id sid tid token lemma pos cord-272759-dqkjofw2 1 1 key key NN cord-272759-dqkjofw2 1 2 : : : cord-272759-dqkjofw2 1 3 cord-272759-dqkjofw2 cord-272759-dqkjofw2 NNP cord-272759-dqkjofw2 1 4 authors author NNS cord-272759-dqkjofw2 1 5 : : : cord-272759-dqkjofw2 1 6 Small small JJ cord-272759-dqkjofw2 1 7 , , , cord-272759-dqkjofw2 1 8 Michael Michael NNP cord-272759-dqkjofw2 1 9 ; ; : cord-272759-dqkjofw2 1 10 Tse Tse NNP cord-272759-dqkjofw2 1 11 , , , cord-272759-dqkjofw2 1 12 C.K. C.K. NNP cord-272759-dqkjofw2 1 13 ; ; : cord-272759-dqkjofw2 1 14 Walker Walker NNP cord-272759-dqkjofw2 1 15 , , , cord-272759-dqkjofw2 1 16 David David NNP cord-272759-dqkjofw2 1 17 M. M. NNP cord-272759-dqkjofw2 2 1 title title NN cord-272759-dqkjofw2 2 2 : : : cord-272759-dqkjofw2 2 3 Super Super NNP cord-272759-dqkjofw2 2 4 - - NNS cord-272759-dqkjofw2 2 5 spreaders spreader NNS cord-272759-dqkjofw2 2 6 and and CC cord-272759-dqkjofw2 2 7 the the DT cord-272759-dqkjofw2 2 8 rate rate NN cord-272759-dqkjofw2 2 9 of of IN cord-272759-dqkjofw2 2 10 transmission transmission NN cord-272759-dqkjofw2 2 11 of of IN cord-272759-dqkjofw2 2 12 the the DT cord-272759-dqkjofw2 2 13 SARS SARS NNP cord-272759-dqkjofw2 2 14 virus virus NN cord-272759-dqkjofw2 2 15 date date NN cord-272759-dqkjofw2 2 16 : : : cord-272759-dqkjofw2 2 17 2006 2006 CD cord-272759-dqkjofw2 2 18 - - HYPH cord-272759-dqkjofw2 2 19 03 03 CD cord-272759-dqkjofw2 2 20 - - SYM cord-272759-dqkjofw2 2 21 15 15 CD cord-272759-dqkjofw2 2 22 journal journal NN cord-272759-dqkjofw2 2 23 : : : cord-272759-dqkjofw2 3 1 Physica Physica NNP cord-272759-dqkjofw2 3 2 D d NN cord-272759-dqkjofw2 3 3 DOI doi NN cord-272759-dqkjofw2 3 4 : : : cord-272759-dqkjofw2 4 1 10.1016 10.1016 CD cord-272759-dqkjofw2 4 2 / / SYM cord-272759-dqkjofw2 4 3 j.physd.2006.01.021 j.physd.2006.01.021 NNP cord-272759-dqkjofw2 4 4 sha sha NNP cord-272759-dqkjofw2 4 5 : : : cord-272759-dqkjofw2 5 1 686b26eb6b82e3a316edbb6625b2f10836165367 686b26eb6b82e3a316edbb6625b2f10836165367 NNP cord-272759-dqkjofw2 5 2 doc_id doc_id CD cord-272759-dqkjofw2 6 1 : : : cord-272759-dqkjofw2 6 2 272759 272759 CD cord-272759-dqkjofw2 6 3 cord_uid cord_uid NNS cord-272759-dqkjofw2 6 4 : : : cord-272759-dqkjofw2 7 1 dqkjofw2 dqkjofw2 NN cord-272759-dqkjofw2 8 1 We -PRON- PRP cord-272759-dqkjofw2 8 2 describe describe VBP cord-272759-dqkjofw2 8 3 a a DT cord-272759-dqkjofw2 8 4 stochastic stochastic JJ cord-272759-dqkjofw2 8 5 small small JJ cord-272759-dqkjofw2 8 6 - - HYPH cord-272759-dqkjofw2 8 7 world world NN cord-272759-dqkjofw2 8 8 network network NN cord-272759-dqkjofw2 8 9 model model NN cord-272759-dqkjofw2 8 10 of of IN cord-272759-dqkjofw2 8 11 transmission transmission NN cord-272759-dqkjofw2 8 12 of of IN cord-272759-dqkjofw2 8 13 the the DT cord-272759-dqkjofw2 8 14 SARS SARS NNP cord-272759-dqkjofw2 8 15 virus virus NN cord-272759-dqkjofw2 8 16 . . . cord-272759-dqkjofw2 9 1 Unlike unlike IN cord-272759-dqkjofw2 9 2 the the DT cord-272759-dqkjofw2 9 3 standard standard JJ cord-272759-dqkjofw2 9 4 Susceptible susceptible JJ cord-272759-dqkjofw2 9 5 - - HYPH cord-272759-dqkjofw2 9 6 Infected Infected NNP cord-272759-dqkjofw2 9 7 - - HYPH cord-272759-dqkjofw2 9 8 Removed remove VBN cord-272759-dqkjofw2 9 9 models model NNS cord-272759-dqkjofw2 9 10 of of IN cord-272759-dqkjofw2 9 11 disease disease NN cord-272759-dqkjofw2 9 12 transmission transmission NN cord-272759-dqkjofw2 9 13 , , , cord-272759-dqkjofw2 9 14 our -PRON- PRP$ cord-272759-dqkjofw2 9 15 model model NN cord-272759-dqkjofw2 9 16 exhibits exhibit VBZ cord-272759-dqkjofw2 9 17 both both DT cord-272759-dqkjofw2 9 18 geographically geographically RB cord-272759-dqkjofw2 9 19 localised localised JJ cord-272759-dqkjofw2 9 20 outbreaks outbreak NNS cord-272759-dqkjofw2 9 21 and and CC cord-272759-dqkjofw2 9 22 “ " `` cord-272759-dqkjofw2 9 23 super super JJ cord-272759-dqkjofw2 9 24 - - NNS cord-272759-dqkjofw2 9 25 spreaders spreader NNS cord-272759-dqkjofw2 9 26 ” " '' cord-272759-dqkjofw2 9 27 . . . cord-272759-dqkjofw2 10 1 Moreover moreover RB cord-272759-dqkjofw2 10 2 , , , cord-272759-dqkjofw2 10 3 the the DT cord-272759-dqkjofw2 10 4 combination combination NN cord-272759-dqkjofw2 10 5 of of IN cord-272759-dqkjofw2 10 6 localised localised JJ cord-272759-dqkjofw2 10 7 and and CC cord-272759-dqkjofw2 10 8 long long JJ cord-272759-dqkjofw2 10 9 range range NN cord-272759-dqkjofw2 10 10 links link NNS cord-272759-dqkjofw2 10 11 allows allow VBZ cord-272759-dqkjofw2 10 12 for for IN cord-272759-dqkjofw2 10 13 more more RBR cord-272759-dqkjofw2 10 14 accurate accurate JJ cord-272759-dqkjofw2 10 15 modelling modelling NN cord-272759-dqkjofw2 10 16 of of IN cord-272759-dqkjofw2 10 17 partial partial JJ cord-272759-dqkjofw2 10 18 isolation isolation NN cord-272759-dqkjofw2 10 19 and and CC cord-272759-dqkjofw2 10 20 various various JJ cord-272759-dqkjofw2 10 21 public public JJ cord-272759-dqkjofw2 10 22 health health NN cord-272759-dqkjofw2 10 23 policies policy NNS cord-272759-dqkjofw2 10 24 . . . cord-272759-dqkjofw2 11 1 From from IN cord-272759-dqkjofw2 11 2 this this DT cord-272759-dqkjofw2 11 3 model model NN cord-272759-dqkjofw2 11 4 , , , cord-272759-dqkjofw2 11 5 we -PRON- PRP cord-272759-dqkjofw2 11 6 derive derive VBP cord-272759-dqkjofw2 11 7 an an DT cord-272759-dqkjofw2 11 8 expression expression NN cord-272759-dqkjofw2 11 9 for for IN cord-272759-dqkjofw2 11 10 the the DT cord-272759-dqkjofw2 11 11 probability probability NN cord-272759-dqkjofw2 11 12 of of IN cord-272759-dqkjofw2 11 13 a a DT cord-272759-dqkjofw2 11 14 widespread widespread JJ cord-272759-dqkjofw2 11 15 outbreak outbreak NN cord-272759-dqkjofw2 11 16 and and CC cord-272759-dqkjofw2 11 17 a a DT cord-272759-dqkjofw2 11 18 condition condition NN cord-272759-dqkjofw2 11 19 to to TO cord-272759-dqkjofw2 11 20 ensure ensure VB cord-272759-dqkjofw2 11 21 that that IN cord-272759-dqkjofw2 11 22 the the DT cord-272759-dqkjofw2 11 23 epidemic epidemic NN cord-272759-dqkjofw2 11 24 is be VBZ cord-272759-dqkjofw2 11 25 controlled control VBN cord-272759-dqkjofw2 11 26 . . . cord-272759-dqkjofw2 12 1 Moreover moreover RB cord-272759-dqkjofw2 12 2 , , , cord-272759-dqkjofw2 12 3 multiple multiple JJ cord-272759-dqkjofw2 12 4 simulations simulation NNS cord-272759-dqkjofw2 12 5 are be VBP cord-272759-dqkjofw2 12 6 used use VBN cord-272759-dqkjofw2 12 7 to to TO cord-272759-dqkjofw2 12 8 make make VB cord-272759-dqkjofw2 12 9 predictions prediction NNS cord-272759-dqkjofw2 12 10 of of IN cord-272759-dqkjofw2 12 11 the the DT cord-272759-dqkjofw2 12 12 likelihood likelihood NN cord-272759-dqkjofw2 12 13 of of IN cord-272759-dqkjofw2 12 14 various various JJ cord-272759-dqkjofw2 12 15 eventual eventual JJ cord-272759-dqkjofw2 12 16 scenarios scenario NNS cord-272759-dqkjofw2 12 17 for for IN cord-272759-dqkjofw2 12 18 fixed fix VBN cord-272759-dqkjofw2 12 19 initial initial JJ cord-272759-dqkjofw2 12 20 conditions condition NNS cord-272759-dqkjofw2 12 21 . . . cord-272759-dqkjofw2 13 1 The the DT cord-272759-dqkjofw2 13 2 main main JJ cord-272759-dqkjofw2 13 3 conclusions conclusion NNS cord-272759-dqkjofw2 13 4 of of IN cord-272759-dqkjofw2 13 5 this this DT cord-272759-dqkjofw2 13 6 study study NN cord-272759-dqkjofw2 13 7 are be VBP cord-272759-dqkjofw2 13 8 : : : cord-272759-dqkjofw2 14 1 ( ( -LRB- cord-272759-dqkjofw2 14 2 i i NN cord-272759-dqkjofw2 14 3 ) ) -RRB- cord-272759-dqkjofw2 14 4 “ " `` cord-272759-dqkjofw2 14 5 super super JJ cord-272759-dqkjofw2 14 6 - - NNS cord-272759-dqkjofw2 14 7 spreaders spreader NNS cord-272759-dqkjofw2 14 8 ” " '' cord-272759-dqkjofw2 14 9 may may MD cord-272759-dqkjofw2 14 10 occur occur VB cord-272759-dqkjofw2 14 11 even even RB cord-272759-dqkjofw2 14 12 if if IN cord-272759-dqkjofw2 14 13 the the DT cord-272759-dqkjofw2 14 14 infectiousness infectiousness NN cord-272759-dqkjofw2 14 15 of of IN cord-272759-dqkjofw2 14 16 all all DT cord-272759-dqkjofw2 14 17 infected infect VBN cord-272759-dqkjofw2 14 18 individuals individual NNS cord-272759-dqkjofw2 14 19 is be VBZ cord-272759-dqkjofw2 14 20 constant constant JJ cord-272759-dqkjofw2 14 21 ; ; , cord-272759-dqkjofw2 14 22 ( ( -LRB- cord-272759-dqkjofw2 14 23 ii ii NN cord-272759-dqkjofw2 14 24 ) ) -RRB- cord-272759-dqkjofw2 14 25 consistent consistent JJ cord-272759-dqkjofw2 14 26 with with IN cord-272759-dqkjofw2 14 27 previous previous JJ cord-272759-dqkjofw2 14 28 reports report NNS cord-272759-dqkjofw2 14 29 , , , cord-272759-dqkjofw2 14 30 extended extended JJ cord-272759-dqkjofw2 14 31 exposure exposure NN cord-272759-dqkjofw2 14 32 time time NN cord-272759-dqkjofw2 14 33 beyond beyond IN cord-272759-dqkjofw2 14 34 3–5 3–5 CD cord-272759-dqkjofw2 14 35 days day NNS cord-272759-dqkjofw2 14 36 ( ( -LRB- cord-272759-dqkjofw2 14 37 i.e. i.e. FW cord-272759-dqkjofw2 14 38 significant significant JJ cord-272759-dqkjofw2 14 39 nosocomial nosocomial JJ cord-272759-dqkjofw2 14 40 transmission transmission NN cord-272759-dqkjofw2 14 41 ) ) -RRB- cord-272759-dqkjofw2 14 42 was be VBD cord-272759-dqkjofw2 14 43 the the DT cord-272759-dqkjofw2 14 44 key key JJ cord-272759-dqkjofw2 14 45 factor factor NN cord-272759-dqkjofw2 14 46 in in IN cord-272759-dqkjofw2 14 47 the the DT cord-272759-dqkjofw2 14 48 severity severity NN cord-272759-dqkjofw2 14 49 of of IN cord-272759-dqkjofw2 14 50 the the DT cord-272759-dqkjofw2 14 51 SARS SARS NNP cord-272759-dqkjofw2 14 52 outbreak outbreak NN cord-272759-dqkjofw2 14 53 in in IN cord-272759-dqkjofw2 14 54 Hong Hong NNP cord-272759-dqkjofw2 14 55 Kong Kong NNP cord-272759-dqkjofw2 14 56 ; ; : cord-272759-dqkjofw2 14 57 and and CC cord-272759-dqkjofw2 14 58 , , , cord-272759-dqkjofw2 14 59 ( ( -LRB- cord-272759-dqkjofw2 14 60 iii iii NN cord-272759-dqkjofw2 14 61 ) ) -RRB- cord-272759-dqkjofw2 15 1 the the DT cord-272759-dqkjofw2 15 2 spread spread NN cord-272759-dqkjofw2 15 3 of of IN cord-272759-dqkjofw2 15 4 SARS SARS NNP cord-272759-dqkjofw2 15 5 can can MD cord-272759-dqkjofw2 15 6 be be VB cord-272759-dqkjofw2 15 7 effectively effectively RB cord-272759-dqkjofw2 15 8 controlled control VBN cord-272759-dqkjofw2 15 9 by by IN cord-272759-dqkjofw2 15 10 either either DT cord-272759-dqkjofw2 15 11 limiting limit VBG cord-272759-dqkjofw2 15 12 long long JJ cord-272759-dqkjofw2 15 13 range range NN cord-272759-dqkjofw2 15 14 links link NNS cord-272759-dqkjofw2 15 15 ( ( -LRB- cord-272759-dqkjofw2 15 16 imposing impose VBG cord-272759-dqkjofw2 15 17 a a DT cord-272759-dqkjofw2 15 18 partial partial JJ cord-272759-dqkjofw2 15 19 quarantine quarantine NN cord-272759-dqkjofw2 15 20 ) ) -RRB- cord-272759-dqkjofw2 15 21 or or CC cord-272759-dqkjofw2 15 22 enforcing enforce VBG cord-272759-dqkjofw2 15 23 rapid rapid JJ cord-272759-dqkjofw2 15 24 hospitalisation hospitalisation NN cord-272759-dqkjofw2 15 25 and and CC cord-272759-dqkjofw2 15 26 isolation isolation NN cord-272759-dqkjofw2 15 27 of of IN cord-272759-dqkjofw2 15 28 symptomatic symptomatic JJ cord-272759-dqkjofw2 15 29 individuals individual NNS cord-272759-dqkjofw2 15 30 . . . cord-272759-dqkjofw2 16 1 The the DT cord-272759-dqkjofw2 16 2 SARS SARS NNP cord-272759-dqkjofw2 16 3 virus virus NN cord-272759-dqkjofw2 16 4 first first RB cord-272759-dqkjofw2 16 5 appeared appear VBD cord-272759-dqkjofw2 16 6 during during IN cord-272759-dqkjofw2 16 7 October October NNP cord-272759-dqkjofw2 16 8 2002 2002 CD cord-272759-dqkjofw2 16 9 in in IN cord-272759-dqkjofw2 16 10 the the DT cord-272759-dqkjofw2 16 11 Guangdong Guangdong NNP cord-272759-dqkjofw2 16 12 province province NN cord-272759-dqkjofw2 16 13 of of IN cord-272759-dqkjofw2 16 14 southern southern JJ cord-272759-dqkjofw2 16 15 China China NNP cord-272759-dqkjofw2 16 16 . . . cord-272759-dqkjofw2 17 1 It -PRON- PRP cord-272759-dqkjofw2 17 2 then then RB cord-272759-dqkjofw2 17 3 passed pass VBD cord-272759-dqkjofw2 17 4 over over RP cord-272759-dqkjofw2 17 5 the the DT cord-272759-dqkjofw2 17 6 border border NN cord-272759-dqkjofw2 17 7 to to IN cord-272759-dqkjofw2 17 8 Hong Hong NNP cord-272759-dqkjofw2 17 9 Kong Kong NNP cord-272759-dqkjofw2 17 10 and and CC cord-272759-dqkjofw2 17 11 from from IN cord-272759-dqkjofw2 17 12 there there EX cord-272759-dqkjofw2 17 13 spread spread VBN cord-272759-dqkjofw2 17 14 to to IN cord-272759-dqkjofw2 17 15 Europe Europe NNP cord-272759-dqkjofw2 17 16 , , , cord-272759-dqkjofw2 17 17 Africa Africa NNP cord-272759-dqkjofw2 17 18 , , , cord-272759-dqkjofw2 17 19 Asia Asia NNP cord-272759-dqkjofw2 17 20 , , , cord-272759-dqkjofw2 17 21 Australia Australia NNP cord-272759-dqkjofw2 17 22 and and CC cord-272759-dqkjofw2 17 23 the the DT cord-272759-dqkjofw2 17 24 Americas Americas NNPS cord-272759-dqkjofw2 17 25 [ [ -LRB- cord-272759-dqkjofw2 17 26 1 1 CD cord-272759-dqkjofw2 17 27 ] ] -RRB- cord-272759-dqkjofw2 17 28 . . . cord-272759-dqkjofw2 18 1 The the DT cord-272759-dqkjofw2 18 2 outbreak outbreak NN cord-272759-dqkjofw2 18 3 in in IN cord-272759-dqkjofw2 18 4 2003 2003 CD cord-272759-dqkjofw2 18 5 infected infected JJ cord-272759-dqkjofw2 18 6 8422 8422 CD cord-272759-dqkjofw2 18 7 , , , cord-272759-dqkjofw2 18 8 killing kill VBG cord-272759-dqkjofw2 18 9 916 916 CD cord-272759-dqkjofw2 18 10 [ [ -LRB- cord-272759-dqkjofw2 18 11 2 2 CD cord-272759-dqkjofw2 18 12 ] ] -RRB- cord-272759-dqkjofw2 18 13 . . . cord-272759-dqkjofw2 19 1 In in IN cord-272759-dqkjofw2 19 2 this this DT cord-272759-dqkjofw2 19 3 paper paper NN cord-272759-dqkjofw2 19 4 we -PRON- PRP cord-272759-dqkjofw2 19 5 focus focus VBP cord-272759-dqkjofw2 19 6 on on IN cord-272759-dqkjofw2 19 7 modelling model VBG cord-272759-dqkjofw2 19 8 the the DT cord-272759-dqkjofw2 19 9 transmission transmission NN cord-272759-dqkjofw2 19 10 of of IN cord-272759-dqkjofw2 19 11 SARS SARS NNP cord-272759-dqkjofw2 19 12 within within IN cord-272759-dqkjofw2 19 13 Hong Hong NNP cord-272759-dqkjofw2 19 14 Kong Kong NNP cord-272759-dqkjofw2 19 15 . . . cord-272759-dqkjofw2 20 1 Beside beside IN cord-272759-dqkjofw2 20 2 mainland mainland NN cord-272759-dqkjofw2 20 3 China China NNP cord-272759-dqkjofw2 20 4 , , , cord-272759-dqkjofw2 20 5 Hong Hong NNP cord-272759-dqkjofw2 20 6 Kong Kong NNP cord-272759-dqkjofw2 20 7 suffered suffer VBD cord-272759-dqkjofw2 20 8 the the DT cord-272759-dqkjofw2 20 9 greatest great JJS cord-272759-dqkjofw2 20 10 casualties casualty NNS cord-272759-dqkjofw2 20 11 [ [ -LRB- cord-272759-dqkjofw2 20 12 2 2 CD cord-272759-dqkjofw2 20 13 ] ] -RRB- cord-272759-dqkjofw2 20 14 . . . cord-272759-dqkjofw2 21 1 In in IN cord-272759-dqkjofw2 21 2 addition addition NN cord-272759-dqkjofw2 21 3 , , , cord-272759-dqkjofw2 21 4 the the DT cord-272759-dqkjofw2 21 5 epidemiological epidemiological JJ cord-272759-dqkjofw2 21 6 data datum NNS cord-272759-dqkjofw2 21 7 currently currently RB cord-272759-dqkjofw2 21 8 available available JJ cord-272759-dqkjofw2 21 9 for for IN cord-272759-dqkjofw2 21 10 Hong Hong NNP cord-272759-dqkjofw2 21 11 Kong Kong NNP cord-272759-dqkjofw2 21 12 is be VBZ cord-272759-dqkjofw2 21 13 far far RB cord-272759-dqkjofw2 21 14 superior superior JJ cord-272759-dqkjofw2 21 15 to to IN cord-272759-dqkjofw2 21 16 that that DT cord-272759-dqkjofw2 21 17 of of IN cord-272759-dqkjofw2 21 18 the the DT cord-272759-dqkjofw2 21 19 Chinese chinese JJ cord-272759-dqkjofw2 21 20 mainland mainland NN cord-272759-dqkjofw2 21 21 . . . cord-272759-dqkjofw2 22 1 1 1 LS cord-272759-dqkjofw2 23 1 Two two CD cord-272759-dqkjofw2 23 2 characteristic characteristic JJ cord-272759-dqkjofw2 23 3 features feature NNS cord-272759-dqkjofw2 23 4 were be VBD cord-272759-dqkjofw2 23 5 observed observe VBN cord-272759-dqkjofw2 23 6 during during IN cord-272759-dqkjofw2 23 7 the the DT cord-272759-dqkjofw2 23 8 SARS SARS NNP cord-272759-dqkjofw2 23 9 outbreak outbreak NN cord-272759-dqkjofw2 23 10 in in IN cord-272759-dqkjofw2 23 11 Hong Hong NNP cord-272759-dqkjofw2 23 12 Kong Kong NNP cord-272759-dqkjofw2 23 13 in in IN cord-272759-dqkjofw2 23 14 2003 2003 CD cord-272759-dqkjofw2 23 15 ( ( -LRB- cord-272759-dqkjofw2 23 16 see see VB cord-272759-dqkjofw2 23 17 Fig Fig NNP cord-272759-dqkjofw2 23 18 . . NNP cord-272759-dqkjofw2 23 19 1 1 CD cord-272759-dqkjofw2 23 20 ) ) -RRB- cord-272759-dqkjofw2 24 1 [ [ -LRB- cord-272759-dqkjofw2 24 2 3 3 CD cord-272759-dqkjofw2 24 3 , , , cord-272759-dqkjofw2 24 4 4 4 CD cord-272759-dqkjofw2 24 5 ] ] -RRB- cord-272759-dqkjofw2 24 6 : : : cord-272759-dqkjofw2 24 7 so so RB cord-272759-dqkjofw2 24 8 - - HYPH cord-272759-dqkjofw2 24 9 called call VBN cord-272759-dqkjofw2 24 10 super super RB cord-272759-dqkjofw2 24 11 - - JJ cord-272759-dqkjofw2 24 12 spread spread JJ cord-272759-dqkjofw2 24 13 events event NNS cord-272759-dqkjofw2 24 14 ( ( -LRB- cord-272759-dqkjofw2 24 15 SSE SSE NNP cord-272759-dqkjofw2 24 16 ) ) -RRB- cord-272759-dqkjofw2 24 17 , , , cord-272759-dqkjofw2 24 18 in in IN cord-272759-dqkjofw2 24 19 which which WDT cord-272759-dqkjofw2 24 20 a a DT cord-272759-dqkjofw2 24 21 single single JJ cord-272759-dqkjofw2 24 22 individual individual NN cord-272759-dqkjofw2 24 23 initiates initiate VBZ cord-272759-dqkjofw2 24 24 a a DT cord-272759-dqkjofw2 24 25 large large JJ cord-272759-dqkjofw2 24 26 number number NN cord-272759-dqkjofw2 24 27 of of IN cord-272759-dqkjofw2 24 28 cases case NNS cord-272759-dqkjofw2 24 29 ; ; : cord-272759-dqkjofw2 24 30 and and CC cord-272759-dqkjofw2 24 31 persistent persistent JJ cord-272759-dqkjofw2 24 32 transmission transmission NN cord-272759-dqkjofw2 24 33 within within IN cord-272759-dqkjofw2 24 34 the the DT cord-272759-dqkjofw2 24 35 community community NN cord-272759-dqkjofw2 24 36 . . . cord-272759-dqkjofw2 25 1 Two two CD cord-272759-dqkjofw2 25 2 widely widely RB cord-272759-dqkjofw2 25 3 cited cite VBN cord-272759-dqkjofw2 25 4 SSEs sse NNS cord-272759-dqkjofw2 25 5 were be VBD cord-272759-dqkjofw2 25 6 observed observe VBN cord-272759-dqkjofw2 25 7 early early RB cord-272759-dqkjofw2 25 8 in in IN cord-272759-dqkjofw2 25 9 the the DT cord-272759-dqkjofw2 25 10 epidemic epidemic NN cord-272759-dqkjofw2 25 11 and and CC cord-272759-dqkjofw2 25 12 have have VBP cord-272759-dqkjofw2 25 13 been be VBN cord-272759-dqkjofw2 25 14 the the DT cord-272759-dqkjofw2 25 15 subject subject NN cord-272759-dqkjofw2 25 16 of of IN cord-272759-dqkjofw2 25 17 much much JJ cord-272759-dqkjofw2 25 18 attention attention NN cord-272759-dqkjofw2 25 19 : : : cord-272759-dqkjofw2 25 20 at at IN cord-272759-dqkjofw2 25 21 the the DT cord-272759-dqkjofw2 25 22 Amoy Amoy NNP cord-272759-dqkjofw2 25 23 Gardens Gardens NNPS cord-272759-dqkjofw2 25 24 housing housing NN cord-272759-dqkjofw2 25 25 estate estate NN cord-272759-dqkjofw2 25 26 and and CC cord-272759-dqkjofw2 25 27 at at IN cord-272759-dqkjofw2 25 28 the the DT cord-272759-dqkjofw2 25 29 Prince Prince NNP cord-272759-dqkjofw2 25 30 of of IN cord-272759-dqkjofw2 25 31 Wales Wales NNP cord-272759-dqkjofw2 25 32 hospital hospital NN cord-272759-dqkjofw2 25 33 . . . cord-272759-dqkjofw2 26 1 Epidemiological epidemiological JJ cord-272759-dqkjofw2 26 2 studies study NNS cord-272759-dqkjofw2 26 3 [ [ -LRB- cord-272759-dqkjofw2 26 4 5 5 CD cord-272759-dqkjofw2 26 5 , , , cord-272759-dqkjofw2 26 6 1 1 CD cord-272759-dqkjofw2 26 7 ] ] -RRB- cord-272759-dqkjofw2 26 8 have have VBP cord-272759-dqkjofw2 26 9 found find VBN cord-272759-dqkjofw2 26 10 that that IN cord-272759-dqkjofw2 26 11 in in IN cord-272759-dqkjofw2 26 12 Hong Hong NNP cord-272759-dqkjofw2 26 13 Kong Kong NNP cord-272759-dqkjofw2 26 14 : : : cord-272759-dqkjofw2 26 15 • • NNP cord-272759-dqkjofw2 26 16 the the DT cord-272759-dqkjofw2 26 17 fatality fatality NN cord-272759-dqkjofw2 26 18 rate rate NN cord-272759-dqkjofw2 26 19 was be VBD cord-272759-dqkjofw2 26 20 approximately approximately RB cord-272759-dqkjofw2 26 21 17 17 CD cord-272759-dqkjofw2 26 22 % % NN cord-272759-dqkjofw2 26 23 ( ( -LRB- cord-272759-dqkjofw2 26 24 compared compare VBN cord-272759-dqkjofw2 26 25 to to IN cord-272759-dqkjofw2 26 26 11 11 CD cord-272759-dqkjofw2 26 27 % % NN cord-272759-dqkjofw2 26 28 globally globally RB cord-272759-dqkjofw2 26 29 ) ) -RRB- cord-272759-dqkjofw2 26 30 ; ; : cord-272759-dqkjofw2 26 31 • • NNP cord-272759-dqkjofw2 26 32 the the DT cord-272759-dqkjofw2 26 33 mean mean JJ cord-272759-dqkjofw2 26 34 incubation incubation NN cord-272759-dqkjofw2 26 35 period period NN cord-272759-dqkjofw2 26 36 was be VBD cord-272759-dqkjofw2 26 37 6.4 6.4 CD cord-272759-dqkjofw2 26 38 days day NNS cord-272759-dqkjofw2 27 1 ( ( -LRB- cord-272759-dqkjofw2 27 2 range range NNP cord-272759-dqkjofw2 27 3 2 2 CD cord-272759-dqkjofw2 27 4 - - SYM cord-272759-dqkjofw2 27 5 10 10 CD cord-272759-dqkjofw2 27 6 days day NNS cord-272759-dqkjofw2 27 7 ) ) -RRB- cord-272759-dqkjofw2 27 8 [ [ -LRB- cord-272759-dqkjofw2 27 9 6 6 CD cord-272759-dqkjofw2 27 10 ] ] -RRB- cord-272759-dqkjofw2 27 11 ; ; . cord-272759-dqkjofw2 28 1 • • NNP cord-272759-dqkjofw2 29 1 the the DT cord-272759-dqkjofw2 29 2 duration duration NN cord-272759-dqkjofw2 29 3 between between IN cord-272759-dqkjofw2 29 4 onset onset NN cord-272759-dqkjofw2 29 5 of of IN cord-272759-dqkjofw2 29 6 symptoms symptom NNS cord-272759-dqkjofw2 29 7 and and CC cord-272759-dqkjofw2 29 8 hospitalisation hospitalisation NN cord-272759-dqkjofw2 29 9 was be VBD cord-272759-dqkjofw2 29 10 3 3 CD cord-272759-dqkjofw2 29 11 - - SYM cord-272759-dqkjofw2 29 12 5 5 CD cord-272759-dqkjofw2 29 13 days day NNS cord-272759-dqkjofw2 29 14 ; ; : cord-272759-dqkjofw2 29 15 and and CC cord-272759-dqkjofw2 29 16 , , , cord-272759-dqkjofw2 29 17 • • XX cord-272759-dqkjofw2 30 1 the the DT cord-272759-dqkjofw2 30 2 mean mean JJ cord-272759-dqkjofw2 30 3 number number NN cord-272759-dqkjofw2 30 4 of of IN cord-272759-dqkjofw2 30 5 individuals individual NNS cord-272759-dqkjofw2 30 6 infected infect VBN cord-272759-dqkjofw2 30 7 by by IN cord-272759-dqkjofw2 30 8 each each DT cord-272759-dqkjofw2 30 9 case case NN cord-272759-dqkjofw2 30 10 during during IN cord-272759-dqkjofw2 30 11 the the DT cord-272759-dqkjofw2 30 12 initial initial JJ cord-272759-dqkjofw2 30 13 phase phase NN cord-272759-dqkjofw2 30 14 of of IN cord-272759-dqkjofw2 30 15 the the DT cord-272759-dqkjofw2 30 16 epidemic epidemic NN cord-272759-dqkjofw2 30 17 ( ( -LRB- cord-272759-dqkjofw2 30 18 excluding exclude VBG cord-272759-dqkjofw2 30 19 SSEs sse NNS cord-272759-dqkjofw2 30 20 ) ) -RRB- cord-272759-dqkjofw2 30 21 was be VBD cord-272759-dqkjofw2 30 22 2.7 2.7 CD cord-272759-dqkjofw2 30 23 [ [ -LRB- cord-272759-dqkjofw2 30 24 4 4 CD cord-272759-dqkjofw2 30 25 ] ] -RRB- cord-272759-dqkjofw2 30 26 . . . cord-272759-dqkjofw2 31 1 Standard standard JJ cord-272759-dqkjofw2 31 2 deterministic deterministic JJ cord-272759-dqkjofw2 31 3 SIR SIR NNP cord-272759-dqkjofw2 31 4 ( ( -LRB- cord-272759-dqkjofw2 31 5 susceptible susceptible JJ cord-272759-dqkjofw2 31 6 - - HYPH cord-272759-dqkjofw2 31 7 infected infect VBN cord-272759-dqkjofw2 31 8 - - HYPH cord-272759-dqkjofw2 31 9 removed remove VBN cord-272759-dqkjofw2 31 10 ) ) -RRB- cord-272759-dqkjofw2 31 11 models model NNS cord-272759-dqkjofw2 31 12 of of IN cord-272759-dqkjofw2 31 13 the the DT cord-272759-dqkjofw2 31 14 spread spread NN cord-272759-dqkjofw2 31 15 of of IN cord-272759-dqkjofw2 31 16 infectious infectious JJ cord-272759-dqkjofw2 31 17 diseases disease NNS cord-272759-dqkjofw2 31 18 [ [ -LRB- cord-272759-dqkjofw2 31 19 7 7 CD cord-272759-dqkjofw2 31 20 ] ] -RRB- cord-272759-dqkjofw2 31 21 make make VB cord-272759-dqkjofw2 31 22 several several JJ cord-272759-dqkjofw2 31 23 important important JJ cord-272759-dqkjofw2 31 24 assumptions assumption NNS cord-272759-dqkjofw2 31 25 . . . cord-272759-dqkjofw2 32 1 An an DT cord-272759-dqkjofw2 32 2 alternative alternative JJ cord-272759-dqkjofw2 32 3 approach approach NN cord-272759-dqkjofw2 32 4 [ [ -LRB- cord-272759-dqkjofw2 32 5 8 8 CD cord-272759-dqkjofw2 32 6 ] ] -RRB- cord-272759-dqkjofw2 32 7 , , , cord-272759-dqkjofw2 32 8 particularly particularly RB cord-272759-dqkjofw2 32 9 popular popular JJ cord-272759-dqkjofw2 32 10 for for IN cord-272759-dqkjofw2 32 11 the the DT cord-272759-dqkjofw2 32 12 study study NN cord-272759-dqkjofw2 32 13 of of IN cord-272759-dqkjofw2 32 14 sexually sexually RB cord-272759-dqkjofw2 32 15 transmitted transmit VBN cord-272759-dqkjofw2 32 16 diseases disease NNS cord-272759-dqkjofw2 32 17 [ [ -LRB- cord-272759-dqkjofw2 32 18 9 9 CD cord-272759-dqkjofw2 32 19 ] ] -RRB- cord-272759-dqkjofw2 32 20 [ [ -LRB- cord-272759-dqkjofw2 32 21 10 10 CD cord-272759-dqkjofw2 32 22 ] ] -RRB- cord-272759-dqkjofw2 32 23 [ [ -LRB- cord-272759-dqkjofw2 32 24 11 11 CD cord-272759-dqkjofw2 32 25 ] ] -RRB- cord-272759-dqkjofw2 32 26 , , , cord-272759-dqkjofw2 32 27 is be VBZ cord-272759-dqkjofw2 32 28 to to TO cord-272759-dqkjofw2 32 29 build build VB cord-272759-dqkjofw2 32 30 an an DT cord-272759-dqkjofw2 32 31 explicit explicit JJ cord-272759-dqkjofw2 32 32 network network NN cord-272759-dqkjofw2 32 33 and and CC cord-272759-dqkjofw2 32 34 model model NN cord-272759-dqkjofw2 32 35 disease disease NN cord-272759-dqkjofw2 32 36 transmission transmission NN cord-272759-dqkjofw2 32 37 along along IN cord-272759-dqkjofw2 32 38 the the DT cord-272759-dqkjofw2 32 39 links link NNS cord-272759-dqkjofw2 32 40 . . . cord-272759-dqkjofw2 33 1 Under under IN cord-272759-dqkjofw2 33 2 certain certain JJ cord-272759-dqkjofw2 33 3 network network NN cord-272759-dqkjofw2 33 4 structures structure NNS cord-272759-dqkjofw2 33 5 , , , cord-272759-dqkjofw2 33 6 it -PRON- PRP cord-272759-dqkjofw2 33 7 is be VBZ cord-272759-dqkjofw2 33 8 then then RB cord-272759-dqkjofw2 33 9 possible possible JJ cord-272759-dqkjofw2 33 10 to to TO cord-272759-dqkjofw2 33 11 obtain obtain VB cord-272759-dqkjofw2 33 12 a a DT cord-272759-dqkjofw2 33 13 closed closed JJ cord-272759-dqkjofw2 33 14 form form NN cord-272759-dqkjofw2 33 15 study study NN cord-272759-dqkjofw2 33 16 of of IN cord-272759-dqkjofw2 33 17 the the DT cord-272759-dqkjofw2 33 18 underlying underlying JJ cord-272759-dqkjofw2 33 19 transmission transmission NN cord-272759-dqkjofw2 33 20 pattern pattern NN cord-272759-dqkjofw2 33 21 [ [ -LRB- cord-272759-dqkjofw2 33 22 10 10 CD cord-272759-dqkjofw2 33 23 , , , cord-272759-dqkjofw2 33 24 12 12 CD cord-272759-dqkjofw2 33 25 ] ] -RRB- cord-272759-dqkjofw2 33 26 . . . cord-272759-dqkjofw2 34 1 In in IN cord-272759-dqkjofw2 34 2 particular particular JJ cord-272759-dqkjofw2 34 3 , , , cord-272759-dqkjofw2 34 4 [ [ -LRB- cord-272759-dqkjofw2 34 5 12 12 CD cord-272759-dqkjofw2 34 6 ] ] -RRB- cord-272759-dqkjofw2 34 7 studied study VBD cord-272759-dqkjofw2 34 8 the the DT cord-272759-dqkjofw2 34 9 transmission transmission NN cord-272759-dqkjofw2 34 10 of of IN cord-272759-dqkjofw2 34 11 an an DT cord-272759-dqkjofw2 34 12 epidemic epidemic NN cord-272759-dqkjofw2 34 13 among among IN cord-272759-dqkjofw2 34 14 a a DT cord-272759-dqkjofw2 34 15 population population NN cord-272759-dqkjofw2 34 16 whose whose WP$ cord-272759-dqkjofw2 34 17 individuals individual NNS cord-272759-dqkjofw2 34 18 are be VBP cord-272759-dqkjofw2 34 19 connected connect VBN cord-272759-dqkjofw2 34 20 both both CC cord-272759-dqkjofw2 34 21 locally locally RB cord-272759-dqkjofw2 34 22 and and CC cord-272759-dqkjofw2 34 23 globally globally RB cord-272759-dqkjofw2 34 24 . . . cord-272759-dqkjofw2 35 1 From from IN cord-272759-dqkjofw2 35 2 this this DT cord-272759-dqkjofw2 35 3 , , , cord-272759-dqkjofw2 35 4 they -PRON- PRP cord-272759-dqkjofw2 35 5 were be VBD cord-272759-dqkjofw2 35 6 able able JJ cord-272759-dqkjofw2 35 7 to to TO cord-272759-dqkjofw2 35 8 obtain obtain VB cord-272759-dqkjofw2 35 9 an an DT cord-272759-dqkjofw2 35 10 approximately approximately RB cord-272759-dqkjofw2 35 11 Poisson Poisson NNP cord-272759-dqkjofw2 35 12 distribution distribution NN cord-272759-dqkjofw2 35 13 for for IN cord-272759-dqkjofw2 35 14 the the DT cord-272759-dqkjofw2 35 15 contact contact NN cord-272759-dqkjofw2 35 16 distribution distribution NN cord-272759-dqkjofw2 35 17 . . . cord-272759-dqkjofw2 36 1 In in IN cord-272759-dqkjofw2 36 2 [ [ -LRB- cord-272759-dqkjofw2 36 3 13 13 CD cord-272759-dqkjofw2 36 4 ] ] -RRB- cord-272759-dqkjofw2 36 5 , , , cord-272759-dqkjofw2 36 6 Hufnagel Hufnagel NNP cord-272759-dqkjofw2 36 7 and and CC cord-272759-dqkjofw2 36 8 co co NNS cord-272759-dqkjofw2 36 9 - - NNS cord-272759-dqkjofw2 36 10 workers worker NNS cord-272759-dqkjofw2 36 11 also also RB cord-272759-dqkjofw2 36 12 studied study VBD cord-272759-dqkjofw2 36 13 the the DT cord-272759-dqkjofw2 36 14 local local JJ cord-272759-dqkjofw2 36 15 and and CC cord-272759-dqkjofw2 36 16 non non JJ cord-272759-dqkjofw2 36 17 - - JJ cord-272759-dqkjofw2 36 18 local local JJ cord-272759-dqkjofw2 36 19 transmission transmission NN cord-272759-dqkjofw2 36 20 of of IN cord-272759-dqkjofw2 36 21 epidemics epidemic NNS cord-272759-dqkjofw2 36 22 . . . cord-272759-dqkjofw2 37 1 The the DT cord-272759-dqkjofw2 37 2 main main JJ cord-272759-dqkjofw2 37 3 features feature NNS cord-272759-dqkjofw2 37 4 modelled model VBN cord-272759-dqkjofw2 37 5 by by IN cord-272759-dqkjofw2 37 6 [ [ -LRB- cord-272759-dqkjofw2 37 7 13 13 CD cord-272759-dqkjofw2 37 8 ] ] -RRB- cord-272759-dqkjofw2 37 9 are be VBP cord-272759-dqkjofw2 37 10 local local JJ cord-272759-dqkjofw2 37 11 SIR SIR NNP cord-272759-dqkjofw2 37 12 infection infection NN cord-272759-dqkjofw2 37 13 ( ( -LRB- cord-272759-dqkjofw2 37 14 with with IN cord-272759-dqkjofw2 37 15 the the DT cord-272759-dqkjofw2 37 16 usual usual JJ cord-272759-dqkjofw2 37 17 stochastic stochastic JJ cord-272759-dqkjofw2 37 18 differential differential JJ cord-272759-dqkjofw2 37 19 equations equation NNS cord-272759-dqkjofw2 37 20 ) ) -RRB- cord-272759-dqkjofw2 37 21 and and CC cord-272759-dqkjofw2 37 22 long long JJ cord-272759-dqkjofw2 37 23 distance distance NN cord-272759-dqkjofw2 37 24 complex complex JJ cord-272759-dqkjofw2 37 25 network network NN cord-272759-dqkjofw2 37 26 links link NNS cord-272759-dqkjofw2 37 27 to to TO cord-272759-dqkjofw2 37 28 model model VB cord-272759-dqkjofw2 37 29 global global JJ cord-272759-dqkjofw2 37 30 aviation aviation NN cord-272759-dqkjofw2 37 31 routes route NNS cord-272759-dqkjofw2 37 32 . . . cord-272759-dqkjofw2 38 1 They -PRON- PRP cord-272759-dqkjofw2 38 2 show show VBP cord-272759-dqkjofw2 38 3 that that IN cord-272759-dqkjofw2 38 4 transmission transmission NN cord-272759-dqkjofw2 38 5 dynamics dynamic NNS cord-272759-dqkjofw2 38 6 with with IN cord-272759-dqkjofw2 38 7 similar similar JJ cord-272759-dqkjofw2 38 8 geographical geographical JJ cord-272759-dqkjofw2 38 9 dispersion dispersion NN cord-272759-dqkjofw2 38 10 to to IN cord-272759-dqkjofw2 38 11 the the DT cord-272759-dqkjofw2 38 12 2003 2003 CD cord-272759-dqkjofw2 38 13 SARS SARS NNP cord-272759-dqkjofw2 38 14 outbreak outbreak NN cord-272759-dqkjofw2 38 15 can can MD cord-272759-dqkjofw2 38 16 develop develop VB cord-272759-dqkjofw2 38 17 in in IN cord-272759-dqkjofw2 38 18 the the DT cord-272759-dqkjofw2 38 19 model model NN cord-272759-dqkjofw2 38 20 . . . cord-272759-dqkjofw2 39 1 In in IN cord-272759-dqkjofw2 39 2 contrast contrast NN cord-272759-dqkjofw2 39 3 to to IN cord-272759-dqkjofw2 39 4 [ [ -LRB- cord-272759-dqkjofw2 39 5 13 13 CD cord-272759-dqkjofw2 39 6 ] ] -RRB- cord-272759-dqkjofw2 39 7 , , , cord-272759-dqkjofw2 39 8 we -PRON- PRP cord-272759-dqkjofw2 39 9 focus focus VBP cord-272759-dqkjofw2 39 10 on on IN cord-272759-dqkjofw2 39 11 abstract abstract JJ cord-272759-dqkjofw2 39 12 network network NN cord-272759-dqkjofw2 39 13 models model NNS cord-272759-dqkjofw2 39 14 within within IN cord-272759-dqkjofw2 39 15 a a DT cord-272759-dqkjofw2 39 16 particular particular JJ cord-272759-dqkjofw2 39 17 community community NN cord-272759-dqkjofw2 39 18 . . . cord-272759-dqkjofw2 40 1 A a DT cord-272759-dqkjofw2 40 2 similar similar JJ cord-272759-dqkjofw2 40 3 global global JJ cord-272759-dqkjofw2 40 4 model model NN cord-272759-dqkjofw2 40 5 of of IN cord-272759-dqkjofw2 40 6 SARS SARS NNP cord-272759-dqkjofw2 40 7 transmission transmission NN cord-272759-dqkjofw2 40 8 could could MD cord-272759-dqkjofw2 40 9 be be VB cord-272759-dqkjofw2 40 10 achieved achieve VBN cord-272759-dqkjofw2 40 11 by by IN cord-272759-dqkjofw2 40 12 introducing introduce VBG cord-272759-dqkjofw2 40 13 an an DT cord-272759-dqkjofw2 40 14 aviation aviation NN cord-272759-dqkjofw2 40 15 network network NN cord-272759-dqkjofw2 40 16 model model NN cord-272759-dqkjofw2 40 17 on on IN cord-272759-dqkjofw2 40 18 top top NN cord-272759-dqkjofw2 40 19 of of IN cord-272759-dqkjofw2 40 20 the the DT cord-272759-dqkjofw2 40 21 models model NNS cord-272759-dqkjofw2 40 22 presented present VBN cord-272759-dqkjofw2 40 23 in in IN cord-272759-dqkjofw2 40 24 this this DT cord-272759-dqkjofw2 40 25 paper paper NN cord-272759-dqkjofw2 40 26 . . . cord-272759-dqkjofw2 41 1 Recently recently RB cord-272759-dqkjofw2 41 2 , , , cord-272759-dqkjofw2 41 3 both both DT cord-272759-dqkjofw2 41 4 small small JJ cord-272759-dqkjofw2 41 5 - - HYPH cord-272759-dqkjofw2 41 6 world world NN cord-272759-dqkjofw2 41 7 ( ( -LRB- cord-272759-dqkjofw2 41 8 SW SW NNP cord-272759-dqkjofw2 41 9 ) ) -RRB- cord-272759-dqkjofw2 41 10 and and CC cord-272759-dqkjofw2 41 11 scale scale NN cord-272759-dqkjofw2 41 12 - - HYPH cord-272759-dqkjofw2 41 13 free free JJ cord-272759-dqkjofw2 41 14 ( ( -LRB- cord-272759-dqkjofw2 41 15 SF SF NNP cord-272759-dqkjofw2 41 16 ) ) -RRB- cord-272759-dqkjofw2 41 17 networks network NNS cord-272759-dqkjofw2 41 18 have have VBP cord-272759-dqkjofw2 41 19 been be VBN cord-272759-dqkjofw2 41 20 observed observe VBN cord-272759-dqkjofw2 41 21 in in IN cord-272759-dqkjofw2 41 22 many many JJ cord-272759-dqkjofw2 41 23 areas area NNS cord-272759-dqkjofw2 41 24 of of IN cord-272759-dqkjofw2 41 25 natural natural JJ cord-272759-dqkjofw2 41 26 and and CC cord-272759-dqkjofw2 41 27 physical physical JJ cord-272759-dqkjofw2 41 28 science science NN cord-272759-dqkjofw2 41 29 , , , cord-272759-dqkjofw2 41 30 including include VBG cord-272759-dqkjofw2 41 31 social social JJ cord-272759-dqkjofw2 41 32 relationships relationship NNS cord-272759-dqkjofw2 41 33 [ [ -LRB- cord-272759-dqkjofw2 41 34 14 14 CD cord-272759-dqkjofw2 41 35 , , , cord-272759-dqkjofw2 41 36 15 15 CD cord-272759-dqkjofw2 41 37 ] ] -RRB- cord-272759-dqkjofw2 41 38 . . . cord-272759-dqkjofw2 42 1 The the DT cord-272759-dqkjofw2 42 2 important important JJ cord-272759-dqkjofw2 42 3 feature feature NN cord-272759-dqkjofw2 42 4 of of IN cord-272759-dqkjofw2 42 5 both both DT cord-272759-dqkjofw2 42 6 SW SW NNP cord-272759-dqkjofw2 42 7 and and CC cord-272759-dqkjofw2 42 8 SF SF NNP cord-272759-dqkjofw2 42 9 networks network NNS cord-272759-dqkjofw2 42 10 is be VBZ cord-272759-dqkjofw2 42 11 that that IN cord-272759-dqkjofw2 42 12 they -PRON- PRP cord-272759-dqkjofw2 42 13 are be VBP cord-272759-dqkjofw2 42 14 highly highly RB cord-272759-dqkjofw2 42 15 connected connect VBN cord-272759-dqkjofw2 42 16 : : : cord-272759-dqkjofw2 42 17 the the DT cord-272759-dqkjofw2 42 18 average average JJ cord-272759-dqkjofw2 42 19 path path NN cord-272759-dqkjofw2 42 20 length length NN cord-272759-dqkjofw2 42 21 between between IN cord-272759-dqkjofw2 42 22 random random JJ cord-272759-dqkjofw2 42 23 individuals individual NNS cord-272759-dqkjofw2 42 24 is be VBZ cord-272759-dqkjofw2 42 25 relatively relatively RB cord-272759-dqkjofw2 42 26 short short JJ cord-272759-dqkjofw2 42 27 . . . cord-272759-dqkjofw2 43 1 Moreover moreover RB cord-272759-dqkjofw2 43 2 , , , cord-272759-dqkjofw2 43 3 for for IN cord-272759-dqkjofw2 43 4 SF SF NNP cord-272759-dqkjofw2 43 5 networks network NNS cord-272759-dqkjofw2 43 6 , , , cord-272759-dqkjofw2 43 7 the the DT cord-272759-dqkjofw2 43 8 node node NN cord-272759-dqkjofw2 43 9 degree degree NN cord-272759-dqkjofw2 43 10 distribution distribution NN cord-272759-dqkjofw2 43 11 follows follow VBZ cord-272759-dqkjofw2 43 12 a a DT cord-272759-dqkjofw2 43 13 scale scale NN cord-272759-dqkjofw2 43 14 - - HYPH cord-272759-dqkjofw2 43 15 free free JJ cord-272759-dqkjofw2 43 16 distribution distribution NN cord-272759-dqkjofw2 43 17 . . . cord-272759-dqkjofw2 44 1 Hence hence RB cord-272759-dqkjofw2 44 2 , , , cord-272759-dqkjofw2 44 3 in in IN cord-272759-dqkjofw2 44 4 many many JJ cord-272759-dqkjofw2 44 5 areas area NNS cord-272759-dqkjofw2 44 6 of of IN cord-272759-dqkjofw2 44 7 natural natural JJ cord-272759-dqkjofw2 44 8 and and CC cord-272759-dqkjofw2 44 9 physical physical JJ cord-272759-dqkjofw2 44 10 science science NN cord-272759-dqkjofw2 44 11 , , , cord-272759-dqkjofw2 44 12 this this DT cord-272759-dqkjofw2 44 13 new new JJ cord-272759-dqkjofw2 44 14 model model NN cord-272759-dqkjofw2 44 15 structure structure NN cord-272759-dqkjofw2 44 16 has have VBZ cord-272759-dqkjofw2 44 17 unveiled unveil VBN cord-272759-dqkjofw2 44 18 a a DT cord-272759-dqkjofw2 44 19 rich rich JJ cord-272759-dqkjofw2 44 20 range range NN cord-272759-dqkjofw2 44 21 of of IN cord-272759-dqkjofw2 44 22 behaviours behaviour NNS cord-272759-dqkjofw2 44 23 . . . cord-272759-dqkjofw2 45 1 In in IN cord-272759-dqkjofw2 45 2 this this DT cord-272759-dqkjofw2 45 3 paper paper NN cord-272759-dqkjofw2 45 4 , , , cord-272759-dqkjofw2 45 5 we -PRON- PRP cord-272759-dqkjofw2 45 6 apply apply VBP cord-272759-dqkjofw2 45 7 these these DT cord-272759-dqkjofw2 45 8 methods method NNS cord-272759-dqkjofw2 45 9 to to IN cord-272759-dqkjofw2 45 10 the the DT cord-272759-dqkjofw2 45 11 modelling modelling NN cord-272759-dqkjofw2 45 12 of of IN cord-272759-dqkjofw2 45 13 the the DT cord-272759-dqkjofw2 45 14 spread spread NN cord-272759-dqkjofw2 45 15 of of IN cord-272759-dqkjofw2 45 16 SARS SARS NNP cord-272759-dqkjofw2 45 17 in in IN cord-272759-dqkjofw2 45 18 Hong Hong NNP cord-272759-dqkjofw2 45 19 Kong Kong NNP cord-272759-dqkjofw2 45 20 ; ; : cord-272759-dqkjofw2 45 21 transmission transmission NN cord-272759-dqkjofw2 45 22 is be VBZ cord-272759-dqkjofw2 45 23 only only RB cord-272759-dqkjofw2 45 24 allowed allow VBN cord-272759-dqkjofw2 45 25 to to TO cord-272759-dqkjofw2 45 26 occur occur VB cord-272759-dqkjofw2 45 27 along along IN cord-272759-dqkjofw2 45 28 a a DT cord-272759-dqkjofw2 45 29 limited limited JJ cord-272759-dqkjofw2 45 30 number number NN cord-272759-dqkjofw2 45 31 of of IN cord-272759-dqkjofw2 45 32 direct direct JJ cord-272759-dqkjofw2 45 33 links link NNS cord-272759-dqkjofw2 45 34 between between IN cord-272759-dqkjofw2 45 35 individuals individual NNS cord-272759-dqkjofw2 45 36 . . . cord-272759-dqkjofw2 46 1 By by IN cord-272759-dqkjofw2 46 2 doing do VBG cord-272759-dqkjofw2 46 3 this this DT cord-272759-dqkjofw2 46 4 , , , cord-272759-dqkjofw2 46 5 we -PRON- PRP cord-272759-dqkjofw2 46 6 will will MD cord-272759-dqkjofw2 46 7 avoid avoid VB cord-272759-dqkjofw2 46 8 making make VBG cord-272759-dqkjofw2 46 9 one one CD cord-272759-dqkjofw2 46 10 of of IN cord-272759-dqkjofw2 46 11 the the DT cord-272759-dqkjofw2 46 12 assumptions assumption NNS cord-272759-dqkjofw2 46 13 underlying underlie VBG cord-272759-dqkjofw2 46 14 standard standard JJ cord-272759-dqkjofw2 46 15 Susceptible susceptible JJ cord-272759-dqkjofw2 46 16 - - HYPH cord-272759-dqkjofw2 46 17 Infected Infected NNP cord-272759-dqkjofw2 46 18 - - HYPH cord-272759-dqkjofw2 46 19 Removed remove VBN cord-272759-dqkjofw2 46 20 ( ( -LRB- cord-272759-dqkjofw2 46 21 SIR SIR NNP cord-272759-dqkjofw2 46 22 ) ) -RRB- cord-272759-dqkjofw2 46 23 models model VBZ cord-272759-dqkjofw2 46 24 : : : cord-272759-dqkjofw2 46 25 a a DT cord-272759-dqkjofw2 46 26 homogeneous homogeneous JJ cord-272759-dqkjofw2 46 27 fully fully RB cord-272759-dqkjofw2 46 28 connected connect VBN cord-272759-dqkjofw2 46 29 population population NN cord-272759-dqkjofw2 46 30 . . . cord-272759-dqkjofw2 47 1 The the DT cord-272759-dqkjofw2 47 2 SIR SIR NNP cord-272759-dqkjofw2 47 3 model model NN cord-272759-dqkjofw2 47 4 assumes assume VBZ cord-272759-dqkjofw2 47 5 that that IN cord-272759-dqkjofw2 47 6 all all DT cord-272759-dqkjofw2 47 7 individuals individual NNS cord-272759-dqkjofw2 47 8 are be VBP cord-272759-dqkjofw2 47 9 susceptible susceptible JJ cord-272759-dqkjofw2 47 10 to to IN cord-272759-dqkjofw2 47 11 the the DT cord-272759-dqkjofw2 47 12 disease disease NN cord-272759-dqkjofw2 47 13 and and CC cord-272759-dqkjofw2 47 14 all all DT cord-272759-dqkjofw2 47 15 suffer suffer VBP cord-272759-dqkjofw2 47 16 an an DT cord-272759-dqkjofw2 47 17 equal equal JJ cord-272759-dqkjofw2 47 18 , , , cord-272759-dqkjofw2 47 19 small small JJ cord-272759-dqkjofw2 47 20 , , , cord-272759-dqkjofw2 47 21 positive positive JJ cord-272759-dqkjofw2 47 22 probability probability NN cord-272759-dqkjofw2 47 23 of of IN cord-272759-dqkjofw2 47 24 contracting contract VBG cord-272759-dqkjofw2 47 25 the the DT cord-272759-dqkjofw2 47 26 virus virus NN cord-272759-dqkjofw2 47 27 . . . cord-272759-dqkjofw2 48 1 This this DT cord-272759-dqkjofw2 48 2 homogeneous homogeneous JJ cord-272759-dqkjofw2 48 3 model model NN cord-272759-dqkjofw2 48 4 leads lead VBZ cord-272759-dqkjofw2 48 5 to to IN cord-272759-dqkjofw2 48 6 a a DT cord-272759-dqkjofw2 48 7 continuous continuous JJ cord-272759-dqkjofw2 48 8 and and CC cord-272759-dqkjofw2 48 9 smooth smooth JJ cord-272759-dqkjofw2 48 10 inter inter JJ cord-272759-dqkjofw2 48 11 - - JJ cord-272759-dqkjofw2 48 12 day day JJ cord-272759-dqkjofw2 48 13 distribution distribution NN cord-272759-dqkjofw2 48 14 of of IN cord-272759-dqkjofw2 48 15 infections infection NNS cord-272759-dqkjofw2 48 16 . . . cord-272759-dqkjofw2 49 1 Irregularities irregularity NNS cord-272759-dqkjofw2 49 2 in in IN cord-272759-dqkjofw2 49 3 this this DT cord-272759-dqkjofw2 49 4 are be VBP cord-272759-dqkjofw2 49 5 usually usually RB cord-272759-dqkjofw2 49 6 attributed attribute VBN cord-272759-dqkjofw2 49 7 to to IN cord-272759-dqkjofw2 49 8 random random JJ cord-272759-dqkjofw2 49 9 variation variation NN cord-272759-dqkjofw2 49 10 and and CC cord-272759-dqkjofw2 49 11 non non JJ cord-272759-dqkjofw2 49 12 - - JJ cord-272759-dqkjofw2 49 13 stationarity stationarity NN cord-272759-dqkjofw2 49 14 in in IN cord-272759-dqkjofw2 49 15 the the DT cord-272759-dqkjofw2 49 16 model model NN cord-272759-dqkjofw2 49 17 parameters parameter NNS cord-272759-dqkjofw2 49 18 . . . cord-272759-dqkjofw2 50 1 In in IN cord-272759-dqkjofw2 50 2 proposing propose VBG cord-272759-dqkjofw2 50 3 an an DT cord-272759-dqkjofw2 50 4 alternative alternative NN cord-272759-dqkjofw2 50 5 to to IN cord-272759-dqkjofw2 50 6 the the DT cord-272759-dqkjofw2 50 7 standard standard JJ cord-272759-dqkjofw2 50 8 SIR SIR NNP cord-272759-dqkjofw2 50 9 model model NN cord-272759-dqkjofw2 50 10 , , , cord-272759-dqkjofw2 50 11 we -PRON- PRP cord-272759-dqkjofw2 50 12 do do VBP cord-272759-dqkjofw2 50 13 not not RB cord-272759-dqkjofw2 50 14 claim claim VB cord-272759-dqkjofw2 50 15 that that IN cord-272759-dqkjofw2 50 16 the the DT cord-272759-dqkjofw2 50 17 SIR SIR NNP cord-272759-dqkjofw2 50 18 model model NN cord-272759-dqkjofw2 50 19 has have VBZ cord-272759-dqkjofw2 50 20 failed fail VBN cord-272759-dqkjofw2 50 21 . . . cord-272759-dqkjofw2 51 1 Certainly certainly RB cord-272759-dqkjofw2 51 2 , , , cord-272759-dqkjofw2 51 3 the the DT cord-272759-dqkjofw2 51 4 power power NN cord-272759-dqkjofw2 51 5 of of IN cord-272759-dqkjofw2 51 6 any any DT cord-272759-dqkjofw2 51 7 model model NN cord-272759-dqkjofw2 51 8 lies lie VBZ cord-272759-dqkjofw2 51 9 in in IN cord-272759-dqkjofw2 51 10 its -PRON- PRP$ cord-272759-dqkjofw2 51 11 simplicity simplicity NN cord-272759-dqkjofw2 51 12 , , , cord-272759-dqkjofw2 51 13 and and CC cord-272759-dqkjofw2 51 14 its -PRON- PRP$ cord-272759-dqkjofw2 51 15 ability ability NN cord-272759-dqkjofw2 51 16 to to TO cord-272759-dqkjofw2 51 17 capture capture VB cord-272759-dqkjofw2 51 18 the the DT cord-272759-dqkjofw2 51 19 important important JJ cord-272759-dqkjofw2 51 20 features feature NNS cord-272759-dqkjofw2 51 21 of of IN cord-272759-dqkjofw2 51 22 a a DT cord-272759-dqkjofw2 51 23 system system NN cord-272759-dqkjofw2 51 24 . . . cord-272759-dqkjofw2 52 1 Hence hence RB cord-272759-dqkjofw2 52 2 , , , cord-272759-dqkjofw2 52 3 like like IN cord-272759-dqkjofw2 52 4 the the DT cord-272759-dqkjofw2 52 5 SIR SIR NNP cord-272759-dqkjofw2 52 6 model model NN cord-272759-dqkjofw2 52 7 , , , cord-272759-dqkjofw2 52 8 the the DT cord-272759-dqkjofw2 52 9 complex complex JJ cord-272759-dqkjofw2 52 10 network network NN cord-272759-dqkjofw2 52 11 model model NN cord-272759-dqkjofw2 52 12 that that WDT cord-272759-dqkjofw2 52 13 we -PRON- PRP cord-272759-dqkjofw2 52 14 describe describe VBP cord-272759-dqkjofw2 52 15 here here RB cord-272759-dqkjofw2 52 16 is be VBZ cord-272759-dqkjofw2 52 17 very very RB cord-272759-dqkjofw2 52 18 simple simple JJ cord-272759-dqkjofw2 52 19 and and CC cord-272759-dqkjofw2 52 20 is be VBZ cord-272759-dqkjofw2 52 21 described describe VBN cord-272759-dqkjofw2 52 22 by by IN cord-272759-dqkjofw2 52 23 a a DT cord-272759-dqkjofw2 52 24 very very RB cord-272759-dqkjofw2 52 25 small small JJ cord-272759-dqkjofw2 52 26 number number NN cord-272759-dqkjofw2 52 27 of of IN cord-272759-dqkjofw2 52 28 parameters parameter NNS cord-272759-dqkjofw2 52 29 . . . cord-272759-dqkjofw2 53 1 Analysis analysis NN cord-272759-dqkjofw2 53 2 of of IN cord-272759-dqkjofw2 53 3 the the DT cord-272759-dqkjofw2 53 4 spread spread NN cord-272759-dqkjofw2 53 5 of of IN cord-272759-dqkjofw2 53 6 SARS SARS NNP cord-272759-dqkjofw2 53 7 with with IN cord-272759-dqkjofw2 53 8 SIR SIR NNP cord-272759-dqkjofw2 53 9 models model NNS cord-272759-dqkjofw2 53 10 shows show VBZ cord-272759-dqkjofw2 53 11 good good JJ cord-272759-dqkjofw2 53 12 correlation correlation NN cord-272759-dqkjofw2 53 13 between between IN cord-272759-dqkjofw2 53 14 decreasing decrease VBG cord-272759-dqkjofw2 53 15 infection infection NN cord-272759-dqkjofw2 53 16 rate rate NN cord-272759-dqkjofw2 53 17 r r NN cord-272759-dqkjofw2 53 18 and and CC cord-272759-dqkjofw2 53 19 the the DT cord-272759-dqkjofw2 53 20 introduction introduction NN cord-272759-dqkjofw2 53 21 of of IN cord-272759-dqkjofw2 53 22 various various JJ cord-272759-dqkjofw2 53 23 governmental governmental JJ cord-272759-dqkjofw2 53 24 control control NN cord-272759-dqkjofw2 53 25 measures measure NNS cord-272759-dqkjofw2 53 26 : : : cord-272759-dqkjofw2 53 27 quarantine quarantine NN cord-272759-dqkjofw2 53 28 and and CC cord-272759-dqkjofw2 53 29 public public JJ cord-272759-dqkjofw2 53 30 awareness awareness NN cord-272759-dqkjofw2 53 31 campaigns campaign NNS cord-272759-dqkjofw2 53 32 [ [ -LRB- cord-272759-dqkjofw2 53 33 16 16 CD cord-272759-dqkjofw2 53 34 ] ] -RRB- cord-272759-dqkjofw2 53 35 . . . cord-272759-dqkjofw2 54 1 However however RB cord-272759-dqkjofw2 54 2 , , , cord-272759-dqkjofw2 54 3 these these DT cord-272759-dqkjofw2 54 4 results result NNS cord-272759-dqkjofw2 54 5 are be VBP cord-272759-dqkjofw2 54 6 based base VBN cord-272759-dqkjofw2 54 7 on on IN cord-272759-dqkjofw2 54 8 a a DT cord-272759-dqkjofw2 54 9 very very RB cord-272759-dqkjofw2 54 10 simplistic simplistic JJ cord-272759-dqkjofw2 54 11 model model NN cord-272759-dqkjofw2 54 12 , , , cord-272759-dqkjofw2 54 13 and and CC cord-272759-dqkjofw2 54 14 localised localise VBN cord-272759-dqkjofw2 54 15 outbreaks outbreak NNS cord-272759-dqkjofw2 54 16 ( ( -LRB- cord-272759-dqkjofw2 54 17 such such JJ cord-272759-dqkjofw2 54 18 as as IN cord-272759-dqkjofw2 54 19 the the DT cord-272759-dqkjofw2 54 20 incident incident NN cord-272759-dqkjofw2 54 21 at at IN cord-272759-dqkjofw2 54 22 Amoy Amoy NNP cord-272759-dqkjofw2 54 23 Gardens Gardens NNP cord-272759-dqkjofw2 54 24 ) ) -RRB- cord-272759-dqkjofw2 54 25 are be VBP cord-272759-dqkjofw2 54 26 not not RB cord-272759-dqkjofw2 54 27 modelled model VBN cord-272759-dqkjofw2 54 28 very very RB cord-272759-dqkjofw2 54 29 well well RB cord-272759-dqkjofw2 54 30 . . . cord-272759-dqkjofw2 55 1 While while IN cord-272759-dqkjofw2 55 2 it -PRON- PRP cord-272759-dqkjofw2 55 3 is be VBZ cord-272759-dqkjofw2 55 4 impossible impossible JJ cord-272759-dqkjofw2 55 5 to to TO cord-272759-dqkjofw2 55 6 predict predict VB cord-272759-dqkjofw2 55 7 the the DT cord-272759-dqkjofw2 55 8 occurrence occurrence NN cord-272759-dqkjofw2 55 9 of of IN cord-272759-dqkjofw2 55 10 such such JJ cord-272759-dqkjofw2 55 11 outbreaks outbreak NNS cord-272759-dqkjofw2 55 12 , , , cord-272759-dqkjofw2 55 13 SW SW NNP cord-272759-dqkjofw2 55 14 - - HYPH cord-272759-dqkjofw2 55 15 SF SF NNP cord-272759-dqkjofw2 55 16 models model NNS cord-272759-dqkjofw2 55 17 provide provide VBP cord-272759-dqkjofw2 55 18 a a DT cord-272759-dqkjofw2 55 19 more more RBR cord-272759-dqkjofw2 55 20 realistic realistic JJ cord-272759-dqkjofw2 55 21 physical physical JJ cord-272759-dqkjofw2 55 22 model model NN cord-272759-dqkjofw2 55 23 of of IN cord-272759-dqkjofw2 55 24 the the DT cord-272759-dqkjofw2 55 25 relationships relationship NNS cord-272759-dqkjofw2 55 26 between between IN cord-272759-dqkjofw2 55 27 individuals individual NNS cord-272759-dqkjofw2 55 28 in in IN cord-272759-dqkjofw2 55 29 a a DT cord-272759-dqkjofw2 55 30 community community NN cord-272759-dqkjofw2 55 31 and and CC cord-272759-dqkjofw2 55 32 will will MD cord-272759-dqkjofw2 55 33 therefore therefore RB cord-272759-dqkjofw2 55 34 provide provide VB cord-272759-dqkjofw2 55 35 a a DT cord-272759-dqkjofw2 55 36 better well JJR cord-272759-dqkjofw2 55 37 picture picture NN cord-272759-dqkjofw2 55 38 of of IN cord-272759-dqkjofw2 55 39 the the DT cord-272759-dqkjofw2 55 40 true true JJ cord-272759-dqkjofw2 55 41 disease disease NN cord-272759-dqkjofw2 55 42 dynamics dynamic NNS cord-272759-dqkjofw2 55 43 . . . cord-272759-dqkjofw2 56 1 Note note VB cord-272759-dqkjofw2 56 2 that that IN cord-272759-dqkjofw2 56 3 , , , cord-272759-dqkjofw2 56 4 since since IN cord-272759-dqkjofw2 56 5 one one PRP cord-272759-dqkjofw2 56 6 can can MD cord-272759-dqkjofw2 56 7 not not RB cord-272759-dqkjofw2 56 8 actually actually RB cord-272759-dqkjofw2 56 9 predict predict VB cord-272759-dqkjofw2 56 10 when when WRB cord-272759-dqkjofw2 56 11 a a DT cord-272759-dqkjofw2 56 12 particular particular JJ cord-272759-dqkjofw2 56 13 SSE SSE NNP cord-272759-dqkjofw2 56 14 will will MD cord-272759-dqkjofw2 56 15 occur occur VB cord-272759-dqkjofw2 56 16 , , , cord-272759-dqkjofw2 56 17 one one PRP cord-272759-dqkjofw2 56 18 can can MD cord-272759-dqkjofw2 56 19 not not RB cord-272759-dqkjofw2 56 20 accurately accurately RB cord-272759-dqkjofw2 56 21 model model VB cord-272759-dqkjofw2 56 22 the the DT cord-272759-dqkjofw2 56 23 timing timing NN cord-272759-dqkjofw2 56 24 of of IN cord-272759-dqkjofw2 56 25 the the DT cord-272759-dqkjofw2 56 26 peak peak NN cord-272759-dqkjofw2 56 27 in in IN cord-272759-dqkjofw2 56 28 the the DT cord-272759-dqkjofw2 56 29 time time NN cord-272759-dqkjofw2 56 30 series series NN cord-272759-dqkjofw2 56 31 of of IN cord-272759-dqkjofw2 56 32 Fig Fig NNP cord-272759-dqkjofw2 56 33 . . . cord-272759-dqkjofw2 57 1 1 1 LS cord-272759-dqkjofw2 57 2 . . . cord-272759-dqkjofw2 58 1 Moreover moreover RB cord-272759-dqkjofw2 58 2 , , , cord-272759-dqkjofw2 58 3 it -PRON- PRP cord-272759-dqkjofw2 58 4 is be VBZ cord-272759-dqkjofw2 58 5 not not RB cord-272759-dqkjofw2 58 6 possible possible JJ cord-272759-dqkjofw2 58 7 to to TO cord-272759-dqkjofw2 58 8 accurately accurately RB cord-272759-dqkjofw2 58 9 model model VB cord-272759-dqkjofw2 58 10 the the DT cord-272759-dqkjofw2 58 11 initial initial JJ cord-272759-dqkjofw2 58 12 SSE SSE NNP cord-272759-dqkjofw2 58 13 at at IN cord-272759-dqkjofw2 58 14 the the DT cord-272759-dqkjofw2 58 15 Prince Prince NNP cord-272759-dqkjofw2 58 16 of of IN cord-272759-dqkjofw2 58 17 Wales Wales NNP cord-272759-dqkjofw2 58 18 hospital hospital NN cord-272759-dqkjofw2 58 19 , , , cord-272759-dqkjofw2 58 20 which which WDT cord-272759-dqkjofw2 58 21 " " `` cord-272759-dqkjofw2 58 22 kick kick NN cord-272759-dqkjofw2 58 23 started start VBD cord-272759-dqkjofw2 58 24 " " `` cord-272759-dqkjofw2 58 25 the the DT cord-272759-dqkjofw2 58 26 SARS SARS NNP cord-272759-dqkjofw2 58 27 outbreak outbreak NN cord-272759-dqkjofw2 58 28 in in IN cord-272759-dqkjofw2 58 29 Hong Hong NNP cord-272759-dqkjofw2 58 30 Kong Kong NNP cord-272759-dqkjofw2 58 31 . . . cord-272759-dqkjofw2 59 1 To to TO cord-272759-dqkjofw2 59 2 include include VB cord-272759-dqkjofw2 59 3 the the DT cord-272759-dqkjofw2 59 4 same same JJ cord-272759-dqkjofw2 59 5 initial initial JJ cord-272759-dqkjofw2 59 6 spread spread NN cord-272759-dqkjofw2 59 7 of of IN cord-272759-dqkjofw2 59 8 SARS SARS NNP cord-272759-dqkjofw2 59 9 in in IN cord-272759-dqkjofw2 59 10 Hong Hong NNP cord-272759-dqkjofw2 59 11 Kong Kong NNP cord-272759-dqkjofw2 59 12 , , , cord-272759-dqkjofw2 59 13 via via IN cord-272759-dqkjofw2 59 14 a a DT cord-272759-dqkjofw2 59 15 rather rather RB cord-272759-dqkjofw2 59 16 singular singular JJ cord-272759-dqkjofw2 59 17 SSE SSE NNP cord-272759-dqkjofw2 59 18 , , , cord-272759-dqkjofw2 59 19 that that IN cord-272759-dqkjofw2 59 20 SSE SSE NNP cord-272759-dqkjofw2 59 21 must must MD cord-272759-dqkjofw2 59 22 be be VB cord-272759-dqkjofw2 59 23 included include VBN cord-272759-dqkjofw2 59 24 explicitly explicitly RB cord-272759-dqkjofw2 59 25 in in IN cord-272759-dqkjofw2 59 26 the the DT cord-272759-dqkjofw2 59 27 model model NN cord-272759-dqkjofw2 59 28 . . . cord-272759-dqkjofw2 60 1 In in IN cord-272759-dqkjofw2 60 2 other other JJ cord-272759-dqkjofw2 60 3 areas area NNS cord-272759-dqkjofw2 60 4 where where WRB cord-272759-dqkjofw2 60 5 SW SW NNP cord-272759-dqkjofw2 60 6 - - HYPH cord-272759-dqkjofw2 60 7 SF SF NNP cord-272759-dqkjofw2 60 8 models model NNS cord-272759-dqkjofw2 60 9 have have VBP cord-272759-dqkjofw2 60 10 been be VBN cord-272759-dqkjofw2 60 11 applied apply VBN cord-272759-dqkjofw2 60 12 , , , cord-272759-dqkjofw2 60 13 a a DT cord-272759-dqkjofw2 60 14 rich rich JJ cord-272759-dqkjofw2 60 15 range range NN cord-272759-dqkjofw2 60 16 of of IN cord-272759-dqkjofw2 60 17 behaviours behaviour NNS cord-272759-dqkjofw2 60 18 has have VBZ cord-272759-dqkjofw2 60 19 been be VBN cord-272759-dqkjofw2 60 20 observed observe VBN cord-272759-dqkjofw2 60 21 . . . cord-272759-dqkjofw2 61 1 Unlike unlike IN cord-272759-dqkjofw2 61 2 standard standard JJ cord-272759-dqkjofw2 61 3 differential differential JJ cord-272759-dqkjofw2 61 4 equation equation NN cord-272759-dqkjofw2 61 5 based base VBN cord-272759-dqkjofw2 61 6 models model NNS cord-272759-dqkjofw2 61 7 , , , cord-272759-dqkjofw2 61 8 SW SW NNP cord-272759-dqkjofw2 61 9 and/or and/or CC cord-272759-dqkjofw2 61 10 SF SF NNP cord-272759-dqkjofw2 61 11 structures structure NNS cord-272759-dqkjofw2 61 12 model model VBP cord-272759-dqkjofw2 61 13 the the DT cord-272759-dqkjofw2 61 14 underlying underlying JJ cord-272759-dqkjofw2 61 15 network network NN cord-272759-dqkjofw2 61 16 of of IN cord-272759-dqkjofw2 61 17 connections connection NNS cord-272759-dqkjofw2 61 18 between between IN cord-272759-dqkjofw2 61 19 individuals individual NNS cord-272759-dqkjofw2 61 20 directly directly RB cord-272759-dqkjofw2 61 21 . . . cord-272759-dqkjofw2 62 1 Our -PRON- PRP$ cord-272759-dqkjofw2 62 2 model model NN cord-272759-dqkjofw2 62 3 is be VBZ cord-272759-dqkjofw2 62 4 designed design VBN cord-272759-dqkjofw2 62 5 to to TO cord-272759-dqkjofw2 62 6 capture capture VB cord-272759-dqkjofw2 62 7 explicitly explicitly RB cord-272759-dqkjofw2 62 8 the the DT cord-272759-dqkjofw2 62 9 small small JJ cord-272759-dqkjofw2 62 10 - - HYPH cord-272759-dqkjofw2 62 11 world world NN cord-272759-dqkjofw2 62 12 features feature NNS cord-272759-dqkjofw2 62 13 of of IN cord-272759-dqkjofw2 62 14 social social JJ cord-272759-dqkjofw2 62 15 interaction interaction NN cord-272759-dqkjofw2 62 16 . . . cord-272759-dqkjofw2 63 1 Our -PRON- PRP$ cord-272759-dqkjofw2 63 2 model model NN cord-272759-dqkjofw2 63 3 is be VBZ cord-272759-dqkjofw2 63 4 not not RB cord-272759-dqkjofw2 63 5 scale scale NN cord-272759-dqkjofw2 63 6 - - HYPH cord-272759-dqkjofw2 63 7 free free JJ cord-272759-dqkjofw2 63 8 . . . cord-272759-dqkjofw2 64 1 To to TO cord-272759-dqkjofw2 64 2 generate generate VB cord-272759-dqkjofw2 64 3 a a DT cord-272759-dqkjofw2 64 4 scale scale NN cord-272759-dqkjofw2 64 5 - - HYPH cord-272759-dqkjofw2 64 6 free free JJ cord-272759-dqkjofw2 64 7 model model NN cord-272759-dqkjofw2 64 8 for for IN cord-272759-dqkjofw2 64 9 disease disease NN cord-272759-dqkjofw2 64 10 epidemics epidemic NNS cord-272759-dqkjofw2 64 11 , , , cord-272759-dqkjofw2 64 12 one one PRP cord-272759-dqkjofw2 64 13 needs need VBZ cord-272759-dqkjofw2 64 14 a a DT cord-272759-dqkjofw2 64 15 power power NN cord-272759-dqkjofw2 64 16 - - HYPH cord-272759-dqkjofw2 64 17 law law NN cord-272759-dqkjofw2 64 18 distribution distribution NN cord-272759-dqkjofw2 64 19 of of IN cord-272759-dqkjofw2 64 20 infection infection NN cord-272759-dqkjofw2 64 21 links link NNS cord-272759-dqkjofw2 64 22 ; ; : cord-272759-dqkjofw2 64 23 we -PRON- PRP cord-272759-dqkjofw2 64 24 consider consider VBP cord-272759-dqkjofw2 64 25 the the DT cord-272759-dqkjofw2 64 26 theoretical theoretical JJ cord-272759-dqkjofw2 64 27 implementation implementation NN cord-272759-dqkjofw2 64 28 of of IN cord-272759-dqkjofw2 64 29 such such PDT cord-272759-dqkjofw2 64 30 a a DT cord-272759-dqkjofw2 64 31 model model NN cord-272759-dqkjofw2 64 32 in in IN cord-272759-dqkjofw2 64 33 a a DT cord-272759-dqkjofw2 64 34 separate separate JJ cord-272759-dqkjofw2 64 35 paper paper NN cord-272759-dqkjofw2 64 36 [ [ -LRB- cord-272759-dqkjofw2 64 37 16 16 CD cord-272759-dqkjofw2 64 38 ] ] -RRB- cord-272759-dqkjofw2 64 39 . . . cord-272759-dqkjofw2 65 1 Finally finally RB cord-272759-dqkjofw2 65 2 , , , cord-272759-dqkjofw2 65 3 we -PRON- PRP cord-272759-dqkjofw2 65 4 will will MD cord-272759-dqkjofw2 65 5 also also RB cord-272759-dqkjofw2 65 6 provide provide VB cord-272759-dqkjofw2 65 7 one one CD cord-272759-dqkjofw2 65 8 possible possible JJ cord-272759-dqkjofw2 65 9 answer answer NN cord-272759-dqkjofw2 65 10 to to IN cord-272759-dqkjofw2 65 11 the the DT cord-272759-dqkjofw2 65 12 question question NN cord-272759-dqkjofw2 65 13 posed pose VBN cord-272759-dqkjofw2 65 14 by by IN cord-272759-dqkjofw2 65 15 Galvani Galvani NNP cord-272759-dqkjofw2 65 16 and and CC cord-272759-dqkjofw2 66 1 May May MD cord-272759-dqkjofw2 66 2 [ [ -LRB- cord-272759-dqkjofw2 66 3 17 17 CD cord-272759-dqkjofw2 66 4 ] ] -RRB- cord-272759-dqkjofw2 67 1 : : : cord-272759-dqkjofw2 67 2 " " `` cord-272759-dqkjofw2 67 3 Were be VBD cord-272759-dqkjofw2 67 4 SARS SARS NNP cord-272759-dqkjofw2 67 5 superspreaders superspreader NNS cord-272759-dqkjofw2 67 6 anomalies anomaly NNS cord-272759-dqkjofw2 67 7 , , , cord-272759-dqkjofw2 67 8 or or CC cord-272759-dqkjofw2 67 9 are be VBP cord-272759-dqkjofw2 67 10 super super JJ cord-272759-dqkjofw2 67 11 - - NNS cord-272759-dqkjofw2 67 12 spreaders spreader NNS cord-272759-dqkjofw2 67 13 characteristic characteristic JJ cord-272759-dqkjofw2 67 14 of of IN cord-272759-dqkjofw2 67 15 most most JJS cord-272759-dqkjofw2 67 16 infectious infectious JJ cord-272759-dqkjofw2 67 17 diseases disease NNS cord-272759-dqkjofw2 67 18 ? ? . cord-272759-dqkjofw2 67 19 " " '' cord-272759-dqkjofw2 68 1 [ [ -LRB- cord-272759-dqkjofw2 68 2 17 17 CD cord-272759-dqkjofw2 68 3 ] ] -RRB- cord-272759-dqkjofw2 68 4 . . . cord-272759-dqkjofw2 69 1 We -PRON- PRP cord-272759-dqkjofw2 69 2 show show VBP cord-272759-dqkjofw2 69 3 that that IN cord-272759-dqkjofw2 69 4 , , , cord-272759-dqkjofw2 69 5 even even RB cord-272759-dqkjofw2 69 6 with with IN cord-272759-dqkjofw2 69 7 uniform uniform JJ cord-272759-dqkjofw2 69 8 rates rate NNS cord-272759-dqkjofw2 69 9 of of IN cord-272759-dqkjofw2 69 10 infection infection NN cord-272759-dqkjofw2 69 11 , , , cord-272759-dqkjofw2 69 12 super super JJ cord-272759-dqkjofw2 69 13 - - NNS cord-272759-dqkjofw2 69 14 spreaders spreader NNS cord-272759-dqkjofw2 69 15 will will MD cord-272759-dqkjofw2 69 16 occur occur VB cord-272759-dqkjofw2 69 17 , , , cord-272759-dqkjofw2 69 18 to to IN cord-272759-dqkjofw2 69 19 varying vary VBG cord-272759-dqkjofw2 69 20 degrees degree NNS cord-272759-dqkjofw2 69 21 , , , cord-272759-dqkjofw2 69 22 in in IN cord-272759-dqkjofw2 69 23 a a DT cord-272759-dqkjofw2 69 24 small small JJ cord-272759-dqkjofw2 69 25 - - HYPH cord-272759-dqkjofw2 69 26 world world NN cord-272759-dqkjofw2 69 27 or or CC cord-272759-dqkjofw2 69 28 scale scale NN cord-272759-dqkjofw2 69 29 - - HYPH cord-272759-dqkjofw2 69 30 free free JJ cord-272759-dqkjofw2 69 31 [ [ -LRB- cord-272759-dqkjofw2 69 32 16 16 CD cord-272759-dqkjofw2 69 33 ] ] -RRB- cord-272759-dqkjofw2 69 34 network network NN cord-272759-dqkjofw2 69 35 . . . cord-272759-dqkjofw2 70 1 The the DT cord-272759-dqkjofw2 70 2 implication implication NN cord-272759-dqkjofw2 70 3 is be VBZ cord-272759-dqkjofw2 70 4 that that IN cord-272759-dqkjofw2 70 5 super super JJ cord-272759-dqkjofw2 70 6 - - NNS cord-272759-dqkjofw2 70 7 spreaders spreader NNS cord-272759-dqkjofw2 70 8 are be VBP cord-272759-dqkjofw2 70 9 not not RB cord-272759-dqkjofw2 70 10 ( ( -LRB- cord-272759-dqkjofw2 70 11 necessarily necessarily RB cord-272759-dqkjofw2 70 12 ) ) -RRB- cord-272759-dqkjofw2 70 13 a a DT cord-272759-dqkjofw2 70 14 result result NN cord-272759-dqkjofw2 70 15 of of IN cord-272759-dqkjofw2 70 16 variable variable JJ cord-272759-dqkjofw2 70 17 rate rate NN cord-272759-dqkjofw2 70 18 of of IN cord-272759-dqkjofw2 70 19 infection infection NN cord-272759-dqkjofw2 70 20 . . . cord-272759-dqkjofw2 71 1 Nonetheless nonetheless RB cord-272759-dqkjofw2 71 2 , , , cord-272759-dqkjofw2 71 3 we -PRON- PRP cord-272759-dqkjofw2 71 4 argue argue VBP cord-272759-dqkjofw2 71 5 that that IN cord-272759-dqkjofw2 71 6 the the DT cord-272759-dqkjofw2 71 7 SARS SARS NNP cord-272759-dqkjofw2 71 8 outbreak outbreak NN cord-272759-dqkjofw2 71 9 in in IN cord-272759-dqkjofw2 71 10 Hong Hong NNP cord-272759-dqkjofw2 71 11 Kong Kong NNP cord-272759-dqkjofw2 71 12 was be VBD cord-272759-dqkjofw2 71 13 initiated initiate VBN cord-272759-dqkjofw2 71 14 by by IN cord-272759-dqkjofw2 71 15 a a DT cord-272759-dqkjofw2 71 16 single single JJ cord-272759-dqkjofw2 71 17 , , , cord-272759-dqkjofw2 71 18 rather rather RB cord-272759-dqkjofw2 71 19 unfortunate unfortunate JJ cord-272759-dqkjofw2 71 20 , , , cord-272759-dqkjofw2 71 21 super super JJ cord-272759-dqkjofw2 71 22 - - JJ cord-272759-dqkjofw2 71 23 spreader spreader JJ cord-272759-dqkjofw2 71 24 event event NN cord-272759-dqkjofw2 71 25 . . . cord-272759-dqkjofw2 72 1 In in IN cord-272759-dqkjofw2 72 2 the the DT cord-272759-dqkjofw2 72 3 next next JJ cord-272759-dqkjofw2 72 4 section section NN cord-272759-dqkjofw2 72 5 , , , cord-272759-dqkjofw2 72 6 we -PRON- PRP cord-272759-dqkjofw2 72 7 describe describe VBP cord-272759-dqkjofw2 72 8 our -PRON- PRP$ cord-272759-dqkjofw2 72 9 model model NN cord-272759-dqkjofw2 72 10 and and CC cord-272759-dqkjofw2 72 11 study study VB cord-272759-dqkjofw2 72 12 its -PRON- PRP$ cord-272759-dqkjofw2 72 13 behaviour behaviour NN cord-272759-dqkjofw2 72 14 analytically analytically RB cord-272759-dqkjofw2 72 15 . . . cord-272759-dqkjofw2 73 1 Subsequent subsequent JJ cord-272759-dqkjofw2 73 2 sections section NNS cord-272759-dqkjofw2 73 3 present present VBP cord-272759-dqkjofw2 73 4 some some DT cord-272759-dqkjofw2 73 5 numerical numerical JJ cord-272759-dqkjofw2 73 6 simulations simulation NNS cord-272759-dqkjofw2 73 7 and and CC cord-272759-dqkjofw2 73 8 a a DT cord-272759-dqkjofw2 73 9 summary summary NN cord-272759-dqkjofw2 73 10 of of IN cord-272759-dqkjofw2 73 11 our -PRON- PRP$ cord-272759-dqkjofw2 73 12 results result NNS cord-272759-dqkjofw2 73 13 . . . cord-272759-dqkjofw2 74 1 In in IN cord-272759-dqkjofw2 74 2 the the DT cord-272759-dqkjofw2 74 3 following follow VBG cord-272759-dqkjofw2 74 4 subsections subsection NNS cord-272759-dqkjofw2 74 5 , , , cord-272759-dqkjofw2 74 6 we -PRON- PRP cord-272759-dqkjofw2 74 7 define define VBP cord-272759-dqkjofw2 74 8 our -PRON- PRP$ cord-272759-dqkjofw2 74 9 model model NN cord-272759-dqkjofw2 74 10 structure structure NN cord-272759-dqkjofw2 74 11 ( ( -LRB- cord-272759-dqkjofw2 74 12 Section section NN cord-272759-dqkjofw2 74 13 2.1 2.1 CD cord-272759-dqkjofw2 74 14 ) ) -RRB- cord-272759-dqkjofw2 74 15 and and CC cord-272759-dqkjofw2 74 16 derive derive VB cord-272759-dqkjofw2 74 17 some some DT cord-272759-dqkjofw2 74 18 analytical analytical JJ cord-272759-dqkjofw2 74 19 results result NNS cord-272759-dqkjofw2 74 20 concerning concern VBG cord-272759-dqkjofw2 74 21 the the DT cord-272759-dqkjofw2 74 22 likelihood likelihood NN cord-272759-dqkjofw2 74 23 of of IN cord-272759-dqkjofw2 74 24 a a DT cord-272759-dqkjofw2 74 25 widespread widespread JJ cord-272759-dqkjofw2 74 26 outbreak outbreak NN cord-272759-dqkjofw2 74 27 ( ( -LRB- cord-272759-dqkjofw2 74 28 Section section NN cord-272759-dqkjofw2 74 29 2.2 2.2 CD cord-272759-dqkjofw2 74 30 ) ) -RRB- cord-272759-dqkjofw2 74 31 . . . cord-272759-dqkjofw2 75 1 Our -PRON- PRP$ cord-272759-dqkjofw2 75 2 aim aim NN cord-272759-dqkjofw2 75 3 is be VBZ cord-272759-dqkjofw2 75 4 to to TO cord-272759-dqkjofw2 75 5 capture capture VB cord-272759-dqkjofw2 75 6 accurately accurately RB cord-272759-dqkjofw2 75 7 the the DT cord-272759-dqkjofw2 75 8 qualitative qualitative JJ cord-272759-dqkjofw2 75 9 features feature NNS cord-272759-dqkjofw2 75 10 of of IN cord-272759-dqkjofw2 75 11 the the DT cord-272759-dqkjofw2 75 12 SARS SARS NNP cord-272759-dqkjofw2 75 13 epidemic epidemic NN cord-272759-dqkjofw2 75 14 with with IN cord-272759-dqkjofw2 75 15 the the DT cord-272759-dqkjofw2 75 16 simplest simple JJS cord-272759-dqkjofw2 75 17 model model NN cord-272759-dqkjofw2 75 18 ( ( -LRB- cord-272759-dqkjofw2 75 19 the the DT cord-272759-dqkjofw2 75 20 fewest few JJS cord-272759-dqkjofw2 75 21 parameters parameter NNS cord-272759-dqkjofw2 75 22 ) ) -RRB- cord-272759-dqkjofw2 75 23 . . . cord-272759-dqkjofw2 76 1 We -PRON- PRP cord-272759-dqkjofw2 76 2 propose propose VBP cord-272759-dqkjofw2 76 3 four four CD cord-272759-dqkjofw2 76 4 distinct distinct JJ cord-272759-dqkjofw2 76 5 states state NNS cord-272759-dqkjofw2 76 6 . . . cord-272759-dqkjofw2 77 1 Individuals individual NNS cord-272759-dqkjofw2 77 2 can can MD cord-272759-dqkjofw2 77 3 be be VB cord-272759-dqkjofw2 77 4 susceptible susceptible JJ cord-272759-dqkjofw2 77 5 ( ( -LRB- cord-272759-dqkjofw2 77 6 S s NN cord-272759-dqkjofw2 77 7 ) ) -RRB- cord-272759-dqkjofw2 77 8 , , , cord-272759-dqkjofw2 77 9 prone prone JJ cord-272759-dqkjofw2 77 10 ( ( -LRB- cord-272759-dqkjofw2 77 11 P p NN cord-272759-dqkjofw2 77 12 ) ) -RRB- cord-272759-dqkjofw2 77 13 , , , cord-272759-dqkjofw2 77 14 infected infect VBN cord-272759-dqkjofw2 77 15 ( ( -LRB- cord-272759-dqkjofw2 77 16 I i NN cord-272759-dqkjofw2 77 17 ) ) -RRB- cord-272759-dqkjofw2 77 18 , , , cord-272759-dqkjofw2 77 19 or or CC cord-272759-dqkjofw2 77 20 removed remove VBN cord-272759-dqkjofw2 77 21 ( ( -LRB- cord-272759-dqkjofw2 77 22 R r NN cord-272759-dqkjofw2 77 23 ) ) -RRB- cord-272759-dqkjofw2 77 24 . . . cord-272759-dqkjofw2 78 1 The the DT cord-272759-dqkjofw2 78 2 transmission transmission NN cord-272759-dqkjofw2 78 3 path path NN cord-272759-dqkjofw2 78 4 is be VBZ cord-272759-dqkjofw2 78 5 depicted depict VBN cord-272759-dqkjofw2 78 6 in in IN cord-272759-dqkjofw2 78 7 Fig Fig NNP cord-272759-dqkjofw2 78 8 . . . cord-272759-dqkjofw2 79 1 2 2 LS cord-272759-dqkjofw2 79 2 . . . cord-272759-dqkjofw2 80 1 Infected infected JJ cord-272759-dqkjofw2 80 2 individuals individual NNS cord-272759-dqkjofw2 80 3 can can MD cord-272759-dqkjofw2 80 4 cause cause VB cord-272759-dqkjofw2 80 5 susceptible susceptible JJ cord-272759-dqkjofw2 80 6 individuals individual NNS cord-272759-dqkjofw2 80 7 , , , cord-272759-dqkjofw2 80 8 to to TO cord-272759-dqkjofw2 80 9 whom whom WP cord-272759-dqkjofw2 80 10 they -PRON- PRP cord-272759-dqkjofw2 80 11 are be VBP cord-272759-dqkjofw2 80 12 linked link VBN cord-272759-dqkjofw2 80 13 , , , cord-272759-dqkjofw2 80 14 to to TO cord-272759-dqkjofw2 80 15 become become VB cord-272759-dqkjofw2 80 16 prone prone JJ cord-272759-dqkjofw2 80 17 with with IN cord-272759-dqkjofw2 80 18 some some DT cord-272759-dqkjofw2 80 19 probability probability NN cord-272759-dqkjofw2 80 20 ( ( -LRB- cord-272759-dqkjofw2 80 21 p p NN cord-272759-dqkjofw2 80 22 1 1 CD cord-272759-dqkjofw2 80 23 or or CC cord-272759-dqkjofw2 80 24 p p NN cord-272759-dqkjofw2 80 25 2 2 CD cord-272759-dqkjofw2 80 26 ) ) -RRB- cord-272759-dqkjofw2 80 27 . . . cord-272759-dqkjofw2 81 1 By by IN cord-272759-dqkjofw2 81 2 infection infection NN cord-272759-dqkjofw2 81 3 we -PRON- PRP cord-272759-dqkjofw2 81 4 mean mean VBP cord-272759-dqkjofw2 81 5 the the DT cord-272759-dqkjofw2 81 6 transition transition NN cord-272759-dqkjofw2 81 7 from from IN cord-272759-dqkjofw2 81 8 the the DT cord-272759-dqkjofw2 81 9 susceptible susceptible JJ cord-272759-dqkjofw2 81 10 state state NN cord-272759-dqkjofw2 81 11 to to IN cord-272759-dqkjofw2 81 12 the the DT cord-272759-dqkjofw2 81 13 prone prone JJ cord-272759-dqkjofw2 81 14 state state NN cord-272759-dqkjofw2 81 15 . . . cord-272759-dqkjofw2 82 1 Infected infected JJ cord-272759-dqkjofw2 82 2 individuals individual NNS cord-272759-dqkjofw2 82 3 can can MD cord-272759-dqkjofw2 82 4 cause cause VB cord-272759-dqkjofw2 82 5 their -PRON- PRP$ cord-272759-dqkjofw2 82 6 immediate immediate JJ cord-272759-dqkjofw2 82 7 neighbours neighbour NNS cord-272759-dqkjofw2 82 8 to to TO cord-272759-dqkjofw2 82 9 become become VB cord-272759-dqkjofw2 82 10 infected infect VBN cord-272759-dqkjofw2 82 11 with with IN cord-272759-dqkjofw2 82 12 probability probability NN cord-272759-dqkjofw2 82 13 p p NN cord-272759-dqkjofw2 82 14 1 1 CD cord-272759-dqkjofw2 82 15 ; ; : cord-272759-dqkjofw2 82 16 long long JJ cord-272759-dqkjofw2 82 17 range range NN cord-272759-dqkjofw2 82 18 links link NNS cord-272759-dqkjofw2 82 19 cause cause VBP cord-272759-dqkjofw2 82 20 infection infection NN cord-272759-dqkjofw2 82 21 with with IN cord-272759-dqkjofw2 82 22 probability probability NN cord-272759-dqkjofw2 82 23 p p NN cord-272759-dqkjofw2 82 24 2 2 CD cord-272759-dqkjofw2 82 25 . . . cord-272759-dqkjofw2 83 1 Prone prone JJ cord-272759-dqkjofw2 83 2 individuals individual NNS cord-272759-dqkjofw2 83 3 become become VBP cord-272759-dqkjofw2 83 4 infected infect VBN cord-272759-dqkjofw2 83 5 with with IN cord-272759-dqkjofw2 83 6 probability probability NN cord-272759-dqkjofw2 83 7 r r NN cord-272759-dqkjofw2 83 8 0 0 CD cord-272759-dqkjofw2 83 9 and and CC cord-272759-dqkjofw2 83 10 , , , cord-272759-dqkjofw2 83 11 finally finally RB cord-272759-dqkjofw2 83 12 , , , cord-272759-dqkjofw2 83 13 infected infected JJ cord-272759-dqkjofw2 83 14 individuals individual NNS cord-272759-dqkjofw2 83 15 become become VBN cord-272759-dqkjofw2 83 16 removed remove VBN cord-272759-dqkjofw2 83 17 with with IN cord-272759-dqkjofw2 83 18 probability probability NN cord-272759-dqkjofw2 83 19 r r NN cord-272759-dqkjofw2 83 20 1 1 CD cord-272759-dqkjofw2 83 21 . . . cord-272759-dqkjofw2 84 1 Just just RB cord-272759-dqkjofw2 84 2 as as IN cord-272759-dqkjofw2 84 3 in in IN cord-272759-dqkjofw2 84 4 the the DT cord-272759-dqkjofw2 84 5 SIR SIR NNP cord-272759-dqkjofw2 84 6 model model NN cord-272759-dqkjofw2 84 7 , , , cord-272759-dqkjofw2 84 8 we -PRON- PRP cord-272759-dqkjofw2 84 9 do do VBP cord-272759-dqkjofw2 84 10 not not RB cord-272759-dqkjofw2 84 11 distinguish distinguish VB cord-272759-dqkjofw2 84 12 fatalities fatality NNS cord-272759-dqkjofw2 84 13 from from IN cord-272759-dqkjofw2 84 14 recoveries recovery NNS cord-272759-dqkjofw2 84 15 : : : cord-272759-dqkjofw2 84 16 in in IN cord-272759-dqkjofw2 84 17 either either DT cord-272759-dqkjofw2 84 18 case case NN cord-272759-dqkjofw2 84 19 , , , cord-272759-dqkjofw2 84 20 the the DT cord-272759-dqkjofw2 84 21 individuals individual NNS cord-272759-dqkjofw2 84 22 are be VBP cord-272759-dqkjofw2 84 23 assumed assume VBN cord-272759-dqkjofw2 84 24 to to TO cord-272759-dqkjofw2 84 25 have have VB cord-272759-dqkjofw2 84 26 acquired acquire VBN cord-272759-dqkjofw2 84 27 immunity immunity NN cord-272759-dqkjofw2 84 28 . . . cord-272759-dqkjofw2 85 1 The the DT cord-272759-dqkjofw2 85 2 model model NN cord-272759-dqkjofw2 85 3 states state VBZ cord-272759-dqkjofw2 85 4 that that IN cord-272759-dqkjofw2 85 5 we -PRON- PRP cord-272759-dqkjofw2 85 6 describe describe VBP cord-272759-dqkjofw2 85 7 here here RB cord-272759-dqkjofw2 85 8 bear bear VBP cord-272759-dqkjofw2 85 9 a a DT cord-272759-dqkjofw2 85 10 close close JJ cord-272759-dqkjofw2 85 11 correspondence correspondence NN cord-272759-dqkjofw2 85 12 to to IN cord-272759-dqkjofw2 85 13 the the DT cord-272759-dqkjofw2 85 14 four four CD cord-272759-dqkjofw2 85 15 states state NNS cord-272759-dqkjofw2 85 16 of of IN cord-272759-dqkjofw2 85 17 the the DT cord-272759-dqkjofw2 85 18 SEIR SEIR NNP cord-272759-dqkjofw2 85 19 model model NN cord-272759-dqkjofw2 85 20 . . . cord-272759-dqkjofw2 86 1 The the DT cord-272759-dqkjofw2 86 2 prone prone JJ cord-272759-dqkjofw2 86 3 state state NN cord-272759-dqkjofw2 86 4 is be VBZ cord-272759-dqkjofw2 86 5 analogous analogous JJ cord-272759-dqkjofw2 86 6 to to IN cord-272759-dqkjofw2 86 7 the the DT cord-272759-dqkjofw2 86 8 exposed expose VBN cord-272759-dqkjofw2 86 9 ( ( -LRB- cord-272759-dqkjofw2 86 10 E e NN cord-272759-dqkjofw2 86 11 ) ) -RRB- cord-272759-dqkjofw2 86 12 state state NN cord-272759-dqkjofw2 86 13 in in IN cord-272759-dqkjofw2 86 14 the the DT cord-272759-dqkjofw2 86 15 SEIR SEIR NNP cord-272759-dqkjofw2 86 16 model model NN cord-272759-dqkjofw2 86 17 . . . cord-272759-dqkjofw2 87 1 We -PRON- PRP cord-272759-dqkjofw2 87 2 choose choose VBP cord-272759-dqkjofw2 87 3 to to TO cord-272759-dqkjofw2 87 4 use use VB cord-272759-dqkjofw2 87 5 the the DT cord-272759-dqkjofw2 87 6 new new JJ cord-272759-dqkjofw2 87 7 term term NN cord-272759-dqkjofw2 87 8 P p NN cord-272759-dqkjofw2 87 9 because because IN cord-272759-dqkjofw2 87 10 the the DT cord-272759-dqkjofw2 87 11 epidemiological epidemiological JJ cord-272759-dqkjofw2 87 12 state state NN cord-272759-dqkjofw2 87 13 is be VBZ cord-272759-dqkjofw2 87 14 slightly slightly RB cord-272759-dqkjofw2 87 15 different different JJ cord-272759-dqkjofw2 87 16 . . . cord-272759-dqkjofw2 88 1 By by IN cord-272759-dqkjofw2 88 2 prone prone JJ cord-272759-dqkjofw2 88 3 we -PRON- PRP cord-272759-dqkjofw2 88 4 mean mean VBP cord-272759-dqkjofw2 88 5 both both CC cord-272759-dqkjofw2 88 6 the the DT cord-272759-dqkjofw2 88 7 infected infected JJ cord-272759-dqkjofw2 88 8 but but CC cord-272759-dqkjofw2 88 9 not not RB cord-272759-dqkjofw2 88 10 infectious infectious JJ cord-272759-dqkjofw2 88 11 ( ( -LRB- cord-272759-dqkjofw2 88 12 incubation incubation NN cord-272759-dqkjofw2 88 13 ) ) -RRB- cord-272759-dqkjofw2 88 14 period period NN cord-272759-dqkjofw2 88 15 and and CC cord-272759-dqkjofw2 88 16 the the DT cord-272759-dqkjofw2 88 17 pre pre JJ cord-272759-dqkjofw2 88 18 - - JJ cord-272759-dqkjofw2 88 19 symptomatic symptomatic JJ cord-272759-dqkjofw2 88 20 period period NN cord-272759-dqkjofw2 88 21 . . . cord-272759-dqkjofw2 89 1 For for IN cord-272759-dqkjofw2 89 2 SARS SARS NNP cord-272759-dqkjofw2 89 3 , , , cord-272759-dqkjofw2 89 4 all all DT cord-272759-dqkjofw2 89 5 infections infection NNS cord-272759-dqkjofw2 89 6 in in IN cord-272759-dqkjofw2 89 7 Hong Hong NNP cord-272759-dqkjofw2 89 8 Kong Kong NNP cord-272759-dqkjofw2 89 9 could could MD cord-272759-dqkjofw2 89 10 be be VB cord-272759-dqkjofw2 89 11 traced trace VBN cord-272759-dqkjofw2 89 12 to to TO cord-272759-dqkjofw2 89 13 contact contact VB cord-272759-dqkjofw2 89 14 with with IN cord-272759-dqkjofw2 89 15 a a DT cord-272759-dqkjofw2 89 16 symptomatic symptomatic JJ cord-272759-dqkjofw2 89 17 individual individual NN cord-272759-dqkjofw2 89 18 . . . cord-272759-dqkjofw2 90 1 2 2 LS cord-272759-dqkjofw2 91 1 Hence hence RB cord-272759-dqkjofw2 91 2 , , , cord-272759-dqkjofw2 91 3 for for IN cord-272759-dqkjofw2 91 4 the the DT cord-272759-dqkjofw2 91 5 purposes purpose NNS cord-272759-dqkjofw2 91 6 of of IN cord-272759-dqkjofw2 91 7 modelling modelling NN cord-272759-dqkjofw2 91 8 transmission transmission NN cord-272759-dqkjofw2 91 9 , , , cord-272759-dqkjofw2 91 10 we -PRON- PRP cord-272759-dqkjofw2 91 11 assume assume VBP cord-272759-dqkjofw2 91 12 that that IN cord-272759-dqkjofw2 91 13 , , , cord-272759-dqkjofw2 91 14 during during IN cord-272759-dqkjofw2 91 15 the the DT cord-272759-dqkjofw2 91 16 pre pre JJ cord-272759-dqkjofw2 91 17 - - JJ cord-272759-dqkjofw2 91 18 symptomatic symptomatic JJ cord-272759-dqkjofw2 91 19 period period NN cord-272759-dqkjofw2 91 20 , , , cord-272759-dqkjofw2 91 21 there there EX cord-272759-dqkjofw2 91 22 is be VBZ cord-272759-dqkjofw2 91 23 no no DT cord-272759-dqkjofw2 91 24 chance chance NN cord-272759-dqkjofw2 91 25 of of IN cord-272759-dqkjofw2 91 26 transmission transmission NN cord-272759-dqkjofw2 91 27 . . . cord-272759-dqkjofw2 92 1 Moreover moreover RB cord-272759-dqkjofw2 92 2 , , , cord-272759-dqkjofw2 92 3 to to TO cord-272759-dqkjofw2 92 4 calibrate calibrate VB cord-272759-dqkjofw2 92 5 our -PRON- PRP$ cord-272759-dqkjofw2 92 6 model model NN cord-272759-dqkjofw2 92 7 with with IN cord-272759-dqkjofw2 92 8 the the DT cord-272759-dqkjofw2 92 9 observed observed JJ cord-272759-dqkjofw2 92 10 data datum NNS cord-272759-dqkjofw2 92 11 ( ( -LRB- cord-272759-dqkjofw2 92 12 which which WDT cord-272759-dqkjofw2 92 13 , , , cord-272759-dqkjofw2 92 14 by by IN cord-272759-dqkjofw2 92 15 definition definition NN cord-272759-dqkjofw2 92 16 , , , cord-272759-dqkjofw2 92 17 are be VBP cord-272759-dqkjofw2 92 18 hospital hospital NN cord-272759-dqkjofw2 92 19 admissions admission NNS cord-272759-dqkjofw2 92 20 ) ) -RRB- cord-272759-dqkjofw2 92 21 , , , cord-272759-dqkjofw2 92 22 we -PRON- PRP cord-272759-dqkjofw2 92 23 further further RB cord-272759-dqkjofw2 92 24 prescribe prescribe VBP cord-272759-dqkjofw2 92 25 that that IN cord-272759-dqkjofw2 92 26 the the DT cord-272759-dqkjofw2 92 27 time time NN cord-272759-dqkjofw2 92 28 between between IN cord-272759-dqkjofw2 92 29 the the DT cord-272759-dqkjofw2 92 30 onset onset NN cord-272759-dqkjofw2 92 31 of of IN cord-272759-dqkjofw2 92 32 symptoms symptom NNS cord-272759-dqkjofw2 92 33 and and CC cord-272759-dqkjofw2 92 34 hospitalisation hospitalisation NN cord-272759-dqkjofw2 92 35 is be VBZ cord-272759-dqkjofw2 92 36 constant constant JJ cord-272759-dqkjofw2 92 37 ( ( -LRB- cord-272759-dqkjofw2 92 38 or or CC cord-272759-dqkjofw2 92 39 , , , cord-272759-dqkjofw2 92 40 equivalently equivalently RB cord-272759-dqkjofw2 92 41 , , , cord-272759-dqkjofw2 92 42 follows follow VBZ cord-272759-dqkjofw2 92 43 a a DT cord-272759-dqkjofw2 92 44 stationary stationary JJ cord-272759-dqkjofw2 92 45 unimodal unimodal JJ cord-272759-dqkjofw2 92 46 distribution distribution NN cord-272759-dqkjofw2 92 47 ) ) -RRB- cord-272759-dqkjofw2 92 48 . . . cord-272759-dqkjofw2 93 1 In in IN cord-272759-dqkjofw2 93 2 our -PRON- PRP$ cord-272759-dqkjofw2 93 3 model model NN cord-272759-dqkjofw2 93 4 we -PRON- PRP cord-272759-dqkjofw2 93 5 explicitly explicitly RB cord-272759-dqkjofw2 93 6 model model VBP cord-272759-dqkjofw2 93 7 the the DT cord-272759-dqkjofw2 93 8 geographical geographical JJ cord-272759-dqkjofw2 93 9 structure structure NN cord-272759-dqkjofw2 93 10 of of IN cord-272759-dqkjofw2 93 11 the the DT cord-272759-dqkjofw2 93 12 population population NN cord-272759-dqkjofw2 93 13 . . . cord-272759-dqkjofw2 94 1 We -PRON- PRP cord-272759-dqkjofw2 94 2 include include VBP cord-272759-dqkjofw2 94 3 both both DT cord-272759-dqkjofw2 94 4 " " `` cord-272759-dqkjofw2 94 5 local local JJ cord-272759-dqkjofw2 94 6 " " '' cord-272759-dqkjofw2 94 7 and and CC cord-272759-dqkjofw2 94 8 " " `` cord-272759-dqkjofw2 94 9 non non JJ cord-272759-dqkjofw2 94 10 - - JJ cord-272759-dqkjofw2 94 11 local local JJ cord-272759-dqkjofw2 94 12 " " '' cord-272759-dqkjofw2 94 13 links link NNS cord-272759-dqkjofw2 94 14 . . . cord-272759-dqkjofw2 95 1 Because because IN cord-272759-dqkjofw2 95 2 of of IN cord-272759-dqkjofw2 95 3 common common JJ cord-272759-dqkjofw2 95 4 transmission transmission NN cord-272759-dqkjofw2 95 5 of of IN cord-272759-dqkjofw2 95 6 SARS SARS NNP cord-272759-dqkjofw2 95 7 within within IN cord-272759-dqkjofw2 95 8 specific specific JJ cord-272759-dqkjofw2 95 9 housing housing NN cord-272759-dqkjofw2 95 10 estates estate NNS cord-272759-dqkjofw2 95 11 and and CC cord-272759-dqkjofw2 95 12 districts district NNS cord-272759-dqkjofw2 95 13 in in IN cord-272759-dqkjofw2 95 14 Hong Hong NNP cord-272759-dqkjofw2 95 15 Kong Kong NNP cord-272759-dqkjofw2 95 16 , , , cord-272759-dqkjofw2 95 17 and and CC cord-272759-dqkjofw2 95 18 the the DT cord-272759-dqkjofw2 95 19 ( ( -LRB- cord-272759-dqkjofw2 95 20 both both DT cord-272759-dqkjofw2 95 21 real real JJ cord-272759-dqkjofw2 95 22 and and CC cord-272759-dqkjofw2 95 23 perceived perceived JJ cord-272759-dqkjofw2 95 24 ) ) -RRB- cord-272759-dqkjofw2 95 25 risk risk NN cord-272759-dqkjofw2 95 26 of of IN cord-272759-dqkjofw2 95 27 transmission transmission NN cord-272759-dqkjofw2 95 28 in in IN cord-272759-dqkjofw2 95 29 workplaces workplace NNS cord-272759-dqkjofw2 95 30 ( ( -LRB- cord-272759-dqkjofw2 95 31 primarily primarily RB cord-272759-dqkjofw2 95 32 hospitals hospital NNS cord-272759-dqkjofw2 95 33 and and CC cord-272759-dqkjofw2 95 34 schools school NNS cord-272759-dqkjofw2 95 35 ) ) -RRB- cord-272759-dqkjofw2 95 36 or or CC cord-272759-dqkjofw2 95 37 other other JJ cord-272759-dqkjofw2 95 38 public public JJ cord-272759-dqkjofw2 95 39 areas area NNS cord-272759-dqkjofw2 95 40 , , , cord-272759-dqkjofw2 95 41 we -PRON- PRP cord-272759-dqkjofw2 95 42 model model VBP cord-272759-dqkjofw2 95 43 these these DT cord-272759-dqkjofw2 95 44 two two CD cord-272759-dqkjofw2 95 45 types type NNS cord-272759-dqkjofw2 95 46 of of IN cord-272759-dqkjofw2 95 47 transmission transmission NN cord-272759-dqkjofw2 95 48 separately separately RB cord-272759-dqkjofw2 95 49 . . . cord-272759-dqkjofw2 96 1 The the DT cord-272759-dqkjofw2 96 2 geographical geographical JJ cord-272759-dqkjofw2 96 3 arrangement arrangement NN cord-272759-dqkjofw2 96 4 of of IN cord-272759-dqkjofw2 96 5 nodes node NNS cord-272759-dqkjofw2 96 6 represents represent VBZ cord-272759-dqkjofw2 96 7 the the DT cord-272759-dqkjofw2 96 8 residence residence NN cord-272759-dqkjofw2 96 9 of of IN cord-272759-dqkjofw2 96 10 each each DT cord-272759-dqkjofw2 96 11 individual individual NN cord-272759-dqkjofw2 96 12 . . . cord-272759-dqkjofw2 97 1 So so RB cord-272759-dqkjofw2 97 2 , , , cord-272759-dqkjofw2 97 3 by by IN cord-272759-dqkjofw2 97 4 " " `` cord-272759-dqkjofw2 97 5 local local JJ cord-272759-dqkjofw2 97 6 " " '' cord-272759-dqkjofw2 97 7 transmission transmission NN cord-272759-dqkjofw2 97 8 , , , cord-272759-dqkjofw2 97 9 we -PRON- PRP cord-272759-dqkjofw2 97 10 mean mean VBP cord-272759-dqkjofw2 97 11 only only RB cord-272759-dqkjofw2 97 12 transmission transmission NN cord-272759-dqkjofw2 97 13 within within IN cord-272759-dqkjofw2 97 14 a a DT cord-272759-dqkjofw2 97 15 family family NN cord-272759-dqkjofw2 97 16 unit unit NN cord-272759-dqkjofw2 97 17 ( ( -LRB- cord-272759-dqkjofw2 97 18 i.e. i.e. FW cord-272759-dqkjofw2 97 19 residents resident NNS cord-272759-dqkjofw2 97 20 of of IN cord-272759-dqkjofw2 97 21 a a DT cord-272759-dqkjofw2 97 22 single single JJ cord-272759-dqkjofw2 97 23 flat flat NN cord-272759-dqkjofw2 97 24 ) ) -RRB- cord-272759-dqkjofw2 97 25 , , , cord-272759-dqkjofw2 97 26 or or CC cord-272759-dqkjofw2 97 27 between between IN cord-272759-dqkjofw2 97 28 adjacent adjacent JJ cord-272759-dqkjofw2 97 29 flats flat NNS cord-272759-dqkjofw2 97 30 . . . cord-272759-dqkjofw2 98 1 3 3 LS cord-272759-dqkjofw2 99 1 Hence hence RB cord-272759-dqkjofw2 99 2 , , , cord-272759-dqkjofw2 99 3 " " `` cord-272759-dqkjofw2 99 4 non non JJ cord-272759-dqkjofw2 99 5 - - JJ cord-272759-dqkjofw2 99 6 local local JJ cord-272759-dqkjofw2 99 7 " " '' cord-272759-dqkjofw2 99 8 transmission transmission NN cord-272759-dqkjofw2 100 1 The the DT cord-272759-dqkjofw2 100 2 top top JJ cord-272759-dqkjofw2 100 3 panel panel NN cord-272759-dqkjofw2 100 4 depicts depict VBZ cord-272759-dqkjofw2 100 5 the the DT cord-272759-dqkjofw2 100 6 transmission transmission NN cord-272759-dqkjofw2 100 7 state state NN cord-272759-dqkjofw2 100 8 diagram diagram NN cord-272759-dqkjofw2 100 9 : : : cord-272759-dqkjofw2 100 10 S s NN cord-272759-dqkjofw2 100 11 to to IN cord-272759-dqkjofw2 100 12 P p NN cord-272759-dqkjofw2 100 13 based base VBN cord-272759-dqkjofw2 100 14 on on IN cord-272759-dqkjofw2 100 15 the the DT cord-272759-dqkjofw2 100 16 SW SW NNP cord-272759-dqkjofw2 100 17 structure structure NN cord-272759-dqkjofw2 100 18 and and CC cord-272759-dqkjofw2 100 19 the the DT cord-272759-dqkjofw2 100 20 infection infection NN cord-272759-dqkjofw2 100 21 probabilities probabilitie VBZ cord-272759-dqkjofw2 100 22 p p NN cord-272759-dqkjofw2 100 23 1,2 1,2 CD cord-272759-dqkjofw2 100 24 ; ; : cord-272759-dqkjofw2 101 1 P p NN cord-272759-dqkjofw2 101 2 to to IN cord-272759-dqkjofw2 101 3 I -PRON- PRP cord-272759-dqkjofw2 101 4 with with IN cord-272759-dqkjofw2 101 5 probability probability NN cord-272759-dqkjofw2 101 6 r r NN cord-272759-dqkjofw2 101 7 0 0 CD cord-272759-dqkjofw2 101 8 ; ; : cord-272759-dqkjofw2 101 9 and and CC cord-272759-dqkjofw2 101 10 I -PRON- PRP cord-272759-dqkjofw2 101 11 to to IN cord-272759-dqkjofw2 101 12 R r NN cord-272759-dqkjofw2 101 13 with with IN cord-272759-dqkjofw2 101 14 probability probability NN cord-272759-dqkjofw2 101 15 r r NN cord-272759-dqkjofw2 101 16 1 1 CD cord-272759-dqkjofw2 101 17 . . . cord-272759-dqkjofw2 102 1 The the DT cord-272759-dqkjofw2 102 2 lower low JJR cord-272759-dqkjofw2 102 3 panel panel NN cord-272759-dqkjofw2 102 4 depicts depict VBZ cord-272759-dqkjofw2 102 5 the the DT cord-272759-dqkjofw2 102 6 distinction distinction NN cord-272759-dqkjofw2 102 7 between between IN cord-272759-dqkjofw2 102 8 " " `` cord-272759-dqkjofw2 102 9 local local JJ cord-272759-dqkjofw2 102 10 " " '' cord-272759-dqkjofw2 102 11 ( ( -LRB- cord-272759-dqkjofw2 102 12 i.e. i.e. FW cord-272759-dqkjofw2 102 13 short short JJ cord-272759-dqkjofw2 102 14 range range NN cord-272759-dqkjofw2 102 15 ) ) -RRB- cord-272759-dqkjofw2 102 16 and and CC cord-272759-dqkjofw2 102 17 " " `` cord-272759-dqkjofw2 102 18 non non JJ cord-272759-dqkjofw2 102 19 - - JJ cord-272759-dqkjofw2 102 20 local local JJ cord-272759-dqkjofw2 102 21 " " '' cord-272759-dqkjofw2 102 22 ( ( -LRB- cord-272759-dqkjofw2 102 23 long long JJ cord-272759-dqkjofw2 102 24 range range NN cord-272759-dqkjofw2 102 25 ) ) -RRB- cord-272759-dqkjofw2 102 26 network network NN cord-272759-dqkjofw2 102 27 links link NNS cord-272759-dqkjofw2 102 28 . . . cord-272759-dqkjofw2 103 1 The the DT cord-272759-dqkjofw2 103 2 lower low JJR cord-272759-dqkjofw2 103 3 panel panel NN cord-272759-dqkjofw2 103 4 shows show VBZ cord-272759-dqkjofw2 103 5 the the DT cord-272759-dqkjofw2 103 6 arrangement arrangement NN cord-272759-dqkjofw2 103 7 of of IN cord-272759-dqkjofw2 103 8 nodes node NNS cord-272759-dqkjofw2 103 9 in in IN cord-272759-dqkjofw2 103 10 a a DT cord-272759-dqkjofw2 103 11 small small JJ cord-272759-dqkjofw2 103 12 - - HYPH cord-272759-dqkjofw2 103 13 world world NN cord-272759-dqkjofw2 103 14 network network NN cord-272759-dqkjofw2 103 15 . . . cord-272759-dqkjofw2 104 1 The the DT cord-272759-dqkjofw2 104 2 black black NN cord-272759-dqkjofw2 104 3 ( ( -LRB- cord-272759-dqkjofw2 104 4 infected infected JJ cord-272759-dqkjofw2 104 5 ) ) -RRB- cord-272759-dqkjofw2 104 6 node node NN cord-272759-dqkjofw2 104 7 may may MD cord-272759-dqkjofw2 104 8 infect infect VB cord-272759-dqkjofw2 104 9 its -PRON- PRP$ cord-272759-dqkjofw2 104 10 four four CD cord-272759-dqkjofw2 104 11 immediate immediate JJ cord-272759-dqkjofw2 104 12 neighbours neighbour NNS cord-272759-dqkjofw2 104 13 with with IN cord-272759-dqkjofw2 104 14 probability probability NN cord-272759-dqkjofw2 104 15 p p NN cord-272759-dqkjofw2 104 16 1 1 CD cord-272759-dqkjofw2 104 17 and and CC cord-272759-dqkjofw2 104 18 three three CD cord-272759-dqkjofw2 104 19 other other JJ cord-272759-dqkjofw2 104 20 nodes node NNS cord-272759-dqkjofw2 104 21 ( ( -LRB- cord-272759-dqkjofw2 104 22 hashed hash VBN cord-272759-dqkjofw2 104 23 ) ) -RRB- cord-272759-dqkjofw2 104 24 with with IN cord-272759-dqkjofw2 104 25 probability probability NN cord-272759-dqkjofw2 104 26 p p NN cord-272759-dqkjofw2 104 27 2 2 CD cord-272759-dqkjofw2 104 28 . . . cord-272759-dqkjofw2 104 29 refers refer VBZ cord-272759-dqkjofw2 104 30 to to IN cord-272759-dqkjofw2 104 31 transmission transmission NN cord-272759-dqkjofw2 104 32 between between IN cord-272759-dqkjofw2 104 33 non non JJ cord-272759-dqkjofw2 104 34 - - JJ cord-272759-dqkjofw2 104 35 family family JJ cord-272759-dqkjofw2 104 36 members member NNS cord-272759-dqkjofw2 104 37 due due JJ cord-272759-dqkjofw2 104 38 to to IN cord-272759-dqkjofw2 104 39 the the DT cord-272759-dqkjofw2 104 40 mixing mixing NN cord-272759-dqkjofw2 104 41 of of IN cord-272759-dqkjofw2 104 42 individuals individual NNS cord-272759-dqkjofw2 104 43 in in IN cord-272759-dqkjofw2 104 44 public public JJ cord-272759-dqkjofw2 104 45 spaces space NNS cord-272759-dqkjofw2 104 46 . . . cord-272759-dqkjofw2 105 1 In in IN cord-272759-dqkjofw2 105 2 the the DT cord-272759-dqkjofw2 105 3 context context NN cord-272759-dqkjofw2 105 4 of of IN cord-272759-dqkjofw2 105 5 the the DT cord-272759-dqkjofw2 105 6 SARS SARS NNP cord-272759-dqkjofw2 105 7 outbreak outbreak NN cord-272759-dqkjofw2 105 8 in in IN cord-272759-dqkjofw2 105 9 Hong Hong NNP cord-272759-dqkjofw2 105 10 Kong Kong NNP cord-272759-dqkjofw2 105 11 , , , cord-272759-dqkjofw2 105 12 this this DT cord-272759-dqkjofw2 105 13 would would MD cord-272759-dqkjofw2 105 14 include include VB cord-272759-dqkjofw2 105 15 transmission transmission NN cord-272759-dqkjofw2 105 16 within within IN cord-272759-dqkjofw2 105 17 hospitals hospital NNS cord-272759-dqkjofw2 105 18 , , , cord-272759-dqkjofw2 105 19 schools school NNS cord-272759-dqkjofw2 105 20 and and CC cord-272759-dqkjofw2 105 21 public public JJ cord-272759-dqkjofw2 105 22 spaces space NNS cord-272759-dqkjofw2 105 23 . . . cord-272759-dqkjofw2 106 1 In in IN cord-272759-dqkjofw2 106 2 our -PRON- PRP$ cord-272759-dqkjofw2 106 3 model model NN cord-272759-dqkjofw2 106 4 , , , cord-272759-dqkjofw2 106 5 we -PRON- PRP cord-272759-dqkjofw2 106 6 expect expect VBP cord-272759-dqkjofw2 106 7 SSE SSE NNP cord-272759-dqkjofw2 106 8 to to TO cord-272759-dqkjofw2 106 9 be be VB cord-272759-dqkjofw2 106 10 represented represent VBN cord-272759-dqkjofw2 106 11 through through IN cord-272759-dqkjofw2 106 12 a a DT cord-272759-dqkjofw2 106 13 single single JJ cord-272759-dqkjofw2 106 14 node node NN cord-272759-dqkjofw2 106 15 with with IN cord-272759-dqkjofw2 106 16 a a DT cord-272759-dqkjofw2 106 17 large large JJ cord-272759-dqkjofw2 106 18 number number NN cord-272759-dqkjofw2 106 19 of of IN cord-272759-dqkjofw2 106 20 non non JJ cord-272759-dqkjofw2 106 21 - - JJ cord-272759-dqkjofw2 106 22 local local JJ cord-272759-dqkjofw2 106 23 connections connection NNS cord-272759-dqkjofw2 106 24 . . . cord-272759-dqkjofw2 107 1 4 4 LS cord-272759-dqkjofw2 108 1 We -PRON- PRP cord-272759-dqkjofw2 108 2 fix fix VBP cord-272759-dqkjofw2 108 3 the the DT cord-272759-dqkjofw2 108 4 population population NN cord-272759-dqkjofw2 108 5 N n CD cord-272759-dqkjofw2 108 6 and and CC cord-272759-dqkjofw2 108 7 assume assume VB cord-272759-dqkjofw2 108 8 that that IN cord-272759-dqkjofw2 108 9 there there EX cord-272759-dqkjofw2 108 10 are be VBP cord-272759-dqkjofw2 108 11 no no DT cord-272759-dqkjofw2 108 12 other other JJ cord-272759-dqkjofw2 108 13 additions addition NNS cord-272759-dqkjofw2 108 14 to to IN cord-272759-dqkjofw2 108 15 , , , cord-272759-dqkjofw2 108 16 or or CC cord-272759-dqkjofw2 108 17 deletions deletion NNS cord-272759-dqkjofw2 108 18 from from IN cord-272759-dqkjofw2 108 19 , , , cord-272759-dqkjofw2 108 20 the the DT cord-272759-dqkjofw2 108 21 population population NN cord-272759-dqkjofw2 108 22 from from IN cord-272759-dqkjofw2 108 23 any any DT cord-272759-dqkjofw2 108 24 other other JJ cord-272759-dqkjofw2 108 25 cause cause NN cord-272759-dqkjofw2 108 26 for for IN cord-272759-dqkjofw2 108 27 the the DT cord-272759-dqkjofw2 108 28 duration duration NN cord-272759-dqkjofw2 108 29 of of IN cord-272759-dqkjofw2 108 30 each each DT cord-272759-dqkjofw2 108 31 simulation simulation NN cord-272759-dqkjofw2 108 32 . . . cord-272759-dqkjofw2 109 1 The the DT cord-272759-dqkjofw2 109 2 population population NN cord-272759-dqkjofw2 109 3 of of IN cord-272759-dqkjofw2 109 4 N n CD cord-272759-dqkjofw2 109 5 nodes node NNS cord-272759-dqkjofw2 109 6 is be VBZ cord-272759-dqkjofw2 109 7 arranged arrange VBN cord-272759-dqkjofw2 109 8 in in IN cord-272759-dqkjofw2 109 9 a a DT cord-272759-dqkjofw2 109 10 regular regular JJ cord-272759-dqkjofw2 109 11 grid grid NN cord-272759-dqkjofw2 109 12 , , , cord-272759-dqkjofw2 109 13 of of IN cord-272759-dqkjofw2 109 14 side side NN cord-272759-dqkjofw2 109 15 length length NN cord-272759-dqkjofw2 109 16 L L NNP cord-272759-dqkjofw2 109 17 ( ( -LRB- cord-272759-dqkjofw2 109 18 L l NN cord-272759-dqkjofw2 109 19 2 2 CD cord-272759-dqkjofw2 109 20 = = SYM cord-272759-dqkjofw2 109 21 N n CD cord-272759-dqkjofw2 109 22 ) ) -RRB- cord-272759-dqkjofw2 109 23 , , , cord-272759-dqkjofw2 109 24 and and CC cord-272759-dqkjofw2 109 25 each each DT cord-272759-dqkjofw2 109 26 node node NN cord-272759-dqkjofw2 109 27 is be VBZ cord-272759-dqkjofw2 109 28 connected connect VBN cord-272759-dqkjofw2 109 29 directly directly RB cord-272759-dqkjofw2 109 30 to to IN cord-272759-dqkjofw2 109 31 n n NN cord-272759-dqkjofw2 109 32 1 1 CD cord-272759-dqkjofw2 109 33 immediate immediate JJ cord-272759-dqkjofw2 109 34 neighbours neighbour NNS cord-272759-dqkjofw2 109 35 . . . cord-272759-dqkjofw2 110 1 5 5 LS cord-272759-dqkjofw2 111 1 An an DT cord-272759-dqkjofw2 111 2 infected infected JJ cord-272759-dqkjofw2 111 3 individual individual NN cord-272759-dqkjofw2 111 4 will will MD cord-272759-dqkjofw2 111 5 infect infect VB cord-272759-dqkjofw2 111 6 each each DT cord-272759-dqkjofw2 111 7 of of IN cord-272759-dqkjofw2 111 8 its -PRON- PRP$ cord-272759-dqkjofw2 111 9 n n NN cord-272759-dqkjofw2 111 10 1 1 CD cord-272759-dqkjofw2 111 11 neighbours neighbour NNS cord-272759-dqkjofw2 111 12 ( ( -LRB- cord-272759-dqkjofw2 111 13 provided provide VBN cord-272759-dqkjofw2 111 14 that that IN cord-272759-dqkjofw2 111 15 they -PRON- PRP cord-272759-dqkjofw2 111 16 are be VBP cord-272759-dqkjofw2 111 17 still still RB cord-272759-dqkjofw2 111 18 susceptible susceptible JJ cord-272759-dqkjofw2 111 19 ) ) -RRB- cord-272759-dqkjofw2 111 20 with with IN cord-272759-dqkjofw2 111 21 probability probability NN cord-272759-dqkjofw2 111 22 p p NN cord-272759-dqkjofw2 111 23 1 1 CD cord-272759-dqkjofw2 111 24 . . . cord-272759-dqkjofw2 112 1 Furthermore furthermore RB cord-272759-dqkjofw2 112 2 , , , cord-272759-dqkjofw2 112 3 each each DT cord-272759-dqkjofw2 112 4 node node NN cord-272759-dqkjofw2 112 5 has have VBZ cord-272759-dqkjofw2 112 6 n n DT cord-272759-dqkjofw2 112 7 2 2 CD cord-272759-dqkjofw2 112 8 non non JJ cord-272759-dqkjofw2 112 9 - - JJ cord-272759-dqkjofw2 112 10 local local JJ cord-272759-dqkjofw2 112 11 ( ( -LRB- cord-272759-dqkjofw2 112 12 i.e. i.e. FW cord-272759-dqkjofw2 112 13 long long JJ cord-272759-dqkjofw2 112 14 distance distance NN cord-272759-dqkjofw2 112 15 ) ) -RRB- cord-272759-dqkjofw2 112 16 links link NNS cord-272759-dqkjofw2 112 17 ( ( -LRB- cord-272759-dqkjofw2 112 18 see see VB cord-272759-dqkjofw2 112 19 Fig Fig NNP cord-272759-dqkjofw2 112 20 . . NNP cord-272759-dqkjofw2 112 21 2 2 CD cord-272759-dqkjofw2 112 22 ) ) -RRB- cord-272759-dqkjofw2 112 23 . . . cord-272759-dqkjofw2 113 1 These these DT cord-272759-dqkjofw2 113 2 are be VBP cord-272759-dqkjofw2 113 3 links link NNS cord-272759-dqkjofw2 113 4 to to IN cord-272759-dqkjofw2 113 5 nodes node NNS cord-272759-dqkjofw2 113 6 that that WDT cord-272759-dqkjofw2 113 7 are be VBP cord-272759-dqkjofw2 113 8 geographically geographically RB cord-272759-dqkjofw2 113 9 remote remote JJ cord-272759-dqkjofw2 113 10 from from IN cord-272759-dqkjofw2 113 11 one one CD cord-272759-dqkjofw2 113 12 another another DT cord-272759-dqkjofw2 113 13 ; ; : cord-272759-dqkjofw2 113 14 infection infection NN cord-272759-dqkjofw2 113 15 occurs occur VBZ cord-272759-dqkjofw2 113 16 along along IN cord-272759-dqkjofw2 113 17 these these DT cord-272759-dqkjofw2 113 18 pathways pathway NNS cord-272759-dqkjofw2 113 19 with with IN cord-272759-dqkjofw2 113 20 probability probability NN cord-272759-dqkjofw2 113 21 p p NN cord-272759-dqkjofw2 113 22 2 2 CD cord-272759-dqkjofw2 113 23 . . . cord-272759-dqkjofw2 114 1 For for IN cord-272759-dqkjofw2 114 2 each each DT cord-272759-dqkjofw2 114 3 node node NN cord-272759-dqkjofw2 114 4 i i PRP cord-272759-dqkjofw2 114 5 , , , cord-272759-dqkjofw2 114 6 the the DT cord-272759-dqkjofw2 114 7 number number NN cord-272759-dqkjofw2 114 8 n n NN cord-272759-dqkjofw2 114 9 ( ( -LRB- cord-272759-dqkjofw2 114 10 i i NN cord-272759-dqkjofw2 114 11 ) ) -RRB- cord-272759-dqkjofw2 114 12 2 2 CD cord-272759-dqkjofw2 114 13 is be VBZ cord-272759-dqkjofw2 114 14 fixed fix VBN cord-272759-dqkjofw2 114 15 , , , cord-272759-dqkjofw2 114 16 and and CC cord-272759-dqkjofw2 114 17 so so RB cord-272759-dqkjofw2 114 18 are be VBP cord-272759-dqkjofw2 114 19 the the DT cord-272759-dqkjofw2 114 20 links link NNS cord-272759-dqkjofw2 114 21 to to IN cord-272759-dqkjofw2 114 22 its -PRON- PRP$ cord-272759-dqkjofw2 114 23 n n NN cord-272759-dqkjofw2 114 24 ( ( -LRB- cord-272759-dqkjofw2 114 25 i i NN cord-272759-dqkjofw2 114 26 ) ) -RRB- cord-272759-dqkjofw2 114 27 2 2 CD cord-272759-dqkjofw2 114 28 remote remote JJ cord-272759-dqkjofw2 114 29 neighbours neighbour NNS cord-272759-dqkjofw2 114 30 once once IN cord-272759-dqkjofw2 114 31 they -PRON- PRP cord-272759-dqkjofw2 114 32 are be VBP cord-272759-dqkjofw2 114 33 established establish VBN cord-272759-dqkjofw2 114 34 . . . cord-272759-dqkjofw2 115 1 The the DT cord-272759-dqkjofw2 115 2 number number NN cord-272759-dqkjofw2 115 3 n n NN cord-272759-dqkjofw2 115 4 ( ( -LRB- cord-272759-dqkjofw2 115 5 i i NN cord-272759-dqkjofw2 115 6 ) ) -RRB- cord-272759-dqkjofw2 115 7 2 2 CD cord-272759-dqkjofw2 115 8 is be VBZ cord-272759-dqkjofw2 115 9 chosen choose VBN cord-272759-dqkjofw2 115 10 to to TO cord-272759-dqkjofw2 115 11 be be VB cord-272759-dqkjofw2 115 12 proportional proportional JJ cord-272759-dqkjofw2 115 13 to to IN cord-272759-dqkjofw2 115 14 a a DT cord-272759-dqkjofw2 115 15 decaying decaying JJ cord-272759-dqkjofw2 115 16 exponential exponential NN cord-272759-dqkjofw2 115 17 f f NN cord-272759-dqkjofw2 115 18 X x NN cord-272759-dqkjofw2 115 19 ( ( -LRB- cord-272759-dqkjofw2 115 20 x x NN cord-272759-dqkjofw2 115 21 ) ) -RRB- cord-272759-dqkjofw2 115 22 ∝ ∝ NN cord-272759-dqkjofw2 115 23 e e NNP cord-272759-dqkjofw2 115 24 − − NN cord-272759-dqkjofw2 115 25 x x SYM cord-272759-dqkjofw2 115 26 µ µ NN cord-272759-dqkjofw2 115 27 with with IN cord-272759-dqkjofw2 115 28 parameter parameter NN cord-272759-dqkjofw2 115 29 µ µ NN cord-272759-dqkjofw2 115 30 proportional proportional JJ cord-272759-dqkjofw2 115 31 to to IN cord-272759-dqkjofw2 115 32 the the DT cord-272759-dqkjofw2 115 33 expected expect VBN cord-272759-dqkjofw2 115 34 ( ( -LRB- cord-272759-dqkjofw2 115 35 average average JJ cord-272759-dqkjofw2 115 36 ) ) -RRB- cord-272759-dqkjofw2 115 37 number number NN cord-272759-dqkjofw2 115 38 of of IN cord-272759-dqkjofw2 115 39 4 4 CD cord-272759-dqkjofw2 115 40 As as IN cord-272759-dqkjofw2 115 41 we -PRON- PRP cord-272759-dqkjofw2 115 42 will will MD cord-272759-dqkjofw2 115 43 see see VB cord-272759-dqkjofw2 115 44 in in IN cord-272759-dqkjofw2 115 45 what what WP cord-272759-dqkjofw2 115 46 follows follow VBZ cord-272759-dqkjofw2 115 47 , , , cord-272759-dqkjofw2 115 48 the the DT cord-272759-dqkjofw2 115 49 number number NN cord-272759-dqkjofw2 115 50 of of IN cord-272759-dqkjofw2 115 51 local local JJ cord-272759-dqkjofw2 115 52 connections connection NNS cord-272759-dqkjofw2 115 53 is be VBZ cord-272759-dqkjofw2 115 54 constant constant JJ cord-272759-dqkjofw2 115 55 for for IN cord-272759-dqkjofw2 115 56 all all DT cord-272759-dqkjofw2 115 57 nodes node NNS cord-272759-dqkjofw2 115 58 . . . cord-272759-dqkjofw2 116 1 5 5 LS cord-272759-dqkjofw2 117 1 The the DT cord-272759-dqkjofw2 117 2 grid grid NN cord-272759-dqkjofw2 117 3 is be VBZ cord-272759-dqkjofw2 117 4 assumed assume VBN cord-272759-dqkjofw2 117 5 to to TO cord-272759-dqkjofw2 117 6 be be VB cord-272759-dqkjofw2 117 7 topologically topologically RB cord-272759-dqkjofw2 117 8 equivalent equivalent JJ cord-272759-dqkjofw2 117 9 to to IN cord-272759-dqkjofw2 117 10 the the DT cord-272759-dqkjofw2 117 11 surface surface NN cord-272759-dqkjofw2 117 12 of of IN cord-272759-dqkjofw2 117 13 an an DT cord-272759-dqkjofw2 117 14 annulus annulus NN cord-272759-dqkjofw2 117 15 in in IN cord-272759-dqkjofw2 117 16 three three CD cord-272759-dqkjofw2 117 17 dimensions dimension NNS cord-272759-dqkjofw2 117 18 , , , cord-272759-dqkjofw2 117 19 that that RB cord-272759-dqkjofw2 117 20 is is RB cord-272759-dqkjofw2 117 21 , , , cord-272759-dqkjofw2 117 22 nodes node NNS cord-272759-dqkjofw2 117 23 ( ( -LRB- cord-272759-dqkjofw2 117 24 1 1 CD cord-272759-dqkjofw2 117 25 , , , cord-272759-dqkjofw2 117 26 1 1 CD cord-272759-dqkjofw2 117 27 ) ) -RRB- cord-272759-dqkjofw2 117 28 and and CC cord-272759-dqkjofw2 117 29 ( ( -LRB- cord-272759-dqkjofw2 117 30 L L NNP cord-272759-dqkjofw2 117 31 , , , cord-272759-dqkjofw2 117 32 L L NNP cord-272759-dqkjofw2 117 33 ) ) -RRB- cord-272759-dqkjofw2 117 34 are be VBP cord-272759-dqkjofw2 117 35 neighbours neighbour NNS cord-272759-dqkjofw2 117 36 . . . cord-272759-dqkjofw2 118 1 links link NNS cord-272759-dqkjofw2 118 2 to to IN cord-272759-dqkjofw2 118 3 remote remote JJ cord-272759-dqkjofw2 118 4 nodes node NNS cord-272759-dqkjofw2 118 5 , , , cord-272759-dqkjofw2 118 6 where where WRB cord-272759-dqkjofw2 118 7 n n LS cord-272759-dqkjofw2 118 8 ( ( -LRB- cord-272759-dqkjofw2 118 9 i i NN cord-272759-dqkjofw2 118 10 ) ) -RRB- cord-272759-dqkjofw2 118 11 It -PRON- PRP cord-272759-dqkjofw2 118 12 is be VBZ cord-272759-dqkjofw2 118 13 the the DT cord-272759-dqkjofw2 118 14 inclusion inclusion NN cord-272759-dqkjofw2 118 15 of of IN cord-272759-dqkjofw2 118 16 non non JJ cord-272759-dqkjofw2 118 17 - - JJ cord-272759-dqkjofw2 118 18 local local JJ cord-272759-dqkjofw2 118 19 links link NNS cord-272759-dqkjofw2 118 20 with with IN cord-272759-dqkjofw2 118 21 a a DT cord-272759-dqkjofw2 118 22 random random JJ cord-272759-dqkjofw2 118 23 number number NN cord-272759-dqkjofw2 118 24 of of IN cord-272759-dqkjofw2 118 25 links link NNS cord-272759-dqkjofw2 118 26 that that WDT cord-272759-dqkjofw2 118 27 can can MD cord-272759-dqkjofw2 118 28 give give VB cord-272759-dqkjofw2 118 29 rise rise NN cord-272759-dqkjofw2 118 30 to to IN cord-272759-dqkjofw2 118 31 the the DT cord-272759-dqkjofw2 118 32 network network NN cord-272759-dqkjofw2 118 33 's 's POS cord-272759-dqkjofw2 118 34 SW SW NNP cord-272759-dqkjofw2 118 35 ( ( -LRB- cord-272759-dqkjofw2 118 36 and and CC cord-272759-dqkjofw2 118 37 , , , cord-272759-dqkjofw2 118 38 in in IN cord-272759-dqkjofw2 118 39 other other JJ cord-272759-dqkjofw2 118 40 cases case NNS cord-272759-dqkjofw2 118 41 not not RB cord-272759-dqkjofw2 118 42 considered consider VBN cord-272759-dqkjofw2 118 43 here here RB cord-272759-dqkjofw2 118 44 , , , cord-272759-dqkjofw2 118 45 SF SF NNP cord-272759-dqkjofw2 118 46 ) ) -RRB- cord-272759-dqkjofw2 118 47 structure structure NN cord-272759-dqkjofw2 118 48 . . . cord-272759-dqkjofw2 119 1 In in IN cord-272759-dqkjofw2 119 2 this this DT cord-272759-dqkjofw2 119 3 paper paper NN cord-272759-dqkjofw2 119 4 , , , cord-272759-dqkjofw2 119 5 we -PRON- PRP cord-272759-dqkjofw2 119 6 assign assign VBP cord-272759-dqkjofw2 119 7 an an DT cord-272759-dqkjofw2 119 8 exponentially exponentially RB cord-272759-dqkjofw2 119 9 decaying decaying JJ cord-272759-dqkjofw2 119 10 probability probability NN cord-272759-dqkjofw2 119 11 distribution distribution NN cord-272759-dqkjofw2 119 12 to to IN cord-272759-dqkjofw2 119 13 any any DT cord-272759-dqkjofw2 119 14 number number NN cord-272759-dqkjofw2 119 15 of of IN cord-272759-dqkjofw2 119 16 links link NNS cord-272759-dqkjofw2 119 17 , , , cord-272759-dqkjofw2 119 18 and and CC cord-272759-dqkjofw2 119 19 ( ( -LRB- cord-272759-dqkjofw2 119 20 for for IN cord-272759-dqkjofw2 119 21 uni uni JJ cord-272759-dqkjofw2 119 22 - - HYPH cord-272759-dqkjofw2 119 23 directional directional JJ cord-272759-dqkjofw2 119 24 links link NNS cord-272759-dqkjofw2 119 25 ) ) -RRB- cord-272759-dqkjofw2 119 26 this this DT cord-272759-dqkjofw2 119 27 is be VBZ cord-272759-dqkjofw2 119 28 sufficient sufficient JJ cord-272759-dqkjofw2 119 29 to to TO cord-272759-dqkjofw2 119 30 generate generate VB cord-272759-dqkjofw2 119 31 the the DT cord-272759-dqkjofw2 119 32 necessary necessary JJ cord-272759-dqkjofw2 119 33 SW SW NNP cord-272759-dqkjofw2 119 34 properties property NNS cord-272759-dqkjofw2 119 35 . . . cord-272759-dqkjofw2 120 1 An an DT cord-272759-dqkjofw2 120 2 SF SF NNP cord-272759-dqkjofw2 120 3 network network NN cord-272759-dqkjofw2 120 4 requires require VBZ cord-272759-dqkjofw2 120 5 a a DT cord-272759-dqkjofw2 120 6 power power NN cord-272759-dqkjofw2 120 7 - - HYPH cord-272759-dqkjofw2 120 8 law law NN cord-272759-dqkjofw2 120 9 distribution distribution NN cord-272759-dqkjofw2 120 10 of of IN cord-272759-dqkjofw2 120 11 the the DT cord-272759-dqkjofw2 120 12 number number NN cord-272759-dqkjofw2 120 13 of of IN cord-272759-dqkjofw2 120 14 links link NNS cord-272759-dqkjofw2 120 15 ( ( -LRB- cord-272759-dqkjofw2 120 16 which which WDT cord-272759-dqkjofw2 120 17 can can MD cord-272759-dqkjofw2 120 18 consequently consequently RB cord-272759-dqkjofw2 120 19 lead lead VB cord-272759-dqkjofw2 120 20 to to IN cord-272759-dqkjofw2 120 21 more more JJR cord-272759-dqkjofw2 120 22 nodes node NNS cord-272759-dqkjofw2 120 23 with with IN cord-272759-dqkjofw2 120 24 many many JJ cord-272759-dqkjofw2 120 25 more more JJR cord-272759-dqkjofw2 120 26 links link NNS cord-272759-dqkjofw2 120 27 ) ) -RRB- cord-272759-dqkjofw2 120 28 and and CC cord-272759-dqkjofw2 120 29 we -PRON- PRP cord-272759-dqkjofw2 120 30 do do VBP cord-272759-dqkjofw2 120 31 not not RB cord-272759-dqkjofw2 120 32 examine examine VB cord-272759-dqkjofw2 120 33 that that DT cord-272759-dqkjofw2 120 34 case case NN cord-272759-dqkjofw2 120 35 here here RB cord-272759-dqkjofw2 120 36 . . . cord-272759-dqkjofw2 121 1 The the DT cord-272759-dqkjofw2 121 2 SF SF NNP cord-272759-dqkjofw2 121 3 distribution distribution NN cord-272759-dqkjofw2 121 4 of of IN cord-272759-dqkjofw2 121 5 the the DT cord-272759-dqkjofw2 121 6 induced induce VBN cord-272759-dqkjofw2 121 7 network network NN cord-272759-dqkjofw2 121 8 of of IN cord-272759-dqkjofw2 121 9 actual actual JJ cord-272759-dqkjofw2 121 10 infections infection NNS cord-272759-dqkjofw2 121 11 has have VBZ cord-272759-dqkjofw2 121 12 been be VBN cord-272759-dqkjofw2 121 13 considered consider VBN cord-272759-dqkjofw2 121 14 elsewhere elsewhere RB cord-272759-dqkjofw2 121 15 [ [ -LRB- cord-272759-dqkjofw2 121 16 16 16 CD cord-272759-dqkjofw2 121 17 ] ] -RRB- cord-272759-dqkjofw2 121 18 . . . cord-272759-dqkjofw2 122 1 It -PRON- PRP cord-272759-dqkjofw2 122 2 is be VBZ cord-272759-dqkjofw2 122 3 worth worth JJ cord-272759-dqkjofw2 122 4 considering consider VBG cord-272759-dqkjofw2 122 5 that that IN cord-272759-dqkjofw2 122 6 , , , cord-272759-dqkjofw2 122 7 for for IN cord-272759-dqkjofw2 122 8 the the DT cord-272759-dqkjofw2 122 9 model model NN cord-272759-dqkjofw2 122 10 that that WDT cord-272759-dqkjofw2 122 11 we -PRON- PRP cord-272759-dqkjofw2 122 12 present present VBP cord-272759-dqkjofw2 122 13 here here RB cord-272759-dqkjofw2 122 14 , , , cord-272759-dqkjofw2 122 15 the the DT cord-272759-dqkjofw2 122 16 links link NNS cord-272759-dqkjofw2 122 17 between between IN cord-272759-dqkjofw2 122 18 nodes node NNS cord-272759-dqkjofw2 122 19 are be VBP cord-272759-dqkjofw2 122 20 uni uni JJ cord-272759-dqkjofw2 122 21 - - HYPH cord-272759-dqkjofw2 122 22 directional directional JJ cord-272759-dqkjofw2 122 23 . . . cord-272759-dqkjofw2 123 1 That that RB cord-272759-dqkjofw2 123 2 is is RB cord-272759-dqkjofw2 123 3 , , , cord-272759-dqkjofw2 123 4 infection infection NN cord-272759-dqkjofw2 123 5 only only RB cord-272759-dqkjofw2 123 6 spreads spread VBZ cord-272759-dqkjofw2 123 7 in in IN cord-272759-dqkjofw2 123 8 one one CD cord-272759-dqkjofw2 123 9 direction direction NN cord-272759-dqkjofw2 123 10 . . . cord-272759-dqkjofw2 124 1 Clearly clearly RB cord-272759-dqkjofw2 124 2 , , , cord-272759-dqkjofw2 124 3 the the DT cord-272759-dqkjofw2 124 4 true true JJ cord-272759-dqkjofw2 124 5 network network NN cord-272759-dqkjofw2 124 6 of of IN cord-272759-dqkjofw2 124 7 social social JJ cord-272759-dqkjofw2 124 8 interaction interaction NN cord-272759-dqkjofw2 124 9 consists consist VBZ cord-272759-dqkjofw2 124 10 of of IN cord-272759-dqkjofw2 124 11 bi bi JJ cord-272759-dqkjofw2 124 12 - - JJ cord-272759-dqkjofw2 124 13 directional directional JJ cord-272759-dqkjofw2 124 14 links link NNS cord-272759-dqkjofw2 124 15 . . . cord-272759-dqkjofw2 125 1 But but CC cord-272759-dqkjofw2 125 2 , , , cord-272759-dqkjofw2 125 3 for for IN cord-272759-dqkjofw2 125 4 the the DT cord-272759-dqkjofw2 125 5 purposes purpose NNS cord-272759-dqkjofw2 125 6 of of IN cord-272759-dqkjofw2 125 7 simulating simulate VBG cord-272759-dqkjofw2 125 8 disease disease NN cord-272759-dqkjofw2 125 9 transmission transmission NN cord-272759-dqkjofw2 125 10 , , , cord-272759-dqkjofw2 125 11 unidirectional unidirectional JJ cord-272759-dqkjofw2 125 12 links link NNS cord-272759-dqkjofw2 125 13 appear appear VBP cord-272759-dqkjofw2 125 14 to to TO cord-272759-dqkjofw2 125 15 be be VB cord-272759-dqkjofw2 125 16 a a DT cord-272759-dqkjofw2 125 17 sufficient sufficient JJ cord-272759-dqkjofw2 125 18 approximation approximation NN cord-272759-dqkjofw2 125 19 . . . cord-272759-dqkjofw2 126 1 The the DT cord-272759-dqkjofw2 126 2 consequence consequence NN cord-272759-dqkjofw2 126 3 of of IN cord-272759-dqkjofw2 126 4 this this DT cord-272759-dqkjofw2 126 5 is be VBZ cord-272759-dqkjofw2 126 6 that that IN cord-272759-dqkjofw2 126 7 it -PRON- PRP cord-272759-dqkjofw2 126 8 becomes become VBZ cord-272759-dqkjofw2 126 9 easier easy JJR cord-272759-dqkjofw2 126 10 to to TO cord-272759-dqkjofw2 126 11 generate generate VB cord-272759-dqkjofw2 126 12 the the DT cord-272759-dqkjofw2 126 13 small small JJ cord-272759-dqkjofw2 126 14 - - HYPH cord-272759-dqkjofw2 126 15 world world NN cord-272759-dqkjofw2 126 16 ( ( -LRB- cord-272759-dqkjofw2 126 17 and and CC cord-272759-dqkjofw2 126 18 elsewhere elsewhere RB cord-272759-dqkjofw2 126 19 the the DT cord-272759-dqkjofw2 126 20 scale scale NN cord-272759-dqkjofw2 126 21 - - HYPH cord-272759-dqkjofw2 126 22 free free JJ cord-272759-dqkjofw2 126 23 ) ) -RRB- cord-272759-dqkjofw2 126 24 network network NN cord-272759-dqkjofw2 126 25 . . . cord-272759-dqkjofw2 127 1 Finally finally RB cord-272759-dqkjofw2 127 2 , , , cord-272759-dqkjofw2 127 3 for for IN cord-272759-dqkjofw2 127 4 each each DT cord-272759-dqkjofw2 127 5 simulation simulation NN cord-272759-dqkjofw2 127 6 we -PRON- PRP cord-272759-dqkjofw2 127 7 seed seed VBP cord-272759-dqkjofw2 127 8 the the DT cord-272759-dqkjofw2 127 9 model model NN cord-272759-dqkjofw2 127 10 with with IN cord-272759-dqkjofw2 127 11 one one CD cord-272759-dqkjofw2 127 12 randomly randomly RB cord-272759-dqkjofw2 127 13 chosen choose VBN cord-272759-dqkjofw2 127 14 initial initial JJ cord-272759-dqkjofw2 127 15 infection infection NN cord-272759-dqkjofw2 127 16 . . . cord-272759-dqkjofw2 128 1 We -PRON- PRP cord-272759-dqkjofw2 128 2 expect expect VBP cord-272759-dqkjofw2 128 3 that that IN cord-272759-dqkjofw2 128 4 computational computational JJ cord-272759-dqkjofw2 128 5 simulations simulation NNS cord-272759-dqkjofw2 128 6 of of IN cord-272759-dqkjofw2 128 7 this this DT cord-272759-dqkjofw2 128 8 network network NN cord-272759-dqkjofw2 128 9 will will MD cord-272759-dqkjofw2 128 10 show show VB cord-272759-dqkjofw2 128 11 that that IN cord-272759-dqkjofw2 128 12 infection infection NN cord-272759-dqkjofw2 128 13 spreads spread VBZ cord-272759-dqkjofw2 128 14 locally locally RB cord-272759-dqkjofw2 128 15 , , , cord-272759-dqkjofw2 128 16 just just RB cord-272759-dqkjofw2 128 17 as as IN cord-272759-dqkjofw2 128 18 SARS SARS NNP cord-272759-dqkjofw2 128 19 spread spread VBD cord-272759-dqkjofw2 128 20 within within IN cord-272759-dqkjofw2 128 21 particular particular JJ cord-272759-dqkjofw2 128 22 geographical geographical JJ cord-272759-dqkjofw2 128 23 regions region NNS cord-272759-dqkjofw2 128 24 of of IN cord-272759-dqkjofw2 128 25 Hong Hong NNP cord-272759-dqkjofw2 128 26 Kong Kong NNP cord-272759-dqkjofw2 128 27 . . . cord-272759-dqkjofw2 129 1 Moreover moreover RB cord-272759-dqkjofw2 129 2 , , , cord-272759-dqkjofw2 129 3 the the DT cord-272759-dqkjofw2 129 4 system system NN cord-272759-dqkjofw2 129 5 can can MD cord-272759-dqkjofw2 129 6 also also RB cord-272759-dqkjofw2 129 7 exhibit exhibit VB cord-272759-dqkjofw2 129 8 non non JJ cord-272759-dqkjofw2 129 9 - - JJ cord-272759-dqkjofw2 129 10 local local JJ cord-272759-dqkjofw2 129 11 infection infection NN cord-272759-dqkjofw2 129 12 , , , cord-272759-dqkjofw2 129 13 as as IN cord-272759-dqkjofw2 129 14 a a DT cord-272759-dqkjofw2 129 15 single single JJ cord-272759-dqkjofw2 129 16 individual individual NN cord-272759-dqkjofw2 129 17 may may MD cord-272759-dqkjofw2 129 18 infect infect VB cord-272759-dqkjofw2 129 19 individuals individual NNS cord-272759-dqkjofw2 129 20 in in IN cord-272759-dqkjofw2 129 21 distant distant JJ cord-272759-dqkjofw2 129 22 communities community NNS cord-272759-dqkjofw2 129 23 . . . cord-272759-dqkjofw2 130 1 Occasionally occasionally RB cord-272759-dqkjofw2 130 2 , , , cord-272759-dqkjofw2 130 3 individuals individual NNS cord-272759-dqkjofw2 130 4 will will MD cord-272759-dqkjofw2 130 5 infect infect VB cord-272759-dqkjofw2 130 6 a a DT cord-272759-dqkjofw2 130 7 large large JJ cord-272759-dqkjofw2 130 8 number number NN cord-272759-dqkjofw2 130 9 of of IN cord-272759-dqkjofw2 130 10 others other NNS cord-272759-dqkjofw2 130 11 , , , cord-272759-dqkjofw2 130 12 exactly exactly RB cord-272759-dqkjofw2 130 13 as as IN cord-272759-dqkjofw2 130 14 was be VBD cord-272759-dqkjofw2 130 15 observed observe VBN cord-272759-dqkjofw2 130 16 at at IN cord-272759-dqkjofw2 130 17 the the DT cord-272759-dqkjofw2 130 18 start start NN cord-272759-dqkjofw2 130 19 of of IN cord-272759-dqkjofw2 130 20 the the DT cord-272759-dqkjofw2 130 21 SARS SARS NNP cord-272759-dqkjofw2 130 22 epidemic epidemic NN cord-272759-dqkjofw2 130 23 in in IN cord-272759-dqkjofw2 130 24 Hong Hong NNP cord-272759-dqkjofw2 130 25 Kong Kong NNP cord-272759-dqkjofw2 130 26 ( ( -LRB- cord-272759-dqkjofw2 130 27 an an DT cord-272759-dqkjofw2 130 28 SSE SSE NNP cord-272759-dqkjofw2 130 29 ) ) -RRB- cord-272759-dqkjofw2 130 30 . . . cord-272759-dqkjofw2 131 1 However however RB cord-272759-dqkjofw2 131 2 , , , cord-272759-dqkjofw2 131 3 unlike unlike IN cord-272759-dqkjofw2 131 4 the the DT cord-272759-dqkjofw2 131 5 start start NN cord-272759-dqkjofw2 131 6 of of IN cord-272759-dqkjofw2 131 7 the the DT cord-272759-dqkjofw2 131 8 SARS SARS NNP cord-272759-dqkjofw2 131 9 epidemic epidemic NN cord-272759-dqkjofw2 131 10 in in IN cord-272759-dqkjofw2 131 11 Hong Hong NNP cord-272759-dqkjofw2 131 12 Kong Kong NNP cord-272759-dqkjofw2 131 13 , , , cord-272759-dqkjofw2 131 14 because because IN cord-272759-dqkjofw2 131 15 we -PRON- PRP cord-272759-dqkjofw2 131 16 seed seed VBP cord-272759-dqkjofw2 131 17 our -PRON- PRP$ cord-272759-dqkjofw2 131 18 population population NN cord-272759-dqkjofw2 131 19 with with IN cord-272759-dqkjofw2 131 20 a a DT cord-272759-dqkjofw2 131 21 single single JJ cord-272759-dqkjofw2 131 22 infectious infectious JJ cord-272759-dqkjofw2 131 23 individual individual NN cord-272759-dqkjofw2 131 24 , , , cord-272759-dqkjofw2 131 25 we -PRON- PRP cord-272759-dqkjofw2 131 26 do do VBP cord-272759-dqkjofw2 131 27 not not RB cord-272759-dqkjofw2 131 28 expect expect VB cord-272759-dqkjofw2 131 29 to to TO cord-272759-dqkjofw2 131 30 see see VB cord-272759-dqkjofw2 131 31 the the DT cord-272759-dqkjofw2 131 32 initial initial JJ cord-272759-dqkjofw2 131 33 SSE SSE NNP cord-272759-dqkjofw2 131 34 triggered trigger VBN cord-272759-dqkjofw2 131 35 by by IN cord-272759-dqkjofw2 131 36 that that DT cord-272759-dqkjofw2 131 37 individual individual NN cord-272759-dqkjofw2 131 38 ( ( -LRB- cord-272759-dqkjofw2 131 39 except except IN cord-272759-dqkjofw2 131 40 by by IN cord-272759-dqkjofw2 131 41 chance chance NN cord-272759-dqkjofw2 131 42 ) ) -RRB- cord-272759-dqkjofw2 131 43 . . . cord-272759-dqkjofw2 132 1 Therefore therefore RB cord-272759-dqkjofw2 132 2 , , , cord-272759-dqkjofw2 132 3 the the DT cord-272759-dqkjofw2 132 4 initial initial JJ cord-272759-dqkjofw2 132 5 growth growth NN cord-272759-dqkjofw2 132 6 of of IN cord-272759-dqkjofw2 132 7 transmission transmission NN cord-272759-dqkjofw2 132 8 in in IN cord-272759-dqkjofw2 132 9 our -PRON- PRP$ cord-272759-dqkjofw2 132 10 model model NN cord-272759-dqkjofw2 132 11 is be VBZ cord-272759-dqkjofw2 132 12 exponential exponential JJ cord-272759-dqkjofw2 132 13 rather rather RB cord-272759-dqkjofw2 132 14 than than IN cord-272759-dqkjofw2 132 15 an an DT cord-272759-dqkjofw2 132 16 SSE SSE NNP cord-272759-dqkjofw2 132 17 . . . cord-272759-dqkjofw2 133 1 The the DT cord-272759-dqkjofw2 133 2 only only JJ cord-272759-dqkjofw2 133 3 way way NN cord-272759-dqkjofw2 133 4 to to TO cord-272759-dqkjofw2 133 5 overcome overcome VB cord-272759-dqkjofw2 133 6 this this DT cord-272759-dqkjofw2 133 7 is be VBZ cord-272759-dqkjofw2 133 8 to to TO cord-272759-dqkjofw2 133 9 include include VB cord-272759-dqkjofw2 133 10 explicitly explicitly RB cord-272759-dqkjofw2 133 11 the the DT cord-272759-dqkjofw2 133 12 " " `` cord-272759-dqkjofw2 133 13 seed seed NN cord-272759-dqkjofw2 133 14 " " '' cord-272759-dqkjofw2 133 15 SSE SSE NNP cord-272759-dqkjofw2 133 16 in in IN cord-272759-dqkjofw2 133 17 the the DT cord-272759-dqkjofw2 133 18 model model NN cord-272759-dqkjofw2 133 19 , , , cord-272759-dqkjofw2 133 20 regardless regardless RB cord-272759-dqkjofw2 133 21 of of IN cord-272759-dqkjofw2 133 22 network network NN cord-272759-dqkjofw2 133 23 topology topology NN cord-272759-dqkjofw2 133 24 . . . cord-272759-dqkjofw2 134 1 The the DT cord-272759-dqkjofw2 134 2 epidemic epidemic NN cord-272759-dqkjofw2 134 3 will will MD cord-272759-dqkjofw2 134 4 eventually eventually RB cord-272759-dqkjofw2 134 5 be be VB cord-272759-dqkjofw2 134 6 contained contain VBN cord-272759-dqkjofw2 134 7 if if IN cord-272759-dqkjofw2 134 8 the the DT cord-272759-dqkjofw2 134 9 rate rate NN cord-272759-dqkjofw2 134 10 of of IN cord-272759-dqkjofw2 134 11 infection infection NN cord-272759-dqkjofw2 134 12 is be VBZ cord-272759-dqkjofw2 134 13 lower low JJR cord-272759-dqkjofw2 134 14 than than IN cord-272759-dqkjofw2 134 15 the the DT cord-272759-dqkjofw2 134 16 rate rate NN cord-272759-dqkjofw2 134 17 of of IN cord-272759-dqkjofw2 134 18 removal removal NN cord-272759-dqkjofw2 134 19 . . . cord-272759-dqkjofw2 135 1 Intuitively intuitively RB cord-272759-dqkjofw2 135 2 , , , cord-272759-dqkjofw2 135 3 provided provide VBN cord-272759-dqkjofw2 135 4 that that IN cord-272759-dqkjofw2 135 5 ( ( -LRB- cord-272759-dqkjofw2 135 6 n n NN cord-272759-dqkjofw2 135 7 1 1 CD cord-272759-dqkjofw2 135 8 p p NN cord-272759-dqkjofw2 135 9 1 1 CD cord-272759-dqkjofw2 135 10 + + CC cord-272759-dqkjofw2 135 11 µp µp NN cord-272759-dqkjofw2 135 12 2 2 CD cord-272759-dqkjofw2 135 13 ) ) -RRB- cord-272759-dqkjofw2 136 1 r r NNP cord-272759-dqkjofw2 136 2 1 1 CD cord-272759-dqkjofw2 136 3 , , , cord-272759-dqkjofw2 136 4 one one PRP cord-272759-dqkjofw2 136 5 would would MD cord-272759-dqkjofw2 136 6 expect expect VB cord-272759-dqkjofw2 136 7 the the DT cord-272759-dqkjofw2 136 8 disease disease NN cord-272759-dqkjofw2 136 9 to to TO cord-272759-dqkjofw2 136 10 become become VB cord-272759-dqkjofw2 136 11 endemic endemic JJ cord-272759-dqkjofw2 136 12 ; ; : cord-272759-dqkjofw2 136 13 conversely conversely RB cord-272759-dqkjofw2 136 14 , , , cord-272759-dqkjofw2 137 1 if if IN cord-272759-dqkjofw2 137 2 ( ( -LRB- cord-272759-dqkjofw2 137 3 n n NN cord-272759-dqkjofw2 137 4 1 1 CD cord-272759-dqkjofw2 137 5 p p NN cord-272759-dqkjofw2 137 6 1 1 CD cord-272759-dqkjofw2 137 7 + + CC cord-272759-dqkjofw2 138 1 µp µp NNP cord-272759-dqkjofw2 138 2 2 2 CD cord-272759-dqkjofw2 138 3 ) ) -RRB- cord-272759-dqkjofw2 139 1 r r NNP cord-272759-dqkjofw2 139 2 1 1 CD cord-272759-dqkjofw2 139 3 , , , cord-272759-dqkjofw2 139 4 the the DT cord-272759-dqkjofw2 139 5 disease disease NN cord-272759-dqkjofw2 139 6 will will MD cord-272759-dqkjofw2 139 7 be be VB cord-272759-dqkjofw2 139 8 contained contain VBN cord-272759-dqkjofw2 139 9 . . . cord-272759-dqkjofw2 140 1 In in IN cord-272759-dqkjofw2 140 2 what what WP cord-272759-dqkjofw2 140 3 follows follow VBZ cord-272759-dqkjofw2 140 4 , , , cord-272759-dqkjofw2 140 5 we -PRON- PRP cord-272759-dqkjofw2 140 6 study study VBP cord-272759-dqkjofw2 140 7 this this DT cord-272759-dqkjofw2 140 8 condition condition NN cord-272759-dqkjofw2 140 9 more more RBR cord-272759-dqkjofw2 140 10 precisely precisely RB cord-272759-dqkjofw2 140 11 . . . cord-272759-dqkjofw2 141 1 Moreover moreover RB cord-272759-dqkjofw2 141 2 , , , cord-272759-dqkjofw2 141 3 with with IN cord-272759-dqkjofw2 141 4 this this DT cord-272759-dqkjofw2 141 5 model model NN cord-272759-dqkjofw2 141 6 we -PRON- PRP cord-272759-dqkjofw2 141 7 can can MD cord-272759-dqkjofw2 141 8 analytically analytically RB cord-272759-dqkjofw2 141 9 compute compute VB cord-272759-dqkjofw2 141 10 the the DT cord-272759-dqkjofw2 141 11 probability probability NN cord-272759-dqkjofw2 141 12 of of IN cord-272759-dqkjofw2 141 13 an an DT cord-272759-dqkjofw2 141 14 outbreak outbreak NN cord-272759-dqkjofw2 141 15 being be VBG cord-272759-dqkjofw2 141 16 self self NN cord-272759-dqkjofw2 141 17 - - HYPH cord-272759-dqkjofw2 141 18 terminating terminate VBG cord-272759-dqkjofw2 141 19 . . . cord-272759-dqkjofw2 142 1 For for IN cord-272759-dqkjofw2 142 2 a a DT cord-272759-dqkjofw2 142 3 single single JJ cord-272759-dqkjofw2 142 4 infectious infectious JJ cord-272759-dqkjofw2 142 5 node node NN cord-272759-dqkjofw2 142 6 , , , cord-272759-dqkjofw2 142 7 the the DT cord-272759-dqkjofw2 142 8 probability probability NN cord-272759-dqkjofw2 142 9 of of IN cord-272759-dqkjofw2 142 10 no no DT cord-272759-dqkjofw2 142 11 further further JJ cord-272759-dqkjofw2 142 12 infections infection NNS cord-272759-dqkjofw2 142 13 on on IN cord-272759-dqkjofw2 142 14 a a DT cord-272759-dqkjofw2 142 15 given give VBN cord-272759-dqkjofw2 142 16 day day NN cord-272759-dqkjofw2 142 17 is be VBZ cord-272759-dqkjofw2 142 18 given give VBN cord-272759-dqkjofw2 142 19 by by IN cord-272759-dqkjofw2 142 20 Hence hence RB cord-272759-dqkjofw2 143 1 the the DT cord-272759-dqkjofw2 143 2 probability probability NN cord-272759-dqkjofw2 143 3 of of IN cord-272759-dqkjofw2 143 4 no no DT cord-272759-dqkjofw2 143 5 further further JJ cord-272759-dqkjofw2 143 6 infections infection NNS cord-272759-dqkjofw2 143 7 from from IN cord-272759-dqkjofw2 143 8 this this DT cord-272759-dqkjofw2 143 9 node node NN cord-272759-dqkjofw2 143 10 can can MD cord-272759-dqkjofw2 143 11 be be VB cord-272759-dqkjofw2 143 12 closely closely RB cord-272759-dqkjofw2 143 13 approximated approximate VBN cord-272759-dqkjofw2 143 14 by by IN cord-272759-dqkjofw2 143 15 the the DT cord-272759-dqkjofw2 143 16 infinite infinite JJ cord-272759-dqkjofw2 143 17 geometric geometric JJ cord-272759-dqkjofw2 143 18 series series NN cord-272759-dqkjofw2 143 19 using use VBG cord-272759-dqkjofw2 143 20 the the DT cord-272759-dqkjofw2 143 21 average average JJ cord-272759-dqkjofw2 143 22 P p NN cord-272759-dqkjofw2 143 23 no1 no1 NN cord-272759-dqkjofw2 143 24 computed compute VBN cord-272759-dqkjofw2 143 25 in in IN cord-272759-dqkjofw2 143 26 Eq Eq NNP cord-272759-dqkjofw2 143 27 . . . cord-272759-dqkjofw2 144 1 ( ( -LRB- cord-272759-dqkjofw2 144 2 2 2 LS cord-272759-dqkjofw2 144 3 ) ) -RRB- cord-272759-dqkjofw2 144 4 : : : cord-272759-dqkjofw2 144 5 provided provide VBN cord-272759-dqkjofw2 144 6 that that IN cord-272759-dqkjofw2 144 7 |P |p CD cord-272759-dqkjofw2 144 8 no1 no1 NN cord-272759-dqkjofw2 144 9 ( ( -LRB- cord-272759-dqkjofw2 144 10 1 1 CD cord-272759-dqkjofw2 144 11 − − NN cord-272759-dqkjofw2 144 12 r r NN cord-272759-dqkjofw2 144 13 1 1 CD cord-272759-dqkjofw2 144 14 ) ) -RRB- cord-272759-dqkjofw2 144 15 | | . cord-272759-dqkjofw2 145 1 < < NNP cord-272759-dqkjofw2 145 2 1 1 CD cord-272759-dqkjofw2 145 3 . . . cord-272759-dqkjofw2 146 1 Upon upon IN cord-272759-dqkjofw2 146 2 substitution substitution NN cord-272759-dqkjofw2 146 3 of of IN cord-272759-dqkjofw2 146 4 Eq Eq NNP cord-272759-dqkjofw2 146 5 . . . cord-272759-dqkjofw2 147 1 ( ( -LRB- cord-272759-dqkjofw2 147 2 2 2 LS cord-272759-dqkjofw2 147 3 ) ) -RRB- cord-272759-dqkjofw2 147 4 into into IN cord-272759-dqkjofw2 147 5 ( ( -LRB- cord-272759-dqkjofw2 147 6 3 3 CD cord-272759-dqkjofw2 147 7 ) ) -RRB- cord-272759-dqkjofw2 147 8 , , , cord-272759-dqkjofw2 147 9 we -PRON- PRP cord-272759-dqkjofw2 147 10 find find VBP cord-272759-dqkjofw2 147 11 that that IN cord-272759-dqkjofw2 147 12 Eq Eq NNP cord-272759-dqkjofw2 147 13 . . . cord-272759-dqkjofw2 148 1 ( ( -LRB- cord-272759-dqkjofw2 148 2 4 4 LS cord-272759-dqkjofw2 148 3 ) ) -RRB- cord-272759-dqkjofw2 148 4 is be VBZ cord-272759-dqkjofw2 148 5 the the DT cord-272759-dqkjofw2 148 6 probability probability NN cord-272759-dqkjofw2 148 7 of of IN cord-272759-dqkjofw2 148 8 no no DT cord-272759-dqkjofw2 148 9 infections infection NNS cord-272759-dqkjofw2 148 10 from from IN cord-272759-dqkjofw2 148 11 a a DT cord-272759-dqkjofw2 148 12 given give VBN cord-272759-dqkjofw2 148 13 individual individual NN cord-272759-dqkjofw2 148 14 , , , cord-272759-dqkjofw2 148 15 and and CC cord-272759-dqkjofw2 148 16 is be VBZ cord-272759-dqkjofw2 148 17 therefore therefore RB cord-272759-dqkjofw2 148 18 a a DT cord-272759-dqkjofw2 148 19 weak weak JJ cord-272759-dqkjofw2 148 20 lower lower RBR cord-272759-dqkjofw2 148 21 bound bind VBN cord-272759-dqkjofw2 148 22 on on IN cord-272759-dqkjofw2 148 23 the the DT cord-272759-dqkjofw2 148 24 probability probability NN cord-272759-dqkjofw2 148 25 of of IN cord-272759-dqkjofw2 148 26 no no DT cord-272759-dqkjofw2 148 27 general general JJ cord-272759-dqkjofw2 148 28 outbreak outbreak NN cord-272759-dqkjofw2 148 29 . . . cord-272759-dqkjofw2 149 1 Now now RB cord-272759-dqkjofw2 149 2 , , , cord-272759-dqkjofw2 149 3 let let VB cord-272759-dqkjofw2 149 4 us -PRON- PRP cord-272759-dqkjofw2 149 5 denote denote VB cord-272759-dqkjofw2 149 6 the the DT cord-272759-dqkjofw2 149 7 probability probability NN cord-272759-dqkjofw2 149 8 of of IN cord-272759-dqkjofw2 149 9 no no DT cord-272759-dqkjofw2 149 10 further further JJ cord-272759-dqkjofw2 149 11 infections infection NNS cord-272759-dqkjofw2 149 12 occurring occur VBG cord-272759-dqkjofw2 149 13 , , , cord-272759-dqkjofw2 149 14 given give VBN cord-272759-dqkjofw2 149 15 that that IN cord-272759-dqkjofw2 149 16 there there EX cord-272759-dqkjofw2 149 17 are be VBP cord-272759-dqkjofw2 149 18 k k XX cord-272759-dqkjofw2 149 19 infectious infectious JJ cord-272759-dqkjofw2 149 20 nodes node NNS cord-272759-dqkjofw2 149 21 by by IN cord-272759-dqkjofw2 149 22 = = NFP cord-272759-dqkjofw2 150 1 P p NN cord-272759-dqkjofw2 151 1 ( ( -LRB- cord-272759-dqkjofw2 151 2 k k NNP cord-272759-dqkjofw2 151 3 ) ) -RRB- cord-272759-dqkjofw2 151 4 none none NN cord-272759-dqkjofw2 151 5 = = NFP cord-272759-dqkjofw2 152 1 Prob(no prob(no VB cord-272759-dqkjofw2 152 2 further further JJ cord-272759-dqkjofw2 152 3 infection infection NN cord-272759-dqkjofw2 152 4 | | CD cord-272759-dqkjofw2 153 1 k k LS cord-272759-dqkjofw2 153 2 infectious infectious JJ cord-272759-dqkjofw2 153 3 nodes node NNS cord-272759-dqkjofw2 153 4 ) ) -RRB- cord-272759-dqkjofw2 153 5 where where WRB cord-272759-dqkjofw2 153 6 , , , cord-272759-dqkjofw2 153 7 for for IN cord-272759-dqkjofw2 153 8 notational notational JJ cord-272759-dqkjofw2 153 9 convenience convenience NN cord-272759-dqkjofw2 153 10 , , , cord-272759-dqkjofw2 153 11 we -PRON- PRP cord-272759-dqkjofw2 153 12 will will MD cord-272759-dqkjofw2 153 13 drop drop VB cord-272759-dqkjofw2 153 14 the the DT cord-272759-dqkjofw2 153 15 subscript subscript NN cord-272759-dqkjofw2 153 16 on on IN cord-272759-dqkjofw2 153 17 P p NN cord-272759-dqkjofw2 153 18 none none NN cord-272759-dqkjofw2 153 19 . . . cord-272759-dqkjofw2 154 1 Treating treat VBG cord-272759-dqkjofw2 154 2 infections infection NNS cord-272759-dqkjofw2 154 3 as as IN cord-272759-dqkjofw2 154 4 discrete discrete JJ cord-272759-dqkjofw2 154 5 events event NNS cord-272759-dqkjofw2 154 6 ( ( -LRB- cord-272759-dqkjofw2 154 7 i.e. i.e. FW cord-272759-dqkjofw2 154 8 they -PRON- PRP cord-272759-dqkjofw2 154 9 occur occur VBP cord-272759-dqkjofw2 154 10 one one CD cord-272759-dqkjofw2 154 11 at at IN cord-272759-dqkjofw2 154 12 a a DT cord-272759-dqkjofw2 154 13 time time NN cord-272759-dqkjofw2 154 14 ) ) -RRB- cord-272759-dqkjofw2 154 15 , , , cord-272759-dqkjofw2 154 16 we -PRON- PRP cord-272759-dqkjofw2 154 17 have have VBP cord-272759-dqkjofw2 154 18 that that DT cord-272759-dqkjofw2 155 1 ( ( -LRB- cord-272759-dqkjofw2 155 2 1− 1− NN cord-272759-dqkjofw2 155 3 P p NN cord-272759-dqkjofw2 155 4 k k NN cord-272759-dqkjofw2 155 5 ) ) -RRB- cord-272759-dqkjofw2 155 6 is be VBZ cord-272759-dqkjofw2 155 7 the the DT cord-272759-dqkjofw2 155 8 probability probability NN cord-272759-dqkjofw2 155 9 of of IN cord-272759-dqkjofw2 155 10 at at RB cord-272759-dqkjofw2 155 11 least least RBS cord-272759-dqkjofw2 155 12 one one CD cord-272759-dqkjofw2 155 13 further further JJ cord-272759-dqkjofw2 155 14 infection infection NN cord-272759-dqkjofw2 155 15 from from IN cord-272759-dqkjofw2 155 16 k k XX cord-272759-dqkjofw2 155 17 infectious infectious JJ cord-272759-dqkjofw2 155 18 nodes node NNS cord-272759-dqkjofw2 155 19 . . . cord-272759-dqkjofw2 156 1 The the DT cord-272759-dqkjofw2 156 2 probability probability NN cord-272759-dqkjofw2 156 3 that that IN cord-272759-dqkjofw2 156 4 the the DT cord-272759-dqkjofw2 156 5 epidemic epidemic NN cord-272759-dqkjofw2 156 6 will will MD cord-272759-dqkjofw2 156 7 terminate terminate VB cord-272759-dqkjofw2 156 8 is be VBZ cord-272759-dqkjofw2 156 9 given give VBN cord-272759-dqkjofw2 156 10 by by IN cord-272759-dqkjofw2 156 11 where where WRB cord-272759-dqkjofw2 156 12 P p NN cord-272759-dqkjofw2 156 13 = = SYM cord-272759-dqkjofw2 156 14 P p NN cord-272759-dqkjofw2 156 15 none none NN cord-272759-dqkjofw2 156 16 is be VBZ cord-272759-dqkjofw2 156 17 given give VBN cord-272759-dqkjofw2 156 18 by by IN cord-272759-dqkjofw2 156 19 Eq Eq NNP cord-272759-dqkjofw2 156 20 . . . cord-272759-dqkjofw2 157 1 ( ( -LRB- cord-272759-dqkjofw2 157 2 4 4 LS cord-272759-dqkjofw2 157 3 ) ) -RRB- cord-272759-dqkjofw2 157 4 . . . cord-272759-dqkjofw2 158 1 By by IN cord-272759-dqkjofw2 158 2 expanding expand VBG cord-272759-dqkjofw2 158 3 Eq Eq NNP cord-272759-dqkjofw2 158 4 . . . cord-272759-dqkjofw2 159 1 ( ( -LRB- cord-272759-dqkjofw2 159 2 5 5 LS cord-272759-dqkjofw2 159 3 ) ) -RRB- cord-272759-dqkjofw2 159 4 and and CC cord-272759-dqkjofw2 159 5 comparing compare VBG cord-272759-dqkjofw2 159 6 to to IN cord-272759-dqkjofw2 159 7 the the DT cord-272759-dqkjofw2 159 8 Pentagonal Pentagonal NNP cord-272759-dqkjofw2 159 9 Number Number NNP cord-272759-dqkjofw2 159 10 Theorem Theorem NNP cord-272759-dqkjofw2 159 11 , , , cord-272759-dqkjofw2 159 12 6 6 CD cord-272759-dqkjofw2 159 13 we -PRON- PRP cord-272759-dqkjofw2 159 14 find find VBP cord-272759-dqkjofw2 159 15 that that IN cord-272759-dqkjofw2 159 16 Eq Eq NNP cord-272759-dqkjofw2 159 17 . . . cord-272759-dqkjofw2 160 1 ( ( -LRB- cord-272759-dqkjofw2 160 2 5 5 LS cord-272759-dqkjofw2 160 3 ) ) -RRB- cord-272759-dqkjofw2 160 4 can can MD cord-272759-dqkjofw2 160 5 be be VB cord-272759-dqkjofw2 160 6 rewritten rewrite VBN cord-272759-dqkjofw2 160 7 as as IN cord-272759-dqkjofw2 160 8 an an DT cord-272759-dqkjofw2 160 9 infinite infinite JJ cord-272759-dqkjofw2 160 10 sum sum NN cord-272759-dqkjofw2 160 11 ( ( -LRB- cord-272759-dqkjofw2 160 12 1 1 CD cord-272759-dqkjofw2 160 13 − − NN cord-272759-dqkjofw2 160 14 P p NN cord-272759-dqkjofw2 160 15 n n NN cord-272759-dqkjofw2 160 16 ) ) -RRB- cord-272759-dqkjofw2 160 17 = = NFP cord-272759-dqkjofw2 161 1 P p NN cord-272759-dqkjofw2 161 2 + + CC cord-272759-dqkjofw2 162 1 P p NN cord-272759-dqkjofw2 162 2 2 2 CD cord-272759-dqkjofw2 162 3 − − NN cord-272759-dqkjofw2 162 4 P p NN cord-272759-dqkjofw2 163 1 5 5 LS cord-272759-dqkjofw2 163 2 − − NN cord-272759-dqkjofw2 163 3 P p NN cord-272759-dqkjofw2 163 4 7 7 CD cord-272759-dqkjofw2 163 5 6 6 CD cord-272759-dqkjofw2 164 1 This this DT cord-272759-dqkjofw2 164 2 result result NN cord-272759-dqkjofw2 164 3 was be VBD cord-272759-dqkjofw2 164 4 originally originally RB cord-272759-dqkjofw2 164 5 proved prove VBN cord-272759-dqkjofw2 164 6 by by IN cord-272759-dqkjofw2 164 7 Euler Euler NNP cord-272759-dqkjofw2 164 8 in in IN cord-272759-dqkjofw2 164 9 1775 1775 CD cord-272759-dqkjofw2 164 10 . . . cord-272759-dqkjofw2 165 1 where where WRB cord-272759-dqkjofw2 165 2 the the DT cord-272759-dqkjofw2 165 3 sequence sequence NN cord-272759-dqkjofw2 165 4 of of IN cord-272759-dqkjofw2 165 5 indices index NNS cord-272759-dqkjofw2 165 6 0 0 CD cord-272759-dqkjofw2 165 7 , , , cord-272759-dqkjofw2 165 8 1 1 CD cord-272759-dqkjofw2 165 9 , , , cord-272759-dqkjofw2 165 10 2 2 CD cord-272759-dqkjofw2 165 11 , , , cord-272759-dqkjofw2 165 12 5 5 CD cord-272759-dqkjofw2 165 13 , , , cord-272759-dqkjofw2 165 14 7 7 CD cord-272759-dqkjofw2 165 15 , , , cord-272759-dqkjofw2 165 16 12 12 CD cord-272759-dqkjofw2 165 17 , , , cord-272759-dqkjofw2 165 18 15 15 CD cord-272759-dqkjofw2 165 19 , , , cord-272759-dqkjofw2 165 20 22 22 CD cord-272759-dqkjofw2 165 21 , , , cord-272759-dqkjofw2 165 22 26 26 CD cord-272759-dqkjofw2 165 23 , , , cord-272759-dqkjofw2 165 24 35 35 CD cord-272759-dqkjofw2 165 25 . . . cord-272759-dqkjofw2 165 26 . . . cord-272759-dqkjofw2 165 27 . . . cord-272759-dqkjofw2 166 1 is be VBZ cord-272759-dqkjofw2 166 2 the the DT cord-272759-dqkjofw2 166 3 generalised generalised JJ cord-272759-dqkjofw2 166 4 pentagonal pentagonal JJ cord-272759-dqkjofw2 166 5 numbers number NNS cord-272759-dqkjofw2 166 6 ( ( -LRB- cord-272759-dqkjofw2 166 7 described describe VBN cord-272759-dqkjofw2 166 8 as as IN cord-272759-dqkjofw2 166 9 sequence sequence NN cord-272759-dqkjofw2 166 10 A001318 A001318 NNP cord-272759-dqkjofw2 166 11 in in IN cord-272759-dqkjofw2 166 12 [ [ -LRB- cord-272759-dqkjofw2 166 13 18 18 CD cord-272759-dqkjofw2 166 14 ] ] -RRB- cord-272759-dqkjofw2 166 15 ) ) -RRB- cord-272759-dqkjofw2 166 16 . . . cord-272759-dqkjofw2 167 1 Eq Eq NNP cord-272759-dqkjofw2 167 2 . . . cord-272759-dqkjofw2 168 1 ( ( -LRB- cord-272759-dqkjofw2 168 2 6 6 LS cord-272759-dqkjofw2 168 3 ) ) -RRB- cord-272759-dqkjofw2 168 4 may may MD cord-272759-dqkjofw2 168 5 also also RB cord-272759-dqkjofw2 168 6 be be VB cord-272759-dqkjofw2 168 7 re re VBN cord-272759-dqkjofw2 168 8 - - VBN cord-272759-dqkjofw2 168 9 written write VBN cord-272759-dqkjofw2 169 1 in in IN cord-272759-dqkjofw2 169 2 terms term NNS cord-272759-dqkjofw2 169 3 of of IN cord-272759-dqkjofw2 169 4 the the DT cord-272759-dqkjofw2 169 5 Dedekind Dedekind NNP cord-272759-dqkjofw2 169 6 eta eta NNP cord-272759-dqkjofw2 169 7 function function NN cord-272759-dqkjofw2 169 8 , , , cord-272759-dqkjofw2 169 9 but but CC cord-272759-dqkjofw2 169 10 for for IN cord-272759-dqkjofw2 169 11 the the DT cord-272759-dqkjofw2 169 12 purposes purpose NNS cord-272759-dqkjofw2 169 13 of of IN cord-272759-dqkjofw2 169 14 this this DT cord-272759-dqkjofw2 169 15 discussion discussion NN cord-272759-dqkjofw2 169 16 it -PRON- PRP cord-272759-dqkjofw2 169 17 is be VBZ cord-272759-dqkjofw2 169 18 unnecessary unnecessary JJ cord-272759-dqkjofw2 169 19 to to TO cord-272759-dqkjofw2 169 20 do do VB cord-272759-dqkjofw2 169 21 so so RB cord-272759-dqkjofw2 169 22 . . . cord-272759-dqkjofw2 170 1 Nonetheless nonetheless RB cord-272759-dqkjofw2 170 2 , , , cord-272759-dqkjofw2 170 3 for for IN cord-272759-dqkjofw2 170 4 0 0 CD cord-272759-dqkjofw2 170 5 ≤ ≤ NN cord-272759-dqkjofw2 170 6 P p NN cord-272759-dqkjofw2 170 7 < < XX cord-272759-dqkjofw2 170 8 1 1 CD cord-272759-dqkjofw2 170 9 this this DT cord-272759-dqkjofw2 170 10 sequence sequence NN cord-272759-dqkjofw2 170 11 converges converge VBZ cord-272759-dqkjofw2 170 12 fairly fairly RB cord-272759-dqkjofw2 170 13 rapidly rapidly RB cord-272759-dqkjofw2 170 14 as as IN cord-272759-dqkjofw2 170 15 the the DT cord-272759-dqkjofw2 170 16 order order NN cord-272759-dqkjofw2 170 17 of of IN cord-272759-dqkjofw2 170 18 the the DT cord-272759-dqkjofw2 170 19 exponent exponent NN cord-272759-dqkjofw2 170 20 increases increase NNS cord-272759-dqkjofw2 170 21 . . . cord-272759-dqkjofw2 171 1 The the DT cord-272759-dqkjofw2 171 2 exact exact JJ cord-272759-dqkjofw2 171 3 7 7 CD cord-272759-dqkjofw2 171 4 probability probability NN cord-272759-dqkjofw2 171 5 of of IN cord-272759-dqkjofw2 171 6 a a DT cord-272759-dqkjofw2 171 7 general general JJ cord-272759-dqkjofw2 171 8 outbreak outbreak NN cord-272759-dqkjofw2 171 9 can can MD cord-272759-dqkjofw2 171 10 alternatively alternatively RB cord-272759-dqkjofw2 171 11 be be VB cord-272759-dqkjofw2 171 12 obtained obtain VBN cord-272759-dqkjofw2 171 13 by by IN cord-272759-dqkjofw2 171 14 using use VBG cord-272759-dqkjofw2 171 15 a a DT cord-272759-dqkjofw2 171 16 branching branch VBG cord-272759-dqkjofw2 171 17 process process NN cord-272759-dqkjofw2 171 18 method method NN cord-272759-dqkjofw2 171 19 . . . cord-272759-dqkjofw2 172 1 Following follow VBG cord-272759-dqkjofw2 172 2 [ [ -LRB- cord-272759-dqkjofw2 172 3 19 19 CD cord-272759-dqkjofw2 172 4 ] ] -RRB- cord-272759-dqkjofw2 172 5 , , , cord-272759-dqkjofw2 172 6 we -PRON- PRP cord-272759-dqkjofw2 172 7 define define VBP cord-272759-dqkjofw2 172 8 the the DT cord-272759-dqkjofw2 172 9 probability probability NN cord-272759-dqkjofw2 172 10 generating generate VBG cord-272759-dqkjofw2 172 11 function function NN cord-272759-dqkjofw2 172 12 for for IN cord-272759-dqkjofw2 172 13 the the DT cord-272759-dqkjofw2 172 14 number number NN cord-272759-dqkjofw2 172 15 of of IN cord-272759-dqkjofw2 172 16 secondary secondary JJ cord-272759-dqkjofw2 172 17 cases case NNS cord-272759-dqkjofw2 172 18 produced produce VBN cord-272759-dqkjofw2 172 19 by by IN cord-272759-dqkjofw2 172 20 a a DT cord-272759-dqkjofw2 172 21 single single JJ cord-272759-dqkjofw2 172 22 infectious infectious JJ cord-272759-dqkjofw2 172 23 case case NN cord-272759-dqkjofw2 172 24 in in IN cord-272759-dqkjofw2 172 25 a a DT cord-272759-dqkjofw2 172 26 day day NN cord-272759-dqkjofw2 172 27 . . . cord-272759-dqkjofw2 173 1 Then then RB cord-272759-dqkjofw2 173 2 the the DT cord-272759-dqkjofw2 173 3 probability probability NN cord-272759-dqkjofw2 173 4 generating generate VBG cord-272759-dqkjofw2 173 5 function function NN cord-272759-dqkjofw2 173 6 for for IN cord-272759-dqkjofw2 173 7 the the DT cord-272759-dqkjofw2 173 8 overall overall JJ cord-272759-dqkjofw2 173 9 number number NN cord-272759-dqkjofw2 173 10 of of IN cord-272759-dqkjofw2 173 11 secondary secondary JJ cord-272759-dqkjofw2 173 12 infections infection NNS cord-272759-dqkjofw2 173 13 from from IN cord-272759-dqkjofw2 173 14 a a DT cord-272759-dqkjofw2 173 15 single single JJ cord-272759-dqkjofw2 173 16 primary primary JJ cord-272759-dqkjofw2 173 17 case case NN cord-272759-dqkjofw2 173 18 is be VBZ cord-272759-dqkjofw2 173 19 One one PRP cord-272759-dqkjofw2 173 20 can can MD cord-272759-dqkjofw2 173 21 then then RB cord-272759-dqkjofw2 173 22 obtain obtain VB cord-272759-dqkjofw2 173 23 the the DT cord-272759-dqkjofw2 173 24 probability probability NN cord-272759-dqkjofw2 173 25 of of IN cord-272759-dqkjofw2 173 26 no no DT cord-272759-dqkjofw2 173 27 general general JJ cord-272759-dqkjofw2 173 28 outbreak outbreak NN cord-272759-dqkjofw2 173 29 ( ( -LRB- cord-272759-dqkjofw2 173 30 i.e. i.e. FW cord-272759-dqkjofw2 173 31 the the DT cord-272759-dqkjofw2 173 32 probability probability NN cord-272759-dqkjofw2 173 33 of of IN cord-272759-dqkjofw2 173 34 the the DT cord-272759-dqkjofw2 173 35 disease disease NN cord-272759-dqkjofw2 173 36 not not RB cord-272759-dqkjofw2 173 37 becoming become VBG cord-272759-dqkjofw2 173 38 endemic endemic JJ cord-272759-dqkjofw2 173 39 ) ) -RRB- cord-272759-dqkjofw2 173 40 as as IN cord-272759-dqkjofw2 173 41 the the DT cord-272759-dqkjofw2 173 42 smallest small JJS cord-272759-dqkjofw2 173 43 solution solution NN cord-272759-dqkjofw2 173 44 x x SYM cord-272759-dqkjofw2 173 45 ∈ ∈ NN cord-272759-dqkjofw2 173 46 [ [ -LRB- cord-272759-dqkjofw2 173 47 0 0 CD cord-272759-dqkjofw2 173 48 , , , cord-272759-dqkjofw2 173 49 1 1 CD cord-272759-dqkjofw2 173 50 ] ] -RRB- cord-272759-dqkjofw2 173 51 of of IN cord-272759-dqkjofw2 173 52 g(x g(x NNP cord-272759-dqkjofw2 173 53 ) ) -RRB- cord-272759-dqkjofw2 173 54 = = NFP cord-272759-dqkjofw2 174 1 x. x. NNP cord-272759-dqkjofw2 175 1 Unfortunately unfortunately RB cord-272759-dqkjofw2 175 2 , , , cord-272759-dqkjofw2 175 3 Eq Eq NNP cord-272759-dqkjofw2 175 4 . . . cord-272759-dqkjofw2 176 1 ( ( -LRB- cord-272759-dqkjofw2 176 2 8) 8) NNP cord-272759-dqkjofw2 176 3 can can MD cord-272759-dqkjofw2 176 4 not not RB cord-272759-dqkjofw2 176 5 be be VB cord-272759-dqkjofw2 176 6 readily readily RB cord-272759-dqkjofw2 176 7 used use VBN cord-272759-dqkjofw2 176 8 for for IN cord-272759-dqkjofw2 176 9 further further JJ cord-272759-dqkjofw2 176 10 analysis analysis NN cord-272759-dqkjofw2 176 11 . . . cord-272759-dqkjofw2 177 1 Similarly similarly RB cord-272759-dqkjofw2 177 2 , , , cord-272759-dqkjofw2 177 3 although although IN cord-272759-dqkjofw2 177 4 Eq Eq NNP cord-272759-dqkjofw2 177 5 . . . cord-272759-dqkjofw2 178 1 ( ( -LRB- cord-272759-dqkjofw2 178 2 5 5 LS cord-272759-dqkjofw2 178 3 ) ) -RRB- cord-272759-dqkjofw2 178 4 can can MD cord-272759-dqkjofw2 178 5 be be VB cord-272759-dqkjofw2 178 6 computed compute VBN cord-272759-dqkjofw2 178 7 easily easily RB cord-272759-dqkjofw2 178 8 , , , cord-272759-dqkjofw2 178 9 it -PRON- PRP cord-272759-dqkjofw2 178 10 is be VBZ cord-272759-dqkjofw2 178 11 not not RB cord-272759-dqkjofw2 178 12 in in IN cord-272759-dqkjofw2 178 13 a a DT cord-272759-dqkjofw2 178 14 form form NN cord-272759-dqkjofw2 178 15 that that WDT cord-272759-dqkjofw2 178 16 is be VBZ cord-272759-dqkjofw2 178 17 immediately immediately RB cord-272759-dqkjofw2 178 18 amenable amenable JJ cord-272759-dqkjofw2 178 19 for for IN cord-272759-dqkjofw2 178 20 further further JJ cord-272759-dqkjofw2 178 21 analysis analysis NN cord-272759-dqkjofw2 178 22 . . . cord-272759-dqkjofw2 179 1 However however RB cord-272759-dqkjofw2 179 2 , , , cord-272759-dqkjofw2 179 3 since since IN cord-272759-dqkjofw2 179 4 P p NN cord-272759-dqkjofw2 179 5 safe safe JJ cord-272759-dqkjofw2 179 6 ≥ ≥ CD cord-272759-dqkjofw2 179 7 P p NN cord-272759-dqkjofw2 179 8 none none NN cord-272759-dqkjofw2 179 9 , , , cord-272759-dqkjofw2 179 10 it -PRON- PRP cord-272759-dqkjofw2 179 11 is be VBZ cord-272759-dqkjofw2 179 12 clear clear JJ cord-272759-dqkjofw2 179 13 that that IN cord-272759-dqkjofw2 179 14 1 1 CD cord-272759-dqkjofw2 179 15 will will MD cord-272759-dqkjofw2 179 16 make make VB cord-272759-dqkjofw2 179 17 P p NN cord-272759-dqkjofw2 179 18 safe safe JJ cord-272759-dqkjofw2 180 1 ≈ ≈ NNP cord-272759-dqkjofw2 180 2 0 0 NFP cord-272759-dqkjofw2 180 3 . . . cord-272759-dqkjofw2 181 1 Hence hence RB cord-272759-dqkjofw2 181 2 , , , cord-272759-dqkjofw2 181 3 either either CC cord-272759-dqkjofw2 181 4 µ µ NN cord-272759-dqkjofw2 181 5 1 1 CD cord-272759-dqkjofw2 181 6 or or CC cord-272759-dqkjofw2 181 7 p p NN cord-272759-dqkjofw2 181 8 2 2 CD cord-272759-dqkjofw2 181 9 ≈ ≈ NNP cord-272759-dqkjofw2 181 10 1 1 CD cord-272759-dqkjofw2 181 11 will will MD cord-272759-dqkjofw2 181 12 lead lead VB cord-272759-dqkjofw2 181 13 to to IN cord-272759-dqkjofw2 181 14 widespread widespread JJ cord-272759-dqkjofw2 181 15 infection infection NN cord-272759-dqkjofw2 181 16 ( ( -LRB- cord-272759-dqkjofw2 181 17 as as IN cord-272759-dqkjofw2 181 18 expected expect VBN cord-272759-dqkjofw2 181 19 ) ) -RRB- cord-272759-dqkjofw2 181 20 . . . cord-272759-dqkjofw2 182 1 Differentiating differentiate VBG cord-272759-dqkjofw2 182 2 ( ( -LRB- cord-272759-dqkjofw2 182 3 5 5 CD cord-272759-dqkjofw2 182 4 ) ) -RRB- cord-272759-dqkjofw2 182 5 with with IN cord-272759-dqkjofw2 182 6 respect respect NN cord-272759-dqkjofw2 182 7 to to IN cord-272759-dqkjofw2 182 8 ( ( -LRB- cord-272759-dqkjofw2 182 9 1 1 CD cord-272759-dqkjofw2 182 10 − − NN cord-272759-dqkjofw2 182 11 p p NN cord-272759-dqkjofw2 182 12 1 1 CD cord-272759-dqkjofw2 182 13 ) ) -RRB- cord-272759-dqkjofw2 182 14 n n NN cord-272759-dqkjofw2 182 15 1 1 CD cord-272759-dqkjofw2 182 16 , , , cord-272759-dqkjofw2 182 17 we -PRON- PRP cord-272759-dqkjofw2 182 18 can can MD cord-272759-dqkjofw2 182 19 easily easily RB cord-272759-dqkjofw2 182 20 verify verify VB cord-272759-dqkjofw2 182 21 that that IN cord-272759-dqkjofw2 182 22 P p NN cord-272759-dqkjofw2 182 23 safe safe NN cord-272759-dqkjofw2 182 24 is be VBZ cord-272759-dqkjofw2 182 25 a a DT cord-272759-dqkjofw2 182 26 monotonic monotonic JJ cord-272759-dqkjofw2 182 27 function function NN cord-272759-dqkjofw2 182 28 of of IN cord-272759-dqkjofw2 182 29 both both DT cord-272759-dqkjofw2 182 30 p p NN cord-272759-dqkjofw2 182 31 1 1 CD cord-272759-dqkjofw2 182 32 and and CC cord-272759-dqkjofw2 182 33 n n NN cord-272759-dqkjofw2 182 34 1 1 CD cord-272759-dqkjofw2 182 35 . . . cord-272759-dqkjofw2 183 1 One one PRP cord-272759-dqkjofw2 183 2 can can MD cord-272759-dqkjofw2 183 3 therefore therefore RB cord-272759-dqkjofw2 183 4 observe observe VB cord-272759-dqkjofw2 183 5 that that IN cord-272759-dqkjofw2 183 6 P p NN cord-272759-dqkjofw2 183 7 safe safe JJ cord-272759-dqkjofw2 183 8 ≈ ≈ NNS cord-272759-dqkjofw2 183 9 0 0 NFP cord-272759-dqkjofw2 183 10 if if IN cord-272759-dqkjofw2 183 11 p p NN cord-272759-dqkjofw2 183 12 1 1 CD cord-272759-dqkjofw2 183 13 ≈ ≈ NNP cord-272759-dqkjofw2 183 14 1 1 CD cord-272759-dqkjofw2 183 15 or or CC cord-272759-dqkjofw2 183 16 n n NN cord-272759-dqkjofw2 183 17 1 1 CD cord-272759-dqkjofw2 183 18 1 1 CD cord-272759-dqkjofw2 183 19 . . . cord-272759-dqkjofw2 184 1 The the DT cord-272759-dqkjofw2 184 2 most most RBS cord-272759-dqkjofw2 184 3 severe severe JJ cord-272759-dqkjofw2 184 4 limitation limitation NN cord-272759-dqkjofw2 184 5 on on IN cord-272759-dqkjofw2 184 6 Eq Eq NNP cord-272759-dqkjofw2 184 7 . . . cord-272759-dqkjofw2 185 1 ( ( -LRB- cord-272759-dqkjofw2 185 2 5 5 LS cord-272759-dqkjofw2 185 3 ) ) -RRB- cord-272759-dqkjofw2 185 4 , , , cord-272759-dqkjofw2 185 5 and and CC cord-272759-dqkjofw2 185 6 also also RB cord-272759-dqkjofw2 185 7 Eqs Eqs NNP cord-272759-dqkjofw2 185 8 . . . cord-272759-dqkjofw2 186 1 ( ( -LRB- cord-272759-dqkjofw2 186 2 7 7 CD cord-272759-dqkjofw2 186 3 ) ) -RRB- cord-272759-dqkjofw2 186 4 and and CC cord-272759-dqkjofw2 186 5 ( ( -LRB- cord-272759-dqkjofw2 186 6 8) 8) NNP cord-272759-dqkjofw2 186 7 , , , cord-272759-dqkjofw2 186 8 is be VBZ cord-272759-dqkjofw2 186 9 that that IN cord-272759-dqkjofw2 186 10 we -PRON- PRP cord-272759-dqkjofw2 186 11 assume assume VBP cord-272759-dqkjofw2 186 12 that that IN cord-272759-dqkjofw2 186 13 no no DT cord-272759-dqkjofw2 186 14 infected infect VBN cord-272759-dqkjofw2 186 15 nodes node NNS cord-272759-dqkjofw2 186 16 have have VBP cord-272759-dqkjofw2 186 17 common common JJ cord-272759-dqkjofw2 186 18 neighbours neighbour NNS cord-272759-dqkjofw2 186 19 , , , cord-272759-dqkjofw2 186 20 and and CC cord-272759-dqkjofw2 186 21 that that IN cord-272759-dqkjofw2 186 22 all all DT cord-272759-dqkjofw2 186 23 of of IN cord-272759-dqkjofw2 186 24 the the DT cord-272759-dqkjofw2 186 25 neighbours neighbour NNS cord-272759-dqkjofw2 186 26 are be VBP cord-272759-dqkjofw2 186 27 susceptible susceptible JJ cord-272759-dqkjofw2 186 28 . . . cord-272759-dqkjofw2 187 1 In in IN cord-272759-dqkjofw2 187 2 reality reality NN cord-272759-dqkjofw2 187 3 , , , cord-272759-dqkjofw2 187 4 the the DT cord-272759-dqkjofw2 187 5 number number NN cord-272759-dqkjofw2 187 6 of of IN cord-272759-dqkjofw2 187 7 potential potential JJ cord-272759-dqkjofw2 187 8 infections infection NNS cord-272759-dqkjofw2 187 9 is be VBZ cord-272759-dqkjofw2 187 10 limited limit VBN cord-272759-dqkjofw2 187 11 by by IN cord-272759-dqkjofw2 187 12 the the DT cord-272759-dqkjofw2 187 13 fact fact NN cord-272759-dqkjofw2 187 14 that that IN cord-272759-dqkjofw2 187 15 some some DT cord-272759-dqkjofw2 187 16 of of IN cord-272759-dqkjofw2 187 17 the the DT cord-272759-dqkjofw2 187 18 potential potential JJ cord-272759-dqkjofw2 187 19 neighbours neighbour NNS cord-272759-dqkjofw2 187 20 are be VBP cord-272759-dqkjofw2 187 21 already already RB cord-272759-dqkjofw2 187 22 infected infect VBN cord-272759-dqkjofw2 187 23 . . . cord-272759-dqkjofw2 188 1 It -PRON- PRP cord-272759-dqkjofw2 188 2 is be VBZ cord-272759-dqkjofw2 188 3 therefore therefore RB cord-272759-dqkjofw2 188 4 important important JJ cord-272759-dqkjofw2 188 5 to to TO cord-272759-dqkjofw2 188 6 estimate estimate VB cord-272759-dqkjofw2 188 7 the the DT cord-272759-dqkjofw2 188 8 number number NN cord-272759-dqkjofw2 188 9 of of IN cord-272759-dqkjofw2 188 10 neighbours neighbour NNS cord-272759-dqkjofw2 188 11 of of IN cord-272759-dqkjofw2 188 12 an an DT cord-272759-dqkjofw2 188 13 infected infected JJ cord-272759-dqkjofw2 188 14 node node NN cord-272759-dqkjofw2 188 15 that that WDT cord-272759-dqkjofw2 188 16 have have VBP cord-272759-dqkjofw2 188 17 not not RB cord-272759-dqkjofw2 188 18 been be VBN cord-272759-dqkjofw2 188 19 infected infect VBN cord-272759-dqkjofw2 188 20 . . . cord-272759-dqkjofw2 189 1 This this DT cord-272759-dqkjofw2 189 2 is be VBZ cord-272759-dqkjofw2 189 3 equivalent equivalent JJ cord-272759-dqkjofw2 189 4 to to IN cord-272759-dqkjofw2 189 5 estimating estimate VBG cord-272759-dqkjofw2 189 6 the the DT cord-272759-dqkjofw2 189 7 ratio ratio NN cord-272759-dqkjofw2 189 8 of of IN cord-272759-dqkjofw2 189 9 local local JJ cord-272759-dqkjofw2 189 10 and and CC cord-272759-dqkjofw2 189 11 non non JJ cord-272759-dqkjofw2 189 12 - - JJ cord-272759-dqkjofw2 189 13 local local JJ cord-272759-dqkjofw2 189 14 infections infection NNS cord-272759-dqkjofw2 189 15 in in IN cord-272759-dqkjofw2 189 16 an an DT cord-272759-dqkjofw2 189 17 epidemic epidemic NN cord-272759-dqkjofw2 189 18 . . . cord-272759-dqkjofw2 190 1 8 8 CD cord-272759-dqkjofw2 191 1 One one PRP cord-272759-dqkjofw2 191 2 can can MD cord-272759-dqkjofw2 191 3 consider consider VB cord-272759-dqkjofw2 191 4 the the DT cord-272759-dqkjofw2 191 5 network network NN cord-272759-dqkjofw2 191 6 of of IN cord-272759-dqkjofw2 191 7 infected infected JJ cord-272759-dqkjofw2 191 8 individuals individual NNS cord-272759-dqkjofw2 191 9 as as IN cord-272759-dqkjofw2 191 10 consisting consist VBG cord-272759-dqkjofw2 191 11 of of IN cord-272759-dqkjofw2 191 12 a a DT cord-272759-dqkjofw2 191 13 number number NN cord-272759-dqkjofw2 191 14 of of IN cord-272759-dqkjofw2 191 15 " " `` cord-272759-dqkjofw2 191 16 clumps clump NNS cord-272759-dqkjofw2 191 17 " " '' cord-272759-dqkjofw2 191 18 : : : cord-272759-dqkjofw2 191 19 one one CD cord-272759-dqkjofw2 191 20 clump clump NN cord-272759-dqkjofw2 191 21 7 7 CD cord-272759-dqkjofw2 191 22 Because because IN cord-272759-dqkjofw2 191 23 of of IN cord-272759-dqkjofw2 191 24 the the DT cord-272759-dqkjofw2 191 25 assumption assumption NN cord-272759-dqkjofw2 191 26 that that IN cord-272759-dqkjofw2 191 27 infections infection NNS cord-272759-dqkjofw2 191 28 occur occur VBP cord-272759-dqkjofw2 191 29 individually individually RB cord-272759-dqkjofw2 191 30 and and CC cord-272759-dqkjofw2 191 31 sequentially sequentially RB cord-272759-dqkjofw2 191 32 , , , cord-272759-dqkjofw2 191 33 the the DT cord-272759-dqkjofw2 191 34 branching branching NN cord-272759-dqkjofw2 191 35 process process NN cord-272759-dqkjofw2 191 36 in in IN cord-272759-dqkjofw2 191 37 Eq Eq NNP cord-272759-dqkjofw2 191 38 . . . cord-272759-dqkjofw2 192 1 ( ( -LRB- cord-272759-dqkjofw2 192 2 5 5 LS cord-272759-dqkjofw2 192 3 ) ) -RRB- cord-272759-dqkjofw2 192 4 is be VBZ cord-272759-dqkjofw2 192 5 only only RB cord-272759-dqkjofw2 192 6 an an DT cord-272759-dqkjofw2 192 7 approximation approximation NN cord-272759-dqkjofw2 192 8 to to IN cord-272759-dqkjofw2 192 9 the the DT cord-272759-dqkjofw2 192 10 solution solution NN cord-272759-dqkjofw2 192 11 of of IN cord-272759-dqkjofw2 192 12 Eq Eq NNP cord-272759-dqkjofw2 192 13 . . . cord-272759-dqkjofw2 193 1 ( ( -LRB- cord-272759-dqkjofw2 193 2 8) 8) NNP cord-272759-dqkjofw2 193 3 . . . cord-272759-dqkjofw2 193 4 8 8 CD cord-272759-dqkjofw2 193 5 We -PRON- PRP cord-272759-dqkjofw2 193 6 can can MD cord-272759-dqkjofw2 193 7 achieve achieve VB cord-272759-dqkjofw2 193 8 this this DT cord-272759-dqkjofw2 193 9 as as IN cord-272759-dqkjofw2 193 10 follows follow VBZ cord-272759-dqkjofw2 193 11 . . . cord-272759-dqkjofw2 194 1 Suppose suppose VB cord-272759-dqkjofw2 194 2 that that IN cord-272759-dqkjofw2 194 3 there there EX cord-272759-dqkjofw2 194 4 are be VBP cord-272759-dqkjofw2 194 5 no no DT cord-272759-dqkjofw2 194 6 non non JJ cord-272759-dqkjofw2 194 7 - - JJ cord-272759-dqkjofw2 194 8 local local JJ cord-272759-dqkjofw2 194 9 infections infection NNS cord-272759-dqkjofw2 194 10 ( ( -LRB- cord-272759-dqkjofw2 194 11 i.e. i.e. FW cord-272759-dqkjofw2 194 12 p p NN cord-272759-dqkjofw2 194 13 2 2 CD cord-272759-dqkjofw2 194 14 = = SYM cord-272759-dqkjofw2 194 15 0 0 CD cord-272759-dqkjofw2 194 16 ) ) -RRB- cord-272759-dqkjofw2 194 17 and and CC cord-272759-dqkjofw2 194 18 that that IN cord-272759-dqkjofw2 194 19 infections infection NNS cord-272759-dqkjofw2 194 20 grow grow VBP cord-272759-dqkjofw2 194 21 in in IN cord-272759-dqkjofw2 194 22 a a DT cord-272759-dqkjofw2 194 23 single single JJ cord-272759-dqkjofw2 194 24 ( ( -LRB- cord-272759-dqkjofw2 194 25 roughly roughly RB cord-272759-dqkjofw2 194 26 spherical spherical JJ cord-272759-dqkjofw2 194 27 ) ) -RRB- cord-272759-dqkjofw2 194 28 " " `` cord-272759-dqkjofw2 194 29 clump clump NN cord-272759-dqkjofw2 194 30 " " '' cord-272759-dqkjofw2 194 31 . . . cord-272759-dqkjofw2 195 1 Then then RB cord-272759-dqkjofw2 195 2 , , , cord-272759-dqkjofw2 195 3 if if IN cord-272759-dqkjofw2 195 4 the the DT cord-272759-dqkjofw2 195 5 clump clump NN cord-272759-dqkjofw2 195 6 consists consist VBZ cord-272759-dqkjofw2 195 7 of of IN cord-272759-dqkjofw2 195 8 I -PRON- PRP cord-272759-dqkjofw2 195 9 ( ( -LRB- cord-272759-dqkjofw2 195 10 t t NN cord-272759-dqkjofw2 195 11 ) ) -RRB- cord-272759-dqkjofw2 195 12 individuals individual NNS cord-272759-dqkjofw2 195 13 , , , cord-272759-dqkjofw2 195 14 then then RB cord-272759-dqkjofw2 195 15 the the DT cord-272759-dqkjofw2 195 16 radius radius NN cord-272759-dqkjofw2 195 17 of of IN cord-272759-dqkjofw2 195 18 this this DT cord-272759-dqkjofw2 195 19 for for IN cord-272759-dqkjofw2 195 20 each each DT cord-272759-dqkjofw2 195 21 non non JJ cord-272759-dqkjofw2 195 22 - - JJ cord-272759-dqkjofw2 195 23 local local JJ cord-272759-dqkjofw2 195 24 infection infection NN cord-272759-dqkjofw2 195 25 ( ( -LRB- cord-272759-dqkjofw2 195 26 i.e. i.e. FW cord-272759-dqkjofw2 195 27 each each DT cord-272759-dqkjofw2 195 28 clump clump NN cord-272759-dqkjofw2 195 29 is be VBZ cord-272759-dqkjofw2 195 30 seeded seed VBN cord-272759-dqkjofw2 195 31 by by IN cord-272759-dqkjofw2 195 32 a a DT cord-272759-dqkjofw2 195 33 nonlocal nonlocal JJ cord-272759-dqkjofw2 195 34 transmission transmission NN cord-272759-dqkjofw2 195 35 ; ; : cord-272759-dqkjofw2 195 36 all all DT cord-272759-dqkjofw2 195 37 other other JJ cord-272759-dqkjofw2 195 38 transmissions transmission NNS cord-272759-dqkjofw2 195 39 within within IN cord-272759-dqkjofw2 195 40 that that DT cord-272759-dqkjofw2 195 41 clump clump NN cord-272759-dqkjofw2 195 42 are be VBP cord-272759-dqkjofw2 195 43 local local JJ cord-272759-dqkjofw2 195 44 ) ) -RRB- cord-272759-dqkjofw2 195 45 . . . cord-272759-dqkjofw2 196 1 Provided provide VBN cord-272759-dqkjofw2 196 2 p p NN cord-272759-dqkjofw2 196 3 2 2 CD cord-272759-dqkjofw2 196 4 > > SYM cord-272759-dqkjofw2 196 5 0 0 NFP cord-272759-dqkjofw2 196 6 , , , cord-272759-dqkjofw2 196 7 this this DT cord-272759-dqkjofw2 196 8 implies imply VBZ cord-272759-dqkjofw2 196 9 that that IN cord-272759-dqkjofw2 196 10 , , , cord-272759-dqkjofw2 196 11 as as IN cord-272759-dqkjofw2 196 12 the the DT cord-272759-dqkjofw2 196 13 clump clump NN cord-272759-dqkjofw2 196 14 gets get VBZ cord-272759-dqkjofw2 196 15 bigger big JJR cord-272759-dqkjofw2 196 16 , , , cord-272759-dqkjofw2 196 17 the the DT cord-272759-dqkjofw2 196 18 probability probability NN cord-272759-dqkjofw2 196 19 of of IN cord-272759-dqkjofw2 196 20 any any DT cord-272759-dqkjofw2 196 21 given give VBN cord-272759-dqkjofw2 196 22 infection infection NN cord-272759-dqkjofw2 196 23 being be VBG cord-272759-dqkjofw2 196 24 a a DT cord-272759-dqkjofw2 196 25 long long JJ cord-272759-dqkjofw2 196 26 range range NN cord-272759-dqkjofw2 196 27 infection infection NN cord-272759-dqkjofw2 196 28 will will MD cord-272759-dqkjofw2 196 29 increase increase VB cord-272759-dqkjofw2 196 30 . . . cord-272759-dqkjofw2 197 1 Conversely conversely RB cord-272759-dqkjofw2 197 2 , , , cord-272759-dqkjofw2 197 3 as as IN cord-272759-dqkjofw2 197 4 the the DT cord-272759-dqkjofw2 197 5 number number NN cord-272759-dqkjofw2 197 6 of of IN cord-272759-dqkjofw2 197 7 clumps clump NNS cord-272759-dqkjofw2 197 8 increases increase NNS cord-272759-dqkjofw2 197 9 , , , cord-272759-dqkjofw2 197 10 the the DT cord-272759-dqkjofw2 197 11 probability probability NN cord-272759-dqkjofw2 197 12 of of IN cord-272759-dqkjofw2 197 13 local local JJ cord-272759-dqkjofw2 197 14 infection infection NN cord-272759-dqkjofw2 197 15 ( ( -LRB- cord-272759-dqkjofw2 197 16 relative relative JJ cord-272759-dqkjofw2 197 17 to to IN cord-272759-dqkjofw2 197 18 nonlocal nonlocal JJ cord-272759-dqkjofw2 197 19 infection infection NN cord-272759-dqkjofw2 197 20 ) ) -RRB- cord-272759-dqkjofw2 197 21 will will MD cord-272759-dqkjofw2 197 22 increase increase VB cord-272759-dqkjofw2 197 23 . . . cord-272759-dqkjofw2 198 1 9 9 CD cord-272759-dqkjofw2 199 1 Let let VB cord-272759-dqkjofw2 199 2 us -PRON- PRP cord-272759-dqkjofw2 199 3 now now RB cord-272759-dqkjofw2 199 4 estimate estimate VB cord-272759-dqkjofw2 199 5 the the DT cord-272759-dqkjofw2 199 6 expected expect VBN cord-272759-dqkjofw2 199 7 number number NN cord-272759-dqkjofw2 199 8 of of IN cord-272759-dqkjofw2 199 9 connections connection NNS cord-272759-dqkjofw2 199 10 from from IN cord-272759-dqkjofw2 199 11 an an DT cord-272759-dqkjofw2 199 12 infected infected JJ cord-272759-dqkjofw2 199 13 node node NN cord-272759-dqkjofw2 199 14 . . . cord-272759-dqkjofw2 200 1 Let let VB cord-272759-dqkjofw2 200 2 N N NNP cord-272759-dqkjofw2 200 3 S S NNP cord-272759-dqkjofw2 200 4 denote denote VB cord-272759-dqkjofw2 200 5 the the DT cord-272759-dqkjofw2 200 6 expected expect VBN cord-272759-dqkjofw2 200 7 number number NN cord-272759-dqkjofw2 200 8 of of IN cord-272759-dqkjofw2 200 9 susceptible susceptible JJ cord-272759-dqkjofw2 200 10 nodes node NNS cord-272759-dqkjofw2 200 11 linked link VBN cord-272759-dqkjofw2 200 12 to to IN cord-272759-dqkjofw2 200 13 a a DT cord-272759-dqkjofw2 200 14 random random JJ cord-272759-dqkjofw2 200 15 node node NN cord-272759-dqkjofw2 200 16 . . . cord-272759-dqkjofw2 201 1 If if IN cord-272759-dqkjofw2 201 2 this this DT cord-272759-dqkjofw2 201 3 node node NN cord-272759-dqkjofw2 201 4 is be VBZ cord-272759-dqkjofw2 201 5 the the DT cord-272759-dqkjofw2 201 6 result result NN cord-272759-dqkjofw2 201 7 of of IN cord-272759-dqkjofw2 201 8 a a DT cord-272759-dqkjofw2 201 9 non non JJ cord-272759-dqkjofw2 201 10 - - JJ cord-272759-dqkjofw2 201 11 local local JJ cord-272759-dqkjofw2 201 12 infection infection NN cord-272759-dqkjofw2 201 13 , , , cord-272759-dqkjofw2 201 14 then then RB cord-272759-dqkjofw2 201 15 we -PRON- PRP cord-272759-dqkjofw2 201 16 suppose suppose VBP cord-272759-dqkjofw2 201 17 that that IN cord-272759-dqkjofw2 201 18 N N NNP cord-272759-dqkjofw2 201 19 S S NNP cord-272759-dqkjofw2 201 20 = = SYM cord-272759-dqkjofw2 201 21 n n NN cord-272759-dqkjofw2 201 22 1 1 CD cord-272759-dqkjofw2 201 23 + + CC cord-272759-dqkjofw2 201 24 µ µ NN cord-272759-dqkjofw2 201 25 ; ; : cord-272759-dqkjofw2 201 26 however however RB cord-272759-dqkjofw2 201 27 , , , cord-272759-dqkjofw2 201 28 if if IN cord-272759-dqkjofw2 201 29 this this DT cord-272759-dqkjofw2 201 30 is be VBZ cord-272759-dqkjofw2 201 31 the the DT cord-272759-dqkjofw2 201 32 result result NN cord-272759-dqkjofw2 201 33 of of IN cord-272759-dqkjofw2 201 34 a a DT cord-272759-dqkjofw2 201 35 short short JJ cord-272759-dqkjofw2 201 36 range range NN cord-272759-dqkjofw2 201 37 infection infection NN cord-272759-dqkjofw2 201 38 , , , cord-272759-dqkjofw2 201 39 then then RB cord-272759-dqkjofw2 201 40 this this DT cord-272759-dqkjofw2 201 41 number number NN cord-272759-dqkjofw2 201 42 should should MD cord-272759-dqkjofw2 201 43 be be VB cord-272759-dqkjofw2 201 44 lower low JJR cord-272759-dqkjofw2 201 45 ( ( -LRB- cord-272759-dqkjofw2 201 46 certainly certainly RB cord-272759-dqkjofw2 201 47 no no DT cord-272759-dqkjofw2 201 48 more more JJR cord-272759-dqkjofw2 201 49 than than IN cord-272759-dqkjofw2 201 50 µ µ NN cord-272759-dqkjofw2 201 51 + + CC cord-272759-dqkjofw2 201 52 n n NN cord-272759-dqkjofw2 201 53 1 1 CD cord-272759-dqkjofw2 201 54 − − CD cord-272759-dqkjofw2 201 55 1 1 CD cord-272759-dqkjofw2 201 56 ) ) -RRB- cord-272759-dqkjofw2 201 57 . . . cord-272759-dqkjofw2 202 1 Now now RB cord-272759-dqkjofw2 202 2 , , , cord-272759-dqkjofw2 202 3 where where WRB cord-272759-dqkjofw2 202 4 k k NNP cord-272759-dqkjofw2 202 5 is be VBZ cord-272759-dqkjofw2 202 6 the the DT cord-272759-dqkjofw2 202 7 proportion proportion NN cord-272759-dqkjofw2 202 8 of of IN cord-272759-dqkjofw2 202 9 local local JJ cord-272759-dqkjofw2 202 10 links link NNS cord-272759-dqkjofw2 202 11 that that WDT cord-272759-dqkjofw2 202 12 support support VBP cord-272759-dqkjofw2 202 13 possible possible JJ cord-272759-dqkjofw2 202 14 infection infection NN cord-272759-dqkjofw2 202 15 and and CC cord-272759-dqkjofw2 202 16 0 0 NFP cord-272759-dqkjofw2 202 17 < < XX cord-272759-dqkjofw2 202 18 k k NNP cord-272759-dqkjofw2 202 19 ≤ ≤ NNP cord-272759-dqkjofw2 202 20 n n NNP cord-272759-dqkjofw2 202 21 1 1 CD cord-272759-dqkjofw2 202 22 −1 −1 NNP cord-272759-dqkjofw2 202 23 n n NN cord-272759-dqkjofw2 202 24 1 1 CD cord-272759-dqkjofw2 202 25 . . . cord-272759-dqkjofw2 203 1 Hence hence RB cord-272759-dqkjofw2 203 2 , , , cord-272759-dqkjofw2 203 3 From from IN cord-272759-dqkjofw2 203 4 the the DT cord-272759-dqkjofw2 203 5 preceding precede VBG cord-272759-dqkjofw2 203 6 geometric geometric JJ cord-272759-dqkjofw2 203 7 argument argument NN cord-272759-dqkjofw2 203 8 , , , cord-272759-dqkjofw2 203 9 if if IN cord-272759-dqkjofw2 203 10 infection infection NN cord-272759-dqkjofw2 203 11 grows grow VBZ cord-272759-dqkjofw2 203 12 in in IN cord-272759-dqkjofw2 203 13 a a DT cord-272759-dqkjofw2 203 14 single single JJ cord-272759-dqkjofw2 203 15 clump clump NN cord-272759-dqkjofw2 203 16 , , , cord-272759-dqkjofw2 203 17 then then RB cord-272759-dqkjofw2 203 18 k k NNP cord-272759-dqkjofw2 203 19 ≈ ≈ NNP cord-272759-dqkjofw2 203 20 1 1 CD cord-272759-dqkjofw2 203 21 2 2 CD cord-272759-dqkjofw2 203 22 . . . cord-272759-dqkjofw2 204 1 Moreover moreover RB cord-272759-dqkjofw2 204 2 , , , cord-272759-dqkjofw2 204 3 k k XX cord-272759-dqkjofw2 204 4 < < XX cord-272759-dqkjofw2 204 5 1 1 CD cord-272759-dqkjofw2 204 6 2 2 CD cord-272759-dqkjofw2 205 1 only only RB cord-272759-dqkjofw2 205 2 if if IN cord-272759-dqkjofw2 205 3 nodes node NNS cord-272759-dqkjofw2 205 4 remain remain VBP cord-272759-dqkjofw2 205 5 infected infected JJ cord-272759-dqkjofw2 205 6 when when WRB cord-272759-dqkjofw2 205 7 they -PRON- PRP cord-272759-dqkjofw2 205 8 are be VBP cord-272759-dqkjofw2 205 9 on on IN cord-272759-dqkjofw2 205 10 the the DT cord-272759-dqkjofw2 205 11 interior interior NN cord-272759-dqkjofw2 205 12 of of IN cord-272759-dqkjofw2 205 13 such such JJ cord-272759-dqkjofw2 205 14 " " `` cord-272759-dqkjofw2 205 15 clump clump NN cord-272759-dqkjofw2 205 16 " " '' cord-272759-dqkjofw2 205 17 ( ( -LRB- cord-272759-dqkjofw2 205 18 i.e. i.e. FW cord-272759-dqkjofw2 205 19 when when WRB cord-272759-dqkjofw2 205 20 r r NNP cord-272759-dqkjofw2 205 21 1 1 CD cord-272759-dqkjofw2 205 22 is be VBZ cord-272759-dqkjofw2 205 23 very very RB cord-272759-dqkjofw2 205 24 low low JJ cord-272759-dqkjofw2 205 25 ) ) -RRB- cord-272759-dqkjofw2 205 26 . . . cord-272759-dqkjofw2 206 1 We -PRON- PRP cord-272759-dqkjofw2 206 2 would would MD cord-272759-dqkjofw2 206 3 therefore therefore RB cord-272759-dqkjofw2 206 4 expect expect VB cord-272759-dqkjofw2 206 5 that that IN cord-272759-dqkjofw2 206 6 1 1 CD cord-272759-dqkjofw2 206 7 2 2 CD cord-272759-dqkjofw2 206 8 ≤ ≤ NN cord-272759-dqkjofw2 206 9 k k NNP cord-272759-dqkjofw2 206 10 ≤ ≤ NNP cord-272759-dqkjofw2 206 11 n n NNP cord-272759-dqkjofw2 206 12 1 1 CD cord-272759-dqkjofw2 206 13 −1 −1 NNP cord-272759-dqkjofw2 206 14 n n NN cord-272759-dqkjofw2 206 15 1 1 CD cord-272759-dqkjofw2 206 16 . . . cord-272759-dqkjofw2 207 1 Note note VB cord-272759-dqkjofw2 207 2 that that IN cord-272759-dqkjofw2 207 3 k k NN cord-272759-dqkjofw2 207 4 is be VBZ cord-272759-dqkjofw2 207 5 not not RB cord-272759-dqkjofw2 207 6 a a DT cord-272759-dqkjofw2 207 7 model model NN cord-272759-dqkjofw2 207 8 parameter parameter NN cord-272759-dqkjofw2 207 9 , , , cord-272759-dqkjofw2 207 10 but but CC cord-272759-dqkjofw2 207 11 rather rather RB cord-272759-dqkjofw2 207 12 it -PRON- PRP cord-272759-dqkjofw2 207 13 is be VBZ cord-272759-dqkjofw2 207 14 a a DT cord-272759-dqkjofw2 207 15 term term NN cord-272759-dqkjofw2 207 16 in in IN cord-272759-dqkjofw2 207 17 the the DT cord-272759-dqkjofw2 207 18 model model NN cord-272759-dqkjofw2 207 19 that that WDT cord-272759-dqkjofw2 207 20 will will MD cord-272759-dqkjofw2 207 21 both both DT cord-272759-dqkjofw2 207 22 depend depend VB cord-272759-dqkjofw2 207 23 on on IN cord-272759-dqkjofw2 207 24 the the DT cord-272759-dqkjofw2 207 25 various various JJ cord-272759-dqkjofw2 207 26 model model NN cord-272759-dqkjofw2 207 27 parameters parameter NNS cord-272759-dqkjofw2 207 28 and and CC cord-272759-dqkjofw2 207 29 vary vary VBP cord-272759-dqkjofw2 207 30 with with IN cord-272759-dqkjofw2 207 31 time time NN cord-272759-dqkjofw2 207 32 . . . cord-272759-dqkjofw2 208 1 Finally finally RB cord-272759-dqkjofw2 208 2 , , , cord-272759-dqkjofw2 208 3 we -PRON- PRP cord-272759-dqkjofw2 208 4 now now RB cord-272759-dqkjofw2 208 5 consider consider VBP cord-272759-dqkjofw2 208 6 the the DT cord-272759-dqkjofw2 208 7 rate rate NN cord-272759-dqkjofw2 208 8 of of IN cord-272759-dqkjofw2 208 9 transmission transmission NN cord-272759-dqkjofw2 208 10 . . . cord-272759-dqkjofw2 209 1 Let let VB cord-272759-dqkjofw2 209 2 P(t P(t NNP cord-272759-dqkjofw2 209 3 ) ) -RRB- cord-272759-dqkjofw2 209 4 , , , cord-272759-dqkjofw2 209 5 I -PRON- PRP cord-272759-dqkjofw2 209 6 ( ( -LRB- cord-272759-dqkjofw2 209 7 t t NN cord-272759-dqkjofw2 209 8 ) ) -RRB- cord-272759-dqkjofw2 209 9 and and CC cord-272759-dqkjofw2 209 10 R(t R(t NNP cord-272759-dqkjofw2 209 11 ) ) -RRB- cord-272759-dqkjofw2 209 12 be be VB cord-272759-dqkjofw2 209 13 the the DT cord-272759-dqkjofw2 209 14 number number NN cord-272759-dqkjofw2 209 15 of of IN cord-272759-dqkjofw2 209 16 prone prone JJ cord-272759-dqkjofw2 209 17 , , , cord-272759-dqkjofw2 209 18 infected infected JJ cord-272759-dqkjofw2 209 19 and and CC cord-272759-dqkjofw2 209 20 removed remove VBN cord-272759-dqkjofw2 209 21 individuals individual NNS cord-272759-dqkjofw2 209 22 at at IN cord-272759-dqkjofw2 209 23 time time NN cord-272759-dqkjofw2 209 24 t t NNP cord-272759-dqkjofw2 209 25 ( ( -LRB- cord-272759-dqkjofw2 209 26 in in IN cord-272759-dqkjofw2 209 27 days day NNS cord-272759-dqkjofw2 209 28 ) ) -RRB- cord-272759-dqkjofw2 209 29 . . . cord-272759-dqkjofw2 210 1 The the DT cord-272759-dqkjofw2 210 2 probabilities probability NNS cord-272759-dqkjofw2 210 3 r r NN cord-272759-dqkjofw2 210 4 0 0 CD cord-272759-dqkjofw2 210 5 and and CC cord-272759-dqkjofw2 210 6 r r NN cord-272759-dqkjofw2 210 7 1 1 CD cord-272759-dqkjofw2 210 8 can can MD cord-272759-dqkjofw2 210 9 therefore therefore RB cord-272759-dqkjofw2 210 10 be be VB cord-272759-dqkjofw2 210 11 considered consider VBN cord-272759-dqkjofw2 210 12 as as IN cord-272759-dqkjofw2 210 13 the the DT cord-272759-dqkjofw2 210 14 rates rate NNS cord-272759-dqkjofw2 210 15 at at IN cord-272759-dqkjofw2 210 16 which which WDT cord-272759-dqkjofw2 210 17 prone prone JJ cord-272759-dqkjofw2 210 18 nodes node NNS cord-272759-dqkjofw2 210 19 become become VBP cord-272759-dqkjofw2 210 20 infectious infectious JJ cord-272759-dqkjofw2 210 21 and and CC cord-272759-dqkjofw2 210 22 infectious infectious JJ cord-272759-dqkjofw2 210 23 nodes node NNS cord-272759-dqkjofw2 210 24 become become VBP cord-272759-dqkjofw2 210 25 removed remove VBN cord-272759-dqkjofw2 210 26 ( ( -LRB- cord-272759-dqkjofw2 210 27 respectively respectively RB cord-272759-dqkjofw2 210 28 ) ) -RRB- cord-272759-dqkjofw2 210 29 . . . cord-272759-dqkjofw2 211 1 Similarly similarly RB cord-272759-dqkjofw2 211 2 , , , cord-272759-dqkjofw2 211 3 ( ( -LRB- cord-272759-dqkjofw2 211 4 n n NN cord-272759-dqkjofw2 211 5 1 1 CD cord-272759-dqkjofw2 211 6 p p NN cord-272759-dqkjofw2 211 7 1 1 CD cord-272759-dqkjofw2 211 8 k+µp k+µp CD cord-272759-dqkjofw2 211 9 2 2 CD cord-272759-dqkjofw2 211 10 ) ) -RRB- cord-272759-dqkjofw2 211 11 S(t)I S(t)I NNP cord-272759-dqkjofw2 211 12 ( ( -LRB- cord-272759-dqkjofw2 211 13 t t NN cord-272759-dqkjofw2 211 14 ) ) -RRB- cord-272759-dqkjofw2 211 15 is be VBZ cord-272759-dqkjofw2 211 16 the the DT cord-272759-dqkjofw2 211 17 expected expect VBN cord-272759-dqkjofw2 211 18 number number NN cord-272759-dqkjofw2 211 19 of of IN cord-272759-dqkjofw2 211 20 new new JJ cord-272759-dqkjofw2 211 21 infections infection NNS cord-272759-dqkjofw2 211 22 . . . cord-272759-dqkjofw2 212 1 Suppose suppose VB cord-272759-dqkjofw2 212 2 that that IN cord-272759-dqkjofw2 212 3 S(t S(t NNS cord-272759-dqkjofw2 212 4 ) ) -RRB- cord-272759-dqkjofw2 212 5 R(t R(t . cord-272759-dqkjofw2 212 6 ) ) -RRB- cord-272759-dqkjofw2 213 1 + + CC cord-272759-dqkjofw2 213 2 I -PRON- PRP cord-272759-dqkjofw2 213 3 ( ( -LRB- cord-272759-dqkjofw2 213 4 t t NN cord-272759-dqkjofw2 213 5 ) ) -RRB- cord-272759-dqkjofw2 213 6 + + . cord-272759-dqkjofw2 214 1 clump clump NN cord-272759-dqkjofw2 214 2 will will MD cord-272759-dqkjofw2 214 3 be be VB cord-272759-dqkjofw2 214 4 I -PRON- PRP cord-272759-dqkjofw2 214 5 ( ( -LRB- cord-272759-dqkjofw2 214 6 t t NN cord-272759-dqkjofw2 214 7 ) ) -RRB- cord-272759-dqkjofw2 215 1 π π NNP cord-272759-dqkjofw2 215 2 and and CC cord-272759-dqkjofw2 215 3 the the DT cord-272759-dqkjofw2 215 4 number number NN cord-272759-dqkjofw2 215 5 of of IN cord-272759-dqkjofw2 215 6 susceptible susceptible JJ cord-272759-dqkjofw2 215 7 individuals individual NNS cord-272759-dqkjofw2 215 8 is be VBZ cord-272759-dqkjofw2 216 1 2 2 LS cord-272759-dqkjofw2 216 2 √ √ NNP cord-272759-dqkjofw2 217 1 I -PRON- PRP cord-272759-dqkjofw2 217 2 ( ( -LRB- cord-272759-dqkjofw2 217 3 t)π t)π NNP cord-272759-dqkjofw2 217 4 . . . cord-272759-dqkjofw2 218 1 Now now RB cord-272759-dqkjofw2 218 2 , , , cord-272759-dqkjofw2 218 3 further further RB cord-272759-dqkjofw2 218 4 suppose suppose VB cord-272759-dqkjofw2 218 5 that that IN cord-272759-dqkjofw2 218 6 all all DT cord-272759-dqkjofw2 218 7 nodes node NNS cord-272759-dqkjofw2 218 8 in in IN cord-272759-dqkjofw2 218 9 the the DT cord-272759-dqkjofw2 218 10 clump clump NN cord-272759-dqkjofw2 218 11 are be VBP cord-272759-dqkjofw2 218 12 infectious infectious JJ cord-272759-dqkjofw2 218 13 ( ( -LRB- cord-272759-dqkjofw2 218 14 i.e. i.e. FW cord-272759-dqkjofw2 218 15 r r NN cord-272759-dqkjofw2 218 16 1 1 CD cord-272759-dqkjofw2 218 17 = = SYM cord-272759-dqkjofw2 218 18 0 0 CD cord-272759-dqkjofw2 218 19 ) ) -RRB- cord-272759-dqkjofw2 218 20 , , , cord-272759-dqkjofw2 218 21 then then RB cord-272759-dqkjofw2 218 22 the the DT cord-272759-dqkjofw2 218 23 mean mean JJ cord-272759-dqkjofw2 218 24 number number NN cord-272759-dqkjofw2 218 25 of of IN cord-272759-dqkjofw2 218 26 links link NNS cord-272759-dqkjofw2 218 27 per per IN cord-272759-dqkjofw2 218 28 infected infected JJ cord-272759-dqkjofw2 218 29 individual individual NN cord-272759-dqkjofw2 218 30 is be VBZ cord-272759-dqkjofw2 218 31 2 2 CD cord-272759-dqkjofw2 219 1 π π LS cord-272759-dqkjofw2 220 1 I -PRON- PRP cord-272759-dqkjofw2 220 2 ( ( -LRB- cord-272759-dqkjofw2 220 3 t t NN cord-272759-dqkjofw2 220 4 ) ) -RRB- cord-272759-dqkjofw2 220 5 . . . cord-272759-dqkjofw2 221 1 Even even RB cord-272759-dqkjofw2 221 2 with with IN cord-272759-dqkjofw2 221 3 r r NN cord-272759-dqkjofw2 221 4 1 1 CD cord-272759-dqkjofw2 221 5 > > SYM cord-272759-dqkjofw2 221 6 0 0 CD cord-272759-dqkjofw2 221 7 , , , cord-272759-dqkjofw2 221 8 as as IN cord-272759-dqkjofw2 221 9 the the DT cord-272759-dqkjofw2 221 10 clump clump NN cord-272759-dqkjofw2 221 11 grows grow VBZ cord-272759-dqkjofw2 221 12 , , , cord-272759-dqkjofw2 221 13 there there EX cord-272759-dqkjofw2 221 14 are be VBP cord-272759-dqkjofw2 221 15 , , , cord-272759-dqkjofw2 221 16 on on IN cord-272759-dqkjofw2 221 17 average average JJ cord-272759-dqkjofw2 221 18 , , , cord-272759-dqkjofw2 221 19 fewer few JJR cord-272759-dqkjofw2 221 20 potential potential JJ cord-272759-dqkjofw2 221 21 infection infection NN cord-272759-dqkjofw2 221 22 paths path NNS cord-272759-dqkjofw2 221 23 . . . cord-272759-dqkjofw2 222 1 9 9 CD cord-272759-dqkjofw2 223 1 Moreover moreover RB cord-272759-dqkjofw2 223 2 , , , cord-272759-dqkjofw2 223 3 one one PRP cord-272759-dqkjofw2 223 4 can can MD cord-272759-dqkjofw2 223 5 estimate estimate VB cord-272759-dqkjofw2 223 6 the the DT cord-272759-dqkjofw2 223 7 number number NN cord-272759-dqkjofw2 223 8 of of IN cord-272759-dqkjofw2 223 9 clumps clump NNS cord-272759-dqkjofw2 223 10 K K NNP cord-272759-dqkjofw2 223 11 . . . cord-272759-dqkjofw2 224 1 Observe observe VB cord-272759-dqkjofw2 224 2 that that IN cord-272759-dqkjofw2 224 3 K K NNP cord-272759-dqkjofw2 224 4 ≈ ≈ NNP cord-272759-dqkjofw2 224 5 µp µp VBD cord-272759-dqkjofw2 224 6 2 2 CD cord-272759-dqkjofw2 224 7 n n NN cord-272759-dqkjofw2 224 8 1 1 CD cord-272759-dqkjofw2 224 9 p p NN cord-272759-dqkjofw2 225 1 1 1 LS cord-272759-dqkjofw2 226 1 + + CC cord-272759-dqkjofw2 226 2 µp µp NN cord-272759-dqkjofw2 226 3 2 2 CD cord-272759-dqkjofw2 226 4 × × NN cord-272759-dqkjofw2 226 5 ( ( -LRB- cord-272759-dqkjofw2 226 6 number number NN cord-272759-dqkjofw2 226 7 of of IN cord-272759-dqkjofw2 226 8 infections infection NNS cord-272759-dqkjofw2 226 9 ) ) -RRB- cord-272759-dqkjofw2 226 10 . . . cord-272759-dqkjofw2 227 1 More more RBR cord-272759-dqkjofw2 227 2 precisely precisely RB cord-272759-dqkjofw2 227 3 , , , cord-272759-dqkjofw2 227 4 n n NN cord-272759-dqkjofw2 227 5 1 1 CD cord-272759-dqkjofw2 227 6 p p NN cord-272759-dqkjofw2 227 7 2 2 CD cord-272759-dqkjofw2 228 1 ( ( -LRB- cord-272759-dqkjofw2 228 2 n n NN cord-272759-dqkjofw2 228 3 1 1 CD cord-272759-dqkjofw2 228 4 k k NN cord-272759-dqkjofw2 228 5 2 2 CD cord-272759-dqkjofw2 228 6 p p NN cord-272759-dqkjofw2 228 7 1 1 CD cord-272759-dqkjofw2 228 8 + + CC cord-272759-dqkjofw2 229 1 µp µp NNP cord-272759-dqkjofw2 229 2 2 2 CD cord-272759-dqkjofw2 229 3 ) ) -RRB- cord-272759-dqkjofw2 230 1 + + CC cord-272759-dqkjofw2 230 2 µp µp NN cord-272759-dqkjofw2 230 3 2 2 CD cord-272759-dqkjofw2 230 4 ( ( -LRB- cord-272759-dqkjofw2 230 5 n n NN cord-272759-dqkjofw2 230 6 1 1 CD cord-272759-dqkjofw2 230 7 kp kp NN cord-272759-dqkjofw2 230 8 1 1 CD cord-272759-dqkjofw2 231 1 + + CC cord-272759-dqkjofw2 232 1 µp µp DT cord-272759-dqkjofw2 232 2 2 2 CD cord-272759-dqkjofw2 232 3 ) ) -RRB- cord-272759-dqkjofw2 232 4 × × NN cord-272759-dqkjofw2 233 1 I -PRON- PRP cord-272759-dqkjofw2 233 2 where where WRB cord-272759-dqkjofw2 233 3 I -PRON- PRP cord-272759-dqkjofw2 233 4 is be VBZ cord-272759-dqkjofw2 233 5 the the DT cord-272759-dqkjofw2 233 6 total total JJ cord-272759-dqkjofw2 233 7 number number NN cord-272759-dqkjofw2 233 8 of of IN cord-272759-dqkjofw2 233 9 infections infection NNS cord-272759-dqkjofw2 233 10 . . . cord-272759-dqkjofw2 234 1 where where WRB cord-272759-dqkjofw2 234 2 n n NN cord-272759-dqkjofw2 234 3 k k NNP cord-272759-dqkjofw2 234 4 = = SYM cord-272759-dqkjofw2 234 5 ( ( -LRB- cord-272759-dqkjofw2 234 6 n n NN cord-272759-dqkjofw2 234 7 1 1 CD cord-272759-dqkjofw2 234 8 p p NN cord-272759-dqkjofw2 235 1 1 1 CD cord-272759-dqkjofw2 235 2 k k NN cord-272759-dqkjofw2 235 3 + + CC cord-272759-dqkjofw2 236 1 µp µp NNP cord-272759-dqkjofw2 236 2 2 2 CD cord-272759-dqkjofw2 236 3 ) ) -RRB- cord-272759-dqkjofw2 236 4 is be VBZ cord-272759-dqkjofw2 236 5 the the DT cord-272759-dqkjofw2 236 6 expected expect VBN cord-272759-dqkjofw2 236 7 number number NN cord-272759-dqkjofw2 236 8 of of IN cord-272759-dqkjofw2 236 9 links link NNS cord-272759-dqkjofw2 236 10 for for IN cord-272759-dqkjofw2 236 11 each each DT cord-272759-dqkjofw2 236 12 infectious infectious JJ cord-272759-dqkjofw2 236 13 node node NN cord-272759-dqkjofw2 236 14 . . . cord-272759-dqkjofw2 237 1 We -PRON- PRP cord-272759-dqkjofw2 237 2 are be VBP cord-272759-dqkjofw2 237 3 now now RB cord-272759-dqkjofw2 237 4 modelling model VBG cord-272759-dqkjofw2 237 5 the the DT cord-272759-dqkjofw2 237 6 inter inter JJ cord-272759-dqkjofw2 237 7 - - JJ cord-272759-dqkjofw2 237 8 day day NN cord-272759-dqkjofw2 237 9 process process NN cord-272759-dqkjofw2 237 10 assuming assume VBG cord-272759-dqkjofw2 237 11 discrete discrete JJ cord-272759-dqkjofw2 237 12 day day NN cord-272759-dqkjofw2 237 13 - - HYPH cord-272759-dqkjofw2 237 14 to to IN cord-272759-dqkjofw2 237 15 - - HYPH cord-272759-dqkjofw2 237 16 day day NN cord-272759-dqkjofw2 237 17 dynamics dynamic NNS cord-272759-dqkjofw2 237 18 . . . cord-272759-dqkjofw2 238 1 The the DT cord-272759-dqkjofw2 238 2 reason reason NN cord-272759-dqkjofw2 238 3 for for IN cord-272759-dqkjofw2 238 4 this this DT cord-272759-dqkjofw2 238 5 approximation approximation NN cord-272759-dqkjofw2 238 6 is be VBZ cord-272759-dqkjofw2 238 7 that that IN cord-272759-dqkjofw2 238 8 the the DT cord-272759-dqkjofw2 238 9 available available JJ cord-272759-dqkjofw2 238 10 time time NN cord-272759-dqkjofw2 238 11 series series NNP cord-272759-dqkjofw2 238 12 data data NNP cord-272759-dqkjofw2 238 13 ( ( -LRB- cord-272759-dqkjofw2 238 14 which which WDT cord-272759-dqkjofw2 238 15 will will MD cord-272759-dqkjofw2 238 16 be be VB cord-272759-dqkjofw2 238 17 the the DT cord-272759-dqkjofw2 238 18 basis basis NN cord-272759-dqkjofw2 238 19 of of IN cord-272759-dqkjofw2 238 20 our -PRON- PRP$ cord-272759-dqkjofw2 238 21 comparison comparison NN cord-272759-dqkjofw2 238 22 ) ) -RRB- cord-272759-dqkjofw2 238 23 is be VBZ cord-272759-dqkjofw2 238 24 similarly similarly RB cord-272759-dqkjofw2 238 25 course course NN cord-272759-dqkjofw2 238 26 - - HYPH cord-272759-dqkjofw2 238 27 grained grain VBN cord-272759-dqkjofw2 238 28 . . . cord-272759-dqkjofw2 239 1 Assuming assume VBG cord-272759-dqkjofw2 239 2 that that IN cord-272759-dqkjofw2 239 3 the the DT cord-272759-dqkjofw2 239 4 population population NN cord-272759-dqkjofw2 239 5 is be VBZ cord-272759-dqkjofw2 239 6 seeded seed VBN cord-272759-dqkjofw2 239 7 with with IN cord-272759-dqkjofw2 239 8 a a DT cord-272759-dqkjofw2 239 9 single single JJ cord-272759-dqkjofw2 239 10 infectious infectious JJ cord-272759-dqkjofw2 239 11 individual individual NN cord-272759-dqkjofw2 239 12 , , , cord-272759-dqkjofw2 239 13 the the DT cord-272759-dqkjofw2 239 14 solution solution NN cord-272759-dqkjofw2 239 15 of of IN cord-272759-dqkjofw2 239 16 Eq Eq NNP cord-272759-dqkjofw2 239 17 . . . cord-272759-dqkjofw2 240 1 ( ( -LRB- cord-272759-dqkjofw2 240 2 11 11 CD cord-272759-dqkjofw2 240 3 ) ) -RRB- cord-272759-dqkjofw2 240 4 is be VBZ cord-272759-dqkjofw2 240 5 given give VBN cord-272759-dqkjofw2 240 6 by by IN cord-272759-dqkjofw2 240 7 where where WRB cord-272759-dqkjofw2 240 8 is be VBZ cord-272759-dqkjofw2 240 9 the the DT cord-272759-dqkjofw2 240 10 matrix matrix NN cord-272759-dqkjofw2 240 11 of of IN cord-272759-dqkjofw2 240 12 eigenvectors eigenvector NNS cord-272759-dqkjofw2 240 13 and and CC cord-272759-dqkjofw2 240 14 is be VBZ cord-272759-dqkjofw2 240 15 formed form VBN cord-272759-dqkjofw2 240 16 from from IN cord-272759-dqkjofw2 240 17 the the DT cord-272759-dqkjofw2 240 18 corresponding correspond VBG cord-272759-dqkjofw2 240 19 eigenvalues eigenvalue NNS cord-272759-dqkjofw2 240 20 , , , cord-272759-dqkjofw2 240 21 given give VBN cord-272759-dqkjofw2 240 22 by by IN cord-272759-dqkjofw2 240 23 It -PRON- PRP cord-272759-dqkjofw2 240 24 then then RB cord-272759-dqkjofw2 240 25 follows follow VBZ cord-272759-dqkjofw2 240 26 that that IN cord-272759-dqkjofw2 240 27 the the DT cord-272759-dqkjofw2 240 28 system system NN cord-272759-dqkjofw2 240 29 has have VBZ cord-272759-dqkjofw2 240 30 a a DT cord-272759-dqkjofw2 240 31 marginally marginally RB cord-272759-dqkjofw2 240 32 stable stable JJ cord-272759-dqkjofw2 240 33 focus focus NN cord-272759-dqkjofw2 240 34 ( ( -LRB- cord-272759-dqkjofw2 240 35 i.e. i.e. FW cord-272759-dqkjofw2 240 36 the the DT cord-272759-dqkjofw2 240 37 epidemic epidemic NN cord-272759-dqkjofw2 240 38 will will MD cord-272759-dqkjofw2 240 39 terminate terminate VB cord-272759-dqkjofw2 240 40 ) ) -RRB- cord-272759-dqkjofw2 240 41 if if IN cord-272759-dqkjofw2 240 42 |λ |λ NNP cord-272759-dqkjofw2 240 43 2,3 2,3 CD cord-272759-dqkjofw2 240 44 | | NNS cord-272759-dqkjofw2 241 1 < < NNP cord-272759-dqkjofw2 241 2 1 1 CD cord-272759-dqkjofw2 241 3 , , , cord-272759-dqkjofw2 242 1 i.e. i.e. FW cord-272759-dqkjofw2 242 2 n n CC cord-272759-dqkjofw2 242 3 k k XX cord-272759-dqkjofw2 242 4 < < XX cord-272759-dqkjofw2 242 5 r r NNP cord-272759-dqkjofw2 242 6 1 1 CD cord-272759-dqkjofw2 242 7 ( ( -LRB- cord-272759-dqkjofw2 242 8 13 13 CD cord-272759-dqkjofw2 242 9 ) ) -RRB- cord-272759-dqkjofw2 242 10 n n NN cord-272759-dqkjofw2 243 1 k k NNP cord-272759-dqkjofw2 243 2 r r NNP cord-272759-dqkjofw2 244 1 0 0 NFP cord-272759-dqkjofw2 244 2 < < XX cord-272759-dqkjofw2 244 3 ( ( -LRB- cord-272759-dqkjofw2 244 4 2 2 CD cord-272759-dqkjofw2 244 5 − − NN cord-272759-dqkjofw2 244 6 r r NN cord-272759-dqkjofw2 244 7 0 0 CD cord-272759-dqkjofw2 244 8 ) ) -RRB- cord-272759-dqkjofw2 245 1 ( ( -LRB- cord-272759-dqkjofw2 245 2 2 2 CD cord-272759-dqkjofw2 245 3 − − NN cord-272759-dqkjofw2 245 4 r r NN cord-272759-dqkjofw2 245 5 1 1 CD cord-272759-dqkjofw2 245 6 ) ) -RRB- cord-272759-dqkjofw2 245 7 . . . cord-272759-dqkjofw2 246 1 The the DT cord-272759-dqkjofw2 246 2 second second JJ cord-272759-dqkjofw2 246 3 condition condition NN cord-272759-dqkjofw2 246 4 ( ( -LRB- cord-272759-dqkjofw2 246 5 14 14 CD cord-272759-dqkjofw2 246 6 ) ) -RRB- cord-272759-dqkjofw2 246 7 is be VBZ cord-272759-dqkjofw2 246 8 only only RB cord-272759-dqkjofw2 246 9 violated violate VBN cord-272759-dqkjofw2 246 10 if if IN cord-272759-dqkjofw2 246 11 n n NN cord-272759-dqkjofw2 246 12 k k XX cord-272759-dqkjofw2 247 1 > > XX cord-272759-dqkjofw2 247 2 1 1 CD cord-272759-dqkjofw2 247 3 , , , cord-272759-dqkjofw2 247 4 which which WDT cord-272759-dqkjofw2 247 5 would would MD cord-272759-dqkjofw2 247 6 also also RB cord-272759-dqkjofw2 247 7 violate violate VB cord-272759-dqkjofw2 247 8 condition condition NN cord-272759-dqkjofw2 247 9 ( ( -LRB- cord-272759-dqkjofw2 247 10 13 13 CD cord-272759-dqkjofw2 247 11 ) ) -RRB- cord-272759-dqkjofw2 247 12 . . . cord-272759-dqkjofw2 248 1 Therefore therefore RB cord-272759-dqkjofw2 248 2 , , , cord-272759-dqkjofw2 248 3 the the DT cord-272759-dqkjofw2 248 4 epidemic epidemic NN cord-272759-dqkjofw2 248 5 is be VBZ cord-272759-dqkjofw2 248 6 controllable controllable JJ cord-272759-dqkjofw2 248 7 provided provide VBN cord-272759-dqkjofw2 248 8 that that IN cord-272759-dqkjofw2 248 9 n n NN cord-272759-dqkjofw2 248 10 k k NN cord-272759-dqkjofw2 248 11 = = SYM cord-272759-dqkjofw2 248 12 n n NN cord-272759-dqkjofw2 248 13 1 1 CD cord-272759-dqkjofw2 248 14 p p NN cord-272759-dqkjofw2 249 1 1 1 LS cord-272759-dqkjofw2 250 1 k k NNP cord-272759-dqkjofw2 250 2 + + CC cord-272759-dqkjofw2 250 3 µp µp NNP cord-272759-dqkjofw2 250 4 2 2 CD cord-272759-dqkjofw2 250 5 < < XX cord-272759-dqkjofw2 250 6 r r NN cord-272759-dqkjofw2 250 7 1 1 CD cord-272759-dqkjofw2 250 8 . . . cord-272759-dqkjofw2 251 1 The the DT cord-272759-dqkjofw2 251 2 right right JJ cord-272759-dqkjofw2 251 3 hand hand NN cord-272759-dqkjofw2 251 4 side side NN cord-272759-dqkjofw2 251 5 of of IN cord-272759-dqkjofw2 251 6 this this DT cord-272759-dqkjofw2 251 7 inequality inequality NN cord-272759-dqkjofw2 251 8 is be VBZ cord-272759-dqkjofw2 251 9 the the DT cord-272759-dqkjofw2 251 10 rate rate NN cord-272759-dqkjofw2 251 11 of of IN cord-272759-dqkjofw2 251 12 infection infection NN cord-272759-dqkjofw2 251 13 and and CC cord-272759-dqkjofw2 251 14 the the DT cord-272759-dqkjofw2 251 15 left left JJ cord-272759-dqkjofw2 251 16 hand hand NN cord-272759-dqkjofw2 251 17 side side NN cord-272759-dqkjofw2 251 18 is be VBZ cord-272759-dqkjofw2 251 19 the the DT cord-272759-dqkjofw2 251 20 rate rate NN cord-272759-dqkjofw2 251 21 of of IN cord-272759-dqkjofw2 251 22 removal removal NN cord-272759-dqkjofw2 251 23 , , , cord-272759-dqkjofw2 251 24 as as IN cord-272759-dqkjofw2 251 25 expected expect VBN cord-272759-dqkjofw2 251 26 . . . cord-272759-dqkjofw2 252 1 In in IN cord-272759-dqkjofw2 252 2 fact fact NN cord-272759-dqkjofw2 252 3 , , , cord-272759-dqkjofw2 252 4 this this DT cord-272759-dqkjofw2 252 5 result result NN cord-272759-dqkjofw2 252 6 is be VBZ cord-272759-dqkjofw2 252 7 exactly exactly RB cord-272759-dqkjofw2 252 8 analogous analogous JJ cord-272759-dqkjofw2 252 9 to to IN cord-272759-dqkjofw2 252 10 the the DT cord-272759-dqkjofw2 252 11 equivalent equivalent JJ cord-272759-dqkjofw2 252 12 result result NN cord-272759-dqkjofw2 252 13 for for IN cord-272759-dqkjofw2 252 14 the the DT cord-272759-dqkjofw2 252 15 continuous continuous JJ cord-272759-dqkjofw2 252 16 SIR SIR NNP cord-272759-dqkjofw2 252 17 model model NN cord-272759-dqkjofw2 252 18 [ [ -LRB- cord-272759-dqkjofw2 252 19 7 7 CD cord-272759-dqkjofw2 252 20 ] ] -RRB- cord-272759-dqkjofw2 252 21 . . . cord-272759-dqkjofw2 253 1 Moreover moreover RB cord-272759-dqkjofw2 253 2 , , , cord-272759-dqkjofw2 253 3 Computationally computationally RB cord-272759-dqkjofw2 253 4 , , , cord-272759-dqkjofw2 253 5 we -PRON- PRP cord-272759-dqkjofw2 253 6 can can MD cord-272759-dqkjofw2 253 7 see see VB cord-272759-dqkjofw2 253 8 that that DT cord-272759-dqkjofw2 253 9 , , , cord-272759-dqkjofw2 253 10 as as IN cord-272759-dqkjofw2 253 11 r r NN cord-272759-dqkjofw2 253 12 0 0 CD cord-272759-dqkjofw2 253 13 or or CC cord-272759-dqkjofw2 253 14 n n NN cord-272759-dqkjofw2 253 15 k k NN cord-272759-dqkjofw2 253 16 increases increase NNS cord-272759-dqkjofw2 253 17 , , , cord-272759-dqkjofw2 253 18 then then RB cord-272759-dqkjofw2 253 19 the the DT cord-272759-dqkjofw2 253 20 rate rate NN cord-272759-dqkjofw2 253 21 of of IN cord-272759-dqkjofw2 253 22 growth growth NN cord-272759-dqkjofw2 253 23 of of IN cord-272759-dqkjofw2 253 24 the the DT cord-272759-dqkjofw2 253 25 epidemic epidemic NN cord-272759-dqkjofw2 253 26 also also RB cord-272759-dqkjofw2 253 27 increases increase VBZ cord-272759-dqkjofw2 253 28 . . . cord-272759-dqkjofw2 254 1 Conversely conversely RB cord-272759-dqkjofw2 254 2 , , , cord-272759-dqkjofw2 254 3 as as IN cord-272759-dqkjofw2 254 4 r r NN cord-272759-dqkjofw2 254 5 1 1 CD cord-272759-dqkjofw2 254 6 increases increase NNS cord-272759-dqkjofw2 254 7 , , , cord-272759-dqkjofw2 254 8 the the DT cord-272759-dqkjofw2 254 9 rate rate NN cord-272759-dqkjofw2 254 10 of of IN cord-272759-dqkjofw2 254 11 growth growth NN cord-272759-dqkjofw2 254 12 decreases decrease NNS cord-272759-dqkjofw2 254 13 . . . cord-272759-dqkjofw2 255 1 This this DT cord-272759-dqkjofw2 255 2 is be VBZ cord-272759-dqkjofw2 255 3 as as IN cord-272759-dqkjofw2 255 4 one one PRP cord-272759-dqkjofw2 255 5 would would MD cord-272759-dqkjofw2 255 6 expect expect VB cord-272759-dqkjofw2 255 7 , , , cord-272759-dqkjofw2 255 8 as as IN cord-272759-dqkjofw2 255 9 increasing increase VBG cord-272759-dqkjofw2 255 10 r r NN cord-272759-dqkjofw2 255 11 1 1 CD cord-272759-dqkjofw2 255 12 will will MD cord-272759-dqkjofw2 255 13 decrease decrease VB cord-272759-dqkjofw2 255 14 the the DT cord-272759-dqkjofw2 255 15 number number NN cord-272759-dqkjofw2 255 16 of of IN cord-272759-dqkjofw2 255 17 infectious infectious JJ cord-272759-dqkjofw2 255 18 individuals individual NNS cord-272759-dqkjofw2 255 19 while while IN cord-272759-dqkjofw2 255 20 increasing increase VBG cord-272759-dqkjofw2 255 21 either either CC cord-272759-dqkjofw2 255 22 r r NN cord-272759-dqkjofw2 255 23 0 0 CD cord-272759-dqkjofw2 255 24 or or CC cord-272759-dqkjofw2 255 25 n n NN cord-272759-dqkjofw2 255 26 k k NN cord-272759-dqkjofw2 255 27 increases increase VBZ cord-272759-dqkjofw2 255 28 this this DT cord-272759-dqkjofw2 255 29 quantity quantity NN cord-272759-dqkjofw2 255 30 . . . cord-272759-dqkjofw2 256 1 In in IN cord-272759-dqkjofw2 256 2 the the DT cord-272759-dqkjofw2 256 3 following follow VBG cord-272759-dqkjofw2 256 4 subsections subsection NNS cord-272759-dqkjofw2 256 5 , , , cord-272759-dqkjofw2 256 6 we -PRON- PRP cord-272759-dqkjofw2 256 7 confirm confirm VBP cord-272759-dqkjofw2 256 8 the the DT cord-272759-dqkjofw2 256 9 preceding precede VBG cord-272759-dqkjofw2 256 10 relationships relationship NNS cord-272759-dqkjofw2 256 11 and and CC cord-272759-dqkjofw2 256 12 numerically numerically RB cord-272759-dqkjofw2 256 13 explore explore VB cord-272759-dqkjofw2 256 14 the the DT cord-272759-dqkjofw2 256 15 behaviour behaviour NN cord-272759-dqkjofw2 256 16 of of IN cord-272759-dqkjofw2 256 17 our -PRON- PRP$ cord-272759-dqkjofw2 256 18 models model NNS cord-272759-dqkjofw2 256 19 under under IN cord-272759-dqkjofw2 256 20 a a DT cord-272759-dqkjofw2 256 21 variety variety NN cord-272759-dqkjofw2 256 22 of of IN cord-272759-dqkjofw2 256 23 conditions condition NNS cord-272759-dqkjofw2 256 24 . . . cord-272759-dqkjofw2 257 1 As as IN cord-272759-dqkjofw2 257 2 stated state VBN cord-272759-dqkjofw2 257 3 , , , cord-272759-dqkjofw2 257 4 our -PRON- PRP$ cord-272759-dqkjofw2 257 5 model model NN cord-272759-dqkjofw2 257 6 has have VBZ cord-272759-dqkjofw2 257 7 seven seven CD cord-272759-dqkjofw2 257 8 explicit explicit JJ cord-272759-dqkjofw2 257 9 parameters parameter NNS cord-272759-dqkjofw2 257 10 : : : cord-272759-dqkjofw2 257 11 L l NN cord-272759-dqkjofw2 257 12 , , , cord-272759-dqkjofw2 257 13 n n NN cord-272759-dqkjofw2 257 14 1 1 CD cord-272759-dqkjofw2 257 15 , , , cord-272759-dqkjofw2 257 16 µ µ NN cord-272759-dqkjofw2 257 17 , , , cord-272759-dqkjofw2 257 18 p p NN cord-272759-dqkjofw2 257 19 1 1 CD cord-272759-dqkjofw2 257 20 , , , cord-272759-dqkjofw2 257 21 p p NN cord-272759-dqkjofw2 257 22 2 2 CD cord-272759-dqkjofw2 257 23 , , , cord-272759-dqkjofw2 257 24 r r NNP cord-272759-dqkjofw2 257 25 1 1 CD cord-272759-dqkjofw2 257 26 , , , cord-272759-dqkjofw2 257 27 and and CC cord-272759-dqkjofw2 257 28 r r NN cord-272759-dqkjofw2 257 29 2 2 CD cord-272759-dqkjofw2 257 30 . . . cord-272759-dqkjofw2 258 1 For for IN cord-272759-dqkjofw2 258 2 the the DT cord-272759-dqkjofw2 258 3 population population NN cord-272759-dqkjofw2 258 4 of of IN cord-272759-dqkjofw2 258 5 Hong Hong NNP cord-272759-dqkjofw2 258 6 Kong Kong NNP cord-272759-dqkjofw2 258 7 , , , cord-272759-dqkjofw2 258 8 we -PRON- PRP cord-272759-dqkjofw2 258 9 set set VBD cord-272759-dqkjofw2 258 10 L l NN cord-272759-dqkjofw2 258 11 = = SYM cord-272759-dqkjofw2 258 12 2700 2700 CD cord-272759-dqkjofw2 259 1 ( ( -LRB- cord-272759-dqkjofw2 259 2 N n NN cord-272759-dqkjofw2 259 3 = = SYM cord-272759-dqkjofw2 259 4 L l NN cord-272759-dqkjofw2 259 5 2 2 CD cord-272759-dqkjofw2 259 6 = = SYM cord-272759-dqkjofw2 259 7 7,290,000 7,290,000 CD cord-272759-dqkjofw2 259 8 ) ) -RRB- cord-272759-dqkjofw2 259 9 . . . cord-272759-dqkjofw2 260 1 We -PRON- PRP cord-272759-dqkjofw2 260 2 arbitrarily arbitrarily RB cord-272759-dqkjofw2 260 3 choose choose VBP cord-272759-dqkjofw2 260 4 n n NN cord-272759-dqkjofw2 260 5 1 1 CD cord-272759-dqkjofw2 260 6 = = SYM cord-272759-dqkjofw2 260 7 4 4 CD cord-272759-dqkjofw2 260 8 and and CC cord-272759-dqkjofw2 260 9 set set VBN cord-272759-dqkjofw2 260 10 E(n E(n NNP cord-272759-dqkjofw2 260 11 2 2 CD cord-272759-dqkjofw2 260 12 ) ) -RRB- cord-272759-dqkjofw2 260 13 = = NFP cord-272759-dqkjofw2 261 1 µ µ NN cord-272759-dqkjofw2 261 2 = = SYM cord-272759-dqkjofw2 261 3 7 7 CD cord-272759-dqkjofw2 261 4 [ [ -LRB- cord-272759-dqkjofw2 261 5 16 16 CD cord-272759-dqkjofw2 261 6 ] ] -RRB- cord-272759-dqkjofw2 261 7 . . . cord-272759-dqkjofw2 262 1 One one CD cord-272759-dqkjofw2 262 2 further further JJ cord-272759-dqkjofw2 262 3 parameter parameter NN cord-272759-dqkjofw2 262 4 is be VBZ cord-272759-dqkjofw2 262 5 the the DT cord-272759-dqkjofw2 262 6 time time NN cord-272759-dqkjofw2 262 7 interval interval NN cord-272759-dqkjofw2 262 8 between between IN cord-272759-dqkjofw2 262 9 successive successive JJ cord-272759-dqkjofw2 262 10 steps step NNS cord-272759-dqkjofw2 262 11 in in IN cord-272759-dqkjofw2 262 12 the the DT cord-272759-dqkjofw2 262 13 discrete discrete JJ cord-272759-dqkjofw2 262 14 time time NN cord-272759-dqkjofw2 262 15 simulations simulation NNS cord-272759-dqkjofw2 262 16 from from IN cord-272759-dqkjofw2 262 17 our -PRON- PRP$ cord-272759-dqkjofw2 262 18 model model NN cord-272759-dqkjofw2 262 19 . . . cord-272759-dqkjofw2 263 1 We -PRON- PRP cord-272759-dqkjofw2 263 2 choose choose VBP cord-272759-dqkjofw2 263 3 the the DT cord-272759-dqkjofw2 263 4 natural natural JJ cord-272759-dqkjofw2 263 5 scale scale NN cord-272759-dqkjofw2 263 6 of of IN cord-272759-dqkjofw2 263 7 one one CD cord-272759-dqkjofw2 263 8 day day NN cord-272759-dqkjofw2 263 9 . . . cord-272759-dqkjofw2 264 1 However however RB cord-272759-dqkjofw2 264 2 , , , cord-272759-dqkjofw2 264 3 it -PRON- PRP cord-272759-dqkjofw2 264 4 is be VBZ cord-272759-dqkjofw2 264 5 not not RB cord-272759-dqkjofw2 264 6 obvious obvious JJ cord-272759-dqkjofw2 264 7 that that IN cord-272759-dqkjofw2 264 8 this this DT cord-272759-dqkjofw2 264 9 is be VBZ cord-272759-dqkjofw2 264 10 the the DT cord-272759-dqkjofw2 264 11 best good JJS cord-272759-dqkjofw2 264 12 choice choice NN cord-272759-dqkjofw2 264 13 . . . cord-272759-dqkjofw2 265 1 Given give VBN cord-272759-dqkjofw2 265 2 that that IN cord-272759-dqkjofw2 265 3 the the DT cord-272759-dqkjofw2 265 4 data data NN cord-272759-dqkjofw2 265 5 is be VBZ cord-272759-dqkjofw2 265 6 discretised discretise VBN cord-272759-dqkjofw2 265 7 to to IN cord-272759-dqkjofw2 265 8 this this DT cord-272759-dqkjofw2 265 9 interval interval NN cord-272759-dqkjofw2 265 10 , , , cord-272759-dqkjofw2 265 11 it -PRON- PRP cord-272759-dqkjofw2 265 12 is be VBZ cord-272759-dqkjofw2 265 13 perhaps perhaps RB cord-272759-dqkjofw2 265 14 the the DT cord-272759-dqkjofw2 265 15 best good JJS cord-272759-dqkjofw2 265 16 choice choice NN cord-272759-dqkjofw2 265 17 in in IN cord-272759-dqkjofw2 265 18 this this DT cord-272759-dqkjofw2 265 19 situation situation NN cord-272759-dqkjofw2 265 20 . . . cord-272759-dqkjofw2 266 1 Nonetheless nonetheless RB cord-272759-dqkjofw2 266 2 , , , cord-272759-dqkjofw2 266 3 to to TO cord-272759-dqkjofw2 266 4 confirm confirm VB cord-272759-dqkjofw2 266 5 that that IN cord-272759-dqkjofw2 266 6 this this DT cord-272759-dqkjofw2 266 7 choice choice NN cord-272759-dqkjofw2 266 8 is be VBZ cord-272759-dqkjofw2 266 9 appropriate appropriate JJ cord-272759-dqkjofw2 266 10 , , , cord-272759-dqkjofw2 266 11 we -PRON- PRP cord-272759-dqkjofw2 266 12 have have VBP cord-272759-dqkjofw2 266 13 repeated repeat VBN cord-272759-dqkjofw2 266 14 our -PRON- PRP$ cord-272759-dqkjofw2 266 15 analysis analysis NN cord-272759-dqkjofw2 266 16 with with IN cord-272759-dqkjofw2 266 17 both both CC cord-272759-dqkjofw2 266 18 longer long JJR cord-272759-dqkjofw2 266 19 and and CC cord-272759-dqkjofw2 266 20 shorter short JJR cord-272759-dqkjofw2 266 21 time time NN cord-272759-dqkjofw2 266 22 steps step NNS cord-272759-dqkjofw2 266 23 . . . cord-272759-dqkjofw2 267 1 The the DT cord-272759-dqkjofw2 267 2 results result NNS cord-272759-dqkjofw2 267 3 are be VBP cord-272759-dqkjofw2 267 4 equivalent equivalent JJ cord-272759-dqkjofw2 267 5 . . . cord-272759-dqkjofw2 268 1 The the DT cord-272759-dqkjofw2 268 2 average average JJ cord-272759-dqkjofw2 268 3 incubation incubation NN cord-272759-dqkjofw2 268 4 period period NN cord-272759-dqkjofw2 268 5 between between IN cord-272759-dqkjofw2 268 6 infection infection NN cord-272759-dqkjofw2 268 7 and and CC cord-272759-dqkjofw2 268 8 an an DT cord-272759-dqkjofw2 268 9 individual individual JJ cord-272759-dqkjofw2 268 10 becoming become VBG cord-272759-dqkjofw2 268 11 symptomatic symptomatic JJ cord-272759-dqkjofw2 268 12 is be VBZ cord-272759-dqkjofw2 268 13 6.4 6.4 CD cord-272759-dqkjofw2 268 14 days day NNS cord-272759-dqkjofw2 268 15 [ [ -LRB- cord-272759-dqkjofw2 268 16 6 6 CD cord-272759-dqkjofw2 268 17 ] ] -RRB- cord-272759-dqkjofw2 268 18 . . . cord-272759-dqkjofw2 269 1 The the DT cord-272759-dqkjofw2 269 2 number number NN cord-272759-dqkjofw2 269 3 of of IN cord-272759-dqkjofw2 269 4 days day NNS cord-272759-dqkjofw2 269 5 in in IN cord-272759-dqkjofw2 269 6 the the DT cord-272759-dqkjofw2 269 7 prone prone JJ cord-272759-dqkjofw2 269 8 state state NN cord-272759-dqkjofw2 269 9 can can MD cord-272759-dqkjofw2 269 10 therefore therefore RB cord-272759-dqkjofw2 269 11 be be VB cord-272759-dqkjofw2 269 12 modelled model VBN cord-272759-dqkjofw2 269 13 as as IN cord-272759-dqkjofw2 269 14 the the DT cord-272759-dqkjofw2 269 15 result result NN cord-272759-dqkjofw2 269 16 of of IN cord-272759-dqkjofw2 269 17 a a DT cord-272759-dqkjofw2 269 18 series series NN cord-272759-dqkjofw2 269 19 of of IN cord-272759-dqkjofw2 269 20 independent independent JJ cord-272759-dqkjofw2 269 21 Bernoulli Bernoulli NNP cord-272759-dqkjofw2 269 22 trials trial NNS cord-272759-dqkjofw2 269 23 with with IN cord-272759-dqkjofw2 269 24 a a DT cord-272759-dqkjofw2 269 25 mean mean JJ cord-272759-dqkjofw2 269 26 1 1 CD cord-272759-dqkjofw2 269 27 r r NN cord-272759-dqkjofw2 269 28 0 0 CD cord-272759-dqkjofw2 270 1 and and CC cord-272759-dqkjofw2 270 2 so so RB cord-272759-dqkjofw2 270 3 it -PRON- PRP cord-272759-dqkjofw2 270 4 follows follow VBZ cord-272759-dqkjofw2 270 5 a a DT cord-272759-dqkjofw2 270 6 geometric geometric JJ cord-272759-dqkjofw2 270 7 distribution distribution NN cord-272759-dqkjofw2 270 8 f f NN cord-272759-dqkjofw2 270 9 X x NN cord-272759-dqkjofw2 270 10 ( ( -LRB- cord-272759-dqkjofw2 270 11 x x NN cord-272759-dqkjofw2 270 12 ) ) -RRB- cord-272759-dqkjofw2 270 13 = = NFP cord-272759-dqkjofw2 270 14 ( ( -LRB- cord-272759-dqkjofw2 270 15 1 1 CD cord-272759-dqkjofw2 270 16 − − NN cord-272759-dqkjofw2 270 17 p p NN cord-272759-dqkjofw2 270 18 ) ) -RRB- cord-272759-dqkjofw2 271 1 x−1 x−1 XX cord-272759-dqkjofw2 272 1 p. p. NN cord-272759-dqkjofw2 272 2 10 10 CD cord-272759-dqkjofw2 273 1 For for IN cord-272759-dqkjofw2 273 2 a a DT cord-272759-dqkjofw2 273 3 general general JJ cord-272759-dqkjofw2 273 4 disease disease NN cord-272759-dqkjofw2 273 5 model model NN cord-272759-dqkjofw2 273 6 , , , cord-272759-dqkjofw2 273 7 it -PRON- PRP cord-272759-dqkjofw2 273 8 would would MD cord-272759-dqkjofw2 273 9 possibly possibly RB cord-272759-dqkjofw2 273 10 be be VB cord-272759-dqkjofw2 273 11 more more RBR cord-272759-dqkjofw2 273 12 appropriate appropriate JJ cord-272759-dqkjofw2 273 13 to to TO cord-272759-dqkjofw2 273 14 have have VB cord-272759-dqkjofw2 273 15 a a DT cord-272759-dqkjofw2 273 16 separate separate JJ cord-272759-dqkjofw2 273 17 state state NN cord-272759-dqkjofw2 273 18 for for IN cord-272759-dqkjofw2 273 19 the the DT cord-272759-dqkjofw2 273 20 pre pre JJ cord-272759-dqkjofw2 273 21 - - JJ cord-272759-dqkjofw2 273 22 symptomatic symptomatic JJ cord-272759-dqkjofw2 273 23 but but CC cord-272759-dqkjofw2 273 24 infectious infectious JJ cord-272759-dqkjofw2 273 25 period period NN cord-272759-dqkjofw2 273 26 . . . cord-272759-dqkjofw2 274 1 Although although IN cord-272759-dqkjofw2 274 2 contact contact NN cord-272759-dqkjofw2 274 3 tracing tracing NN cord-272759-dqkjofw2 274 4 of of IN cord-272759-dqkjofw2 274 5 all all DT cord-272759-dqkjofw2 274 6 SARS SARS NNP cord-272759-dqkjofw2 274 7 patients patient NNS cord-272759-dqkjofw2 274 8 in in IN cord-272759-dqkjofw2 274 9 Hong Hong NNP cord-272759-dqkjofw2 274 10 Kong Kong NNP cord-272759-dqkjofw2 274 11 has have VBZ cord-272759-dqkjofw2 274 12 demonstrated demonstrate VBN cord-272759-dqkjofw2 274 13 that that IN cord-272759-dqkjofw2 274 14 this this DT cord-272759-dqkjofw2 274 15 is be VBZ cord-272759-dqkjofw2 274 16 not not RB cord-272759-dqkjofw2 274 17 a a DT cord-272759-dqkjofw2 274 18 significant significant JJ cord-272759-dqkjofw2 274 19 period period NN cord-272759-dqkjofw2 274 20 for for IN cord-272759-dqkjofw2 274 21 SARS SARS NNP cord-272759-dqkjofw2 274 22 , , , cord-272759-dqkjofw2 274 23 we -PRON- PRP cord-272759-dqkjofw2 274 24 have have VBP cord-272759-dqkjofw2 274 25 repeated repeat VBN cord-272759-dqkjofw2 274 26 the the DT cord-272759-dqkjofw2 274 27 simulations simulation NNS cord-272759-dqkjofw2 274 28 with with IN cord-272759-dqkjofw2 274 29 this this DT cord-272759-dqkjofw2 274 30 state state NN cord-272759-dqkjofw2 274 31 . . . cord-272759-dqkjofw2 275 1 If if IN cord-272759-dqkjofw2 275 2 the the DT cord-272759-dqkjofw2 275 3 hiatus hiatus NN cord-272759-dqkjofw2 275 4 in in IN cord-272759-dqkjofw2 275 5 this this DT cord-272759-dqkjofw2 275 6 state state NN cord-272759-dqkjofw2 275 7 is be VBZ cord-272759-dqkjofw2 275 8 relatively relatively RB cord-272759-dqkjofw2 275 9 short short JJ cord-272759-dqkjofw2 275 10 , , , cord-272759-dqkjofw2 275 11 the the DT cord-272759-dqkjofw2 275 12 results result NNS cord-272759-dqkjofw2 275 13 are be VBP cord-272759-dqkjofw2 275 14 not not RB cord-272759-dqkjofw2 275 15 altered alter VBN cord-272759-dqkjofw2 275 16 significantly significantly RB cord-272759-dqkjofw2 275 17 . . . cord-272759-dqkjofw2 276 1 In in IN cord-272759-dqkjofw2 276 2 a a DT cord-272759-dqkjofw2 276 3 similar similar JJ cord-272759-dqkjofw2 276 4 spirit spirit NN cord-272759-dqkjofw2 276 5 , , , cord-272759-dqkjofw2 276 6 the the DT cord-272759-dqkjofw2 276 7 time time NN cord-272759-dqkjofw2 276 8 before before IN cord-272759-dqkjofw2 276 9 hospitalisation hospitalisation NN cord-272759-dqkjofw2 276 10 is be VBZ cord-272759-dqkjofw2 276 11 3 3 CD cord-272759-dqkjofw2 276 12 - - SYM cord-272759-dqkjofw2 276 13 5 5 CD cord-272759-dqkjofw2 276 14 days day NNS cord-272759-dqkjofw2 276 15 , , , cord-272759-dqkjofw2 276 16 and and CC cord-272759-dqkjofw2 276 17 we -PRON- PRP cord-272759-dqkjofw2 276 18 model model VBP cord-272759-dqkjofw2 276 19 this this DT cord-272759-dqkjofw2 276 20 as as IN cord-272759-dqkjofw2 276 21 a a DT cord-272759-dqkjofw2 276 22 series series NN cord-272759-dqkjofw2 276 23 of of IN cord-272759-dqkjofw2 276 24 independent independent JJ cord-272759-dqkjofw2 276 25 Bernoulli Bernoulli NNP cord-272759-dqkjofw2 276 26 trials trial NNS cord-272759-dqkjofw2 276 27 . . . cord-272759-dqkjofw2 277 1 In in IN cord-272759-dqkjofw2 277 2 an an DT cord-272759-dqkjofw2 277 3 effort effort NN cord-272759-dqkjofw2 277 4 to to TO cord-272759-dqkjofw2 277 5 establish establish VB cord-272759-dqkjofw2 277 6 the the DT cord-272759-dqkjofw2 277 7 degree degree NN cord-272759-dqkjofw2 277 8 to to TO cord-272759-dqkjofw2 277 9 which which WDT cord-272759-dqkjofw2 277 10 hospital hospital NN cord-272759-dqkjofw2 277 11 transmission transmission NN cord-272759-dqkjofw2 277 12 in in IN cord-272759-dqkjofw2 277 13 our -PRON- PRP$ cord-272759-dqkjofw2 277 14 model model NN cord-272759-dqkjofw2 277 15 matches match NNS cord-272759-dqkjofw2 277 16 what what WP cord-272759-dqkjofw2 277 17 was be VBD cord-272759-dqkjofw2 277 18 observed observe VBN cord-272759-dqkjofw2 277 19 , , , cord-272759-dqkjofw2 277 20 we -PRON- PRP cord-272759-dqkjofw2 277 21 first first RB cord-272759-dqkjofw2 277 22 assume assume VBP cord-272759-dqkjofw2 277 23 that that IN cord-272759-dqkjofw2 277 24 hospitalisation hospitalisation NN cord-272759-dqkjofw2 277 25 is be VBZ cord-272759-dqkjofw2 277 26 equivalent equivalent JJ cord-272759-dqkjofw2 277 27 to to IN cord-272759-dqkjofw2 277 28 isolation isolation NN cord-272759-dqkjofw2 277 29 of of IN cord-272759-dqkjofw2 277 30 infectious infectious JJ cord-272759-dqkjofw2 277 31 individuals individual NNS cord-272759-dqkjofw2 277 32 . . . cord-272759-dqkjofw2 278 1 That that RB cord-272759-dqkjofw2 278 2 is is RB cord-272759-dqkjofw2 278 3 , , , cord-272759-dqkjofw2 278 4 we -PRON- PRP cord-272759-dqkjofw2 278 5 suppose suppose VBP cord-272759-dqkjofw2 278 6 that that IN cord-272759-dqkjofw2 278 7 infectious infectious JJ cord-272759-dqkjofw2 278 8 individuals individual NNS cord-272759-dqkjofw2 278 9 are be VBP cord-272759-dqkjofw2 278 10 only only RB cord-272759-dqkjofw2 278 11 infectious infectious JJ cord-272759-dqkjofw2 278 12 for for IN cord-272759-dqkjofw2 278 13 3 3 CD cord-272759-dqkjofw2 278 14 - - SYM cord-272759-dqkjofw2 278 15 5 5 CD cord-272759-dqkjofw2 278 16 days day NNS cord-272759-dqkjofw2 278 17 . . . cord-272759-dqkjofw2 279 1 The the DT cord-272759-dqkjofw2 279 2 current current JJ cord-272759-dqkjofw2 279 3 weight weight NN cord-272759-dqkjofw2 279 4 of of IN cord-272759-dqkjofw2 279 5 evidence evidence NN cord-272759-dqkjofw2 279 6 suggests suggest VBZ cord-272759-dqkjofw2 279 7 that that IN cord-272759-dqkjofw2 279 8 hospital hospital NN cord-272759-dqkjofw2 279 9 transmission transmission NN cord-272759-dqkjofw2 279 10 was be VBD cord-272759-dqkjofw2 279 11 a a DT cord-272759-dqkjofw2 279 12 crucial crucial JJ cord-272759-dqkjofw2 279 13 factor factor NN cord-272759-dqkjofw2 279 14 for for IN cord-272759-dqkjofw2 279 15 the the DT cord-272759-dqkjofw2 279 16 SARS SARS NNP cord-272759-dqkjofw2 279 17 outbreak outbreak NN cord-272759-dqkjofw2 279 18 in in IN cord-272759-dqkjofw2 279 19 Hong Hong NNP cord-272759-dqkjofw2 279 20 Kong Kong NNP cord-272759-dqkjofw2 279 21 during during IN cord-272759-dqkjofw2 279 22 2003 2003 CD cord-272759-dqkjofw2 279 23 . . . cord-272759-dqkjofw2 280 1 We -PRON- PRP cord-272759-dqkjofw2 280 2 will will MD cord-272759-dqkjofw2 280 3 show show VB cord-272759-dqkjofw2 280 4 that that IN cord-272759-dqkjofw2 280 5 this this DT cord-272759-dqkjofw2 280 6 is be VBZ cord-272759-dqkjofw2 280 7 also also RB cord-272759-dqkjofw2 280 8 the the DT cord-272759-dqkjofw2 280 9 case case NN cord-272759-dqkjofw2 280 10 for for IN cord-272759-dqkjofw2 280 11 our -PRON- PRP$ cord-272759-dqkjofw2 280 12 model model NN cord-272759-dqkjofw2 280 13 . . . cord-272759-dqkjofw2 281 1 Hence hence RB cord-272759-dqkjofw2 281 2 , , , cord-272759-dqkjofw2 281 3 we -PRON- PRP cord-272759-dqkjofw2 281 4 suppose suppose VBP cord-272759-dqkjofw2 281 5 for for IN cord-272759-dqkjofw2 281 6 now now RB cord-272759-dqkjofw2 281 7 that that IN cord-272759-dqkjofw2 281 8 the the DT cord-272759-dqkjofw2 281 9 average average JJ cord-272759-dqkjofw2 281 10 amount amount NN cord-272759-dqkjofw2 281 11 of of IN cord-272759-dqkjofw2 281 12 time time NN cord-272759-dqkjofw2 281 13 prior prior RB cord-272759-dqkjofw2 281 14 to to IN cord-272759-dqkjofw2 281 15 isolation isolation NN cord-272759-dqkjofw2 281 16 is be VBZ cord-272759-dqkjofw2 281 17 4 4 CD cord-272759-dqkjofw2 281 18 days day NNS cord-272759-dqkjofw2 281 19 ( ( -LRB- cord-272759-dqkjofw2 281 20 we -PRON- PRP cord-272759-dqkjofw2 281 21 will will MD cord-272759-dqkjofw2 281 22 consider consider VB cord-272759-dqkjofw2 281 23 larger large JJR cord-272759-dqkjofw2 281 24 values value NNS cord-272759-dqkjofw2 281 25 later later RB cord-272759-dqkjofw2 281 26 ) ) -RRB- cord-272759-dqkjofw2 281 27 . . . cord-272759-dqkjofw2 282 1 In in IN cord-272759-dqkjofw2 282 2 our -PRON- PRP$ cord-272759-dqkjofw2 282 3 model model NN cord-272759-dqkjofw2 282 4 , , , cord-272759-dqkjofw2 282 5 the the DT cord-272759-dqkjofw2 282 6 number number NN cord-272759-dqkjofw2 282 7 of of IN cord-272759-dqkjofw2 282 8 days day NNS cord-272759-dqkjofw2 282 9 prior prior RB cord-272759-dqkjofw2 282 10 to to IN cord-272759-dqkjofw2 282 11 hospitalisation hospitalisation NN cord-272759-dqkjofw2 282 12 is be VBZ cord-272759-dqkjofw2 282 13 also also RB cord-272759-dqkjofw2 282 14 made make VBN cord-272759-dqkjofw2 282 15 to to TO cord-272759-dqkjofw2 282 16 follow follow VB cord-272759-dqkjofw2 282 17 a a DT cord-272759-dqkjofw2 282 18 geometric geometric JJ cord-272759-dqkjofw2 282 19 distribution distribution NN cord-272759-dqkjofw2 282 20 with with IN cord-272759-dqkjofw2 282 21 mean mean JJ cord-272759-dqkjofw2 282 22 1 1 CD cord-272759-dqkjofw2 282 23 r r NN cord-272759-dqkjofw2 282 24 1 1 CD cord-272759-dqkjofw2 282 25 . . . cord-272759-dqkjofw2 283 1 Hence hence RB cord-272759-dqkjofw2 283 2 , , , cord-272759-dqkjofw2 283 3 the the DT cord-272759-dqkjofw2 283 4 only only JJ cord-272759-dqkjofw2 283 5 free free JJ cord-272759-dqkjofw2 283 6 parameters parameter NNS cord-272759-dqkjofw2 283 7 are be VBP cord-272759-dqkjofw2 283 8 µ µ NN cord-272759-dqkjofw2 283 9 , , , cord-272759-dqkjofw2 283 10 p p NN cord-272759-dqkjofw2 283 11 1 1 CD cord-272759-dqkjofw2 283 12 and and CC cord-272759-dqkjofw2 283 13 p p CD cord-272759-dqkjofw2 283 14 2 2 CD cord-272759-dqkjofw2 283 15 . . . cord-272759-dqkjofw2 284 1 Without without IN cord-272759-dqkjofw2 284 2 active active JJ cord-272759-dqkjofw2 284 3 control control NN cord-272759-dqkjofw2 284 4 , , , cord-272759-dqkjofw2 284 5 we -PRON- PRP cord-272759-dqkjofw2 284 6 also also RB cord-272759-dqkjofw2 284 7 know know VBP cord-272759-dqkjofw2 284 8 that that IN cord-272759-dqkjofw2 284 9 the the DT cord-272759-dqkjofw2 284 10 average average JJ cord-272759-dqkjofw2 284 11 number number NN cord-272759-dqkjofw2 284 12 of of IN cord-272759-dqkjofw2 284 13 new new JJ cord-272759-dqkjofw2 284 14 infections infection NNS cord-272759-dqkjofw2 284 15 per per IN cord-272759-dqkjofw2 284 16 case case NN cord-272759-dqkjofw2 284 17 ( ( -LRB- cord-272759-dqkjofw2 284 18 excluding exclude VBG cord-272759-dqkjofw2 284 19 SSEs SSEs NNP cord-272759-dqkjofw2 284 20 ) ) -RRB- cord-272759-dqkjofw2 284 21 is be VBZ cord-272759-dqkjofw2 284 22 2.7 2.7 CD cord-272759-dqkjofw2 284 23 [ [ -LRB- cord-272759-dqkjofw2 284 24 4 4 CD cord-272759-dqkjofw2 284 25 ] ] -RRB- cord-272759-dqkjofw2 284 26 . . . cord-272759-dqkjofw2 285 1 In in IN cord-272759-dqkjofw2 285 2 this this DT cord-272759-dqkjofw2 285 3 state state NN cord-272759-dqkjofw2 285 4 , , , cord-272759-dqkjofw2 285 5 each each DT cord-272759-dqkjofw2 285 6 infectious infectious JJ cord-272759-dqkjofw2 285 7 individual individual NN cord-272759-dqkjofw2 285 8 will will MD cord-272759-dqkjofw2 285 9 infect infect VB cord-272759-dqkjofw2 285 10 , , , cord-272759-dqkjofw2 285 11 on on IN cord-272759-dqkjofw2 285 12 average average JJ cord-272759-dqkjofw2 285 13 , , , cord-272759-dqkjofw2 285 14 n n NN cord-272759-dqkjofw2 285 15 1 1 CD cord-272759-dqkjofw2 285 16 p p NN cord-272759-dqkjofw2 285 17 1 1 CD cord-272759-dqkjofw2 286 1 + + CC cord-272759-dqkjofw2 287 1 E(n E(n NNP cord-272759-dqkjofw2 287 2 2 2 CD cord-272759-dqkjofw2 287 3 ) ) -RRB- cord-272759-dqkjofw2 288 1 = = NFP cord-272759-dqkjofw2 289 1 µ µ NNP cord-272759-dqkjofw2 289 2 and and CC cord-272759-dqkjofw2 289 3 we -PRON- PRP cord-272759-dqkjofw2 289 4 suppose suppose VBP cord-272759-dqkjofw2 289 5 that that IN cord-272759-dqkjofw2 289 6 the the DT cord-272759-dqkjofw2 289 7 time time NN cord-272759-dqkjofw2 289 8 before before IN cord-272759-dqkjofw2 289 9 hospitalisation hospitalisation NN cord-272759-dqkjofw2 289 10 is be VBZ cord-272759-dqkjofw2 289 11 d d NNP cord-272759-dqkjofw2 289 12 days day NNS cord-272759-dqkjofw2 289 13 , , , cord-272759-dqkjofw2 289 14 we -PRON- PRP cord-272759-dqkjofw2 289 15 have have VBP cord-272759-dqkjofw2 289 16 We -PRON- PRP cord-272759-dqkjofw2 289 17 set set VBN cord-272759-dqkjofw2 289 18 d d XX cord-272759-dqkjofw2 290 1 = = SYM cord-272759-dqkjofw2 290 2 4 4 CD cord-272759-dqkjofw2 290 3 and and CC cord-272759-dqkjofw2 290 4 therefore therefore RB cord-272759-dqkjofw2 290 5 p p NN cord-272759-dqkjofw2 290 6 1 1 CD cord-272759-dqkjofw2 290 7 ≈ ≈ NNP cord-272759-dqkjofw2 290 8 1 1 CD cord-272759-dqkjofw2 290 9 n n NN cord-272759-dqkjofw2 290 10 1 1 CD cord-272759-dqkjofw2 290 11 ( ( -LRB- cord-272759-dqkjofw2 290 12 0.675 0.675 CD cord-272759-dqkjofw2 290 13 − − NN cord-272759-dqkjofw2 291 1 µp µp NNP cord-272759-dqkjofw2 291 2 2 2 CD cord-272759-dqkjofw2 291 3 ) ) -RRB- cord-272759-dqkjofw2 291 4 = = SYM cord-272759-dqkjofw2 291 5 0.135 0.135 CD cord-272759-dqkjofw2 291 6 − − NN cord-272759-dqkjofw2 291 7 µ µ NN cord-272759-dqkjofw2 291 8 n n NN cord-272759-dqkjofw2 291 9 1 1 CD cord-272759-dqkjofw2 291 10 p p NN cord-272759-dqkjofw2 291 11 2 2 CD cord-272759-dqkjofw2 291 12 . . . cord-272759-dqkjofw2 292 1 In in IN cord-272759-dqkjofw2 292 2 subsequent subsequent JJ cord-272759-dqkjofw2 292 3 simulations simulation NNS cord-272759-dqkjofw2 292 4 , , , cord-272759-dqkjofw2 292 5 we -PRON- PRP cord-272759-dqkjofw2 292 6 also also RB cord-272759-dqkjofw2 292 7 consider consider VBP cord-272759-dqkjofw2 292 8 d d NN cord-272759-dqkjofw2 292 9 = = SYM cord-272759-dqkjofw2 292 10 3 3 CD cord-272759-dqkjofw2 292 11 , , , cord-272759-dqkjofw2 292 12 4 4 CD cord-272759-dqkjofw2 292 13 , , , cord-272759-dqkjofw2 292 14 6 6 CD cord-272759-dqkjofw2 292 15 and and CC cord-272759-dqkjofw2 292 16 also also RB cord-272759-dqkjofw2 292 17 a a DT cord-272759-dqkjofw2 292 18 larger large JJR cord-272759-dqkjofw2 292 19 number number NN cord-272759-dqkjofw2 292 20 of of IN cord-272759-dqkjofw2 292 21 new new JJ cord-272759-dqkjofw2 292 22 infections infection NNS cord-272759-dqkjofw2 292 23 than than IN cord-272759-dqkjofw2 292 24 2.7 2.7 CD cord-272759-dqkjofw2 292 25 . . . cord-272759-dqkjofw2 293 1 10 10 CD cord-272759-dqkjofw2 294 1 We -PRON- PRP cord-272759-dqkjofw2 294 2 do do VBP cord-272759-dqkjofw2 294 3 it -PRON- PRP cord-272759-dqkjofw2 294 4 this this DT cord-272759-dqkjofw2 294 5 way way NN cord-272759-dqkjofw2 294 6 simply simply RB cord-272759-dqkjofw2 294 7 because because IN cord-272759-dqkjofw2 294 8 it -PRON- PRP cord-272759-dqkjofw2 294 9 is be VBZ cord-272759-dqkjofw2 294 10 convenient convenient JJ cord-272759-dqkjofw2 294 11 to to TO cord-272759-dqkjofw2 294 12 do do VB cord-272759-dqkjofw2 294 13 so so RB cord-272759-dqkjofw2 294 14 . . . cord-272759-dqkjofw2 295 1 For for IN cord-272759-dqkjofw2 295 2 simulation simulation NN cord-272759-dqkjofw2 295 3 purposes purpose NNS cord-272759-dqkjofw2 295 4 , , , cord-272759-dqkjofw2 295 5 this this DT cord-272759-dqkjofw2 295 6 sequence sequence NN cord-272759-dqkjofw2 295 7 of of IN cord-272759-dqkjofw2 295 8 Bernoulli Bernoulli NNP cord-272759-dqkjofw2 295 9 trials trial NNS cord-272759-dqkjofw2 295 10 is be VBZ cord-272759-dqkjofw2 295 11 both both DT cord-272759-dqkjofw2 295 12 easy easy JJ cord-272759-dqkjofw2 295 13 to to TO cord-272759-dqkjofw2 295 14 implement implement VB cord-272759-dqkjofw2 295 15 and and CC cord-272759-dqkjofw2 295 16 ( ( -LRB- cord-272759-dqkjofw2 295 17 more more RBR cord-272759-dqkjofw2 295 18 importantly importantly RB cord-272759-dqkjofw2 295 19 ) ) -RRB- cord-272759-dqkjofw2 295 20 requires require VBZ cord-272759-dqkjofw2 295 21 very very RB cord-272759-dqkjofw2 295 22 modest modest JJ cord-272759-dqkjofw2 295 23 computational computational JJ cord-272759-dqkjofw2 295 24 storage storage NN cord-272759-dqkjofw2 295 25 resources resource NNS cord-272759-dqkjofw2 295 26 . . . cord-272759-dqkjofw2 296 1 In in IN cord-272759-dqkjofw2 296 2 each each DT cord-272759-dqkjofw2 296 3 case case NN cord-272759-dqkjofw2 296 4 , , , cord-272759-dqkjofw2 296 5 the the DT cord-272759-dqkjofw2 296 6 results result NNS cord-272759-dqkjofw2 296 7 are be VBP cord-272759-dqkjofw2 296 8 equivalent equivalent JJ cord-272759-dqkjofw2 296 9 to to IN cord-272759-dqkjofw2 296 10 those those DT cord-272759-dqkjofw2 296 11 presented present VBN cord-272759-dqkjofw2 296 12 here here RB cord-272759-dqkjofw2 296 13 . . . cord-272759-dqkjofw2 297 1 However however RB cord-272759-dqkjofw2 297 2 , , , cord-272759-dqkjofw2 297 3 we -PRON- PRP cord-272759-dqkjofw2 297 4 maintain maintain VBP cord-272759-dqkjofw2 297 5 the the DT cord-272759-dqkjofw2 297 6 values value NNS cord-272759-dqkjofw2 297 7 described describe VBN cord-272759-dqkjofw2 297 8 above above RB cord-272759-dqkjofw2 297 9 in in IN cord-272759-dqkjofw2 297 10 the the DT cord-272759-dqkjofw2 297 11 following follow VBG cord-272759-dqkjofw2 297 12 discussion discussion NN cord-272759-dqkjofw2 297 13 . . . cord-272759-dqkjofw2 298 1 Any any DT cord-272759-dqkjofw2 298 2 deviation deviation NN cord-272759-dqkjofw2 298 3 of of IN cord-272759-dqkjofw2 298 4 results result NNS cord-272759-dqkjofw2 298 5 between between IN cord-272759-dqkjofw2 298 6 these these DT cord-272759-dqkjofw2 298 7 and and CC cord-272759-dqkjofw2 298 8 other other JJ cord-272759-dqkjofw2 298 9 values value NNS cord-272759-dqkjofw2 298 10 will will MD cord-272759-dqkjofw2 298 11 be be VB cord-272759-dqkjofw2 298 12 highlighted highlight VBN cord-272759-dqkjofw2 298 13 in in IN cord-272759-dqkjofw2 298 14 the the DT cord-272759-dqkjofw2 298 15 text text NN cord-272759-dqkjofw2 298 16 . . . cord-272759-dqkjofw2 299 1 Our -PRON- PRP$ cord-272759-dqkjofw2 299 2 initial initial JJ cord-272759-dqkjofw2 299 3 model model NN cord-272759-dqkjofw2 299 4 parameters parameter NNS cord-272759-dqkjofw2 299 5 are be VBP cord-272759-dqkjofw2 299 6 therefore therefore RB cord-272759-dqkjofw2 299 7 [ [ -LRB- cord-272759-dqkjofw2 299 8 16 16 CD cord-272759-dqkjofw2 299 9 ] ] -RRB- cord-272759-dqkjofw2 299 10 : : : cord-272759-dqkjofw2 300 1 Note note VB cord-272759-dqkjofw2 300 2 that that IN cord-272759-dqkjofw2 300 3 , , , cord-272759-dqkjofw2 300 4 because because IN cord-272759-dqkjofw2 300 5 we -PRON- PRP cord-272759-dqkjofw2 300 6 have have VBP cord-272759-dqkjofw2 300 7 the the DT cord-272759-dqkjofw2 300 8 possibility possibility NN cord-272759-dqkjofw2 300 9 of of IN cord-272759-dqkjofw2 300 10 P p NN cord-272759-dqkjofw2 300 11 to to IN cord-272759-dqkjofw2 300 12 I -PRON- PRP cord-272759-dqkjofw2 300 13 transition transition VBP cord-272759-dqkjofw2 300 14 after after IN cord-272759-dqkjofw2 300 15 zero zero CD cord-272759-dqkjofw2 300 16 days day NNS cord-272759-dqkjofw2 300 17 , , , cord-272759-dqkjofw2 300 18 r r NN cord-272759-dqkjofw2 300 19 0 0 CD cord-272759-dqkjofw2 300 20 = = SYM cord-272759-dqkjofw2 300 21 1 1 CD cord-272759-dqkjofw2 300 22 7.4 7.4 CD cord-272759-dqkjofw2 300 23 rather rather RB cord-272759-dqkjofw2 300 24 than than IN cord-272759-dqkjofw2 300 25 1 1 CD cord-272759-dqkjofw2 300 26 6.4 6.4 CD cord-272759-dqkjofw2 300 27 . . . cord-272759-dqkjofw2 301 1 This this DT cord-272759-dqkjofw2 301 2 does do VBZ cord-272759-dqkjofw2 301 3 not not RB cord-272759-dqkjofw2 301 4 have have VB cord-272759-dqkjofw2 301 5 a a DT cord-272759-dqkjofw2 301 6 significant significant JJ cord-272759-dqkjofw2 301 7 effect effect NN cord-272759-dqkjofw2 301 8 on on IN cord-272759-dqkjofw2 301 9 our -PRON- PRP$ cord-272759-dqkjofw2 301 10 results result NNS cord-272759-dqkjofw2 301 11 ; ; : cord-272759-dqkjofw2 301 12 it -PRON- PRP cord-272759-dqkjofw2 301 13 is be VBZ cord-272759-dqkjofw2 301 14 merely merely RB cord-272759-dqkjofw2 301 15 a a DT cord-272759-dqkjofw2 301 16 computational computational JJ cord-272759-dqkjofw2 301 17 convenience convenience NN cord-272759-dqkjofw2 301 18 . . . cord-272759-dqkjofw2 302 1 Now now RB cord-272759-dqkjofw2 302 2 , , , cord-272759-dqkjofw2 302 3 from from IN cord-272759-dqkjofw2 302 4 Eq Eq NNP cord-272759-dqkjofw2 302 5 . . . cord-272759-dqkjofw2 303 1 ( ( -LRB- cord-272759-dqkjofw2 303 2 15 15 LS cord-272759-dqkjofw2 303 3 ) ) -RRB- cord-272759-dqkjofw2 303 4 we -PRON- PRP cord-272759-dqkjofw2 303 5 can can MD cord-272759-dqkjofw2 303 6 deduce deduce VB cord-272759-dqkjofw2 303 7 that that IN cord-272759-dqkjofw2 303 8 the the DT cord-272759-dqkjofw2 303 9 rate rate NN cord-272759-dqkjofw2 303 10 of of IN cord-272759-dqkjofw2 303 11 growth growth NN cord-272759-dqkjofw2 303 12 of of IN cord-272759-dqkjofw2 303 13 infection infection NN cord-272759-dqkjofw2 303 14 is be VBZ cord-272759-dqkjofw2 303 15 approximately approximately RB cord-272759-dqkjofw2 303 16 which which WDT cord-272759-dqkjofw2 303 17 , , , cord-272759-dqkjofw2 303 18 for for IN cord-272759-dqkjofw2 303 19 r r NN cord-272759-dqkjofw2 303 20 1 1 CD cord-272759-dqkjofw2 303 21 = = SYM cord-272759-dqkjofw2 303 22 0.25 0.25 CD cord-272759-dqkjofw2 303 23 , , , cord-272759-dqkjofw2 303 24 yields yield NNS cord-272759-dqkjofw2 303 25 either either CC cord-272759-dqkjofw2 303 26 a a DT cord-272759-dqkjofw2 303 27 growth growth NN cord-272759-dqkjofw2 303 28 rate rate NN cord-272759-dqkjofw2 303 29 significantly significantly RB cord-272759-dqkjofw2 303 30 less less RBR cord-272759-dqkjofw2 303 31 than than IN cord-272759-dqkjofw2 303 32 exhibited exhibit VBN cord-272759-dqkjofw2 303 33 in in IN cord-272759-dqkjofw2 303 34 the the DT cord-272759-dqkjofw2 303 35 data datum NNS cord-272759-dqkjofw2 303 36 or or CC cord-272759-dqkjofw2 303 37 rates rate NNS cord-272759-dqkjofw2 303 38 of of IN cord-272759-dqkjofw2 303 39 infection infection NN cord-272759-dqkjofw2 303 40 significantly significantly RB cord-272759-dqkjofw2 303 41 greater great JJR cord-272759-dqkjofw2 303 42 . . . cord-272759-dqkjofw2 304 1 Even even RB cord-272759-dqkjofw2 304 2 for for IN cord-272759-dqkjofw2 304 3 reasonable reasonable JJ cord-272759-dqkjofw2 304 4 variation variation NN cord-272759-dqkjofw2 304 5 of of IN cord-272759-dqkjofw2 304 6 d d NN cord-272759-dqkjofw2 304 7 and and CC cord-272759-dqkjofw2 304 8 the the DT cord-272759-dqkjofw2 304 9 average average JJ cord-272759-dqkjofw2 304 10 number number NN cord-272759-dqkjofw2 304 11 of of IN cord-272759-dqkjofw2 304 12 secondary secondary JJ cord-272759-dqkjofw2 304 13 infections infection NNS cord-272759-dqkjofw2 304 14 , , , cord-272759-dqkjofw2 304 15 we -PRON- PRP cord-272759-dqkjofw2 304 16 obtain obtain VBP cord-272759-dqkjofw2 304 17 similar similar JJ cord-272759-dqkjofw2 304 18 results result NNS cord-272759-dqkjofw2 304 19 . . . cord-272759-dqkjofw2 305 1 Hence hence RB cord-272759-dqkjofw2 305 2 , , , cord-272759-dqkjofw2 305 3 we -PRON- PRP cord-272759-dqkjofw2 305 4 conclude conclude VBP cord-272759-dqkjofw2 305 5 that that IN cord-272759-dqkjofw2 305 6 the the DT cord-272759-dqkjofw2 305 7 assumption assumption NN cord-272759-dqkjofw2 305 8 of of IN cord-272759-dqkjofw2 305 9 no no DT cord-272759-dqkjofw2 305 10 nosocomial nosocomial JJ cord-272759-dqkjofw2 305 11 transmission transmission NN cord-272759-dqkjofw2 305 12 is be VBZ cord-272759-dqkjofw2 305 13 inconsistent inconsistent JJ cord-272759-dqkjofw2 305 14 with with IN cord-272759-dqkjofw2 305 15 the the DT cord-272759-dqkjofw2 305 16 observed observed JJ cord-272759-dqkjofw2 305 17 data datum NNS cord-272759-dqkjofw2 305 18 . . . cord-272759-dqkjofw2 306 1 Increasing increase VBG cord-272759-dqkjofw2 306 2 the the DT cord-272759-dqkjofw2 306 3 average average JJ cord-272759-dqkjofw2 306 4 infectious infectious JJ cord-272759-dqkjofw2 306 5 time time NN cord-272759-dqkjofw2 306 6 to to IN cord-272759-dqkjofw2 306 7 6 6 CD cord-272759-dqkjofw2 306 8 days day NNS cord-272759-dqkjofw2 306 9 gives give VBZ cord-272759-dqkjofw2 306 10 a a DT cord-272759-dqkjofw2 306 11 substantially substantially RB cord-272759-dqkjofw2 306 12 higher high JJR cord-272759-dqkjofw2 306 13 rate rate NN cord-272759-dqkjofw2 306 14 of of IN cord-272759-dqkjofw2 306 15 infection infection NN cord-272759-dqkjofw2 306 16 : : : cord-272759-dqkjofw2 306 17 consistent consistent JJ cord-272759-dqkjofw2 306 18 with with IN cord-272759-dqkjofw2 306 19 the the DT cord-272759-dqkjofw2 306 20 observed observed JJ cord-272759-dqkjofw2 306 21 data datum NNS cord-272759-dqkjofw2 306 22 . . . cord-272759-dqkjofw2 307 1 Subject subject JJ cord-272759-dqkjofw2 307 2 to to IN cord-272759-dqkjofw2 307 3 Eq Eq NNP cord-272759-dqkjofw2 307 4 . . . cord-272759-dqkjofw2 308 1 ( ( -LRB- cord-272759-dqkjofw2 308 2 5 5 LS cord-272759-dqkjofw2 308 3 ) ) -RRB- cord-272759-dqkjofw2 308 4 , , , cord-272759-dqkjofw2 308 5 we -PRON- PRP cord-272759-dqkjofw2 308 6 explore explore VBP cord-272759-dqkjofw2 308 7 which which WDT cord-272759-dqkjofw2 308 8 parameter parameter NN cord-272759-dqkjofw2 308 9 values value NNS cord-272759-dqkjofw2 308 10 give give VBP cord-272759-dqkjofw2 308 11 a a DT cord-272759-dqkjofw2 308 12 significant significant JJ cord-272759-dqkjofw2 308 13 probability probability NN cord-272759-dqkjofw2 308 14 of of IN cord-272759-dqkjofw2 308 15 the the DT cord-272759-dqkjofw2 308 16 epidemic epidemic NN cord-272759-dqkjofw2 308 17 becoming become VBG cord-272759-dqkjofw2 308 18 endemic endemic JJ cord-272759-dqkjofw2 308 19 . . . cord-272759-dqkjofw2 309 1 From from IN cord-272759-dqkjofw2 309 2 Eq Eq NNP cord-272759-dqkjofw2 309 3 . . . cord-272759-dqkjofw2 310 1 ( ( -LRB- cord-272759-dqkjofw2 310 2 13 13 CD cord-272759-dqkjofw2 310 3 ) ) -RRB- cord-272759-dqkjofw2 310 4 , , , cord-272759-dqkjofw2 310 5 we -PRON- PRP cord-272759-dqkjofw2 310 6 have have VBP cord-272759-dqkjofw2 310 7 that that DT cord-272759-dqkjofw2 310 8 P p NN cord-272759-dqkjofw2 310 9 safe safe NN cord-272759-dqkjofw2 310 10 = = SYM cord-272759-dqkjofw2 310 11 1 1 CD cord-272759-dqkjofw2 310 12 if if IN cord-272759-dqkjofw2 311 1 n n CC cord-272759-dqkjofw2 311 2 k k XX cord-272759-dqkjofw2 311 3 < < XX cord-272759-dqkjofw2 311 4 r r NNP cord-272759-dqkjofw2 311 5 1 1 CD cord-272759-dqkjofw2 311 6 . . . cord-272759-dqkjofw2 312 1 Consistent consistent JJ cord-272759-dqkjofw2 312 2 with with IN cord-272759-dqkjofw2 312 3 the the DT cord-272759-dqkjofw2 312 4 discussion discussion NN cord-272759-dqkjofw2 312 5 of of IN cord-272759-dqkjofw2 312 6 the the DT cord-272759-dqkjofw2 312 7 preceding precede VBG cord-272759-dqkjofw2 312 8 section section NN cord-272759-dqkjofw2 312 9 , , , cord-272759-dqkjofw2 312 10 we -PRON- PRP cord-272759-dqkjofw2 312 11 start start VBP cord-272759-dqkjofw2 312 12 with with IN cord-272759-dqkjofw2 312 13 the the DT cord-272759-dqkjofw2 312 14 assumption assumption NN cord-272759-dqkjofw2 312 15 that that IN cord-272759-dqkjofw2 312 16 k k NNP cord-272759-dqkjofw2 312 17 = = SYM cord-272759-dqkjofw2 312 18 n n NN cord-272759-dqkjofw2 312 19 1 1 CD cord-272759-dqkjofw2 312 20 −1 −1 NNP cord-272759-dqkjofw2 312 21 n n NN cord-272759-dqkjofw2 312 22 1 1 CD cord-272759-dqkjofw2 312 23 and and CC cord-272759-dqkjofw2 312 24 set set VBD cord-272759-dqkjofw2 312 25 n n NN cord-272759-dqkjofw2 312 26 1 1 CD cord-272759-dqkjofw2 312 27 = = SYM cord-272759-dqkjofw2 312 28 4 4 CD cord-272759-dqkjofw2 312 29 and and CC cord-272759-dqkjofw2 312 30 µ µ NN cord-272759-dqkjofw2 312 31 = = SYM cord-272759-dqkjofw2 312 32 7 7 CD cord-272759-dqkjofw2 312 33 . . . cord-272759-dqkjofw2 313 1 Fig Fig NNP cord-272759-dqkjofw2 313 2 . . . cord-272759-dqkjofw2 314 1 3 3 CD cord-272759-dqkjofw2 314 2 is be VBZ cord-272759-dqkjofw2 314 3 a a DT cord-272759-dqkjofw2 314 4 plot plot NN cord-272759-dqkjofw2 314 5 of of IN cord-272759-dqkjofw2 314 6 the the DT cord-272759-dqkjofw2 314 7 probability probability NN cord-272759-dqkjofw2 314 8 of of IN cord-272759-dqkjofw2 314 9 complete complete JJ cord-272759-dqkjofw2 314 10 infection infection NN cord-272759-dqkjofw2 314 11 for for IN cord-272759-dqkjofw2 314 12 various various JJ cord-272759-dqkjofw2 314 13 parameter parameter NN cord-272759-dqkjofw2 314 14 values value NNS cord-272759-dqkjofw2 314 15 estimated estimate VBN cord-272759-dqkjofw2 314 16 from from IN cord-272759-dqkjofw2 314 17 the the DT cord-272759-dqkjofw2 314 18 data datum NNS cord-272759-dqkjofw2 314 19 and and CC cord-272759-dqkjofw2 314 20 Eq Eq NNP cord-272759-dqkjofw2 314 21 . . . cord-272759-dqkjofw2 315 1 ( ( -LRB- cord-272759-dqkjofw2 315 2 5 5 LS cord-272759-dqkjofw2 315 3 ) ) -RRB- cord-272759-dqkjofw2 315 4 . . . cord-272759-dqkjofw2 316 1 We -PRON- PRP cord-272759-dqkjofw2 316 2 see see VBP cord-272759-dqkjofw2 316 3 that that IN cord-272759-dqkjofw2 316 4 there there EX cord-272759-dqkjofw2 316 5 is be VBZ cord-272759-dqkjofw2 316 6 close close JJ cord-272759-dqkjofw2 316 7 agreement agreement NN cord-272759-dqkjofw2 316 8 between between IN cord-272759-dqkjofw2 316 9 the the DT cord-272759-dqkjofw2 316 10 theoretical theoretical JJ cord-272759-dqkjofw2 316 11 and and CC cord-272759-dqkjofw2 316 12 experimental experimental JJ cord-272759-dqkjofw2 316 13 results result NNS cord-272759-dqkjofw2 316 14 . . . cord-272759-dqkjofw2 317 1 Moreover moreover RB cord-272759-dqkjofw2 317 2 , , , cord-272759-dqkjofw2 317 3 we -PRON- PRP cord-272759-dqkjofw2 317 4 note note VBP cord-272759-dqkjofw2 317 5 that that IN cord-272759-dqkjofw2 317 6 a a DT cord-272759-dqkjofw2 317 7 smaller small JJR cord-272759-dqkjofw2 317 8 value value NN cord-272759-dqkjofw2 317 9 of of IN cord-272759-dqkjofw2 317 10 k k NNP cord-272759-dqkjofw2 317 11 is be VBZ cord-272759-dqkjofw2 317 12 appropriate appropriate JJ cord-272759-dqkjofw2 317 13 for for IN cord-272759-dqkjofw2 317 14 scenarios scenario NNS cord-272759-dqkjofw2 317 15 with with IN cord-272759-dqkjofw2 317 16 a a DT cord-272759-dqkjofw2 317 17 relatively relatively RB cord-272759-dqkjofw2 317 18 high high JJ cord-272759-dqkjofw2 317 19 proportion proportion NN cord-272759-dqkjofw2 317 20 of of IN cord-272759-dqkjofw2 317 21 local local JJ cord-272759-dqkjofw2 317 22 spreading spreading NN cord-272759-dqkjofw2 317 23 ( ( -LRB- cord-272759-dqkjofw2 317 24 i.e. i.e. FW cord-272759-dqkjofw2 317 25 p p NN cord-272759-dqkjofw2 317 26 1 1 CD cord-272759-dqkjofw2 317 27 larger large JJR cord-272759-dqkjofw2 317 28 and and CC cord-272759-dqkjofw2 317 29 p p NN cord-272759-dqkjofw2 317 30 2 2 CD cord-272759-dqkjofw2 317 31 ≈ ≈ NNP cord-272759-dqkjofw2 317 32 0 0 CD cord-272759-dqkjofw2 317 33 ) ) -RRB- cord-272759-dqkjofw2 317 34 . . . cord-272759-dqkjofw2 318 1 This this DT cord-272759-dqkjofw2 318 2 is be VBZ cord-272759-dqkjofw2 318 3 consistent consistent JJ cord-272759-dqkjofw2 318 4 with with IN cord-272759-dqkjofw2 318 5 the the DT cord-272759-dqkjofw2 318 6 case case NN cord-272759-dqkjofw2 318 7 of of IN cord-272759-dqkjofw2 318 8 spreading spread VBG cord-272759-dqkjofw2 318 9 within within IN cord-272759-dqkjofw2 318 10 a a DT cord-272759-dqkjofw2 318 11 single single JJ cord-272759-dqkjofw2 318 12 clump clump NN cord-272759-dqkjofw2 318 13 , , , cord-272759-dqkjofw2 318 14 and and CC cord-272759-dqkjofw2 318 15 we -PRON- PRP cord-272759-dqkjofw2 318 16 approach approach VBP cord-272759-dqkjofw2 318 17 the the DT cord-272759-dqkjofw2 318 18 situation situation NN cord-272759-dqkjofw2 318 19 of of IN cord-272759-dqkjofw2 318 20 k k NN cord-272759-dqkjofw2 318 21 = = SYM cord-272759-dqkjofw2 318 22 1 1 CD cord-272759-dqkjofw2 318 23 2 2 CD cord-272759-dqkjofw2 318 24 . . . cord-272759-dqkjofw2 319 1 However however RB cord-272759-dqkjofw2 319 2 , , , cord-272759-dqkjofw2 319 3 in in IN cord-272759-dqkjofw2 319 4 these these DT cord-272759-dqkjofw2 319 5 simulations simulation NNS cord-272759-dqkjofw2 319 6 the the DT cord-272759-dqkjofw2 319 7 best good JJS cord-272759-dqkjofw2 319 8 choice choice NN cord-272759-dqkjofw2 319 9 is be VBZ cord-272759-dqkjofw2 319 10 k k NN cord-272759-dqkjofw2 319 11 > > XX cord-272759-dqkjofw2 319 12 1 1 CD cord-272759-dqkjofw2 319 13 2 2 CD cord-272759-dqkjofw2 319 14 in in IN cord-272759-dqkjofw2 319 15 all all DT cord-272759-dqkjofw2 319 16 cases case NNS cord-272759-dqkjofw2 319 17 . . . cord-272759-dqkjofw2 320 1 Only only RB cord-272759-dqkjofw2 320 2 for for IN cord-272759-dqkjofw2 320 3 extremely extremely RB cord-272759-dqkjofw2 320 4 small small JJ cord-272759-dqkjofw2 320 5 values value NNS cord-272759-dqkjofw2 320 6 of of IN cord-272759-dqkjofw2 320 7 r r NN cord-272759-dqkjofw2 320 8 1 1 CD cord-272759-dqkjofw2 320 9 and and CC cord-272759-dqkjofw2 320 10 p p NN cord-272759-dqkjofw2 320 11 2 2 CD cord-272759-dqkjofw2 320 12 would would MD cord-272759-dqkjofw2 320 13 we -PRON- PRP cord-272759-dqkjofw2 320 14 expect expect VB cord-272759-dqkjofw2 320 15 smaller small JJR cord-272759-dqkjofw2 320 16 values value NNS cord-272759-dqkjofw2 320 17 of of IN cord-272759-dqkjofw2 320 18 k. k. NNP cord-272759-dqkjofw2 320 19 Typically typically RB cord-272759-dqkjofw2 320 20 , , , cord-272759-dqkjofw2 320 21 k k NNP cord-272759-dqkjofw2 320 22 = = SYM cord-272759-dqkjofw2 320 23 n n NN cord-272759-dqkjofw2 320 24 1 1 CD cord-272759-dqkjofw2 320 25 −1 −1 NNP cord-272759-dqkjofw2 320 26 n n NN cord-272759-dqkjofw2 320 27 1 1 CD cord-272759-dqkjofw2 320 28 = = SYM cord-272759-dqkjofw2 320 29 3 3 CD cord-272759-dqkjofw2 320 30 4 4 CD cord-272759-dqkjofw2 320 31 seems seem VBZ cord-272759-dqkjofw2 320 32 to to TO cord-272759-dqkjofw2 320 33 be be VB cord-272759-dqkjofw2 320 34 a a DT cord-272759-dqkjofw2 320 35 good good JJ cord-272759-dqkjofw2 320 36 choice choice NN cord-272759-dqkjofw2 320 37 . . . cord-272759-dqkjofw2 321 1 Furthermore furthermore RB cord-272759-dqkjofw2 321 2 , , , cord-272759-dqkjofw2 321 3 in in IN cord-272759-dqkjofw2 321 4 Fig Fig NNP cord-272759-dqkjofw2 321 5 . . . cord-272759-dqkjofw2 322 1 3 3 LS cord-272759-dqkjofw2 323 1 it -PRON- PRP cord-272759-dqkjofw2 323 2 is be VBZ cord-272759-dqkjofw2 323 3 evident evident JJ cord-272759-dqkjofw2 323 4 that that IN cord-272759-dqkjofw2 323 5 the the DT cord-272759-dqkjofw2 323 6 greatest great JJS cord-272759-dqkjofw2 323 7 probability probability NN cord-272759-dqkjofw2 323 8 of of IN cord-272759-dqkjofw2 323 9 an an DT cord-272759-dqkjofw2 323 10 epidemic epidemic NN cord-272759-dqkjofw2 323 11 becoming become VBG cord-272759-dqkjofw2 323 12 endemic endemic JJ cord-272759-dqkjofw2 323 13 is be VBZ cord-272759-dqkjofw2 323 14 when when WRB cord-272759-dqkjofw2 323 15 there there EX cord-272759-dqkjofw2 323 16 is be VBZ cord-272759-dqkjofw2 323 17 both both CC cord-272759-dqkjofw2 323 18 local local JJ cord-272759-dqkjofw2 323 19 and and CC cord-272759-dqkjofw2 323 20 non non JJ cord-272759-dqkjofw2 323 21 - - JJ cord-272759-dqkjofw2 323 22 local local JJ cord-272759-dqkjofw2 323 23 infection infection NN cord-272759-dqkjofw2 323 24 . . . cord-272759-dqkjofw2 324 1 In in IN cord-272759-dqkjofw2 324 2 the the DT cord-272759-dqkjofw2 324 3 model model NN cord-272759-dqkjofw2 324 4 that that WDT cord-272759-dqkjofw2 324 5 we -PRON- PRP cord-272759-dqkjofw2 324 6 have have VBP cord-272759-dqkjofw2 324 7 constructed construct VBN cord-272759-dqkjofw2 324 8 here here RB cord-272759-dqkjofw2 324 9 , , , cord-272759-dqkjofw2 324 10 local local JJ cord-272759-dqkjofw2 324 11 infection infection NN cord-272759-dqkjofw2 324 12 spreads spread VBZ cord-272759-dqkjofw2 324 13 approximately approximately RB cord-272759-dqkjofw2 324 14 geometrically geometrically RB cord-272759-dqkjofw2 324 15 , , , cord-272759-dqkjofw2 324 16 11 11 CD cord-272759-dqkjofw2 324 17 while while IN cord-272759-dqkjofw2 324 18 non non JJ cord-272759-dqkjofw2 324 19 - - JJ cord-272759-dqkjofw2 324 20 local local JJ cord-272759-dqkjofw2 324 21 infection infection NN cord-272759-dqkjofw2 324 22 spreads spread VBZ cord-272759-dqkjofw2 324 23 exponentially exponentially RB cord-272759-dqkjofw2 324 24 . . . cord-272759-dqkjofw2 325 1 Yet yet CC cord-272759-dqkjofw2 325 2 , , , cord-272759-dqkjofw2 325 3 it -PRON- PRP cord-272759-dqkjofw2 325 4 is be VBZ cord-272759-dqkjofw2 325 5 some some DT cord-272759-dqkjofw2 325 6 combination combination NN cord-272759-dqkjofw2 325 7 of of IN cord-272759-dqkjofw2 325 8 both both DT cord-272759-dqkjofw2 325 9 that that WDT cord-272759-dqkjofw2 325 10 provided provide VBD cord-272759-dqkjofw2 325 11 the the DT cord-272759-dqkjofw2 325 12 greatest great JJS cord-272759-dqkjofw2 325 13 possibility possibility NN cord-272759-dqkjofw2 325 14 of of IN cord-272759-dqkjofw2 325 15 an an DT cord-272759-dqkjofw2 325 16 outbreak outbreak NN cord-272759-dqkjofw2 325 17 spreading spread VBG cord-272759-dqkjofw2 325 18 without without IN cord-272759-dqkjofw2 325 19 control control NN cord-272759-dqkjofw2 325 20 . . . cord-272759-dqkjofw2 326 1 Clearly clearly RB cord-272759-dqkjofw2 326 2 , , , cord-272759-dqkjofw2 326 3 exponential exponential JJ cord-272759-dqkjofw2 326 4 growth growth NN cord-272759-dqkjofw2 326 5 will will MD cord-272759-dqkjofw2 326 6 lead lead VB cord-272759-dqkjofw2 326 7 ( ( -LRB- cord-272759-dqkjofw2 326 8 all all DT cord-272759-dqkjofw2 326 9 else else RB cord-272759-dqkjofw2 326 10 being be VBG cord-272759-dqkjofw2 326 11 equal equal JJ cord-272759-dqkjofw2 326 12 ) ) -RRB- cord-272759-dqkjofw2 326 13 to to IN cord-272759-dqkjofw2 326 14 more more RBR cord-272759-dqkjofw2 326 15 rapid rapid JJ cord-272759-dqkjofw2 326 16 growth growth NN cord-272759-dqkjofw2 326 17 of of IN cord-272759-dqkjofw2 326 18 an an DT cord-272759-dqkjofw2 326 19 epidemic epidemic NN cord-272759-dqkjofw2 326 20 than than IN cord-272759-dqkjofw2 326 21 geometric geometric JJ cord-272759-dqkjofw2 326 22 growth growth NN cord-272759-dqkjofw2 326 23 . . . cord-272759-dqkjofw2 327 1 But but CC cord-272759-dqkjofw2 327 2 , , , cord-272759-dqkjofw2 327 3 by by IN cord-272759-dqkjofw2 327 4 combining combine VBG cord-272759-dqkjofw2 327 5 some some DT cord-272759-dqkjofw2 327 6 geometric geometric JJ cord-272759-dqkjofw2 327 7 growth growth NN cord-272759-dqkjofw2 327 8 , , , cord-272759-dqkjofw2 327 9 the the DT cord-272759-dqkjofw2 327 10 epidemic epidemic NN cord-272759-dqkjofw2 327 11 becomes become VBZ cord-272759-dqkjofw2 327 12 even even RB cord-272759-dqkjofw2 327 13 more more RBR cord-272759-dqkjofw2 327 14 dangerous dangerous JJ cord-272759-dqkjofw2 327 15 . . . cord-272759-dqkjofw2 328 1 It -PRON- PRP cord-272759-dqkjofw2 328 2 seems seem VBZ cord-272759-dqkjofw2 328 3 that that IN cord-272759-dqkjofw2 328 4 the the DT cord-272759-dqkjofw2 328 5 additional additional JJ cord-272759-dqkjofw2 328 6 local local JJ cord-272759-dqkjofw2 328 7 transmissions transmission NNS cord-272759-dqkjofw2 328 8 allow allow VBP cord-272759-dqkjofw2 328 9 each each DT cord-272759-dqkjofw2 328 10 nonlocal nonlocal JJ cord-272759-dqkjofw2 328 11 transmission transmission NN cord-272759-dqkjofw2 328 12 the the DT cord-272759-dqkjofw2 328 13 possibility possibility NN cord-272759-dqkjofw2 328 14 of of IN cord-272759-dqkjofw2 328 15 seeding seed VBG cord-272759-dqkjofw2 328 16 a a DT cord-272759-dqkjofw2 328 17 new new JJ cord-272759-dqkjofw2 328 18 infection infection NN cord-272759-dqkjofw2 328 19 cluster cluster NN cord-272759-dqkjofw2 328 20 ( ( -LRB- cord-272759-dqkjofw2 328 21 rather rather RB cord-272759-dqkjofw2 328 22 than than IN cord-272759-dqkjofw2 328 23 just just RB cord-272759-dqkjofw2 328 24 a a DT cord-272759-dqkjofw2 328 25 single single JJ cord-272759-dqkjofw2 328 26 point point NN cord-272759-dqkjofw2 328 27 ) ) -RRB- cord-272759-dqkjofw2 328 28 , , , cord-272759-dqkjofw2 328 29 and and CC cord-272759-dqkjofw2 328 30 each each DT cord-272759-dqkjofw2 328 31 new new JJ cord-272759-dqkjofw2 328 32 cluster cluster NN cord-272759-dqkjofw2 328 33 is be VBZ cord-272759-dqkjofw2 328 34 more more RBR cord-272759-dqkjofw2 328 35 difficult difficult JJ cord-272759-dqkjofw2 328 36 to to TO cord-272759-dqkjofw2 328 37 eradicate eradicate VB cord-272759-dqkjofw2 328 38 than than IN cord-272759-dqkjofw2 328 39 a a DT cord-272759-dqkjofw2 328 40 single single JJ cord-272759-dqkjofw2 328 41 point point NN cord-272759-dqkjofw2 328 42 infection infection NN cord-272759-dqkjofw2 328 43 . . . cord-272759-dqkjofw2 329 1 Fig Fig NNP cord-272759-dqkjofw2 329 2 . . . cord-272759-dqkjofw2 330 1 4 4 LS cord-272759-dqkjofw2 330 2 depicts depict VBZ cord-272759-dqkjofw2 330 3 level level NN cord-272759-dqkjofw2 330 4 curves curve NNS cord-272759-dqkjofw2 330 5 for for IN cord-272759-dqkjofw2 330 6 the the DT cord-272759-dqkjofw2 330 7 probability probability NN cord-272759-dqkjofw2 330 8 of of IN cord-272759-dqkjofw2 330 9 fixed fix VBN cord-272759-dqkjofw2 330 10 levels level NNS cord-272759-dqkjofw2 330 11 of of IN cord-272759-dqkjofw2 330 12 infection infection NN cord-272759-dqkjofw2 330 13 . . . cord-272759-dqkjofw2 331 1 That that RB cord-272759-dqkjofw2 331 2 is is RB cord-272759-dqkjofw2 331 3 , , , cord-272759-dqkjofw2 331 4 we -PRON- PRP cord-272759-dqkjofw2 331 5 compute compute VBP cord-272759-dqkjofw2 331 6 the the DT cord-272759-dqkjofw2 331 7 parameter parameter NN cord-272759-dqkjofw2 331 8 values value NNS cord-272759-dqkjofw2 331 9 p p NN cord-272759-dqkjofw2 331 10 1,2 1,2 CD cord-272759-dqkjofw2 331 11 ∈ ∈ VBP cord-272759-dqkjofw2 331 12 [ [ -LRB- cord-272759-dqkjofw2 331 13 0 0 CD cord-272759-dqkjofw2 331 14 , , , cord-272759-dqkjofw2 331 15 1 1 CD cord-272759-dqkjofw2 331 16 ] ] -RRB- cord-272759-dqkjofw2 331 17 and and CC cord-272759-dqkjofw2 331 18 r r NN cord-272759-dqkjofw2 331 19 1 1 CD cord-272759-dqkjofw2 331 20 ∈ ∈ NN cord-272759-dqkjofw2 331 21 [ [ -LRB- cord-272759-dqkjofw2 331 22 0.1 0.1 CD cord-272759-dqkjofw2 331 23 , , , cord-272759-dqkjofw2 331 24 0.5 0.5 CD cord-272759-dqkjofw2 331 25 ] ] -RRB- cord-272759-dqkjofw2 331 26 required require VBN cord-272759-dqkjofw2 331 27 to to TO cord-272759-dqkjofw2 331 28 achieve achieve VB cord-272759-dqkjofw2 331 29 specific specific JJ cord-272759-dqkjofw2 331 30 values value NNS cord-272759-dqkjofw2 331 31 of of IN cord-272759-dqkjofw2 331 32 P p NN cord-272759-dqkjofw2 331 33 safe safe JJ cord-272759-dqkjofw2 331 34 . . . cord-272759-dqkjofw2 332 1 We -PRON- PRP cord-272759-dqkjofw2 332 2 see see VBP cord-272759-dqkjofw2 332 3 that that IN cord-272759-dqkjofw2 332 4 only only RB cord-272759-dqkjofw2 332 5 for for IN cord-272759-dqkjofw2 332 6 p p NN cord-272759-dqkjofw2 332 7 1,2 1,2 CD cord-272759-dqkjofw2 332 8 0.2 0.2 CD cord-272759-dqkjofw2 332 9 is be VBZ cord-272759-dqkjofw2 332 10 the the DT cord-272759-dqkjofw2 332 11 outbreak outbreak NN cord-272759-dqkjofw2 332 12 likely likely JJ cord-272759-dqkjofw2 332 13 to to TO cord-272759-dqkjofw2 332 14 be be VB cord-272759-dqkjofw2 332 15 controlled control VBN cord-272759-dqkjofw2 332 16 . . . cord-272759-dqkjofw2 333 1 Moreover moreover RB cord-272759-dqkjofw2 333 2 , , , cord-272759-dqkjofw2 333 3 the the DT cord-272759-dqkjofw2 333 4 variation variation NN cord-272759-dqkjofw2 333 5 with with IN cord-272759-dqkjofw2 333 6 r r NNP cord-272759-dqkjofw2 333 7 1 1 CD cord-272759-dqkjofw2 333 8 is be VBZ cord-272759-dqkjofw2 333 9 not not RB cord-272759-dqkjofw2 333 10 critical critical JJ cord-272759-dqkjofw2 333 11 i.e. i.e. FW cord-272759-dqkjofw2 333 12 the the DT cord-272759-dqkjofw2 333 13 range range NN cord-272759-dqkjofw2 333 14 of of IN cord-272759-dqkjofw2 333 15 behaviour behaviour NN cord-272759-dqkjofw2 333 16 for for IN cord-272759-dqkjofw2 333 17 specific specific JJ cord-272759-dqkjofw2 333 18 p p NN cord-272759-dqkjofw2 333 19 1,2 1,2 CD cord-272759-dqkjofw2 333 20 is be VBZ cord-272759-dqkjofw2 333 21 not not RB cord-272759-dqkjofw2 333 22 great great JJ cord-272759-dqkjofw2 333 23 . . . cord-272759-dqkjofw2 334 1 Finally finally RB cord-272759-dqkjofw2 334 2 , , , cord-272759-dqkjofw2 334 3 in in IN cord-272759-dqkjofw2 334 4 Fig Fig NNP cord-272759-dqkjofw2 334 5 . . . cord-272759-dqkjofw2 335 1 5 5 LS cord-272759-dqkjofw2 336 1 we -PRON- PRP cord-272759-dqkjofw2 336 2 plot plot VBP cord-272759-dqkjofw2 336 3 the the DT cord-272759-dqkjofw2 336 4 probability probability NN cord-272759-dqkjofw2 336 5 of of IN cord-272759-dqkjofw2 336 6 the the DT cord-272759-dqkjofw2 336 7 epidemic epidemic NN cord-272759-dqkjofw2 336 8 being be VBG cord-272759-dqkjofw2 336 9 controlled control VBN cord-272759-dqkjofw2 336 10 for for IN cord-272759-dqkjofw2 336 11 various various JJ cord-272759-dqkjofw2 336 12 values value NNS cord-272759-dqkjofw2 336 13 of of IN cord-272759-dqkjofw2 336 14 µ µ NN cord-272759-dqkjofw2 336 15 with with IN cord-272759-dqkjofw2 336 16 p p NN cord-272759-dqkjofw2 336 17 1,2 1,2 CD cord-272759-dqkjofw2 336 18 ∈ ∈ VB cord-272759-dqkjofw2 336 19 [ [ -LRB- cord-272759-dqkjofw2 336 20 0 0 CD cord-272759-dqkjofw2 336 21 , , , cord-272759-dqkjofw2 336 22 1 1 CD cord-272759-dqkjofw2 336 23 ] ] -RRB- cord-272759-dqkjofw2 336 24 , , . cord-272759-dqkjofw2 337 1 r r LS cord-272759-dqkjofw2 337 2 0 0 CD cord-272759-dqkjofw2 337 3 = = SYM cord-272759-dqkjofw2 337 4 0.1 0.1 CD cord-272759-dqkjofw2 337 5 and and CC cord-272759-dqkjofw2 337 6 r r NN cord-272759-dqkjofw2 337 7 1 1 CD cord-272759-dqkjofw2 337 8 = = SYM cord-272759-dqkjofw2 337 9 0.25 0.25 CD cord-272759-dqkjofw2 337 10 . . . cord-272759-dqkjofw2 338 1 Consistent consistent JJ cord-272759-dqkjofw2 338 2 with with IN cord-272759-dqkjofw2 338 3 Fig Fig NNP cord-272759-dqkjofw2 338 4 . . . cord-272759-dqkjofw2 339 1 4 4 LS cord-272759-dqkjofw2 339 2 , , , cord-272759-dqkjofw2 339 3 results result NNS cord-272759-dqkjofw2 339 4 for for IN cord-272759-dqkjofw2 339 5 different different JJ cord-272759-dqkjofw2 339 6 values value NNS cord-272759-dqkjofw2 339 7 of of IN cord-272759-dqkjofw2 339 8 r r NN cord-272759-dqkjofw2 339 9 0,1 0,1 CD cord-272759-dqkjofw2 339 10 did do VBD cord-272759-dqkjofw2 339 11 not not RB cord-272759-dqkjofw2 339 12 change change VB cord-272759-dqkjofw2 339 13 significantly significantly RB cord-272759-dqkjofw2 339 14 . . . cord-272759-dqkjofw2 340 1 Moreover moreover RB cord-272759-dqkjofw2 340 2 , , , cord-272759-dqkjofw2 340 3 from from IN cord-272759-dqkjofw2 340 4 Fig Fig NNP cord-272759-dqkjofw2 340 5 . . . cord-272759-dqkjofw2 341 1 5 5 LS cord-272759-dqkjofw2 342 1 we -PRON- PRP cord-272759-dqkjofw2 342 2 see see VBP cord-272759-dqkjofw2 342 3 that that IN cord-272759-dqkjofw2 342 4 only only RB cord-272759-dqkjofw2 342 5 for for IN cord-272759-dqkjofw2 342 6 µ µ NN cord-272759-dqkjofw2 342 7 > > XX cord-272759-dqkjofw2 342 8 2 2 CD cord-272759-dqkjofw2 342 9 does do VBZ cord-272759-dqkjofw2 342 10 the the DT cord-272759-dqkjofw2 342 11 infection infection NN cord-272759-dqkjofw2 342 12 probability probability NN cord-272759-dqkjofw2 342 13 p p NN cord-272759-dqkjofw2 342 14 2 2 CD cord-272759-dqkjofw2 342 15 have have VBP cord-272759-dqkjofw2 342 16 a a DT cord-272759-dqkjofw2 342 17 significant significant JJ cord-272759-dqkjofw2 342 18 effect effect NN cord-272759-dqkjofw2 342 19 . . . cord-272759-dqkjofw2 343 1 That that RB cord-272759-dqkjofw2 343 2 is is RB cord-272759-dqkjofw2 343 3 , , , cord-272759-dqkjofw2 343 4 to to TO cord-272759-dqkjofw2 343 5 limit limit VB cord-272759-dqkjofw2 343 6 long long JJ cord-272759-dqkjofw2 343 7 range range NN cord-272759-dqkjofw2 343 8 infection infection NN cord-272759-dqkjofw2 343 9 , , , cord-272759-dqkjofw2 343 10 one one PRP cord-272759-dqkjofw2 343 11 should should MD cord-272759-dqkjofw2 343 12 aim aim VB cord-272759-dqkjofw2 343 13 to to TO cord-272759-dqkjofw2 343 14 reduce reduce VB cord-272759-dqkjofw2 343 15 the the DT cord-272759-dqkjofw2 343 16 average average JJ cord-272759-dqkjofw2 343 17 number number NN cord-272759-dqkjofw2 343 18 of of IN cord-272759-dqkjofw2 343 19 long long JJ cord-272759-dqkjofw2 343 20 range range NN cord-272759-dqkjofw2 343 21 links link NNS cord-272759-dqkjofw2 343 22 below below IN cord-272759-dqkjofw2 343 23 2 2 CD cord-272759-dqkjofw2 343 24 . . . cord-272759-dqkjofw2 344 1 We -PRON- PRP cord-272759-dqkjofw2 344 2 find find VBP cord-272759-dqkjofw2 344 3 that that IN cord-272759-dqkjofw2 344 4 , , , cord-272759-dqkjofw2 344 5 for for IN cord-272759-dqkjofw2 344 6 all all DT cord-272759-dqkjofw2 344 7 values value NNS cord-272759-dqkjofw2 344 8 of of IN cord-272759-dqkjofw2 344 9 p p NN cord-272759-dqkjofw2 344 10 1,2 1,2 CD cord-272759-dqkjofw2 344 11 and and CC cord-272759-dqkjofw2 344 12 µ µ NN cord-272759-dqkjofw2 344 13 > > XX cord-272759-dqkjofw2 344 14 2 2 CD cord-272759-dqkjofw2 344 15 , , , cord-272759-dqkjofw2 344 16 there there EX cord-272759-dqkjofw2 344 17 was be VBD cord-272759-dqkjofw2 344 18 remarkably remarkably RB cord-272759-dqkjofw2 344 19 little little JJ cord-272759-dqkjofw2 344 20 variation variation NN cord-272759-dqkjofw2 344 21 in in IN cord-272759-dqkjofw2 344 22 the the DT cord-272759-dqkjofw2 344 23 value value NN cord-272759-dqkjofw2 344 24 of of IN cord-272759-dqkjofw2 344 25 P p NN cord-272759-dqkjofw2 344 26 safe safe JJ cord-272759-dqkjofw2 344 27 . . . cord-272759-dqkjofw2 345 1 However however RB cord-272759-dqkjofw2 345 2 , , , cord-272759-dqkjofw2 345 3 the the DT cord-272759-dqkjofw2 345 4 rate rate NN cord-272759-dqkjofw2 345 5 of of IN cord-272759-dqkjofw2 345 6 infection infection NN cord-272759-dqkjofw2 345 7 ( ( -LRB- cord-272759-dqkjofw2 345 8 Eq Eq NNP cord-272759-dqkjofw2 345 9 . . . cord-272759-dqkjofw2 345 10 ( ( -LRB- cord-272759-dqkjofw2 345 11 15 15 CD cord-272759-dqkjofw2 345 12 ) ) -RRB- cord-272759-dqkjofw2 345 13 ) ) -RRB- cord-272759-dqkjofw2 345 14 did do VBD cord-272759-dqkjofw2 345 15 change change VB cord-272759-dqkjofw2 345 16 significantly significantly RB cord-272759-dqkjofw2 345 17 . . . cord-272759-dqkjofw2 346 1 Subject subject JJ cord-272759-dqkjofw2 346 2 to to IN cord-272759-dqkjofw2 346 3 the the DT cord-272759-dqkjofw2 346 4 choice choice NN cord-272759-dqkjofw2 346 5 of of IN cord-272759-dqkjofw2 346 6 parameters parameter NNS cord-272759-dqkjofw2 346 7 in in IN cord-272759-dqkjofw2 346 8 the the DT cord-272759-dqkjofw2 346 9 previous previous JJ cord-272759-dqkjofw2 346 10 sections section NNS cord-272759-dqkjofw2 346 11 , , , cord-272759-dqkjofw2 346 12 we -PRON- PRP cord-272759-dqkjofw2 346 13 now now RB cord-272759-dqkjofw2 346 14 simulate simulate VBP cord-272759-dqkjofw2 346 15 the the DT cord-272759-dqkjofw2 346 16 expected expect VBN cord-272759-dqkjofw2 346 17 dynamics dynamic NNS cord-272759-dqkjofw2 346 18 and and CC cord-272759-dqkjofw2 346 19 compare compare VB cord-272759-dqkjofw2 346 20 this this DT cord-272759-dqkjofw2 346 21 to to IN cord-272759-dqkjofw2 346 22 the the DT cord-272759-dqkjofw2 346 23 theoretical theoretical JJ cord-272759-dqkjofw2 346 24 bounds bound NNS cord-272759-dqkjofw2 346 25 of of IN cord-272759-dqkjofw2 346 26 Section section NN cord-272759-dqkjofw2 346 27 2.2 2.2 CD cord-272759-dqkjofw2 346 28 . . . cord-272759-dqkjofw2 347 1 According accord VBG cord-272759-dqkjofw2 347 2 to to IN cord-272759-dqkjofw2 347 3 theory theory NN cord-272759-dqkjofw2 347 4 , , , cord-272759-dqkjofw2 347 5 restricting restrict VBG cord-272759-dqkjofw2 347 6 the the DT cord-272759-dqkjofw2 347 7 infectious infectious JJ cord-272759-dqkjofw2 347 8 period period NN cord-272759-dqkjofw2 347 9 to to IN cord-272759-dqkjofw2 347 10 five five CD cord-272759-dqkjofw2 347 11 or or CC cord-272759-dqkjofw2 347 12 fewer few JJR cord-272759-dqkjofw2 347 13 days day NNS cord-272759-dqkjofw2 347 14 does do VBZ cord-272759-dqkjofw2 347 15 not not RB cord-272759-dqkjofw2 347 16 yield yield VB cord-272759-dqkjofw2 347 17 a a DT cord-272759-dqkjofw2 347 18 growth growth NN cord-272759-dqkjofw2 347 19 rate rate NN cord-272759-dqkjofw2 347 20 large large JJ cord-272759-dqkjofw2 347 21 enough enough RB cord-272759-dqkjofw2 347 22 to to TO cord-272759-dqkjofw2 347 23 be be VB cord-272759-dqkjofw2 347 24 consistent consistent JJ cord-272759-dqkjofw2 347 25 with with IN cord-272759-dqkjofw2 347 26 the the DT cord-272759-dqkjofw2 347 27 observed observed JJ cord-272759-dqkjofw2 347 28 data datum NNS cord-272759-dqkjofw2 347 29 . . . cord-272759-dqkjofw2 348 1 We -PRON- PRP cord-272759-dqkjofw2 348 2 test test VBP cord-272759-dqkjofw2 348 3 that that DT cord-272759-dqkjofw2 348 4 assertion assertion NN cord-272759-dqkjofw2 348 5 numerically numerically RB cord-272759-dqkjofw2 348 6 and and CC cord-272759-dqkjofw2 348 7 find find VB cord-272759-dqkjofw2 348 8 that that IN cord-272759-dqkjofw2 348 9 the the DT cord-272759-dqkjofw2 348 10 observed observed JJ cord-272759-dqkjofw2 348 11 data datum NNS cord-272759-dqkjofw2 348 12 ( ( -LRB- cord-272759-dqkjofw2 348 13 over over IN cord-272759-dqkjofw2 348 14 1000 1000 CD cord-272759-dqkjofw2 348 15 individuals individual NNS cord-272759-dqkjofw2 348 16 infected infect VBN cord-272759-dqkjofw2 348 17 after after IN cord-272759-dqkjofw2 348 18 50 50 CD cord-272759-dqkjofw2 348 19 days day NNS cord-272759-dqkjofw2 348 20 ) ) -RRB- cord-272759-dqkjofw2 348 21 is be VBZ cord-272759-dqkjofw2 348 22 inconsistent inconsistent JJ cord-272759-dqkjofw2 348 23 with with IN cord-272759-dqkjofw2 348 24 the the DT cord-272759-dqkjofw2 348 25 simulation simulation NN cord-272759-dqkjofw2 348 26 for for IN cord-272759-dqkjofw2 348 27 r r NN cord-272759-dqkjofw2 348 28 1 1 CD cord-272759-dqkjofw2 348 29 = = SYM cord-272759-dqkjofw2 348 30 0.25 0.25 CD cord-272759-dqkjofw2 348 31 . . . cord-272759-dqkjofw2 349 1 However however RB cord-272759-dqkjofw2 349 2 , , , cord-272759-dqkjofw2 349 3 by by IN cord-272759-dqkjofw2 349 4 lowering lower VBG cord-272759-dqkjofw2 349 5 r r NN cord-272759-dqkjofw2 349 6 1 1 CD cord-272759-dqkjofw2 349 7 to to IN cord-272759-dqkjofw2 349 8 0.165 0.165 CD cord-272759-dqkjofw2 349 9 ( ( -LRB- cord-272759-dqkjofw2 349 10 and and CC cord-272759-dqkjofw2 349 11 therefore therefore RB cord-272759-dqkjofw2 349 12 increasing increase VBG cord-272759-dqkjofw2 349 13 the the DT cord-272759-dqkjofw2 349 14 mean mean JJ cord-272759-dqkjofw2 349 15 infectious infectious JJ cord-272759-dqkjofw2 349 16 period period NN cord-272759-dqkjofw2 349 17 to to IN cord-272759-dqkjofw2 349 18 six six CD cord-272759-dqkjofw2 349 19 days day NNS cord-272759-dqkjofw2 349 20 , , , cord-272759-dqkjofw2 349 21 we -PRON- PRP cord-272759-dqkjofw2 349 22 achieve achieve VBP cord-272759-dqkjofw2 349 23 results result NNS cord-272759-dqkjofw2 349 24 more more RBR cord-272759-dqkjofw2 349 25 consistent consistent JJ cord-272759-dqkjofw2 349 26 with with IN cord-272759-dqkjofw2 349 27 the the DT cord-272759-dqkjofw2 349 28 observed observed JJ cord-272759-dqkjofw2 349 29 data datum NNS cord-272759-dqkjofw2 349 30 . . . cord-272759-dqkjofw2 350 1 We -PRON- PRP cord-272759-dqkjofw2 350 2 see see VBP cord-272759-dqkjofw2 350 3 that that IN cord-272759-dqkjofw2 350 4 only only RB cord-272759-dqkjofw2 350 5 with with IN cord-272759-dqkjofw2 350 6 r r NN cord-272759-dqkjofw2 350 7 1 1 CD cord-272759-dqkjofw2 350 8 ≥ ≥ CD cord-272759-dqkjofw2 350 9 0.165 0.165 CD cord-272759-dqkjofw2 350 10 do do VBP cord-272759-dqkjofw2 350 11 we -PRON- PRP cord-272759-dqkjofw2 350 12 obtain obtain VB cord-272759-dqkjofw2 350 13 results result NNS cord-272759-dqkjofw2 350 14 for for IN cord-272759-dqkjofw2 350 15 which which WDT cord-272759-dqkjofw2 350 16 the the DT cord-272759-dqkjofw2 350 17 true true JJ cord-272759-dqkjofw2 350 18 data data NN cord-272759-dqkjofw2 350 19 is be VBZ cord-272759-dqkjofw2 350 20 not not RB cord-272759-dqkjofw2 350 21 statistically statistically RB cord-272759-dqkjofw2 350 22 atypical atypical JJ cord-272759-dqkjofw2 350 23 . . . cord-272759-dqkjofw2 351 1 Moreover moreover RB cord-272759-dqkjofw2 351 2 , , , cord-272759-dqkjofw2 351 3 this this DT cord-272759-dqkjofw2 351 4 result result NN cord-272759-dqkjofw2 351 5 is be VBZ cord-272759-dqkjofw2 351 6 robust robust JJ cord-272759-dqkjofw2 351 7 to to TO cord-272759-dqkjofw2 351 8 moderate moderate JJ cord-272759-dqkjofw2 351 9 changes change NNS cord-272759-dqkjofw2 351 10 of of IN cord-272759-dqkjofw2 351 11 the the DT cord-272759-dqkjofw2 351 12 other other JJ cord-272759-dqkjofw2 351 13 relevant relevant JJ cord-272759-dqkjofw2 351 14 parameters parameter NNS cord-272759-dqkjofw2 351 15 , , , cord-272759-dqkjofw2 351 16 as as IN cord-272759-dqkjofw2 351 17 illustrated illustrate VBN cord-272759-dqkjofw2 351 18 in in IN cord-272759-dqkjofw2 351 19 Fig Fig NNP cord-272759-dqkjofw2 351 20 . . . cord-272759-dqkjofw2 352 1 6 6 LS cord-272759-dqkjofw2 352 2 . . . cord-272759-dqkjofw2 353 1 We -PRON- PRP cord-272759-dqkjofw2 353 2 conclude conclude VBP cord-272759-dqkjofw2 353 3 that that IN cord-272759-dqkjofw2 353 4 the the DT cord-272759-dqkjofw2 353 5 obtained obtain VBN cord-272759-dqkjofw2 353 6 results result NNS cord-272759-dqkjofw2 353 7 for for IN cord-272759-dqkjofw2 353 8 which which WDT cord-272759-dqkjofw2 353 9 the the DT cord-272759-dqkjofw2 353 10 true true JJ cord-272759-dqkjofw2 353 11 data data NN cord-272759-dqkjofw2 353 12 is be VBZ cord-272759-dqkjofw2 353 13 not not RB cord-272759-dqkjofw2 353 14 atypical atypical JJ cord-272759-dqkjofw2 353 15 ; ; : cord-272759-dqkjofw2 353 16 we -PRON- PRP cord-272759-dqkjofw2 353 17 require require VBP cord-272759-dqkjofw2 353 18 r r NN cord-272759-dqkjofw2 353 19 1 1 CD cord-272759-dqkjofw2 353 20 ≥ ≥ CD cord-272759-dqkjofw2 353 21 0.165 0.165 CD cord-272759-dqkjofw2 353 22 ( ( -LRB- cord-272759-dqkjofw2 353 23 i.e. i.e. FW cord-272759-dqkjofw2 353 24 a a DT cord-272759-dqkjofw2 353 25 mean mean JJ cord-272759-dqkjofw2 353 26 exposure exposure NN cord-272759-dqkjofw2 353 27 time time NN cord-272759-dqkjofw2 353 28 of of IN cord-272759-dqkjofw2 353 29 six six CD cord-272759-dqkjofw2 353 30 or or CC cord-272759-dqkjofw2 353 31 more more JJR cord-272759-dqkjofw2 353 32 days day NNS cord-272759-dqkjofw2 353 33 ) ) -RRB- cord-272759-dqkjofw2 353 34 . . . cord-272759-dqkjofw2 354 1 Moreover moreover RB cord-272759-dqkjofw2 354 2 , , , cord-272759-dqkjofw2 354 3 we -PRON- PRP cord-272759-dqkjofw2 354 4 see see VBP cord-272759-dqkjofw2 354 5 from from IN cord-272759-dqkjofw2 354 6 Fig Fig NNP cord-272759-dqkjofw2 354 7 . . . cord-272759-dqkjofw2 354 8 6 6 CD cord-272759-dqkjofw2 354 9 that that DT cord-272759-dqkjofw2 354 10 widespread widespread JJ cord-272759-dqkjofw2 354 11 infection infection NN cord-272759-dqkjofw2 354 12 is be VBZ cord-272759-dqkjofw2 354 13 associated associate VBN cord-272759-dqkjofw2 354 14 with with IN cord-272759-dqkjofw2 354 15 a a DT cord-272759-dqkjofw2 354 16 large large JJ cord-272759-dqkjofw2 354 17 number number NN cord-272759-dqkjofw2 354 18 of of IN cord-272759-dqkjofw2 354 19 clusters cluster NNS cord-272759-dqkjofw2 354 20 . . . cord-272759-dqkjofw2 355 1 The the DT cord-272759-dqkjofw2 355 2 results result NNS cord-272759-dqkjofw2 355 3 of of IN cord-272759-dqkjofw2 355 4 the the DT cord-272759-dqkjofw2 355 5 next next JJ cord-272759-dqkjofw2 355 6 section section NN cord-272759-dqkjofw2 355 7 corroborate corroborate VBP cord-272759-dqkjofw2 355 8 this this DT cord-272759-dqkjofw2 355 9 . . . cord-272759-dqkjofw2 356 1 To to TO cord-272759-dqkjofw2 356 2 examine examine VB cord-272759-dqkjofw2 356 3 the the DT cord-272759-dqkjofw2 356 4 role role NN cord-272759-dqkjofw2 356 5 of of IN cord-272759-dqkjofw2 356 6 clustering cluster VBG cord-272759-dqkjofw2 356 7 more more RBR cord-272759-dqkjofw2 356 8 closely closely RB cord-272759-dqkjofw2 356 9 , , , cord-272759-dqkjofw2 356 10 Fig Fig NNP cord-272759-dqkjofw2 356 11 . . NNP cord-272759-dqkjofw2 356 12 7 7 CD cord-272759-dqkjofw2 356 13 is be VBZ cord-272759-dqkjofw2 356 14 a a DT cord-272759-dqkjofw2 356 15 snapshot snapshot NN cord-272759-dqkjofw2 356 16 of of IN cord-272759-dqkjofw2 356 17 a a DT cord-272759-dqkjofw2 356 18 single single JJ cord-272759-dqkjofw2 356 19 simulation simulation NN cord-272759-dqkjofw2 356 20 for for IN cord-272759-dqkjofw2 356 21 parameter parameter NN cord-272759-dqkjofw2 356 22 values value NNS cord-272759-dqkjofw2 356 23 r r NN cord-272759-dqkjofw2 356 24 1 1 CD cord-272759-dqkjofw2 356 25 = = SYM cord-272759-dqkjofw2 356 26 0.25 0.25 CD cord-272759-dqkjofw2 356 27 and and CC cord-272759-dqkjofw2 356 28 p p NN cord-272759-dqkjofw2 356 29 2 2 CD cord-272759-dqkjofw2 356 30 = = SYM cord-272759-dqkjofw2 356 31 0.006 0.006 CD cord-272759-dqkjofw2 356 32 . . . cord-272759-dqkjofw2 357 1 This this DT cord-272759-dqkjofw2 357 2 simulation simulation NN cord-272759-dqkjofw2 357 3 shows show VBZ cord-272759-dqkjofw2 357 4 SSE SSE NNP cord-272759-dqkjofw2 357 5 resulting result VBG cord-272759-dqkjofw2 357 6 from from IN cord-272759-dqkjofw2 357 7 clustering cluster VBG cord-272759-dqkjofw2 357 8 and and CC cord-272759-dqkjofw2 357 9 highly highly RB cord-272759-dqkjofw2 357 10 connected connect VBN cord-272759-dqkjofw2 357 11 nodes node NNS cord-272759-dqkjofw2 357 12 . . . cord-272759-dqkjofw2 358 1 Moreover moreover RB cord-272759-dqkjofw2 358 2 , , , cord-272759-dqkjofw2 358 3 the the DT cord-272759-dqkjofw2 358 4 gradual gradual JJ cord-272759-dqkjofw2 358 5 spread spread NN cord-272759-dqkjofw2 358 6 of of IN cord-272759-dqkjofw2 358 7 the the DT cord-272759-dqkjofw2 358 8 disease disease NN cord-272759-dqkjofw2 358 9 within within IN cord-272759-dqkjofw2 358 10 a a DT cord-272759-dqkjofw2 358 11 single single JJ cord-272759-dqkjofw2 358 12 cluster cluster NN cord-272759-dqkjofw2 358 13 is be VBZ cord-272759-dqkjofw2 358 14 evident evident JJ cord-272759-dqkjofw2 358 15 ; ; : cord-272759-dqkjofw2 358 16 one one PRP cord-272759-dqkjofw2 358 17 can can MD cord-272759-dqkjofw2 358 18 see see VB cord-272759-dqkjofw2 358 19 that that IN cord-272759-dqkjofw2 358 20 the the DT cord-272759-dqkjofw2 358 21 number number NN cord-272759-dqkjofw2 358 22 of of IN cord-272759-dqkjofw2 358 23 clusters cluster NNS cord-272759-dqkjofw2 358 24 is be VBZ cord-272759-dqkjofw2 358 25 far far RB cord-272759-dqkjofw2 358 26 less less JJR cord-272759-dqkjofw2 358 27 than than IN cord-272759-dqkjofw2 358 28 the the DT cord-272759-dqkjofw2 358 29 number number NN cord-272759-dqkjofw2 358 30 of of IN cord-272759-dqkjofw2 358 31 infections infection NNS cord-272759-dqkjofw2 358 32 . . . cord-272759-dqkjofw2 359 1 Time Time NNP cord-272759-dqkjofw2 359 2 series series NN cord-272759-dqkjofw2 359 3 of of IN cord-272759-dqkjofw2 359 4 the the DT cord-272759-dqkjofw2 359 5 infection infection NN cord-272759-dqkjofw2 359 6 total total NN cord-272759-dqkjofw2 359 7 appear appear VBP cord-272759-dqkjofw2 359 8 qualitatively qualitatively RB cord-272759-dqkjofw2 359 9 similar similar JJ cord-272759-dqkjofw2 359 10 to to IN cord-272759-dqkjofw2 359 11 the the DT cord-272759-dqkjofw2 359 12 Hong Hong NNP cord-272759-dqkjofw2 359 13 Kong Kong NNP cord-272759-dqkjofw2 359 14 SARS SARS NNP cord-272759-dqkjofw2 359 15 data datum NNS cord-272759-dqkjofw2 359 16 . . . cord-272759-dqkjofw2 360 1 Specifically specifically RB cord-272759-dqkjofw2 360 2 , , , cord-272759-dqkjofw2 360 3 burstiness burstiness NN cord-272759-dqkjofw2 360 4 typical typical JJ cord-272759-dqkjofw2 360 5 of of IN cord-272759-dqkjofw2 360 6 SSEs SSEs NNP cord-272759-dqkjofw2 360 7 is be VBZ cord-272759-dqkjofw2 360 8 evident evident JJ cord-272759-dqkjofw2 360 9 . . . cord-272759-dqkjofw2 361 1 However however RB cord-272759-dqkjofw2 361 2 , , , cord-272759-dqkjofw2 361 3 the the DT cord-272759-dqkjofw2 361 4 quantitative quantitative JJ cord-272759-dqkjofw2 361 5 behaviour behaviour NN cord-272759-dqkjofw2 361 6 of of IN cord-272759-dqkjofw2 361 7 this this DT cord-272759-dqkjofw2 361 8 model model NN cord-272759-dqkjofw2 361 9 is be VBZ cord-272759-dqkjofw2 361 10 remarkably remarkably RB cord-272759-dqkjofw2 361 11 different different JJ cord-272759-dqkjofw2 361 12 to to IN cord-272759-dqkjofw2 361 13 the the DT cord-272759-dqkjofw2 361 14 dynamics dynamic NNS cord-272759-dqkjofw2 361 15 observed observe VBN cord-272759-dqkjofw2 361 16 in in IN cord-272759-dqkjofw2 361 17 the the DT cord-272759-dqkjofw2 361 18 SARS SARS NNP cord-272759-dqkjofw2 361 19 outbreak outbreak NN cord-272759-dqkjofw2 361 20 . . . cord-272759-dqkjofw2 362 1 The the DT cord-272759-dqkjofw2 362 2 daily daily JJ cord-272759-dqkjofw2 362 3 number number NN cord-272759-dqkjofw2 362 4 of of IN cord-272759-dqkjofw2 362 5 reported report VBN cord-272759-dqkjofw2 362 6 infections infection NNS cord-272759-dqkjofw2 362 7 in in IN cord-272759-dqkjofw2 362 8 Fig Fig NNP cord-272759-dqkjofw2 362 9 . . . cord-272759-dqkjofw2 363 1 1 1 LS cord-272759-dqkjofw2 363 2 far far RB cord-272759-dqkjofw2 363 3 exceeds exceed VBZ cord-272759-dqkjofw2 363 4 the the DT cord-272759-dqkjofw2 363 5 total total JJ cord-272759-dqkjofw2 363 6 number number NN cord-272759-dqkjofw2 363 7 of of IN cord-272759-dqkjofw2 363 8 active active JJ cord-272759-dqkjofw2 363 9 infected infected JJ cord-272759-dqkjofw2 363 10 and and CC cord-272759-dqkjofw2 363 11 prone prone JJ cord-272759-dqkjofw2 363 12 individuals individual NNS cord-272759-dqkjofw2 363 13 in in IN cord-272759-dqkjofw2 363 14 Fig Fig NNP cord-272759-dqkjofw2 363 15 . . . cord-272759-dqkjofw2 364 1 7 7 CD cord-272759-dqkjofw2 364 2 . . . cord-272759-dqkjofw2 365 1 Finally finally RB cord-272759-dqkjofw2 365 2 , , , cord-272759-dqkjofw2 365 3 we -PRON- PRP cord-272759-dqkjofw2 365 4 provide provide VBP cord-272759-dqkjofw2 365 5 simulations simulation NNS cord-272759-dqkjofw2 365 6 of of IN cord-272759-dqkjofw2 365 7 the the DT cord-272759-dqkjofw2 365 8 Hong Hong NNP cord-272759-dqkjofw2 365 9 Kong Kong NNP cord-272759-dqkjofw2 365 10 epidemic epidemic NN cord-272759-dqkjofw2 365 11 and and CC cord-272759-dqkjofw2 365 12 from from IN cord-272759-dqkjofw2 365 13 multiple multiple JJ cord-272759-dqkjofw2 365 14 simulations simulation NNS cord-272759-dqkjofw2 365 15 estimate estimate VBP cord-272759-dqkjofw2 365 16 the the DT cord-272759-dqkjofw2 365 17 likelihood likelihood NN cord-272759-dqkjofw2 365 18 of of IN cord-272759-dqkjofw2 365 19 various various JJ cord-272759-dqkjofw2 365 20 outcomes outcome NNS cord-272759-dqkjofw2 365 21 based base VBN cord-272759-dqkjofw2 365 22 on on IN cord-272759-dqkjofw2 365 23 the the DT cord-272759-dqkjofw2 365 24 model model NN cord-272759-dqkjofw2 365 25 . . . cord-272759-dqkjofw2 366 1 We -PRON- PRP cord-272759-dqkjofw2 366 2 initiate initiate VBP cord-272759-dqkjofw2 366 3 the the DT cord-272759-dqkjofw2 366 4 model model NN cord-272759-dqkjofw2 366 5 with with IN cord-272759-dqkjofw2 366 6 a a DT cord-272759-dqkjofw2 366 7 single single JJ cord-272759-dqkjofw2 366 8 infected infected JJ cord-272759-dqkjofw2 366 9 individual individual NN cord-272759-dqkjofw2 366 10 and and CC cord-272759-dqkjofw2 366 11 a a DT cord-272759-dqkjofw2 366 12 relatively relatively RB cord-272759-dqkjofw2 366 13 low low JJ cord-272759-dqkjofw2 366 14 removal removal NN cord-272759-dqkjofw2 366 15 rate rate NN cord-272759-dqkjofw2 366 16 r r NN cord-272759-dqkjofw2 366 17 1 1 CD cord-272759-dqkjofw2 366 18 . . . cord-272759-dqkjofw2 367 1 Fig Fig NNP cord-272759-dqkjofw2 367 2 . . . cord-272759-dqkjofw2 368 1 8 8 CD cord-272759-dqkjofw2 368 2 depicts depict VBZ cord-272759-dqkjofw2 368 3 our -PRON- PRP$ cord-272759-dqkjofw2 368 4 results result NNS cord-272759-dqkjofw2 368 5 . . . cord-272759-dqkjofw2 369 1 We -PRON- PRP cord-272759-dqkjofw2 369 2 can can MD cord-272759-dqkjofw2 369 3 see see VB cord-272759-dqkjofw2 369 4 from from IN cord-272759-dqkjofw2 369 5 Fig Fig NNP cord-272759-dqkjofw2 369 6 . . . cord-272759-dqkjofw2 370 1 8 8 CD cord-272759-dqkjofw2 370 2 that that IN cord-272759-dqkjofw2 370 3 many many JJ cord-272759-dqkjofw2 370 4 of of IN cord-272759-dqkjofw2 370 5 the the DT cord-272759-dqkjofw2 370 6 features feature NNS cord-272759-dqkjofw2 370 7 of of IN cord-272759-dqkjofw2 370 8 the the DT cord-272759-dqkjofw2 370 9 true true JJ cord-272759-dqkjofw2 370 10 data datum NNS cord-272759-dqkjofw2 370 11 are be VBP cord-272759-dqkjofw2 370 12 reproduced reproduce VBN cord-272759-dqkjofw2 370 13 well well RB cord-272759-dqkjofw2 370 14 in in IN cord-272759-dqkjofw2 370 15 the the DT cord-272759-dqkjofw2 370 16 simulations simulation NNS cord-272759-dqkjofw2 370 17 . . . cord-272759-dqkjofw2 371 1 However however RB cord-272759-dqkjofw2 371 2 , , , cord-272759-dqkjofw2 371 3 two two CD cord-272759-dqkjofw2 371 4 important important JJ cord-272759-dqkjofw2 371 5 aspects aspect NNS cord-272759-dqkjofw2 371 6 of of IN cord-272759-dqkjofw2 371 7 the the DT cord-272759-dqkjofw2 371 8 simulations simulation NNS cord-272759-dqkjofw2 371 9 are be VBP cord-272759-dqkjofw2 371 10 not not RB cord-272759-dqkjofw2 371 11 sufficiently sufficiently RB cord-272759-dqkjofw2 371 12 similar similar JJ cord-272759-dqkjofw2 371 13 to to IN cord-272759-dqkjofw2 371 14 the the DT cord-272759-dqkjofw2 371 15 data datum NNS cord-272759-dqkjofw2 371 16 . . . cord-272759-dqkjofw2 372 1 Firstly firstly RB cord-272759-dqkjofw2 372 2 , , , cord-272759-dqkjofw2 372 3 the the DT cord-272759-dqkjofw2 372 4 initial initial JJ cord-272759-dqkjofw2 372 5 spreading spreading NN cord-272759-dqkjofw2 372 6 of of IN cord-272759-dqkjofw2 372 7 the the DT cord-272759-dqkjofw2 372 8 disease disease NN cord-272759-dqkjofw2 372 9 is be VBZ cord-272759-dqkjofw2 372 10 exponential exponential JJ cord-272759-dqkjofw2 372 11 , , , cord-272759-dqkjofw2 372 12 rather rather RB cord-272759-dqkjofw2 372 13 than than IN cord-272759-dqkjofw2 372 14 the the DT cord-272759-dqkjofw2 372 15 single single JJ cord-272759-dqkjofw2 372 16 SSE SSE NNP cord-272759-dqkjofw2 372 17 observed observe VBD cord-272759-dqkjofw2 372 18 in in IN cord-272759-dqkjofw2 372 19 the the DT cord-272759-dqkjofw2 372 20 real real JJ cord-272759-dqkjofw2 372 21 data datum NNS cord-272759-dqkjofw2 372 22 . . . cord-272759-dqkjofw2 373 1 Secondly secondly RB cord-272759-dqkjofw2 373 2 , , , cord-272759-dqkjofw2 373 3 the the DT cord-272759-dqkjofw2 373 4 magnitude magnitude NN cord-272759-dqkjofw2 373 5 of of IN cord-272759-dqkjofw2 373 6 the the DT cord-272759-dqkjofw2 373 7 SSEs sse NNS cord-272759-dqkjofw2 373 8 in in IN cord-272759-dqkjofw2 373 9 the the DT cord-272759-dqkjofw2 373 10 simulations simulation NNS cord-272759-dqkjofw2 373 11 is be VBZ cord-272759-dqkjofw2 373 12 somewhat somewhat RB cord-272759-dqkjofw2 373 13 smaller small JJR cord-272759-dqkjofw2 373 14 than than IN cord-272759-dqkjofw2 373 15 the the DT cord-272759-dqkjofw2 373 16 largest large JJS cord-272759-dqkjofw2 373 17 SSEs sse NNS cord-272759-dqkjofw2 373 18 in in IN cord-272759-dqkjofw2 373 19 the the DT cord-272759-dqkjofw2 373 20 data datum NNS cord-272759-dqkjofw2 373 21 . . . cord-272759-dqkjofw2 374 1 This this DT cord-272759-dqkjofw2 374 2 second second JJ cord-272759-dqkjofw2 374 3 aspect aspect NN cord-272759-dqkjofw2 374 4 can can MD cord-272759-dqkjofw2 374 5 be be VB cord-272759-dqkjofw2 374 6 overcome overcome VBN cord-272759-dqkjofw2 374 7 by by IN cord-272759-dqkjofw2 374 8 simply simply RB cord-272759-dqkjofw2 374 9 altering alter VBG cord-272759-dqkjofw2 374 10 the the DT cord-272759-dqkjofw2 374 11 distribution distribution NN cord-272759-dqkjofw2 374 12 of of IN cord-272759-dqkjofw2 374 13 non non JJ cord-272759-dqkjofw2 374 14 - - JJ cord-272759-dqkjofw2 374 15 local local JJ cord-272759-dqkjofw2 374 16 links link NNS cord-272759-dqkjofw2 374 17 . . . cord-272759-dqkjofw2 375 1 In in IN cord-272759-dqkjofw2 375 2 [ [ -LRB- cord-272759-dqkjofw2 375 3 16 16 CD cord-272759-dqkjofw2 375 4 ] ] -RRB- cord-272759-dqkjofw2 375 5 we -PRON- PRP cord-272759-dqkjofw2 375 6 describe describe VBP cord-272759-dqkjofw2 375 7 how how WRB cord-272759-dqkjofw2 375 8 a a DT cord-272759-dqkjofw2 375 9 power power NN cord-272759-dqkjofw2 375 10 - - HYPH cord-272759-dqkjofw2 375 11 law law NN cord-272759-dqkjofw2 375 12 distribution distribution NN cord-272759-dqkjofw2 375 13 of of IN cord-272759-dqkjofw2 375 14 links link NNS cord-272759-dqkjofw2 375 15 can can MD cord-272759-dqkjofw2 375 16 lead lead VB cord-272759-dqkjofw2 375 17 to to IN cord-272759-dqkjofw2 375 18 many many JJ cord-272759-dqkjofw2 375 19 more more JJR cord-272759-dqkjofw2 375 20 extreme extreme JJ cord-272759-dqkjofw2 375 21 events event NNS cord-272759-dqkjofw2 375 22 . . . cord-272759-dqkjofw2 376 1 Conversely conversely RB cord-272759-dqkjofw2 376 2 , , , cord-272759-dqkjofw2 376 3 the the DT cord-272759-dqkjofw2 376 4 initial initial JJ cord-272759-dqkjofw2 376 5 SSE SSE NNP cord-272759-dqkjofw2 376 6 in in IN cord-272759-dqkjofw2 376 7 the the DT cord-272759-dqkjofw2 376 8 data datum NNS cord-272759-dqkjofw2 376 9 can can MD cord-272759-dqkjofw2 376 10 not not RB cord-272759-dqkjofw2 376 11 be be VB cord-272759-dqkjofw2 376 12 modelled model VBN cord-272759-dqkjofw2 376 13 well well RB cord-272759-dqkjofw2 376 14 by by IN cord-272759-dqkjofw2 376 15 our -PRON- PRP$ cord-272759-dqkjofw2 376 16 simulations simulation NNS cord-272759-dqkjofw2 376 17 , , , cord-272759-dqkjofw2 376 18 except except IN cord-272759-dqkjofw2 376 19 by by IN cord-272759-dqkjofw2 376 20 chance chance NN cord-272759-dqkjofw2 376 21 . . . cord-272759-dqkjofw2 377 1 Therefore therefore RB cord-272759-dqkjofw2 377 2 , , , cord-272759-dqkjofw2 377 3 to to TO cord-272759-dqkjofw2 377 4 achieve achieve VB cord-272759-dqkjofw2 377 5 similar similar JJ cord-272759-dqkjofw2 377 6 initial initial JJ cord-272759-dqkjofw2 377 7 events event NNS cord-272759-dqkjofw2 377 8 , , , cord-272759-dqkjofw2 377 9 we -PRON- PRP cord-272759-dqkjofw2 377 10 would would MD cord-272759-dqkjofw2 377 11 expect expect VB cord-272759-dqkjofw2 377 12 that that IN cord-272759-dqkjofw2 377 13 we -PRON- PRP cord-272759-dqkjofw2 377 14 would would MD cord-272759-dqkjofw2 377 15 have have VB cord-272759-dqkjofw2 377 16 to to TO cord-272759-dqkjofw2 377 17 execute execute VB cord-272759-dqkjofw2 377 18 many many JJ cord-272759-dqkjofw2 377 19 simulations simulation NNS cord-272759-dqkjofw2 377 20 ( ( -LRB- cord-272759-dqkjofw2 377 21 and and CC cord-272759-dqkjofw2 377 22 choose choose VB cord-272759-dqkjofw2 377 23 only only RB cord-272759-dqkjofw2 377 24 those those DT cord-272759-dqkjofw2 377 25 that that WDT cord-272759-dqkjofw2 377 26 suit suit VBP cord-272759-dqkjofw2 377 27 our -PRON- PRP$ cord-272759-dqkjofw2 377 28 purpose purpose NN cord-272759-dqkjofw2 377 29 ) ) -RRB- cord-272759-dqkjofw2 377 30 , , , cord-272759-dqkjofw2 377 31 or or CC cord-272759-dqkjofw2 377 32 simply simply RB cord-272759-dqkjofw2 377 33 build build VB cord-272759-dqkjofw2 377 34 the the DT cord-272759-dqkjofw2 377 35 SSE SSE NNP cord-272759-dqkjofw2 377 36 into into IN cord-272759-dqkjofw2 377 37 the the DT cord-272759-dqkjofw2 377 38 model model NN cord-272759-dqkjofw2 377 39 . . . cord-272759-dqkjofw2 378 1 Neither neither DT cord-272759-dqkjofw2 378 2 of of IN cord-272759-dqkjofw2 378 3 these these DT cord-272759-dqkjofw2 378 4 approaches approach NNS cord-272759-dqkjofw2 378 5 are be VBP cord-272759-dqkjofw2 378 6 desirable desirable JJ cord-272759-dqkjofw2 378 7 . . . cord-272759-dqkjofw2 379 1 We -PRON- PRP cord-272759-dqkjofw2 379 2 prefer prefer VBP cord-272759-dqkjofw2 379 3 to to TO cord-272759-dqkjofw2 379 4 focus focus VB cord-272759-dqkjofw2 379 5 on on IN cord-272759-dqkjofw2 379 6 the the DT cord-272759-dqkjofw2 379 7 possibility possibility NN cord-272759-dqkjofw2 379 8 of of IN cord-272759-dqkjofw2 379 9 SSEs sse NNS cord-272759-dqkjofw2 379 10 occurring occur VBG cord-272759-dqkjofw2 379 11 randomly randomly RB cord-272759-dqkjofw2 379 12 , , , cord-272759-dqkjofw2 379 13 without without IN cord-272759-dqkjofw2 379 14 explicitly explicitly RB cord-272759-dqkjofw2 379 15 adding add VBG cord-272759-dqkjofw2 379 16 them -PRON- PRP cord-272759-dqkjofw2 379 17 in in IN cord-272759-dqkjofw2 379 18 the the DT cord-272759-dqkjofw2 379 19 model model NN cord-272759-dqkjofw2 379 20 . . . cord-272759-dqkjofw2 380 1 Hence hence RB cord-272759-dqkjofw2 380 2 , , , cord-272759-dqkjofw2 380 3 we -PRON- PRP cord-272759-dqkjofw2 380 4 do do VBP cord-272759-dqkjofw2 380 5 see see VB cord-272759-dqkjofw2 380 6 SSEs sse NNS cord-272759-dqkjofw2 380 7 , , , cord-272759-dqkjofw2 380 8 but but CC cord-272759-dqkjofw2 380 9 not not RB cord-272759-dqkjofw2 380 10 necessarily necessarily RB cord-272759-dqkjofw2 380 11 immediately immediately RB cord-272759-dqkjofw2 380 12 after after IN cord-272759-dqkjofw2 380 13 the the DT cord-272759-dqkjofw2 380 14 start start NN cord-272759-dqkjofw2 380 15 of of IN cord-272759-dqkjofw2 380 16 the the DT cord-272759-dqkjofw2 380 17 simulation simulation NN cord-272759-dqkjofw2 380 18 ( ( -LRB- cord-272759-dqkjofw2 380 19 as as IN cord-272759-dqkjofw2 380 20 we -PRON- PRP cord-272759-dqkjofw2 380 21 suppose suppose VBP cord-272759-dqkjofw2 380 22 occurred occur VBD cord-272759-dqkjofw2 380 23 in in IN cord-272759-dqkjofw2 380 24 the the DT cord-272759-dqkjofw2 380 25 true true JJ cord-272759-dqkjofw2 380 26 data datum NNS cord-272759-dqkjofw2 380 27 ) ) -RRB- cord-272759-dqkjofw2 380 28 . . . cord-272759-dqkjofw2 381 1 We -PRON- PRP cord-272759-dqkjofw2 381 2 now now RB cord-272759-dqkjofw2 381 3 wish wish VBP cord-272759-dqkjofw2 381 4 to to TO cord-272759-dqkjofw2 381 5 demonstrated demonstrate VBN cord-272759-dqkjofw2 381 6 how how WRB cord-272759-dqkjofw2 381 7 the the DT cord-272759-dqkjofw2 381 8 SW SW NNP cord-272759-dqkjofw2 381 9 model model NN cord-272759-dqkjofw2 381 10 described describe VBN cord-272759-dqkjofw2 381 11 here here RB cord-272759-dqkjofw2 381 12 improves improve VBZ cord-272759-dqkjofw2 381 13 on on IN cord-272759-dqkjofw2 381 14 stochastic stochastic JJ cord-272759-dqkjofw2 381 15 SIR sir NN cord-272759-dqkjofw2 381 16 - - HYPH cord-272759-dqkjofw2 381 17 type type NN cord-272759-dqkjofw2 381 18 models model NNS cord-272759-dqkjofw2 381 19 [ [ -LRB- cord-272759-dqkjofw2 381 20 7 7 CD cord-272759-dqkjofw2 381 21 ] ] -RRB- cord-272759-dqkjofw2 381 22 . . . cord-272759-dqkjofw2 382 1 One one CD cord-272759-dqkjofw2 382 2 very very RB cord-272759-dqkjofw2 382 3 simple simple JJ cord-272759-dqkjofw2 382 4 way way NN cord-272759-dqkjofw2 382 5 to to TO cord-272759-dqkjofw2 382 6 achieve achieve VB cord-272759-dqkjofw2 382 7 this this DT cord-272759-dqkjofw2 382 8 is be VBZ cord-272759-dqkjofw2 382 9 to to TO cord-272759-dqkjofw2 382 10 compare compare VB cord-272759-dqkjofw2 382 11 the the DT cord-272759-dqkjofw2 382 12 distribution distribution NN cord-272759-dqkjofw2 382 13 of of IN cord-272759-dqkjofw2 382 14 statistic statistic NN cord-272759-dqkjofw2 382 15 values value NNS cord-272759-dqkjofw2 382 16 measured measure VBN cord-272759-dqkjofw2 382 17 from from IN cord-272759-dqkjofw2 382 18 simulations simulation NNS cord-272759-dqkjofw2 382 19 of of IN cord-272759-dqkjofw2 382 20 either either DT cord-272759-dqkjofw2 382 21 type type NN cord-272759-dqkjofw2 382 22 of of IN cord-272759-dqkjofw2 382 23 model model NN cord-272759-dqkjofw2 382 24 to to IN cord-272759-dqkjofw2 382 25 the the DT cord-272759-dqkjofw2 382 26 true true JJ cord-272759-dqkjofw2 382 27 data datum NNS cord-272759-dqkjofw2 382 28 . . . cord-272759-dqkjofw2 383 1 In in IN cord-272759-dqkjofw2 383 2 Fig Fig NNP cord-272759-dqkjofw2 383 3 . . . cord-272759-dqkjofw2 384 1 9 9 CD cord-272759-dqkjofw2 385 1 we -PRON- PRP cord-272759-dqkjofw2 385 2 do do VBP cord-272759-dqkjofw2 385 3 this this DT cord-272759-dqkjofw2 385 4 , , , cord-272759-dqkjofw2 385 5 and and CC cord-272759-dqkjofw2 385 6 we -PRON- PRP cord-272759-dqkjofw2 385 7 find find VBP cord-272759-dqkjofw2 385 8 that that IN cord-272759-dqkjofw2 385 9 the the DT cord-272759-dqkjofw2 385 10 small small JJ cord-272759-dqkjofw2 385 11 - - HYPH cord-272759-dqkjofw2 385 12 world world NN cord-272759-dqkjofw2 385 13 model model NN cord-272759-dqkjofw2 385 14 exhibits exhibit VBZ cord-272759-dqkjofw2 385 15 statistical statistical JJ cord-272759-dqkjofw2 385 16 properties property NNS cord-272759-dqkjofw2 385 17 much much RB cord-272759-dqkjofw2 385 18 closer close JJR cord-272759-dqkjofw2 385 19 to to IN cord-272759-dqkjofw2 385 20 the the DT cord-272759-dqkjofw2 385 21 observed observed JJ cord-272759-dqkjofw2 385 22 data datum NNS cord-272759-dqkjofw2 385 23 . . . cord-272759-dqkjofw2 386 1 In in IN cord-272759-dqkjofw2 386 2 Fig Fig NNP cord-272759-dqkjofw2 386 3 . . . cord-272759-dqkjofw2 387 1 9 9 CD cord-272759-dqkjofw2 388 1 we -PRON- PRP cord-272759-dqkjofw2 388 2 compare compare VBP cord-272759-dqkjofw2 388 3 the the DT cord-272759-dqkjofw2 388 4 results result NNS cord-272759-dqkjofw2 388 5 for for IN cord-272759-dqkjofw2 388 6 the the DT cord-272759-dqkjofw2 388 7 SIRtype SIRtype NNP cord-272759-dqkjofw2 388 8 model model NN cord-272759-dqkjofw2 388 9 ( ( -LRB- cord-272759-dqkjofw2 388 10 with with IN cord-272759-dqkjofw2 388 11 stochastic stochastic JJ cord-272759-dqkjofw2 388 12 inputs input NNS cord-272759-dqkjofw2 388 13 ) ) -RRB- cord-272759-dqkjofw2 388 14 to to IN cord-272759-dqkjofw2 388 15 the the DT cord-272759-dqkjofw2 388 16 SW SW NNP cord-272759-dqkjofw2 388 17 model model NN cord-272759-dqkjofw2 388 18 described describe VBN cord-272759-dqkjofw2 388 19 in in IN cord-272759-dqkjofw2 388 20 this this DT cord-272759-dqkjofw2 388 21 paper paper NN cord-272759-dqkjofw2 388 22 . . . cord-272759-dqkjofw2 389 1 By by IN cord-272759-dqkjofw2 389 2 generating generate VBG cord-272759-dqkjofw2 389 3 multiple multiple JJ cord-272759-dqkjofw2 389 4 simulations simulation NNS cord-272759-dqkjofw2 389 5 of of IN cord-272759-dqkjofw2 389 6 both both DT cord-272759-dqkjofw2 389 7 models model NNS cord-272759-dqkjofw2 389 8 and and CC cord-272759-dqkjofw2 389 9 estimating estimate VBG cord-272759-dqkjofw2 389 10 simple simple JJ cord-272759-dqkjofw2 389 11 statistical statistical JJ cord-272759-dqkjofw2 389 12 measures measure NNS cord-272759-dqkjofw2 389 13 from from IN cord-272759-dqkjofw2 389 14 both both DT cord-272759-dqkjofw2 389 15 sets set NNS cord-272759-dqkjofw2 389 16 of of IN cord-272759-dqkjofw2 389 17 simulations simulation NNS cord-272759-dqkjofw2 389 18 , , , cord-272759-dqkjofw2 389 19 we -PRON- PRP cord-272759-dqkjofw2 389 20 see see VBP cord-272759-dqkjofw2 389 21 that that IN cord-272759-dqkjofw2 389 22 the the DT cord-272759-dqkjofw2 389 23 model model NN cord-272759-dqkjofw2 389 24 dynamics dynamic NNS cord-272759-dqkjofw2 389 25 of of IN cord-272759-dqkjofw2 389 26 the the DT cord-272759-dqkjofw2 389 27 SW SW NNP cord-272759-dqkjofw2 389 28 model model NN cord-272759-dqkjofw2 389 29 are be VBP cord-272759-dqkjofw2 389 30 much much RB cord-272759-dqkjofw2 389 31 closer close JJR cord-272759-dqkjofw2 389 32 to to IN cord-272759-dqkjofw2 389 33 the the DT cord-272759-dqkjofw2 389 34 true true JJ cord-272759-dqkjofw2 389 35 data datum NNS cord-272759-dqkjofw2 389 36 . . . cord-272759-dqkjofw2 390 1 Assuming assume VBG cord-272759-dqkjofw2 390 2 that that IN cord-272759-dqkjofw2 390 3 this this DT cord-272759-dqkjofw2 390 4 model model NN cord-272759-dqkjofw2 390 5 and and CC cord-272759-dqkjofw2 390 6 parameters parameter NNS cord-272759-dqkjofw2 390 7 are be VBP cord-272759-dqkjofw2 390 8 accurate accurate JJ cord-272759-dqkjofw2 390 9 , , , cord-272759-dqkjofw2 390 10 or or CC cord-272759-dqkjofw2 390 11 at at IN cord-272759-dqkjofw2 390 12 least least JJS cord-272759-dqkjofw2 390 13 appropriate appropriate JJ cord-272759-dqkjofw2 390 14 , , , cord-272759-dqkjofw2 390 15 we -PRON- PRP cord-272759-dqkjofw2 390 16 compute compute VBP cord-272759-dqkjofw2 390 17 the the DT cord-272759-dqkjofw2 390 18 likely likely JJ cord-272759-dqkjofw2 390 19 behaviour behaviour NN cord-272759-dqkjofw2 390 20 for for IN cord-272759-dqkjofw2 390 21 various various JJ cord-272759-dqkjofw2 390 22 epidemics epidemic NNS cord-272759-dqkjofw2 390 23 . . . cord-272759-dqkjofw2 391 1 We -PRON- PRP cord-272759-dqkjofw2 391 2 generated generate VBD cord-272759-dqkjofw2 391 3 1000 1000 CD cord-272759-dqkjofw2 391 4 realisations realisation NNS cord-272759-dqkjofw2 391 5 of of IN cord-272759-dqkjofw2 391 6 the the DT cord-272759-dqkjofw2 391 7 model model NN cord-272759-dqkjofw2 391 8 depicted depict VBN cord-272759-dqkjofw2 391 9 in in IN cord-272759-dqkjofw2 391 10 Fig Fig NNP cord-272759-dqkjofw2 391 11 . . NNP cord-272759-dqkjofw2 391 12 8 8 CD cord-272759-dqkjofw2 391 13 and and CC cord-272759-dqkjofw2 391 14 computed compute VBD cord-272759-dqkjofw2 391 15 the the DT cord-272759-dqkjofw2 391 16 total total JJ cord-272759-dqkjofw2 391 17 number number NN cord-272759-dqkjofw2 391 18 of of IN cord-272759-dqkjofw2 391 19 casualties casualty NNS cord-272759-dqkjofw2 391 20 . . . cord-272759-dqkjofw2 392 1 Fig Fig NNP cord-272759-dqkjofw2 392 2 . . . cord-272759-dqkjofw2 393 1 10 10 CD cord-272759-dqkjofw2 393 2 is be VBZ cord-272759-dqkjofw2 393 3 a a DT cord-272759-dqkjofw2 393 4 plot plot NN cord-272759-dqkjofw2 393 5 of of IN cord-272759-dqkjofw2 393 6 the the DT cord-272759-dqkjofw2 393 7 probability probability NN cord-272759-dqkjofw2 393 8 distribution distribution NN cord-272759-dqkjofw2 393 9 of of IN cord-272759-dqkjofw2 393 10 the the DT cord-272759-dqkjofw2 393 11 number number NN cord-272759-dqkjofw2 393 12 of of IN cord-272759-dqkjofw2 393 13 fatalities fatality NNS cord-272759-dqkjofw2 393 14 for for IN cord-272759-dqkjofw2 393 15 these these DT cord-272759-dqkjofw2 393 16 simulations simulation NNS cord-272759-dqkjofw2 393 17 , , , cord-272759-dqkjofw2 393 18 and and CC cord-272759-dqkjofw2 393 19 Fig Fig NNP cord-272759-dqkjofw2 393 20 . . . cord-272759-dqkjofw2 394 1 11 11 CD cord-272759-dqkjofw2 394 2 is be VBZ cord-272759-dqkjofw2 394 3 the the DT cord-272759-dqkjofw2 394 4 probability probability NN cord-272759-dqkjofw2 394 5 distribution distribution NN cord-272759-dqkjofw2 394 6 for for IN cord-272759-dqkjofw2 394 7 the the DT cord-272759-dqkjofw2 394 8 daily daily JJ cord-272759-dqkjofw2 394 9 number number NN cord-272759-dqkjofw2 394 10 of of IN cord-272759-dqkjofw2 394 11 infections infection NNS cord-272759-dqkjofw2 394 12 . . . cord-272759-dqkjofw2 395 1 We -PRON- PRP cord-272759-dqkjofw2 395 2 found find VBD cord-272759-dqkjofw2 395 3 that that IN cord-272759-dqkjofw2 395 4 the the DT cord-272759-dqkjofw2 395 5 probability probability NN cord-272759-dqkjofw2 395 6 of of IN cord-272759-dqkjofw2 395 7 infecting infect VBG cord-272759-dqkjofw2 395 8 fewer few JJR cord-272759-dqkjofw2 395 9 than than IN cord-272759-dqkjofw2 395 10 20 20 CD cord-272759-dqkjofw2 395 11 people people NNS cord-272759-dqkjofw2 395 12 was be VBD cord-272759-dqkjofw2 395 13 approximately approximately RB cord-272759-dqkjofw2 395 14 0.18 0.18 CD cord-272759-dqkjofw2 395 15 , , , cord-272759-dqkjofw2 395 16 while while IN cord-272759-dqkjofw2 395 17 the the DT cord-272759-dqkjofw2 395 18 probability probability NN cord-272759-dqkjofw2 395 19 of of IN cord-272759-dqkjofw2 395 20 infecting infect VBG cord-272759-dqkjofw2 395 21 more more JJR cord-272759-dqkjofw2 395 22 than than IN cord-272759-dqkjofw2 395 23 1000 1000 CD cord-272759-dqkjofw2 395 24 was be VBD cord-272759-dqkjofw2 395 25 0.27 0.27 CD cord-272759-dqkjofw2 395 26 . . . cord-272759-dqkjofw2 396 1 One one PRP cord-272759-dqkjofw2 396 2 can can MD cord-272759-dqkjofw2 396 3 see see VB cord-272759-dqkjofw2 396 4 that that IN cord-272759-dqkjofw2 396 5 , , , cord-272759-dqkjofw2 396 6 with with IN cord-272759-dqkjofw2 396 7 respect respect NN cord-272759-dqkjofw2 396 8 to to IN cord-272759-dqkjofw2 396 9 these these DT cord-272759-dqkjofw2 396 10 gross gross JJ cord-272759-dqkjofw2 396 11 statistics statistic NNS cord-272759-dqkjofw2 396 12 , , , cord-272759-dqkjofw2 396 13 the the DT cord-272759-dqkjofw2 396 14 true true JJ cord-272759-dqkjofw2 396 15 situation situation NN cord-272759-dqkjofw2 396 16 for for IN cord-272759-dqkjofw2 396 17 Hong Hong NNP cord-272759-dqkjofw2 396 18 Kong Kong NNP cord-272759-dqkjofw2 396 19 ( ( -LRB- cord-272759-dqkjofw2 396 20 1755 1755 CD cord-272759-dqkjofw2 396 21 casualties casualty NNS cord-272759-dqkjofw2 396 22 ) ) -RRB- cord-272759-dqkjofw2 396 23 is be VBZ cord-272759-dqkjofw2 396 24 quite quite RB cord-272759-dqkjofw2 396 25 typical typical JJ cord-272759-dqkjofw2 396 26 . . . cord-272759-dqkjofw2 397 1 12 12 CD cord-272759-dqkjofw2 398 1 It -PRON- PRP cord-272759-dqkjofw2 398 2 is be VBZ cord-272759-dqkjofw2 398 3 interesting interesting JJ cord-272759-dqkjofw2 398 4 to to TO cord-272759-dqkjofw2 398 5 note note VB cord-272759-dqkjofw2 398 6 , , , cord-272759-dqkjofw2 398 7 however however RB cord-272759-dqkjofw2 398 8 , , , cord-272759-dqkjofw2 398 9 that that IN cord-272759-dqkjofw2 398 10 there there EX cord-272759-dqkjofw2 398 11 is be VBZ cord-272759-dqkjofw2 398 12 a a DT cord-272759-dqkjofw2 398 13 large large JJ cord-272759-dqkjofw2 398 14 variation variation NN cord-272759-dqkjofw2 398 15 in in IN cord-272759-dqkjofw2 398 16 the the DT cord-272759-dqkjofw2 398 17 number number NN cord-272759-dqkjofw2 398 18 of of IN cord-272759-dqkjofw2 398 19 casualties casualty NNS cord-272759-dqkjofw2 398 20 . . . cord-272759-dqkjofw2 399 1 In in IN cord-272759-dqkjofw2 399 2 all all DT cord-272759-dqkjofw2 399 3 cases case NNS cord-272759-dqkjofw2 399 4 , , , cord-272759-dqkjofw2 399 5 the the DT cord-272759-dqkjofw2 399 6 parameter parameter NN cord-272759-dqkjofw2 399 7 values value NNS cord-272759-dqkjofw2 399 8 of of IN cord-272759-dqkjofw2 399 9 Fig Fig NNP cord-272759-dqkjofw2 399 10 . . . cord-272759-dqkjofw2 399 11 8 8 CD cord-272759-dqkjofw2 399 12 provided provide VBD cord-272759-dqkjofw2 399 13 effective effective JJ cord-272759-dqkjofw2 399 14 control control NN cord-272759-dqkjofw2 399 15 of of IN cord-272759-dqkjofw2 399 16 SARS SARS NNP cord-272759-dqkjofw2 399 17 transmission transmission NN cord-272759-dqkjofw2 399 18 after after IN cord-272759-dqkjofw2 399 19 approximately approximately RB cord-272759-dqkjofw2 399 20 150 150 CD cord-272759-dqkjofw2 399 21 days day NNS cord-272759-dqkjofw2 399 22 . . . cord-272759-dqkjofw2 400 1 From from IN cord-272759-dqkjofw2 400 2 these these DT cord-272759-dqkjofw2 400 3 simulations simulation NNS cord-272759-dqkjofw2 400 4 , , , cord-272759-dqkjofw2 400 5 we -PRON- PRP cord-272759-dqkjofw2 400 6 therefore therefore RB cord-272759-dqkjofw2 400 7 conclude conclude VBP cord-272759-dqkjofw2 400 8 that that IN cord-272759-dqkjofw2 400 9 , , , cord-272759-dqkjofw2 400 10 with with IN cord-272759-dqkjofw2 400 11 effective effective JJ cord-272759-dqkjofw2 400 12 control control NN cord-272759-dqkjofw2 400 13 measures measure NNS cord-272759-dqkjofw2 400 14 in in IN cord-272759-dqkjofw2 400 15 place place NN cord-272759-dqkjofw2 400 16 , , , cord-272759-dqkjofw2 400 17 the the DT cord-272759-dqkjofw2 400 18 likelihood likelihood NN cord-272759-dqkjofw2 400 19 of of IN cord-272759-dqkjofw2 400 20 a a DT cord-272759-dqkjofw2 400 21 significant significant JJ cord-272759-dqkjofw2 400 22 outbreak outbreak NN cord-272759-dqkjofw2 400 23 is be VBZ cord-272759-dqkjofw2 400 24 low low JJ cord-272759-dqkjofw2 400 25 . . . cord-272759-dqkjofw2 401 1 12 12 CD cord-272759-dqkjofw2 402 1 From from IN cord-272759-dqkjofw2 402 2 1000 1000 CD cord-272759-dqkjofw2 402 3 simulations simulation NNS cord-272759-dqkjofw2 402 4 , , , cord-272759-dqkjofw2 402 5 106 106 CD cord-272759-dqkjofw2 402 6 exhibited exhibit VBD cord-272759-dqkjofw2 402 7 a a DT cord-272759-dqkjofw2 402 8 larger large JJR cord-272759-dqkjofw2 402 9 number number NN cord-272759-dqkjofw2 402 10 of of IN cord-272759-dqkjofw2 402 11 casualties casualty NNS cord-272759-dqkjofw2 402 12 . . . cord-272759-dqkjofw2 403 1 We -PRON- PRP cord-272759-dqkjofw2 403 2 summarise summarise VBP cord-272759-dqkjofw2 403 3 the the DT cord-272759-dqkjofw2 403 4 main main JJ cord-272759-dqkjofw2 403 5 results result NNS cord-272759-dqkjofw2 403 6 of of IN cord-272759-dqkjofw2 403 7 the the DT cord-272759-dqkjofw2 403 8 preceding precede VBG cord-272759-dqkjofw2 403 9 sections section NNS cord-272759-dqkjofw2 403 10 as as IN cord-272759-dqkjofw2 403 11 follows follow VBZ cord-272759-dqkjofw2 403 12 . . . cord-272759-dqkjofw2 404 1 • • NNP cord-272759-dqkjofw2 405 1 The the DT cord-272759-dqkjofw2 405 2 probability probability NN cord-272759-dqkjofw2 405 3 of of IN cord-272759-dqkjofw2 405 4 the the DT cord-272759-dqkjofw2 405 5 disease disease NN cord-272759-dqkjofw2 405 6 spread spread VBD cord-272759-dqkjofw2 405 7 being be VBG cord-272759-dqkjofw2 405 8 controlled control VBN cord-272759-dqkjofw2 405 9 , , , cord-272759-dqkjofw2 405 10 P p NN cord-272759-dqkjofw2 405 11 safe safe JJ cord-272759-dqkjofw2 405 12 , , , cord-272759-dqkjofw2 405 13 is be VBZ cord-272759-dqkjofw2 405 14 approximately approximately RB cord-272759-dqkjofw2 406 1 • • NNP cord-272759-dqkjofw2 407 1 The the DT cord-272759-dqkjofw2 407 2 epidemic epidemic NN cord-272759-dqkjofw2 407 3 is be VBZ cord-272759-dqkjofw2 407 4 under under IN cord-272759-dqkjofw2 407 5 control control NN cord-272759-dqkjofw2 407 6 if if IN cord-272759-dqkjofw2 407 7 n n NN cord-272759-dqkjofw2 407 8 k k NNP cord-272759-dqkjofw2 407 9 = = SYM cord-272759-dqkjofw2 407 10 n n NN cord-272759-dqkjofw2 407 11 1 1 CD cord-272759-dqkjofw2 407 12 kp kp NNP cord-272759-dqkjofw2 407 13 1 1 CD cord-272759-dqkjofw2 407 14 + + SYM cord-272759-dqkjofw2 407 15 µp µp NN cord-272759-dqkjofw2 407 16 2 2 CD cord-272759-dqkjofw2 408 1 < < XX cord-272759-dqkjofw2 408 2 r r NNP cord-272759-dqkjofw2 408 3 1 1 CD cord-272759-dqkjofw2 408 4 ( ( -LRB- cord-272759-dqkjofw2 408 5 Section section NN cord-272759-dqkjofw2 408 6 2.2 2.2 CD cord-272759-dqkjofw2 408 7 ) ) -RRB- cord-272759-dqkjofw2 408 8 . . . cord-272759-dqkjofw2 409 1 • • NNP cord-272759-dqkjofw2 410 1 For for IN cord-272759-dqkjofw2 410 2 the the DT cord-272759-dqkjofw2 410 3 endemic endemic JJ cord-272759-dqkjofw2 410 4 case case NN cord-272759-dqkjofw2 410 5 , , , cord-272759-dqkjofw2 410 6 the the DT cord-272759-dqkjofw2 410 7 rate rate NN cord-272759-dqkjofw2 410 8 of of IN cord-272759-dqkjofw2 410 9 growth growth NN cord-272759-dqkjofw2 410 10 of of IN cord-272759-dqkjofw2 410 11 infection infection NN cord-272759-dqkjofw2 410 12 is be VBZ cord-272759-dqkjofw2 410 13 • • NNP cord-272759-dqkjofw2 411 1 This this DT cord-272759-dqkjofw2 411 2 model model NN cord-272759-dqkjofw2 411 3 exhibits exhibit VBZ cord-272759-dqkjofw2 411 4 behaviour behaviour NN cord-272759-dqkjofw2 411 5 consistent consistent JJ cord-272759-dqkjofw2 411 6 with with IN cord-272759-dqkjofw2 411 7 both both CC cord-272759-dqkjofw2 411 8 SSEs sse NNS cord-272759-dqkjofw2 411 9 and and CC cord-272759-dqkjofw2 411 10 persistent persistent JJ cord-272759-dqkjofw2 411 11 localised localised JJ cord-272759-dqkjofw2 411 12 transmission transmission NN cord-272759-dqkjofw2 411 13 ( ( -LRB- cord-272759-dqkjofw2 411 14 Section section NN cord-272759-dqkjofw2 411 15 3.4 3.4 CD cord-272759-dqkjofw2 411 16 ) ) -RRB- cord-272759-dqkjofw2 411 17 . . . cord-272759-dqkjofw2 412 1 More more RBR cord-272759-dqkjofw2 412 2 extreme extreme JJ cord-272759-dqkjofw2 412 3 SSEs sse NNS cord-272759-dqkjofw2 412 4 can can MD cord-272759-dqkjofw2 412 5 be be VB cord-272759-dqkjofw2 412 6 observed observe VBN cord-272759-dqkjofw2 412 7 simply simply RB cord-272759-dqkjofw2 412 8 by by IN cord-272759-dqkjofw2 412 9 fattening fatten VBG cord-272759-dqkjofw2 412 10 the the DT cord-272759-dqkjofw2 412 11 tail tail NN cord-272759-dqkjofw2 412 12 of of IN cord-272759-dqkjofw2 412 13 the the DT cord-272759-dqkjofw2 412 14 distribution distribution NN cord-272759-dqkjofw2 412 15 of of IN cord-272759-dqkjofw2 412 16 links link NNS cord-272759-dqkjofw2 412 17 . . . cord-272759-dqkjofw2 413 1 By by IN cord-272759-dqkjofw2 413 2 assigning assign VBG cord-272759-dqkjofw2 413 3 a a DT cord-272759-dqkjofw2 413 4 power power NN cord-272759-dqkjofw2 413 5 - - HYPH cord-272759-dqkjofw2 413 6 law law NN cord-272759-dqkjofw2 413 7 distribution distribution NN cord-272759-dqkjofw2 413 8 to to IN cord-272759-dqkjofw2 413 9 the the DT cord-272759-dqkjofw2 413 10 number number NN cord-272759-dqkjofw2 413 11 of of IN cord-272759-dqkjofw2 413 12 nonlocal nonlocal JJ cord-272759-dqkjofw2 413 13 links link NNS cord-272759-dqkjofw2 413 14 that that WDT cord-272759-dqkjofw2 413 15 a a DT cord-272759-dqkjofw2 413 16 node node NN cord-272759-dqkjofw2 413 17 has have VBZ cord-272759-dqkjofw2 413 18 , , , cord-272759-dqkjofw2 413 19 one one PRP cord-272759-dqkjofw2 413 20 can can MD cord-272759-dqkjofw2 413 21 readily readily RB cord-272759-dqkjofw2 413 22 obtain obtain VB cord-272759-dqkjofw2 413 23 SSE SSE NNP cord-272759-dqkjofw2 413 24 involving involve VBG cord-272759-dqkjofw2 413 25 many many JJ cord-272759-dqkjofw2 413 26 hundreds hundred NNS cord-272759-dqkjofw2 413 27 of of IN cord-272759-dqkjofw2 413 28 secondary secondary JJ cord-272759-dqkjofw2 413 29 infections infection NNS cord-272759-dqkjofw2 413 30 from from IN cord-272759-dqkjofw2 413 31 a a DT cord-272759-dqkjofw2 413 32 single single JJ cord-272759-dqkjofw2 413 33 source source NN cord-272759-dqkjofw2 413 34 . . . cord-272759-dqkjofw2 414 1 • • NNP cord-272759-dqkjofw2 415 1 An an DT cord-272759-dqkjofw2 415 2 SSE SSE NNP cord-272759-dqkjofw2 415 3 does do VBZ cord-272759-dqkjofw2 415 4 not not RB cord-272759-dqkjofw2 415 5 imply imply VB cord-272759-dqkjofw2 415 6 highly highly RB cord-272759-dqkjofw2 415 7 infectious infectious JJ cord-272759-dqkjofw2 415 8 individuals individual NNS cord-272759-dqkjofw2 415 9 , , , cord-272759-dqkjofw2 415 10 only only RB cord-272759-dqkjofw2 415 11 highly highly RB cord-272759-dqkjofw2 415 12 connected connect VBN cord-272759-dqkjofw2 415 13 ones one NNS cord-272759-dqkjofw2 415 14 ( ( -LRB- cord-272759-dqkjofw2 415 15 Section section NN cord-272759-dqkjofw2 415 16 3.4 3.4 CD cord-272759-dqkjofw2 415 17 ) ) -RRB- cord-272759-dqkjofw2 415 18 . . . cord-272759-dqkjofw2 416 1 • • NNP cord-272759-dqkjofw2 417 1 Theoretical theoretical JJ cord-272759-dqkjofw2 417 2 results result NNS cord-272759-dqkjofw2 417 3 and and CC cord-272759-dqkjofw2 417 4 model model NN cord-272759-dqkjofw2 417 5 simulations simulation NNS cord-272759-dqkjofw2 417 6 are be VBP cord-272759-dqkjofw2 417 7 unlike unlike IN cord-272759-dqkjofw2 417 8 the the DT cord-272759-dqkjofw2 417 9 true true JJ cord-272759-dqkjofw2 417 10 data datum NNS cord-272759-dqkjofw2 417 11 , , , cord-272759-dqkjofw2 417 12 unless unless IN cord-272759-dqkjofw2 417 13 exposure exposure NN cord-272759-dqkjofw2 417 14 time time NN cord-272759-dqkjofw2 417 15 is be VBZ cord-272759-dqkjofw2 417 16 significantly significantly RB cord-272759-dqkjofw2 417 17 greater great JJR cord-272759-dqkjofw2 417 18 than than IN cord-272759-dqkjofw2 417 19 an an DT cord-272759-dqkjofw2 417 20 average average NN cord-272759-dqkjofw2 417 21 of of IN cord-272759-dqkjofw2 417 22 three three CD cord-272759-dqkjofw2 417 23 days day NNS cord-272759-dqkjofw2 417 24 ( ( -LRB- cord-272759-dqkjofw2 417 25 Sections section NNS cord-272759-dqkjofw2 417 26 2.2 2.2 CD cord-272759-dqkjofw2 417 27 and and CC cord-272759-dqkjofw2 417 28 3.3 3.3 CD cord-272759-dqkjofw2 417 29 ) ) -RRB- cord-272759-dqkjofw2 417 30 . . . cord-272759-dqkjofw2 418 1 If if IN cord-272759-dqkjofw2 418 2 the the DT cord-272759-dqkjofw2 418 3 exposure exposure NN cord-272759-dqkjofw2 418 4 time time NN cord-272759-dqkjofw2 418 5 is be VBZ cord-272759-dqkjofw2 418 6 three three CD cord-272759-dqkjofw2 418 7 days day NNS cord-272759-dqkjofw2 418 8 or or CC cord-272759-dqkjofw2 418 9 less less JJR cord-272759-dqkjofw2 418 10 , , , cord-272759-dqkjofw2 418 11 the the DT cord-272759-dqkjofw2 418 12 rate rate NN cord-272759-dqkjofw2 418 13 of of IN cord-272759-dqkjofw2 418 14 growth growth NN cord-272759-dqkjofw2 418 15 of of IN cord-272759-dqkjofw2 418 16 the the DT cord-272759-dqkjofw2 418 17 epidemic epidemic NN cord-272759-dqkjofw2 418 18 is be VBZ cord-272759-dqkjofw2 418 19 significantly significantly RB cord-272759-dqkjofw2 418 20 lower low JJR cord-272759-dqkjofw2 418 21 than than IN cord-272759-dqkjofw2 418 22 that that DT cord-272759-dqkjofw2 418 23 observed observe VBD cord-272759-dqkjofw2 418 24 in in IN cord-272759-dqkjofw2 418 25 the the DT cord-272759-dqkjofw2 418 26 true true JJ cord-272759-dqkjofw2 418 27 data datum NNS cord-272759-dqkjofw2 418 28 . . . cord-272759-dqkjofw2 419 1 • • NNP cord-272759-dqkjofw2 420 1 Nosocomial nosocomial JJ cord-272759-dqkjofw2 420 2 transmission transmission NN cord-272759-dqkjofw2 420 3 was be VBD cord-272759-dqkjofw2 420 4 therefore therefore RB cord-272759-dqkjofw2 420 5 a a DT cord-272759-dqkjofw2 420 6 key key JJ cord-272759-dqkjofw2 420 7 factor factor NN cord-272759-dqkjofw2 420 8 in in IN cord-272759-dqkjofw2 420 9 the the DT cord-272759-dqkjofw2 420 10 acuteness acuteness NN cord-272759-dqkjofw2 420 11 of of IN cord-272759-dqkjofw2 420 12 the the DT cord-272759-dqkjofw2 420 13 SARS SARS NNP cord-272759-dqkjofw2 420 14 epidemic epidemic NN cord-272759-dqkjofw2 420 15 in in IN cord-272759-dqkjofw2 420 16 Hong Hong NNP cord-272759-dqkjofw2 420 17 Kong Kong NNP cord-272759-dqkjofw2 420 18 in in IN cord-272759-dqkjofw2 420 19 2003 2003 CD cord-272759-dqkjofw2 420 20 . . . cord-272759-dqkjofw2 421 1 Effective effective JJ cord-272759-dqkjofw2 421 2 control control NN cord-272759-dqkjofw2 421 3 of of IN cord-272759-dqkjofw2 421 4 hospital hospital NN cord-272759-dqkjofw2 421 5 transmissions transmission NNS cord-272759-dqkjofw2 421 6 would would MD cord-272759-dqkjofw2 421 7 have have VB cord-272759-dqkjofw2 421 8 prevented prevent VBN cord-272759-dqkjofw2 421 9 a a DT cord-272759-dqkjofw2 421 10 serious serious JJ cord-272759-dqkjofw2 421 11 outbreak outbreak NN cord-272759-dqkjofw2 421 12 ( ( -LRB- cord-272759-dqkjofw2 421 13 Section section NN cord-272759-dqkjofw2 421 14 3.3 3.3 CD cord-272759-dqkjofw2 421 15 ) ) -RRB- cord-272759-dqkjofw2 421 16 . . . cord-272759-dqkjofw2 422 1 With with IN cord-272759-dqkjofw2 422 2 respect respect NN cord-272759-dqkjofw2 422 3 to to IN cord-272759-dqkjofw2 422 4 nosocomial nosocomial JJ cord-272759-dqkjofw2 422 5 transmission transmission NN cord-272759-dqkjofw2 422 6 , , , cord-272759-dqkjofw2 422 7 our -PRON- PRP$ cord-272759-dqkjofw2 422 8 model model NN cord-272759-dqkjofw2 422 9 therefore therefore RB cord-272759-dqkjofw2 422 10 confirms confirm VBZ cord-272759-dqkjofw2 422 11 what what WP cord-272759-dqkjofw2 422 12 has have VBZ cord-272759-dqkjofw2 422 13 been be VBN cord-272759-dqkjofw2 422 14 observed observe VBN cord-272759-dqkjofw2 422 15 independently independently RB cord-272759-dqkjofw2 422 16 , , , cord-272759-dqkjofw2 422 17 and and CC cord-272759-dqkjofw2 422 18 suggested suggest VBN cord-272759-dqkjofw2 422 19 by by IN cord-272759-dqkjofw2 422 20 many many JJ cord-272759-dqkjofw2 422 21 authors author NNS cord-272759-dqkjofw2 422 22 . . . cord-272759-dqkjofw2 423 1 • • NNP cord-272759-dqkjofw2 423 2 Simulations simulation NNS cord-272759-dqkjofw2 423 3 of of IN cord-272759-dqkjofw2 423 4 our -PRON- PRP$ cord-272759-dqkjofw2 423 5 model model NN cord-272759-dqkjofw2 423 6 , , , cord-272759-dqkjofw2 423 7 with with IN cord-272759-dqkjofw2 423 8 minimal minimal JJ cord-272759-dqkjofw2 423 9 parameter parameter NN cord-272759-dqkjofw2 423 10 variation variation NN cord-272759-dqkjofw2 423 11 , , , cord-272759-dqkjofw2 423 12 produced produce VBN cord-272759-dqkjofw2 423 13 dynamics dynamic NNS cord-272759-dqkjofw2 423 14 indistinguishable indistinguishable JJ cord-272759-dqkjofw2 423 15 from from IN cord-272759-dqkjofw2 423 16 the the DT cord-272759-dqkjofw2 423 17 true true JJ cord-272759-dqkjofw2 423 18 data datum NNS cord-272759-dqkjofw2 423 19 . . . cord-272759-dqkjofw2 424 1 These these DT cord-272759-dqkjofw2 424 2 same same JJ cord-272759-dqkjofw2 424 3 parameter parameter NN cord-272759-dqkjofw2 424 4 values value NNS cord-272759-dqkjofw2 424 5 exhibit exhibit VBP cord-272759-dqkjofw2 424 6 a a DT cord-272759-dqkjofw2 424 7 wide wide JJ cord-272759-dqkjofw2 424 8 variety variety NN cord-272759-dqkjofw2 424 9 of of IN cord-272759-dqkjofw2 424 10 behaviours behaviour NNS cord-272759-dqkjofw2 424 11 ( ( -LRB- cord-272759-dqkjofw2 424 12 Section section NN cord-272759-dqkjofw2 424 13 3.5 3.5 CD cord-272759-dqkjofw2 424 14 ) ) -RRB- cord-272759-dqkjofw2 424 15 . . . cord-272759-dqkjofw2 425 1 Hence hence RB cord-272759-dqkjofw2 425 2 , , , cord-272759-dqkjofw2 425 3 any any DT cord-272759-dqkjofw2 425 4 effort effort NN cord-272759-dqkjofw2 425 5 to to TO cord-272759-dqkjofw2 425 6 actually actually RB cord-272759-dqkjofw2 425 7 obtain obtain VB cord-272759-dqkjofw2 425 8 maximum maximum JJ cord-272759-dqkjofw2 425 9 likelihood likelihood NN cord-272759-dqkjofw2 425 10 parameter parameter NN cord-272759-dqkjofw2 425 11 estimates estimate NNS cord-272759-dqkjofw2 425 12 from from IN cord-272759-dqkjofw2 425 13 the the DT cord-272759-dqkjofw2 425 14 observed observed JJ cord-272759-dqkjofw2 425 15 data data NN cord-272759-dqkjofw2 425 16 is be VBZ cord-272759-dqkjofw2 425 17 futile futile JJ cord-272759-dqkjofw2 425 18 . . . cord-272759-dqkjofw2 426 1 Despite despite IN cord-272759-dqkjofw2 426 2 this this DT cord-272759-dqkjofw2 426 3 , , , cord-272759-dqkjofw2 426 4 our -PRON- PRP$ cord-272759-dqkjofw2 426 5 calculations calculation NNS cord-272759-dqkjofw2 426 6 show show VBP cord-272759-dqkjofw2 426 7 that that IN cord-272759-dqkjofw2 426 8 the the DT cord-272759-dqkjofw2 426 9 true true JJ cord-272759-dqkjofw2 426 10 data data NN cord-272759-dqkjofw2 426 11 is be VBZ cord-272759-dqkjofw2 426 12 certainly certainly RB cord-272759-dqkjofw2 426 13 typical typical JJ cord-272759-dqkjofw2 426 14 of of IN cord-272759-dqkjofw2 426 15 our -PRON- PRP$ cord-272759-dqkjofw2 426 16 models model NNS cord-272759-dqkjofw2 426 17 . . . cord-272759-dqkjofw2 427 1 Moreover moreover RB cord-272759-dqkjofw2 427 2 , , , cord-272759-dqkjofw2 427 3 our -PRON- PRP$ cord-272759-dqkjofw2 427 4 models model NNS cord-272759-dqkjofw2 427 5 exhibit exhibit VBP cord-272759-dqkjofw2 427 6 a a DT cord-272759-dqkjofw2 427 7 marked marked JJ cord-272759-dqkjofw2 427 8 long long JJ cord-272759-dqkjofw2 427 9 - - HYPH cord-272759-dqkjofw2 427 10 tailedness tailedness NN cord-272759-dqkjofw2 427 11 both both DT cord-272759-dqkjofw2 427 12 in in IN cord-272759-dqkjofw2 427 13 infection infection NN cord-272759-dqkjofw2 427 14 times time NNS cord-272759-dqkjofw2 427 15 and and CC cord-272759-dqkjofw2 427 16 epidemic epidemic NN cord-272759-dqkjofw2 427 17 lifetimes lifetime NNS cord-272759-dqkjofw2 427 18 . . . cord-272759-dqkjofw2 428 1 • • NNP cord-272759-dqkjofw2 429 1 The the DT cord-272759-dqkjofw2 429 2 likelihood likelihood NN cord-272759-dqkjofw2 429 3 of of IN cord-272759-dqkjofw2 429 4 infecting infect VBG cord-272759-dqkjofw2 429 5 fewer few JJR cord-272759-dqkjofw2 429 6 than than IN cord-272759-dqkjofw2 429 7 20 20 CD cord-272759-dqkjofw2 429 8 people people NNS cord-272759-dqkjofw2 429 9 was be VBD cord-272759-dqkjofw2 429 10 approximately approximately RB cord-272759-dqkjofw2 429 11 0.18 0.18 CD cord-272759-dqkjofw2 429 12 , , , cord-272759-dqkjofw2 429 13 and and CC cord-272759-dqkjofw2 429 14 the the DT cord-272759-dqkjofw2 429 15 likelihood likelihood NN cord-272759-dqkjofw2 429 16 of of IN cord-272759-dqkjofw2 429 17 infecting infect VBG cord-272759-dqkjofw2 429 18 more more JJR cord-272759-dqkjofw2 429 19 than than IN cord-272759-dqkjofw2 429 20 1000 1000 CD cord-272759-dqkjofw2 429 21 was be VBD cord-272759-dqkjofw2 429 22 0.27 0.27 CD cord-272759-dqkjofw2 429 23 ( ( -LRB- cord-272759-dqkjofw2 429 24 Section section NN cord-272759-dqkjofw2 429 25 3.5 3.5 CD cord-272759-dqkjofw2 429 26 ) ) -RRB- cord-272759-dqkjofw2 429 27 . . . cord-272759-dqkjofw2 430 1 Apart apart RB cord-272759-dqkjofw2 430 2 from from IN cord-272759-dqkjofw2 430 3 deriving derive VBG cord-272759-dqkjofw2 430 4 analytic analytic JJ cord-272759-dqkjofw2 430 5 expression expression NN cord-272759-dqkjofw2 430 6 for for IN cord-272759-dqkjofw2 430 7 the the DT cord-272759-dqkjofw2 430 8 spreading spreading NN cord-272759-dqkjofw2 430 9 and and CC cord-272759-dqkjofw2 430 10 control control NN cord-272759-dqkjofw2 430 11 of of IN cord-272759-dqkjofw2 430 12 an an DT cord-272759-dqkjofw2 430 13 epidemic epidemic NN cord-272759-dqkjofw2 430 14 , , , cord-272759-dqkjofw2 430 15 the the DT cord-272759-dqkjofw2 430 16 main main JJ cord-272759-dqkjofw2 430 17 results result NNS cord-272759-dqkjofw2 430 18 of of IN cord-272759-dqkjofw2 430 19 this this DT cord-272759-dqkjofw2 430 20 study study NN cord-272759-dqkjofw2 430 21 , , , cord-272759-dqkjofw2 430 22 when when WRB cord-272759-dqkjofw2 430 23 applied apply VBN cord-272759-dqkjofw2 430 24 to to IN cord-272759-dqkjofw2 430 25 the the DT cord-272759-dqkjofw2 430 26 SARS SARS NNP cord-272759-dqkjofw2 430 27 epidemic epidemic NN cord-272759-dqkjofw2 430 28 in in IN cord-272759-dqkjofw2 430 29 Hong Hong NNP cord-272759-dqkjofw2 430 30 Kong Kong NNP cord-272759-dqkjofw2 430 31 in in IN cord-272759-dqkjofw2 430 32 2003 2003 CD cord-272759-dqkjofw2 430 33 , , , cord-272759-dqkjofw2 430 34 is be VBZ cord-272759-dqkjofw2 430 35 that that IN cord-272759-dqkjofw2 430 36 our -PRON- PRP$ cord-272759-dqkjofw2 430 37 data data NN cord-272759-dqkjofw2 430 38 is be VBZ cord-272759-dqkjofw2 430 39 consistent consistent JJ cord-272759-dqkjofw2 430 40 with with IN cord-272759-dqkjofw2 430 41 the the DT cord-272759-dqkjofw2 430 42 observation observation NN cord-272759-dqkjofw2 430 43 that that IN cord-272759-dqkjofw2 430 44 the the DT cord-272759-dqkjofw2 430 45 epidemic epidemic NN cord-272759-dqkjofw2 430 46 that that WDT cord-272759-dqkjofw2 430 47 occurred occur VBD cord-272759-dqkjofw2 430 48 was be VBD cord-272759-dqkjofw2 430 49 largely largely RB cord-272759-dqkjofw2 430 50 preventable preventable JJ cord-272759-dqkjofw2 430 51 . . . cord-272759-dqkjofw2 431 1 The the DT cord-272759-dqkjofw2 431 2 primary primary JJ cord-272759-dqkjofw2 431 3 factor factor NN cord-272759-dqkjofw2 431 4 for for IN cord-272759-dqkjofw2 431 5 the the DT cord-272759-dqkjofw2 431 6 severity severity NN cord-272759-dqkjofw2 431 7 of of IN cord-272759-dqkjofw2 431 8 the the DT cord-272759-dqkjofw2 431 9 outbreak outbreak NN cord-272759-dqkjofw2 431 10 was be VBD cord-272759-dqkjofw2 431 11 poor poor JJ cord-272759-dqkjofw2 431 12 infection infection NN cord-272759-dqkjofw2 431 13 control control NN cord-272759-dqkjofw2 431 14 in in IN cord-272759-dqkjofw2 431 15 the the DT cord-272759-dqkjofw2 431 16 hospital hospital NN cord-272759-dqkjofw2 431 17 setting setting NN cord-272759-dqkjofw2 431 18 and and CC cord-272759-dqkjofw2 431 19 the the DT cord-272759-dqkjofw2 431 20 delayed delay VBN cord-272759-dqkjofw2 431 21 introduction introduction NN cord-272759-dqkjofw2 431 22 of of IN cord-272759-dqkjofw2 431 23 quarantine quarantine NN cord-272759-dqkjofw2 431 24 and and CC cord-272759-dqkjofw2 431 25 community community NN cord-272759-dqkjofw2 431 26 isolation isolation NN cord-272759-dqkjofw2 431 27 practices practice NNS cord-272759-dqkjofw2 431 28 . . . cord-272759-dqkjofw2 432 1 This this DT cord-272759-dqkjofw2 432 2 is be VBZ cord-272759-dqkjofw2 432 3 consistent consistent JJ cord-272759-dqkjofw2 432 4 with with IN cord-272759-dqkjofw2 432 5 various various JJ cord-272759-dqkjofw2 432 6 discussions discussion NNS cord-272759-dqkjofw2 432 7 presented present VBN cord-272759-dqkjofw2 432 8 elsewhere elsewhere RB cord-272759-dqkjofw2 432 9 . . . cord-272759-dqkjofw2 433 1 However however RB cord-272759-dqkjofw2 433 2 , , , cord-272759-dqkjofw2 433 3 we -PRON- PRP cord-272759-dqkjofw2 433 4 note note VBP cord-272759-dqkjofw2 433 5 that that IN cord-272759-dqkjofw2 433 6 nosocomial nosocomial JJ cord-272759-dqkjofw2 433 7 transmission transmission NN cord-272759-dqkjofw2 433 8 was be VBD cord-272759-dqkjofw2 433 9 considered consider VBN cord-272759-dqkjofw2 433 10 only only RB cord-272759-dqkjofw2 433 11 by by IN cord-272759-dqkjofw2 433 12 supposing suppose VBG cord-272759-dqkjofw2 433 13 ( ( -LRB- cord-272759-dqkjofw2 433 14 admittedly admittedly RB cord-272759-dqkjofw2 433 15 erroneously erroneously RB cord-272759-dqkjofw2 433 16 ) ) -RRB- cord-272759-dqkjofw2 433 17 that that IN cord-272759-dqkjofw2 433 18 the the DT cord-272759-dqkjofw2 433 19 time time NN cord-272759-dqkjofw2 433 20 between between IN cord-272759-dqkjofw2 433 21 becoming become VBG cord-272759-dqkjofw2 433 22 symptomatic symptomatic JJ cord-272759-dqkjofw2 433 23 ( ( -LRB- cord-272759-dqkjofw2 433 24 and and CC cord-272759-dqkjofw2 433 25 infectious infectious JJ cord-272759-dqkjofw2 433 26 ) ) -RRB- cord-272759-dqkjofw2 433 27 and and CC cord-272759-dqkjofw2 433 28 hospitalisation hospitalisation NN cord-272759-dqkjofw2 433 29 is be VBZ cord-272759-dqkjofw2 433 30 constant constant JJ cord-272759-dqkjofw2 433 31 . . . cord-272759-dqkjofw2 434 1 Nosocomial nosocomial JJ cord-272759-dqkjofw2 434 2 transmission transmission NN cord-272759-dqkjofw2 434 3 is be VBZ cord-272759-dqkjofw2 434 4 simulated simulate VBN cord-272759-dqkjofw2 434 5 by by IN cord-272759-dqkjofw2 434 6 changing change VBG cord-272759-dqkjofw2 434 7 the the DT cord-272759-dqkjofw2 434 8 expected expect VBN cord-272759-dqkjofw2 434 9 duration duration NN cord-272759-dqkjofw2 434 10 between between IN cord-272759-dqkjofw2 434 11 becoming become VBG cord-272759-dqkjofw2 434 12 symptomatic symptomatic JJ cord-272759-dqkjofw2 434 13 ( ( -LRB- cord-272759-dqkjofw2 434 14 I i NN cord-272759-dqkjofw2 434 15 ) ) -RRB- cord-272759-dqkjofw2 434 16 and and CC cord-272759-dqkjofw2 434 17 becoming become VBG cord-272759-dqkjofw2 434 18 removed remove VBN cord-272759-dqkjofw2 434 19 ( ( -LRB- cord-272759-dqkjofw2 434 20 R r NN cord-272759-dqkjofw2 434 21 ) ) -RRB- cord-272759-dqkjofw2 434 22 . . . cord-272759-dqkjofw2 435 1 Although although IN cord-272759-dqkjofw2 435 2 this this DT cord-272759-dqkjofw2 435 3 is be VBZ cord-272759-dqkjofw2 435 4 perhaps perhaps RB cord-272759-dqkjofw2 435 5 unconventional unconventional JJ cord-272759-dqkjofw2 435 6 from from IN cord-272759-dqkjofw2 435 7 an an DT cord-272759-dqkjofw2 435 8 epidemiological epidemiological JJ cord-272759-dqkjofw2 435 9 viewpoint viewpoint NN cord-272759-dqkjofw2 435 10 , , , cord-272759-dqkjofw2 435 11 it -PRON- PRP cord-272759-dqkjofw2 435 12 is be VBZ cord-272759-dqkjofw2 435 13 probably probably RB cord-272759-dqkjofw2 435 14 the the DT cord-272759-dqkjofw2 435 15 best good JJS cord-272759-dqkjofw2 435 16 that that IN cord-272759-dqkjofw2 435 17 we -PRON- PRP cord-272759-dqkjofw2 435 18 can can MD cord-272759-dqkjofw2 435 19 do do VB cord-272759-dqkjofw2 435 20 , , , cord-272759-dqkjofw2 435 21 as as IN cord-272759-dqkjofw2 435 22 the the DT cord-272759-dqkjofw2 435 23 only only JJ cord-272759-dqkjofw2 435 24 data datum NNS cord-272759-dqkjofw2 435 25 that that WDT cord-272759-dqkjofw2 435 26 we -PRON- PRP cord-272759-dqkjofw2 435 27 have have VBP cord-272759-dqkjofw2 435 28 to to TO cord-272759-dqkjofw2 435 29 work work VB cord-272759-dqkjofw2 435 30 from from IN cord-272759-dqkjofw2 435 31 is be VBZ cord-272759-dqkjofw2 435 32 the the DT cord-272759-dqkjofw2 435 33 date date NN cord-272759-dqkjofw2 435 34 of of IN cord-272759-dqkjofw2 435 35 hospital hospital NN cord-272759-dqkjofw2 435 36 admission admission NN cord-272759-dqkjofw2 435 37 . . . cord-272759-dqkjofw2 436 1 This this DT cord-272759-dqkjofw2 436 2 conclusion conclusion NN cord-272759-dqkjofw2 436 3 is be VBZ cord-272759-dqkjofw2 436 4 in in IN cord-272759-dqkjofw2 436 5 contrast contrast NN cord-272759-dqkjofw2 436 6 with with IN cord-272759-dqkjofw2 436 7 work work NN cord-272759-dqkjofw2 436 8 done do VBN cord-272759-dqkjofw2 436 9 by by IN cord-272759-dqkjofw2 436 10 Pastor Pastor NNP cord-272759-dqkjofw2 436 11 - - HYPH cord-272759-dqkjofw2 436 12 Satorras Satorras NNP cord-272759-dqkjofw2 436 13 and and CC cord-272759-dqkjofw2 436 14 colleagues colleague NNS cord-272759-dqkjofw2 436 15 [ [ -LRB- cord-272759-dqkjofw2 436 16 20 20 CD cord-272759-dqkjofw2 436 17 , , , cord-272759-dqkjofw2 436 18 21 21 CD cord-272759-dqkjofw2 436 19 ] ] -RRB- cord-272759-dqkjofw2 436 20 with with IN cord-272759-dqkjofw2 436 21 scale scale NN cord-272759-dqkjofw2 436 22 - - HYPH cord-272759-dqkjofw2 436 23 free free JJ cord-272759-dqkjofw2 436 24 SIS SIS NNP cord-272759-dqkjofw2 436 25 type type NN cord-272759-dqkjofw2 436 26 [ [ -LRB- cord-272759-dqkjofw2 436 27 7 7 CD cord-272759-dqkjofw2 436 28 ] ] -RRB- cord-272759-dqkjofw2 436 29 disease disease NN cord-272759-dqkjofw2 436 30 models model NNS cord-272759-dqkjofw2 436 31 . . . cord-272759-dqkjofw2 437 1 In in IN cord-272759-dqkjofw2 437 2 that that DT cord-272759-dqkjofw2 437 3 case case NN cord-272759-dqkjofw2 437 4 , , , cord-272759-dqkjofw2 437 5 they -PRON- PRP cord-272759-dqkjofw2 437 6 found find VBD cord-272759-dqkjofw2 437 7 that that IN cord-272759-dqkjofw2 437 8 the the DT cord-272759-dqkjofw2 437 9 disease disease NN cord-272759-dqkjofw2 437 10 would would MD cord-272759-dqkjofw2 437 11 almost almost RB cord-272759-dqkjofw2 437 12 always always RB cord-272759-dqkjofw2 437 13 persist persist VB cord-272759-dqkjofw2 437 14 and and CC cord-272759-dqkjofw2 437 15 that that IN cord-272759-dqkjofw2 437 16 random random JJ cord-272759-dqkjofw2 437 17 immunisation immunisation NN cord-272759-dqkjofw2 437 18 was be VBD cord-272759-dqkjofw2 437 19 ineffective ineffective JJ cord-272759-dqkjofw2 437 20 [ [ -LRB- cord-272759-dqkjofw2 437 21 21 21 CD cord-272759-dqkjofw2 437 22 ] ] -RRB- cord-272759-dqkjofw2 437 23 . . . cord-272759-dqkjofw2 438 1 The the DT cord-272759-dqkjofw2 438 2 model model NN cord-272759-dqkjofw2 438 3 presented present VBN cord-272759-dqkjofw2 438 4 here here RB cord-272759-dqkjofw2 438 5 emphasised emphasise VBD cord-272759-dqkjofw2 438 6 the the DT cord-272759-dqkjofw2 438 7 small small JJ cord-272759-dqkjofw2 438 8 - - HYPH cord-272759-dqkjofw2 438 9 world world NN cord-272759-dqkjofw2 438 10 transmission transmission NN cord-272759-dqkjofw2 438 11 dynamics dynamic NNS cord-272759-dqkjofw2 438 12 created create VBN cord-272759-dqkjofw2 438 13 by by IN cord-272759-dqkjofw2 438 14 providing provide VBG cord-272759-dqkjofw2 438 15 a a DT cord-272759-dqkjofw2 438 16 small small JJ cord-272759-dqkjofw2 438 17 number number NN cord-272759-dqkjofw2 438 18 of of IN cord-272759-dqkjofw2 438 19 highly highly RB cord-272759-dqkjofw2 438 20 connected connect VBN cord-272759-dqkjofw2 438 21 nodes node NNS cord-272759-dqkjofw2 438 22 . . . cord-272759-dqkjofw2 439 1 We -PRON- PRP cord-272759-dqkjofw2 439 2 model model VBP cord-272759-dqkjofw2 439 3 the the DT cord-272759-dqkjofw2 439 4 inter inter JJ cord-272759-dqkjofw2 439 5 - - JJ cord-272759-dqkjofw2 439 6 connection connection NN cord-272759-dqkjofw2 439 7 between between IN cord-272759-dqkjofw2 439 8 nodes node NNS cord-272759-dqkjofw2 439 9 with with IN cord-272759-dqkjofw2 439 10 one one CD cord-272759-dqkjofw2 439 11 - - HYPH cord-272759-dqkjofw2 439 12 directional directional JJ cord-272759-dqkjofw2 439 13 links link NNS cord-272759-dqkjofw2 439 14 ( ( -LRB- cord-272759-dqkjofw2 439 15 rather rather RB cord-272759-dqkjofw2 439 16 than than IN cord-272759-dqkjofw2 439 17 the the DT cord-272759-dqkjofw2 439 18 bi bi JJ cord-272759-dqkjofw2 439 19 - - JJ cord-272759-dqkjofw2 439 20 directional directional JJ cord-272759-dqkjofw2 439 21 links link NNS cord-272759-dqkjofw2 439 22 we -PRON- PRP cord-272759-dqkjofw2 439 23 would would MD cord-272759-dqkjofw2 439 24 expect expect VB cord-272759-dqkjofw2 439 25 for for IN cord-272759-dqkjofw2 439 26 social social JJ cord-272759-dqkjofw2 439 27 contacts contact NNS cord-272759-dqkjofw2 439 28 ) ) -RRB- cord-272759-dqkjofw2 439 29 because because IN cord-272759-dqkjofw2 439 30 this this DT cord-272759-dqkjofw2 439 31 makes make VBZ cord-272759-dqkjofw2 439 32 the the DT cord-272759-dqkjofw2 439 33 network network NN cord-272759-dqkjofw2 439 34 much much RB cord-272759-dqkjofw2 439 35 easier easy JJR cord-272759-dqkjofw2 439 36 to to TO cord-272759-dqkjofw2 439 37 construct construct VB cord-272759-dqkjofw2 439 38 , , , cord-272759-dqkjofw2 439 39 without without IN cord-272759-dqkjofw2 439 40 sacrificing sacrifice VBG cord-272759-dqkjofw2 439 41 any any DT cord-272759-dqkjofw2 439 42 realism realism NN cord-272759-dqkjofw2 439 43 . . . cord-272759-dqkjofw2 440 1 This this DT cord-272759-dqkjofw2 440 2 model model NN cord-272759-dqkjofw2 440 3 could could MD cord-272759-dqkjofw2 440 4 easily easily RB cord-272759-dqkjofw2 440 5 be be VB cord-272759-dqkjofw2 440 6 extended extend VBN cord-272759-dqkjofw2 440 7 to to TO cord-272759-dqkjofw2 440 8 exhibit exhibit VB cord-272759-dqkjofw2 440 9 scale scale NN cord-272759-dqkjofw2 440 10 - - HYPH cord-272759-dqkjofw2 440 11 free free JJ cord-272759-dqkjofw2 440 12 characteristics characteristic NNS cord-272759-dqkjofw2 440 13 , , , cord-272759-dqkjofw2 440 14 by by IN cord-272759-dqkjofw2 440 15 simply simply RB cord-272759-dqkjofw2 440 16 altering alter VBG cord-272759-dqkjofw2 440 17 the the DT cord-272759-dqkjofw2 440 18 distribution distribution NN cord-272759-dqkjofw2 440 19 of of IN cord-272759-dqkjofw2 440 20 non non JJ cord-272759-dqkjofw2 440 21 - - JJ cord-272759-dqkjofw2 440 22 local local JJ cord-272759-dqkjofw2 440 23 links link NNS cord-272759-dqkjofw2 440 24 ( ( -LRB- cord-272759-dqkjofw2 440 25 to to TO cord-272759-dqkjofw2 440 26 follow follow VB cord-272759-dqkjofw2 440 27 a a DT cord-272759-dqkjofw2 440 28 power power NN cord-272759-dqkjofw2 440 29 - - HYPH cord-272759-dqkjofw2 440 30 law law NN cord-272759-dqkjofw2 440 31 distribution distribution NN cord-272759-dqkjofw2 440 32 ) ) -RRB- cord-272759-dqkjofw2 440 33 . . . cord-272759-dqkjofw2 441 1 Doing do VBG cord-272759-dqkjofw2 441 2 so so RB cord-272759-dqkjofw2 441 3 would would MD cord-272759-dqkjofw2 441 4 produce produce VB cord-272759-dqkjofw2 441 5 simulations simulation NNS cord-272759-dqkjofw2 441 6 with with IN cord-272759-dqkjofw2 441 7 a a DT cord-272759-dqkjofw2 441 8 larger large JJR cord-272759-dqkjofw2 441 9 number number NN cord-272759-dqkjofw2 441 10 of of IN cord-272759-dqkjofw2 441 11 highly highly RB cord-272759-dqkjofw2 441 12 connected connect VBN cord-272759-dqkjofw2 441 13 individuals individual NNS cord-272759-dqkjofw2 441 14 , , , cord-272759-dqkjofw2 441 15 and and CC cord-272759-dqkjofw2 441 16 therefore therefore RB cord-272759-dqkjofw2 441 17 we -PRON- PRP cord-272759-dqkjofw2 441 18 could could MD cord-272759-dqkjofw2 441 19 simulate simulate VB cord-272759-dqkjofw2 441 20 the the DT cord-272759-dqkjofw2 441 21 largest large JJS cord-272759-dqkjofw2 441 22 SSEs sse NNS cord-272759-dqkjofw2 441 23 in in IN cord-272759-dqkjofw2 441 24 the the DT cord-272759-dqkjofw2 441 25 data datum NNS cord-272759-dqkjofw2 441 26 . . . cord-272759-dqkjofw2 442 1 The the DT cord-272759-dqkjofw2 442 2 results result NNS cord-272759-dqkjofw2 442 3 presented present VBN cord-272759-dqkjofw2 442 4 in in IN cord-272759-dqkjofw2 442 5 this this DT cord-272759-dqkjofw2 442 6 paper paper NN cord-272759-dqkjofw2 442 7 show show VBP cord-272759-dqkjofw2 442 8 small small JJ cord-272759-dqkjofw2 442 9 ( ( -LRB- cord-272759-dqkjofw2 442 10 less less JJR cord-272759-dqkjofw2 442 11 than than IN cord-272759-dqkjofw2 442 12 100 100 CD cord-272759-dqkjofw2 442 13 individuals individual NNS cord-272759-dqkjofw2 442 14 ) ) -RRB- cord-272759-dqkjofw2 442 15 SSEs SSEs NNP cord-272759-dqkjofw2 442 16 ; ; : cord-272759-dqkjofw2 442 17 extension extension NN cord-272759-dqkjofw2 442 18 to to IN cord-272759-dqkjofw2 442 19 the the DT cord-272759-dqkjofw2 442 20 power power NN cord-272759-dqkjofw2 442 21 - - HYPH cord-272759-dqkjofw2 442 22 law law NN cord-272759-dqkjofw2 442 23 distribution distribution NN cord-272759-dqkjofw2 442 24 would would MD cord-272759-dqkjofw2 442 25 provide provide VB cord-272759-dqkjofw2 442 26 SSEs sse NNS cord-272759-dqkjofw2 442 27 with with IN cord-272759-dqkjofw2 442 28 a a DT cord-272759-dqkjofw2 442 29 larger large JJR cord-272759-dqkjofw2 442 30 number number NN cord-272759-dqkjofw2 442 31 of of IN cord-272759-dqkjofw2 442 32 secondary secondary JJ cord-272759-dqkjofw2 442 33 infections infection NNS cord-272759-dqkjofw2 442 34 . . . cord-272759-dqkjofw2 443 1 We -PRON- PRP cord-272759-dqkjofw2 443 2 should should MD cord-272759-dqkjofw2 443 3 note note VB cord-272759-dqkjofw2 443 4 that that IN cord-272759-dqkjofw2 443 5 it -PRON- PRP cord-272759-dqkjofw2 443 6 is be VBZ cord-272759-dqkjofw2 443 7 very very RB cord-272759-dqkjofw2 443 8 difficult difficult JJ cord-272759-dqkjofw2 443 9 to to TO cord-272759-dqkjofw2 443 10 reliably reliably RB cord-272759-dqkjofw2 443 11 and and CC cord-272759-dqkjofw2 443 12 accurately accurately RB cord-272759-dqkjofw2 443 13 fit fit VB cord-272759-dqkjofw2 443 14 even even RB cord-272759-dqkjofw2 443 15 a a DT cord-272759-dqkjofw2 443 16 moderate moderate JJ cord-272759-dqkjofw2 443 17 number number NN cord-272759-dqkjofw2 443 18 of of IN cord-272759-dqkjofw2 443 19 parameters parameter NNS cord-272759-dqkjofw2 443 20 to to IN cord-272759-dqkjofw2 443 21 a a DT cord-272759-dqkjofw2 443 22 stochastic stochastic JJ cord-272759-dqkjofw2 443 23 model model NN cord-272759-dqkjofw2 443 24 from from IN cord-272759-dqkjofw2 443 25 such such JJ cord-272759-dqkjofw2 443 26 limited limited JJ cord-272759-dqkjofw2 443 27 data datum NNS cord-272759-dqkjofw2 443 28 . . . cord-272759-dqkjofw2 444 1 Especially especially RB cord-272759-dqkjofw2 444 2 when when WRB cord-272759-dqkjofw2 444 3 the the DT cord-272759-dqkjofw2 444 4 model model NN cord-272759-dqkjofw2 444 5 , , , cord-272759-dqkjofw2 444 6 for for IN cord-272759-dqkjofw2 444 7 the the DT cord-272759-dqkjofw2 444 8 same same JJ cord-272759-dqkjofw2 444 9 parameter parameter NN cord-272759-dqkjofw2 444 10 values value NNS cord-272759-dqkjofw2 444 11 , , , cord-272759-dqkjofw2 444 12 can can MD cord-272759-dqkjofw2 444 13 exhibit exhibit VB cord-272759-dqkjofw2 444 14 a a DT cord-272759-dqkjofw2 444 15 wide wide JJ cord-272759-dqkjofw2 444 16 variety variety NN cord-272759-dqkjofw2 444 17 of of IN cord-272759-dqkjofw2 444 18 behaviour behaviour NN cord-272759-dqkjofw2 444 19 . . . cord-272759-dqkjofw2 445 1 To to TO cord-272759-dqkjofw2 445 2 overcome overcome VB cord-272759-dqkjofw2 445 3 this this DT cord-272759-dqkjofw2 445 4 , , , cord-272759-dqkjofw2 445 5 we -PRON- PRP cord-272759-dqkjofw2 445 6 ( ( -LRB- cord-272759-dqkjofw2 445 7 a a LS cord-272759-dqkjofw2 445 8 ) ) -RRB- cord-272759-dqkjofw2 445 9 make make VB cord-272759-dqkjofw2 445 10 our -PRON- PRP$ cord-272759-dqkjofw2 445 11 model model NN cord-272759-dqkjofw2 445 12 so so RB cord-272759-dqkjofw2 445 13 simple simple JJ cord-272759-dqkjofw2 445 14 that that IN cord-272759-dqkjofw2 445 15 the the DT cord-272759-dqkjofw2 445 16 number number NN cord-272759-dqkjofw2 445 17 of of IN cord-272759-dqkjofw2 445 18 parameters parameter NNS cord-272759-dqkjofw2 445 19 is be VBZ cord-272759-dqkjofw2 445 20 very very RB cord-272759-dqkjofw2 445 21 few few JJ cord-272759-dqkjofw2 445 22 ( ( -LRB- cord-272759-dqkjofw2 445 23 certainly certainly RB cord-272759-dqkjofw2 445 24 comparable comparable JJ cord-272759-dqkjofw2 445 25 in in IN cord-272759-dqkjofw2 445 26 number number NN cord-272759-dqkjofw2 445 27 to to IN cord-272759-dqkjofw2 445 28 ordinary ordinary JJ cord-272759-dqkjofw2 445 29 SIR SIR NNP cord-272759-dqkjofw2 445 30 ) ) -RRB- cord-272759-dqkjofw2 445 31 , , , cord-272759-dqkjofw2 445 32 and and CC cord-272759-dqkjofw2 445 33 ( ( -LRB- cord-272759-dqkjofw2 445 34 b b LS cord-272759-dqkjofw2 445 35 ) ) -RRB- cord-272759-dqkjofw2 445 36 only only RB cord-272759-dqkjofw2 445 37 " " `` cord-272759-dqkjofw2 445 38 fit fit JJ cord-272759-dqkjofw2 445 39 " " '' cord-272759-dqkjofw2 445 40 the the DT cord-272759-dqkjofw2 445 41 model model NN cord-272759-dqkjofw2 445 42 with with IN cord-272759-dqkjofw2 445 43 typical typical JJ cord-272759-dqkjofw2 445 44 parameter parameter NN cord-272759-dqkjofw2 445 45 values value NNS cord-272759-dqkjofw2 445 46 and and CC cord-272759-dqkjofw2 445 47 test test VBP cord-272759-dqkjofw2 445 48 that that DT cord-272759-dqkjofw2 445 49 , , , cord-272759-dqkjofw2 445 50 for for IN cord-272759-dqkjofw2 445 51 these these DT cord-272759-dqkjofw2 445 52 parameter parameter NN cord-272759-dqkjofw2 445 53 values value NNS cord-272759-dqkjofw2 445 54 , , , cord-272759-dqkjofw2 445 55 the the DT cord-272759-dqkjofw2 445 56 observed observed JJ cord-272759-dqkjofw2 445 57 data data NN cord-272759-dqkjofw2 445 58 is be VBZ cord-272759-dqkjofw2 445 59 typical typical JJ cord-272759-dqkjofw2 445 60 . . . cord-272759-dqkjofw2 446 1 Certainly certainly RB cord-272759-dqkjofw2 446 2 , , , cord-272759-dqkjofw2 446 3 we -PRON- PRP cord-272759-dqkjofw2 446 4 can can MD cord-272759-dqkjofw2 446 5 not not RB cord-272759-dqkjofw2 446 6 exclude exclude VB cord-272759-dqkjofw2 446 7 the the DT cord-272759-dqkjofw2 446 8 ( ( -LRB- cord-272759-dqkjofw2 446 9 quite quite RB cord-272759-dqkjofw2 446 10 likely likely JJ cord-272759-dqkjofw2 446 11 ) ) -RRB- cord-272759-dqkjofw2 446 12 probability probability NN cord-272759-dqkjofw2 446 13 that that WDT cord-272759-dqkjofw2 446 14 other other JJ cord-272759-dqkjofw2 446 15 parameter parameter NN cord-272759-dqkjofw2 446 16 values value NNS cord-272759-dqkjofw2 446 17 also also RB cord-272759-dqkjofw2 446 18 produce produce VBP cord-272759-dqkjofw2 446 19 behaviour behaviour NN cord-272759-dqkjofw2 446 20 of of IN cord-272759-dqkjofw2 446 21 which which WDT cord-272759-dqkjofw2 446 22 the the DT cord-272759-dqkjofw2 446 23 observed observed JJ cord-272759-dqkjofw2 446 24 data data NN cord-272759-dqkjofw2 446 25 is be VBZ cord-272759-dqkjofw2 446 26 typical typical JJ cord-272759-dqkjofw2 446 27 . . . cord-272759-dqkjofw2 447 1 Therefore therefore RB cord-272759-dqkjofw2 447 2 , , , cord-272759-dqkjofw2 447 3 in in IN cord-272759-dqkjofw2 447 4 this this DT cord-272759-dqkjofw2 447 5 paper paper NN cord-272759-dqkjofw2 447 6 we -PRON- PRP cord-272759-dqkjofw2 447 7 only only RB cord-272759-dqkjofw2 447 8 draw draw VBP cord-272759-dqkjofw2 447 9 conclusions conclusion NNS cord-272759-dqkjofw2 447 10 based base VBN cord-272759-dqkjofw2 447 11 on on IN cord-272759-dqkjofw2 447 12 our -PRON- PRP$ cord-272759-dqkjofw2 447 13 observations observation NNS cord-272759-dqkjofw2 447 14 of of IN cord-272759-dqkjofw2 447 15 parameters parameter NNS cord-272759-dqkjofw2 447 16 that that WDT cord-272759-dqkjofw2 447 17 produce produce VBP cord-272759-dqkjofw2 447 18 behaviours behaviour NNS cord-272759-dqkjofw2 447 19 that that WDT cord-272759-dqkjofw2 447 20 are be VBP cord-272759-dqkjofw2 447 21 either either CC cord-272759-dqkjofw2 447 22 typical typical JJ cord-272759-dqkjofw2 447 23 or or CC cord-272759-dqkjofw2 447 24 ( ( -LRB- cord-272759-dqkjofw2 447 25 more more RBR cord-272759-dqkjofw2 447 26 importantly importantly RB cord-272759-dqkjofw2 447 27 ) ) -RRB- cord-272759-dqkjofw2 447 28 atypical atypical JJ cord-272759-dqkjofw2 447 29 of of IN cord-272759-dqkjofw2 447 30 the the DT cord-272759-dqkjofw2 447 31 observed observed JJ cord-272759-dqkjofw2 447 32 data datum NNS cord-272759-dqkjofw2 447 33 . . . cord-272759-dqkjofw2 448 1 Although although IN cord-272759-dqkjofw2 448 2 we -PRON- PRP cord-272759-dqkjofw2 448 3 have have VBP cord-272759-dqkjofw2 448 4 observed observe VBN cord-272759-dqkjofw2 448 5 that that IN cord-272759-dqkjofw2 448 6 our -PRON- PRP$ cord-272759-dqkjofw2 448 7 model model NN cord-272759-dqkjofw2 448 8 exhibits exhibit VBZ cord-272759-dqkjofw2 448 9 more more RBR cord-272759-dqkjofw2 448 10 realistic realistic JJ cord-272759-dqkjofw2 448 11 dynamics dynamic NNS cord-272759-dqkjofw2 448 12 than than IN cord-272759-dqkjofw2 448 13 SIR SIR NNP cord-272759-dqkjofw2 448 14 models model NNS cord-272759-dqkjofw2 448 15 , , , cord-272759-dqkjofw2 448 16 it -PRON- PRP cord-272759-dqkjofw2 448 17 is be VBZ cord-272759-dqkjofw2 448 18 only only RB cord-272759-dqkjofw2 448 19 a a DT cord-272759-dqkjofw2 448 20 model model NN cord-272759-dqkjofw2 448 21 . . . cord-272759-dqkjofw2 449 1 And and CC cord-272759-dqkjofw2 449 2 , , , cord-272759-dqkjofw2 449 3 like like IN cord-272759-dqkjofw2 449 4 the the DT cord-272759-dqkjofw2 449 5 SIR SIR NNP cord-272759-dqkjofw2 449 6 model model NN cord-272759-dqkjofw2 449 7 , , , cord-272759-dqkjofw2 449 8 our -PRON- PRP$ cord-272759-dqkjofw2 449 9 model model NN cord-272759-dqkjofw2 449 10 is be VBZ cord-272759-dqkjofw2 449 11 a a DT cord-272759-dqkjofw2 449 12 compromise compromise NN cord-272759-dqkjofw2 449 13 between between IN cord-272759-dqkjofw2 449 14 complexity complexity NN cord-272759-dqkjofw2 449 15 and and CC cord-272759-dqkjofw2 449 16 realism realism NN cord-272759-dqkjofw2 449 17 . . . cord-272759-dqkjofw2 450 1 We -PRON- PRP cord-272759-dqkjofw2 450 2 intend intend VBP cord-272759-dqkjofw2 450 3 to to TO cord-272759-dqkjofw2 450 4 address address VB cord-272759-dqkjofw2 450 5 this this DT cord-272759-dqkjofw2 450 6 problem problem NN cord-272759-dqkjofw2 450 7 in in IN cord-272759-dqkjofw2 450 8 the the DT cord-272759-dqkjofw2 450 9 future future NN cord-272759-dqkjofw2 450 10 by by IN cord-272759-dqkjofw2 450 11 applying apply VBG cord-272759-dqkjofw2 450 12 Monte Monte NNP cord-272759-dqkjofw2 450 13 Carlo Carlo NNP cord-272759-dqkjofw2 450 14 Markov Markov NNP cord-272759-dqkjofw2 450 15 Chain Chain NNP cord-272759-dqkjofw2 450 16 models model NNS cord-272759-dqkjofw2 450 17 [ [ -LRB- cord-272759-dqkjofw2 450 18 22 22 CD cord-272759-dqkjofw2 450 19 ] ] -RRB- cord-272759-dqkjofw2 450 20 to to IN cord-272759-dqkjofw2 450 21 this this DT cord-272759-dqkjofw2 450 22 sparse sparse JJ cord-272759-dqkjofw2 450 23 data datum NNS cord-272759-dqkjofw2 450 24 [ [ -LRB- cord-272759-dqkjofw2 450 25 23 23 CD cord-272759-dqkjofw2 450 26 ] ] -RRB- cord-272759-dqkjofw2 450 27 . . . cord-272759-dqkjofw2 451 1 Even even RB cord-272759-dqkjofw2 451 2 our -PRON- PRP$ cord-272759-dqkjofw2 451 3 choice choice NN cord-272759-dqkjofw2 451 4 of of IN cord-272759-dqkjofw2 451 5 a a DT cord-272759-dqkjofw2 451 6 discrete discrete JJ cord-272759-dqkjofw2 451 7 time time NN cord-272759-dqkjofw2 451 8 model model NN cord-272759-dqkjofw2 451 9 is be VBZ cord-272759-dqkjofw2 451 10 open open JJ cord-272759-dqkjofw2 451 11 to to IN cord-272759-dqkjofw2 451 12 debate debate NN cord-272759-dqkjofw2 451 13 . . . cord-272759-dqkjofw2 452 1 The the DT cord-272759-dqkjofw2 452 2 choice choice NN cord-272759-dqkjofw2 452 3 , , , cord-272759-dqkjofw2 452 4 with with IN cord-272759-dqkjofw2 452 5 a a DT cord-272759-dqkjofw2 452 6 time time NN cord-272759-dqkjofw2 452 7 interval interval NN cord-272759-dqkjofw2 452 8 chosen choose VBN cord-272759-dqkjofw2 452 9 as as IN cord-272759-dqkjofw2 452 10 one one CD cord-272759-dqkjofw2 452 11 day day NN cord-272759-dqkjofw2 452 12 , , , cord-272759-dqkjofw2 452 13 was be VBD cord-272759-dqkjofw2 452 14 motivated motivate VBN cord-272759-dqkjofw2 452 15 by by IN cord-272759-dqkjofw2 452 16 the the DT cord-272759-dqkjofw2 452 17 data datum NNS cord-272759-dqkjofw2 452 18 and and CC cord-272759-dqkjofw2 452 19 what what WP cord-272759-dqkjofw2 452 20 was be VBD cord-272759-dqkjofw2 452 21 more more RBR cord-272759-dqkjofw2 452 22 intuitive intuitive JJ cord-272759-dqkjofw2 452 23 to to IN cord-272759-dqkjofw2 452 24 us -PRON- PRP cord-272759-dqkjofw2 452 25 . . . cord-272759-dqkjofw2 453 1 We -PRON- PRP cord-272759-dqkjofw2 453 2 have have VBP cord-272759-dqkjofw2 453 3 conducted conduct VBN cord-272759-dqkjofw2 453 4 calculations calculation NNS cord-272759-dqkjofw2 453 5 with with IN cord-272759-dqkjofw2 453 6 both both CC cord-272759-dqkjofw2 453 7 longer long JJR cord-272759-dqkjofw2 453 8 and and CC cord-272759-dqkjofw2 453 9 shorter short JJR cord-272759-dqkjofw2 453 10 interinterval interinterval NN cord-272759-dqkjofw2 453 11 time time NN cord-272759-dqkjofw2 453 12 scales scale NNS cord-272759-dqkjofw2 453 13 and and CC cord-272759-dqkjofw2 453 14 find find VB cord-272759-dqkjofw2 453 15 that that IN cord-272759-dqkjofw2 453 16 the the DT cord-272759-dqkjofw2 453 17 results result NNS cord-272759-dqkjofw2 453 18 are be VBP cord-272759-dqkjofw2 453 19 invariant invariant JJ cord-272759-dqkjofw2 453 20 under under IN cord-272759-dqkjofw2 453 21 a a DT cord-272759-dqkjofw2 453 22 suitable suitable JJ cord-272759-dqkjofw2 453 23 change change NN cord-272759-dqkjofw2 453 24 in in IN cord-272759-dqkjofw2 453 25 time time NN cord-272759-dqkjofw2 453 26 scale scale NN cord-272759-dqkjofw2 453 27 ( ( -LRB- cord-272759-dqkjofw2 453 28 i.e. i.e. FW cord-272759-dqkjofw2 453 29 we -PRON- PRP cord-272759-dqkjofw2 453 30 get get VBP cord-272759-dqkjofw2 453 31 equivalent equivalent JJ cord-272759-dqkjofw2 453 32 results result NNS cord-272759-dqkjofw2 453 33 by by IN cord-272759-dqkjofw2 453 34 using use VBG cord-272759-dqkjofw2 453 35 a a DT cord-272759-dqkjofw2 453 36 shorter short JJR cord-272759-dqkjofw2 453 37 time time NN cord-272759-dqkjofw2 453 38 step step NN cord-272759-dqkjofw2 453 39 ) ) -RRB- cord-272759-dqkjofw2 453 40 . . . cord-272759-dqkjofw2 454 1 Moreover moreover RB cord-272759-dqkjofw2 454 2 , , , cord-272759-dqkjofw2 454 3 recent recent JJ cord-272759-dqkjofw2 454 4 epidemiological epidemiological JJ cord-272759-dqkjofw2 454 5 case case NN cord-272759-dqkjofw2 454 6 studies study NNS cord-272759-dqkjofw2 454 7 have have VBP cord-272759-dqkjofw2 454 8 found find VBN cord-272759-dqkjofw2 454 9 that that IN cord-272759-dqkjofw2 454 10 , , , cord-272759-dqkjofw2 454 11 overall overall RB cord-272759-dqkjofw2 454 12 , , , cord-272759-dqkjofw2 454 13 in in IN cord-272759-dqkjofw2 454 14 Hong Hong NNP cord-272759-dqkjofw2 454 15 Kong Kong NNP cord-272759-dqkjofw2 454 16 8 8 CD cord-272759-dqkjofw2 454 17 % % NN cord-272759-dqkjofw2 454 18 of of IN cord-272759-dqkjofw2 454 19 individuals individual NNS cord-272759-dqkjofw2 454 20 sharing share VBG cord-272759-dqkjofw2 454 21 a a DT cord-272759-dqkjofw2 454 22 flat flat NN cord-272759-dqkjofw2 454 23 with with IN cord-272759-dqkjofw2 454 24 a a DT cord-272759-dqkjofw2 454 25 SARS SARS NNP cord-272759-dqkjofw2 454 26 patient patient NN cord-272759-dqkjofw2 454 27 contracted contract VBN cord-272759-dqkjofw2 454 28 SARS SARS NNP cord-272759-dqkjofw2 454 29 [ [ -LRB- cord-272759-dqkjofw2 454 30 24 24 CD cord-272759-dqkjofw2 454 31 ] ] -RRB- cord-272759-dqkjofw2 454 32 . . . cord-272759-dqkjofw2 455 1 Given give VBN cord-272759-dqkjofw2 455 2 an an DT cord-272759-dqkjofw2 455 3 average average JJ cord-272759-dqkjofw2 455 4 infectious infectious JJ cord-272759-dqkjofw2 455 5 period period NN cord-272759-dqkjofw2 455 6 of of IN cord-272759-dqkjofw2 455 7 four four CD cord-272759-dqkjofw2 455 8 days day NNS cord-272759-dqkjofw2 455 9 ( ( -LRB- cord-272759-dqkjofw2 455 10 prior prior RB cord-272759-dqkjofw2 455 11 to to IN cord-272759-dqkjofw2 455 12 hospitalisation hospitalisation NN cord-272759-dqkjofw2 455 13 ) ) -RRB- cord-272759-dqkjofw2 455 14 , , , cord-272759-dqkjofw2 455 15 this this DT cord-272759-dqkjofw2 455 16 implies imply VBZ cord-272759-dqkjofw2 455 17 that that IN cord-272759-dqkjofw2 455 18 the the DT cord-272759-dqkjofw2 455 19 daily daily JJ cord-272759-dqkjofw2 455 20 probability probability NN cord-272759-dqkjofw2 455 21 of of IN cord-272759-dqkjofw2 455 22 transmission transmission NN cord-272759-dqkjofw2 455 23 is be VBZ cord-272759-dqkjofw2 455 24 0.02 0.02 CD cord-272759-dqkjofw2 455 25 . . . cord-272759-dqkjofw2 456 1 This this DT cord-272759-dqkjofw2 456 2 is be VBZ cord-272759-dqkjofw2 456 3 approximately approximately RB cord-272759-dqkjofw2 456 4 consistent consistent JJ cord-272759-dqkjofw2 456 5 with with IN cord-272759-dqkjofw2 456 6 the the DT cord-272759-dqkjofw2 456 7 values value NNS cord-272759-dqkjofw2 456 8 of of IN cord-272759-dqkjofw2 456 9 p p NN cord-272759-dqkjofw2 456 10 1 1 CD cord-272759-dqkjofw2 456 11 used use VBN cord-272759-dqkjofw2 456 12 in in IN cord-272759-dqkjofw2 456 13 this this DT cord-272759-dqkjofw2 456 14 study study NN cord-272759-dqkjofw2 456 15 , , , cord-272759-dqkjofw2 456 16 and and CC cord-272759-dqkjofw2 456 17 therefore therefore RB cord-272759-dqkjofw2 456 18 provides provide VBZ cord-272759-dqkjofw2 456 19 further further JJ cord-272759-dqkjofw2 456 20 support support NN cord-272759-dqkjofw2 456 21 of of IN cord-272759-dqkjofw2 456 22 our -PRON- PRP$ cord-272759-dqkjofw2 456 23 results result NNS cord-272759-dqkjofw2 456 24 . . . cord-272759-dqkjofw2 457 1 Conversely conversely RB cord-272759-dqkjofw2 457 2 , , , cord-272759-dqkjofw2 457 3 analysis analysis NN cord-272759-dqkjofw2 457 4 of of IN cord-272759-dqkjofw2 457 5 the the DT cord-272759-dqkjofw2 457 6 SSE SSE NNP cord-272759-dqkjofw2 457 7 at at IN cord-272759-dqkjofw2 457 8 the the DT cord-272759-dqkjofw2 457 9 Prince Prince NNP cord-272759-dqkjofw2 457 10 of of IN cord-272759-dqkjofw2 457 11 Wales Wales NNP cord-272759-dqkjofw2 457 12 Hospital Hospital NNP cord-272759-dqkjofw2 457 13 found find VBD cord-272759-dqkjofw2 457 14 that that IN cord-272759-dqkjofw2 457 15 , , , cord-272759-dqkjofw2 457 16 for for IN cord-272759-dqkjofw2 457 17 a a DT cord-272759-dqkjofw2 457 18 group group NN cord-272759-dqkjofw2 457 19 of of IN cord-272759-dqkjofw2 457 20 medical medical JJ cord-272759-dqkjofw2 457 21 students student NNS cord-272759-dqkjofw2 457 22 , , , cord-272759-dqkjofw2 457 23 the the DT cord-272759-dqkjofw2 457 24 probability probability NN cord-272759-dqkjofw2 457 25 of of IN cord-272759-dqkjofw2 457 26 direct direct JJ cord-272759-dqkjofw2 457 27 contact contact NN cord-272759-dqkjofw2 457 28 with with IN cord-272759-dqkjofw2 457 29 the the DT cord-272759-dqkjofw2 457 30 index index NN cord-272759-dqkjofw2 457 31 patient patient NN cord-272759-dqkjofw2 457 32 leading lead VBG cord-272759-dqkjofw2 457 33 to to IN cord-272759-dqkjofw2 457 34 SARS SARS NNP cord-272759-dqkjofw2 457 35 infection infection NN cord-272759-dqkjofw2 457 36 was be VBD cord-272759-dqkjofw2 457 37 10 10 CD cord-272759-dqkjofw2 457 38 27 27 CD cord-272759-dqkjofw2 457 39 [ [ -LRB- cord-272759-dqkjofw2 457 40 5 5 CD cord-272759-dqkjofw2 457 41 ] ] -RRB- cord-272759-dqkjofw2 457 42 . . . cord-272759-dqkjofw2 458 1 As as IN cord-272759-dqkjofw2 458 2 this this DT cord-272759-dqkjofw2 458 3 study study NN cord-272759-dqkjofw2 458 4 dealt deal VBD cord-272759-dqkjofw2 458 5 with with IN cord-272759-dqkjofw2 458 6 a a DT cord-272759-dqkjofw2 458 7 single single JJ cord-272759-dqkjofw2 458 8 meeting meeting NN cord-272759-dqkjofw2 458 9 , , , cord-272759-dqkjofw2 458 10 this this DT cord-272759-dqkjofw2 458 11 implies imply VBZ cord-272759-dqkjofw2 458 12 a a DT cord-272759-dqkjofw2 458 13 daily daily JJ cord-272759-dqkjofw2 458 14 infection infection NN cord-272759-dqkjofw2 458 15 probability probability NN cord-272759-dqkjofw2 458 16 of of IN cord-272759-dqkjofw2 458 17 approximately approximately RB cord-272759-dqkjofw2 458 18 0.371 0.371 CD cord-272759-dqkjofw2 458 19 : : : cord-272759-dqkjofw2 458 20 significantly significantly RB cord-272759-dqkjofw2 458 21 higher high JJR cord-272759-dqkjofw2 458 22 than than IN cord-272759-dqkjofw2 458 23 p p NN cord-272759-dqkjofw2 458 24 2 2 CD cord-272759-dqkjofw2 458 25 in in IN cord-272759-dqkjofw2 458 26 our -PRON- PRP$ cord-272759-dqkjofw2 458 27 simulations simulation NNS cord-272759-dqkjofw2 458 28 . . . cord-272759-dqkjofw2 459 1 Hence hence RB cord-272759-dqkjofw2 459 2 , , , cord-272759-dqkjofw2 459 3 although although IN cord-272759-dqkjofw2 459 4 we -PRON- PRP cord-272759-dqkjofw2 459 5 have have VBP cord-272759-dqkjofw2 459 6 concluded conclude VBN cord-272759-dqkjofw2 459 7 that that IN cord-272759-dqkjofw2 459 8 SSEs sse NNS cord-272759-dqkjofw2 459 9 may may MD cord-272759-dqkjofw2 459 10 occur occur VB cord-272759-dqkjofw2 459 11 without without IN cord-272759-dqkjofw2 459 12 individuals individual NNS cord-272759-dqkjofw2 459 13 necessarily necessarily RB cord-272759-dqkjofw2 459 14 being be VBG cord-272759-dqkjofw2 459 15 highly highly RB cord-272759-dqkjofw2 459 16 infectious infectious JJ cord-272759-dqkjofw2 459 17 , , , cord-272759-dqkjofw2 459 18 epidemiological epidemiological JJ cord-272759-dqkjofw2 459 19 evidence evidence NN cord-272759-dqkjofw2 459 20 suggests suggest VBZ cord-272759-dqkjofw2 459 21 that that IN cord-272759-dqkjofw2 459 22 , , , cord-272759-dqkjofw2 459 23 in in IN cord-272759-dqkjofw2 459 24 some some DT cord-272759-dqkjofw2 459 25 cases case NNS cord-272759-dqkjofw2 459 26 , , , cord-272759-dqkjofw2 459 27 this this DT cord-272759-dqkjofw2 459 28 may may MD cord-272759-dqkjofw2 459 29 still still RB cord-272759-dqkjofw2 459 30 be be VB cord-272759-dqkjofw2 459 31 the the DT cord-272759-dqkjofw2 459 32 case case NN cord-272759-dqkjofw2 459 33 . . . cord-272759-dqkjofw2 460 1 Finally finally RB cord-272759-dqkjofw2 460 2 , , , cord-272759-dqkjofw2 460 3 we -PRON- PRP cord-272759-dqkjofw2 460 4 note note VBP cord-272759-dqkjofw2 460 5 that that IN cord-272759-dqkjofw2 460 6 , , , cord-272759-dqkjofw2 460 7 although although IN cord-272759-dqkjofw2 460 8 the the DT cord-272759-dqkjofw2 460 9 methods method NNS cord-272759-dqkjofw2 460 10 presented present VBN cord-272759-dqkjofw2 460 11 here here RB cord-272759-dqkjofw2 460 12 are be VBP cord-272759-dqkjofw2 460 13 applied apply VBN cord-272759-dqkjofw2 460 14 only only RB cord-272759-dqkjofw2 460 15 to to IN cord-272759-dqkjofw2 460 16 the the DT cord-272759-dqkjofw2 460 17 SARS SARS NNP cord-272759-dqkjofw2 460 18 outbreak outbreak NN cord-272759-dqkjofw2 460 19 in in IN cord-272759-dqkjofw2 460 20 Hong Hong NNP cord-272759-dqkjofw2 460 21 Kong Kong NNP cord-272759-dqkjofw2 460 22 in in IN cord-272759-dqkjofw2 460 23 2003 2003 CD cord-272759-dqkjofw2 460 24 , , , cord-272759-dqkjofw2 460 25 these these DT cord-272759-dqkjofw2 460 26 methods method NNS cord-272759-dqkjofw2 460 27 are be VBP cord-272759-dqkjofw2 460 28 not not RB cord-272759-dqkjofw2 460 29 limited limited JJ cord-272759-dqkjofw2 460 30 to to IN cord-272759-dqkjofw2 460 31 this this DT cord-272759-dqkjofw2 460 32 situation situation NN cord-272759-dqkjofw2 460 33 . . . cord-272759-dqkjofw2 461 1 Apart apart RB cord-272759-dqkjofw2 461 2 from from IN cord-272759-dqkjofw2 461 3 repeating repeat VBG cord-272759-dqkjofw2 461 4 , , , cord-272759-dqkjofw2 461 5 or or CC cord-272759-dqkjofw2 461 6 modifying modify VBG cord-272759-dqkjofw2 461 7 , , , cord-272759-dqkjofw2 461 8 this this DT cord-272759-dqkjofw2 461 9 analysis analysis NN cord-272759-dqkjofw2 461 10 for for IN cord-272759-dqkjofw2 461 11 different different JJ cord-272759-dqkjofw2 461 12 infectious infectious JJ cord-272759-dqkjofw2 461 13 diseases disease NNS cord-272759-dqkjofw2 461 14 ( ( -LRB- cord-272759-dqkjofw2 461 15 such such JJ cord-272759-dqkjofw2 461 16 as as IN cord-272759-dqkjofw2 461 17 HIV HIV NNP cord-272759-dqkjofw2 461 18 AIDS AIDS NNP cord-272759-dqkjofw2 461 19 ) ) -RRB- cord-272759-dqkjofw2 461 20 , , , cord-272759-dqkjofw2 461 21 we -PRON- PRP cord-272759-dqkjofw2 461 22 imagine imagine VBP cord-272759-dqkjofw2 461 23 that that IN cord-272759-dqkjofw2 461 24 these these DT cord-272759-dqkjofw2 461 25 techniques technique NNS cord-272759-dqkjofw2 461 26 could could MD cord-272759-dqkjofw2 461 27 be be VB cord-272759-dqkjofw2 461 28 useful useful JJ cord-272759-dqkjofw2 461 29 in in IN cord-272759-dqkjofw2 461 30 the the DT cord-272759-dqkjofw2 461 31 theoretical theoretical JJ cord-272759-dqkjofw2 461 32 study study NN cord-272759-dqkjofw2 461 33 of of IN cord-272759-dqkjofw2 461 34 quarantine quarantine NN cord-272759-dqkjofw2 461 35 and and CC cord-272759-dqkjofw2 461 36 isolation isolation NN cord-272759-dqkjofw2 461 37 practices practice NNS cord-272759-dqkjofw2 461 38 , , , cord-272759-dqkjofw2 461 39 as as RB cord-272759-dqkjofw2 461 40 well well RB cord-272759-dqkjofw2 461 41 as as IN cord-272759-dqkjofw2 461 42 disease disease NN cord-272759-dqkjofw2 461 43 transmission transmission NN cord-272759-dqkjofw2 461 44 among among IN cord-272759-dqkjofw2 461 45 isolated isolate VBN cord-272759-dqkjofw2 461 46 communities community NNS cord-272759-dqkjofw2 461 47 . . . cord-272759-dqkjofw2 462 1 Quarantine quarantine NN cord-272759-dqkjofw2 462 2 can can MD cord-272759-dqkjofw2 462 3 be be VB cord-272759-dqkjofw2 462 4 effectively effectively RB cord-272759-dqkjofw2 462 5 modelled model VBN cord-272759-dqkjofw2 462 6 as as IN cord-272759-dqkjofw2 462 7 a a DT cord-272759-dqkjofw2 462 8 limitation limitation NN cord-272759-dqkjofw2 462 9 of of IN cord-272759-dqkjofw2 462 10 long long JJ cord-272759-dqkjofw2 462 11 range range NN cord-272759-dqkjofw2 462 12 transmission transmission NN cord-272759-dqkjofw2 462 13 . . . cord-272759-dqkjofw2 463 1 One one PRP cord-272759-dqkjofw2 463 2 can can MD cord-272759-dqkjofw2 463 3 easily easily RB cord-272759-dqkjofw2 463 4 model model VB cord-272759-dqkjofw2 463 5 change change NN cord-272759-dqkjofw2 463 6 in in IN cord-272759-dqkjofw2 463 7 quarantine quarantine NN cord-272759-dqkjofw2 463 8 by by IN cord-272759-dqkjofw2 463 9 varying vary VBG cord-272759-dqkjofw2 463 10 the the DT cord-272759-dqkjofw2 463 11 parameter parameter NN cord-272759-dqkjofw2 463 12 µ µ NN cord-272759-dqkjofw2 463 13 ( ( -LRB- cord-272759-dqkjofw2 463 14 or or CC cord-272759-dqkjofw2 463 15 alternatively alternatively RB cord-272759-dqkjofw2 463 16 , , , cord-272759-dqkjofw2 463 17 but but CC cord-272759-dqkjofw2 463 18 not not RB cord-272759-dqkjofw2 463 19 equivalently equivalently RB cord-272759-dqkjofw2 463 20 , , , cord-272759-dqkjofw2 463 21 p p NN cord-272759-dqkjofw2 463 22 2 2 CD cord-272759-dqkjofw2 463 23 ) ) -RRB- cord-272759-dqkjofw2 463 24 . . . cord-272759-dqkjofw2 464 1 This this DT cord-272759-dqkjofw2 464 2 should should MD cord-272759-dqkjofw2 464 3 provide provide VB cord-272759-dqkjofw2 464 4 a a DT cord-272759-dqkjofw2 464 5 new new JJ cord-272759-dqkjofw2 464 6 , , , cord-272759-dqkjofw2 464 7 simpler simple JJR cord-272759-dqkjofw2 464 8 approach approach NN cord-272759-dqkjofw2 464 9 to to IN cord-272759-dqkjofw2 464 10 the the DT cord-272759-dqkjofw2 464 11 study study NN cord-272759-dqkjofw2 464 12 of of IN cord-272759-dqkjofw2 464 13 quarantine quarantine NN cord-272759-dqkjofw2 464 14 to to TO cord-272759-dqkjofw2 464 15 supplement supplement VB cord-272759-dqkjofw2 464 16 compartmental compartmental JJ cord-272759-dqkjofw2 464 17 models model NNS cord-272759-dqkjofw2 464 18 such such JJ cord-272759-dqkjofw2 464 19 as as IN cord-272759-dqkjofw2 464 20 those those DT cord-272759-dqkjofw2 464 21 described describe VBN cord-272759-dqkjofw2 464 22 in in IN cord-272759-dqkjofw2 464 23 [ [ -LRB- cord-272759-dqkjofw2 464 24 25 25 CD cord-272759-dqkjofw2 464 25 ] ] -RRB- cord-272759-dqkjofw2 464 26 . . . cord-272759-dqkjofw2 465 1 World World NNP cord-272759-dqkjofw2 465 2 Health Health NNP cord-272759-dqkjofw2 465 3 Organisation Organisation NNP cord-272759-dqkjofw2 465 4 , , , cord-272759-dqkjofw2 465 5 Consensus Consensus NNP cord-272759-dqkjofw2 465 6 document document NN cord-272759-dqkjofw2 465 7 on on IN cord-272759-dqkjofw2 465 8 the the DT cord-272759-dqkjofw2 465 9 epidemiology epidemiology NN cord-272759-dqkjofw2 465 10 of of IN cord-272759-dqkjofw2 465 11 SARS SARS NNP cord-272759-dqkjofw2 465 12 Report Report NNP cord-272759-dqkjofw2 465 13 of of IN cord-272759-dqkjofw2 465 14 the the DT cord-272759-dqkjofw2 465 15 severe severe JJ cord-272759-dqkjofw2 465 16 acute acute JJ cord-272759-dqkjofw2 465 17 respiratory respiratory JJ cord-272759-dqkjofw2 465 18 syndrome syndrome NN cord-272759-dqkjofw2 465 19 expert expert NN cord-272759-dqkjofw2 465 20 committee committee NN cord-272759-dqkjofw2 465 21 Transmission Transmission NNP cord-272759-dqkjofw2 465 22 dynamics dynamic NNS cord-272759-dqkjofw2 465 23 of of IN cord-272759-dqkjofw2 465 24 the the DT cord-272759-dqkjofw2 465 25 etiological etiological JJ cord-272759-dqkjofw2 465 26 agent agent NN cord-272759-dqkjofw2 465 27 of of IN cord-272759-dqkjofw2 465 28 SARS SARS NNP cord-272759-dqkjofw2 465 29 in in IN cord-272759-dqkjofw2 465 30 Hong Hong NNP cord-272759-dqkjofw2 465 31 Kong Kong NNP cord-272759-dqkjofw2 465 32 : : : cord-272759-dqkjofw2 465 33 impact impact NN cord-272759-dqkjofw2 465 34 of of IN cord-272759-dqkjofw2 465 35 public public JJ cord-272759-dqkjofw2 465 36 health health NN cord-272759-dqkjofw2 465 37 interventions intervention NNS cord-272759-dqkjofw2 465 38 Cluster Cluster NNP cord-272759-dqkjofw2 465 39 of of IN cord-272759-dqkjofw2 465 40 SARS SARS NNP cord-272759-dqkjofw2 465 41 among among IN cord-272759-dqkjofw2 465 42 medical medical JJ cord-272759-dqkjofw2 465 43 students student NNS cord-272759-dqkjofw2 465 44 exposed expose VBN cord-272759-dqkjofw2 465 45 to to IN cord-272759-dqkjofw2 465 46 single single JJ cord-272759-dqkjofw2 465 47 patient patient JJ cord-272759-dqkjofw2 465 48 Epidemiological epidemiological JJ cord-272759-dqkjofw2 465 49 determinants determinant NNS cord-272759-dqkjofw2 465 50 of of IN cord-272759-dqkjofw2 465 51 spread spread NN cord-272759-dqkjofw2 465 52 of of IN cord-272759-dqkjofw2 465 53 causal causal JJ cord-272759-dqkjofw2 465 54 agent agent NN cord-272759-dqkjofw2 465 55 of of IN cord-272759-dqkjofw2 465 56 severe severe JJ cord-272759-dqkjofw2 465 57 acute acute JJ cord-272759-dqkjofw2 465 58 respiratory respiratory JJ cord-272759-dqkjofw2 465 59 syndrome syndrome NN cord-272759-dqkjofw2 465 60 in in IN cord-272759-dqkjofw2 465 61 Hong Hong NNP cord-272759-dqkjofw2 465 62 Kong Kong NNP cord-272759-dqkjofw2 465 63 Mathematical Mathematical NNP cord-272759-dqkjofw2 465 64 Biology Biology NNP cord-272759-dqkjofw2 465 65 Modeling Modeling NNP cord-272759-dqkjofw2 465 66 infection infection NN cord-272759-dqkjofw2 465 67 transmission transmission NN cord-272759-dqkjofw2 465 68 More more RBR cord-272759-dqkjofw2 465 69 realistic realistic JJ cord-272759-dqkjofw2 465 70 models model NNS cord-272759-dqkjofw2 465 71 of of IN cord-272759-dqkjofw2 465 72 sexually sexually RB cord-272759-dqkjofw2 465 73 transmitted transmit VBN cord-272759-dqkjofw2 465 74 disease disease NN cord-272759-dqkjofw2 465 75 transmission transmission NN cord-272759-dqkjofw2 465 76 dynamics dynamic NNS cord-272759-dqkjofw2 465 77 : : : cord-272759-dqkjofw2 465 78 Sexual sexual JJ cord-272759-dqkjofw2 465 79 partnership partnership NN cord-272759-dqkjofw2 465 80 networks network NNS cord-272759-dqkjofw2 465 81 , , , cord-272759-dqkjofw2 465 82 pair pair NN cord-272759-dqkjofw2 465 83 models model NNS cord-272759-dqkjofw2 465 84 and and CC cord-272759-dqkjofw2 465 85 moment moment NN cord-272759-dqkjofw2 465 86 closure closure NN cord-272759-dqkjofw2 466 1 A a DT cord-272759-dqkjofw2 466 2 versatile versatile JJ cord-272759-dqkjofw2 466 3 ODE ode NN cord-272759-dqkjofw2 466 4 approximation approximation NN cord-272759-dqkjofw2 466 5 to to IN cord-272759-dqkjofw2 466 6 a a DT cord-272759-dqkjofw2 466 7 network network NN cord-272759-dqkjofw2 466 8 model model NN cord-272759-dqkjofw2 466 9 for for IN cord-272759-dqkjofw2 466 10 the the DT cord-272759-dqkjofw2 466 11 spread spread NN cord-272759-dqkjofw2 466 12 of of IN cord-272759-dqkjofw2 466 13 sexually sexually RB cord-272759-dqkjofw2 466 14 transmitted transmit VBN cord-272759-dqkjofw2 466 15 diseases disease NNS cord-272759-dqkjofw2 466 16 Likelihood likelihood NN cord-272759-dqkjofw2 466 17 - - HYPH cord-272759-dqkjofw2 466 18 based base VBN cord-272759-dqkjofw2 466 19 inference inference NN cord-272759-dqkjofw2 466 20 for for IN cord-272759-dqkjofw2 466 21 stochastic stochastic JJ cord-272759-dqkjofw2 466 22 models model NNS cord-272759-dqkjofw2 466 23 of of IN cord-272759-dqkjofw2 466 24 sexual sexual JJ cord-272759-dqkjofw2 466 25 network network NN cord-272759-dqkjofw2 466 26 formation formation NN cord-272759-dqkjofw2 466 27 , , , cord-272759-dqkjofw2 466 28 Theor Theor NNP cord-272759-dqkjofw2 466 29 Poisson Poisson NNP cord-272759-dqkjofw2 466 30 approximation approximation NN cord-272759-dqkjofw2 466 31 for for IN cord-272759-dqkjofw2 466 32 epidemics epidemic NNS cord-272759-dqkjofw2 466 33 with with IN cord-272759-dqkjofw2 466 34 two two CD cord-272759-dqkjofw2 466 35 levels level NNS cord-272759-dqkjofw2 466 36 of of IN cord-272759-dqkjofw2 466 37 mixing mix VBG cord-272759-dqkjofw2 466 38 Forecast forecast NN cord-272759-dqkjofw2 466 39 and and CC cord-272759-dqkjofw2 466 40 control control NN cord-272759-dqkjofw2 466 41 of of IN cord-272759-dqkjofw2 466 42 epidemics epidemic NNS cord-272759-dqkjofw2 466 43 in in IN cord-272759-dqkjofw2 466 44 a a DT cord-272759-dqkjofw2 466 45 globalized globalized JJ cord-272759-dqkjofw2 466 46 world world NN cord-272759-dqkjofw2 466 47 Six six CD cord-272759-dqkjofw2 466 48 Degrees degree NNS cord-272759-dqkjofw2 466 49 : : : cord-272759-dqkjofw2 467 1 The the DT cord-272759-dqkjofw2 467 2 Science Science NNP cord-272759-dqkjofw2 467 3 of of IN cord-272759-dqkjofw2 467 4 a a DT cord-272759-dqkjofw2 467 5 Connected Connected NNP cord-272759-dqkjofw2 467 6 Age Age NNP cord-272759-dqkjofw2 467 7 Collective collective JJ cord-272759-dqkjofw2 467 8 dynamics dynamic NNS cord-272759-dqkjofw2 467 9 of of IN cord-272759-dqkjofw2 467 10 ' ' `` cord-272759-dqkjofw2 467 11 small small JJ cord-272759-dqkjofw2 467 12 - - HYPH cord-272759-dqkjofw2 467 13 world world NN cord-272759-dqkjofw2 467 14 ' ' '' cord-272759-dqkjofw2 467 15 networks network NNS cord-272759-dqkjofw2 467 16 Small small JJ cord-272759-dqkjofw2 467 17 world world NN cord-272759-dqkjofw2 467 18 and and CC cord-272759-dqkjofw2 467 19 scale scale VB cord-272759-dqkjofw2 467 20 free free JJ cord-272759-dqkjofw2 467 21 model model NN cord-272759-dqkjofw2 467 22 for for IN cord-272759-dqkjofw2 467 23 transmission transmission NN cord-272759-dqkjofw2 467 24 of of IN cord-272759-dqkjofw2 467 25 SARS SARS NNP cord-272759-dqkjofw2 467 26 Dimensions Dimensions NNPS cord-272759-dqkjofw2 467 27 of of IN cord-272759-dqkjofw2 467 28 superspreading superspreade VBG cord-272759-dqkjofw2 467 29 On on IN cord-272759-dqkjofw2 467 30 - - HYPH cord-272759-dqkjofw2 467 31 line line NN cord-272759-dqkjofw2 467 32 encyclopedia encyclopedia NN cord-272759-dqkjofw2 467 33 of of IN cord-272759-dqkjofw2 467 34 integer integer NN cord-272759-dqkjofw2 467 35 sequences sequence NNS cord-272759-dqkjofw2 467 36 , , , cord-272759-dqkjofw2 467 37 Online Online NNP cord-272759-dqkjofw2 467 38 Mathematical Mathematical NNP cord-272759-dqkjofw2 467 39 Epidemiology Epidemiology NNP cord-272759-dqkjofw2 467 40 of of IN cord-272759-dqkjofw2 467 41 Infectious Infectious NNP cord-272759-dqkjofw2 467 42 Diseases Diseases NNPS cord-272759-dqkjofw2 467 43 Epidemic epidemic NN cord-272759-dqkjofw2 467 44 spreading spread VBG cord-272759-dqkjofw2 467 45 in in IN cord-272759-dqkjofw2 467 46 scale scale NN cord-272759-dqkjofw2 467 47 - - HYPH cord-272759-dqkjofw2 467 48 free free JJ cord-272759-dqkjofw2 467 49 networks network NNS cord-272759-dqkjofw2 467 50 Epidemic epidemic NN cord-272759-dqkjofw2 467 51 dynamics dynamic NNS cord-272759-dqkjofw2 467 52 and and CC cord-272759-dqkjofw2 467 53 endemic endemic JJ cord-272759-dqkjofw2 467 54 states state NNS cord-272759-dqkjofw2 467 55 in in IN cord-272759-dqkjofw2 467 56 complex complex JJ cord-272759-dqkjofw2 467 57 networks network NNS cord-272759-dqkjofw2 467 58 Bayesian bayesian JJ cord-272759-dqkjofw2 467 59 inference inference NN cord-272759-dqkjofw2 467 60 for for IN cord-272759-dqkjofw2 467 61 partially partially RB cord-272759-dqkjofw2 467 62 observed observe VBN cord-272759-dqkjofw2 467 63 stochastic stochastic JJ cord-272759-dqkjofw2 467 64 epidemics epidemic NNS cord-272759-dqkjofw2 467 65 Stochastic stochastic JJ cord-272759-dqkjofw2 467 66 modelling modelling NN cord-272759-dqkjofw2 467 67 of of IN cord-272759-dqkjofw2 467 68 ecological ecological JJ cord-272759-dqkjofw2 467 69 processes process NNS cord-272759-dqkjofw2 467 70 using use VBG cord-272759-dqkjofw2 467 71 hybrid hybrid JJ cord-272759-dqkjofw2 467 72 Gibbs Gibbs NNP cord-272759-dqkjofw2 467 73 samplers sampler NNS cord-272759-dqkjofw2 467 74 Probable probable JJ cord-272759-dqkjofw2 467 75 secondary secondary JJ cord-272759-dqkjofw2 467 76 infections infection NNS cord-272759-dqkjofw2 467 77 in in IN cord-272759-dqkjofw2 467 78 households household NNS cord-272759-dqkjofw2 467 79 of of IN cord-272759-dqkjofw2 467 80 SARS SARS NNP cord-272759-dqkjofw2 467 81 patients patient NNS cord-272759-dqkjofw2 467 82 in in IN cord-272759-dqkjofw2 467 83 Hong Hong NNP cord-272759-dqkjofw2 467 84 Kong Kong NNP cord-272759-dqkjofw2 467 85 Simulating simulate VBG cord-272759-dqkjofw2 467 86 the the DT cord-272759-dqkjofw2 467 87 effect effect NN cord-272759-dqkjofw2 467 88 of of IN cord-272759-dqkjofw2 467 89 quarantine quarantine NN cord-272759-dqkjofw2 467 90 on on IN cord-272759-dqkjofw2 467 91 the the DT cord-272759-dqkjofw2 467 92 spread spread NN cord-272759-dqkjofw2 467 93 of of IN cord-272759-dqkjofw2 467 94 the the DT cord-272759-dqkjofw2 467 95 1918 1918 CD cord-272759-dqkjofw2 467 96 - - SYM cord-272759-dqkjofw2 467 97 19 19 CD cord-272759-dqkjofw2 467 98 flu flu NN cord-272759-dqkjofw2 467 99 in in IN cord-272759-dqkjofw2 467 100 central central JJ cord-272759-dqkjofw2 467 101 Canada Canada NNP cord-272759-dqkjofw2 468 1 This this DT cord-272759-dqkjofw2 468 2 work work NN cord-272759-dqkjofw2 468 3 is be VBZ cord-272759-dqkjofw2 468 4 supported support VBN cord-272759-dqkjofw2 468 5 by by IN cord-272759-dqkjofw2 468 6 funding fund VBG cord-272759-dqkjofw2 468 7 from from IN cord-272759-dqkjofw2 468 8 the the DT cord-272759-dqkjofw2 468 9 Health Health NNP cord-272759-dqkjofw2 468 10 , , , cord-272759-dqkjofw2 468 11 Welfare Welfare NNP cord-272759-dqkjofw2 468 12 and and CC cord-272759-dqkjofw2 468 13 Food Food NNP cord-272759-dqkjofw2 468 14 Bureau Bureau NNP cord-272759-dqkjofw2 468 15 of of IN cord-272759-dqkjofw2 468 16 the the DT cord-272759-dqkjofw2 468 17 government government NN cord-272759-dqkjofw2 468 18 of of IN cord-272759-dqkjofw2 468 19 the the DT cord-272759-dqkjofw2 468 20 Hong Hong NNP cord-272759-dqkjofw2 468 21 Kong Kong NNP cord-272759-dqkjofw2 468 22 Special Special NNP cord-272759-dqkjofw2 468 23 Administrative Administrative NNP cord-272759-dqkjofw2 468 24 Region Region NNP cord-272759-dqkjofw2 468 25 under under IN cord-272759-dqkjofw2 468 26 the the DT cord-272759-dqkjofw2 468 27 Research Research NNP cord-272759-dqkjofw2 468 28 Fund Fund NNP cord-272759-dqkjofw2 468 29 for for IN cord-272759-dqkjofw2 468 30 Control Control NNP cord-272759-dqkjofw2 468 31 of of IN cord-272759-dqkjofw2 468 32 Infectious Infectious NNP cord-272759-dqkjofw2 468 33 Diseases Diseases NNPS cord-272759-dqkjofw2 468 34 ( ( -LRB- cord-272759-dqkjofw2 468 35 RFCID RFCID NNP cord-272759-dqkjofw2 468 36 ) ) -RRB- cord-272759-dqkjofw2 468 37 . . . cord-272759-dqkjofw2 469 1 DW DW NNP cord-272759-dqkjofw2 469 2 thanks thank NNS cord-272759-dqkjofw2 469 3 the the DT cord-272759-dqkjofw2 469 4 Scottish Scottish NNP cord-272759-dqkjofw2 469 5 Executive Executive NNP cord-272759-dqkjofw2 469 6 Environment Environment NNP cord-272759-dqkjofw2 469 7 and and CC cord-272759-dqkjofw2 469 8 Rural Rural NNP cord-272759-dqkjofw2 469 9 Affairs Affairs NNPS cord-272759-dqkjofw2 469 10 Department Department NNP cord-272759-dqkjofw2 469 11 ( ( -LRB- cord-272759-dqkjofw2 469 12 SEERAD SEERAD NNP cord-272759-dqkjofw2 469 13 ) ) -RRB- cord-272759-dqkjofw2 469 14 for for IN cord-272759-dqkjofw2 469 15 support support NN cord-272759-dqkjofw2 469 16 . . .