601	432	39	of	of	IN
cord-004615-xfi3p601	432	40	one	one	CD
cord-004615-xfi3p601	432	41	infected	infected	JJ
cord-004615-xfi3p601	432	42	herd	herd	NN
cord-004615-xfi3p601	432	43	.	.	.
cord-004615-xfi3p601	433	1	In	in	IN
cord-004615-xfi3p601	433	2	the	the	DT
cord-004615-xfi3p601	433	3	same	same	JJ
cord-004615-xfi3p601	433	4	way	way	NN
cord-004615-xfi3p601	433	5	we	-PRON-	PRP
cord-004615-xfi3p601	433	6	can	can	MD
cord-004615-xfi3p601	433	7	estimate	estimate	VB
cord-004615-xfi3p601	433	8	the	the	DT
cord-004615-xfi3p601	433	9	probability	probability	NN
cord-004615-xfi3p601	433	10	of	of	IN
cord-004615-xfi3p601	433	11	extinction	extinction	NN
cord-004615-xfi3p601	433	12	by	by	IN
cord-004615-xfi3p601	433	13	the	the	DT
cord-004615-xfi3p601	433	14	computed	compute	VBN
cord-004615-xfi3p601	433	15	probability	probability	NN
cord-004615-xfi3p601	433	16	for	for	IN
cord-004615-xfi3p601	433	17	one	one	CD
cord-004615-xfi3p601	433	18	herd	herd	NN
cord-004615-xfi3p601	433	19	,	,	,
cord-004615-xfi3p601	433	20	to	to	IN
cord-004615-xfi3p601	433	21	the	the	DT
cord-004615-xfi3p601	433	22	power	power	NN
cord-004615-xfi3p601	433	23	of	of	IN
cord-004615-xfi3p601	433	24	the	the	DT
cord-004615-xfi3p601	433	25	number	number	NN
cord-004615-xfi3p601	433	26	of	of	IN
cord-004615-xfi3p601	433	27	initially	initially	RB
cord-004615-xfi3p601	433	28	infected	infect	VBN
cord-004615-xfi3p601	433	29	herds	herd	NNS
cord-004615-xfi3p601	433	30	.	.	.
cord-004615-xfi3p601	434	1	From	from	IN
cord-004615-xfi3p601	434	2	previous	previous	JJ
cord-004615-xfi3p601	434	3	outbreaks	outbreak	NNS
cord-004615-xfi3p601	434	4	of	of	IN
cord-004615-xfi3p601	434	5	FMD	FMD	NNP
cord-004615-xfi3p601	434	6	,	,	,
cord-004615-xfi3p601	434	7	CSF	CSF	NNP
cord-004615-xfi3p601	434	8	and	and	CC
cord-004615-xfi3p601	434	9	AI	AI	NNP
cord-004615-xfi3p601	434	10	in	in	IN
cord-004615-xfi3p601	434	11	the	the	DT
cord-004615-xfi3p601	434	12	Netherlands	Netherlands	NNP
cord-004615-xfi3p601	434	13	,	,	,
cord-004615-xfi3p601	434	14	one	one	PRP
cord-004615-xfi3p601	434	15	can	can	MD
cord-004615-xfi3p601	434	16	see	see	VB
cord-004615-xfi3p601	434	17	that	that	IN
cord-004615-xfi3p601	434	18	as	as	IN
cord-004615-xfi3p601	434	19	a	a	DT
cord-004615-xfi3p601	434	20	rule	rule	NN
cord-004615-xfi3p601	434	21	several	several	JJ
cord-004615-xfi3p601	434	22	farms	farm	NNS
cord-004615-xfi3p601	434	23	are	be	VBP
cord-004615-xfi3p601	434	24	already	already	RB
cord-004615-xfi3p601	434	25	infected	infect	VBN
cord-004615-xfi3p601	434	26	at	at	IN
cord-004615-xfi3p601	434	27	the	the	DT
cord-004615-xfi3p601	434	28	moment	moment	NN
cord-004615-xfi3p601	434	29	the	the	DT
cord-004615-xfi3p601	434	30	first	first	JJ
cord-004615-xfi3p601	434	31	case	case	NN
cord-004615-xfi3p601	434	32	is	be	VBZ
cord-004615-xfi3p601	434	33	suspected	suspect	VBN
cord-004615-xfi3p601	434	34	or	or	CC
cord-004615-xfi3p601	434	35	confirmed	confirm	VBN
cord-004615-xfi3p601	434	36	.	.	.
cord-004615-xfi3p601	435	1	3	3	LS
cord-004615-xfi3p601	435	2	.	.	.
cord-004615-xfi3p601	436	1	The	the	DT
cord-004615-xfi3p601	436	2	results	result	NNS
cord-004615-xfi3p601	436	3	are	be	VBP
cord-004615-xfi3p601	436	4	very	very	RB
cord-004615-xfi3p601	436	5	much	much	RB
cord-004615-xfi3p601	436	6	the	the	DT
cord-004615-xfi3p601	436	7	same	same	JJ
cord-004615-xfi3p601	436	8	as	as	IN
cord-004615-xfi3p601	436	9	the	the	DT
cord-004615-xfi3p601	436	10	results	result	NNS
cord-004615-xfi3p601	436	11	of	of	IN
cord-004615-xfi3p601	436	12	Klinkenberg	Klinkenberg	NNP
cord-004615-xfi3p601	436	13	et	et	FW
cord-004615-xfi3p601	436	14	al	al	NNP
cord-004615-xfi3p601	436	15	.	.	.
cord-004615-xfi3p601	437	1	but	but	CC
cord-004615-xfi3p601	437	2	we	-PRON-	PRP
cord-004615-xfi3p601	437	3	do	do	VBP
cord-004615-xfi3p601	437	4	not	not	RB
cord-004615-xfi3p601	437	5	need	need	VB
cord-004615-xfi3p601	437	6	simulations	simulation	NNS
cord-004615-xfi3p601	437	7	to	to	TO
cord-004615-xfi3p601	437	8	estimate	estimate	VB
cord-004615-xfi3p601	437	9	the	the	DT
cord-004615-xfi3p601	437	10	properties	property	NNS
cord-004615-xfi3p601	437	11	.	.	.
cord-004615-xfi3p601	438	1	Also	also	RB
cord-004615-xfi3p601	438	2	,	,	,
cord-004615-xfi3p601	438	3	our	-PRON-	PRP$
cord-004615-xfi3p601	438	4	method	method	NN
cord-004615-xfi3p601	438	5	is	be	VBZ
cord-004615-xfi3p601	438	6	much	much	RB
cord-004615-xfi3p601	438	7	faster	fast	JJR
cord-004615-xfi3p601	438	8	than	than	IN
cord-004615-xfi3p601	438	9	using	use	VBG
cord-004615-xfi3p601	438	10	simulations	simulation	NNS
cord-004615-xfi3p601	438	11	.	.	.
cord-004615-xfi3p601	439	1	In	in	IN
cord-004615-xfi3p601	439	2	Table	Table	NNP
cord-004615-xfi3p601	439	3	6	6	CD
cord-004615-xfi3p601	439	4	of	of	IN
cord-004615-xfi3p601	439	5	[	[	-LRB-
cord-004615-xfi3p601	439	6	1	1	CD
cord-004615-xfi3p601	439	7	]	]	-RRB-
cord-004615-xfi3p601	439	8	it	-PRON-	PRP
cord-004615-xfi3p601	439	9	is	be	VBZ
cord-004615-xfi3p601	439	10	suggested	suggest	VBN
cord-004615-xfi3p601	439	11	that	that	IN
cord-004615-xfi3p601	439	12	the	the	DT
cord-004615-xfi3p601	439	13	expected	expect	VBN
cord-004615-xfi3p601	439	14	final	final	JJ
cord-004615-xfi3p601	439	15	size	size	NN
cord-004615-xfi3p601	439	16	,	,	,
cord-004615-xfi3p601	439	17	with	with	IN
cord-004615-xfi3p601	439	18	initially	initially	RB
cord-004615-xfi3p601	439	19	five	five	CD
cord-004615-xfi3p601	439	20	infected	infected	JJ
cord-004615-xfi3p601	439	21	multipliers	multiplier	NNS
cord-004615-xfi3p601	439	22	and	and	CC
cord-004615-xfi3p601	439	23	five	five	CD
cord-004615-xfi3p601	439	24	infected	infected	JJ
cord-004615-xfi3p601	439	25	finishers	finisher	NNS
cord-004615-xfi3p601	439	26	,	,	,
cord-004615-xfi3p601	439	27	is	be	VBZ
cord-004615-xfi3p601	439	28	estimated	estimate	VBN
cord-004615-xfi3p601	439	29	by	by	IN
cord-004615-xfi3p601	439	30	simulations	simulation	NNS
cord-004615-xfi3p601	439	31	.	.	.
cord-004615-xfi3p601	440	1	In	in	IN
cord-004615-xfi3p601	440	2	reality	reality	NN
cord-004615-xfi3p601	440	3	the	the	DT
cord-004615-xfi3p601	440	4	median	median	NN
cord-004615-xfi3p601	440	5	of	of	IN
cord-004615-xfi3p601	440	6	1000	1000	CD
cord-004615-xfi3p601	440	7	simulations	simulation	NNS
cord-004615-xfi3p601	440	8	is	be	VBZ
cord-004615-xfi3p601	440	9	used	use	VBN
cord-004615-xfi3p601	440	10	in	in	IN
cord-004615-xfi3p601	440	11	that	that	DT
cord-004615-xfi3p601	440	12	paper	paper	NN
cord-004615-xfi3p601	440	13	.	.	.
cord-004615-xfi3p601	441	1	This	this	DT
cord-004615-xfi3p601	441	2	explains	explain	VBZ
cord-004615-xfi3p601	441	3	why	why	WRB
cord-004615-xfi3p601	441	4	our	-PRON-	PRP$
cord-004615-xfi3p601	441	5	results	result	NNS
cord-004615-xfi3p601	441	6	differ	differ	VBP
cord-004615-xfi3p601	441	7	on	on	IN
cord-004615-xfi3p601	441	8	that	that	DT
cord-004615-xfi3p601	441	9	point	point	NN
cord-004615-xfi3p601	441	10	.	.	.
cord-004615-xfi3p601	442	1	4	4	LS
cord-004615-xfi3p601	442	2	.	.	.
cord-004615-xfi3p601	443	1	Note	note	VB
cord-004615-xfi3p601	443	2	that	that	DT
cord-004615-xfi3p601	443	3	strategy	strategy	NN
cord-004615-xfi3p601	443	4	ABC	ABC	NNP
cord-004615-xfi3p601	443	5	gives	give	VBZ
cord-004615-xfi3p601	443	6	an	an	DT
cord-004615-xfi3p601	443	7	extremely	extremely	RB
cord-004615-xfi3p601	443	8	high	high	JJ
cord-004615-xfi3p601	443	9	expected	expect	VBN
cord-004615-xfi3p601	443	10	final	final	JJ
cord-004615-xfi3p601	443	11	size	size	NN
cord-004615-xfi3p601	443	12	.	.	.
cord-004615-xfi3p601	444	1	Klinkenberg	Klinkenberg	NNP
cord-004615-xfi3p601	444	2	et	et	FW
cord-004615-xfi3p601	444	3	al	al	NNP
cord-004615-xfi3p601	444	4	.	.	.
cord-004615-xfi3p601	445	1	[	[	-LRB-
cord-004615-xfi3p601	445	2	1	1	CD
cord-004615-xfi3p601	445	3	]	]	-RRB-
cord-004615-xfi3p601	445	4	did	do	VBD
cord-004615-xfi3p601	445	5	not	not	RB
cord-004615-xfi3p601	445	6	even	even	RB
cord-004615-xfi3p601	445	7	give	give	VB
cord-004615-xfi3p601	445	8	this	this	DT
cord-004615-xfi3p601	445	9	final	final	JJ
cord-004615-xfi3p601	445	10	size	size	NN
cord-004615-xfi3p601	445	11	.	.	.
cord-004615-xfi3p601	446	1	This	this	DT
cord-004615-xfi3p601	446	2	is	be	VBZ
cord-004615-xfi3p601	446	3	because	because	IN
cord-004615-xfi3p601	446	4	for	for	IN
cord-004615-xfi3p601	446	5	the	the	DT
cord-004615-xfi3p601	446	6	given	give	VBN
cord-004615-xfi3p601	446	7	parameters	parameter	NNS
cord-004615-xfi3p601	446	8	the	the	DT
cord-004615-xfi3p601	446	9	process	process	NN
cord-004615-xfi3p601	446	10	is	be	VBZ
cord-004615-xfi3p601	446	11	very	very	RB
cord-004615-xfi3p601	446	12	near	near	JJ
cord-004615-xfi3p601	446	13	to	to	IN
cord-004615-xfi3p601	446	14	a	a	DT
cord-004615-xfi3p601	446	15	process	process	NN
cord-004615-xfi3p601	446	16	with	with	IN
cord-004615-xfi3p601	446	17	a	a	DT
cord-004615-xfi3p601	446	18	positive	positive	JJ
cord-004615-xfi3p601	446	19	probability	probability	NN
cord-004615-xfi3p601	446	20	of	of	IN
cord-004615-xfi3p601	446	21	surviving	survive	VBG
cord-004615-xfi3p601	446	22	i.e.	i.e.	FW
cord-004615-xfi3p601	446	23	a	a	DT
cord-004615-xfi3p601	446	24	positive	positive	JJ
cord-004615-xfi3p601	446	25	probability	probability	NN
cord-004615-xfi3p601	446	26	of	of	IN
cord-004615-xfi3p601	446	27	an	an	DT
cord-004615-xfi3p601	446	28	infinite	infinite	JJ
cord-004615-xfi3p601	446	29	final	final	JJ
cord-004615-xfi3p601	446	30	size	size	NN
cord-004615-xfi3p601	446	31	.	.	.
cord-004615-xfi3p601	447	1	5	5	LS
cord-004615-xfi3p601	447	2	.	.	.
cord-004615-xfi3p601	448	1	Using	use	VBG
cord-004615-xfi3p601	448	2	the	the	DT
cord-004615-xfi3p601	448	3	expected	expect	VBN
cord-004615-xfi3p601	448	4	size	size	NN
cord-004615-xfi3p601	448	5	at	at	IN
cord-004615-xfi3p601	448	6	t	t	NN
cord-004615-xfi3p601	448	7	=	=	SYM
cord-004615-xfi3p601	448	8	T	T	NNP
cord-004615-xfi3p601	448	9	and	and	CC
cord-004615-xfi3p601	448	10	the	the	DT
cord-004615-xfi3p601	448	11	variance	variance	NN
cord-004615-xfi3p601	448	12	of	of	IN
cord-004615-xfi3p601	448	13	this	this	DT
cord-004615-xfi3p601	448	14	size	size	NN
cord-004615-xfi3p601	448	15	,	,	,
cord-004615-xfi3p601	448	16	we	-PRON-	PRP
cord-004615-xfi3p601	448	17	see	see	VBP
cord-004615-xfi3p601	448	18	that	that	IN
cord-004615-xfi3p601	448	19	the	the	DT
cord-004615-xfi3p601	448	20	expected	expect	VBN
cord-004615-xfi3p601	448	21	final	final	JJ
cord-004615-xfi3p601	448	22	size	size	NN
cord-004615-xfi3p601	448	23	is	be	VBZ
cord-004615-xfi3p601	448	24	not	not	RB
cord-004615-xfi3p601	448	25	very	very	RB
cord-004615-xfi3p601	448	26	informative	informative	JJ
cord-004615-xfi3p601	448	27	in	in	IN
cord-004615-xfi3p601	448	28	some	some	DT
cord-004615-xfi3p601	448	29	scenarios	scenario	NNS
cord-004615-xfi3p601	448	30	.	.	.
cord-004615-xfi3p601	449	1	Large	large	JJ
cord-004615-xfi3p601	449	2	variance	variance	NN
cord-004615-xfi3p601	449	3	may	may	MD
cord-004615-xfi3p601	449	4	imply	imply	VB
cord-004615-xfi3p601	449	5	that	that	IN
cord-004615-xfi3p601	449	6	a	a	DT
cord-004615-xfi3p601	449	7	large	large	JJ
cord-004615-xfi3p601	449	8	set	set	NN
cord-004615-xfi3p601	449	9	of	of	IN
cord-004615-xfi3p601	449	10	"	"	``
cord-004615-xfi3p601	449	11	numbers	number	NNS
cord-004615-xfi3p601	449	12	of	of	IN
cord-004615-xfi3p601	449	13	infected	infected	JJ
cord-004615-xfi3p601	449	14	herds	herd	NNS
cord-004615-xfi3p601	449	15	"	"	``
cord-004615-xfi3p601	449	16	have	have	VBP
cord-004615-xfi3p601	449	17	a	a	DT
cord-004615-xfi3p601	449	18	not	not	RB
cord-004615-xfi3p601	449	19	-	-	HYPH
cord-004615-xfi3p601	449	20	ignorable	ignorable	JJ
cord-004615-xfi3p601	449	21	probability	probability	NN
cord-004615-xfi3p601	449	22	,	,	,
cord-004615-xfi3p601	449	23	even	even	RB
cord-004615-xfi3p601	449	24	if	if	IN
cord-004615-xfi3p601	449	25	we	-PRON-	PRP
cord-004615-xfi3p601	449	26	know	know	VBP
cord-004615-xfi3p601	449	27	the	the	DT
cord-004615-xfi3p601	449	28	exact	exact	JJ
cord-004615-xfi3p601	449	29	parameters	parameter	NNS
cord-004615-xfi3p601	449	30	.	.	.
cord-004615-xfi3p601	450	1	6	6	LS
cord-004615-xfi3p601	450	2	.	.	.
cord-004615-xfi3p601	451	1	The	the	DT
cord-004615-xfi3p601	451	2	computed	compute	VBN
cord-004615-xfi3p601	451	3	covariance	covariance	NN
cord-004615-xfi3p601	451	4	matrices	matrix	NNS
cord-004615-xfi3p601	451	5	do	do	VBP
cord-004615-xfi3p601	451	6	have	have	VB
cord-004615-xfi3p601	451	7	values	value	NNS
cord-004615-xfi3p601	451	8	of	of	IN
cord-004615-xfi3p601	451	9	different	different	JJ
cord-004615-xfi3p601	451	10	order	order	NN
cord-004615-xfi3p601	451	11	in	in	IN
cord-004615-xfi3p601	451	12	them	-PRON-	PRP
cord-004615-xfi3p601	451	13	.	.	.
cord-004615-xfi3p601	452	1	Consider	consider	VB
cord-004615-xfi3p601	452	2	for	for	IN
cord-004615-xfi3p601	452	3	instance	instance	NN
cord-004615-xfi3p601	452	4	strategy	strategy	NN
cord-004615-xfi3p601	453	1	B.	B.	NNP
cord-004615-xfi3p601	454	1	The	the	DT
cord-004615-xfi3p601	454	2	variance	variance	NN
cord-004615-xfi3p601	454	3	of	of	IN
cord-004615-xfi3p601	454	4	the	the	DT
cord-004615-xfi3p601	454	5	number	number	NN
cord-004615-xfi3p601	454	6	of	of	IN
cord-004615-xfi3p601	454	7	finishers	finisher	NNS
cord-004615-xfi3p601	454	8	and	and	CC
cord-004615-xfi3p601	454	9	multipliers	multiplier	NNS
cord-004615-xfi3p601	454	10	already	already	RB
cord-004615-xfi3p601	454	11	detected	detect	VBN
cord-004615-xfi3p601	454	12	is	be	VBZ
cord-004615-xfi3p601	454	13	much	much	RB
cord-004615-xfi3p601	454	14	higher	high	JJR
cord-004615-xfi3p601	454	15	than	than	IN
cord-004615-xfi3p601	454	16	the	the	DT
cord-004615-xfi3p601	454	17	variance	variance	NN
cord-004615-xfi3p601	454	18	of	of	IN
cord-004615-xfi3p601	454	19	the	the	DT
cord-004615-xfi3p601	454	20	number	number	NN
cord-004615-xfi3p601	454	21	of	of	IN
cord-004615-xfi3p601	454	22	finishers	finisher	NNS
cord-004615-xfi3p601	454	23	and	and	CC
cord-004615-xfi3p601	454	24	multipliers	multiplier	NNS
cord-004615-xfi3p601	454	25	that	that	WDT
cord-004615-xfi3p601	454	26	are	be	VBP
cord-004615-xfi3p601	454	27	still	still	RB
cord-004615-xfi3p601	454	28	alive	alive	JJ
cord-004615-xfi3p601	454	29	at	at	IN
cord-004615-xfi3p601	454	30	time	time	NN
cord-004615-xfi3p601	454	31	t	t	NN
cord-004615-xfi3p601	454	32	=	=	SYM
cord-004615-xfi3p601	454	33	T	T	NNP
cord-004615-xfi3p601	454	34	.	.	.
cord-004615-xfi3p601	455	1	This	this	DT
cord-004615-xfi3p601	455	2	is	be	VBZ
cord-004615-xfi3p601	455	3	because	because	IN
cord-004615-xfi3p601	455	4	the	the	DT
cord-004615-xfi3p601	455	5	infection	infection	NN
cord-004615-xfi3p601	455	6	rate	rate	NN
cord-004615-xfi3p601	455	7	decreases	decrease	VBZ
cord-004615-xfi3p601	455	8	for	for	IN
cord-004615-xfi3p601	455	9	this	this	DT
cord-004615-xfi3p601	455	10	strategy	strategy	NN
cord-004615-xfi3p601	455	11	.	.	.
cord-004615-xfi3p601	456	1	At	at	IN
cord-004615-xfi3p601	456	2	the	the	DT
cord-004615-xfi3p601	456	3	start	start	NN
cord-004615-xfi3p601	456	4	of	of	IN
cord-004615-xfi3p601	456	5	the	the	DT
cord-004615-xfi3p601	456	6	process	process	NN
cord-004615-xfi3p601	456	7	one	one	CD
cord-004615-xfi3p601	456	8	infective	infective	JJ
cord-004615-xfi3p601	456	9	herd	herd	NN
cord-004615-xfi3p601	456	10	may	may	MD
cord-004615-xfi3p601	456	11	infect	infect	VB
cord-004615-xfi3p601	456	12	several	several	JJ
cord-004615-xfi3p601	456	13	other	other	JJ
cord-004615-xfi3p601	456	14	herds	herd	NNS
cord-004615-xfi3p601	456	15	with	with	IN
cord-004615-xfi3p601	456	16	a	a	DT
cord-004615-xfi3p601	456	17	relatively	relatively	RB
cord-004615-xfi3p601	456	18	high	high	JJ
cord-004615-xfi3p601	456	19	probability	probability	NN
cord-004615-xfi3p601	456	20	,	,	,
cord-004615-xfi3p601	456	21	while	while	IN
cord-004615-xfi3p601	456	22	after	after	IN
cord-004615-xfi3p601	456	23	some	some	DT
cord-004615-xfi3p601	456	24	time	time	NN
cord-004615-xfi3p601	456	25	infections	infection	NNS
cord-004615-xfi3p601	456	26	become	become	VBP
cord-004615-xfi3p601	456	27	rare	rare	JJ
cord-004615-xfi3p601	456	28	.	.	.
cord-004615-xfi3p601	457	1	This	this	DT
cord-004615-xfi3p601	457	2	is	be	VBZ
cord-004615-xfi3p601	457	3	why	why	WRB
cord-004615-xfi3p601	457	4	the	the	DT
cord-004615-xfi3p601	457	5	expected	expect	VBN
cord-004615-xfi3p601	457	6	number	number	NN
cord-004615-xfi3p601	457	7	of	of	IN
cord-004615-xfi3p601	457	8	infective	infective	JJ
cord-004615-xfi3p601	457	9	herds	herd	NNS
cord-004615-xfi3p601	457	10	at	at	IN
cord-004615-xfi3p601	457	11	t	t	NN
cord-004615-xfi3p601	457	12	=	=	SYM
cord-004615-xfi3p601	457	13	T	T	NNP
cord-004615-xfi3p601	457	14	is	be	VBZ
cord-004615-xfi3p601	457	15	much	much	RB
cord-004615-xfi3p601	457	16	less	less	JJR
cord-004615-xfi3p601	457	17	than	than	IN
cord-004615-xfi3p601	457	18	the	the	DT
cord-004615-xfi3p601	457	19	expected	expect	VBN
cord-004615-xfi3p601	457	20	number	number	NN
cord-004615-xfi3p601	457	21	of	of	IN
cord-004615-xfi3p601	457	22	infected	infected	JJ
cord-004615-xfi3p601	457	23	herds	herd	NNS
cord-004615-xfi3p601	457	24	.	.	.
cord-004615-xfi3p601	458	1	7	7	CD
cord-004615-xfi3p601	458	2	.	.	.
cord-004615-xfi3p601	459	1	For	for	IN
cord-004615-xfi3p601	459	2	constant	constant	JJ
cord-004615-xfi3p601	459	3	environments	environment	NNS
cord-004615-xfi3p601	459	4	we	-PRON-	PRP
cord-004615-xfi3p601	459	5	are	be	VBP
cord-004615-xfi3p601	459	6	interested	interested	JJ
cord-004615-xfi3p601	459	7	in	in	IN
cord-004615-xfi3p601	459	8	the	the	DT
cord-004615-xfi3p601	459	9	variance	variance	NN
cord-004615-xfi3p601	459	10	of	of	IN
cord-004615-xfi3p601	459	11	the	the	DT
cord-004615-xfi3p601	459	12	final	final	JJ
cord-004615-xfi3p601	459	13	size	size	NN
cord-004615-xfi3p601	459	14	.	.	.
cord-004615-xfi3p601	460	1	Note	note	VB
cord-004615-xfi3p601	460	2	that	that	IN
cord-004615-xfi3p601	460	3	in	in	IN
cord-004615-xfi3p601	460	4	all	all	DT
cord-004615-xfi3p601	460	5	of	of	IN
cord-004615-xfi3p601	460	6	the	the	DT
cord-004615-xfi3p601	460	7	strategies	strategy	NNS
cord-004615-xfi3p601	460	8	with	with	IN
cord-004615-xfi3p601	460	9	almost	almost	RB
cord-004615-xfi3p601	460	10	sure	sure	JJ
cord-004615-xfi3p601	460	11	extinction	extinction	NN
cord-004615-xfi3p601	460	12	in	in	IN
cord-004615-xfi3p601	460	13	a	a	DT
cord-004615-xfi3p601	460	14	constant	constant	JJ
cord-004615-xfi3p601	460	15	environment	environment	NN
cord-004615-xfi3p601	460	16	,	,	,
cord-004615-xfi3p601	460	17	only	only	RB
cord-004615-xfi3p601	460	18	one	one	CD
cord-004615-xfi3p601	460	19	type	type	NN
cord-004615-xfi3p601	460	20	of	of	IN
cord-004615-xfi3p601	460	21	herd	herd	NN
cord-004615-xfi3p601	460	22	can	can	MD
cord-004615-xfi3p601	460	23	be	be	VB
cord-004615-xfi3p601	460	24	infected	infect	VBN
cord-004615-xfi3p601	460	25	,	,	,
cord-004615-xfi3p601	460	26	so	so	RB
cord-004615-xfi3p601	460	27	we	-PRON-	PRP
cord-004615-xfi3p601	460	28	only	only	RB
cord-004615-xfi3p601	460	29	have	have	VBP
cord-004615-xfi3p601	460	30	to	to	TO
cord-004615-xfi3p601	460	31	deal	deal	VB
cord-004615-xfi3p601	460	32	with	with	IN
cord-004615-xfi3p601	460	33	one	one	CD
cord-004615-xfi3p601	460	34	type	type	NN
cord-004615-xfi3p601	460	35	of	of	IN
cord-004615-xfi3p601	460	36	herd	herd	NN
cord-004615-xfi3p601	460	37	.	.	.
cord-004615-xfi3p601	461	1	We	-PRON-	PRP
cord-004615-xfi3p601	461	2	use	use	VBP
cord-004615-xfi3p601	461	3	the	the	DT
cord-004615-xfi3p601	461	4	underlying	underlie	VBG
cord-004615-xfi3p601	461	5	Galton	Galton	NNP
cord-004615-xfi3p601	461	6	-	-	HYPH
cord-004615-xfi3p601	461	7	Watson	Watson	NNP
cord-004615-xfi3p601	461	8	process	process	VBP
cord-004615-xfi3p601	461	9	to	to	TO
cord-004615-xfi3p601	461	10	deduce	deduce	VB
cord-004615-xfi3p601	461	11	the	the	DT
cord-004615-xfi3p601	461	12	variance	variance	NN
cord-004615-xfi3p601	461	13	of	of	IN
cord-004615-xfi3p601	461	14	the	the	DT
cord-004615-xfi3p601	461	15	final	final	JJ
cord-004615-xfi3p601	461	16	size	size	NN
cord-004615-xfi3p601	461	17	(	(	-LRB-
cord-004615-xfi3p601	461	18	see	see	VB
cord-004615-xfi3p601	461	19	Section	section	NN
cord-004615-xfi3p601	461	20	2.11	2.11	CD
cord-004615-xfi3p601	461	21	of	of	IN
cord-004615-xfi3p601	461	22	[	[	-LRB-
cord-004615-xfi3p601	461	23	4	4	CD
cord-004615-xfi3p601	461	24	]	]	-RRB-
cord-004615-xfi3p601	461	25	)	)	-RRB-
cord-004615-xfi3p601	461	26	.	.	.
cord-004615-xfi3p601	462	1	If	if	IN
cord-004615-xfi3p601	462	2	we	-PRON-	PRP
cord-004615-xfi3p601	462	3	take	take	VBP
cord-004615-xfi3p601	462	4	m	m	NN
cord-004615-xfi3p601	462	5	for	for	IN
cord-004615-xfi3p601	462	6	the	the	DT
cord-004615-xfi3p601	462	7	expected	expect	VBN
cord-004615-xfi3p601	462	8	number	number	NN
cord-004615-xfi3p601	462	9	of	of	IN
cord-004615-xfi3p601	462	10	direct	direct	JJ
cord-004615-xfi3p601	462	11	infections	infection	NNS
cord-004615-xfi3p601	462	12	by	by	IN
cord-004615-xfi3p601	462	13	one	one	CD
cord-004615-xfi3p601	462	14	infective	infective	JJ
cord-004615-xfi3p601	462	15	herd	herd	NN
cord-004615-xfi3p601	462	16	,	,	,
cord-004615-xfi3p601	462	17	the	the	DT
cord-004615-xfi3p601	462	18	expected	expect	VBN
cord-004615-xfi3p601	462	19	final	final	JJ
cord-004615-xfi3p601	462	20	size	size	NN
cord-004615-xfi3p601	462	21	is	be	VBZ
cord-004615-xfi3p601	462	22	1	1	CD
cord-004615-xfi3p601	462	23	1−m	1−m	CD
cord-004615-xfi3p601	462	24	and	and	CC
cord-004615-xfi3p601	462	25	the	the	DT
cord-004615-xfi3p601	462	26	variance	variance	NN
cord-004615-xfi3p601	462	27	is	be	VBZ
cord-004615-xfi3p601	462	28	m(1+m	m(1+m	NNP
cord-004615-xfi3p601	462	29	)	)	-RRB-
cord-004615-xfi3p601	462	30	(	(	-LRB-
cord-004615-xfi3p601	462	31	1−m	1−m	CD
cord-004615-xfi3p601	462	32	)	)	-RRB-
cord-004615-xfi3p601	462	33	2	2	CD
cord-004615-xfi3p601	462	34	.	.	.
cord-004615-xfi3p601	463	1	Note	note	VB
cord-004615-xfi3p601	463	2	that	that	IN
cord-004615-xfi3p601	463	3	for	for	IN
cord-004615-xfi3p601	463	4	a	a	DT
cord-004615-xfi3p601	463	5	large	large	JJ
cord-004615-xfi3p601	463	6	expected	expect	VBN
cord-004615-xfi3p601	463	7	final	final	JJ
cord-004615-xfi3p601	463	8	size	size	NN
cord-004615-xfi3p601	463	9	,	,	,
cord-004615-xfi3p601	463	10	the	the	DT
cord-004615-xfi3p601	463	11	variance	variance	NN
cord-004615-xfi3p601	463	12	will	will	MD
cord-004615-xfi3p601	463	13	be	be	VB
cord-004615-xfi3p601	463	14	of	of	IN
cord-004615-xfi3p601	463	15	the	the	DT
cord-004615-xfi3p601	463	16	square	square	JJ
cord-004615-xfi3p601	463	17	order	order	NN
cord-004615-xfi3p601	463	18	of	of	IN
cord-004615-xfi3p601	463	19	the	the	DT
cord-004615-xfi3p601	463	20	final	final	JJ
cord-004615-xfi3p601	463	21	size	size	NN
cord-004615-xfi3p601	463	22	.	.	.
cord-004615-xfi3p601	464	1	Due	due	IN
cord-004615-xfi3p601	464	2	to	to	IN
cord-004615-xfi3p601	464	3	this	this	DT
cord-004615-xfi3p601	464	4	large	large	JJ
cord-004615-xfi3p601	464	5	variance	variance	NN
cord-004615-xfi3p601	464	6	,	,	,
cord-004615-xfi3p601	464	7	we	-PRON-	PRP
cord-004615-xfi3p601	464	8	can	can	MD
cord-004615-xfi3p601	464	9	not	not	RB
cord-004615-xfi3p601	464	10	give	give	VB
cord-004615-xfi3p601	464	11	exact	exact	JJ
cord-004615-xfi3p601	464	12	quantitative	quantitative	JJ
cord-004615-xfi3p601	464	13	predictions	prediction	NNS
cord-004615-xfi3p601	464	14	about	about	IN
cord-004615-xfi3p601	464	15	the	the	DT
cord-004615-xfi3p601	464	16	final	final	JJ
cord-004615-xfi3p601	464	17	size	size	NN
cord-004615-xfi3p601	464	18	of	of	IN
cord-004615-xfi3p601	464	19	an	an	DT
cord-004615-xfi3p601	464	20	epidemic	epidemic	NN
cord-004615-xfi3p601	464	21	.	.	.
cord-004615-xfi3p601	465	1	This	this	DT
cord-004615-xfi3p601	465	2	also	also	RB
cord-004615-xfi3p601	465	3	indicates	indicate	VBZ
cord-004615-xfi3p601	465	4	that	that	IN
cord-004615-xfi3p601	465	5	there	there	EX
cord-004615-xfi3p601	465	6	is	be	VBZ
cord-004615-xfi3p601	465	7	a	a	DT
cord-004615-xfi3p601	465	8	large	large	JJ
cord-004615-xfi3p601	465	9	intrinsic	intrinsic	JJ
cord-004615-xfi3p601	465	10	uncertainty	uncertainty	NN
cord-004615-xfi3p601	465	11	in	in	IN
cord-004615-xfi3p601	465	12	the	the	DT
cord-004615-xfi3p601	465	13	problem	problem	NN
cord-004615-xfi3p601	465	14	.	.	.
cord-004615-xfi3p601	466	1	8	8	CD
cord-004615-xfi3p601	466	2	.	.	.
cord-004615-xfi3p601	467	1	If	if	IN
cord-004615-xfi3p601	467	2	the	the	DT
cord-004615-xfi3p601	467	3	infection	infection	NN
cord-004615-xfi3p601	467	4	rates	rate	NNS
cord-004615-xfi3p601	467	5	are	be	VBP
cord-004615-xfi3p601	467	6	increasing	increase	VBG
cord-004615-xfi3p601	467	7	in	in	IN
cord-004615-xfi3p601	467	8	time	time	NN
cord-004615-xfi3p601	467	9	,	,	,
cord-004615-xfi3p601	467	10	the	the	DT
cord-004615-xfi3p601	467	11	expected	expect	VBN
cord-004615-xfi3p601	467	12	final	final	JJ
cord-004615-xfi3p601	467	13	size	size	NN
cord-004615-xfi3p601	467	14	will	will	MD
cord-004615-xfi3p601	467	15	decrease	decrease	VB
cord-004615-xfi3p601	467	16	for	for	IN
cord-004615-xfi3p601	467	17	increasing	increase	VBG
cord-004615-xfi3p601	467	18	r	r	NN
cord-004615-xfi3p601	467	19	,	,	,
cord-004615-xfi3p601	467	20	while	while	IN
cord-004615-xfi3p601	467	21	for	for	IN
cord-004615-xfi3p601	467	22	decreasing	decrease	VBG
cord-004615-xfi3p601	467	23	infection	infection	NN
cord-004615-xfi3p601	467	24	rates	rate	NNS
cord-004615-xfi3p601	467	25	the	the	DT
cord-004615-xfi3p601	467	26	expected	expect	VBN
cord-004615-xfi3p601	467	27	final	final	JJ
cord-004615-xfi3p601	467	28	size	size	NN
cord-004615-xfi3p601	467	29	will	will	MD
cord-004615-xfi3p601	467	30	increase	increase	VB
cord-004615-xfi3p601	467	31	for	for	IN
cord-004615-xfi3p601	467	32	increasing	increase	VBG
cord-004615-xfi3p601	467	33	r.	r.	NNP
cord-004615-xfi3p601	468	1	This	this	DT
cord-004615-xfi3p601	468	2	is	be	VBZ
cord-004615-xfi3p601	468	3	because	because	IN
cord-004615-xfi3p601	468	4	r	r	NNP
cord-004615-xfi3p601	468	5	can	can	MD
cord-004615-xfi3p601	468	6	be	be	VB
cord-004615-xfi3p601	468	7	seen	see	VBN
cord-004615-xfi3p601	468	8	as	as	IN
cord-004615-xfi3p601	468	9	a	a	DT
cord-004615-xfi3p601	468	10	parameter	parameter	NN
cord-004615-xfi3p601	468	11	describing	describe	VBG
cord-004615-xfi3p601	468	12	the	the	DT
cord-004615-xfi3p601	468	13	speed	speed	NN
cord-004615-xfi3p601	468	14	of	of	IN
cord-004615-xfi3p601	468	15	the	the	DT
cord-004615-xfi3p601	468	16	process	process	NN
cord-004615-xfi3p601	468	17	in	in	IN
cord-004615-xfi3p601	468	18	a	a	DT
cord-004615-xfi3p601	468	19	constant	constant	JJ
cord-004615-xfi3p601	468	20	environment	environment	NN
cord-004615-xfi3p601	468	21	.	.	.
cord-004615-xfi3p601	469	1	Large	large	JJ
cord-004615-xfi3p601	469	2	values	value	NNS
cord-004615-xfi3p601	469	3	of	of	IN
cord-004615-xfi3p601	469	4	r	r	NN
cord-004615-xfi3p601	469	5	correspond	correspond	VB
cord-004615-xfi3p601	469	6	to	to	IN
cord-004615-xfi3p601	469	7	short	short	JJ
cord-004615-xfi3p601	469	8	generation	generation	NN
cord-004615-xfi3p601	469	9	lengths	length	NNS
cord-004615-xfi3p601	469	10	compared	compare	VBN
cord-004615-xfi3p601	469	11	to	to	IN
cord-004615-xfi3p601	469	12	small	small	JJ
cord-004615-xfi3p601	469	13	r.	r.	NNP
cord-004615-xfi3p601	470	1	So	so	RB
cord-004615-xfi3p601	470	2	,	,	,
cord-004615-xfi3p601	470	3	if	if	IN
cord-004615-xfi3p601	470	4	the	the	DT
cord-004615-xfi3p601	470	5	infection	infection	NN
cord-004615-xfi3p601	470	6	rate	rate	NN
cord-004615-xfi3p601	470	7	is	be	VBZ
cord-004615-xfi3p601	470	8	increasing	increase	VBG
cord-004615-xfi3p601	470	9	in	in	IN
cord-004615-xfi3p601	470	10	time	time	NN
cord-004615-xfi3p601	470	11	,	,	,
cord-004615-xfi3p601	470	12	the	the	DT
cord-004615-xfi3p601	470	13	n	n	NN
cord-004615-xfi3p601	470	14	-	-	HYPH
cord-004615-xfi3p601	470	15	th	th	RP
cord-004615-xfi3p601	470	16	generation	generation	NN
cord-004615-xfi3p601	470	17	for	for	IN
cord-004615-xfi3p601	470	18	small	small	JJ
cord-004615-xfi3p601	470	19	values	value	NNS
cord-004615-xfi3p601	470	20	of	of	IN
cord-004615-xfi3p601	470	21	r	r	NNP
cord-004615-xfi3p601	470	22	will	will	MD
cord-004615-xfi3p601	470	23	have	have	VB
cord-004615-xfi3p601	470	24	a	a	DT
cord-004615-xfi3p601	470	25	larger	large	JJR
cord-004615-xfi3p601	470	26	infection	infection	NN
cord-004615-xfi3p601	470	27	rate	rate	NN
cord-004615-xfi3p601	470	28	than	than	IN
cord-004615-xfi3p601	470	29	the	the	DT
cord-004615-xfi3p601	470	30	n	n	NN
cord-004615-xfi3p601	470	31	-	-	HYPH
cord-004615-xfi3p601	470	32	th	th	RP
cord-004615-xfi3p601	470	33	generation	generation	NN
cord-004615-xfi3p601	470	34	for	for	IN
cord-004615-xfi3p601	470	35	large	large	JJ
cord-004615-xfi3p601	470	36	r.	r.	NNP
cord-004615-xfi3p601	471	1	The	the	DT
cord-004615-xfi3p601	471	2	effect	effect	NN
cord-004615-xfi3p601	471	3	of	of	IN
cord-004615-xfi3p601	471	4	decreasing	decrease	VBG
cord-004615-xfi3p601	471	5	R	r	NN
cord-004615-xfi3p601	471	6	,	,	,
cord-004615-xfi3p601	471	7	the	the	DT
cord-004615-xfi3p601	471	8	parameter	parameter	NN
cord-004615-xfi3p601	471	9	describing	describe	VBG
cord-004615-xfi3p601	471	10	the	the	DT
cord-004615-xfi3p601	471	11	random	random	JJ
cord-004615-xfi3p601	471	12	effects	effect	NNS
cord-004615-xfi3p601	471	13	at	at	IN
cord-004615-xfi3p601	471	14	the	the	DT
cord-004615-xfi3p601	471	15	start	start	NN
cord-004615-xfi3p601	471	16	of	of	IN
cord-004615-xfi3p601	471	17	the	the	DT
cord-004615-xfi3p601	471	18	within	within	JJ
cord-004615-xfi3p601	471	19	-	-	HYPH
cord-004615-xfi3p601	471	20	herd	herd	NN
cord-004615-xfi3p601	471	21	spread	spread	NN
cord-004615-xfi3p601	471	22	,	,	,
cord-004615-xfi3p601	471	23	is	be	VBZ
cord-004615-xfi3p601	471	24	less	less	RBR
cord-004615-xfi3p601	471	25	clear	clear	JJ
cord-004615-xfi3p601	471	26	from	from	IN
cord-004615-xfi3p601	471	27	formulae	formula	NNS
cord-004615-xfi3p601	471	28	and	and	CC
cord-004615-xfi3p601	471	29	definitions	definition	NNS
cord-004615-xfi3p601	471	30	.	.	.
cord-004615-xfi3p601	472	1	From	from	IN
cord-004615-xfi3p601	472	2	the	the	DT
cord-004615-xfi3p601	472	3	figures	figure	NNS
cord-004615-xfi3p601	472	4	we	-PRON-	PRP
cord-004615-xfi3p601	472	5	can	can	MD
cord-004615-xfi3p601	472	6	only	only	RB
cord-004615-xfi3p601	472	7	see	see	VB
cord-004615-xfi3p601	472	8	that	that	IN
cord-004615-xfi3p601	472	9	R	r	NN
cord-004615-xfi3p601	472	10	has	have	VBZ
cord-004615-xfi3p601	472	11	relative	relative	JJ
cord-004615-xfi3p601	472	12	small	small	JJ
cord-004615-xfi3p601	472	13	effect	effect	NN
cord-004615-xfi3p601	472	14	on	on	IN
cord-004615-xfi3p601	472	15	the	the	DT
cord-004615-xfi3p601	472	16	expected	expect	VBN
cord-004615-xfi3p601	472	17	final	final	JJ
cord-004615-xfi3p601	472	18	size	size	NN
cord-004615-xfi3p601	472	19	and	and	CC
cord-004615-xfi3p601	472	20	the	the	DT
cord-004615-xfi3p601	472	21	probability	probability	NN
cord-004615-xfi3p601	472	22	of	of	IN
cord-004615-xfi3p601	472	23	extinction	extinction	NN
cord-004615-xfi3p601	472	24	.	.	.
cord-004615-xfi3p601	473	1	9	9	LS
cord-004615-xfi3p601	473	2	.	.	.
cord-004615-xfi3p601	474	1	Some	some	DT
cord-004615-xfi3p601	474	2	parameters	parameter	NNS
cord-004615-xfi3p601	474	3	heavily	heavily	RB
cord-004615-xfi3p601	474	4	influence	influence	VBP
cord-004615-xfi3p601	474	5	the	the	DT
cord-004615-xfi3p601	474	6	expected	expect	VBN
cord-004615-xfi3p601	474	7	final	final	JJ
cord-004615-xfi3p601	474	8	size	size	NN
cord-004615-xfi3p601	474	9	and	and	CC
cord-004615-xfi3p601	474	10	the	the	DT
cord-004615-xfi3p601	474	11	probability	probability	NN
cord-004615-xfi3p601	474	12	of	of	IN
cord-004615-xfi3p601	474	13	extinction	extinction	NN
cord-004615-xfi3p601	474	14	.	.	.
cord-004615-xfi3p601	475	1	We	-PRON-	PRP
cord-004615-xfi3p601	475	2	have	have	VBP
cord-004615-xfi3p601	475	3	already	already	RB
cord-004615-xfi3p601	475	4	seen	see	VBN
cord-004615-xfi3p601	475	5	that	that	IN
cord-004615-xfi3p601	475	6	in	in	IN
cord-004615-xfi3p601	475	7	a	a	DT
cord-004615-xfi3p601	475	8	constant	constant	JJ
cord-004615-xfi3p601	475	9	environment	environment	NN
cord-004615-xfi3p601	475	10	r	r	NN
cord-004615-xfi3p601	475	11	and	and	CC
cord-004615-xfi3p601	475	12	R	r	NN
cord-004615-xfi3p601	475	13	do	do	VBP
cord-004615-xfi3p601	475	14	not	not	RB
cord-004615-xfi3p601	475	15	influence	influence	VB
cord-004615-xfi3p601	475	16	these	these	DT
cord-004615-xfi3p601	475	17	quantities	quantity	NNS
cord-004615-xfi3p601	475	18	.	.	.
cord-004615-xfi3p601	476	1	For	for	IN
cord-004615-xfi3p601	476	2	predictions	prediction	NNS
cord-004615-xfi3p601	476	3	the	the	DT
cord-004615-xfi3p601	476	4	ratios	ratio	NNS
cord-004615-xfi3p601	476	5	β	β	NN
cord-004615-xfi3p601	476	6	:	:	:
cord-004615-xfi3p601	477	1	β	β	NNP
cord-004615-xfi3p601	477	2	tr	tr	NN
cord-004615-xfi3p601	477	3	:	:	:
cord-004615-xfi3p601	477	4	α	α	NN
cord-004615-xfi3p601	477	5	are	be	VBP
cord-004615-xfi3p601	477	6	most	most	RBS
cord-004615-xfi3p601	477	7	important	important	JJ
cord-004615-xfi3p601	477	8	.	.	.
cord-004615-xfi3p601	478	1	So	so	RB
cord-004615-xfi3p601	478	2	the	the	DT
cord-004615-xfi3p601	478	3	estimation	estimation	NN
cord-004615-xfi3p601	478	4	effort	effort	NN
cord-004615-xfi3p601	478	5	is	be	VBZ
cord-004615-xfi3p601	478	6	best	well	RBS
cord-004615-xfi3p601	478	7	devoted	devoted	JJ
cord-004615-xfi3p601	478	8	towards	towards	IN
cord-004615-xfi3p601	478	9	estimating	estimate	VBG
cord-004615-xfi3p601	478	10	these	these	DT
cord-004615-xfi3p601	478	11	ratios	ratio	NNS
cord-004615-xfi3p601	478	12	.	.	.
cord-004615-xfi3p601	479	1	By	by	IN
cord-004615-xfi3p601	479	2	using	use	VBG
cord-004615-xfi3p601	479	3	a	a	DT
cord-004615-xfi3p601	479	4	stochastic	stochastic	JJ
cord-004615-xfi3p601	479	5	model	model	NN
cord-004615-xfi3p601	479	6	,	,	,
cord-004615-xfi3p601	479	7	we	-PRON-	PRP
cord-004615-xfi3p601	479	8	could	could	MD
cord-004615-xfi3p601	479	9	estimate	estimate	VB
cord-004615-xfi3p601	479	10	the	the	DT
cord-004615-xfi3p601	479	11	probability	probability	NN
cord-004615-xfi3p601	479	12	of	of	IN
cord-004615-xfi3p601	479	13	extinction	extinction	NN
cord-004615-xfi3p601	479	14	and	and	CC
cord-004615-xfi3p601	479	15	the	the	DT
cord-004615-xfi3p601	479	16	expectation	expectation	NN
cord-004615-xfi3p601	479	17	of	of	IN
cord-004615-xfi3p601	479	18	the	the	DT
cord-004615-xfi3p601	479	19	final	final	JJ
cord-004615-xfi3p601	479	20	size	size	NN
cord-004615-xfi3p601	479	21	of	of	IN
cord-004615-xfi3p601	479	22	an	an	DT
cord-004615-xfi3p601	479	23	epidemic	epidemic	NN
cord-004615-xfi3p601	479	24	in	in	IN
cord-004615-xfi3p601	479	25	a	a	DT
cord-004615-xfi3p601	479	26	varying	vary	VBG
cord-004615-xfi3p601	479	27	environment	environment	NN
cord-004615-xfi3p601	479	28	.	.	.
cord-004615-xfi3p601	480	1	We	-PRON-	PRP
cord-004615-xfi3p601	480	2	only	only	RB
cord-004615-xfi3p601	480	3	need	need	VBP
cord-004615-xfi3p601	480	4	that	that	IN
cord-004615-xfi3p601	480	5	the	the	DT
cord-004615-xfi3p601	480	6	environment	environment	NN
cord-004615-xfi3p601	480	7	is	be	VBZ
cord-004615-xfi3p601	480	8	not	not	RB
cord-004615-xfi3p601	480	9	varying	vary	VBG
cord-004615-xfi3p601	480	10	anymore	anymore	RB
cord-004615-xfi3p601	480	11	after	after	IN
cord-004615-xfi3p601	480	12	some	some	DT
cord-004615-xfi3p601	480	13	given	give	VBN
cord-004615-xfi3p601	480	14	time	time	NN
cord-004615-xfi3p601	480	15	.	.	.
cord-004615-xfi3p601	481	1	We	-PRON-	PRP
cord-004615-xfi3p601	481	2	use	use	VBP
cord-004615-xfi3p601	481	3	a	a	DT
cord-004615-xfi3p601	481	4	branching	branch	VBG
cord-004615-xfi3p601	481	5	process	process	NN
cord-004615-xfi3p601	481	6	in	in	IN
cord-004615-xfi3p601	481	7	varying	vary	VBG
cord-004615-xfi3p601	481	8	environments	environment	NNS
cord-004615-xfi3p601	481	9	,	,	,
cord-004615-xfi3p601	481	10	depending	depend	VBG
cord-004615-xfi3p601	481	11	on	on	IN
cord-004615-xfi3p601	481	12	the	the	DT
cord-004615-xfi3p601	481	13	age	age	NN
cord-004615-xfi3p601	481	14	of	of	IN
cord-004615-xfi3p601	481	15	the	the	DT
cord-004615-xfi3p601	481	16	particles	particle	NNS
cord-004615-xfi3p601	481	17	.	.	.
cord-004615-xfi3p601	482	1	In	in	IN
cord-004615-xfi3p601	482	2	the	the	DT
cord-004615-xfi3p601	482	3	constant	constant	JJ
cord-004615-xfi3p601	482	4	environment	environment	NN
cord-004615-xfi3p601	482	5	the	the	DT
cord-004615-xfi3p601	482	6	probability	probability	NN
cord-004615-xfi3p601	482	7	of	of	IN
cord-004615-xfi3p601	482	8	extinction	extinction	NN
cord-004615-xfi3p601	482	9	and	and	CC
cord-004615-xfi3p601	482	10	the	the	DT
cord-004615-xfi3p601	482	11	final	final	JJ
cord-004615-xfi3p601	482	12	size	size	NN
cord-004615-xfi3p601	482	13	are	be	VBP
cord-004615-xfi3p601	482	14	known	know	VBN
cord-004615-xfi3p601	482	15	.	.	.
cord-004615-xfi3p601	483	1	By	by	IN
cord-004615-xfi3p601	483	2	using	use	VBG
cord-004615-xfi3p601	483	3	an	an	DT
cord-004615-xfi3p601	483	4	iterative	iterative	JJ
cord-004615-xfi3p601	483	5	process	process	NN
cord-004615-xfi3p601	483	6	,	,	,
cord-004615-xfi3p601	483	7	we	-PRON-	PRP
cord-004615-xfi3p601	483	8	computed	compute	VBD
cord-004615-xfi3p601	483	9	this	this	DT
cord-004615-xfi3p601	483	10	probability	probability	NN
cord-004615-xfi3p601	483	11	and	and	CC
cord-004615-xfi3p601	483	12	size	size	NN
cord-004615-xfi3p601	483	13	for	for	IN
cord-004615-xfi3p601	483	14	the	the	DT
cord-004615-xfi3p601	483	15	time	time	NN
cord-004615-xfi3p601	483	16	the	the	DT
cord-004615-xfi3p601	483	17	environment	environment	NN
cord-004615-xfi3p601	483	18	is	be	VBZ
cord-004615-xfi3p601	483	19	still	still	RB
cord-004615-xfi3p601	483	20	varying	vary	VBG
cord-004615-xfi3p601	483	21	.	.	.
cord-004615-xfi3p601	484	1	By	by	IN
cord-004615-xfi3p601	484	2	using	use	VBG
cord-004615-xfi3p601	484	3	generating	generating	NN
cord-004615-xfi3p601	484	4	functions	function	NNS
cord-004615-xfi3p601	484	5	,	,	,
cord-004615-xfi3p601	484	6	we	-PRON-	PRP
cord-004615-xfi3p601	484	7	can	can	MD
cord-004615-xfi3p601	484	8	compute	compute	VB
cord-004615-xfi3p601	484	9	many	many	JJ
cord-004615-xfi3p601	484	10	important	important	JJ
cord-004615-xfi3p601	484	11	properties	property	NNS
cord-004615-xfi3p601	484	12	,	,	,
cord-004615-xfi3p601	484	13	like	like	IN
cord-004615-xfi3p601	484	14	the	the	DT
cord-004615-xfi3p601	484	15	moments	moment	NNS
cord-004615-xfi3p601	484	16	of	of	IN
cord-004615-xfi3p601	484	17	the	the	DT
cord-004615-xfi3p601	484	18	final	final	JJ
cord-004615-xfi3p601	484	19	size	size	NN
cord-004615-xfi3p601	484	20	,	,	,
cord-004615-xfi3p601	484	21	and	and	CC
cord-004615-xfi3p601	484	22	a	a	DT
cord-004615-xfi3p601	484	23	lower	lower	RBR
cord-004615-xfi3p601	484	24	bound	bind	VBN
cord-004615-xfi3p601	484	25	for	for	IN
cord-004615-xfi3p601	484	26	the	the	DT
cord-004615-xfi3p601	484	27	probability	probability	NN
cord-004615-xfi3p601	484	28	that	that	IN
cord-004615-xfi3p601	484	29	the	the	DT
cord-004615-xfi3p601	484	30	process	process	NN
cord-004615-xfi3p601	484	31	has	have	VBZ
cord-004615-xfi3p601	484	32	gone	go	VBN
cord-004615-xfi3p601	484	33	extinct	extinct	JJ
cord-004615-xfi3p601	484	34	after	after	IN
cord-004615-xfi3p601	484	35	a	a	DT
cord-004615-xfi3p601	484	36	given	give	VBN
cord-004615-xfi3p601	484	37	time	time	NN
cord-004615-xfi3p601	484	38	.	.	.
cord-004615-xfi3p601	485	1	These	these	DT
cord-004615-xfi3p601	485	2	generating	generating	NN
cord-004615-xfi3p601	485	3	functions	function	NNS
cord-004615-xfi3p601	485	4	are	be	VBP
cord-004615-xfi3p601	485	5	very	very	RB
cord-004615-xfi3p601	485	6	useful	useful	JJ
cord-004615-xfi3p601	485	7	especially	especially	RB
cord-004615-xfi3p601	485	8	if	if	IN
cord-004615-xfi3p601	485	9	in	in	IN
cord-004615-xfi3p601	485	10	a	a	DT
cord-004615-xfi3p601	485	11	constant	constant	JJ
cord-004615-xfi3p601	485	12	environment	environment	NN
cord-004615-xfi3p601	485	13	the	the	DT
cord-004615-xfi3p601	485	14	expected	expect	VBN
cord-004615-xfi3p601	485	15	number	number	NN
cord-004615-xfi3p601	485	16	of	of	IN
cord-004615-xfi3p601	485	17	infections	infection	NNS
cord-004615-xfi3p601	485	18	after	after	IN
cord-004615-xfi3p601	485	19	a	a	DT
cord-004615-xfi3p601	485	20	certain	certain	JJ
cord-004615-xfi3p601	485	21	age	age	NN
cord-004615-xfi3p601	485	22	does	do	VBZ
cord-004615-xfi3p601	485	23	not	not	RB
cord-004615-xfi3p601	485	24	depend	depend	VB
cord-004615-xfi3p601	485	25	on	on	IN
cord-004615-xfi3p601	485	26	that	that	DT
cord-004615-xfi3p601	485	27	age	age	NN
cord-004615-xfi3p601	485	28	.	.	.
cord-004615-xfi3p601	486	1	This	this	DT
cord-004615-xfi3p601	486	2	only	only	RB
cord-004615-xfi3p601	486	3	holds	hold	VBZ
cord-004615-xfi3p601	486	4	if	if	IN
cord-004615-xfi3p601	486	5	the	the	DT
cord-004615-xfi3p601	486	6	infection	infection	NN
cord-004615-xfi3p601	486	7	and	and	CC
cord-004615-xfi3p601	486	8	detection	detection	NN
cord-004615-xfi3p601	486	9	rate	rate	NN
cord-004615-xfi3p601	486	10	are	be	VBP
cord-004615-xfi3p601	486	11	in	in	IN
cord-004615-xfi3p601	486	12	direct	direct	JJ
cord-004615-xfi3p601	486	13	proportion	proportion	NN
cord-004615-xfi3p601	486	14	,	,	,
cord-004615-xfi3p601	486	15	for	for	IN
cord-004615-xfi3p601	486	16	the	the	DT
cord-004615-xfi3p601	486	17	non	non	JJ
cord-004615-xfi3p601	486	18	-	-	JJ
cord-004615-xfi3p601	486	19	varying	varying	JJ
cord-004615-xfi3p601	486	20	environment	environment	NN
cord-004615-xfi3p601	486	21	.	.	.
cord-004615-xfi3p601	487	1	It	-PRON-	PRP
cord-004615-xfi3p601	487	2	is	be	VBZ
cord-004615-xfi3p601	487	3	difficult	difficult	JJ
cord-004615-xfi3p601	487	4	to	to	TO
cord-004615-xfi3p601	487	5	estimate	estimate	VB
cord-004615-xfi3p601	487	6	the	the	DT
cord-004615-xfi3p601	487	7	parameters	parameter	NNS
cord-004615-xfi3p601	487	8	for	for	IN
cord-004615-xfi3p601	487	9	the	the	DT
cord-004615-xfi3p601	487	10	computations	computation	NNS
cord-004615-xfi3p601	487	11	.	.	.
cord-004615-xfi3p601	488	1	Some	some	DT
cord-004615-xfi3p601	488	2	of	of	IN
cord-004615-xfi3p601	488	3	the	the	DT
cord-004615-xfi3p601	488	4	properties	property	NNS
cord-004615-xfi3p601	488	5	computed	compute	VBN
cord-004615-xfi3p601	488	6	in	in	IN
cord-004615-xfi3p601	488	7	this	this	DT
cord-004615-xfi3p601	488	8	model	model	NN
cord-004615-xfi3p601	488	9	,	,	,
cord-004615-xfi3p601	488	10	like	like	IN
cord-004615-xfi3p601	488	11	the	the	DT
cord-004615-xfi3p601	488	12	probability	probability	NN
cord-004615-xfi3p601	488	13	of	of	IN
cord-004615-xfi3p601	488	14	extinction	extinction	NN
cord-004615-xfi3p601	488	15	heavily	heavily	RB
cord-004615-xfi3p601	488	16	depend	depend	VBP
cord-004615-xfi3p601	488	17	on	on	IN
cord-004615-xfi3p601	488	18	the	the	DT
cord-004615-xfi3p601	488	19	parameters	parameter	NNS
cord-004615-xfi3p601	488	20	α	α	NN
cord-004615-xfi3p601	488	21	and	and	CC
cord-004615-xfi3p601	488	22	β	β	NN
cord-004615-xfi3p601	488	23	,	,	,
cord-004615-xfi3p601	488	24	describing	describe	VBG
cord-004615-xfi3p601	488	25	the	the	DT
cord-004615-xfi3p601	488	26	infection	infection	NN
cord-004615-xfi3p601	488	27	and	and	CC
cord-004615-xfi3p601	488	28	detection	detection	NN
cord-004615-xfi3p601	488	29	rate	rate	NN
cord-004615-xfi3p601	488	30	.	.	.
cord-004615-xfi3p601	489	1	The	the	DT
cord-004615-xfi3p601	489	2	model	model	NN
cord-004615-xfi3p601	489	3	presented	present	VBN
cord-004615-xfi3p601	489	4	in	in	IN
cord-004615-xfi3p601	489	5	this	this	DT
cord-004615-xfi3p601	489	6	paper	paper	NN
cord-004615-xfi3p601	489	7	may	may	MD
cord-004615-xfi3p601	489	8	be	be	VB
cord-004615-xfi3p601	489	9	useful	useful	JJ
cord-004615-xfi3p601	489	10	to	to	TO
cord-004615-xfi3p601	489	11	compare	compare	VB
cord-004615-xfi3p601	489	12	the	the	DT
cord-004615-xfi3p601	489	13	effect	effect	NN
cord-004615-xfi3p601	489	14	of	of	IN
cord-004615-xfi3p601	489	15	different	different	JJ
cord-004615-xfi3p601	489	16	measures	measure	NNS
cord-004615-xfi3p601	489	17	,	,	,
cord-004615-xfi3p601	489	18	but	but	CC
cord-004615-xfi3p601	489	19	it	-PRON-	PRP
cord-004615-xfi3p601	489	20	is	be	VBZ
cord-004615-xfi3p601	489	21	very	very	RB
cord-004615-xfi3p601	489	22	dangerous	dangerous	JJ
cord-004615-xfi3p601	489	23	to	to	TO
cord-004615-xfi3p601	489	24	use	use	VB
cord-004615-xfi3p601	489	25	this	this	DT
cord-004615-xfi3p601	489	26	model	model	NN
cord-004615-xfi3p601	489	27	for	for	IN
cord-004615-xfi3p601	489	28	absolute	absolute	JJ
cord-004615-xfi3p601	489	29	quantitative	quantitative	JJ
cord-004615-xfi3p601	489	30	predictions	prediction	NNS
cord-004615-xfi3p601	489	31	.	.	.
cord-004615-xfi3p601	490	1	We	-PRON-	PRP
cord-004615-xfi3p601	490	2	used	use	VBD
cord-004615-xfi3p601	490	3	the	the	DT
cord-004615-xfi3p601	490	4	model	model	NN
cord-004615-xfi3p601	490	5	to	to	TO
cord-004615-xfi3p601	490	6	describe	describe	VB
cord-004615-xfi3p601	490	7	the	the	DT
cord-004615-xfi3p601	490	8	spread	spread	NN
cord-004615-xfi3p601	490	9	of	of	IN
cord-004615-xfi3p601	490	10	classical	classical	JJ
cord-004615-xfi3p601	490	11	swine	swine	NN
cord-004615-xfi3p601	490	12	fever	fever	NN
cord-004615-xfi3p601	490	13	.	.	.
cord-004615-xfi3p601	491	1	It	-PRON-	PRP
cord-004615-xfi3p601	491	2	is	be	VBZ
cord-004615-xfi3p601	491	3	worth	worth	JJ
cord-004615-xfi3p601	491	4	investigating	investigate	VBG
cord-004615-xfi3p601	491	5	if	if	IN
cord-004615-xfi3p601	491	6	the	the	DT
cord-004615-xfi3p601	491	7	same	same	JJ
cord-004615-xfi3p601	491	8	model	model	NN
cord-004615-xfi3p601	491	9	,	,	,
cord-004615-xfi3p601	491	10	with	with	IN
cord-004615-xfi3p601	491	11	other	other	JJ
cord-004615-xfi3p601	491	12	parameters	parameter	NNS
cord-004615-xfi3p601	491	13	,	,	,
cord-004615-xfi3p601	491	14	may	may	MD
cord-004615-xfi3p601	491	15	be	be	VB
cord-004615-xfi3p601	491	16	used	use	VBN
cord-004615-xfi3p601	491	17	to	to	TO
cord-004615-xfi3p601	491	18	describe	describe	VB
cord-004615-xfi3p601	491	19	the	the	DT
cord-004615-xfi3p601	491	20	spread	spread	NN
cord-004615-xfi3p601	491	21	of	of	IN
cord-004615-xfi3p601	491	22	other	other	JJ
cord-004615-xfi3p601	491	23	animal	animal	NN
cord-004615-xfi3p601	491	24	diseases	disease	NNS
cord-004615-xfi3p601	491	25	,	,	,
cord-004615-xfi3p601	491	26	with	with	IN
cord-004615-xfi3p601	491	27	culling	cull	VBG
cord-004615-xfi3p601	491	28	at	at	IN
cord-004615-xfi3p601	491	29	detection	detection	NN
cord-004615-xfi3p601	491	30	,	,	,
cord-004615-xfi3p601	491	31	or	or	CC
cord-004615-xfi3p601	491	32	even	even	RB
cord-004615-xfi3p601	491	33	human	human	JJ
cord-004615-xfi3p601	491	34	diseases	disease	NNS
cord-004615-xfi3p601	491	35	,	,	,
cord-004615-xfi3p601	491	36	which	which	WDT
cord-004615-xfi3p601	491	37	lead	lead	VBP
cord-004615-xfi3p601	491	38	to	to	IN
cord-004615-xfi3p601	491	39	strict	strict	JJ
cord-004615-xfi3p601	491	40	quarantine	quarantine	NN
cord-004615-xfi3p601	491	41	of	of	IN
cord-004615-xfi3p601	491	42	detected	detect	VBN
cord-004615-xfi3p601	491	43	infected	infect	VBN
cord-004615-xfi3p601	491	44	individuals	individual	NNS
cord-004615-xfi3p601	491	45	(	(	-LRB-
cord-004615-xfi3p601	491	46	and	and	CC
cord-004615-xfi3p601	491	47	suspected	suspect	VBN
cord-004615-xfi3p601	491	48	cases	case	NNS
cord-004615-xfi3p601	491	49	)	)	-RRB-
cord-004615-xfi3p601	491	50	and	and	CC
cord-004615-xfi3p601	491	51	contact	contact	NN
cord-004615-xfi3p601	491	52	and	and	CC
cord-004615-xfi3p601	491	53	movement	movement	NN
cord-004615-xfi3p601	491	54	restrictions	restriction	NNS
cord-004615-xfi3p601	491	55	.	.	.
cord-004615-xfi3p601	492	1	Emerging	emerge	VBG
cord-004615-xfi3p601	492	2	infections	infection	NNS
cord-004615-xfi3p601	492	3	such	such	JJ
cord-004615-xfi3p601	492	4	as	as	IN
cord-004615-xfi3p601	492	5	SARS	SARS	NNP
cord-004615-xfi3p601	492	6	are	be	VBP
cord-004615-xfi3p601	492	7	possible	possible	JJ
cord-004615-xfi3p601	492	8	examples	example	NNS
cord-004615-xfi3p601	492	9	of	of	IN
cord-004615-xfi3p601	492	10	this	this	DT
cord-004615-xfi3p601	492	11	.	.	.
cord-004615-xfi3p601	493	1	Quantification	quantification	NN
cord-004615-xfi3p601	493	2	of	of	IN
cord-004615-xfi3p601	493	3	the	the	DT
cord-004615-xfi3p601	493	4	Effects	effect	NNS
cord-004615-xfi3p601	493	5	of	of	IN
cord-004615-xfi3p601	493	6	Control	Control	NNP
cord-004615-xfi3p601	493	7	Strategies	Strategies	NNPS
cord-004615-xfi3p601	493	8	on	on	IN
cord-004615-xfi3p601	493	9	Classical	Classical	NNP
cord-004615-xfi3p601	493	10	Swine	Swine	NNP
cord-004615-xfi3p601	493	11	Fever	fever	NN
cord-004615-xfi3p601	493	12	Epidemics	epidemic	NNS
cord-004615-xfi3p601	494	1	Mathematical	mathematical	JJ
cord-004615-xfi3p601	494	2	Epidemiology	Epidemiology	NNP
cord-004615-xfi3p601	494	3	of	of	IN
cord-004615-xfi3p601	494	4	Infectious	Infectious	NNP
cord-004615-xfi3p601	494	5	Diseases	Diseases	NNPS
cord-004615-xfi3p601	495	1	Probability	probability	NN
cord-004615-xfi3p601	495	2	and	and	CC
cord-004615-xfi3p601	495	3	Random	Random	NNP
cord-004615-xfi3p601	495	4	Processes	Processes	NNPS
cord-004615-xfi3p601	495	5	Branching	branch	VBG
cord-004615-xfi3p601	495	6	Processes	process	NNS
cord-004615-xfi3p601	495	7	with	with	IN
cord-004615-xfi3p601	495	8	Biological	Biological	NNP
cord-004615-xfi3p601	495	9	Applications	Applications	NNPS
cord-004615-xfi3p601	496	1	The	the	DT
cord-004615-xfi3p601	496	2	Foot	Foot	NNP
cord-004615-xfi3p601	496	3	-	-	HYPH
cord-004615-xfi3p601	496	4	and	and	CC
cord-004615-xfi3p601	496	5	-	-	HYPH
cord-004615-xfi3p601	496	6	Mouth	Mouth	NNP
cord-004615-xfi3p601	496	7	Epidemic	epidemic	NN
cord-004615-xfi3p601	496	8	in	in	IN
cord-004615-xfi3p601	496	9	Great	Great	NNP
cord-004615-xfi3p601	496	10	Britain	Britain	NNP
cord-004615-xfi3p601	496	11	:	:	:
cord-004615-xfi3p601	496	12	Pattern	Pattern	NNP
cord-004615-xfi3p601	496	13	of	of	IN
cord-004615-xfi3p601	496	14	Spread	Spread	NNP
cord-004615-xfi3p601	496	15	and	and	CC
cord-004615-xfi3p601	496	16	Impact	Impact	NNP
cord-004615-xfi3p601	496	17	of	of	IN
cord-004615-xfi3p601	496	18	Interventions	Interventions	NNPS
cord-004615-xfi3p601	496	19	Transmission	Transmission	NNP
cord-004615-xfi3p601	496	20	Intensity	Intensity	NNP
cord-004615-xfi3p601	496	21	and	and	CC
cord-004615-xfi3p601	496	22	Impact	Impact	NNP
cord-004615-xfi3p601	496	23	of	of	IN
cord-004615-xfi3p601	496	24	Control	Control	NNP
cord-004615-xfi3p601	496	25	Policies	Policies	NNPS
cord-004615-xfi3p601	496	26	on	on	IN
cord-004615-xfi3p601	496	27	the	the	DT
cord-004615-xfi3p601	496	28	Foot	Foot	NNP
cord-004615-xfi3p601	496	29	and	and	CC
cord-004615-xfi3p601	496	30	Mouth	Mouth	NNP
cord-004615-xfi3p601	496	31	Epidemic	Epidemic	NNP
cord-004615-xfi3p601	496	32	in	in	IN
cord-004615-xfi3p601	496	33	Great	Great	NNP
cord-004615-xfi3p601	496	34	-	-	HYPH
cord-004615-xfi3p601	496	35	Britain	Britain	NNP
cord-004615-xfi3p601	496	36	Branching	Branching	NNP
cord-004615-xfi3p601	496	37	Processes	process	NNS
cord-004615-xfi3p601	496	38	with	with	IN
cord-004615-xfi3p601	496	39	Deteriorating	deteriorate	VBG
cord-004615-xfi3p601	496	40	Random	random	JJ
cord-004615-xfi3p601	496	41	Environments	environment	NNS
cord-004615-xfi3p601	497	1	The	the	DT
cord-004615-xfi3p601	497	2	Role	role	NN
cord-004615-xfi3p601	497	3	of	of	IN
cord-004615-xfi3p601	497	4	Mathematical	Mathematical	NNP
cord-004615-xfi3p601	497	5	Modelling	Modelling	NNP
cord-004615-xfi3p601	497	6	in	in	IN
cord-004615-xfi3p601	497	7	the	the	DT
cord-004615-xfi3p601	497	8	Control	Control	NNP
cord-004615-xfi3p601	497	9	of	of	IN
cord-004615-xfi3p601	497	10	the	the	DT
cord-004615-xfi3p601	497	11	2001	2001	CD
cord-004615-xfi3p601	497	12	FMD	FMD	NNP
cord-004615-xfi3p601	497	13	Epidemic	Epidemic	NNP
cord-004615-xfi3p601	497	14	in	in	IN
cord-004615-xfi3p601	497	15	the	the	DT
cord-004615-xfi3p601	497	16	UK	UK	NNP
cord-004615-xfi3p601	497	17	Dynamics	Dynamics	NNPS
cord-004615-xfi3p601	497	18	of	of	IN
cord-004615-xfi3p601	497	19	the	the	DT
cord-004615-xfi3p601	497	20	2001	2001	CD
cord-004615-xfi3p601	497	21	UK	UK	NNP
cord-004615-xfi3p601	497	22	Foot	Foot	NNP
cord-004615-xfi3p601	497	23	and	and	CC
cord-004615-xfi3p601	497	24	Mouth	Mouth	NNP
cord-004615-xfi3p601	497	25	Epidemic	Epidemic	NNP
cord-004615-xfi3p601	497	26	-Dispersal	-Dispersal	.
cord-004615-xfi3p601	497	27	in	in	IN
cord-004615-xfi3p601	497	28	a	a	DT
cord-004615-xfi3p601	497	29	Heterogeneous	Heterogeneous	NNP
cord-004615-xfi3p601	497	30	Landscape	Landscape	NNP
cord-004615-xfi3p601	497	31	Modelling	Modelling	NNP
cord-004615-xfi3p601	497	32	and	and	CC
cord-004615-xfi3p601	497	33	Prediction	Prediction	NNP
cord-004615-xfi3p601	497	34	of	of	IN
cord-004615-xfi3p601	497	35	Classical	Classical	NNP
cord-004615-xfi3p601	497	36	Swine	Swine	NNP
cord-004615-xfi3p601	497	37	Fever	Fever	NNP
cord-004615-xfi3p601	497	38	Epidemics	epidemic	NNS
cord-004615-xfi3p601	497	39	Quantification	quantification	NN
cord-004615-xfi3p601	497	40	of	of	IN
cord-004615-xfi3p601	497	41	the	the	DT
cord-004615-xfi3p601	497	42	Transmission	Transmission	NNP
cord-004615-xfi3p601	497	43	of	of	IN
cord-004615-xfi3p601	497	44	Classical	Classical	NNP
cord-004615-xfi3p601	497	45	Swine	Swine	NNP
cord-004615-xfi3p601	497	46	Fever	Fever	NNP
cord-004615-xfi3p601	497	47	Virus	virus	NN
cord-004615-xfi3p601	497	48	between	between	IN
cord-004615-xfi3p601	497	49	Herds	Herds	NNPS
cord-004615-xfi3p601	497	50	during	during	IN
cord-004615-xfi3p601	497	51	the	the	DT
cord-004615-xfi3p601	497	52	1997	1997	CD
cord-004615-xfi3p601	497	53	-	-	SYM
cord-004615-xfi3p601	497	54	1998	1998	CD
cord-004615-xfi3p601	497	55	Epidemic	epidemic	NN
cord-004615-xfi3p601	497	56	in	in	IN
cord-004615-xfi3p601	497	57	The	the	DT
cord-004615-xfi3p601	497	58	Netherlands	Netherlands	NNP