id	sid	tid	token	lemma	pos
cord-221131-44n5pojb	1	1	key	key	NN
cord-221131-44n5pojb	1	2	:	:	:
cord-221131-44n5pojb	2	1	cord-221131	cord-221131	JJ
cord-221131-44n5pojb	2	2	-	-	HYPH
cord-221131-44n5pojb	2	3	44n5pojb	44n5pojb	CD
cord-221131-44n5pojb	2	4	authors	author	NNS
cord-221131-44n5pojb	2	5	:	:	:
cord-221131-44n5pojb	2	6	Zullo	Zullo	NNP
cord-221131-44n5pojb	2	7	,	,	,
cord-221131-44n5pojb	2	8	Federico	Federico	NNP
cord-221131-44n5pojb	2	9	title	title	NN
cord-221131-44n5pojb	2	10	:	:	:
cord-221131-44n5pojb	3	1	Some	some	DT
cord-221131-44n5pojb	3	2	numerical	numerical	JJ
cord-221131-44n5pojb	3	3	observations	observation	NNS
cord-221131-44n5pojb	3	4	about	about	IN
cord-221131-44n5pojb	3	5	the	the	DT
cord-221131-44n5pojb	3	6	COVID-19	covid-19	JJ
cord-221131-44n5pojb	3	7	epidemic	epidemic	NN
cord-221131-44n5pojb	3	8	in	in	IN
cord-221131-44n5pojb	3	9	Italy	Italy	NNP
cord-221131-44n5pojb	3	10	date	date	NN
cord-221131-44n5pojb	3	11	:	:	:
cord-221131-44n5pojb	3	12	2020	2020	CD
cord-221131-44n5pojb	3	13	-	-	HYPH
cord-221131-44n5pojb	3	14	03	03	CD
cord-221131-44n5pojb	3	15	-	-	SYM
cord-221131-44n5pojb	3	16	25	25	CD
cord-221131-44n5pojb	3	17	journal	journal	NN
cord-221131-44n5pojb	3	18	:	:	:
cord-221131-44n5pojb	4	1	nan	nan	NNP
cord-221131-44n5pojb	4	2	DOI	DOI	NNP
cord-221131-44n5pojb	4	3	:	:	:
cord-221131-44n5pojb	4	4	nan	nan	NNP
cord-221131-44n5pojb	4	5	sha	sha	NNP
cord-221131-44n5pojb	4	6	:	:	:
cord-221131-44n5pojb	4	7	0940e70d9d7ae49cab612c8f5c22957601152aa7	0940e70d9d7ae49cab612c8f5c22957601152aa7	NFP
cord-221131-44n5pojb	4	8	doc_id	doc_id	CD
cord-221131-44n5pojb	4	9	:	:	:
cord-221131-44n5pojb	5	1	221131	221131	CD
cord-221131-44n5pojb	5	2	cord_uid	cord_uid	NNS
cord-221131-44n5pojb	5	3	:	:	:
cord-221131-44n5pojb	5	4	44n5pojb	44n5pojb	CD
cord-221131-44n5pojb	6	1	We	-PRON-	PRP
cord-221131-44n5pojb	6	2	give	give	VBP
cord-221131-44n5pojb	6	3	some	some	DT
cord-221131-44n5pojb	6	4	numerical	numerical	JJ
cord-221131-44n5pojb	6	5	observations	observation	NNS
cord-221131-44n5pojb	6	6	on	on	IN
cord-221131-44n5pojb	6	7	the	the	DT
cord-221131-44n5pojb	6	8	total	total	JJ
cord-221131-44n5pojb	6	9	number	number	NN
cord-221131-44n5pojb	6	10	of	of	IN
cord-221131-44n5pojb	6	11	infected	infect	VBN
cord-221131-44n5pojb	6	12	by	by	IN
cord-221131-44n5pojb	6	13	the	the	DT
cord-221131-44n5pojb	6	14	SARS	SARS	NNP
cord-221131-44n5pojb	6	15	-	-	HYPH
cord-221131-44n5pojb	6	16	CoV-2	CoV-2	NNP
cord-221131-44n5pojb	6	17	in	in	IN
cord-221131-44n5pojb	6	18	Italy	Italy	NNP
cord-221131-44n5pojb	6	19	.	.	.
cord-221131-44n5pojb	7	1	The	the	DT
cord-221131-44n5pojb	7	2	analysis	analysis	NN
cord-221131-44n5pojb	7	3	is	be	VBZ
cord-221131-44n5pojb	7	4	based	base	VBN
cord-221131-44n5pojb	7	5	on	on	IN
cord-221131-44n5pojb	7	6	a	a	DT
cord-221131-44n5pojb	7	7	tanh	tanh	NN
cord-221131-44n5pojb	7	8	formula	formula	NN
cord-221131-44n5pojb	7	9	involving	involve	VBG
cord-221131-44n5pojb	7	10	two	two	CD
cord-221131-44n5pojb	7	11	parameters	parameter	NNS
cord-221131-44n5pojb	7	12	.	.	.
cord-221131-44n5pojb	8	1	A	a	DT
cord-221131-44n5pojb	8	2	polynomial	polynomial	JJ
cord-221131-44n5pojb	8	3	correlation	correlation	NN
cord-221131-44n5pojb	8	4	between	between	IN
cord-221131-44n5pojb	8	5	the	the	DT
cord-221131-44n5pojb	8	6	parameters	parameter	NNS
cord-221131-44n5pojb	8	7	gives	give	VBZ
cord-221131-44n5pojb	8	8	an	an	DT
cord-221131-44n5pojb	8	9	upper	upper	JJ
cord-221131-44n5pojb	8	10	bound	bind	VBN
cord-221131-44n5pojb	8	11	for	for	IN
cord-221131-44n5pojb	8	12	the	the	DT
cord-221131-44n5pojb	8	13	time	time	NN
cord-221131-44n5pojb	8	14	of	of	IN
cord-221131-44n5pojb	8	15	the	the	DT
cord-221131-44n5pojb	8	16	peak	peak	NN
cord-221131-44n5pojb	8	17	of	of	IN
cord-221131-44n5pojb	8	18	new	new	JJ
cord-221131-44n5pojb	8	19	infected	infect	VBN
cord-221131-44n5pojb	8	20	.	.	.
cord-221131-44n5pojb	9	1	A	a	DT
cord-221131-44n5pojb	9	2	numerical	numerical	JJ
cord-221131-44n5pojb	9	3	indicator	indicator	NN
cord-221131-44n5pojb	9	4	of	of	IN
cord-221131-44n5pojb	9	5	the	the	DT
cord-221131-44n5pojb	9	6	temporal	temporal	JJ
cord-221131-44n5pojb	9	7	variability	variability	NN
cord-221131-44n5pojb	9	8	of	of	IN
cord-221131-44n5pojb	9	9	the	the	DT
cord-221131-44n5pojb	9	10	upper	upper	JJ
cord-221131-44n5pojb	9	11	bound	bind	VBN
cord-221131-44n5pojb	9	12	is	be	VBZ
cord-221131-44n5pojb	9	13	introduced	introduce	VBN
cord-221131-44n5pojb	9	14	.	.	.
cord-221131-44n5pojb	10	1	The	the	DT
cord-221131-44n5pojb	10	2	result	result	NN
cord-221131-44n5pojb	10	3	and	and	CC
cord-221131-44n5pojb	10	4	the	the	DT
cord-221131-44n5pojb	10	5	possibility	possibility	NN
cord-221131-44n5pojb	10	6	to	to	TO
cord-221131-44n5pojb	10	7	extend	extend	VB
cord-221131-44n5pojb	10	8	the	the	DT
cord-221131-44n5pojb	10	9	analysis	analysis	NN
cord-221131-44n5pojb	10	10	to	to	IN
cord-221131-44n5pojb	10	11	other	other	JJ
cord-221131-44n5pojb	10	12	countries	country	NNS
cord-221131-44n5pojb	10	13	are	be	VBP
cord-221131-44n5pojb	10	14	discussed	discuss	VBN
cord-221131-44n5pojb	10	15	in	in	IN
cord-221131-44n5pojb	10	16	the	the	DT
cord-221131-44n5pojb	10	17	conclusions	conclusion	NNS
cord-221131-44n5pojb	10	18	.	.	.
cord-221131-44n5pojb	11	1	The	the	DT
cord-221131-44n5pojb	11	2	coronavirus	coronavirus	NN
cord-221131-44n5pojb	11	3	disease	disease	NN
cord-221131-44n5pojb	11	4	2019	2019	CD
cord-221131-44n5pojb	11	5	(	(	-LRB-
cord-221131-44n5pojb	11	6	COVID-19	COVID-19	NNP
cord-221131-44n5pojb	11	7	)	)	-RRB-
cord-221131-44n5pojb	11	8	has	have	VBZ
cord-221131-44n5pojb	11	9	been	be	VBN
cord-221131-44n5pojb	11	10	recognized	recognize	VBN
cord-221131-44n5pojb	11	11	in	in	IN
cord-221131-44n5pojb	11	12	Italy	Italy	NNP
cord-221131-44n5pojb	11	13	starting	start	VBG
cord-221131-44n5pojb	11	14	from	from	IN
cord-221131-44n5pojb	11	15	31st	31st	JJ
cord-221131-44n5pojb	11	16	January	January	NNP
cord-221131-44n5pojb	11	17	2020	2020	CD
cord-221131-44n5pojb	11	18	,	,	,
cord-221131-44n5pojb	11	19	also	also	RB
cord-221131-44n5pojb	11	20	if	if	IN
cord-221131-44n5pojb	11	21	there	there	EX
cord-221131-44n5pojb	11	22	are	be	VBP
cord-221131-44n5pojb	11	23	some	some	DT
cord-221131-44n5pojb	11	24	evidences	evidence	NNS
cord-221131-44n5pojb	11	25	that	that	IN
cord-221131-44n5pojb	11	26	the	the	DT
cord-221131-44n5pojb	11	27	first	first	JJ
cord-221131-44n5pojb	11	28	cases	case	NNS
cord-221131-44n5pojb	11	29	started	start	VBD
cord-221131-44n5pojb	11	30	some	some	DT
cord-221131-44n5pojb	11	31	time	time	NN
cord-221131-44n5pojb	11	32	earlier	early	RBR
cord-221131-44n5pojb	11	33	[	[	-LRB-
cord-221131-44n5pojb	11	34	3	3	CD
cord-221131-44n5pojb	11	35	]	]	-RRB-
cord-221131-44n5pojb	11	36	.	.	.
cord-221131-44n5pojb	12	1	The	the	DT
cord-221131-44n5pojb	12	2	spread	spread	NN
cord-221131-44n5pojb	12	3	of	of	IN
cord-221131-44n5pojb	12	4	the	the	DT
cord-221131-44n5pojb	12	5	disease	disease	NN
cord-221131-44n5pojb	12	6	started	start	VBD
cord-221131-44n5pojb	12	7	from	from	IN
cord-221131-44n5pojb	12	8	the	the	DT
cord-221131-44n5pojb	12	9	northern	northern	JJ
cord-221131-44n5pojb	12	10	regions	region	NNS
cord-221131-44n5pojb	12	11	of	of	IN
cord-221131-44n5pojb	12	12	Italy	Italy	NNP
cord-221131-44n5pojb	12	13	,	,	,
cord-221131-44n5pojb	12	14	Lombardy	Lombardy	NNP
cord-221131-44n5pojb	12	15	and	and	CC
cord-221131-44n5pojb	12	16	Veneto	Veneto	NNP
cord-221131-44n5pojb	12	17	on	on	IN
cord-221131-44n5pojb	12	18	the	the	DT
cord-221131-44n5pojb	12	19	21st	21st	NN
cord-221131-44n5pojb	12	20	of	of	IN
cord-221131-44n5pojb	12	21	February	February	NNP
cord-221131-44n5pojb	12	22	2020	2020	CD
cord-221131-44n5pojb	12	23	:	:	:
cord-221131-44n5pojb	12	24	after	after	IN
cord-221131-44n5pojb	12	25	about	about	RB
cord-221131-44n5pojb	12	26	twenty	twenty	CD
cord-221131-44n5pojb	12	27	positive	positive	JJ
cord-221131-44n5pojb	12	28	cases	case	NNS
cord-221131-44n5pojb	12	29	,	,	,
cord-221131-44n5pojb	12	30	two	two	CD
cord-221131-44n5pojb	12	31	small	small	JJ
cord-221131-44n5pojb	12	32	areas	area	NNS
cord-221131-44n5pojb	12	33	had	have	VBD
cord-221131-44n5pojb	12	34	been	be	VBN
cord-221131-44n5pojb	12	35	put	put	VBN
cord-221131-44n5pojb	12	36	in	in	IN
cord-221131-44n5pojb	12	37	quarantine	quarantine	NN
cord-221131-44n5pojb	12	38	but	but	CC
cord-221131-44n5pojb	12	39	,	,	,
cord-221131-44n5pojb	12	40	since	since	IN
cord-221131-44n5pojb	12	41	then	then	RB
cord-221131-44n5pojb	12	42	,	,	,
cord-221131-44n5pojb	12	43	the	the	DT
cord-221131-44n5pojb	12	44	number	number	NN
cord-221131-44n5pojb	12	45	of	of	IN
cord-221131-44n5pojb	12	46	infected	infected	JJ
cord-221131-44n5pojb	12	47	increased	increase	VBN
cord-221131-44n5pojb	12	48	exponentially	exponentially	RB
cord-221131-44n5pojb	12	49	in	in	IN
cord-221131-44n5pojb	12	50	this	this	DT
cord-221131-44n5pojb	12	51	two	two	CD
cord-221131-44n5pojb	12	52	districts	district	NNS
cord-221131-44n5pojb	12	53	.	.	.
cord-221131-44n5pojb	13	1	From	from	IN
cord-221131-44n5pojb	13	2	the	the	DT
cord-221131-44n5pojb	13	3	localities	locality	NNS
cord-221131-44n5pojb	13	4	situated	situate	VBN
cord-221131-44n5pojb	13	5	farthest	farthest	RBS
cord-221131-44n5pojb	13	6	south	south	RB
cord-221131-44n5pojb	13	7	in	in	IN
cord-221131-44n5pojb	13	8	Lombardy	Lombardy	NNP
cord-221131-44n5pojb	13	9	the	the	DT
cord-221131-44n5pojb	13	10	disease	disease	NN
cord-221131-44n5pojb	13	11	spread	spread	VBD
cord-221131-44n5pojb	13	12	in	in	IN
cord-221131-44n5pojb	13	13	closest	close	JJS
cord-221131-44n5pojb	13	14	regions	region	NNS
cord-221131-44n5pojb	13	15	,	,	,
cord-221131-44n5pojb	13	16	Emilia	Emilia	NNP
cord-221131-44n5pojb	13	17	-	-	HYPH
cord-221131-44n5pojb	13	18	Romagna	Romagna	NNP
cord-221131-44n5pojb	13	19	above	above	IN
cord-221131-44n5pojb	13	20	all	all	DT
cord-221131-44n5pojb	13	21	,	,	,
cord-221131-44n5pojb	13	22	with	with	IN
cord-221131-44n5pojb	13	23	the	the	DT
cord-221131-44n5pojb	13	24	provinces	province	NNS
cord-221131-44n5pojb	13	25	of	of	IN
cord-221131-44n5pojb	13	26	Piacenza	Piacenza	NNP
cord-221131-44n5pojb	13	27	,	,	,
cord-221131-44n5pojb	13	28	Parma	Parma	NNP
cord-221131-44n5pojb	13	29	,	,	,
cord-221131-44n5pojb	13	30	Modena	Modena	NNP
cord-221131-44n5pojb	13	31	,	,	,
cord-221131-44n5pojb	13	32	Rimini	Rimini	NNP
cord-221131-44n5pojb	13	33	,	,	,
cord-221131-44n5pojb	13	34	but	but	CC
cord-221131-44n5pojb	13	35	soon	soon	RB
cord-221131-44n5pojb	13	36	after	after	IN
cord-221131-44n5pojb	13	37	also	also	RB
cord-221131-44n5pojb	13	38	in	in	IN
cord-221131-44n5pojb	13	39	other	other	JJ
cord-221131-44n5pojb	13	40	provinces	province	NNS
cord-221131-44n5pojb	13	41	of	of	IN
cord-221131-44n5pojb	13	42	Lombardy	Lombardy	NNP
cord-221131-44n5pojb	14	1	(	(	-LRB-
cord-221131-44n5pojb	14	2	e.g.	e.g.	RB
cord-221131-44n5pojb	14	3	in	in	IN
cord-221131-44n5pojb	14	4	the	the	DT
cord-221131-44n5pojb	14	5	province	province	NN
cord-221131-44n5pojb	14	6	of	of	IN
cord-221131-44n5pojb	14	7	Bergamo	Bergamo	NNP
cord-221131-44n5pojb	14	8	)	)	-RRB-
cord-221131-44n5pojb	14	9	.	.	.
cord-221131-44n5pojb	15	1	On	on	IN
cord-221131-44n5pojb	15	2	the	the	DT
cord-221131-44n5pojb	15	3	8th	8th	NN
cord-221131-44n5pojb	15	4	of	of	IN
cord-221131-44n5pojb	15	5	March	March	NNP
cord-221131-44n5pojb	15	6	a	a	DT
cord-221131-44n5pojb	15	7	lockdown	lockdown	NN
cord-221131-44n5pojb	15	8	for	for	IN
cord-221131-44n5pojb	15	9	the	the	DT
cord-221131-44n5pojb	15	10	entire	entire	JJ
cord-221131-44n5pojb	15	11	region	region	NN
cord-221131-44n5pojb	15	12	of	of	IN
cord-221131-44n5pojb	15	13	Lombardy	Lombardy	NNP
cord-221131-44n5pojb	15	14	(	(	-LRB-
cord-221131-44n5pojb	15	15	with	with	IN
cord-221131-44n5pojb	15	16	a	a	DT
cord-221131-44n5pojb	15	17	population	population	NN
cord-221131-44n5pojb	15	18	of	of	IN
cord-221131-44n5pojb	15	19	about	about	RB
cord-221131-44n5pojb	15	20	10	10	CD
cord-221131-44n5pojb	15	21	millions	million	NNS
cord-221131-44n5pojb	15	22	of	of	IN
cord-221131-44n5pojb	15	23	inhabitants	inhabitant	NNS
cord-221131-44n5pojb	15	24	)	)	-RRB-
cord-221131-44n5pojb	15	25	and	and	CC
cord-221131-44n5pojb	15	26	other	other	JJ
cord-221131-44n5pojb	15	27	fourteen	fourteen	CD
cord-221131-44n5pojb	15	28	provinces	province	NNS
cord-221131-44n5pojb	15	29	(	(	-LRB-
cord-221131-44n5pojb	15	30	population	population	NN
cord-221131-44n5pojb	15	31	of	of	IN
cord-221131-44n5pojb	15	32	about	about	RB
cord-221131-44n5pojb	15	33	six	six	CD
cord-221131-44n5pojb	15	34	millions	million	NNS
cord-221131-44n5pojb	15	35	of	of	IN
cord-221131-44n5pojb	15	36	inhabitants	inhabitant	NNS
cord-221131-44n5pojb	15	37	)	)	-RRB-
cord-221131-44n5pojb	15	38	was	be	VBD
cord-221131-44n5pojb	15	39	imposed	impose	VBN
cord-221131-44n5pojb	15	40	by	by	IN
cord-221131-44n5pojb	15	41	the	the	DT
cord-221131-44n5pojb	15	42	central	central	JJ
cord-221131-44n5pojb	15	43	government	government	NN
cord-221131-44n5pojb	15	44	of	of	IN
cord-221131-44n5pojb	15	45	Italy	Italy	NNP
cord-221131-44n5pojb	15	46	and	and	CC
cord-221131-44n5pojb	15	47	then	then	RB
cord-221131-44n5pojb	15	48	extended	extend	VBD
cord-221131-44n5pojb	15	49	,	,	,
cord-221131-44n5pojb	15	50	on	on	IN
cord-221131-44n5pojb	15	51	the	the	DT
cord-221131-44n5pojb	15	52	9th	9th	NN
cord-221131-44n5pojb	15	53	of	of	IN
cord-221131-44n5pojb	15	54	March	March	NNP
cord-221131-44n5pojb	15	55	,	,	,
cord-221131-44n5pojb	15	56	to	to	IN
cord-221131-44n5pojb	15	57	the	the	DT
cord-221131-44n5pojb	15	58	entire	entire	JJ
cord-221131-44n5pojb	15	59	country	country	NN
cord-221131-44n5pojb	15	60	.	.	.
cord-221131-44n5pojb	16	1	Up	up	IN
cord-221131-44n5pojb	16	2	to	to	IN
cord-221131-44n5pojb	16	3	the	the	DT
cord-221131-44n5pojb	16	4	23rd	23rd	NN
cord-221131-44n5pojb	16	5	of	of	IN
cord-221131-44n5pojb	16	6	March	March	NNP
cord-221131-44n5pojb	16	7	,	,	,
cord-221131-44n5pojb	16	8	the	the	DT
cord-221131-44n5pojb	16	9	total	total	JJ
cord-221131-44n5pojb	16	10	number	number	NN
cord-221131-44n5pojb	16	11	of	of	IN
cord-221131-44n5pojb	16	12	infected	infect	VBN
cord-221131-44n5pojb	16	13	is	be	VBZ
cord-221131-44n5pojb	16	14	63927	63927	CD
cord-221131-44n5pojb	16	15	,	,	,
cord-221131-44n5pojb	16	16	of	of	IN
cord-221131-44n5pojb	16	17	which	which	WDT
cord-221131-44n5pojb	16	18	28761	28761	CD
cord-221131-44n5pojb	16	19	in	in	IN
cord-221131-44n5pojb	16	20	the	the	DT
cord-221131-44n5pojb	16	21	Lombardy	Lombardy	NNP
cord-221131-44n5pojb	16	22	region	region	NN
cord-221131-44n5pojb	16	23	.	.	.
cord-221131-44n5pojb	17	1	Since	since	IN
cord-221131-44n5pojb	17	2	the	the	DT
cord-221131-44n5pojb	17	3	start	start	NN
cord-221131-44n5pojb	17	4	of	of	IN
cord-221131-44n5pojb	17	5	the	the	DT
cord-221131-44n5pojb	17	6	epidemic	epidemic	NN
cord-221131-44n5pojb	17	7	in	in	IN
cord-221131-44n5pojb	17	8	China	China	NNP
cord-221131-44n5pojb	17	9	,	,	,
cord-221131-44n5pojb	17	10	a	a	DT
cord-221131-44n5pojb	17	11	certain	certain	JJ
cord-221131-44n5pojb	17	12	number	number	NN
cord-221131-44n5pojb	17	13	of	of	IN
cord-221131-44n5pojb	17	14	studies	study	NNS
cord-221131-44n5pojb	17	15	appeared	appear	VBD
cord-221131-44n5pojb	17	16	in	in	IN
cord-221131-44n5pojb	17	17	the	the	DT
cord-221131-44n5pojb	17	18	mathematical	mathematical	JJ
cord-221131-44n5pojb	17	19	community	community	NN
cord-221131-44n5pojb	17	20	about	about	IN
cord-221131-44n5pojb	17	21	this	this	DT
cord-221131-44n5pojb	17	22	subject	subject	NN
cord-221131-44n5pojb	17	23	:	:	:
cord-221131-44n5pojb	17	24	the	the	DT
cord-221131-44n5pojb	17	25	description	description	NN
cord-221131-44n5pojb	17	26	of	of	IN
cord-221131-44n5pojb	17	27	the	the	DT
cord-221131-44n5pojb	17	28	spatial	spatial	JJ
cord-221131-44n5pojb	17	29	or	or	CC
cord-221131-44n5pojb	17	30	temporal	temporal	JJ
cord-221131-44n5pojb	17	31	diffusion	diffusion	NN
cord-221131-44n5pojb	17	32	of	of	IN
cord-221131-44n5pojb	17	33	the	the	DT
cord-221131-44n5pojb	17	34	infected	infect	VBN
cord-221131-44n5pojb	17	35	in	in	IN
cord-221131-44n5pojb	17	36	given	give	VBN
cord-221131-44n5pojb	17	37	regions	region	NNS
cord-221131-44n5pojb	17	38	[	[	-LRB-
cord-221131-44n5pojb	17	39	4	4	CD
cord-221131-44n5pojb	17	40	]	]	-RRB-
cord-221131-44n5pojb	17	41	,	,	,
cord-221131-44n5pojb	17	42	[	[	-LRB-
cord-221131-44n5pojb	17	43	8	8	CD
cord-221131-44n5pojb	17	44	]	]	-RRB-
cord-221131-44n5pojb	17	45	-	-	:
cord-221131-44n5pojb	17	46	[	[	-LRB-
cord-221131-44n5pojb	17	47	10	10	CD
cord-221131-44n5pojb	17	48	]	]	-RRB-
cord-221131-44n5pojb	17	49	,	,	,
cord-221131-44n5pojb	17	50	the	the	DT
cord-221131-44n5pojb	17	51	transmission	transmission	NN
cord-221131-44n5pojb	17	52	dynamics	dynamic	NNS
cord-221131-44n5pojb	17	53	of	of	IN
cord-221131-44n5pojb	17	54	the	the	DT
cord-221131-44n5pojb	17	55	infection	infection	NN
cord-221131-44n5pojb	17	56	[	[	-LRB-
cord-221131-44n5pojb	17	57	6	6	CD
cord-221131-44n5pojb	17	58	]	]	-RRB-
cord-221131-44n5pojb	17	59	,	,	,
cord-221131-44n5pojb	17	60	the	the	DT
cord-221131-44n5pojb	17	61	economic	economic	JJ
cord-221131-44n5pojb	17	62	and	and	CC
cord-221131-44n5pojb	17	63	financial	financial	JJ
cord-221131-44n5pojb	17	64	consequences	consequence	NNS
cord-221131-44n5pojb	17	65	of	of	IN
cord-221131-44n5pojb	17	66	the	the	DT
cord-221131-44n5pojb	17	67	epidemic	epidemic	NN
cord-221131-44n5pojb	17	68	[	[	-LRB-
cord-221131-44n5pojb	17	69	1	1	CD
cord-221131-44n5pojb	17	70	]	]	-RRB-
cord-221131-44n5pojb	17	71	,	,	,
cord-221131-44n5pojb	17	72	the	the	DT
cord-221131-44n5pojb	17	73	effect	effect	NN
cord-221131-44n5pojb	17	74	of	of	IN
cord-221131-44n5pojb	17	75	atmospheric	atmospheric	JJ
cord-221131-44n5pojb	17	76	indicators	indicator	NNS
cord-221131-44n5pojb	17	77	on	on	IN
cord-221131-44n5pojb	17	78	the	the	DT
cord-221131-44n5pojb	17	79	spread	spread	NN
cord-221131-44n5pojb	17	80	of	of	IN
cord-221131-44n5pojb	17	81	the	the	DT
cord-221131-44n5pojb	17	82	virus	virus	NN
cord-221131-44n5pojb	17	83	[	[	-LRB-
cord-221131-44n5pojb	17	84	5	5	CD
cord-221131-44n5pojb	17	85	]	]	-RRB-
cord-221131-44n5pojb	17	86	,	,	,
cord-221131-44n5pojb	17	87	are	be	VBP
cord-221131-44n5pojb	17	88	only	only	RB
cord-221131-44n5pojb	17	89	a	a	DT
cord-221131-44n5pojb	17	90	fraction	fraction	NN
cord-221131-44n5pojb	17	91	of	of	IN
cord-221131-44n5pojb	17	92	the	the	DT
cord-221131-44n5pojb	17	93	topics	topic	NNS
cord-221131-44n5pojb	17	94	under	under	IN
cord-221131-44n5pojb	17	95	investigation	investigation	NN
cord-221131-44n5pojb	17	96	in	in	IN
cord-221131-44n5pojb	17	97	these	these	DT
cord-221131-44n5pojb	17	98	days	day	NNS
cord-221131-44n5pojb	17	99	.	.	.
cord-221131-44n5pojb	18	1	One	one	CD
cord-221131-44n5pojb	18	2	of	of	IN
cord-221131-44n5pojb	18	3	the	the	DT
cord-221131-44n5pojb	18	4	simplest	simple	JJS
cord-221131-44n5pojb	18	5	non	non	JJ
cord-221131-44n5pojb	18	6	-	-	JJ
cord-221131-44n5pojb	18	7	linear	linear	JJ
cord-221131-44n5pojb	18	8	deterministic	deterministic	JJ
cord-221131-44n5pojb	18	9	continuous	continuous	JJ
cord-221131-44n5pojb	18	10	(	(	-LRB-
cord-221131-44n5pojb	18	11	in	in	IN
cord-221131-44n5pojb	18	12	time	time	NN
cord-221131-44n5pojb	18	13	)	)	-RRB-
cord-221131-44n5pojb	18	14	model	model	NN
cord-221131-44n5pojb	18	15	of	of	IN
cord-221131-44n5pojb	18	16	epidemiology	epidemiology	NN
cord-221131-44n5pojb	18	17	is	be	VBZ
cord-221131-44n5pojb	18	18	the	the	DT
cord-221131-44n5pojb	18	19	SIR	SIR	NNP
cord-221131-44n5pojb	18	20	model	model	NN
cord-221131-44n5pojb	18	21	,	,	,
cord-221131-44n5pojb	18	22	in	in	IN
cord-221131-44n5pojb	18	23	which	which	WDT
cord-221131-44n5pojb	18	24	the	the	DT
cord-221131-44n5pojb	18	25	overall	overall	JJ
cord-221131-44n5pojb	18	26	population	population	NN
cord-221131-44n5pojb	18	27	is	be	VBZ
cord-221131-44n5pojb	18	28	divided	divide	VBN
cord-221131-44n5pojb	18	29	in	in	IN
cord-221131-44n5pojb	18	30	three	three	CD
cord-221131-44n5pojb	18	31	disjoint	disjoint	JJ
cord-221131-44n5pojb	18	32	classes	class	NNS
cord-221131-44n5pojb	18	33	:	:	:
cord-221131-44n5pojb	18	34	S	S	NNP
cord-221131-44n5pojb	18	35	is	be	VBZ
cord-221131-44n5pojb	18	36	the	the	DT
cord-221131-44n5pojb	18	37	number	number	NN
cord-221131-44n5pojb	18	38	of	of	IN
cord-221131-44n5pojb	18	39	susceptible	susceptible	JJ
cord-221131-44n5pojb	18	40	individuals	individual	NNS
cord-221131-44n5pojb	18	41	,	,	,
cord-221131-44n5pojb	18	42	I	-PRON-	PRP
cord-221131-44n5pojb	18	43	the	the	DT
cord-221131-44n5pojb	18	44	number	number	NN
cord-221131-44n5pojb	18	45	of	of	IN
cord-221131-44n5pojb	18	46	infectious	infectious	JJ
cord-221131-44n5pojb	18	47	individuals	individual	NNS
cord-221131-44n5pojb	18	48	and	and	CC
cord-221131-44n5pojb	18	49	R	r	VB
cord-221131-44n5pojb	18	50	the	the	DT
cord-221131-44n5pojb	18	51	number	number	NN
cord-221131-44n5pojb	18	52	of	of	IN
cord-221131-44n5pojb	18	53	recovered	recover	VBN
cord-221131-44n5pojb	18	54	individuals	individual	NNS
cord-221131-44n5pojb	18	55	.	.	.
cord-221131-44n5pojb	19	1	Albeit	albeit	IN
cord-221131-44n5pojb	19	2	its	-PRON-	PRP$
cord-221131-44n5pojb	19	3	non	non	JJ
cord-221131-44n5pojb	19	4	-	-	NN
cord-221131-44n5pojb	19	5	linearity	linearity	NN
cord-221131-44n5pojb	19	6	,	,	,
cord-221131-44n5pojb	19	7	the	the	DT
cord-221131-44n5pojb	19	8	dynamic	dynamic	NN
cord-221131-44n5pojb	19	9	of	of	IN
cord-221131-44n5pojb	19	10	the	the	DT
cord-221131-44n5pojb	19	11	model	model	NN
cord-221131-44n5pojb	19	12	is	be	VBZ
cord-221131-44n5pojb	19	13	fairly	fairly	RB
cord-221131-44n5pojb	19	14	uncomplicated	uncomplicated	JJ
cord-221131-44n5pojb	19	15	and	and	CC
cord-221131-44n5pojb	19	16	manageable	manageable	JJ
cord-221131-44n5pojb	19	17	from	from	IN
cord-221131-44n5pojb	19	18	an	an	DT
cord-221131-44n5pojb	19	19	analytical	analytical	JJ
cord-221131-44n5pojb	19	20	point	point	NN
cord-221131-44n5pojb	19	21	of	of	IN
cord-221131-44n5pojb	19	22	view	view	NN
cord-221131-44n5pojb	19	23	,	,	,
cord-221131-44n5pojb	19	24	and	and	CC
cord-221131-44n5pojb	19	25	displays	display	VBZ
cord-221131-44n5pojb	19	26	very	very	RB
cord-221131-44n5pojb	19	27	interesting	interesting	JJ
cord-221131-44n5pojb	19	28	properties	property	NNS
cord-221131-44n5pojb	19	29	such	such	JJ
cord-221131-44n5pojb	19	30	as	as	IN
cord-221131-44n5pojb	19	31	the	the	DT
cord-221131-44n5pojb	19	32	existence	existence	NN
cord-221131-44n5pojb	19	33	of	of	IN
cord-221131-44n5pojb	19	34	an	an	DT
cord-221131-44n5pojb	19	35	epidemic	epidemic	NN
cord-221131-44n5pojb	19	36	threshold	threshold	NN
cord-221131-44n5pojb	19	37	(	(	-LRB-
cord-221131-44n5pojb	19	38	see	see	VB
cord-221131-44n5pojb	19	39	e.g.	e.g.	RB
cord-221131-44n5pojb	19	40	[	[	-LRB-
cord-221131-44n5pojb	19	41	11	11	CD
cord-221131-44n5pojb	19	42	]	]	-RRB-
cord-221131-44n5pojb	19	43	)	)	-RRB-
cord-221131-44n5pojb	19	44	,	,	,
cord-221131-44n5pojb	19	45	making	make	VBG
cord-221131-44n5pojb	19	46	it	-PRON-	PRP
cord-221131-44n5pojb	19	47	a	a	DT
cord-221131-44n5pojb	19	48	very	very	RB
cord-221131-44n5pojb	19	49	reasonable	reasonable	JJ
cord-221131-44n5pojb	19	50	model	model	NN
cord-221131-44n5pojb	19	51	.	.	.
cord-221131-44n5pojb	20	1	In	in	IN
cord-221131-44n5pojb	20	2	section	section	NN
cord-221131-44n5pojb	20	3	(	(	-LRB-
cord-221131-44n5pojb	20	4	2	2	LS
cord-221131-44n5pojb	20	5	)	)	-RRB-
cord-221131-44n5pojb	20	6	the	the	DT
cord-221131-44n5pojb	20	7	SIR	SIR	NNP
cord-221131-44n5pojb	20	8	model	model	NN
cord-221131-44n5pojb	20	9	is	be	VBZ
cord-221131-44n5pojb	20	10	introduced	introduce	VBN
cord-221131-44n5pojb	20	11	and	and	CC
cord-221131-44n5pojb	20	12	briefly	briefly	RB
cord-221131-44n5pojb	20	13	discussed	discuss	VBD
cord-221131-44n5pojb	20	14	,	,	,
cord-221131-44n5pojb	20	15	in	in	IN
cord-221131-44n5pojb	20	16	section	section	NN
cord-221131-44n5pojb	20	17	(	(	-LRB-
cord-221131-44n5pojb	20	18	3	3	LS
cord-221131-44n5pojb	20	19	)	)	-RRB-
cord-221131-44n5pojb	20	20	we	-PRON-	PRP
cord-221131-44n5pojb	20	21	will	will	MD
cord-221131-44n5pojb	20	22	analyze	analyze	VB
cord-221131-44n5pojb	20	23	the	the	DT
cord-221131-44n5pojb	20	24	data	datum	NNS
cord-221131-44n5pojb	20	25	of	of	IN
cord-221131-44n5pojb	20	26	the	the	DT
cord-221131-44n5pojb	20	27	cumulative	cumulative	JJ
cord-221131-44n5pojb	20	28	number	number	NN
cord-221131-44n5pojb	20	29	of	of	IN
cord-221131-44n5pojb	20	30	infected	infect	VBN
cord-221131-44n5pojb	20	31	in	in	IN
cord-221131-44n5pojb	20	32	Italy	Italy	NNP
cord-221131-44n5pojb	20	33	on	on	IN
cord-221131-44n5pojb	20	34	the	the	DT
cord-221131-44n5pojb	20	35	base	base	NN
cord-221131-44n5pojb	20	36	of	of	IN
cord-221131-44n5pojb	20	37	two	two	CD
cord-221131-44n5pojb	20	38	simple	simple	JJ
cord-221131-44n5pojb	20	39	hypotheses	hypothesis	NNS
cord-221131-44n5pojb	20	40	.	.	.
cord-221131-44n5pojb	21	1	An	an	DT
cord-221131-44n5pojb	21	2	upper	upper	JJ
cord-221131-44n5pojb	21	3	bound	bind	VBN
cord-221131-44n5pojb	21	4	for	for	IN
cord-221131-44n5pojb	21	5	the	the	DT
cord-221131-44n5pojb	21	6	timing	timing	NN
cord-221131-44n5pojb	21	7	of	of	IN
cord-221131-44n5pojb	21	8	the	the	DT
cord-221131-44n5pojb	21	9	peak	peak	NN
cord-221131-44n5pojb	21	10	of	of	IN
cord-221131-44n5pojb	21	11	new	new	JJ
cord-221131-44n5pojb	21	12	number	number	NN
cord-221131-44n5pojb	21	13	of	of	IN
cord-221131-44n5pojb	21	14	infected	infected	JJ
cord-221131-44n5pojb	21	15	is	be	VBZ
cord-221131-44n5pojb	21	16	obtained	obtain	VBN
cord-221131-44n5pojb	21	17	.	.	.
cord-221131-44n5pojb	22	1	In	in	IN
cord-221131-44n5pojb	22	2	the	the	DT
cord-221131-44n5pojb	22	3	conclusions	conclusion	NNS
cord-221131-44n5pojb	22	4	we	-PRON-	PRP
cord-221131-44n5pojb	22	5	will	will	MD
cord-221131-44n5pojb	22	6	comment	comment	VB
cord-221131-44n5pojb	22	7	about	about	IN
cord-221131-44n5pojb	22	8	the	the	DT
cord-221131-44n5pojb	22	9	results	result	NNS
cord-221131-44n5pojb	22	10	and	and	CC
cord-221131-44n5pojb	22	11	look	look	VB
cord-221131-44n5pojb	22	12	for	for	IN
cord-221131-44n5pojb	22	13	possible	possible	JJ
cord-221131-44n5pojb	22	14	extensions	extension	NNS
cord-221131-44n5pojb	22	15	.	.	.
cord-221131-44n5pojb	23	1	The	the	DT
cord-221131-44n5pojb	23	2	SIR	SIR	NNP
cord-221131-44n5pojb	23	3	model	model	NN
cord-221131-44n5pojb	23	4	describes	describe	VBZ
cord-221131-44n5pojb	23	5	the	the	DT
cord-221131-44n5pojb	23	6	evolution	evolution	NN
cord-221131-44n5pojb	23	7	of	of	IN
cord-221131-44n5pojb	23	8	the	the	DT
cord-221131-44n5pojb	23	9	individuals	individual	NNS
cord-221131-44n5pojb	23	10	in	in	IN
cord-221131-44n5pojb	23	11	the	the	DT
cord-221131-44n5pojb	23	12	susceptible	susceptible	JJ
cord-221131-44n5pojb	23	13	,	,	,
cord-221131-44n5pojb	23	14	infectious	infectious	JJ
cord-221131-44n5pojb	23	15	or	or	CC
cord-221131-44n5pojb	23	16	recovered	recovered	JJ
cord-221131-44n5pojb	23	17	classes	class	NNS
cord-221131-44n5pojb	23	18	with	with	IN
cord-221131-44n5pojb	23	19	the	the	DT
cord-221131-44n5pojb	23	20	following	follow	VBG
cord-221131-44n5pojb	23	21	differential	differential	JJ
cord-221131-44n5pojb	23	22	equations	equation	NNS
cord-221131-44n5pojb	23	23	:	:	:
cord-221131-44n5pojb	23	24	The	the	DT
cord-221131-44n5pojb	23	25	total	total	JJ
cord-221131-44n5pojb	23	26	population	population	NN
cord-221131-44n5pojb	23	27	N	n	NN
cord-221131-44n5pojb	23	28	=	=	SYM
cord-221131-44n5pojb	23	29	S	s	NN
cord-221131-44n5pojb	23	30	+	+	CC
cord-221131-44n5pojb	24	1	R	r	NN
cord-221131-44n5pojb	25	1	+	+	CC
cord-221131-44n5pojb	25	2	I	-PRON-	PRP
cord-221131-44n5pojb	25	3	is	be	VBZ
cord-221131-44n5pojb	25	4	a	a	DT
cord-221131-44n5pojb	25	5	conserved	conserved	JJ
cord-221131-44n5pojb	25	6	quantity	quantity	NN
cord-221131-44n5pojb	25	7	from	from	IN
cord-221131-44n5pojb	25	8	the	the	DT
cord-221131-44n5pojb	25	9	dynamical	dynamical	JJ
cord-221131-44n5pojb	25	10	point	point	NN
cord-221131-44n5pojb	25	11	of	of	IN
cord-221131-44n5pojb	25	12	view	view	NN
cord-221131-44n5pojb	25	13	,	,	,
cord-221131-44n5pojb	25	14	meaning	mean	VBG
cord-221131-44n5pojb	25	15	that	that	IN
cord-221131-44n5pojb	25	16	there	there	EX
cord-221131-44n5pojb	25	17	are	be	VBP
cord-221131-44n5pojb	25	18	only	only	RB
cord-221131-44n5pojb	25	19	two	two	CD
cord-221131-44n5pojb	25	20	independent	independent	JJ
cord-221131-44n5pojb	25	21	variables	variable	NNS
cord-221131-44n5pojb	25	22	in	in	IN
cord-221131-44n5pojb	25	23	the	the	DT
cord-221131-44n5pojb	25	24	set	set	NN
cord-221131-44n5pojb	25	25	of	of	IN
cord-221131-44n5pojb	25	26	equations	equation	NNS
cord-221131-44n5pojb	25	27	(	(	-LRB-
cord-221131-44n5pojb	25	28	1	1	CD
cord-221131-44n5pojb	25	29	)	)	-RRB-
cord-221131-44n5pojb	25	30	.	.	.
cord-221131-44n5pojb	26	1	The	the	DT
cord-221131-44n5pojb	26	2	characteristics	characteristic	NNS
cord-221131-44n5pojb	26	3	of	of	IN
cord-221131-44n5pojb	26	4	this	this	DT
cord-221131-44n5pojb	26	5	model	model	NN
cord-221131-44n5pojb	26	6	are	be	VBP
cord-221131-44n5pojb	26	7	well	well	RB
cord-221131-44n5pojb	26	8	-	-	HYPH
cord-221131-44n5pojb	26	9	known	know	VBN
cord-221131-44n5pojb	26	10	and	and	CC
cord-221131-44n5pojb	26	11	the	the	DT
cord-221131-44n5pojb	26	12	interested	interested	JJ
cord-221131-44n5pojb	26	13	readers	reader	NNS
cord-221131-44n5pojb	26	14	can	can	MD
cord-221131-44n5pojb	26	15	look	look	VB
cord-221131-44n5pojb	26	16	for	for	IN
cord-221131-44n5pojb	26	17	example	example	NN
cord-221131-44n5pojb	26	18	at	at	IN
cord-221131-44n5pojb	26	19	the	the	DT
cord-221131-44n5pojb	26	20	discussions	discussion	NNS
cord-221131-44n5pojb	26	21	in	in	IN
cord-221131-44n5pojb	26	22	the	the	DT
cord-221131-44n5pojb	26	23	classical	classical	JJ
cord-221131-44n5pojb	26	24	books	book	NNS
cord-221131-44n5pojb	26	25	of	of	IN
cord-221131-44n5pojb	26	26	Braun	Braun	NNP
cord-221131-44n5pojb	26	27	[	[	-LRB-
cord-221131-44n5pojb	26	28	2	2	CD
cord-221131-44n5pojb	26	29	]	]	-RRB-
cord-221131-44n5pojb	26	30	and	and	CC
cord-221131-44n5pojb	26	31	Murrray	Murrray	NNP
cord-221131-44n5pojb	26	32	[	[	-LRB-
cord-221131-44n5pojb	26	33	11	11	CD
cord-221131-44n5pojb	26	34	]	]	-RRB-
cord-221131-44n5pojb	26	35	.	.	.
cord-221131-44n5pojb	27	1	Here	here	RB
cord-221131-44n5pojb	27	2	we	-PRON-	PRP
cord-221131-44n5pojb	27	3	will	will	MD
cord-221131-44n5pojb	27	4	make	make	VB
cord-221131-44n5pojb	27	5	only	only	JJ
cord-221131-44n5pojb	27	6	few	few	JJ
cord-221131-44n5pojb	27	7	observations	observation	NNS
cord-221131-44n5pojb	27	8	,	,	,
cord-221131-44n5pojb	27	9	relevant	relevant	JJ
cord-221131-44n5pojb	27	10	for	for	IN
cord-221131-44n5pojb	27	11	the	the	DT
cord-221131-44n5pojb	27	12	next	next	JJ
cord-221131-44n5pojb	27	13	sections	section	NNS
cord-221131-44n5pojb	27	14	.	.	.
cord-221131-44n5pojb	28	1	Some	some	DT
cord-221131-44n5pojb	28	2	authors	author	NNS
cord-221131-44n5pojb	28	3	do	do	VBP
cord-221131-44n5pojb	28	4	not	not	RB
cord-221131-44n5pojb	28	5	include	include	VB
cord-221131-44n5pojb	28	6	the	the	DT
cord-221131-44n5pojb	28	7	denominator	denominator	NN
cord-221131-44n5pojb	28	8	N	n	NN
cord-221131-44n5pojb	28	9	on	on	IN
cord-221131-44n5pojb	28	10	the	the	DT
cord-221131-44n5pojb	28	11	right	right	JJ
cord-221131-44n5pojb	28	12	hand	hand	NN
cord-221131-44n5pojb	28	13	side	side	NN
cord-221131-44n5pojb	28	14	of	of	IN
cord-221131-44n5pojb	28	15	(	(	-LRB-
cord-221131-44n5pojb	28	16	1	1	CD
cord-221131-44n5pojb	28	17	)	)	-RRB-
cord-221131-44n5pojb	28	18	,	,	,
cord-221131-44n5pojb	28	19	since	since	IN
cord-221131-44n5pojb	28	20	it	-PRON-	PRP
cord-221131-44n5pojb	28	21	is	be	VBZ
cord-221131-44n5pojb	28	22	a	a	DT
cord-221131-44n5pojb	28	23	constant	constant	JJ
cord-221131-44n5pojb	28	24	and	and	CC
cord-221131-44n5pojb	28	25	can	can	MD
cord-221131-44n5pojb	28	26	be	be	VB
cord-221131-44n5pojb	28	27	absorbed	absorb	VBN
cord-221131-44n5pojb	28	28	by	by	IN
cord-221131-44n5pojb	28	29	a	a	DT
cord-221131-44n5pojb	28	30	re	re	NN
cord-221131-44n5pojb	28	31	-	-	NN
cord-221131-44n5pojb	28	32	definition	definition	NN
cord-221131-44n5pojb	29	1	of	of	IN
cord-221131-44n5pojb	29	2	the	the	DT
cord-221131-44n5pojb	29	3	parameter	parameter	NN
cord-221131-44n5pojb	29	4	r.	r.	NNP
cord-221131-44n5pojb	30	1	However	however	RB
cord-221131-44n5pojb	30	2	,	,	,
cord-221131-44n5pojb	30	3	we	-PRON-	PRP
cord-221131-44n5pojb	30	4	will	will	MD
cord-221131-44n5pojb	30	5	keep	keep	VB
cord-221131-44n5pojb	30	6	it	-PRON-	PRP
cord-221131-44n5pojb	30	7	:	:	:
cord-221131-44n5pojb	30	8	in	in	IN
cord-221131-44n5pojb	30	9	this	this	DT
cord-221131-44n5pojb	30	10	way	way	NN
cord-221131-44n5pojb	30	11	it	-PRON-	PRP
cord-221131-44n5pojb	30	12	is	be	VBZ
cord-221131-44n5pojb	30	13	evident	evident	JJ
cord-221131-44n5pojb	30	14	the	the	DT
cord-221131-44n5pojb	30	15	scaling	scale	VBG
cord-221131-44n5pojb	30	16	property	property	NN
cord-221131-44n5pojb	30	17	of	of	IN
cord-221131-44n5pojb	30	18	this	this	DT
cord-221131-44n5pojb	30	19	model	model	NN
cord-221131-44n5pojb	30	20	:	:	:
cord-221131-44n5pojb	30	21	if	if	IN
cord-221131-44n5pojb	30	22	the	the	DT
cord-221131-44n5pojb	30	23	initial	initial	JJ
cord-221131-44n5pojb	30	24	conditions	condition	NNS
cord-221131-44n5pojb	30	25	(	(	-LRB-
cord-221131-44n5pojb	30	26	S	s	NN
cord-221131-44n5pojb	30	27	0	0	CD
cord-221131-44n5pojb	30	28	,	,	,
cord-221131-44n5pojb	30	29	I	-PRON-	PRP
cord-221131-44n5pojb	30	30	0	0	CD
cord-221131-44n5pojb	30	31	,	,	,
cord-221131-44n5pojb	30	32	R	r	NN
cord-221131-44n5pojb	30	33	0	0	CD
cord-221131-44n5pojb	30	34	)	)	-RRB-
cord-221131-44n5pojb	30	35	are	be	VBP
cord-221131-44n5pojb	30	36	scaled	scale	VBN
cord-221131-44n5pojb	30	37	by	by	IN
cord-221131-44n5pojb	30	38	a	a	DT
cord-221131-44n5pojb	30	39	common	common	JJ
cord-221131-44n5pojb	30	40	constant	constant	JJ
cord-221131-44n5pojb	30	41	factor	factor	NN
cord-221131-44n5pojb	30	42	α	α	NN
cord-221131-44n5pojb	30	43	,	,	,
cord-221131-44n5pojb	30	44	(	(	-LRB-
cord-221131-44n5pojb	30	45	and	and	CC
cord-221131-44n5pojb	30	46	so	so	RB
cord-221131-44n5pojb	30	47	the	the	DT
cord-221131-44n5pojb	30	48	total	total	JJ
cord-221131-44n5pojb	30	49	population	population	NN
cord-221131-44n5pojb	30	50	is	be	VBZ
cord-221131-44n5pojb	30	51	scaled	scale	VBN
cord-221131-44n5pojb	30	52	by	by	IN
cord-221131-44n5pojb	30	53	a	a	DT
cord-221131-44n5pojb	30	54	factor	factor	NN
cord-221131-44n5pojb	30	55	α	α	NN
cord-221131-44n5pojb	30	56	)	)	-RRB-
cord-221131-44n5pojb	30	57	,	,	,
cord-221131-44n5pojb	30	58	the	the	DT
cord-221131-44n5pojb	30	59	solution	solution	NN
cord-221131-44n5pojb	30	60	is	be	VBZ
cord-221131-44n5pojb	30	61	scaled	scale	VBN
cord-221131-44n5pojb	30	62	by	by	IN
cord-221131-44n5pojb	30	63	the	the	DT
cord-221131-44n5pojb	30	64	same	same	JJ
cord-221131-44n5pojb	30	65	factor	factor	NN
cord-221131-44n5pojb	30	66	.	.	.
cord-221131-44n5pojb	31	1	Some	some	DT
cord-221131-44n5pojb	31	2	temporal	temporal	JJ
cord-221131-44n5pojb	31	3	properties	property	NNS
cord-221131-44n5pojb	31	4	of	of	IN
cord-221131-44n5pojb	31	5	this	this	DT
cord-221131-44n5pojb	31	6	model	model	NN
cord-221131-44n5pojb	31	7	,	,	,
cord-221131-44n5pojb	31	8	like	like	IN
cord-221131-44n5pojb	31	9	the	the	DT
cord-221131-44n5pojb	31	10	time	time	NN
cord-221131-44n5pojb	31	11	corresponding	correspond	VBG
cord-221131-44n5pojb	31	12	to	to	IN
cord-221131-44n5pojb	31	13	a	a	DT
cord-221131-44n5pojb	31	14	maximum	maximum	NN
cord-221131-44n5pojb	31	15	in	in	IN
cord-221131-44n5pojb	31	16	I	-PRON-	PRP
cord-221131-44n5pojb	31	17	(	(	-LRB-
cord-221131-44n5pojb	31	18	the	the	DT
cord-221131-44n5pojb	31	19	time	time	NN
cord-221131-44n5pojb	31	20	of	of	IN
cord-221131-44n5pojb	31	21	the	the	DT
cord-221131-44n5pojb	31	22	peak	peak	NN
cord-221131-44n5pojb	31	23	of	of	IN
cord-221131-44n5pojb	31	24	the	the	DT
cord-221131-44n5pojb	31	25	infected	infected	JJ
cord-221131-44n5pojb	31	26	)	)	-RRB-
cord-221131-44n5pojb	31	27	,	,	,
cord-221131-44n5pojb	31	28	do	do	VBP
cord-221131-44n5pojb	31	29	not	not	RB
cord-221131-44n5pojb	31	30	depend	depend	VB
cord-221131-44n5pojb	31	31	on	on	IN
cord-221131-44n5pojb	31	32	the	the	DT
cord-221131-44n5pojb	31	33	scaling	scaling	NN
cord-221131-44n5pojb	31	34	.	.	.
cord-221131-44n5pojb	32	1	This	this	DT
cord-221131-44n5pojb	32	2	property	property	NN
cord-221131-44n5pojb	32	3	is	be	VBZ
cord-221131-44n5pojb	32	4	very	very	RB
cord-221131-44n5pojb	32	5	useful	useful	JJ
cord-221131-44n5pojb	32	6	,	,	,
cord-221131-44n5pojb	32	7	since	since	IN
cord-221131-44n5pojb	32	8	the	the	DT
cord-221131-44n5pojb	32	9	actual	actual	JJ
cord-221131-44n5pojb	32	10	number	number	NN
cord-221131-44n5pojb	32	11	of	of	IN
cord-221131-44n5pojb	32	12	infected	infected	JJ
cord-221131-44n5pojb	32	13	or	or	CC
cord-221131-44n5pojb	32	14	susceptible	susceptible	JJ
cord-221131-44n5pojb	32	15	(	(	-LRB-
cord-221131-44n5pojb	32	16	and	and	CC
cord-221131-44n5pojb	32	17	then	then	RB
cord-221131-44n5pojb	32	18	of	of	IN
cord-221131-44n5pojb	32	19	recovered	recover	VBN
cord-221131-44n5pojb	32	20	)	)	-RRB-
cord-221131-44n5pojb	32	21	is	be	VBZ
cord-221131-44n5pojb	32	22	in	in	IN
cord-221131-44n5pojb	32	23	general	general	JJ
cord-221131-44n5pojb	32	24	not	not	RB
cord-221131-44n5pojb	32	25	known	know	VBN
cord-221131-44n5pojb	32	26	.	.	.
cord-221131-44n5pojb	33	1	The	the	DT
cord-221131-44n5pojb	33	2	reasonable	reasonable	JJ
cord-221131-44n5pojb	33	3	assumption	assumption	NN
cord-221131-44n5pojb	33	4	that	that	IN
cord-221131-44n5pojb	33	5	the	the	DT
cord-221131-44n5pojb	33	6	same	same	JJ
cord-221131-44n5pojb	33	7	fraction	fraction	NN
cord-221131-44n5pojb	33	8	(	(	-LRB-
cord-221131-44n5pojb	33	9	with	with	IN
cord-221131-44n5pojb	33	10	respect	respect	NN
cord-221131-44n5pojb	33	11	to	to	IN
cord-221131-44n5pojb	33	12	the	the	DT
cord-221131-44n5pojb	33	13	total	total	NN
cord-221131-44n5pojb	33	14	)	)	-RRB-
cord-221131-44n5pojb	33	15	of	of	IN
cord-221131-44n5pojb	33	16	infected	infect	VBN
cord-221131-44n5pojb	33	17	,	,	,
cord-221131-44n5pojb	33	18	susceptible	susceptible	JJ
cord-221131-44n5pojb	33	19	and	and	CC
cord-221131-44n5pojb	33	20	recovered	recover	VBN
cord-221131-44n5pojb	33	21	individuals	individual	NNS
cord-221131-44n5pojb	33	22	are	be	VBP
cord-221131-44n5pojb	33	23	known	know	VBN
cord-221131-44n5pojb	33	24	,	,	,
cord-221131-44n5pojb	33	25	gives	give	VBZ
cord-221131-44n5pojb	33	26	the	the	DT
cord-221131-44n5pojb	33	27	possibility	possibility	NN
cord-221131-44n5pojb	33	28	,	,	,
cord-221131-44n5pojb	33	29	in	in	IN
cord-221131-44n5pojb	33	30	this	this	DT
cord-221131-44n5pojb	33	31	case	case	NN
cord-221131-44n5pojb	33	32	,	,	,
cord-221131-44n5pojb	33	33	to	to	TO
cord-221131-44n5pojb	33	34	compare	compare	VB
cord-221131-44n5pojb	33	35	the	the	DT
cord-221131-44n5pojb	33	36	measured	measure	VBN
cord-221131-44n5pojb	33	37	data	datum	NNS
cord-221131-44n5pojb	33	38	with	with	IN
cord-221131-44n5pojb	33	39	the	the	DT
cord-221131-44n5pojb	33	40	properties	property	NNS
cord-221131-44n5pojb	33	41	that	that	WDT
cord-221131-44n5pojb	33	42	are	be	VBP
cord-221131-44n5pojb	33	43	scale	scale	NN
cord-221131-44n5pojb	33	44	-	-	HYPH
cord-221131-44n5pojb	33	45	independent	independent	JJ
cord-221131-44n5pojb	33	46	.	.	.
cord-221131-44n5pojb	34	1	The	the	DT
cord-221131-44n5pojb	34	2	solution	solution	NN
cord-221131-44n5pojb	34	3	of	of	IN
cord-221131-44n5pojb	34	4	the	the	DT
cord-221131-44n5pojb	34	5	system	system	NN
cord-221131-44n5pojb	34	6	(	(	-LRB-
cord-221131-44n5pojb	34	7	1	1	CD
cord-221131-44n5pojb	34	8	)	)	-RRB-
cord-221131-44n5pojb	34	9	can	can	MD
cord-221131-44n5pojb	34	10	be	be	VB
cord-221131-44n5pojb	34	11	written	write	VBN
cord-221131-44n5pojb	34	12	in	in	IN
cord-221131-44n5pojb	34	13	terms	term	NNS
cord-221131-44n5pojb	34	14	of	of	IN
cord-221131-44n5pojb	34	15	just	just	RB
cord-221131-44n5pojb	34	16	one	one	CD
cord-221131-44n5pojb	34	17	variable	variable	NN
cord-221131-44n5pojb	34	18	:	:	:
cord-221131-44n5pojb	34	19	if	if	IN
cord-221131-44n5pojb	34	20	R(t	R(t	NNP
cord-221131-44n5pojb	34	21	)	)	-RRB-
cord-221131-44n5pojb	34	22	is	be	VBZ
cord-221131-44n5pojb	34	23	known	know	VBN
cord-221131-44n5pojb	34	24	,	,	,
cord-221131-44n5pojb	34	25	I(t	I(t	NNP
cord-221131-44n5pojb	34	26	)	)	-RRB-
cord-221131-44n5pojb	34	27	can	can	MD
cord-221131-44n5pojb	34	28	be	be	VB
cord-221131-44n5pojb	34	29	obtained	obtain	VBN
cord-221131-44n5pojb	34	30	by	by	IN
cord-221131-44n5pojb	34	31	the	the	DT
cord-221131-44n5pojb	34	32	third	third	JJ
cord-221131-44n5pojb	34	33	equation	equation	NN
cord-221131-44n5pojb	34	34	and	and	CC
cord-221131-44n5pojb	34	35	S(t	S(t	NNP
cord-221131-44n5pojb	34	36	)	)	-RRB-
cord-221131-44n5pojb	34	37	from	from	IN
cord-221131-44n5pojb	34	38	the	the	DT
cord-221131-44n5pojb	34	39	first	first	JJ
cord-221131-44n5pojb	34	40	one	one	CD
cord-221131-44n5pojb	34	41	or	or	CC
cord-221131-44n5pojb	34	42	from	from	IN
cord-221131-44n5pojb	34	43	the	the	DT
cord-221131-44n5pojb	34	44	constrain	constrain	NN
cord-221131-44n5pojb	34	45	N	n	NN
cord-221131-44n5pojb	34	46	=	=	SYM
cord-221131-44n5pojb	34	47	S(t	S(t	NNS
cord-221131-44n5pojb	34	48	)	)	-RRB-
cord-221131-44n5pojb	35	1	+	+	CC
cord-221131-44n5pojb	35	2	I(t	I(t	NNP
cord-221131-44n5pojb	35	3	)	)	-RRB-
cord-221131-44n5pojb	36	1	+	+	CC
cord-221131-44n5pojb	36	2	R(t	r(t	NN
cord-221131-44n5pojb	36	3	)	)	-RRB-
cord-221131-44n5pojb	36	4	.	.	.
cord-221131-44n5pojb	37	1	If	if	IN
cord-221131-44n5pojb	37	2	the	the	DT
cord-221131-44n5pojb	37	3	epidemic	epidemic	NN
cord-221131-44n5pojb	37	4	is	be	VBZ
cord-221131-44n5pojb	37	5	not	not	RB
cord-221131-44n5pojb	37	6	severe	severe	JJ
cord-221131-44n5pojb	37	7	(	(	-LRB-
cord-221131-44n5pojb	37	8	the	the	DT
cord-221131-44n5pojb	37	9	number	number	NN
cord-221131-44n5pojb	37	10	R(t	R(t	NNP
cord-221131-44n5pojb	37	11	)	)	-RRB-
cord-221131-44n5pojb	37	12	can	can	MD
cord-221131-44n5pojb	37	13	be	be	VB
cord-221131-44n5pojb	37	14	considered	consider	VBN
cord-221131-44n5pojb	37	15	small	small	JJ
cord-221131-44n5pojb	37	16	compared	compare	VBN
cord-221131-44n5pojb	37	17	to	to	IN
cord-221131-44n5pojb	37	18	the	the	DT
cord-221131-44n5pojb	37	19	overall	overall	JJ
cord-221131-44n5pojb	37	20	population	population	NN
cord-221131-44n5pojb	37	21	)	)	-RRB-
cord-221131-44n5pojb	37	22	,	,	,
cord-221131-44n5pojb	37	23	an	an	DT
cord-221131-44n5pojb	37	24	explicit	explicit	JJ
cord-221131-44n5pojb	37	25	formula	formula	NN
cord-221131-44n5pojb	37	26	for	for	IN
cord-221131-44n5pojb	37	27	the	the	DT
cord-221131-44n5pojb	37	28	number	number	NN
cord-221131-44n5pojb	37	29	of	of	IN
cord-221131-44n5pojb	37	30	recovered	recover	VBN
cord-221131-44n5pojb	37	31	can	can	MD
cord-221131-44n5pojb	37	32	be	be	VB
cord-221131-44n5pojb	37	33	obtained	obtain	VBN
cord-221131-44n5pojb	37	34	in	in	IN
cord-221131-44n5pojb	37	35	terms	term	NNS
cord-221131-44n5pojb	37	36	of	of	IN
cord-221131-44n5pojb	37	37	the	the	DT
cord-221131-44n5pojb	37	38	hyperbolic	hyperbolic	JJ
cord-221131-44n5pojb	37	39	tangent	tangent	JJ
cord-221131-44n5pojb	37	40	function	function	NN
cord-221131-44n5pojb	37	41	.	.	.
cord-221131-44n5pojb	38	1	The	the	DT
cord-221131-44n5pojb	38	2	functions	function	NNS
cord-221131-44n5pojb	38	3	reads	read	VBZ
cord-221131-44n5pojb	38	4	as	as	IN
cord-221131-44n5pojb	38	5	where	where	WRB
cord-221131-44n5pojb	38	6	we	-PRON-	PRP
cord-221131-44n5pojb	38	7	used	use	VBD
cord-221131-44n5pojb	38	8	the	the	DT
cord-221131-44n5pojb	38	9	initial	initial	JJ
cord-221131-44n5pojb	38	10	value	value	NN
cord-221131-44n5pojb	38	11	R(0	R(0	NNP
cord-221131-44n5pojb	38	12	)	)	-RRB-
cord-221131-44n5pojb	39	1	=	=	NFP
cord-221131-44n5pojb	40	1	0	0	NFP
cord-221131-44n5pojb	41	1	and	and	CC
cord-221131-44n5pojb	41	2	the	the	DT
cord-221131-44n5pojb	41	3	parameters	parameter	NNS
cord-221131-44n5pojb	41	4	(	(	-LRB-
cord-221131-44n5pojb	41	5	α	α	NNP
cord-221131-44n5pojb	41	6	,	,	,
cord-221131-44n5pojb	41	7	β	β	NN
cord-221131-44n5pojb	41	8	,	,	,
cord-221131-44n5pojb	41	9	c	c	NNP
cord-221131-44n5pojb	41	10	)	)	-RRB-
cord-221131-44n5pojb	41	11	can	can	MD
cord-221131-44n5pojb	41	12	be	be	VB
cord-221131-44n5pojb	41	13	made	make	VBN
cord-221131-44n5pojb	41	14	explicit	explicit	JJ
cord-221131-44n5pojb	41	15	in	in	IN
cord-221131-44n5pojb	41	16	terms	term	NNS
cord-221131-44n5pojb	41	17	of	of	IN
cord-221131-44n5pojb	41	18	the	the	DT
cord-221131-44n5pojb	41	19	parameters	parameter	NNS
cord-221131-44n5pojb	41	20	appearing	appear	VBG
cord-221131-44n5pojb	41	21	in	in	IN
cord-221131-44n5pojb	41	22	(	(	-LRB-
cord-221131-44n5pojb	41	23	1	1	CD
cord-221131-44n5pojb	41	24	)	)	-RRB-
cord-221131-44n5pojb	41	25	.	.	.
cord-221131-44n5pojb	42	1	The	the	DT
cord-221131-44n5pojb	42	2	previous	previous	JJ
cord-221131-44n5pojb	42	3	is	be	VBZ
cord-221131-44n5pojb	42	4	one	one	CD
cord-221131-44n5pojb	42	5	of	of	IN
cord-221131-44n5pojb	42	6	the	the	DT
cord-221131-44n5pojb	42	7	example	example	NN
cord-221131-44n5pojb	42	8	of	of	IN
cord-221131-44n5pojb	42	9	the	the	DT
cord-221131-44n5pojb	42	10	so	so	RB
cord-221131-44n5pojb	42	11	-	-	HYPH
cord-221131-44n5pojb	42	12	called	call	VBN
cord-221131-44n5pojb	42	13	s	s	NN
cord-221131-44n5pojb	42	14	-	-	HYPH
cord-221131-44n5pojb	42	15	shaped	shape	VBN
cord-221131-44n5pojb	42	16	epidemiological	epidemiological	JJ
cord-221131-44n5pojb	42	17	curve	curve	NN
cord-221131-44n5pojb	42	18	(	(	-LRB-
cord-221131-44n5pojb	42	19	with	with	IN
cord-221131-44n5pojb	42	20	a	a	DT
cord-221131-44n5pojb	42	21	"	"	``
cord-221131-44n5pojb	42	22	peaked	peaked	JJ
cord-221131-44n5pojb	42	23	"	"	''
cord-221131-44n5pojb	42	24	derivative	derivative	JJ
cord-221131-44n5pojb	42	25	,	,	,
cord-221131-44n5pojb	42	26	the	the	DT
cord-221131-44n5pojb	42	27	function	function	NN
cord-221131-44n5pojb	42	28	sech	sech	NNP
cord-221131-44n5pojb	42	29	2	2	CD
cord-221131-44n5pojb	42	30	)	)	-RRB-
cord-221131-44n5pojb	42	31	that	that	WDT
cord-221131-44n5pojb	42	32	universally	universally	RB
cord-221131-44n5pojb	42	33	describes	describe	VBZ
cord-221131-44n5pojb	42	34	an	an	DT
cord-221131-44n5pojb	42	35	infection	infection	NN
cord-221131-44n5pojb	42	36	disease	disease	NN
cord-221131-44n5pojb	42	37	.	.	.
cord-221131-44n5pojb	43	1	The	the	DT
cord-221131-44n5pojb	43	2	value	value	NN
cord-221131-44n5pojb	43	3	of	of	IN
cord-221131-44n5pojb	43	4	the	the	DT
cord-221131-44n5pojb	43	5	number	number	NN
cord-221131-44n5pojb	43	6	of	of	IN
cord-221131-44n5pojb	43	7	infected	infected	JJ
cord-221131-44n5pojb	43	8	can	can	MD
cord-221131-44n5pojb	43	9	be	be	VB
cord-221131-44n5pojb	43	10	obtained	obtain	VBN
cord-221131-44n5pojb	43	11	by	by	IN
cord-221131-44n5pojb	43	12	derivation	derivation	NN
cord-221131-44n5pojb	43	13	,	,	,
cord-221131-44n5pojb	43	14	i.e.	i.e.	FW
cord-221131-44n5pojb	43	15	I(t	I(t	NNP
cord-221131-44n5pojb	43	16	)	)	-RRB-
cord-221131-44n5pojb	43	17	=	=	NFP
cord-221131-44n5pojb	44	1	αβsech(βt	αβsech(βt	NNP
cord-221131-44n5pojb	44	2	−	−	CD
cord-221131-44n5pojb	44	3	c	c	NN
cord-221131-44n5pojb	44	4	)	)	-RRB-
cord-221131-44n5pojb	44	5	2	2	CD
cord-221131-44n5pojb	44	6	.	.	.
cord-221131-44n5pojb	45	1	When	when	WRB
cord-221131-44n5pojb	45	2	considering	consider	VBG
cord-221131-44n5pojb	45	3	the	the	DT
cord-221131-44n5pojb	45	4	cumulative	cumulative	JJ
cord-221131-44n5pojb	45	5	number	number	NN
cord-221131-44n5pojb	45	6	of	of	IN
cord-221131-44n5pojb	45	7	infected	infect	VBN
cord-221131-44n5pojb	45	8	,	,	,
cord-221131-44n5pojb	45	9	R	r	NN
cord-221131-44n5pojb	45	10	+	+	CC
cord-221131-44n5pojb	45	11	I	i	NN
cord-221131-44n5pojb	45	12	,	,	,
cord-221131-44n5pojb	45	13	the	the	DT
cord-221131-44n5pojb	45	14	contribution	contribution	NN
cord-221131-44n5pojb	45	15	of	of	IN
cord-221131-44n5pojb	45	16	sech	sech	NNP
cord-221131-44n5pojb	45	17	2	2	CD
cord-221131-44n5pojb	45	18	is	be	VBZ
cord-221131-44n5pojb	45	19	negligible	negligible	JJ
cord-221131-44n5pojb	45	20	on	on	IN
cord-221131-44n5pojb	45	21	the	the	DT
cord-221131-44n5pojb	45	22	tails	tail	NNS
cord-221131-44n5pojb	45	23	,	,	,
cord-221131-44n5pojb	45	24	whereas	whereas	IN
cord-221131-44n5pojb	45	25	it	-PRON-	PRP
cord-221131-44n5pojb	45	26	is	be	VBZ
cord-221131-44n5pojb	45	27	more	more	RBR
cord-221131-44n5pojb	45	28	pronounced	pronounced	JJ
cord-221131-44n5pojb	45	29	in	in	IN
cord-221131-44n5pojb	45	30	correspondence	correspondence	NN
cord-221131-44n5pojb	45	31	of	of	IN
cord-221131-44n5pojb	45	32	the	the	DT
cord-221131-44n5pojb	45	33	maximum	maximum	NN
cord-221131-44n5pojb	45	34	of	of	IN
cord-221131-44n5pojb	45	35	sech	sech	NNP
cord-221131-44n5pojb	45	36	2	2	CD
cord-221131-44n5pojb	45	37	,	,	,
cord-221131-44n5pojb	45	38	but	but	CC
cord-221131-44n5pojb	45	39	it	-PRON-	PRP
cord-221131-44n5pojb	45	40	is	be	VBZ
cord-221131-44n5pojb	45	41	however	however	RB
cord-221131-44n5pojb	45	42	small	small	JJ
cord-221131-44n5pojb	45	43	if	if	IN
cord-221131-44n5pojb	45	44	the	the	DT
cord-221131-44n5pojb	45	45	value	value	NN
cord-221131-44n5pojb	45	46	of	of	IN
cord-221131-44n5pojb	45	47	the	the	DT
cord-221131-44n5pojb	45	48	parameter	parameter	NN
cord-221131-44n5pojb	45	49	β	β	NN
cord-221131-44n5pojb	45	50	is	be	VBZ
cord-221131-44n5pojb	45	51	less	less	JJR
cord-221131-44n5pojb	45	52	than	than	IN
cord-221131-44n5pojb	45	53	one	one	CD
cord-221131-44n5pojb	45	54	.	.	.
cord-221131-44n5pojb	46	1	In	in	IN
cord-221131-44n5pojb	46	2	this	this	DT
cord-221131-44n5pojb	46	3	case	case	NN
cord-221131-44n5pojb	46	4	,	,	,
cord-221131-44n5pojb	46	5	the	the	DT
cord-221131-44n5pojb	46	6	value	value	NN
cord-221131-44n5pojb	46	7	of	of	IN
cord-221131-44n5pojb	46	8	R	r	NN
cord-221131-44n5pojb	46	9	+	+	CC
cord-221131-44n5pojb	46	10	I	-PRON-	PRP
cord-221131-44n5pojb	46	11	is	be	VBZ
cord-221131-44n5pojb	46	12	well	well	RB
cord-221131-44n5pojb	46	13	approximated	approximate	VBN
cord-221131-44n5pojb	46	14	by	by	IN
cord-221131-44n5pojb	46	15	a	a	DT
cord-221131-44n5pojb	46	16	tanh	tanh	NN
cord-221131-44n5pojb	46	17	formula	formula	NN
cord-221131-44n5pojb	46	18	like	like	IN
cord-221131-44n5pojb	46	19	(	(	-LRB-
cord-221131-44n5pojb	46	20	2	2	CD
cord-221131-44n5pojb	46	21	)	)	-RRB-
cord-221131-44n5pojb	46	22	,	,	,
cord-221131-44n5pojb	46	23	with	with	IN
cord-221131-44n5pojb	46	24	a	a	DT
cord-221131-44n5pojb	46	25	certain	certain	JJ
cord-221131-44n5pojb	46	26	different	different	JJ
cord-221131-44n5pojb	46	27	value	value	NN
cord-221131-44n5pojb	46	28	of	of	IN
cord-221131-44n5pojb	46	29	c.	c.	NN
cord-221131-44n5pojb	47	1	This	this	DT
cord-221131-44n5pojb	47	2	is	be	VBZ
cord-221131-44n5pojb	47	3	what	what	WP
cord-221131-44n5pojb	47	4	we	-PRON-	PRP
cord-221131-44n5pojb	47	5	will	will	MD
cord-221131-44n5pojb	47	6	assume	assume	VB
cord-221131-44n5pojb	47	7	in	in	IN
cord-221131-44n5pojb	47	8	the	the	DT
cord-221131-44n5pojb	47	9	next	next	JJ
cord-221131-44n5pojb	47	10	section	section	NN
cord-221131-44n5pojb	47	11	.	.	.
cord-221131-44n5pojb	48	1	It	-PRON-	PRP
cord-221131-44n5pojb	48	2	is	be	VBZ
cord-221131-44n5pojb	48	3	clear	clear	JJ
cord-221131-44n5pojb	48	4	that	that	IN
cord-221131-44n5pojb	48	5	the	the	DT
cord-221131-44n5pojb	48	6	description	description	NN
cord-221131-44n5pojb	48	7	made	make	VBN
cord-221131-44n5pojb	48	8	in	in	IN
cord-221131-44n5pojb	48	9	the	the	DT
cord-221131-44n5pojb	48	10	previous	previous	JJ
cord-221131-44n5pojb	48	11	section	section	NN
cord-221131-44n5pojb	48	12	is	be	VBZ
cord-221131-44n5pojb	48	13	very	very	RB
cord-221131-44n5pojb	48	14	basic	basic	JJ
cord-221131-44n5pojb	48	15	.	.	.
cord-221131-44n5pojb	49	1	However	however	RB
cord-221131-44n5pojb	49	2	it	-PRON-	PRP
cord-221131-44n5pojb	49	3	has	have	VBZ
cord-221131-44n5pojb	49	4	the	the	DT
cord-221131-44n5pojb	49	5	advantage	advantage	NN
cord-221131-44n5pojb	49	6	to	to	TO
cord-221131-44n5pojb	49	7	be	be	VB
cord-221131-44n5pojb	49	8	manageable	manageable	JJ
cord-221131-44n5pojb	49	9	and	and	CC
cord-221131-44n5pojb	49	10	to	to	TO
cord-221131-44n5pojb	49	11	incorporate	incorporate	VB
cord-221131-44n5pojb	49	12	the	the	DT
cord-221131-44n5pojb	49	13	main	main	JJ
cord-221131-44n5pojb	49	14	properties	property	NNS
cord-221131-44n5pojb	49	15	of	of	IN
cord-221131-44n5pojb	49	16	the	the	DT
cord-221131-44n5pojb	49	17	SIR	SIR	NNP
cord-221131-44n5pojb	49	18	model	model	NN
cord-221131-44n5pojb	49	19	.	.	.
cord-221131-44n5pojb	50	1	It	-PRON-	PRP
cord-221131-44n5pojb	50	2	is	be	VBZ
cord-221131-44n5pojb	50	3	not	not	RB
cord-221131-44n5pojb	50	4	by	by	IN
cord-221131-44n5pojb	50	5	chance	chance	NN
cord-221131-44n5pojb	50	6	that	that	IN
cord-221131-44n5pojb	50	7	the	the	DT
cord-221131-44n5pojb	50	8	first	first	JJ
cord-221131-44n5pojb	50	9	application	application	NN
cord-221131-44n5pojb	50	10	of	of	IN
cord-221131-44n5pojb	50	11	the	the	DT
cord-221131-44n5pojb	50	12	SIR	SIR	NNP
cord-221131-44n5pojb	50	13	model	model	NN
cord-221131-44n5pojb	50	14	(	(	-LRB-
cord-221131-44n5pojb	50	15	the	the	DT
cord-221131-44n5pojb	50	16	Bombay	Bombay	NNP
cord-221131-44n5pojb	50	17	plague	plague	NN
cord-221131-44n5pojb	50	18	of	of	IN
cord-221131-44n5pojb	50	19	1905	1905	CD
cord-221131-44n5pojb	50	20	)	)	-RRB-
cord-221131-44n5pojb	50	21	by	by	IN
cord-221131-44n5pojb	50	22	Kermack	Kermack	NNP
cord-221131-44n5pojb	50	23	and	and	CC
cord-221131-44n5pojb	50	24	McKendrick	McKendrick	NNP
cord-221131-44n5pojb	50	25	[	[	-LRB-
cord-221131-44n5pojb	50	26	7	7	CD
cord-221131-44n5pojb	50	27	]	]	-RRB-
cord-221131-44n5pojb	50	28	used	use	VBD
cord-221131-44n5pojb	50	29	precisely	precisely	RB
cord-221131-44n5pojb	50	30	the	the	DT
cord-221131-44n5pojb	50	31	tanh	tanh	NN
cord-221131-44n5pojb	50	32	formula	formula	NN
cord-221131-44n5pojb	50	33	above	above	RB
cord-221131-44n5pojb	50	34	.	.	.
cord-221131-44n5pojb	51	1	In	in	IN
cord-221131-44n5pojb	51	2	the	the	DT
cord-221131-44n5pojb	51	3	following	following	NN
cord-221131-44n5pojb	51	4	we	-PRON-	PRP
cord-221131-44n5pojb	51	5	will	will	MD
cord-221131-44n5pojb	51	6	base	base	VB
cord-221131-44n5pojb	51	7	our	-PRON-	PRP$
cord-221131-44n5pojb	51	8	analysis	analysis	NN
cord-221131-44n5pojb	51	9	on	on	IN
cord-221131-44n5pojb	51	10	two	two	CD
cord-221131-44n5pojb	51	11	hypothesis	hypothesis	NN
cord-221131-44n5pojb	51	12	:	:	:
cord-221131-44n5pojb	51	13	(	(	-LRB-
cord-221131-44n5pojb	51	14	i	i	NN
cord-221131-44n5pojb	51	15	)	)	-RRB-
cord-221131-44n5pojb	52	1	We	-PRON-	PRP
cord-221131-44n5pojb	52	2	assume	assume	VBP
cord-221131-44n5pojb	52	3	that	that	IN
cord-221131-44n5pojb	52	4	the	the	DT
cord-221131-44n5pojb	52	5	cumulative	cumulative	JJ
cord-221131-44n5pojb	52	6	number	number	NN
cord-221131-44n5pojb	52	7	of	of	IN
cord-221131-44n5pojb	52	8	infected	infect	VBN
cord-221131-44n5pojb	52	9	is	be	VBZ
cord-221131-44n5pojb	52	10	described	describe	VBN
cord-221131-44n5pojb	52	11	by	by	IN
cord-221131-44n5pojb	52	12	a	a	DT
cord-221131-44n5pojb	52	13	tanh	tanh	NN
cord-221131-44n5pojb	52	14	model	model	NN
cord-221131-44n5pojb	52	15	.	.	.
cord-221131-44n5pojb	53	1	This	this	DT
cord-221131-44n5pojb	53	2	assumption	assumption	NN
cord-221131-44n5pojb	53	3	is	be	VBZ
cord-221131-44n5pojb	53	4	independent	independent	JJ
cord-221131-44n5pojb	53	5	on	on	IN
cord-221131-44n5pojb	53	6	the	the	DT
cord-221131-44n5pojb	53	7	underlying	underlying	JJ
cord-221131-44n5pojb	53	8	dynamical	dynamical	JJ
cord-221131-44n5pojb	53	9	model	model	NN
cord-221131-44n5pojb	53	10	considered	consider	VBN
cord-221131-44n5pojb	53	11	,	,	,
cord-221131-44n5pojb	53	12	but	but	CC
cord-221131-44n5pojb	53	13	may	may	MD
cord-221131-44n5pojb	53	14	be	be	VB
cord-221131-44n5pojb	53	15	justified	justify	VBN
cord-221131-44n5pojb	53	16	on	on	IN
cord-221131-44n5pojb	53	17	the	the	DT
cord-221131-44n5pojb	53	18	base	base	NN
cord-221131-44n5pojb	53	19	of	of	IN
cord-221131-44n5pojb	53	20	some	some	DT
cord-221131-44n5pojb	53	21	of	of	IN
cord-221131-44n5pojb	53	22	them	-PRON-	PRP
cord-221131-44n5pojb	53	23	(	(	-LRB-
cord-221131-44n5pojb	53	24	e.g.	e.g.	IN
cord-221131-44n5pojb	53	25	the	the	DT
cord-221131-44n5pojb	53	26	SIR	SIR	NNP
cord-221131-44n5pojb	53	27	model	model	NN
cord-221131-44n5pojb	53	28	,	,	,
cord-221131-44n5pojb	53	29	as	as	IN
cord-221131-44n5pojb	53	30	shown	show	VBN
cord-221131-44n5pojb	53	31	in	in	IN
cord-221131-44n5pojb	53	32	the	the	DT
cord-221131-44n5pojb	53	33	previous	previous	JJ
cord-221131-44n5pojb	53	34	section	section	NN
cord-221131-44n5pojb	53	35	)	)	-RRB-
cord-221131-44n5pojb	53	36	.	.	.
cord-221131-44n5pojb	54	1	(	(	-LRB-
cord-221131-44n5pojb	54	2	ii	ii	NN
cord-221131-44n5pojb	54	3	)	)	-RRB-
cord-221131-44n5pojb	55	1	We	-PRON-	PRP
cord-221131-44n5pojb	55	2	assume	assume	VBP
cord-221131-44n5pojb	55	3	that	that	IN
cord-221131-44n5pojb	55	4	,	,	,
cord-221131-44n5pojb	55	5	whatever	whatever	WDT
cord-221131-44n5pojb	55	6	it	-PRON-	PRP
cord-221131-44n5pojb	55	7	is	be	VBZ
cord-221131-44n5pojb	55	8	the	the	DT
cord-221131-44n5pojb	55	9	underlying	underlying	JJ
cord-221131-44n5pojb	55	10	model	model	NN
cord-221131-44n5pojb	55	11	describing	describe	VBG
cord-221131-44n5pojb	55	12	the	the	DT
cord-221131-44n5pojb	55	13	evolution	evolution	NN
cord-221131-44n5pojb	55	14	of	of	IN
cord-221131-44n5pojb	55	15	the	the	DT
cord-221131-44n5pojb	55	16	number	number	NN
cord-221131-44n5pojb	55	17	of	of	IN
cord-221131-44n5pojb	55	18	infected	infect	VBN
cord-221131-44n5pojb	55	19	,	,	,
cord-221131-44n5pojb	55	20	this	this	DT
cord-221131-44n5pojb	55	21	model	model	NN
cord-221131-44n5pojb	55	22	is	be	VBZ
cord-221131-44n5pojb	55	23	scale	scale	NN
cord-221131-44n5pojb	55	24	invariant	invariant	JJ
cord-221131-44n5pojb	55	25	,	,	,
cord-221131-44n5pojb	55	26	in	in	IN
cord-221131-44n5pojb	55	27	the	the	DT
cord-221131-44n5pojb	55	28	sense	sense	NN
cord-221131-44n5pojb	55	29	specified	specify	VBN
cord-221131-44n5pojb	55	30	in	in	IN
cord-221131-44n5pojb	55	31	the	the	DT
cord-221131-44n5pojb	55	32	previous	previous	JJ
cord-221131-44n5pojb	55	33	section	section	NN
cord-221131-44n5pojb	55	34	.	.	.
cord-221131-44n5pojb	56	1	The	the	DT
cord-221131-44n5pojb	56	2	second	second	JJ
cord-221131-44n5pojb	56	3	hypothesis	hypothesis	NN
cord-221131-44n5pojb	56	4	is	be	VBZ
cord-221131-44n5pojb	56	5	fundamental	fundamental	JJ
cord-221131-44n5pojb	56	6	since	since	IN
cord-221131-44n5pojb	56	7	we	-PRON-	PRP
cord-221131-44n5pojb	56	8	are	be	VBP
cord-221131-44n5pojb	56	9	going	go	VBG
cord-221131-44n5pojb	56	10	to	to	TO
cord-221131-44n5pojb	56	11	look	look	VB
cord-221131-44n5pojb	56	12	at	at	IN
cord-221131-44n5pojb	56	13	scale	scale	NN
cord-221131-44n5pojb	56	14	-	-	HYPH
cord-221131-44n5pojb	56	15	independent	independent	JJ
cord-221131-44n5pojb	56	16	quantities	quantity	NNS
cord-221131-44n5pojb	56	17	:	:	:
cord-221131-44n5pojb	56	18	even	even	RB
cord-221131-44n5pojb	56	19	in	in	IN
cord-221131-44n5pojb	56	20	the	the	DT
cord-221131-44n5pojb	56	21	case	case	NN
cord-221131-44n5pojb	56	22	the	the	DT
cord-221131-44n5pojb	56	23	measured	measure	VBN
cord-221131-44n5pojb	56	24	number	number	NN
cord-221131-44n5pojb	56	25	of	of	IN
cord-221131-44n5pojb	56	26	infected	infected	JJ
cord-221131-44n5pojb	56	27	and	and	CC
cord-221131-44n5pojb	56	28	recovered	recover	VBN
cord-221131-44n5pojb	56	29	individuals	individual	NNS
cord-221131-44n5pojb	56	30	are	be	VBP
cord-221131-44n5pojb	56	31	different	different	JJ
cord-221131-44n5pojb	56	32	from	from	IN
cord-221131-44n5pojb	56	33	the	the	DT
cord-221131-44n5pojb	56	34	actual	actual	JJ
cord-221131-44n5pojb	56	35	values	value	NNS
cord-221131-44n5pojb	56	36	,	,	,
cord-221131-44n5pojb	56	37	it	-PRON-	PRP
cord-221131-44n5pojb	56	38	is	be	VBZ
cord-221131-44n5pojb	56	39	possible	possible	JJ
cord-221131-44n5pojb	56	40	to	to	TO
cord-221131-44n5pojb	56	41	estimate	estimate	VB
cord-221131-44n5pojb	56	42	these	these	DT
cord-221131-44n5pojb	56	43	quantities	quantity	NNS
cord-221131-44n5pojb	56	44	.	.	.
cord-221131-44n5pojb	57	1	The	the	DT
cord-221131-44n5pojb	57	2	cumulative	cumulative	JJ
cord-221131-44n5pojb	57	3	total	total	JJ
cord-221131-44n5pojb	57	4	number	number	NN
cord-221131-44n5pojb	57	5	of	of	IN
cord-221131-44n5pojb	57	6	infected	infect	VBN
cord-221131-44n5pojb	57	7	that	that	WDT
cord-221131-44n5pojb	57	8	will	will	MD
cord-221131-44n5pojb	57	9	be	be	VB
cord-221131-44n5pojb	57	10	considered	consider	VBN
cord-221131-44n5pojb	57	11	in	in	IN
cord-221131-44n5pojb	57	12	the	the	DT
cord-221131-44n5pojb	57	13	next	next	JJ
cord-221131-44n5pojb	57	14	lines	line	NNS
cord-221131-44n5pojb	57	15	are	be	VBP
cord-221131-44n5pojb	57	16	those	those	DT
cord-221131-44n5pojb	57	17	of	of	IN
cord-221131-44n5pojb	57	18	entire	entire	JJ
cord-221131-44n5pojb	57	19	Italy	Italy	NNP
cord-221131-44n5pojb	57	20	territory	territory	NN
cord-221131-44n5pojb	57	21	.	.	.
cord-221131-44n5pojb	58	1	There	there	EX
cord-221131-44n5pojb	58	2	are	be	VBP
cord-221131-44n5pojb	58	3	at	at	RB
cord-221131-44n5pojb	58	4	least	least	RBS
cord-221131-44n5pojb	58	5	two	two	CD
cord-221131-44n5pojb	58	6	reasons	reason	NNS
cord-221131-44n5pojb	58	7	that	that	WDT
cord-221131-44n5pojb	58	8	suggested	suggest	VBD
cord-221131-44n5pojb	58	9	to	to	TO
cord-221131-44n5pojb	58	10	not	not	RB
cord-221131-44n5pojb	58	11	take	take	VB
cord-221131-44n5pojb	58	12	regional	regional	JJ
cord-221131-44n5pojb	58	13	or	or	CC
cord-221131-44n5pojb	58	14	local	local	JJ
cord-221131-44n5pojb	58	15	data	datum	NNS
cord-221131-44n5pojb	58	16	:	:	:
cord-221131-44n5pojb	58	17	the	the	DT
cord-221131-44n5pojb	58	18	first	first	JJ
cord-221131-44n5pojb	58	19	one	one	NN
cord-221131-44n5pojb	58	20	is	be	VBZ
cord-221131-44n5pojb	58	21	that	that	IN
cord-221131-44n5pojb	58	22	the	the	DT
cord-221131-44n5pojb	58	23	epidemic	epidemic	NN
cord-221131-44n5pojb	58	24	started	start	VBD
cord-221131-44n5pojb	58	25	to	to	TO
cord-221131-44n5pojb	58	26	spread	spread	VB
cord-221131-44n5pojb	58	27	across	across	IN
cord-221131-44n5pojb	58	28	three	three	CD
cord-221131-44n5pojb	58	29	different	different	JJ
cord-221131-44n5pojb	58	30	regions	region	NNS
cord-221131-44n5pojb	58	31	(	(	-LRB-
cord-221131-44n5pojb	58	32	Lombardy	Lombardy	NNP
cord-221131-44n5pojb	58	33	,	,	,
cord-221131-44n5pojb	58	34	Veneto	Veneto	NNP
cord-221131-44n5pojb	58	35	and	and	CC
cord-221131-44n5pojb	58	36	Emilia	Emilia	NNP
cord-221131-44n5pojb	58	37	-	-	HYPH
cord-221131-44n5pojb	58	38	Romagna	Romagna	NNP
cord-221131-44n5pojb	58	39	)	)	-RRB-
cord-221131-44n5pojb	58	40	and	and	CC
cord-221131-44n5pojb	58	41	there	there	EX
cord-221131-44n5pojb	58	42	could	could	MD
cord-221131-44n5pojb	58	43	not	not	RB
cord-221131-44n5pojb	58	44	be	be	VB
cord-221131-44n5pojb	58	45	a	a	DT
cord-221131-44n5pojb	58	46	correspondence	correspondence	NN
cord-221131-44n5pojb	58	47	between	between	IN
cord-221131-44n5pojb	58	48	the	the	DT
cord-221131-44n5pojb	58	49	locality	locality	NN
cord-221131-44n5pojb	58	50	where	where	WRB
cord-221131-44n5pojb	58	51	a	a	DT
cord-221131-44n5pojb	58	52	certain	certain	JJ
cord-221131-44n5pojb	58	53	fraction	fraction	NN
cord-221131-44n5pojb	58	54	of	of	IN
cord-221131-44n5pojb	58	55	inhabitants	inhabitant	NNS
cord-221131-44n5pojb	58	56	reside	reside	VBP
cord-221131-44n5pojb	58	57	and	and	CC
cord-221131-44n5pojb	58	58	the	the	DT
cord-221131-44n5pojb	58	59	region	region	NN
cord-221131-44n5pojb	58	60	where	where	WRB
cord-221131-44n5pojb	58	61	this	this	DT
cord-221131-44n5pojb	58	62	fraction	fraction	NN
cord-221131-44n5pojb	58	63	was	be	VBD
cord-221131-44n5pojb	58	64	infected	infect	VBN
cord-221131-44n5pojb	58	65	.	.	.
cord-221131-44n5pojb	59	1	This	this	DT
cord-221131-44n5pojb	59	2	is	be	VBZ
cord-221131-44n5pojb	59	3	also	also	RB
cord-221131-44n5pojb	59	4	true	true	JJ
cord-221131-44n5pojb	59	5	at	at	IN
cord-221131-44n5pojb	59	6	a	a	DT
cord-221131-44n5pojb	59	7	national	national	JJ
cord-221131-44n5pojb	59	8	level	level	NN
cord-221131-44n5pojb	59	9	,	,	,
cord-221131-44n5pojb	59	10	but	but	CC
cord-221131-44n5pojb	59	11	the	the	DT
cord-221131-44n5pojb	59	12	fraction	fraction	NN
cord-221131-44n5pojb	59	13	is	be	VBZ
cord-221131-44n5pojb	59	14	assumed	assume	VBN
cord-221131-44n5pojb	59	15	to	to	TO
cord-221131-44n5pojb	59	16	be	be	VB
cord-221131-44n5pojb	59	17	smaller	small	JJR
cord-221131-44n5pojb	59	18	.	.	.
cord-221131-44n5pojb	60	1	The	the	DT
cord-221131-44n5pojb	60	2	second	second	JJ
cord-221131-44n5pojb	60	3	reason	reason	NN
cord-221131-44n5pojb	60	4	is	be	VBZ
cord-221131-44n5pojb	60	5	that	that	IN
cord-221131-44n5pojb	60	6	a	a	DT
cord-221131-44n5pojb	60	7	non	non	JJ
cord-221131-44n5pojb	60	8	negligible	negligible	JJ
cord-221131-44n5pojb	60	9	number	number	NN
cord-221131-44n5pojb	60	10	of	of	IN
cord-221131-44n5pojb	60	11	workers	worker	NNS
cord-221131-44n5pojb	60	12	and	and	CC
cord-221131-44n5pojb	60	13	students	student	NNS
cord-221131-44n5pojb	60	14	moved	move	VBD
cord-221131-44n5pojb	60	15	,	,	,
cord-221131-44n5pojb	60	16	just	just	RB
cord-221131-44n5pojb	60	17	before	before	IN
cord-221131-44n5pojb	60	18	the	the	DT
cord-221131-44n5pojb	60	19	lockdown	lockdown	NN
cord-221131-44n5pojb	60	20	,	,	,
cord-221131-44n5pojb	60	21	from	from	IN
cord-221131-44n5pojb	60	22	the	the	DT
cord-221131-44n5pojb	60	23	regions	region	NNS
cord-221131-44n5pojb	60	24	in	in	IN
cord-221131-44n5pojb	60	25	the	the	DT
cord-221131-44n5pojb	60	26	north	north	NN
cord-221131-44n5pojb	60	27	of	of	IN
cord-221131-44n5pojb	60	28	Italy	Italy	NNP
cord-221131-44n5pojb	60	29	to	to	IN
cord-221131-44n5pojb	60	30	their	-PRON-	PRP$
cord-221131-44n5pojb	60	31	regions	region	NNS
cord-221131-44n5pojb	60	32	of	of	IN
cord-221131-44n5pojb	60	33	origin	origin	NN
cord-221131-44n5pojb	60	34	in	in	IN
cord-221131-44n5pojb	60	35	the	the	DT
cord-221131-44n5pojb	60	36	center	center	NN
cord-221131-44n5pojb	60	37	and	and	CC
cord-221131-44n5pojb	60	38	south	south	NN
cord-221131-44n5pojb	60	39	of	of	IN
cord-221131-44n5pojb	60	40	Italy	Italy	NNP
cord-221131-44n5pojb	60	41	.	.	.
cord-221131-44n5pojb	61	1	The	the	DT
cord-221131-44n5pojb	61	2	possibility	possibility	NN
cord-221131-44n5pojb	61	3	that	that	IN
cord-221131-44n5pojb	61	4	a	a	DT
cord-221131-44n5pojb	61	5	non	non	JJ
cord-221131-44n5pojb	61	6	negligible	negligible	JJ
cord-221131-44n5pojb	61	7	flow	flow	NN
cord-221131-44n5pojb	61	8	of	of	IN
cord-221131-44n5pojb	61	9	infected	infected	JJ
cord-221131-44n5pojb	61	10	people	people	NNS
cord-221131-44n5pojb	61	11	passed	pass	VBD
cord-221131-44n5pojb	61	12	from	from	IN
cord-221131-44n5pojb	61	13	the	the	DT
cord-221131-44n5pojb	61	14	north	north	NN
cord-221131-44n5pojb	61	15	to	to	IN
cord-221131-44n5pojb	61	16	other	other	JJ
cord-221131-44n5pojb	61	17	regions	region	NNS
cord-221131-44n5pojb	61	18	should	should	MD
cord-221131-44n5pojb	61	19	be	be	VB
cord-221131-44n5pojb	61	20	taken	take	VBN
cord-221131-44n5pojb	61	21	into	into	IN
cord-221131-44n5pojb	61	22	consideration	consideration	NN
cord-221131-44n5pojb	61	23	.	.	.
cord-221131-44n5pojb	62	1	By	by	IN
cord-221131-44n5pojb	62	2	taking	take	VBG
cord-221131-44n5pojb	62	3	the	the	DT
cord-221131-44n5pojb	62	4	entire	entire	JJ
cord-221131-44n5pojb	62	5	national	national	JJ
cord-221131-44n5pojb	62	6	set	set	NN
cord-221131-44n5pojb	62	7	of	of	IN
cord-221131-44n5pojb	62	8	data	datum	NNS
cord-221131-44n5pojb	62	9	we	-PRON-	PRP
cord-221131-44n5pojb	62	10	overpass	overpass	VBP
cord-221131-44n5pojb	62	11	the	the	DT
cord-221131-44n5pojb	62	12	above	above	JJ
cord-221131-44n5pojb	62	13	issues	issue	NNS
cord-221131-44n5pojb	62	14	.	.	.
cord-221131-44n5pojb	63	1	The	the	DT
cord-221131-44n5pojb	63	2	data	datum	NNS
cord-221131-44n5pojb	63	3	can	can	MD
cord-221131-44n5pojb	63	4	be	be	VB
cord-221131-44n5pojb	63	5	taken	take	VBN
cord-221131-44n5pojb	63	6	for	for	IN
cord-221131-44n5pojb	63	7	example	example	NN
cord-221131-44n5pojb	63	8	from	from	IN
cord-221131-44n5pojb	63	9	Italian	italian	JJ
cord-221131-44n5pojb	63	10	Protezione	Protezione	NNP
cord-221131-44n5pojb	63	11	Civile	Civile	NNP
cord-221131-44n5pojb	63	12	[	[	-LRB-
cord-221131-44n5pojb	63	13	12	12	CD
cord-221131-44n5pojb	63	14	]	]	-RRB-
cord-221131-44n5pojb	63	15	or	or	CC
cord-221131-44n5pojb	63	16	from	from	IN
cord-221131-44n5pojb	63	17	WHO	who	WP
cord-221131-44n5pojb	63	18	[	[	-LRB-
cord-221131-44n5pojb	63	19	13	13	CD
cord-221131-44n5pojb	63	20	]	]	-RRB-
cord-221131-44n5pojb	63	21	.	.	.
cord-221131-44n5pojb	64	1	The	the	DT
cord-221131-44n5pojb	64	2	cumulative	cumulative	JJ
cord-221131-44n5pojb	64	3	total	total	JJ
cord-221131-44n5pojb	64	4	number	number	NN
cord-221131-44n5pojb	64	5	of	of	IN
cord-221131-44n5pojb	64	6	infected	infected	JJ
cord-221131-44n5pojb	64	7	will	will	MD
cord-221131-44n5pojb	64	8	be	be	VB
cord-221131-44n5pojb	64	9	indicated	indicate	VBN
cord-221131-44n5pojb	64	10	by	by	IN
cord-221131-44n5pojb	64	11	F	F	NNP
cord-221131-44n5pojb	64	12	n	n	NNP
cord-221131-44n5pojb	64	13	,	,	,
cord-221131-44n5pojb	64	14	with	with	IN
cord-221131-44n5pojb	64	15	F	F	NNP
cord-221131-44n5pojb	64	16	1	1	CD
cord-221131-44n5pojb	64	17	=	=	SYM
cord-221131-44n5pojb	64	18	20	20	CD
cord-221131-44n5pojb	64	19	corresponding	correspond	VBG
cord-221131-44n5pojb	64	20	to	to	IN
cord-221131-44n5pojb	64	21	the	the	DT
cord-221131-44n5pojb	64	22	number	number	NN
cord-221131-44n5pojb	64	23	of	of	IN
cord-221131-44n5pojb	64	24	infected	infect	VBN
cord-221131-44n5pojb	64	25	on	on	IN
cord-221131-44n5pojb	64	26	21st	21st	NN
cord-221131-44n5pojb	64	27	of	of	IN
cord-221131-44n5pojb	64	28	February	February	NNP
cord-221131-44n5pojb	64	29	2020	2020	CD
cord-221131-44n5pojb	64	30	.	.	.
cord-221131-44n5pojb	65	1	The	the	DT
cord-221131-44n5pojb	65	2	subscript	subscript	NN
cord-221131-44n5pojb	65	3	n	n	NN
cord-221131-44n5pojb	65	4	stays	stay	VBZ
cord-221131-44n5pojb	65	5	for	for	IN
cord-221131-44n5pojb	65	6	the	the	DT
cord-221131-44n5pojb	65	7	number	number	NN
cord-221131-44n5pojb	65	8	of	of	IN
cord-221131-44n5pojb	65	9	days	day	NNS
cord-221131-44n5pojb	65	10	from	from	IN
cord-221131-44n5pojb	65	11	the	the	DT
cord-221131-44n5pojb	65	12	starting	starting	NN
cord-221131-44n5pojb	65	13	of	of	IN
cord-221131-44n5pojb	65	14	epidemic	epidemic	NN
cord-221131-44n5pojb	65	15	.	.	.
cord-221131-44n5pojb	66	1	These	these	DT
cord-221131-44n5pojb	66	2	data	datum	NNS
cord-221131-44n5pojb	66	3	will	will	MD
cord-221131-44n5pojb	66	4	be	be	VB
cord-221131-44n5pojb	66	5	opposed	oppose	VBN
cord-221131-44n5pojb	66	6	to	to	IN
cord-221131-44n5pojb	66	7	the	the	DT
cord-221131-44n5pojb	66	8	continuous	continuous	JJ
cord-221131-44n5pojb	66	9	formula	formula	NN
cord-221131-44n5pojb	66	10	The	the	DT
cord-221131-44n5pojb	66	11	value	value	NN
cord-221131-44n5pojb	66	12	of	of	IN
cord-221131-44n5pojb	66	13	β	β	NN
cord-221131-44n5pojb	66	14	will	will	MD
cord-221131-44n5pojb	66	15	be	be	VB
cord-221131-44n5pojb	66	16	taken	take	VBN
cord-221131-44n5pojb	66	17	to	to	TO
cord-221131-44n5pojb	66	18	be	be	VB
cord-221131-44n5pojb	66	19	constrained	constrain	VBN
cord-221131-44n5pojb	66	20	by	by	IN
cord-221131-44n5pojb	66	21	the	the	DT
cord-221131-44n5pojb	66	22	equation	equation	NN
cord-221131-44n5pojb	66	23	The	the	DT
cord-221131-44n5pojb	66	24	function	function	NN
cord-221131-44n5pojb	66	25	f	f	NNP
cord-221131-44n5pojb	66	26	(	(	-LRB-
cord-221131-44n5pojb	66	27	3	3	LS
cord-221131-44n5pojb	66	28	)	)	-RRB-
cord-221131-44n5pojb	66	29	then	then	RB
cord-221131-44n5pojb	66	30	depends	depend	VBZ
cord-221131-44n5pojb	66	31	on	on	IN
cord-221131-44n5pojb	66	32	two	two	CD
cord-221131-44n5pojb	66	33	parameters	parameter	NNS
cord-221131-44n5pojb	66	34	,	,	,
cord-221131-44n5pojb	66	35	α	α	NN
cord-221131-44n5pojb	66	36	and	and	CC
cord-221131-44n5pojb	66	37	c.	c.	NN
cord-221131-44n5pojb	67	1	When	when	WRB
cord-221131-44n5pojb	67	2	necessary	necessary	JJ
cord-221131-44n5pojb	67	3	,	,	,
cord-221131-44n5pojb	67	4	to	to	TO
cord-221131-44n5pojb	67	5	stress	stress	VB
cord-221131-44n5pojb	67	6	the	the	DT
cord-221131-44n5pojb	67	7	dependence	dependence	NN
cord-221131-44n5pojb	67	8	on	on	IN
cord-221131-44n5pojb	67	9	these	these	DT
cord-221131-44n5pojb	67	10	parameters	parameter	NNS
cord-221131-44n5pojb	67	11	,	,	,
cord-221131-44n5pojb	67	12	we	-PRON-	PRP
cord-221131-44n5pojb	67	13	will	will	MD
cord-221131-44n5pojb	67	14	denote	denote	VB
cord-221131-44n5pojb	67	15	the	the	DT
cord-221131-44n5pojb	67	16	function	function	NN
cord-221131-44n5pojb	67	17	with	with	IN
cord-221131-44n5pojb	67	18	f	f	NNP
cord-221131-44n5pojb	67	19	α	α	NNP
cord-221131-44n5pojb	67	20	,	,	,
cord-221131-44n5pojb	67	21	c	c	NNP
cord-221131-44n5pojb	67	22	(	(	-LRB-
cord-221131-44n5pojb	67	23	t	t	NN
cord-221131-44n5pojb	67	24	)	)	-RRB-
cord-221131-44n5pojb	67	25	.	.	.
cord-221131-44n5pojb	68	1	The	the	DT
cord-221131-44n5pojb	68	2	cumulative	cumulative	JJ
cord-221131-44n5pojb	68	3	final	final	JJ
cord-221131-44n5pojb	68	4	number	number	NN
cord-221131-44n5pojb	68	5	of	of	IN
cord-221131-44n5pojb	68	6	infected	infected	JJ
cord-221131-44n5pojb	68	7	expected	expect	VBN
cord-221131-44n5pojb	68	8	from	from	IN
cord-221131-44n5pojb	68	9	formula	formula	NN
cord-221131-44n5pojb	68	10	(	(	-LRB-
cord-221131-44n5pojb	68	11	3	3	LS
cord-221131-44n5pojb	68	12	)	)	-RRB-
cord-221131-44n5pojb	68	13	is	be	VBZ
cord-221131-44n5pojb	68	14	given	give	VBN
cord-221131-44n5pojb	68	15	by	by	IN
cord-221131-44n5pojb	68	16	f	f	NNP
cord-221131-44n5pojb	68	17	∞	∞	NNP
cord-221131-44n5pojb	68	18	=	=	:
cord-221131-44n5pojb	68	19	α(1	α(1	NNP
cord-221131-44n5pojb	68	20	+	+	CC
cord-221131-44n5pojb	68	21	tanh(c	tanh(c	NN
cord-221131-44n5pojb	68	22	)	)	-RRB-
cord-221131-44n5pojb	68	23	)	)	-RRB-
cord-221131-44n5pojb	68	24	.	.	.
cord-221131-44n5pojb	69	1	It	-PRON-	PRP
cord-221131-44n5pojb	69	2	is	be	VBZ
cord-221131-44n5pojb	69	3	possible	possible	JJ
cord-221131-44n5pojb	69	4	to	to	TO
cord-221131-44n5pojb	69	5	estimate	estimate	VB
cord-221131-44n5pojb	69	6	the	the	DT
cord-221131-44n5pojb	69	7	parameters	parameter	NNS
cord-221131-44n5pojb	69	8	α	α	NN
cord-221131-44n5pojb	69	9	and	and	CC
cord-221131-44n5pojb	69	10	c	c	NN
cord-221131-44n5pojb	69	11	by	by	IN
cord-221131-44n5pojb	69	12	minimizing	minimize	VBG
cord-221131-44n5pojb	69	13	the	the	DT
cord-221131-44n5pojb	69	14	difference	difference	NN
cord-221131-44n5pojb	69	15	between	between	IN
cord-221131-44n5pojb	69	16	the	the	DT
cord-221131-44n5pojb	69	17	actual	actual	JJ
cord-221131-44n5pojb	69	18	and	and	CC
cord-221131-44n5pojb	69	19	predicted	predict	VBN
cord-221131-44n5pojb	69	20	number	number	NN
cord-221131-44n5pojb	69	21	of	of	IN
cord-221131-44n5pojb	69	22	cases	case	NNS
cord-221131-44n5pojb	69	23	,	,	,
cord-221131-44n5pojb	69	24	i.e.	i.e.	FW
cord-221131-44n5pojb	69	25	minimizing	minimize	VBG
cord-221131-44n5pojb	69	26	In	in	IN
cord-221131-44n5pojb	69	27	order	order	NN
cord-221131-44n5pojb	69	28	to	to	TO
cord-221131-44n5pojb	69	29	have	have	VB
cord-221131-44n5pojb	69	30	a	a	DT
cord-221131-44n5pojb	69	31	reasonable	reasonable	JJ
cord-221131-44n5pojb	69	32	minimum	minimum	JJ
cord-221131-44n5pojb	69	33	number	number	NN
cord-221131-44n5pojb	69	34	of	of	IN
cord-221131-44n5pojb	69	35	data	datum	NNS
cord-221131-44n5pojb	69	36	,	,	,
cord-221131-44n5pojb	69	37	we	-PRON-	PRP
cord-221131-44n5pojb	69	38	start	start	VBP
cord-221131-44n5pojb	69	39	the	the	DT
cord-221131-44n5pojb	69	40	analysis	analysis	NN
cord-221131-44n5pojb	69	41	by	by	IN
cord-221131-44n5pojb	69	42	taking	take	VBG
cord-221131-44n5pojb	69	43	n	n	NNP
cord-221131-44n5pojb	69	44	≥	≥	CD
cord-221131-44n5pojb	69	45	15	15	CD
cord-221131-44n5pojb	69	46	.	.	.
cord-221131-44n5pojb	70	1	The	the	DT
cord-221131-44n5pojb	70	2	values	value	NNS
cord-221131-44n5pojb	70	3	of	of	IN
cord-221131-44n5pojb	70	4	the	the	DT
cord-221131-44n5pojb	70	5	parameters	parameter	NNS
cord-221131-44n5pojb	70	6	minimizing	minimize	VBG
cord-221131-44n5pojb	70	7	the	the	DT
cord-221131-44n5pojb	70	8	sum	sum	NN
cord-221131-44n5pojb	70	9	S	S	NNP
cord-221131-44n5pojb	70	10	n	n	NNP
cord-221131-44n5pojb	70	11	are	be	VBP
cord-221131-44n5pojb	70	12	reported	report	VBN
cord-221131-44n5pojb	70	13	in	in	IN
cord-221131-44n5pojb	70	14	table	table	NN
cord-221131-44n5pojb	70	15	(	(	-LRB-
cord-221131-44n5pojb	70	16	1	1	CD
cord-221131-44n5pojb	70	17	)	)	-RRB-
cord-221131-44n5pojb	71	1	At	at	IN
cord-221131-44n5pojb	71	2	the	the	DT
cord-221131-44n5pojb	71	3	31st	31st	JJ
cord-221131-44n5pojb	71	4	day	day	NN
cord-221131-44n5pojb	71	5	of	of	IN
cord-221131-44n5pojb	71	6	epidemic	epidemic	NN
cord-221131-44n5pojb	71	7	the	the	DT
cord-221131-44n5pojb	71	8	final	final	JJ
cord-221131-44n5pojb	71	9	number	number	NN
cord-221131-44n5pojb	71	10	of	of	IN
cord-221131-44n5pojb	71	11	infected	infect	VBN
cord-221131-44n5pojb	71	12	is	be	VBZ
cord-221131-44n5pojb	71	13	estimated	estimate	VBN
cord-221131-44n5pojb	71	14	to	to	TO
cord-221131-44n5pojb	71	15	be	be	VB
cord-221131-44n5pojb	71	16	76193	76193	CD
cord-221131-44n5pojb	71	17	,	,	,
cord-221131-44n5pojb	71	18	but	but	CC
cord-221131-44n5pojb	71	19	this	this	DT
cord-221131-44n5pojb	71	20	is	be	VBZ
cord-221131-44n5pojb	71	21	only	only	RB
cord-221131-44n5pojb	71	22	a	a	DT
cord-221131-44n5pojb	71	23	lower	lower	RBR
cord-221131-44n5pojb	71	24	bound	bind	VBN
cord-221131-44n5pojb	71	25	since	since	IN
cord-221131-44n5pojb	71	26	the	the	DT
cord-221131-44n5pojb	71	27	values	value	NNS
cord-221131-44n5pojb	71	28	of	of	IN
cord-221131-44n5pojb	71	29	α	α	NNP
cord-221131-44n5pojb	71	30	n	n	NN
cord-221131-44n5pojb	71	31	and	and	CC
cord-221131-44n5pojb	71	32	c	c	NNP
cord-221131-44n5pojb	71	33	n	n	NNP
cord-221131-44n5pojb	71	34	are	be	VBP
cord-221131-44n5pojb	71	35	increasing	increase	VBG
cord-221131-44n5pojb	71	36	.	.	.
cord-221131-44n5pojb	72	1	A	a	DT
cord-221131-44n5pojb	72	2	plot	plot	NN
cord-221131-44n5pojb	72	3	of	of	IN
cord-221131-44n5pojb	72	4	f	f	NNP
cord-221131-44n5pojb	72	5	α	α	NNP
cord-221131-44n5pojb	72	6	31	31	CD
cord-221131-44n5pojb	72	7	,	,	,
cord-221131-44n5pojb	72	8	c	c	NNP
cord-221131-44n5pojb	72	9	31	31	CD
cord-221131-44n5pojb	72	10	(	(	-LRB-
cord-221131-44n5pojb	72	11	t	t	NN
cord-221131-44n5pojb	72	12	)	)	-RRB-
cord-221131-44n5pojb	72	13	and	and	CC
cord-221131-44n5pojb	72	14	of	of	IN
cord-221131-44n5pojb	72	15	the	the	DT
cord-221131-44n5pojb	72	16	cumulative	cumulative	JJ
cord-221131-44n5pojb	72	17	number	number	NN
cord-221131-44n5pojb	72	18	of	of	IN
cord-221131-44n5pojb	72	19	infected	infect	VBN
cord-221131-44n5pojb	72	20	is	be	VBZ
cord-221131-44n5pojb	72	21	reported	report	VBN
cord-221131-44n5pojb	72	22	in	in	IN
cord-221131-44n5pojb	72	23	figure	figure	NN
cord-221131-44n5pojb	72	24	(	(	-LRB-
cord-221131-44n5pojb	72	25	1	1	CD
cord-221131-44n5pojb	72	26	)	)	-RRB-
cord-221131-44n5pojb	72	27	.	.	.
cord-221131-44n5pojb	73	1	A	a	DT
cord-221131-44n5pojb	73	2	fundamental	fundamental	JJ
cord-221131-44n5pojb	73	3	observation	observation	NN
cord-221131-44n5pojb	73	4	is	be	VBZ
cord-221131-44n5pojb	73	5	that	that	IN
cord-221131-44n5pojb	73	6	the	the	DT
cord-221131-44n5pojb	73	7	function	function	NN
cord-221131-44n5pojb	73	8	S	s	NN
cord-221131-44n5pojb	73	9	n	n	NNP
cord-221131-44n5pojb	73	10	actually	actually	RB
cord-221131-44n5pojb	73	11	has	have	VBZ
cord-221131-44n5pojb	73	12	a	a	DT
cord-221131-44n5pojb	73	13	basin	basin	NN
cord-221131-44n5pojb	73	14	of	of	IN
cord-221131-44n5pojb	73	15	depressed	depressed	JJ
cord-221131-44n5pojb	73	16	values	value	NNS
cord-221131-44n5pojb	73	17	,	,	,
cord-221131-44n5pojb	73	18	showed	show	VBD
cord-221131-44n5pojb	73	19	in	in	IN
cord-221131-44n5pojb	73	20	detail	detail	NN
cord-221131-44n5pojb	73	21	in	in	IN
cord-221131-44n5pojb	73	22	figure	figure	NN
cord-221131-44n5pojb	73	23	(	(	-LRB-
cord-221131-44n5pojb	73	24	2	2	LS
cord-221131-44n5pojb	73	25	)	)	-RRB-
cord-221131-44n5pojb	73	26	for	for	IN
cord-221131-44n5pojb	73	27	a	a	DT
cord-221131-44n5pojb	73	28	given	give	VBN
cord-221131-44n5pojb	73	29	value	value	NN
cord-221131-44n5pojb	73	30	of	of	IN
cord-221131-44n5pojb	73	31	n.	n.	NN
cord-221131-44n5pojb	74	1	This	this	DT
cord-221131-44n5pojb	74	2	basin	basin	NN
cord-221131-44n5pojb	74	3	of	of	IN
cord-221131-44n5pojb	74	4	minimum	minimum	NN
cord-221131-44n5pojb	74	5	seems	seem	VBZ
cord-221131-44n5pojb	74	6	to	to	TO
cord-221131-44n5pojb	74	7	indicate	indicate	VB
cord-221131-44n5pojb	74	8	that	that	IN
cord-221131-44n5pojb	74	9	there	there	EX
cord-221131-44n5pojb	74	10	is	be	VBZ
cord-221131-44n5pojb	74	11	a	a	DT
cord-221131-44n5pojb	74	12	given	give	VBN
cord-221131-44n5pojb	74	13	function	function	NN
cord-221131-44n5pojb	74	14	α(c	α(c	XX
cord-221131-44n5pojb	74	15	)	)	-RRB-
cord-221131-44n5pojb	74	16	giving	give	VBG
cord-221131-44n5pojb	74	17	a	a	DT
cord-221131-44n5pojb	74	18	family	family	NN
cord-221131-44n5pojb	74	19	of	of	IN
cord-221131-44n5pojb	74	20	tanh	tanh	NN
cord-221131-44n5pojb	74	21	curves	curve	NNS
cord-221131-44n5pojb	74	22	with	with	IN
cord-221131-44n5pojb	74	23	 	 	_SP
cord-221131-44n5pojb	74	24	Clearly	clearly	RB
cord-221131-44n5pojb	74	25	,	,	,
cord-221131-44n5pojb	74	26	by	by	IN
cord-221131-44n5pojb	74	27	considering	consider	VBG
cord-221131-44n5pojb	74	28	a	a	DT
cord-221131-44n5pojb	74	29	number	number	NN
cord-221131-44n5pojb	74	30	N	n	NN
cord-221131-44n5pojb	74	31	of	of	IN
cord-221131-44n5pojb	74	32	values	value	NNS
cord-221131-44n5pojb	74	33	of	of	IN
cord-221131-44n5pojb	74	34	α	α	NNP
cord-221131-44n5pojb	74	35	n	n	NN
cord-221131-44n5pojb	74	36	and	and	CC
cord-221131-44n5pojb	74	37	c	c	NNP
cord-221131-44n5pojb	74	38	n	n	NN
cord-221131-44n5pojb	74	39	to	to	TO
cord-221131-44n5pojb	74	40	fit	fit	VB
cord-221131-44n5pojb	74	41	a	a	DT
cord-221131-44n5pojb	74	42	k	k	NN
cord-221131-44n5pojb	74	43	,	,	,
cord-221131-44n5pojb	74	44	k=0	k=0	UH
cord-221131-44n5pojb	74	45	,	,	,
cord-221131-44n5pojb	74	46	...	...	:
cord-221131-44n5pojb	75	1	,	,	,
cord-221131-44n5pojb	75	2	3	3	CD
cord-221131-44n5pojb	75	3	,	,	,
cord-221131-44n5pojb	75	4	we	-PRON-	PRP
cord-221131-44n5pojb	75	5	will	will	MD
cord-221131-44n5pojb	75	6	obtain	obtain	VB
cord-221131-44n5pojb	75	7	a	a	DT
cord-221131-44n5pojb	75	8	set	set	NN
cord-221131-44n5pojb	75	9	of	of	IN
cord-221131-44n5pojb	75	10	values	value	NNS
cord-221131-44n5pojb	75	11	{	{	-LRB-
cord-221131-44n5pojb	75	12	a	a	DT
cord-221131-44n5pojb	75	13	k	k	NN
cord-221131-44n5pojb	75	14	,	,	,
cord-221131-44n5pojb	75	15	N	N	NNP
cord-221131-44n5pojb	75	16	}	}	-RRB-
cord-221131-44n5pojb	75	17	.	.	.
cord-221131-44n5pojb	76	1	By	by	IN
cord-221131-44n5pojb	76	2	fitting	fit	VBG
cord-221131-44n5pojb	76	3	all	all	PDT
cord-221131-44n5pojb	76	4	the	the	DT
cord-221131-44n5pojb	76	5	data	datum	NNS
cord-221131-44n5pojb	76	6	available	available	JJ
cord-221131-44n5pojb	76	7	(	(	-LRB-
cord-221131-44n5pojb	76	8	i.e.	i.e.	FW
cord-221131-44n5pojb	76	9	by	by	IN
cord-221131-44n5pojb	76	10	taking	take	VBG
cord-221131-44n5pojb	76	11	N	n	NN
cord-221131-44n5pojb	76	12	=	=	SYM
cord-221131-44n5pojb	76	13	17	17	CD
cord-221131-44n5pojb	76	14	)	)	-RRB-
cord-221131-44n5pojb	76	15	,	,	,
cord-221131-44n5pojb	76	16	we	-PRON-	PRP
cord-221131-44n5pojb	76	17	get	get	VBP
cord-221131-44n5pojb	76	18	the	the	DT
cord-221131-44n5pojb	76	19	following	follow	VBG
cord-221131-44n5pojb	76	20	values	value	NNS
cord-221131-44n5pojb	76	21	for	for	IN
cord-221131-44n5pojb	76	22	the	the	DT
cord-221131-44n5pojb	76	23	coefficients	coefficient	NNS
cord-221131-44n5pojb	76	24	a	a	DT
cord-221131-44n5pojb	76	25	k	k	XX
cord-221131-44n5pojb	76	26	:	:	:
cord-221131-44n5pojb	76	27	It	-PRON-	PRP
cord-221131-44n5pojb	76	28	is	be	VBZ
cord-221131-44n5pojb	76	29	possible	possible	JJ
cord-221131-44n5pojb	76	30	to	to	TO
cord-221131-44n5pojb	76	31	get	get	VB
cord-221131-44n5pojb	76	32	more	more	JJR
cord-221131-44n5pojb	76	33	terms	term	NNS
cord-221131-44n5pojb	76	34	in	in	IN
cord-221131-44n5pojb	76	35	the	the	DT
cord-221131-44n5pojb	76	36	sum	sum	NN
cord-221131-44n5pojb	76	37	(	(	-LRB-
cord-221131-44n5pojb	76	38	6	6	CD
cord-221131-44n5pojb	76	39	)	)	-RRB-
cord-221131-44n5pojb	76	40	,	,	,
cord-221131-44n5pojb	76	41	but	but	CC
cord-221131-44n5pojb	76	42	the	the	DT
cord-221131-44n5pojb	76	43	cubic	cubic	JJ
cord-221131-44n5pojb	76	44	term	term	NN
cord-221131-44n5pojb	76	45	is	be	VBZ
cord-221131-44n5pojb	76	46	sufficient	sufficient	JJ
cord-221131-44n5pojb	76	47	to	to	TO
cord-221131-44n5pojb	76	48	get	get	VB
cord-221131-44n5pojb	76	49	a	a	DT
cord-221131-44n5pojb	76	50	formula	formula	NN
cord-221131-44n5pojb	76	51	accurate	accurate	JJ
cord-221131-44n5pojb	76	52	enough	enough	RB
cord-221131-44n5pojb	76	53	to	to	IN
cord-221131-44n5pojb	76	54	what	what	WP
cord-221131-44n5pojb	76	55	we	-PRON-	PRP
cord-221131-44n5pojb	76	56	are	be	VBP
cord-221131-44n5pojb	76	57	going	go	VBG
cord-221131-44n5pojb	76	58	to	to	TO
cord-221131-44n5pojb	76	59	say	say	VB
cord-221131-44n5pojb	76	60	.	.	.
cord-221131-44n5pojb	77	1	The	the	DT
cord-221131-44n5pojb	77	2	plot	plot	NN
cord-221131-44n5pojb	77	3	of	of	IN
cord-221131-44n5pojb	77	4	the	the	DT
cord-221131-44n5pojb	77	5	fit	fit	NN
cord-221131-44n5pojb	77	6	is	be	VBZ
cord-221131-44n5pojb	77	7	given	give	VBN
cord-221131-44n5pojb	77	8	in	in	IN
cord-221131-44n5pojb	77	9	figure	figure	NN
cord-221131-44n5pojb	77	10	(	(	-LRB-
cord-221131-44n5pojb	77	11	5	5	CD
cord-221131-44n5pojb	77	12	)	)	-RRB-
cord-221131-44n5pojb	77	13	,	,	,
cord-221131-44n5pojb	77	14	together	together	RB
cord-221131-44n5pojb	77	15	with	with	IN
cord-221131-44n5pojb	77	16	the	the	DT
cord-221131-44n5pojb	77	17	values	value	NNS
cord-221131-44n5pojb	77	18	of	of	IN
cord-221131-44n5pojb	77	19	the	the	DT
cord-221131-44n5pojb	77	20	residuals	residual	NNS
cord-221131-44n5pojb	77	21	α	α	NN
cord-221131-44n5pojb	77	22	n	n	NN
cord-221131-44n5pojb	77	23	−	−	NN
cord-221131-44n5pojb	77	24	3	3	CD
cord-221131-44n5pojb	77	25	k=0	k=0	NN
cord-221131-44n5pojb	78	1	a	a	DT
cord-221131-44n5pojb	78	2	k	k	NNP
cord-221131-44n5pojb	78	3	c	c	NN
cord-221131-44n5pojb	78	4	k	k	NNP
cord-221131-44n5pojb	78	5	n	n	NNP
cord-221131-44n5pojb	78	6	,	,	,
cord-221131-44n5pojb	78	7	where	where	WRB
cord-221131-44n5pojb	78	8	the	the	DT
cord-221131-44n5pojb	78	9	values	value	NNS
cord-221131-44n5pojb	78	10	a	a	DT
cord-221131-44n5pojb	78	11	k	k	NN
cord-221131-44n5pojb	78	12	are	be	VBP
cord-221131-44n5pojb	78	13	those	those	DT
cord-221131-44n5pojb	78	14	given	give	VBN
cord-221131-44n5pojb	78	15	in	in	IN
cord-221131-44n5pojb	78	16	equation	equation	NN
cord-221131-44n5pojb	78	17	(	(	-LRB-
cord-221131-44n5pojb	78	18	7	7	CD
cord-221131-44n5pojb	78	19	)	)	-RRB-
cord-221131-44n5pojb	78	20	.	.	.
cord-221131-44n5pojb	79	1	A	a	DT
cord-221131-44n5pojb	79	2	comparison	comparison	NN
cord-221131-44n5pojb	79	3	between	between	IN
cord-221131-44n5pojb	79	4	the	the	DT
cord-221131-44n5pojb	79	5	curve	curve	NN
cord-221131-44n5pojb	79	6	α(c	α(c	XX
cord-221131-44n5pojb	79	7	)	)	-RRB-
cord-221131-44n5pojb	79	8	and	and	CC
cord-221131-44n5pojb	79	9	the	the	DT
cord-221131-44n5pojb	79	10	basin	basin	NN
cord-221131-44n5pojb	79	11	of	of	IN
cord-221131-44n5pojb	79	12	minima	minima	NNP
cord-221131-44n5pojb	79	13	for	for	IN
cord-221131-44n5pojb	79	14	S	S	NNP
cord-221131-44n5pojb	79	15	n	n	NNP
cord-221131-44n5pojb	79	16	has	have	VBZ
cord-221131-44n5pojb	79	17	been	be	VBN
cord-221131-44n5pojb	79	18	plotted	plot	VBN
cord-221131-44n5pojb	79	19	in	in	IN
cord-221131-44n5pojb	79	20	figure	figure	NN
cord-221131-44n5pojb	79	21	(	(	-LRB-
cord-221131-44n5pojb	79	22	6	6	CD
cord-221131-44n5pojb	79	23	)	)	-RRB-
cord-221131-44n5pojb	79	24	:	:	:
cord-221131-44n5pojb	79	25	the	the	DT
cord-221131-44n5pojb	79	26	red	red	JJ
cord-221131-44n5pojb	79	27	curve	curve	NN
cord-221131-44n5pojb	79	28	is	be	VBZ
cord-221131-44n5pojb	79	29	the	the	DT
cord-221131-44n5pojb	79	30	function	function	NN
cord-221131-44n5pojb	79	31	(	(	-LRB-
cord-221131-44n5pojb	79	32	6	6	CD
cord-221131-44n5pojb	79	33	)	)	-RRB-
cord-221131-44n5pojb	79	34	with	with	IN
cord-221131-44n5pojb	79	35	the	the	DT
cord-221131-44n5pojb	79	36	black	black	JJ
cord-221131-44n5pojb	79	37	dots	dot	NNS
cord-221131-44n5pojb	79	38	giving	give	VBG
cord-221131-44n5pojb	79	39	the	the	DT
cord-221131-44n5pojb	79	40	actual	actual	JJ
cord-221131-44n5pojb	79	41	values	value	NNS
cord-221131-44n5pojb	79	42	of	of	IN
cord-221131-44n5pojb	79	43	(	(	-LRB-
cord-221131-44n5pojb	79	44	c	c	NNP
cord-221131-44n5pojb	79	45	n	n	NNP
cord-221131-44n5pojb	79	46	,	,	,
cord-221131-44n5pojb	79	47	α	α	NNP
cord-221131-44n5pojb	79	48	n	n	NN
cord-221131-44n5pojb	79	49	)	)	-RRB-
cord-221131-44n5pojb	79	50	in	in	IN
cord-221131-44n5pojb	79	51	table	table	NN
cord-221131-44n5pojb	79	52	(	(	-LRB-
cord-221131-44n5pojb	79	53	1	1	CD
cord-221131-44n5pojb	79	54	)	)	-RRB-
cord-221131-44n5pojb	79	55	.	.	.
cord-221131-44n5pojb	80	1	The	the	DT
cord-221131-44n5pojb	80	2	function	function	NN
cord-221131-44n5pojb	80	3	α(c	α(c	XX
cord-221131-44n5pojb	80	4	)	)	-RRB-
cord-221131-44n5pojb	80	5	denotes	denote	VBZ
cord-221131-44n5pojb	80	6	a	a	DT
cord-221131-44n5pojb	80	7	trend	trend	NN
cord-221131-44n5pojb	80	8	in	in	IN
cord-221131-44n5pojb	80	9	the	the	DT
cord-221131-44n5pojb	80	10	data	datum	NNS
cord-221131-44n5pojb	80	11	that	that	WDT
cord-221131-44n5pojb	80	12	may	may	MD
cord-221131-44n5pojb	80	13	be	be	VB
cord-221131-44n5pojb	80	14	useful	useful	JJ
cord-221131-44n5pojb	80	15	.	.	.
cord-221131-44n5pojb	81	1	If	if	IN
cord-221131-44n5pojb	81	2	in	in	IN
cord-221131-44n5pojb	81	3	the	the	DT
cord-221131-44n5pojb	81	4	next	next	JJ
cord-221131-44n5pojb	81	5	days	day	NNS
cord-221131-44n5pojb	81	6	the	the	DT
cord-221131-44n5pojb	81	7	values	value	NNS
cord-221131-44n5pojb	81	8	of	of	IN
cord-221131-44n5pojb	81	9	the	the	DT
cord-221131-44n5pojb	81	10	infection	infection	NN
cord-221131-44n5pojb	81	11	continue	continue	VBP
cord-221131-44n5pojb	81	12	to	to	TO
cord-221131-44n5pojb	81	13	rise	rise	VB
cord-221131-44n5pojb	81	14	,	,	,
cord-221131-44n5pojb	81	15	it	-PRON-	PRP
cord-221131-44n5pojb	81	16	is	be	VBZ
cord-221131-44n5pojb	81	17	reasonable	reasonable	JJ
cord-221131-44n5pojb	81	18	to	to	TO
cord-221131-44n5pojb	81	19	expect	expect	VB
cord-221131-44n5pojb	81	20	that	that	IN
cord-221131-44n5pojb	81	21	the	the	DT
cord-221131-44n5pojb	81	22	values	value	NNS
cord-221131-44n5pojb	81	23	of	of	IN
cord-221131-44n5pojb	81	24	α	α	NN
cord-221131-44n5pojb	81	25	and	and	CC
cord-221131-44n5pojb	81	26	c	c	NN
cord-221131-44n5pojb	81	27	will	will	MD
cord-221131-44n5pojb	81	28	be	be	VB
cord-221131-44n5pojb	81	29	constrained	constrain	VBN
cord-221131-44n5pojb	81	30	closely	closely	RB
cord-221131-44n5pojb	81	31	by	by	IN
cord-221131-44n5pojb	81	32	the	the	DT
cord-221131-44n5pojb	81	33	same	same	JJ
cord-221131-44n5pojb	81	34	curve	curve	NN
cord-221131-44n5pojb	81	35	.	.	.
cord-221131-44n5pojb	82	1	Clearly	clearly	RB
cord-221131-44n5pojb	82	2	the	the	DT
cord-221131-44n5pojb	82	3	model	model	NN
cord-221131-44n5pojb	82	4	used	use	VBN
cord-221131-44n5pojb	82	5	here	here	RB
cord-221131-44n5pojb	82	6	is	be	VBZ
cord-221131-44n5pojb	82	7	rough	rough	JJ
cord-221131-44n5pojb	82	8	,	,	,
cord-221131-44n5pojb	82	9	but	but	CC
cord-221131-44n5pojb	82	10	it	-PRON-	PRP
cord-221131-44n5pojb	82	11	can	can	MD
cord-221131-44n5pojb	82	12	give	give	VB
cord-221131-44n5pojb	82	13	at	at	IN
cord-221131-44n5pojb	82	14	least	least	JJS
cord-221131-44n5pojb	82	15	an	an	DT
cord-221131-44n5pojb	82	16	idea	idea	NN
cord-221131-44n5pojb	82	17	about	about	IN
cord-221131-44n5pojb	82	18	the	the	DT
cord-221131-44n5pojb	82	19	future	future	JJ
cord-221131-44n5pojb	82	20	trend	trend	NN
cord-221131-44n5pojb	82	21	of	of	IN
cord-221131-44n5pojb	82	22	the	the	DT
cord-221131-44n5pojb	82	23	data	datum	NNS
cord-221131-44n5pojb	82	24	.	.	.
cord-221131-44n5pojb	83	1	We	-PRON-	PRP
cord-221131-44n5pojb	83	2	are	be	VBP
cord-221131-44n5pojb	83	3	tacitly	tacitly	RB
cord-221131-44n5pojb	83	4	assuming	assume	VBG
cord-221131-44n5pojb	83	5	that	that	IN
cord-221131-44n5pojb	83	6	there	there	EX
cord-221131-44n5pojb	83	7	will	will	MD
cord-221131-44n5pojb	83	8	be	be	VB
cord-221131-44n5pojb	83	9	no	no	DT
cord-221131-44n5pojb	83	10	other	other	JJ
cord-221131-44n5pojb	83	11	cluster	cluster	NN
cord-221131-44n5pojb	83	12	of	of	IN
cord-221131-44n5pojb	83	13	infection	infection	NN
cord-221131-44n5pojb	83	14	around	around	IN
cord-221131-44n5pojb	83	15	Italy	Italy	NNP
cord-221131-44n5pojb	83	16	in	in	IN
cord-221131-44n5pojb	83	17	the	the	DT
cord-221131-44n5pojb	83	18	next	next	JJ
cord-221131-44n5pojb	83	19	days	day	NNS
cord-221131-44n5pojb	83	20	:	:	:
cord-221131-44n5pojb	83	21	the	the	DT
cord-221131-44n5pojb	83	22	point	point	NN
cord-221131-44n5pojb	83	23	will	will	MD
cord-221131-44n5pojb	83	24	be	be	VB
cord-221131-44n5pojb	83	25	discussed	discuss	VBN
cord-221131-44n5pojb	83	26	later	later	RB
cord-221131-44n5pojb	83	27	.	.	.
cord-221131-44n5pojb	84	1	Now	now	RB
cord-221131-44n5pojb	84	2	we	-PRON-	PRP
cord-221131-44n5pojb	84	3	consider	consider	VBP
cord-221131-44n5pojb	84	4	the	the	DT
cord-221131-44n5pojb	84	5	function	function	NN
cord-221131-44n5pojb	84	6	f	f	XX
cord-221131-44n5pojb	84	7	in	in	IN
cord-221131-44n5pojb	84	8	(	(	-LRB-
cord-221131-44n5pojb	84	9	3	3	CD
cord-221131-44n5pojb	84	10	)	)	-RRB-
cord-221131-44n5pojb	84	11	as	as	IN
cord-221131-44n5pojb	84	12	a	a	DT
cord-221131-44n5pojb	84	13	function	function	NN
cord-221131-44n5pojb	84	14	of	of	IN
cord-221131-44n5pojb	84	15	t	t	NN
cord-221131-44n5pojb	84	16	and	and	CC
cord-221131-44n5pojb	84	17	c	c	NN
cord-221131-44n5pojb	84	18	alone	alone	RB
cord-221131-44n5pojb	84	19	,	,	,
cord-221131-44n5pojb	84	20	since	since	IN
cord-221131-44n5pojb	84	21	the	the	DT
cord-221131-44n5pojb	84	22	value	value	NN
cord-221131-44n5pojb	84	23	of	of	IN
cord-221131-44n5pojb	84	24	a	a	DT
cord-221131-44n5pojb	84	25	is	be	VBZ
cord-221131-44n5pojb	84	26	constrained	constrain	VBN
cord-221131-44n5pojb	84	27	by	by	IN
cord-221131-44n5pojb	84	28	the	the	DT
cord-221131-44n5pojb	84	29	curve	curve	NN
cord-221131-44n5pojb	84	30	(	(	-LRB-
cord-221131-44n5pojb	84	31	6	6	CD
cord-221131-44n5pojb	84	32	)	)	-RRB-
cord-221131-44n5pojb	84	33	.	.	.
cord-221131-44n5pojb	85	1	The	the	DT
cord-221131-44n5pojb	85	2	plot	plot	NN
cord-221131-44n5pojb	85	3	of	of	IN
cord-221131-44n5pojb	85	4	the	the	DT
cord-221131-44n5pojb	85	5	derivative	derivative	NN
cord-221131-44n5pojb	85	6	of	of	IN
cord-221131-44n5pojb	85	7	this	this	DT
cord-221131-44n5pojb	85	8	function	function	NN
cord-221131-44n5pojb	85	9	(	(	-LRB-
cord-221131-44n5pojb	85	10	with	with	IN
cord-221131-44n5pojb	85	11	respect	respect	NN
cord-221131-44n5pojb	85	12	to	to	IN
cord-221131-44n5pojb	85	13	t	t	NN
cord-221131-44n5pojb	85	14	)	)	-RRB-
cord-221131-44n5pojb	85	15	gives	give	VBZ
cord-221131-44n5pojb	85	16	the	the	DT
cord-221131-44n5pojb	85	17	time	time	NN
cord-221131-44n5pojb	85	18	of	of	IN
cord-221131-44n5pojb	85	19	the	the	DT
cord-221131-44n5pojb	85	20	peak	peak	NN
cord-221131-44n5pojb	85	21	of	of	IN
cord-221131-44n5pojb	85	22	infections	infection	NNS
cord-221131-44n5pojb	85	23	.	.	.
cord-221131-44n5pojb	86	1	The	the	DT
cord-221131-44n5pojb	86	2	plot	plot	NN
cord-221131-44n5pojb	86	3	is	be	VBZ
cord-221131-44n5pojb	86	4	reported	report	VBN
cord-221131-44n5pojb	86	5	in	in	IN
cord-221131-44n5pojb	86	6	figure	figure	NN
cord-221131-44n5pojb	86	7	(	(	-LRB-
cord-221131-44n5pojb	86	8	7	7	CD
cord-221131-44n5pojb	86	9	)	)	-RRB-
cord-221131-44n5pojb	86	10	:	:	:
cord-221131-44n5pojb	86	11	we	-PRON-	PRP
cord-221131-44n5pojb	86	12	notice	notice	VBP
cord-221131-44n5pojb	86	13	that	that	IN
cord-221131-44n5pojb	86	14	the	the	DT
cord-221131-44n5pojb	86	15	maximum	maximum	NN
cord-221131-44n5pojb	86	16	of	of	IN
cord-221131-44n5pojb	86	17	the	the	DT
cord-221131-44n5pojb	86	18	derivative	derivative	NN
cord-221131-44n5pojb	86	19	of	of	IN
cord-221131-44n5pojb	86	20	the	the	DT
cord-221131-44n5pojb	86	21	cumulative	cumulative	JJ
cord-221131-44n5pojb	86	22	number	number	NN
cord-221131-44n5pojb	86	23	of	of	IN
cord-221131-44n5pojb	86	24	infected	infected	JJ
cord-221131-44n5pojb	86	25	increases	increase	NNS
cord-221131-44n5pojb	86	26	with	with	IN
cord-221131-44n5pojb	86	27	n	n	NN
cord-221131-44n5pojb	86	28	up	up	RB
cord-221131-44n5pojb	86	29	to	to	IN
cord-221131-44n5pojb	86	30	c	c	NNP
cord-221131-44n5pojb	86	31	∼	∼	NNP
cord-221131-44n5pojb	86	32	4.15	4.15	CD
cord-221131-44n5pojb	86	33	and	and	CC
cord-221131-44n5pojb	86	34	then	then	RB
cord-221131-44n5pojb	86	35	decreases	decrease	VBZ
cord-221131-44n5pojb	86	36	by	by	IN
cord-221131-44n5pojb	86	37	increasing	increase	VBG
cord-221131-44n5pojb	86	38	c.	c.	NN
cord-221131-44n5pojb	87	1	This	this	DT
cord-221131-44n5pojb	87	2	gives	give	VBZ
cord-221131-44n5pojb	87	3	an	an	DT
cord-221131-44n5pojb	87	4	upper	upper	JJ
cord-221131-44n5pojb	87	5	bound	bind	VBN
cord-221131-44n5pojb	87	6	for	for	IN
cord-221131-44n5pojb	87	7	the	the	DT
cord-221131-44n5pojb	87	8	peak	peak	NN
cord-221131-44n5pojb	87	9	of	of	IN
cord-221131-44n5pojb	87	10	new	new	JJ
cord-221131-44n5pojb	87	11	number	number	NN
cord-221131-44n5pojb	87	12	of	of	IN
cord-221131-44n5pojb	87	13	infected	infect	VBN
cord-221131-44n5pojb	87	14	(	(	-LRB-
cord-221131-44n5pojb	87	15	the	the	DT
cord-221131-44n5pojb	87	16	point	point	NN
cord-221131-44n5pojb	87	17	where	where	WRB
cord-221131-44n5pojb	87	18	the	the	DT
cord-221131-44n5pojb	87	19	second	second	JJ
cord-221131-44n5pojb	87	20	derivative	derivative	NN
cord-221131-44n5pojb	87	21	of	of	IN
cord-221131-44n5pojb	87	22	f	f	NNP
cord-221131-44n5pojb	87	23	(	(	-LRB-
cord-221131-44n5pojb	87	24	t	t	NN
cord-221131-44n5pojb	87	25	)	)	-RRB-
cord-221131-44n5pojb	87	26	(	(	-LRB-
cord-221131-44n5pojb	87	27	3	3	LS
cord-221131-44n5pojb	87	28	)	)	-RRB-
cord-221131-44n5pojb	87	29	is	be	VBZ
cord-221131-44n5pojb	87	30	zero	zero	CD
cord-221131-44n5pojb	87	31	)	)	-RRB-
cord-221131-44n5pojb	87	32	,	,	,
cord-221131-44n5pojb	87	33	given	give	VBN
cord-221131-44n5pojb	87	34	by	by	IN
cord-221131-44n5pojb	87	35	32	32	CD
cord-221131-44n5pojb	87	36	days	day	NNS
cord-221131-44n5pojb	87	37	after	after	IN
cord-221131-44n5pojb	87	38	the	the	DT
cord-221131-44n5pojb	87	39	first	first	JJ
cord-221131-44n5pojb	87	40	infection	infection	NN
cord-221131-44n5pojb	87	41	.	.	.
cord-221131-44n5pojb	88	1	In	in	IN
cord-221131-44n5pojb	88	2	the	the	DT
cord-221131-44n5pojb	88	3	next	next	JJ
cord-221131-44n5pojb	88	4	days	day	NNS
cord-221131-44n5pojb	88	5	(	(	-LRB-
cord-221131-44n5pojb	88	6	at	at	IN
cord-221131-44n5pojb	88	7	the	the	DT
cord-221131-44n5pojb	88	8	moment	moment	NN
cord-221131-44n5pojb	88	9	of	of	IN
cord-221131-44n5pojb	88	10	writing	writing	NN
cord-221131-44n5pojb	88	11	we	-PRON-	PRP
cord-221131-44n5pojb	88	12	are	be	VBP
cord-221131-44n5pojb	88	13	exactly	exactly	RB
cord-221131-44n5pojb	88	14	at	at	IN
cord-221131-44n5pojb	88	15	the	the	DT
cord-221131-44n5pojb	88	16	24th	24th	NN
cord-221131-44n5pojb	88	17	of	of	IN
cord-221131-44n5pojb	88	18	March	March	NNP
cord-221131-44n5pojb	88	19	,	,	,
cord-221131-44n5pojb	88	20	exactly	exactly	RB
cord-221131-44n5pojb	88	21	at	at	IN
cord-221131-44n5pojb	88	22	32	32	CD
cord-221131-44n5pojb	88	23	days	day	NNS
cord-221131-44n5pojb	88	24	)	)	-RRB-
cord-221131-44n5pojb	89	1	the	the	DT
cord-221131-44n5pojb	89	2	description	description	NN
cord-221131-44n5pojb	89	3	above	above	RB
cord-221131-44n5pojb	89	4	can	can	MD
cord-221131-44n5pojb	89	5	be	be	VB
cord-221131-44n5pojb	89	6	tested	test	VBN
cord-221131-44n5pojb	89	7	.	.	.
cord-221131-44n5pojb	90	1	The	the	DT
cord-221131-44n5pojb	90	2	above	above	JJ
cord-221131-44n5pojb	90	3	analysis	analysis	NN
cord-221131-44n5pojb	90	4	,	,	,
cord-221131-44n5pojb	90	5	despite	despite	IN
cord-221131-44n5pojb	90	6	using	use	VBG
cord-221131-44n5pojb	90	7	a	a	DT
cord-221131-44n5pojb	90	8	rough	rough	JJ
cord-221131-44n5pojb	90	9	function	function	NN
cord-221131-44n5pojb	90	10	for	for	IN
cord-221131-44n5pojb	90	11	the	the	DT
cord-221131-44n5pojb	90	12	total	total	JJ
cord-221131-44n5pojb	90	13	number	number	NN
cord-221131-44n5pojb	90	14	of	of	IN
cord-221131-44n5pojb	90	15	infected	infect	VBN
cord-221131-44n5pojb	90	16	,	,	,
cord-221131-44n5pojb	90	17	is	be	VBZ
cord-221131-44n5pojb	90	18	able	able	JJ
cord-221131-44n5pojb	90	19	to	to	TO
cord-221131-44n5pojb	90	20	give	give	VB
cord-221131-44n5pojb	90	21	an	an	DT
cord-221131-44n5pojb	90	22	upper	upper	JJ
cord-221131-44n5pojb	90	23	bound	bind	VBN
cord-221131-44n5pojb	90	24	for	for	IN
cord-221131-44n5pojb	90	25	the	the	DT
cord-221131-44n5pojb	90	26	time	time	NN
cord-221131-44n5pojb	90	27	of	of	IN
cord-221131-44n5pojb	90	28	the	the	DT
cord-221131-44n5pojb	90	29	peak	peak	NN
cord-221131-44n5pojb	90	30	of	of	IN
cord-221131-44n5pojb	90	31	new	new	JJ
cord-221131-44n5pojb	90	32	infected	infect	VBN
cord-221131-44n5pojb	90	33	(	(	-LRB-
cord-221131-44n5pojb	90	34	around	around	IN
cord-221131-44n5pojb	90	35	23rd	23rd	NN
cord-221131-44n5pojb	90	36	of	of	IN
cord-221131-44n5pojb	90	37	March	March	NNP
cord-221131-44n5pojb	90	38	)	)	-RRB-
cord-221131-44n5pojb	90	39	thanks	thank	NNS
cord-221131-44n5pojb	90	40	to	to	IN
cord-221131-44n5pojb	90	41	the	the	DT
cord-221131-44n5pojb	90	42	observation	observation	NN
cord-221131-44n5pojb	90	43	that	that	IN
cord-221131-44n5pojb	90	44	the	the	DT
cord-221131-44n5pojb	90	45	values	value	NNS
cord-221131-44n5pojb	90	46	of	of	IN
cord-221131-44n5pojb	90	47	α	α	NNP
cord-221131-44n5pojb	90	48	n	n	NN
cord-221131-44n5pojb	90	49	are	be	VBP
cord-221131-44n5pojb	90	50	,	,	,
cord-221131-44n5pojb	90	51	in	in	IN
cord-221131-44n5pojb	90	52	a	a	DT
cord-221131-44n5pojb	90	53	certain	certain	JJ
cord-221131-44n5pojb	90	54	sense	sense	NN
cord-221131-44n5pojb	90	55	,	,	,
cord-221131-44n5pojb	90	56	not	not	RB
cord-221131-44n5pojb	90	57	independent	independent	JJ
cord-221131-44n5pojb	90	58	on	on	IN
cord-221131-44n5pojb	90	59	the	the	DT
cord-221131-44n5pojb	90	60	values	value	NNS
cord-221131-44n5pojb	90	61	of	of	IN
cord-221131-44n5pojb	90	62	c	c	NN
cord-221131-44n5pojb	90	63	n	n	NN
cord-221131-44n5pojb	90	64	and	and	CC
cord-221131-44n5pojb	90	65	are	be	VBP
cord-221131-44n5pojb	90	66	well	well	RB
cord-221131-44n5pojb	90	67	described	describe	VBN
cord-221131-44n5pojb	90	68	by	by	IN
cord-221131-44n5pojb	90	69	a	a	DT
cord-221131-44n5pojb	90	70	polynomial	polynomial	JJ
cord-221131-44n5pojb	90	71	interpolation	interpolation	NN
cord-221131-44n5pojb	90	72	with	with	IN
cord-221131-44n5pojb	90	73	linear	linear	JJ
cord-221131-44n5pojb	90	74	coefficient	coefficient	NN
cord-221131-44n5pojb	90	75	.	.	.
cord-221131-44n5pojb	91	1	The	the	DT
cord-221131-44n5pojb	91	2	hypothesis	hypothesis	NN
cord-221131-44n5pojb	91	3	about	about	IN
cord-221131-44n5pojb	91	4	the	the	DT
cord-221131-44n5pojb	91	5	scale	scale	NN
cord-221131-44n5pojb	91	6	invariance	invariance	NN
cord-221131-44n5pojb	91	7	of	of	IN
cord-221131-44n5pojb	91	8	the	the	DT
cord-221131-44n5pojb	91	9	underlying	underlying	JJ
cord-221131-44n5pojb	91	10	model	model	NN
cord-221131-44n5pojb	91	11	(	(	-LRB-
cord-221131-44n5pojb	91	12	that	that	DT
cord-221131-44n5pojb	91	13	,	,	,
cord-221131-44n5pojb	91	14	we	-PRON-	PRP
cord-221131-44n5pojb	91	15	repeat	repeat	VBP
cord-221131-44n5pojb	91	16	,	,	,
cord-221131-44n5pojb	91	17	not	not	RB
cord-221131-44n5pojb	91	18	necessarily	necessarily	RB
cord-221131-44n5pojb	91	19	is	be	VBZ
cord-221131-44n5pojb	91	20	represented	represent	VBN
cord-221131-44n5pojb	91	21	by	by	IN
cord-221131-44n5pojb	91	22	the	the	DT
cord-221131-44n5pojb	91	23	SIR	SIR	NNP
cord-221131-44n5pojb	91	24	model	model	NN
cord-221131-44n5pojb	91	25	)	)	-RRB-
cord-221131-44n5pojb	91	26	is	be	VBZ
cord-221131-44n5pojb	91	27	fundamental	fundamental	JJ
cord-221131-44n5pojb	91	28	for	for	IN
cord-221131-44n5pojb	91	29	the	the	DT
cord-221131-44n5pojb	91	30	accuracy	accuracy	NN
cord-221131-44n5pojb	91	31	of	of	IN
cord-221131-44n5pojb	91	32	the	the	DT
cord-221131-44n5pojb	91	33	result	result	NN
cord-221131-44n5pojb	91	34	.	.	.
cord-221131-44n5pojb	92	1	Another	another	DT
cord-221131-44n5pojb	92	2	underlying	underlying	JJ
cord-221131-44n5pojb	92	3	assumption	assumption	NN
cord-221131-44n5pojb	92	4	is	be	VBZ
cord-221131-44n5pojb	92	5	that	that	IN
cord-221131-44n5pojb	92	6	the	the	DT
cord-221131-44n5pojb	92	7	restrictive	restrictive	JJ
cord-221131-44n5pojb	92	8	measures	measure	NNS
cord-221131-44n5pojb	92	9	will	will	MD
cord-221131-44n5pojb	92	10	be	be	VB
cord-221131-44n5pojb	92	11	kept	keep	VBN
cord-221131-44n5pojb	92	12	and	and	CC
cord-221131-44n5pojb	92	13	observed	observe	VBN
cord-221131-44n5pojb	92	14	in	in	IN
cord-221131-44n5pojb	92	15	the	the	DT
cord-221131-44n5pojb	92	16	next	next	JJ
cord-221131-44n5pojb	92	17	days	day	NNS
cord-221131-44n5pojb	92	18	and	and	CC
cord-221131-44n5pojb	92	19	there	there	EX
cord-221131-44n5pojb	92	20	will	will	MD
cord-221131-44n5pojb	92	21	be	be	VB
cord-221131-44n5pojb	92	22	no	no	DT
cord-221131-44n5pojb	92	23	other	other	JJ
cord-221131-44n5pojb	92	24	clusters	cluster	NNS
cord-221131-44n5pojb	92	25	in	in	IN
cord-221131-44n5pojb	92	26	the	the	DT
cord-221131-44n5pojb	92	27	south	south	NN
cord-221131-44n5pojb	92	28	of	of	IN
cord-221131-44n5pojb	92	29	Italy	Italy	NNP
cord-221131-44n5pojb	92	30	(	(	-LRB-
cord-221131-44n5pojb	92	31	in	in	IN
cord-221131-44n5pojb	92	32	the	the	DT
cord-221131-44n5pojb	92	33	SIR	SIR	NNP
cord-221131-44n5pojb	92	34	model	model	NN
cord-221131-44n5pojb	92	35	language	language	NN
cord-221131-44n5pojb	92	36	,	,	,
cord-221131-44n5pojb	92	37	the	the	DT
cord-221131-44n5pojb	92	38	values	value	NNS
cord-221131-44n5pojb	92	39	of	of	IN
cord-221131-44n5pojb	92	40	S	s	NN
cord-221131-44n5pojb	92	41	0	0	CD
cord-221131-44n5pojb	92	42	are	be	VBP
cord-221131-44n5pojb	92	43	below	below	IN
cord-221131-44n5pojb	92	44	the	the	DT
cord-221131-44n5pojb	92	45	epidemic	epidemic	NN
cord-221131-44n5pojb	92	46	threshold	threshold	NN
cord-221131-44n5pojb	92	47	,	,	,
cord-221131-44n5pojb	92	48	see	see	VB
cord-221131-44n5pojb	92	49	e.g.	e.g.	RB
cord-221131-44n5pojb	92	50	[	[	-LRB-
cord-221131-44n5pojb	92	51	11	11	CD
cord-221131-44n5pojb	92	52	]	]	-RRB-
cord-221131-44n5pojb	92	53	)	)	-RRB-
cord-221131-44n5pojb	92	54	.	.	.
cord-221131-44n5pojb	93	1	In	in	IN
cord-221131-44n5pojb	93	2	the	the	DT
cord-221131-44n5pojb	93	3	unfortunate	unfortunate	JJ
cord-221131-44n5pojb	93	4	case	case	NN
cord-221131-44n5pojb	93	5	that	that	IN
cord-221131-44n5pojb	93	6	there	there	EX
cord-221131-44n5pojb	93	7	will	will	MD
cord-221131-44n5pojb	93	8	be	be	VB
cord-221131-44n5pojb	93	9	other	other	JJ
cord-221131-44n5pojb	93	10	clusters	cluster	NNS
cord-221131-44n5pojb	93	11	,	,	,
cord-221131-44n5pojb	93	12	it	-PRON-	PRP
cord-221131-44n5pojb	93	13	is	be	VBZ
cord-221131-44n5pojb	93	14	possible	possible	JJ
cord-221131-44n5pojb	93	15	to	to	TO
cord-221131-44n5pojb	93	16	think	think	VB
cord-221131-44n5pojb	93	17	at	at	IN
cord-221131-44n5pojb	93	18	a	a	DT
cord-221131-44n5pojb	93	19	substitution	substitution	NN
cord-221131-44n5pojb	93	20	of	of	IN
cord-221131-44n5pojb	93	21	the	the	DT
cord-221131-44n5pojb	93	22	tanh	tanh	NN
cord-221131-44n5pojb	93	23	curve	curve	NN
cord-221131-44n5pojb	93	24	by	by	IN
cord-221131-44n5pojb	93	25	a	a	DT
cord-221131-44n5pojb	93	26	combination	combination	NN
cord-221131-44n5pojb	93	27	of	of	IN
cord-221131-44n5pojb	93	28	such	such	JJ
cord-221131-44n5pojb	93	29	functions	function	NNS
cord-221131-44n5pojb	93	30	:	:	:
cord-221131-44n5pojb	93	31	if	if	IN
cord-221131-44n5pojb	93	32	there	there	EX
cord-221131-44n5pojb	93	33	are	be	VBP
cord-221131-44n5pojb	93	34	two	two	CD
cord-221131-44n5pojb	93	35	clusters	cluster	NNS
cord-221131-44n5pojb	93	36	of	of	IN
cord-221131-44n5pojb	93	37	comparable	comparable	JJ
cord-221131-44n5pojb	93	38	magnitude	magnitude	NN
cord-221131-44n5pojb	93	39	,	,	,
cord-221131-44n5pojb	93	40	then	then	RB
cord-221131-44n5pojb	93	41	we	-PRON-	PRP
cord-221131-44n5pojb	93	42	will	will	MD
cord-221131-44n5pojb	93	43	have	have	VB
cord-221131-44n5pojb	93	44	f	f	NNP
cord-221131-44n5pojb	93	45	(	(	-LRB-
cord-221131-44n5pojb	93	46	t	t	NN
cord-221131-44n5pojb	93	47	)	)	-RRB-
cord-221131-44n5pojb	93	48	=	=	NFP
cord-221131-44n5pojb	94	1	α	α	NN
cord-221131-44n5pojb	94	2	1	1	CD
cord-221131-44n5pojb	94	3	tanh(β	tanh(β	NNP
cord-221131-44n5pojb	94	4	1	1	CD
cord-221131-44n5pojb	94	5	t	t	NN
cord-221131-44n5pojb	94	6	−	−	NN
cord-221131-44n5pojb	94	7	c	c	NN
cord-221131-44n5pojb	94	8	1	1	CD
cord-221131-44n5pojb	94	9	)	)	-RRB-
cord-221131-44n5pojb	94	10	+	+	CC
cord-221131-44n5pojb	94	11	α	α	NN
cord-221131-44n5pojb	94	12	1	1	CD
cord-221131-44n5pojb	94	13	tanh(c	tanh(c	JJ
cord-221131-44n5pojb	94	14	1	1	CD
cord-221131-44n5pojb	94	15	)	)	-RRB-
cord-221131-44n5pojb	94	16	+	+	CC
cord-221131-44n5pojb	94	17	α	α	NN
cord-221131-44n5pojb	94	18	2	2	CD
cord-221131-44n5pojb	94	19	tanh(β	tanh(β	NNP
cord-221131-44n5pojb	94	20	2	2	CD
cord-221131-44n5pojb	94	21	t	t	NN
cord-221131-44n5pojb	94	22	−	−	NN
cord-221131-44n5pojb	94	23	c	c	NN
cord-221131-44n5pojb	94	24	2	2	CD
cord-221131-44n5pojb	94	25	)	)	-RRB-
cord-221131-44n5pojb	94	26	+	+	CC
cord-221131-44n5pojb	94	27	α	α	NN
cord-221131-44n5pojb	94	28	2	2	CD
cord-221131-44n5pojb	94	29	tanh(c	tanh(c	CD
cord-221131-44n5pojb	94	30	2	2	CD
cord-221131-44n5pojb	94	31	)	)	-RRB-
cord-221131-44n5pojb	95	1	In	in	IN
cord-221131-44n5pojb	95	2	a	a	DT
cord-221131-44n5pojb	95	3	next	next	JJ
cord-221131-44n5pojb	95	4	paper	paper	NN
cord-221131-44n5pojb	95	5	other	other	JJ
cord-221131-44n5pojb	95	6	sets	set	NNS
cord-221131-44n5pojb	95	7	of	of	IN
cord-221131-44n5pojb	95	8	data	datum	NNS
cord-221131-44n5pojb	95	9	will	will	MD
cord-221131-44n5pojb	95	10	be	be	VB
cord-221131-44n5pojb	95	11	analyzed	analyze	VBN
cord-221131-44n5pojb	95	12	,	,	,
cord-221131-44n5pojb	95	13	whereas	whereas	IN
cord-221131-44n5pojb	95	14	the	the	DT
cord-221131-44n5pojb	95	15	above	above	JJ
cord-221131-44n5pojb	95	16	analysis	analysis	NN
cord-221131-44n5pojb	95	17	will	will	MD
cord-221131-44n5pojb	95	18	be	be	VB
cord-221131-44n5pojb	95	19	updated	update	VBN
cord-221131-44n5pojb	95	20	if	if	IN
cord-221131-44n5pojb	95	21	necessary	necessary	JJ
cord-221131-44n5pojb	95	22	.	.	.
cord-221131-44n5pojb	96	1	Coronavirus	Coronavirus	NNP
cord-221131-44n5pojb	96	2	and	and	CC
cord-221131-44n5pojb	96	3	oil	oil	NN
cord-221131-44n5pojb	96	4	price	price	NN
cord-221131-44n5pojb	96	5	crash	crash	NN
cord-221131-44n5pojb	96	6	Differential	Differential	NNP
cord-221131-44n5pojb	96	7	Equations	Equations	NNPS
cord-221131-44n5pojb	96	8	and	and	CC
cord-221131-44n5pojb	96	9	Their	-PRON-	PRP$
cord-221131-44n5pojb	96	10	Applications	application	NNS
cord-221131-44n5pojb	96	11	:	:	:
cord-221131-44n5pojb	97	1	An	an	DT
cord-221131-44n5pojb	97	2	Introduction	introduction	NN
cord-221131-44n5pojb	97	3	to	to	IN
cord-221131-44n5pojb	97	4	Applied	Applied	NNP
cord-221131-44n5pojb	97	5	Mathematics	Mathematics	NNP
cord-221131-44n5pojb	97	6	Early	Early	NNP
cord-221131-44n5pojb	97	7	phylogenetic	phylogenetic	JJ
cord-221131-44n5pojb	97	8	estimate	estimate	NN
cord-221131-44n5pojb	97	9	of	of	IN
cord-221131-44n5pojb	97	10	the	the	DT
cord-221131-44n5pojb	97	11	effective	effective	JJ
cord-221131-44n5pojb	97	12	reproduction	reproduction	NN
cord-221131-44n5pojb	97	13	number	number	NN
cord-221131-44n5pojb	97	14	of	of	IN
cord-221131-44n5pojb	97	15	SARSCoV2	SARSCoV2	NNP
cord-221131-44n5pojb	97	16	Analysis	Analysis	NNP
cord-221131-44n5pojb	97	17	and	and	CC
cord-221131-44n5pojb	97	18	forecast	forecast	NN
cord-221131-44n5pojb	97	19	of	of	IN
cord-221131-44n5pojb	97	20	COVID-19	COVID-19	NNP
cord-221131-44n5pojb	97	21	spreading	spreading	NN
cord-221131-44n5pojb	97	22	in	in	IN
cord-221131-44n5pojb	97	23	China	China	NNP
cord-221131-44n5pojb	97	24	Weifeng	Weifeng	NNP
cord-221131-44n5pojb	97	25	Lv	Lv	NNP
cord-221131-44n5pojb	97	26	:	:	:
cord-221131-44n5pojb	98	1	High	high	JJ
cord-221131-44n5pojb	98	2	Temperature	temperature	NN
cord-221131-44n5pojb	98	3	and	and	CC
cord-221131-44n5pojb	98	4	High	high	JJ
cord-221131-44n5pojb	98	5	Humidity	humidity	NN
cord-221131-44n5pojb	98	6	Reduce	reduce	VBP
cord-221131-44n5pojb	98	7	the	the	DT
cord-221131-44n5pojb	98	8	Transmission	Transmission	NNP
cord-221131-44n5pojb	98	9	of	of	IN
cord-221131-44n5pojb	98	10	COVID-19	COVID-19	NNP
cord-221131-44n5pojb	98	11	Early	early	JJ
cord-221131-44n5pojb	98	12	dynamics	dynamic	NNS
cord-221131-44n5pojb	98	13	of	of	IN
cord-221131-44n5pojb	98	14	transmission	transmission	NN
cord-221131-44n5pojb	98	15	and	and	CC
cord-221131-44n5pojb	98	16	control	control	NN
cord-221131-44n5pojb	98	17	of	of	IN
cord-221131-44n5pojb	98	18	COVID-19	COVID-19	NNP
cord-221131-44n5pojb	98	19	:	:	:
cord-221131-44n5pojb	98	20	a	a	DT
cord-221131-44n5pojb	98	21	mathematical	mathematical	JJ
cord-221131-44n5pojb	98	22	modelling	modelling	NN
cord-221131-44n5pojb	98	23	study	study	NN
cord-221131-44n5pojb	99	1	A	a	DT
cord-221131-44n5pojb	99	2	Contribution	contribution	NN
cord-221131-44n5pojb	99	3	to	to	IN
cord-221131-44n5pojb	99	4	the	the	DT
cord-221131-44n5pojb	99	5	Mathematical	Mathematical	NNP
cord-221131-44n5pojb	99	6	Theory	Theory	NNP
cord-221131-44n5pojb	99	7	of	of	IN
cord-221131-44n5pojb	99	8	Epidemics	Epidemics	NNP
cord-221131-44n5pojb	99	9	Data	Data	NNP
cord-221131-44n5pojb	99	10	analysis	analysis	NN
cord-221131-44n5pojb	99	11	for	for	IN
cord-221131-44n5pojb	99	12	the	the	DT
cord-221131-44n5pojb	99	13	COVID-19	COVID-19	NNP
cord-221131-44n5pojb	99	14	early	early	JJ
cord-221131-44n5pojb	99	15	dynamics	dynamic	NNS
cord-221131-44n5pojb	99	16	in	in	IN
cord-221131-44n5pojb	99	17	Northern	Northern	NNP
cord-221131-44n5pojb	99	18	Italy	Italy	NNP
cord-221131-44n5pojb	99	19	Data	Data	NNP
cord-221131-44n5pojb	99	20	Analysis	Analysis	NNP
cord-221131-44n5pojb	99	21	for	for	IN
cord-221131-44n5pojb	99	22	the	the	DT
cord-221131-44n5pojb	99	23	COVID-19	covid-19	JJ
cord-221131-44n5pojb	99	24	early	early	JJ
cord-221131-44n5pojb	99	25	dynamics	dynamic	NNS
cord-221131-44n5pojb	99	26	in	in	IN
cord-221131-44n5pojb	99	27	Northern	Northern	NNP
cord-221131-44n5pojb	99	28	Italy	Italy	NNP
cord-221131-44n5pojb	99	29	.	.	.
cord-221131-44n5pojb	100	1	The	the	DT
cord-221131-44n5pojb	100	2	effect	effect	NN
cord-221131-44n5pojb	100	3	of	of	IN
cord-221131-44n5pojb	100	4	first	first	JJ
cord-221131-44n5pojb	100	5	restrictive	restrictive	JJ
cord-221131-44n5pojb	100	6	measures	measure	NNS
cord-221131-44n5pojb	100	7	Modelling	modelling	NN
cord-221131-44n5pojb	100	8	and	and	CC
cord-221131-44n5pojb	100	9	predicting	predict	VBG
cord-221131-44n5pojb	100	10	the	the	DT
cord-221131-44n5pojb	100	11	spatio	spatio	JJ
cord-221131-44n5pojb	100	12	-	-	HYPH
cord-221131-44n5pojb	100	13	temporal	temporal	JJ
cord-221131-44n5pojb	100	14	spread	spread	NN
cord-221131-44n5pojb	100	15	of	of	IN
cord-221131-44n5pojb	100	16	Coronavirus	Coronavirus	NNP
cord-221131-44n5pojb	100	17	disease	disease	NN
cord-221131-44n5pojb	100	18	2019	2019	CD
cord-221131-44n5pojb	100	19	(	(	-LRB-
cord-221131-44n5pojb	100	20	COVID-19	COVID-19	NNP
cord-221131-44n5pojb	100	21	)	)	-RRB-
cord-221131-44n5pojb	100	22	in	in	IN
cord-221131-44n5pojb	100	23	Italy	Italy	NNP