id sid tid token lemma pos cord-335886-m0d72ntg 1 1 key key JJ cord-335886-m0d72ntg 1 2 : : : cord-335886-m0d72ntg 1 3 cord-335886-m0d72ntg cord-335886-m0d72ntg NNP cord-335886-m0d72ntg 1 4 authors author NNS cord-335886-m0d72ntg 1 5 : : : cord-335886-m0d72ntg 1 6 Tomie Tomie NNP cord-335886-m0d72ntg 1 7 , , , cord-335886-m0d72ntg 1 8 Toshihisa Toshihisa NNP cord-335886-m0d72ntg 1 9 title title NN cord-335886-m0d72ntg 1 10 : : : cord-335886-m0d72ntg 1 11 Relations relation NNS cord-335886-m0d72ntg 1 12 of of IN cord-335886-m0d72ntg 1 13 parameters parameter NNS cord-335886-m0d72ntg 1 14 for for IN cord-335886-m0d72ntg 1 15 describing describe VBG cord-335886-m0d72ntg 1 16 the the DT cord-335886-m0d72ntg 1 17 epidemic epidemic NN cord-335886-m0d72ntg 1 18 of of IN cord-335886-m0d72ntg 1 19 COVID―19 COVID―19 NNP cord-335886-m0d72ntg 1 20 by by IN cord-335886-m0d72ntg 1 21 the the DT cord-335886-m0d72ntg 1 22 Kermack―McKendrick Kermack―McKendrick NNP cord-335886-m0d72ntg 1 23 model model NN cord-335886-m0d72ntg 1 24 date date NN cord-335886-m0d72ntg 1 25 : : : cord-335886-m0d72ntg 1 26 2020 2020 CD cord-335886-m0d72ntg 1 27 - - HYPH cord-335886-m0d72ntg 1 28 03 03 CD cord-335886-m0d72ntg 1 29 - - HYPH cord-335886-m0d72ntg 1 30 03 03 CD cord-335886-m0d72ntg 1 31 journal journal NN cord-335886-m0d72ntg 1 32 : : : cord-335886-m0d72ntg 1 33 nan nan NNP cord-335886-m0d72ntg 1 34 DOI DOI NNP cord-335886-m0d72ntg 1 35 : : : cord-335886-m0d72ntg 1 36 10.1101/2020.02.26.20027797 10.1101/2020.02.26.20027797 CD cord-335886-m0d72ntg 1 37 sha sha NNP cord-335886-m0d72ntg 1 38 : : : cord-335886-m0d72ntg 1 39 7344c6de7ce2258e74ce131bed72e6ad465f0ce8 7344c6de7ce2258e74ce131bed72e6ad465f0ce8 CD cord-335886-m0d72ntg 1 40 doc_id doc_id CD cord-335886-m0d72ntg 1 41 : : : cord-335886-m0d72ntg 1 42 335886 335886 CD cord-335886-m0d72ntg 1 43 cord_uid cord_uid NNS cord-335886-m0d72ntg 1 44 : : : cord-335886-m0d72ntg 1 45 m0d72ntg m0d72ntg NNP cord-335886-m0d72ntg 2 1 In in IN cord-335886-m0d72ntg 2 2 order order NN cord-335886-m0d72ntg 2 3 to to TO cord-335886-m0d72ntg 2 4 quantitatively quantitatively RB cord-335886-m0d72ntg 2 5 characterize characterize VB cord-335886-m0d72ntg 2 6 the the DT cord-335886-m0d72ntg 2 7 epidemic epidemic NN cord-335886-m0d72ntg 2 8 of of IN cord-335886-m0d72ntg 2 9 COVID―19 COVID―19 NNP cord-335886-m0d72ntg 2 10 , , , cord-335886-m0d72ntg 2 11 useful useful JJ cord-335886-m0d72ntg 2 12 relations relation NNS cord-335886-m0d72ntg 2 13 among among IN cord-335886-m0d72ntg 2 14 parameters parameter NNS cord-335886-m0d72ntg 2 15 describing describe VBG cord-335886-m0d72ntg 2 16 an an DT cord-335886-m0d72ntg 2 17 epidemic epidemic NN cord-335886-m0d72ntg 2 18 in in IN cord-335886-m0d72ntg 2 19 general general JJ cord-335886-m0d72ntg 2 20 are be VBP cord-335886-m0d72ntg 2 21 derived derive VBN cord-335886-m0d72ntg 2 22 based base VBN cord-335886-m0d72ntg 2 23 on on IN cord-335886-m0d72ntg 2 24 the the DT cord-335886-m0d72ntg 2 25 Kermack Kermack NNP cord-335886-m0d72ntg 2 26 - - HYPH cord-335886-m0d72ntg 2 27 McKendrick McKendrick NNP cord-335886-m0d72ntg 2 28 model model NN cord-335886-m0d72ntg 2 29 . . . cord-335886-m0d72ntg 3 1 The the DT cord-335886-m0d72ntg 3 2 first first JJ cord-335886-m0d72ntg 3 3 relation relation NN cord-335886-m0d72ntg 3 4 is be VBZ cord-335886-m0d72ntg 3 5 1 1 CD cord-335886-m0d72ntg 3 6 / / SYM cord-335886-m0d72ntg 3 7 τgrow=1 τgrow=1 NNS cord-335886-m0d72ntg 3 8 / / SYM cord-335886-m0d72ntg 3 9 τtrans−1 τtrans−1 NNP cord-335886-m0d72ntg 3 10 / / SYM cord-335886-m0d72ntg 3 11 τinf τinf NNP cord-335886-m0d72ntg 3 12 , , , cord-335886-m0d72ntg 3 13 where where WRB cord-335886-m0d72ntg 3 14 τgrow τgrow NNP cord-335886-m0d72ntg 3 15 is be VBZ cord-335886-m0d72ntg 3 16 the the DT cord-335886-m0d72ntg 3 17 time time NN cord-335886-m0d72ntg 3 18 constant constant JJ cord-335886-m0d72ntg 3 19 of of IN cord-335886-m0d72ntg 3 20 the the DT cord-335886-m0d72ntg 3 21 exponential exponential JJ cord-335886-m0d72ntg 3 22 growth growth NN cord-335886-m0d72ntg 3 23 of of IN cord-335886-m0d72ntg 3 24 an an DT cord-335886-m0d72ntg 3 25 epidemic epidemic NN cord-335886-m0d72ntg 3 26 , , , cord-335886-m0d72ntg 3 27 τtrans τtrans NNP cord-335886-m0d72ntg 3 28 is be VBZ cord-335886-m0d72ntg 3 29 the the DT cord-335886-m0d72ntg 3 30 time time NN cord-335886-m0d72ntg 3 31 for for IN cord-335886-m0d72ntg 3 32 a a DT cord-335886-m0d72ntg 3 33 pathogen pathogen NN cord-335886-m0d72ntg 3 34 to to TO cord-335886-m0d72ntg 3 35 be be VB cord-335886-m0d72ntg 3 36 transmitted transmit VBN cord-335886-m0d72ntg 3 37 from from IN cord-335886-m0d72ntg 3 38 one one CD cord-335886-m0d72ntg 3 39 patient patient NN cord-335886-m0d72ntg 3 40 to to IN cord-335886-m0d72ntg 3 41 uninfected uninfected JJ cord-335886-m0d72ntg 3 42 person person NN cord-335886-m0d72ntg 3 43 , , , cord-335886-m0d72ntg 3 44 and and CC cord-335886-m0d72ntg 3 45 the the DT cord-335886-m0d72ntg 3 46 infectious infectious JJ cord-335886-m0d72ntg 3 47 time time NN cord-335886-m0d72ntg 3 48 τinf τinf NNP cord-335886-m0d72ntg 3 49 is be VBZ cord-335886-m0d72ntg 3 50 the the DT cord-335886-m0d72ntg 3 51 time time NN cord-335886-m0d72ntg 3 52 during during IN cord-335886-m0d72ntg 3 53 which which WDT cord-335886-m0d72ntg 3 54 the the DT cord-335886-m0d72ntg 3 55 pathogen pathogen NN cord-335886-m0d72ntg 3 56 keeps keep VBZ cord-335886-m0d72ntg 3 57 its -PRON- PRP$ cord-335886-m0d72ntg 3 58 power power NN cord-335886-m0d72ntg 3 59 of of IN cord-335886-m0d72ntg 3 60 transmission transmission NN cord-335886-m0d72ntg 3 61 . . . cord-335886-m0d72ntg 4 1 The the DT cord-335886-m0d72ntg 4 2 second second JJ cord-335886-m0d72ntg 4 3 relation relation NN cord-335886-m0d72ntg 4 4 p(∞ p(∞ VBN cord-335886-m0d72ntg 4 5 ) ) -RRB- cord-335886-m0d72ntg 4 6 ≈1−exp(−(R0−1)/0.60 ≈1−exp(−(r0−1)/0.60 NN cord-335886-m0d72ntg 4 7 ) ) -RRB- cord-335886-m0d72ntg 4 8 is be VBZ cord-335886-m0d72ntg 4 9 the the DT cord-335886-m0d72ntg 4 10 relation relation NN cord-335886-m0d72ntg 4 11 between between IN cord-335886-m0d72ntg 4 12 p(∞ p(∞ NNP cord-335886-m0d72ntg 4 13 ) ) -RRB- cord-335886-m0d72ntg 4 14 , , , cord-335886-m0d72ntg 4 15 the the DT cord-335886-m0d72ntg 4 16 final final JJ cord-335886-m0d72ntg 4 17 size size NN cord-335886-m0d72ntg 4 18 of of IN cord-335886-m0d72ntg 4 19 the the DT cord-335886-m0d72ntg 4 20 disaster disaster NN cord-335886-m0d72ntg 4 21 defined define VBN cord-335886-m0d72ntg 4 22 by by IN cord-335886-m0d72ntg 4 23 the the DT cord-335886-m0d72ntg 4 24 ratio ratio NN cord-335886-m0d72ntg 4 25 of of IN cord-335886-m0d72ntg 4 26 the the DT cord-335886-m0d72ntg 4 27 total total JJ cord-335886-m0d72ntg 4 28 infected infected JJ cord-335886-m0d72ntg 4 29 people people NNS cord-335886-m0d72ntg 4 30 to to IN cord-335886-m0d72ntg 4 31 the the DT cord-335886-m0d72ntg 4 32 population population NN cord-335886-m0d72ntg 4 33 of of IN cord-335886-m0d72ntg 4 34 the the DT cord-335886-m0d72ntg 4 35 society society NN cord-335886-m0d72ntg 4 36 , , , cord-335886-m0d72ntg 4 37 and and CC cord-335886-m0d72ntg 4 38 the the DT cord-335886-m0d72ntg 4 39 basic basic JJ cord-335886-m0d72ntg 4 40 reproduction reproduction NN cord-335886-m0d72ntg 4 41 number number NN cord-335886-m0d72ntg 4 42 , , , cord-335886-m0d72ntg 4 43 R0 R0 NNP cord-335886-m0d72ntg 4 44 , , , cord-335886-m0d72ntg 4 45 which which WDT cord-335886-m0d72ntg 4 46 is be VBZ cord-335886-m0d72ntg 4 47 the the DT cord-335886-m0d72ntg 4 48 number number NN cord-335886-m0d72ntg 4 49 of of IN cord-335886-m0d72ntg 4 50 persons person NNS cord-335886-m0d72ntg 4 51 infected infect VBN cord-335886-m0d72ntg 4 52 by by IN cord-335886-m0d72ntg 4 53 the the DT cord-335886-m0d72ntg 4 54 transmission transmission NN cord-335886-m0d72ntg 4 55 of of IN cord-335886-m0d72ntg 4 56 the the DT cord-335886-m0d72ntg 4 57 pathogen pathogen NN cord-335886-m0d72ntg 4 58 from from IN cord-335886-m0d72ntg 4 59 one one CD cord-335886-m0d72ntg 4 60 infected infected JJ cord-335886-m0d72ntg 4 61 person person NN cord-335886-m0d72ntg 4 62 during during IN cord-335886-m0d72ntg 4 63 the the DT cord-335886-m0d72ntg 4 64 infectious infectious JJ cord-335886-m0d72ntg 4 65 time time NN cord-335886-m0d72ntg 4 66 . . . cord-335886-m0d72ntg 5 1 The the DT cord-335886-m0d72ntg 5 2 third third JJ cord-335886-m0d72ntg 5 3 relation relation NN cord-335886-m0d72ntg 5 4 1 1 CD cord-335886-m0d72ntg 5 5 / / SYM cord-335886-m0d72ntg 5 6 τend=1 τend=1 NNS cord-335886-m0d72ntg 5 7 / / SYM cord-335886-m0d72ntg 5 8 τinf−(1−p(∞))/τtrans τinf−(1−p(∞))/τtrans NNPS cord-335886-m0d72ntg 5 9 gives give VBZ cord-335886-m0d72ntg 5 10 the the DT cord-335886-m0d72ntg 5 11 decay decay NN cord-335886-m0d72ntg 5 12 time time NN cord-335886-m0d72ntg 5 13 constant constant JJ cord-335886-m0d72ntg 5 14 τend τend NN cord-335886-m0d72ntg 5 15 at at IN cord-335886-m0d72ntg 5 16 the the DT cord-335886-m0d72ntg 5 17 ending end VBG cord-335886-m0d72ntg 5 18 stage stage NN cord-335886-m0d72ntg 5 19 of of IN cord-335886-m0d72ntg 5 20 the the DT cord-335886-m0d72ntg 5 21 epidemic epidemic NN cord-335886-m0d72ntg 5 22 . . . cord-335886-m0d72ntg 6 1 Derived derived JJ cord-335886-m0d72ntg 6 2 relations relation NNS cord-335886-m0d72ntg 6 3 are be VBP cord-335886-m0d72ntg 6 4 applied apply VBN cord-335886-m0d72ntg 6 5 to to IN cord-335886-m0d72ntg 6 6 influenza influenza NN cord-335886-m0d72ntg 6 7 in in IN cord-335886-m0d72ntg 6 8 Japan Japan NNP cord-335886-m0d72ntg 6 9 in in IN cord-335886-m0d72ntg 6 10 2019 2019 CD cord-335886-m0d72ntg 6 11 for for IN cord-335886-m0d72ntg 6 12 characterizing characterize VBG cord-335886-m0d72ntg 6 13 the the DT cord-335886-m0d72ntg 6 14 epidemic epidemic NN cord-335886-m0d72ntg 6 15 . . . cord-335886-m0d72ntg 7 1 We -PRON- PRP cord-335886-m0d72ntg 7 2 reported report VBD cord-335886-m0d72ntg 7 3 the the DT cord-335886-m0d72ntg 7 4 understanding understanding NN cord-335886-m0d72ntg 7 5 of of IN cord-335886-m0d72ntg 7 6 the the DT cord-335886-m0d72ntg 7 7 present present JJ cord-335886-m0d72ntg 7 8 status status NN cord-335886-m0d72ntg 7 9 and and CC cord-335886-m0d72ntg 7 10 forecasting forecasting NN cord-335886-m0d72ntg 7 11 of of IN cord-335886-m0d72ntg 7 12 pneumonia pneumonia NN cord-335886-m0d72ntg 7 13 by by IN cord-335886-m0d72ntg 7 14 in in IN cord-335886-m0d72ntg 7 15 China China NNP cord-335886-m0d72ntg 7 16 which which WDT cord-335886-m0d72ntg 7 17 is be VBZ cord-335886-m0d72ntg 7 18 supposed suppose VBN cord-335886-m0d72ntg 7 19 to to TO cord-335886-m0d72ntg 7 20 have have VB cord-335886-m0d72ntg 7 21 originated originate VBN cord-335886-m0d72ntg 7 22 in in IN cord-335886-m0d72ntg 7 23 Wuhan Wuhan NNP cord-335886-m0d72ntg 7 24 by by IN cord-335886-m0d72ntg 7 25 analyzing analyze VBG cord-335886-m0d72ntg 7 26 the the DT cord-335886-m0d72ntg 7 27 data datum NNS cord-335886-m0d72ntg 7 28 up up IN cord-335886-m0d72ntg 7 29 to to IN cord-335886-m0d72ntg 7 30 February February NNP cord-335886-m0d72ntg 7 31 11 11 CD cord-335886-m0d72ntg 7 32 ( ( -LRB- cord-335886-m0d72ntg 7 33 ref.1 ref.1 NNP cord-335886-m0d72ntg 7 34 ) ) -RRB- cord-335886-m0d72ntg 7 35 . . . cord-335886-m0d72ntg 8 1 In in IN cord-335886-m0d72ntg 8 2 ref ref NN cord-335886-m0d72ntg 8 3 . . . cord-335886-m0d72ntg 9 1 1 1 LS cord-335886-m0d72ntg 9 2 , , , cord-335886-m0d72ntg 9 3 we -PRON- PRP cord-335886-m0d72ntg 9 4 clarified clarify VBD cord-335886-m0d72ntg 9 5 that that IN cord-335886-m0d72ntg 9 6 the the DT cord-335886-m0d72ntg 9 7 behavior behavior NN cord-335886-m0d72ntg 9 8 of of IN cord-335886-m0d72ntg 9 9 the the DT cord-335886-m0d72ntg 9 10 epidemic epidemic NN cord-335886-m0d72ntg 9 11 was be VBD cord-335886-m0d72ntg 9 12 different different JJ cord-335886-m0d72ntg 9 13 in in IN cord-335886-m0d72ntg 9 14 different different JJ cord-335886-m0d72ntg 9 15 regions region NNS cord-335886-m0d72ntg 9 16 and and CC cord-335886-m0d72ntg 9 17 that that IN cord-335886-m0d72ntg 9 18 the the DT cord-335886-m0d72ntg 9 19 outbreak outbreak NN cord-335886-m0d72ntg 9 20 was be VBD cord-335886-m0d72ntg 9 21 well well RB cord-335886-m0d72ntg 9 22 described describe VBN cord-335886-m0d72ntg 9 23 by by IN cord-335886-m0d72ntg 9 24 a a DT cord-335886-m0d72ntg 9 25 Gaussian Gaussian NNP cord-335886-m0d72ntg 9 26 as as IN cord-335886-m0d72ntg 9 27 was be VBD cord-335886-m0d72ntg 9 28 for for IN cord-335886-m0d72ntg 9 29 influenza influenza NN cord-335886-m0d72ntg 9 30 in in IN cord-335886-m0d72ntg 9 31 Japan Japan NNP cord-335886-m0d72ntg 9 32 . . . cord-335886-m0d72ntg 10 1 We -PRON- PRP cord-335886-m0d72ntg 10 2 reported report VBD cord-335886-m0d72ntg 10 3 the the DT cord-335886-m0d72ntg 10 4 following follow VBG cord-335886-m0d72ntg 10 5 ; ; : cord-335886-m0d72ntg 10 6 1 1 CD cord-335886-m0d72ntg 10 7 . . . cord-335886-m0d72ntg 11 1 the the DT cord-335886-m0d72ntg 11 2 epidemic epidemic NN cord-335886-m0d72ntg 11 3 in in IN cord-335886-m0d72ntg 11 4 China China NNP cord-335886-m0d72ntg 11 5 passed pass VBD cord-335886-m0d72ntg 11 6 the the DT cord-335886-m0d72ntg 11 7 peak peak NN cord-335886-m0d72ntg 11 8 in in IN cord-335886-m0d72ntg 11 9 the the DT cord-335886-m0d72ntg 11 10 beginning beginning NN cord-335886-m0d72ntg 11 11 of of IN cord-335886-m0d72ntg 11 12 February February NNP cord-335886-m0d72ntg 11 13 , , , cord-335886-m0d72ntg 11 14 2 2 CD cord-335886-m0d72ntg 11 15 . . . cord-335886-m0d72ntg 12 1 the the DT cord-335886-m0d72ntg 12 2 date date NN cord-335886-m0d72ntg 12 3 of of IN cord-335886-m0d72ntg 12 4 the the DT cord-335886-m0d72ntg 12 5 epidemic epidemic NN cord-335886-m0d72ntg 12 6 peak peak NN cord-335886-m0d72ntg 12 7 was be VBD cord-335886-m0d72ntg 12 8 different different JJ cord-335886-m0d72ntg 12 9 by by IN cord-335886-m0d72ntg 12 10 region region NN cord-335886-m0d72ntg 12 11 and and CC cord-335886-m0d72ntg 12 12 was be VBD cord-335886-m0d72ntg 12 13 the the DT cord-335886-m0d72ntg 12 14 latest late JJS cord-335886-m0d72ntg 12 15 in in IN cord-335886-m0d72ntg 12 16 Wuhan Wuhan NNP cord-335886-m0d72ntg 12 17 . . . cord-335886-m0d72ntg 13 1 For for IN cord-335886-m0d72ntg 13 2 more more JJR cord-335886-m0d72ntg 13 3 than than IN cord-335886-m0d72ntg 13 4 10 10 CD cord-335886-m0d72ntg 13 5 days day NNS cord-335886-m0d72ntg 13 6 after after IN cord-335886-m0d72ntg 13 7 our -PRON- PRP$ cord-335886-m0d72ntg 13 8 forecast forecast NN cord-335886-m0d72ntg 13 9 , , , cord-335886-m0d72ntg 13 10 the the DT cord-335886-m0d72ntg 13 11 epidemic epidemic NN cord-335886-m0d72ntg 13 12 closely closely RB cord-335886-m0d72ntg 13 13 followed follow VBD cord-335886-m0d72ntg 13 14 our -PRON- PRP$ cord-335886-m0d72ntg 13 15 forecast forecast NN cord-335886-m0d72ntg 13 16 . . . cord-335886-m0d72ntg 14 1 The the DT cord-335886-m0d72ntg 14 2 new new JJ cord-335886-m0d72ntg 14 3 patients patient NNS cord-335886-m0d72ntg 14 4 outside outside IN cord-335886-m0d72ntg 14 5 Wuhan Wuhan NNP cord-335886-m0d72ntg 14 6 decreased decrease VBD cord-335886-m0d72ntg 14 7 to to IN cord-335886-m0d72ntg 14 8 less less JJR cord-335886-m0d72ntg 14 9 than than IN cord-335886-m0d72ntg 14 10 4 4 CD cord-335886-m0d72ntg 14 11 % % NN cord-335886-m0d72ntg 14 12 of of IN cord-335886-m0d72ntg 14 13 that that DT cord-335886-m0d72ntg 14 14 at at IN cord-335886-m0d72ntg 14 15 the the DT cord-335886-m0d72ntg 14 16 peak peak NN cord-335886-m0d72ntg 14 17 around around IN cord-335886-m0d72ntg 14 18 February February NNP cord-335886-m0d72ntg 14 19 5 5 CD cord-335886-m0d72ntg 14 20 . . . cord-335886-m0d72ntg 15 1 Although although IN cord-335886-m0d72ntg 15 2 the the DT cord-335886-m0d72ntg 15 3 epidemic epidemic NN cord-335886-m0d72ntg 15 4 in in IN cord-335886-m0d72ntg 15 5 China China NNP cord-335886-m0d72ntg 15 6 is be VBZ cord-335886-m0d72ntg 15 7 near near IN cord-335886-m0d72ntg 15 8 the the DT cord-335886-m0d72ntg 15 9 end end NN cord-335886-m0d72ntg 15 10 , , , cord-335886-m0d72ntg 15 11 patients patient NNS cord-335886-m0d72ntg 15 12 by by IN cord-335886-m0d72ntg 15 13 COVID-19 COVID-19 NNP cord-335886-m0d72ntg 15 14 are be VBP cord-335886-m0d72ntg 15 15 found find VBN cord-335886-m0d72ntg 15 16 in in IN cord-335886-m0d72ntg 15 17 many many JJ cord-335886-m0d72ntg 15 18 other other JJ cord-335886-m0d72ntg 15 19 countries country NNS cord-335886-m0d72ntg 15 20 , , , cord-335886-m0d72ntg 15 21 and and CC cord-335886-m0d72ntg 15 22 COVID-19 COVID-19 NNP cord-335886-m0d72ntg 15 23 is be VBZ cord-335886-m0d72ntg 15 24 still still RB cord-335886-m0d72ntg 15 25 a a DT cord-335886-m0d72ntg 15 26 big big JJ cord-335886-m0d72ntg 15 27 fear fear NN cord-335886-m0d72ntg 15 28 of of IN cord-335886-m0d72ntg 15 29 the the DT cord-335886-m0d72ntg 15 30 people people NNS cord-335886-m0d72ntg 15 31 over over IN cord-335886-m0d72ntg 15 32 the the DT cord-335886-m0d72ntg 15 33 world world NN cord-335886-m0d72ntg 15 34 . . . cord-335886-m0d72ntg 16 1 In in IN cord-335886-m0d72ntg 16 2 order order NN cord-335886-m0d72ntg 16 3 to to TO cord-335886-m0d72ntg 16 4 forecast forecast VB cord-335886-m0d72ntg 16 5 the the DT cord-335886-m0d72ntg 16 6 epidemic epidemic NN cord-335886-m0d72ntg 16 7 of of IN cord-335886-m0d72ntg 16 8 COVID-19 covid-19 CD cord-335886-m0d72ntg 16 9 in in IN cord-335886-m0d72ntg 16 10 other other JJ cord-335886-m0d72ntg 16 11 countries country NNS cord-335886-m0d72ntg 16 12 , , , cord-335886-m0d72ntg 16 13 we -PRON- PRP cord-335886-m0d72ntg 16 14 need need VBP cord-335886-m0d72ntg 16 15 to to TO cord-335886-m0d72ntg 16 16 theoretically theoretically RB cord-335886-m0d72ntg 16 17 characterize characterize VB cord-335886-m0d72ntg 16 18 the the DT cord-335886-m0d72ntg 16 19 COVID-19 covid-19 JJ cord-335886-m0d72ntg 16 20 epidemic epidemic NN cord-335886-m0d72ntg 16 21 by by IN cord-335886-m0d72ntg 16 22 fitting fit VBG cord-335886-m0d72ntg 16 23 a a DT cord-335886-m0d72ntg 16 24 model model NN cord-335886-m0d72ntg 16 25 calculation calculation NN cord-335886-m0d72ntg 16 26 to to IN cord-335886-m0d72ntg 16 27 the the DT cord-335886-m0d72ntg 16 28 data datum NNS cord-335886-m0d72ntg 16 29 observed observe VBN cord-335886-m0d72ntg 16 30 in in IN cord-335886-m0d72ntg 16 31 China China NNP cord-335886-m0d72ntg 16 32 . . . cord-335886-m0d72ntg 17 1 We -PRON- PRP cord-335886-m0d72ntg 17 2 choose choose VBP cord-335886-m0d72ntg 17 3 the the DT cord-335886-m0d72ntg 17 4 Kermack- Kermack- NNP cord-335886-m0d72ntg 17 5 2 2 CD cord-335886-m0d72ntg 17 6 ) ) -RRB- cord-335886-m0d72ntg 17 7 for for IN cord-335886-m0d72ntg 17 8 our -PRON- PRP$ cord-335886-m0d72ntg 17 9 analysis analysis NN cord-335886-m0d72ntg 17 10 . . . cord-335886-m0d72ntg 18 1 The the DT cord-335886-m0d72ntg 18 2 Kermack Kermack NNP cord-335886-m0d72ntg 18 3 - - HYPH cord-335886-m0d72ntg 18 4 McKendrick McKendrick NNP cord-335886-m0d72ntg 18 5 model model NN cord-335886-m0d72ntg 18 6 was be VBD cord-335886-m0d72ntg 18 7 proposed propose VBN cord-335886-m0d72ntg 18 8 as as RB cord-335886-m0d72ntg 18 9 early early RB cord-335886-m0d72ntg 18 10 as as IN cord-335886-m0d72ntg 18 11 1927 1927 CD cord-335886-m0d72ntg 18 12 , , , cord-335886-m0d72ntg 18 13 but but CC cord-335886-m0d72ntg 18 14 still still RB cord-335886-m0d72ntg 18 15 , , , cord-335886-m0d72ntg 18 16 it -PRON- PRP cord-335886-m0d72ntg 18 17 is be VBZ cord-335886-m0d72ntg 18 18 the the DT cord-335886-m0d72ntg 18 19 basis basis NN cord-335886-m0d72ntg 18 20 of of IN cord-335886-m0d72ntg 18 21 many many JJ cord-335886-m0d72ntg 18 22 modified modify VBN cord-335886-m0d72ntg 18 23 models model NNS cord-335886-m0d72ntg 18 24 for for IN cord-335886-m0d72ntg 18 25 describing describe VBG cord-335886-m0d72ntg 18 26 epidemics epidemic NNS cord-335886-m0d72ntg 18 27 . . . cord-335886-m0d72ntg 19 1 We -PRON- PRP cord-335886-m0d72ntg 19 2 want want VBP cord-335886-m0d72ntg 19 3 to to TO cord-335886-m0d72ntg 19 4 analyze analyze VB cord-335886-m0d72ntg 19 5 the the DT cord-335886-m0d72ntg 19 6 epidemic epidemic NN cord-335886-m0d72ntg 19 7 of of IN cord-335886-m0d72ntg 19 8 COVID-19 COVID-19 NNP cord-335886-m0d72ntg 19 9 in in IN cord-335886-m0d72ntg 19 10 detail detail NN cord-335886-m0d72ntg 19 11 by by IN cord-335886-m0d72ntg 19 12 applying apply VBG cord-335886-m0d72ntg 19 13 a a DT cord-335886-m0d72ntg 19 14 model model NN cord-335886-m0d72ntg 19 15 . . . cord-335886-m0d72ntg 20 1 As as IN cord-335886-m0d72ntg 20 2 a a DT cord-335886-m0d72ntg 20 3 preparation preparation NN cord-335886-m0d72ntg 20 4 of of IN cord-335886-m0d72ntg 20 5 the the DT cord-335886-m0d72ntg 20 6 analysis analysis NN cord-335886-m0d72ntg 20 7 , , , cord-335886-m0d72ntg 20 8 useful useful JJ cord-335886-m0d72ntg 20 9 relations relation NNS cord-335886-m0d72ntg 20 10 of of IN cord-335886-m0d72ntg 20 11 parameters parameter NNS cord-335886-m0d72ntg 20 12 describing describe VBG cord-335886-m0d72ntg 20 13 an an DT cord-335886-m0d72ntg 20 14 epidemic epidemic NN cord-335886-m0d72ntg 20 15 are be VBP cord-335886-m0d72ntg 20 16 derived derive VBN cord-335886-m0d72ntg 20 17 in in IN cord-335886-m0d72ntg 20 18 the the DT cord-335886-m0d72ntg 20 19 present present JJ cord-335886-m0d72ntg 20 20 paper paper NN cord-335886-m0d72ntg 20 21 . . . cord-335886-m0d72ntg 21 1 Useful useful JJ cord-335886-m0d72ntg 21 2 relations relation NNS cord-335886-m0d72ntg 21 3 of of IN cord-335886-m0d72ntg 21 4 parameters parameter NNS cord-335886-m0d72ntg 21 5 of of IN cord-335886-m0d72ntg 21 6 an an DT cord-335886-m0d72ntg 21 7 epidemic epidemic NN cord-335886-m0d72ntg 21 8 are be VBP cord-335886-m0d72ntg 21 9 Eqs Eqs NNP cord-335886-m0d72ntg 21 10 . . . cord-335886-m0d72ntg 22 1 ( ( -LRB- cord-335886-m0d72ntg 22 2 7 7 CD cord-335886-m0d72ntg 22 3 ) ) -RRB- cord-335886-m0d72ntg 22 4 to to IN cord-335886-m0d72ntg 22 5 ( ( -LRB- cord-335886-m0d72ntg 22 6 10 10 CD cord-335886-m0d72ntg 22 7 ) ) -RRB- cord-335886-m0d72ntg 22 8 in in IN cord-335886-m0d72ntg 22 9 the the DT cord-335886-m0d72ntg 22 10 following following NN cord-335886-m0d72ntg 22 11 , , , cord-335886-m0d72ntg 22 12 which which WDT cord-335886-m0d72ntg 22 13 are be VBP cord-335886-m0d72ntg 22 14 derived derive VBN cord-335886-m0d72ntg 22 15 from from IN cord-335886-m0d72ntg 22 16 the the DT cord-335886-m0d72ntg 22 17 Kermack Kermack NNP cord-335886-m0d72ntg 22 18 - - HYPH cord-335886-m0d72ntg 22 19 McKendrick McKendrick NNP cord-335886-m0d72ntg 22 20 model model NN cord-335886-m0d72ntg 22 21 ( ( -LRB- cord-335886-m0d72ntg 22 22 ref.2 ref.2 NNP cord-335886-m0d72ntg 22 23 ) ) -RRB- cord-335886-m0d72ntg 22 24 . . . cord-335886-m0d72ntg 23 1 The the DT cord-335886-m0d72ntg 23 2 number number NN cord-335886-m0d72ntg 23 3 of of IN cord-335886-m0d72ntg 23 4 susceptible susceptible JJ cord-335886-m0d72ntg 23 5 people people NNS cord-335886-m0d72ntg 23 6 in in IN cord-335886-m0d72ntg 23 7 the the DT cord-335886-m0d72ntg 23 8 group group NN cord-335886-m0d72ntg 23 9 is be VBZ cord-335886-m0d72ntg 23 10 set set VBN cord-335886-m0d72ntg 23 11 as as IN cord-335886-m0d72ntg 23 12 S S NNP cord-335886-m0d72ntg 23 13 0 0 CD cord-335886-m0d72ntg 23 14 , , , cord-335886-m0d72ntg 23 15 the the DT cord-335886-m0d72ntg 23 16 number number NN cord-335886-m0d72ntg 23 17 of of IN cord-335886-m0d72ntg 23 18 infected infected JJ cord-335886-m0d72ntg 23 19 persons person NNS cord-335886-m0d72ntg 23 20 is be VBZ cord-335886-m0d72ntg 23 21 I(t I(t NNP cord-335886-m0d72ntg 23 22 ) ) -RRB- cord-335886-m0d72ntg 23 23 , , , cord-335886-m0d72ntg 23 24 the the DT cord-335886-m0d72ntg 23 25 number number NN cord-335886-m0d72ntg 23 26 of of IN cord-335886-m0d72ntg 23 27 persons person NNS cord-335886-m0d72ntg 23 28 who who WP cord-335886-m0d72ntg 23 29 have have VBP cord-335886-m0d72ntg 23 30 been be VBN cord-335886-m0d72ntg 23 31 infected infect VBN cord-335886-m0d72ntg 23 32 and and CC cord-335886-m0d72ntg 23 33 recovered recover VBN cord-335886-m0d72ntg 23 34 to to TO cord-335886-m0d72ntg 23 35 obtain obtain VB cord-335886-m0d72ntg 23 36 immunity immunity NN cord-335886-m0d72ntg 23 37 or or CC cord-335886-m0d72ntg 23 38 have have VBP cord-335886-m0d72ntg 23 39 died die VBN cord-335886-m0d72ntg 23 40 is be VBZ cord-335886-m0d72ntg 23 41 R(t R(t NNP cord-335886-m0d72ntg 23 42 ) ) -RRB- cord-335886-m0d72ntg 23 43 , , , cord-335886-m0d72ntg 23 44 the the DT cord-335886-m0d72ntg 23 45 number number NN cord-335886-m0d72ntg 23 46 of of IN cord-335886-m0d72ntg 23 47 persons person NNS cord-335886-m0d72ntg 23 48 who who WP cord-335886-m0d72ntg 23 49 is be VBZ cord-335886-m0d72ntg 23 50 susceptible susceptible JJ cord-335886-m0d72ntg 23 51 but but CC cord-335886-m0d72ntg 23 52 not not RB cord-335886-m0d72ntg 23 53 yet yet RB cord-335886-m0d72ntg 23 54 infected infect VBN cord-335886-m0d72ntg 23 55 is be VBZ cord-335886-m0d72ntg 23 56 S(t S(t NNP cord-335886-m0d72ntg 23 57 ) ) -RRB- cord-335886-m0d72ntg 23 58 . . . cord-335886-m0d72ntg 24 1 S s NN cord-335886-m0d72ntg 24 2 0 0 CD cord-335886-m0d72ntg 25 1 = = SYM cord-335886-m0d72ntg 25 2 S(t S(t NNP cord-335886-m0d72ntg 25 3 ) ) -RRB- cord-335886-m0d72ntg 25 4 + + CC cord-335886-m0d72ntg 25 5 I(t I(t NNP cord-335886-m0d72ntg 25 6 ) ) -RRB- cord-335886-m0d72ntg 26 1 + + CC cord-335886-m0d72ntg 26 2 R(t r(t NN cord-335886-m0d72ntg 26 3 ) ) -RRB- cord-335886-m0d72ntg 26 4 . . . cord-335886-m0d72ntg 27 1 When when WRB cord-335886-m0d72ntg 27 2 the the DT cord-335886-m0d72ntg 27 3 transmission transmission NN cord-335886-m0d72ntg 27 4 power power NN cord-335886-m0d72ntg 27 5 of of IN cord-335886-m0d72ntg 27 6 the the DT cord-335886-m0d72ntg 27 7 disease disease NN cord-335886-m0d72ntg 27 8 is be VBZ cord-335886-m0d72ntg 27 9 set set VBN cord-335886-m0d72ntg 27 10 as as IN cord-335886-m0d72ntg 27 11 β β NN cord-335886-m0d72ntg 27 12 and and CC cord-335886-m0d72ntg 27 13 the the DT cord-335886-m0d72ntg 27 14 recovery recovery NN cord-335886-m0d72ntg 27 15 rate rate NN cord-335886-m0d72ntg 27 16 from from IN cord-335886-m0d72ntg 27 17 the the DT cord-335886-m0d72ntg 27 18 infection infection NN cord-335886-m0d72ntg 27 19 is be VBZ cord-335886-m0d72ntg 27 20 γ γ NN cord-335886-m0d72ntg 27 21 , , , cord-335886-m0d72ntg 27 22 the the DT cord-335886-m0d72ntg 27 23 epidemic epidemic NN cord-335886-m0d72ntg 27 24 of of IN cord-335886-m0d72ntg 27 25 the the DT cord-335886-m0d72ntg 27 26 disease disease NN cord-335886-m0d72ntg 27 27 is be VBZ cord-335886-m0d72ntg 27 28 given give VBN cord-335886-m0d72ntg 27 29 by by IN cord-335886-m0d72ntg 27 30 the the DT cord-335886-m0d72ntg 27 31 following following JJ cord-335886-m0d72ntg 27 32 three three CD cord-335886-m0d72ntg 27 33 differential differential JJ cord-335886-m0d72ntg 27 34 equations equation NNS cord-335886-m0d72ntg 27 35 . . . cord-335886-m0d72ntg 28 1 the the DT cord-335886-m0d72ntg 28 2 author author NN cord-335886-m0d72ntg 28 3 / / SYM cord-335886-m0d72ntg 28 4 funder funder NN cord-335886-m0d72ntg 28 5 , , , cord-335886-m0d72ntg 28 6 who who WP cord-335886-m0d72ntg 28 7 has have VBZ cord-335886-m0d72ntg 28 8 granted grant VBN cord-335886-m0d72ntg 28 9 medRxiv medRxiv NNS cord-335886-m0d72ntg 28 10 a a DT cord-335886-m0d72ntg 28 11 license license NN cord-335886-m0d72ntg 28 12 to to TO cord-335886-m0d72ntg 28 13 display display VB cord-335886-m0d72ntg 28 14 the the DT cord-335886-m0d72ntg 28 15 preprint preprint NN cord-335886-m0d72ntg 28 16 in in IN cord-335886-m0d72ntg 28 17 perpetuity perpetuity NN cord-335886-m0d72ntg 28 18 . . . cord-335886-m0d72ntg 29 1 The the DT cord-335886-m0d72ntg 29 2 copyright copyright NN cord-335886-m0d72ntg 29 3 holder holder NN cord-335886-m0d72ntg 29 4 for for IN cord-335886-m0d72ntg 29 5 this this DT cord-335886-m0d72ntg 29 6 preprint preprint NN cord-335886-m0d72ntg 29 7 ( ( -LRB- cord-335886-m0d72ntg 29 8 which which WDT cord-335886-m0d72ntg 29 9 was be VBD cord-335886-m0d72ntg 29 10 not not RB cord-335886-m0d72ntg 29 11 peer peer NN cord-335886-m0d72ntg 29 12 - - HYPH cord-335886-m0d72ntg 29 13 reviewed review VBN cord-335886-m0d72ntg 29 14 ) ) -RRB- cord-335886-m0d72ntg 29 15 is be VBZ cord-335886-m0d72ntg 29 16 . . . cord-335886-m0d72ntg 30 1 https://doi.org/10.1101/2020.02.26.20027797 https://doi.org/10.1101/2020.02.26.20027797 '' cord-335886-m0d72ntg 31 1 doi doi NNP cord-335886-m0d72ntg 31 2 : : : cord-335886-m0d72ntg 32 1 medRxiv medRxiv NNP cord-335886-m0d72ntg 32 2 preprint preprint NNP cord-335886-m0d72ntg 33 1 We -PRON- PRP cord-335886-m0d72ntg 33 2 define define VBP cord-335886-m0d72ntg 33 3 the the DT cord-335886-m0d72ntg 33 4 initial initial JJ cord-335886-m0d72ntg 33 5 transmission transmission NN cord-335886-m0d72ntg 33 6 time time NN cord-335886-m0d72ntg 33 7 constant constant JJ cord-335886-m0d72ntg 33 8 , , , cord-335886-m0d72ntg 33 9 τ τ NN cord-335886-m0d72ntg 33 10 trans trans NNP cord-335886-m0d72ntg 33 11 , , , cord-335886-m0d72ntg 33 12 after after IN cord-335886-m0d72ntg 33 13 which which WDT cord-335886-m0d72ntg 33 14 a a DT cord-335886-m0d72ntg 33 15 pathogen pathogen NN cord-335886-m0d72ntg 33 16 is be VBZ cord-335886-m0d72ntg 33 17 transmitted transmit VBN cord-335886-m0d72ntg 33 18 to to IN cord-335886-m0d72ntg 33 19 one one CD cord-335886-m0d72ntg 33 20 susceptible susceptible JJ cord-335886-m0d72ntg 33 21 host host NN cord-335886-m0d72ntg 33 22 in in IN cord-335886-m0d72ntg 33 23 the the DT cord-335886-m0d72ntg 33 24 early early JJ cord-335886-m0d72ntg 33 25 stage stage NN cord-335886-m0d72ntg 33 26 of of IN cord-335886-m0d72ntg 33 27 the the DT cord-335886-m0d72ntg 33 28 epidemic epidemic NN cord-335886-m0d72ntg 33 29 and and CC cord-335886-m0d72ntg 33 30 the the DT cord-335886-m0d72ntg 33 31 infectious infectious JJ cord-335886-m0d72ntg 33 32 time time NN cord-335886-m0d72ntg 33 33 of of IN cord-335886-m0d72ntg 33 34 a a DT cord-335886-m0d72ntg 33 35 pathogen pathogen NN cord-335886-m0d72ntg 33 36 , , , cord-335886-m0d72ntg 33 37 τ τ NN cord-335886-m0d72ntg 33 38 inf inf NNP cord-335886-m0d72ntg 33 39 , , , cord-335886-m0d72ntg 33 40 after after IN cord-335886-m0d72ntg 33 41 which which WDT cord-335886-m0d72ntg 33 42 the the DT cord-335886-m0d72ntg 33 43 pathogen pathogen NN cord-335886-m0d72ntg 33 44 loses lose VBZ cord-335886-m0d72ntg 33 45 the the DT cord-335886-m0d72ntg 33 46 power power NN cord-335886-m0d72ntg 33 47 of of IN cord-335886-m0d72ntg 33 48 transmission transmission NN cord-335886-m0d72ntg 33 49 as as IN cord-335886-m0d72ntg 33 50 follows follow VBZ cord-335886-m0d72ntg 33 51 , , , cord-335886-m0d72ntg 33 52 The the DT cord-335886-m0d72ntg 33 53 basic basic JJ cord-335886-m0d72ntg 33 54 reproduction reproduction NN cord-335886-m0d72ntg 33 55 number number NN cord-335886-m0d72ntg 33 56 , , , cord-335886-m0d72ntg 33 57 R R NNP cord-335886-m0d72ntg 33 58 0 0 CD cord-335886-m0d72ntg 33 59 , , , cord-335886-m0d72ntg 33 60 which which WDT cord-335886-m0d72ntg 33 61 is be VBZ cord-335886-m0d72ntg 33 62 the the DT cord-335886-m0d72ntg 33 63 number number NN cord-335886-m0d72ntg 33 64 of of IN cord-335886-m0d72ntg 33 65 persons person NNS cord-335886-m0d72ntg 33 66 infected infect VBN cord-335886-m0d72ntg 33 67 by by IN cord-335886-m0d72ntg 33 68 the the DT cord-335886-m0d72ntg 33 69 transmission transmission NN cord-335886-m0d72ntg 33 70 of of IN cord-335886-m0d72ntg 33 71 a a DT cord-335886-m0d72ntg 33 72 pathogen pathogen NN cord-335886-m0d72ntg 33 73 from from IN cord-335886-m0d72ntg 33 74 one one CD cord-335886-m0d72ntg 33 75 infected infected JJ cord-335886-m0d72ntg 33 76 person person NN cord-335886-m0d72ntg 33 77 during during IN cord-335886-m0d72ntg 33 78 the the DT cord-335886-m0d72ntg 33 79 infectious infectious JJ cord-335886-m0d72ntg 33 80 time time NN cord-335886-m0d72ntg 33 81 , , , cord-335886-m0d72ntg 33 82 is be VBZ cord-335886-m0d72ntg 33 83 given give VBN cord-335886-m0d72ntg 33 84 by by IN cord-335886-m0d72ntg 34 1 In in IN cord-335886-m0d72ntg 34 2 the the DT cord-335886-m0d72ntg 34 3 following following NN cord-335886-m0d72ntg 34 4 , , , cord-335886-m0d72ntg 34 5 we -PRON- PRP cord-335886-m0d72ntg 34 6 see see VBP cord-335886-m0d72ntg 34 7 that that IN cord-335886-m0d72ntg 34 8 an an DT cord-335886-m0d72ntg 34 9 epidemic epidemic NN cord-335886-m0d72ntg 34 10 starts start VBZ cord-335886-m0d72ntg 34 11 with with IN cord-335886-m0d72ntg 34 12 exponential exponential JJ cord-335886-m0d72ntg 34 13 growth growth NN cord-335886-m0d72ntg 34 14 with with IN cord-335886-m0d72ntg 34 15 a a DT cord-335886-m0d72ntg 34 16 time time NN cord-335886-m0d72ntg 34 17 constant constant JJ cord-335886-m0d72ntg 34 18 τ τ NN cord-335886-m0d72ntg 34 19 grow grow VB cord-335886-m0d72ntg 34 20 given give VBN cord-335886-m0d72ntg 34 21 by by IN cord-335886-m0d72ntg 34 22 and and CC cord-335886-m0d72ntg 34 23 decays decay VBZ cord-335886-m0d72ntg 34 24 exponentially exponentially RB cord-335886-m0d72ntg 34 25 with with IN cord-335886-m0d72ntg 34 26 a a DT cord-335886-m0d72ntg 34 27 time time NN cord-335886-m0d72ntg 34 28 constant constant JJ cord-335886-m0d72ntg 34 29 τ τ NN cord-335886-m0d72ntg 34 30 end end VB cord-335886-m0d72ntg 34 31 given give VBN cord-335886-m0d72ntg 34 32 by by IN cord-335886-m0d72ntg 34 33 Here here RB cord-335886-m0d72ntg 34 34 , , , cord-335886-m0d72ntg 34 35 p(∞ p(∞ ADD cord-335886-m0d72ntg 34 36 ) ) -RRB- cord-335886-m0d72ntg 35 1 is be VBZ cord-335886-m0d72ntg 35 2 the the DT cord-335886-m0d72ntg 35 3 final final JJ cord-335886-m0d72ntg 35 4 size size NN cord-335886-m0d72ntg 35 5 of of IN cord-335886-m0d72ntg 35 6 the the DT cord-335886-m0d72ntg 35 7 disaster disaster NN cord-335886-m0d72ntg 35 8 which which WDT cord-335886-m0d72ntg 35 9 is be VBZ cord-335886-m0d72ntg 35 10 defined define VBN cord-335886-m0d72ntg 35 11 by by IN cord-335886-m0d72ntg 35 12 the the DT cord-335886-m0d72ntg 35 13 ratio ratio NN cord-335886-m0d72ntg 35 14 of of IN cord-335886-m0d72ntg 35 15 the the DT cord-335886-m0d72ntg 35 16 total total JJ cord-335886-m0d72ntg 35 17 number number NN cord-335886-m0d72ntg 35 18 of of IN cord-335886-m0d72ntg 35 19 the the DT cord-335886-m0d72ntg 35 20 infected infected JJ cord-335886-m0d72ntg 35 21 people people NNS cord-335886-m0d72ntg 35 22 , , , cord-335886-m0d72ntg 35 23 R(∞ R(∞ NNP cord-335886-m0d72ntg 35 24 ) ) -RRB- cord-335886-m0d72ntg 35 25 , , , cord-335886-m0d72ntg 35 26 to to IN cord-335886-m0d72ntg 35 27 the the DT cord-335886-m0d72ntg 35 28 population population NN cord-335886-m0d72ntg 35 29 of of IN cord-335886-m0d72ntg 35 30 the the DT cord-335886-m0d72ntg 35 31 society society NN cord-335886-m0d72ntg 35 32 , , , cord-335886-m0d72ntg 35 33 S S NNP cord-335886-m0d72ntg 35 34 0 0 CD cord-335886-m0d72ntg 35 35 . . . cord-335886-m0d72ntg 36 1 As as IN cord-335886-m0d72ntg 36 2 shown show VBN cord-335886-m0d72ntg 36 3 later later RB cord-335886-m0d72ntg 36 4 , , , cord-335886-m0d72ntg 36 5 p(∞ p(∞ VBN cord-335886-m0d72ntg 36 6 ) ) -RRB- cord-335886-m0d72ntg 36 7 is be VBZ cord-335886-m0d72ntg 36 8 approximated approximate VBN cord-335886-m0d72ntg 36 9 as as IN cord-335886-m0d72ntg 36 10 , , , cord-335886-m0d72ntg 36 11 By by IN cord-335886-m0d72ntg 36 12 using use VBG cord-335886-m0d72ntg 36 13 R r NN cord-335886-m0d72ntg 36 14 0 0 CD cord-335886-m0d72ntg 36 15 , , , cord-335886-m0d72ntg 36 16 Eq Eq NNP cord-335886-m0d72ntg 36 17 . . . cord-335886-m0d72ntg 37 1 ( ( -LRB- cord-335886-m0d72ntg 37 2 7 7 LS cord-335886-m0d72ntg 37 3 ) ) -RRB- cord-335886-m0d72ntg 37 4 is be VBZ cord-335886-m0d72ntg 37 5 rewritten rewrite VBN cord-335886-m0d72ntg 37 6 as as IN cord-335886-m0d72ntg 37 7 R r NN cord-335886-m0d72ntg 37 8 0 0 CD cord-335886-m0d72ntg 37 9 , , , cord-335886-m0d72ntg 37 10 τ τ NN cord-335886-m0d72ntg 37 11 inf inf NNP cord-335886-m0d72ntg 37 12 , , , cord-335886-m0d72ntg 37 13 and and CC cord-335886-m0d72ntg 37 14 p(∞ p(∞ NNP cord-335886-m0d72ntg 37 15 ) ) -RRB- cord-335886-m0d72ntg 37 16 are be VBP cord-335886-m0d72ntg 37 17 parameters parameter NNS cord-335886-m0d72ntg 37 18 describing describe VBG cord-335886-m0d72ntg 37 19 an an DT cord-335886-m0d72ntg 37 20 epidemic epidemic NN cord-335886-m0d72ntg 37 21 . . . cord-335886-m0d72ntg 38 1 The the DT cord-335886-m0d72ntg 38 2 above above JJ cord-335886-m0d72ntg 38 3 relations relation NNS cord-335886-m0d72ntg 38 4 , , , cord-335886-m0d72ntg 38 5 Eqs Eqs NNP cord-335886-m0d72ntg 38 6 . . . cord-335886-m0d72ntg 39 1 ( ( -LRB- cord-335886-m0d72ntg 39 2 7 7 CD cord-335886-m0d72ntg 39 3 ) ) -RRB- cord-335886-m0d72ntg 39 4 to to IN cord-335886-m0d72ntg 39 5 ( ( -LRB- cord-335886-m0d72ntg 39 6 10 10 CD cord-335886-m0d72ntg 39 7 ) ) -RRB- cord-335886-m0d72ntg 39 8 , , , cord-335886-m0d72ntg 39 9 are be VBP cord-335886-m0d72ntg 39 10 derived derive VBN cord-335886-m0d72ntg 39 11 as as IN cord-335886-m0d72ntg 39 12 follows follow VBZ cord-335886-m0d72ntg 39 13 . . . cord-335886-m0d72ntg 40 1 In in IN cord-335886-m0d72ntg 40 2 the the DT cord-335886-m0d72ntg 40 3 beginning beginning NN cord-335886-m0d72ntg 40 4 of of IN cord-335886-m0d72ntg 40 5 the the DT cord-335886-m0d72ntg 40 6 epidemic epidemic NN cord-335886-m0d72ntg 40 7 , , , cord-335886-m0d72ntg 40 8 I(t I(t NNP cord-335886-m0d72ntg 40 9 ) ) -RRB- cord-335886-m0d72ntg 40 10 and and CC cord-335886-m0d72ntg 40 11 R(t R(t NNP cord-335886-m0d72ntg 40 12 ) ) -RRB- cord-335886-m0d72ntg 40 13 are be VBP cord-335886-m0d72ntg 40 14 negligible negligible JJ cord-335886-m0d72ntg 40 15 compared compare VBN cord-335886-m0d72ntg 40 16 to to IN cord-335886-m0d72ntg 40 17 S S NNP cord-335886-m0d72ntg 40 18 0 0 CD cord-335886-m0d72ntg 40 19 , , , cord-335886-m0d72ntg 40 20 and and CC cord-335886-m0d72ntg 40 21 Eq Eq NNP cord-335886-m0d72ntg 40 22 . . . cord-335886-m0d72ntg 41 1 the the DT cord-335886-m0d72ntg 41 2 author author NN cord-335886-m0d72ntg 41 3 / / SYM cord-335886-m0d72ntg 41 4 funder funder NN cord-335886-m0d72ntg 41 5 , , , cord-335886-m0d72ntg 41 6 who who WP cord-335886-m0d72ntg 41 7 has have VBZ cord-335886-m0d72ntg 41 8 granted grant VBN cord-335886-m0d72ntg 41 9 medRxiv medRxiv NNS cord-335886-m0d72ntg 41 10 a a DT cord-335886-m0d72ntg 41 11 license license NN cord-335886-m0d72ntg 41 12 to to TO cord-335886-m0d72ntg 41 13 display display VB cord-335886-m0d72ntg 41 14 the the DT cord-335886-m0d72ntg 41 15 preprint preprint NN cord-335886-m0d72ntg 41 16 in in IN cord-335886-m0d72ntg 41 17 perpetuity perpetuity NN cord-335886-m0d72ntg 41 18 . . . cord-335886-m0d72ntg 42 1 The the DT cord-335886-m0d72ntg 42 2 copyright copyright NN cord-335886-m0d72ntg 42 3 holder holder NN cord-335886-m0d72ntg 42 4 for for IN cord-335886-m0d72ntg 42 5 this this DT cord-335886-m0d72ntg 42 6 preprint preprint NN cord-335886-m0d72ntg 42 7 ( ( -LRB- cord-335886-m0d72ntg 42 8 which which WDT cord-335886-m0d72ntg 42 9 was be VBD cord-335886-m0d72ntg 42 10 not not RB cord-335886-m0d72ntg 42 11 peer peer NN cord-335886-m0d72ntg 42 12 - - HYPH cord-335886-m0d72ntg 42 13 reviewed review VBN cord-335886-m0d72ntg 42 14 ) ) -RRB- cord-335886-m0d72ntg 42 15 is be VBZ cord-335886-m0d72ntg 42 16 which which WDT cord-335886-m0d72ntg 42 17 gives give VBZ cord-335886-m0d72ntg 42 18 exponential exponential JJ cord-335886-m0d72ntg 42 19 decay decay NN cord-335886-m0d72ntg 42 20 of of IN cord-335886-m0d72ntg 42 21 the the DT cord-335886-m0d72ntg 42 22 patients patient NNS cord-335886-m0d72ntg 42 23 . . . cord-335886-m0d72ntg 43 1 The the DT cord-335886-m0d72ntg 43 2 time time NN cord-335886-m0d72ntg 43 3 constant constant JJ cord-335886-m0d72ntg 43 4 of of IN cord-335886-m0d72ntg 43 5 the the DT cord-335886-m0d72ntg 43 6 decay decay NN cord-335886-m0d72ntg 43 7 τ τ NN cord-335886-m0d72ntg 43 8 end end NN cord-335886-m0d72ntg 43 9 is be VBZ cord-335886-m0d72ntg 43 10 given give VBN cord-335886-m0d72ntg 43 11 by by IN cord-335886-m0d72ntg 43 12 Thus thus RB cord-335886-m0d72ntg 43 13 , , , cord-335886-m0d72ntg 43 14 Eq Eq NNP cord-335886-m0d72ntg 43 15 . . . cord-335886-m0d72ntg 44 1 ( ( -LRB- cord-335886-m0d72ntg 44 2 8) 8) NNP cord-335886-m0d72ntg 44 3 is be VBZ cord-335886-m0d72ntg 44 4 derived derive VBN cord-335886-m0d72ntg 44 5 . . . cord-335886-m0d72ntg 45 1 The the DT cord-335886-m0d72ntg 45 2 final final JJ cord-335886-m0d72ntg 45 3 size size NN cord-335886-m0d72ntg 45 4 equation equation NN cord-335886-m0d72ntg 45 5 was be VBD cord-335886-m0d72ntg 45 6 numerically numerically RB cord-335886-m0d72ntg 45 7 solved solve VBN cord-335886-m0d72ntg 45 8 and and CC cord-335886-m0d72ntg 45 9 the the DT cord-335886-m0d72ntg 45 10 result result NN cord-335886-m0d72ntg 45 11 is be VBZ cord-335886-m0d72ntg 45 12 shown show VBN cord-335886-m0d72ntg 45 13 by by IN cord-335886-m0d72ntg 45 14 the the DT cord-335886-m0d72ntg 45 15 solid solid JJ cord-335886-m0d72ntg 45 16 curve curve NN cord-335886-m0d72ntg 45 17 in in IN cord-335886-m0d72ntg 45 18 Fig.2 Fig.2 NNP cord-335886-m0d72ntg 45 19 . . . cord-335886-m0d72ntg 46 1 As as IN cord-335886-m0d72ntg 46 2 R r NN cord-335886-m0d72ntg 46 3 0 0 CD cord-335886-m0d72ntg 46 4 increases increase NNS cord-335886-m0d72ntg 46 5 from from IN cord-335886-m0d72ntg 46 6 1 1 CD cord-335886-m0d72ntg 46 7 , , , cord-335886-m0d72ntg 46 8 p p NN cord-335886-m0d72ntg 46 9 ( ( -LRB- cord-335886-m0d72ntg 46 10 ∞ ∞ NNP cord-335886-m0d72ntg 46 11 ) ) -RRB- cord-335886-m0d72ntg 46 12 increases increase VBZ cord-335886-m0d72ntg 46 13 from from IN cord-335886-m0d72ntg 46 14 zero zero CD cord-335886-m0d72ntg 46 15 and and CC cord-335886-m0d72ntg 46 16 saturates saturate VBZ cord-335886-m0d72ntg 46 17 at at IN cord-335886-m0d72ntg 46 18 a a DT cord-335886-m0d72ntg 46 19 large large JJ cord-335886-m0d72ntg 46 20 R r NN cord-335886-m0d72ntg 46 21 0 0 CD cord-335886-m0d72ntg 46 22 . . . cord-335886-m0d72ntg 47 1 When when WRB cord-335886-m0d72ntg 47 2 R r NN cord-335886-m0d72ntg 47 3 0 0 CD cord-335886-m0d72ntg 47 4 is be VBZ cord-335886-m0d72ntg 47 5 larger large JJR cord-335886-m0d72ntg 47 6 than than IN cord-335886-m0d72ntg 47 7 2.5 2.5 CD cord-335886-m0d72ntg 47 8 , , , cord-335886-m0d72ntg 47 9 more more JJR cord-335886-m0d72ntg 47 10 than than IN cord-335886-m0d72ntg 47 11 90 90 CD cord-335886-m0d72ntg 47 12 % % NN cord-335886-m0d72ntg 47 13 of of IN cord-335886-m0d72ntg 47 14 people people NNS cord-335886-m0d72ntg 47 15 in in IN cord-335886-m0d72ntg 47 16 the the DT cord-335886-m0d72ntg 47 17 group group NN cord-335886-m0d72ntg 47 18 are be VBP cord-335886-m0d72ntg 47 19 _SP cord-335886-m0d72ntg 48 1 We -PRON- PRP cord-335886-m0d72ntg 48 2 apply apply VBP cord-335886-m0d72ntg 48 3 the the DT cord-335886-m0d72ntg 48 4 above above JJ cord-335886-m0d72ntg 48 5 model model NN cord-335886-m0d72ntg 48 6 to to IN cord-335886-m0d72ntg 48 7 the the DT cord-335886-m0d72ntg 48 8 epidemic epidemic NN cord-335886-m0d72ntg 48 9 of of IN cord-335886-m0d72ntg 48 10 influenza influenza NN cord-335886-m0d72ntg 48 11 in in IN cord-335886-m0d72ntg 48 12 Japan Japan NNP cord-335886-m0d72ntg 48 13 as as IN cord-335886-m0d72ntg 48 14 cited cite VBN cord-335886-m0d72ntg 48 15 in in IN cord-335886-m0d72ntg 48 16 ref.1 ref.1 NNP cord-335886-m0d72ntg 48 17 as as IN cord-335886-m0d72ntg 48 18 a a DT cord-335886-m0d72ntg 48 19 reference reference NN cord-335886-m0d72ntg 48 20 for for IN cord-335886-m0d72ntg 48 21 the the DT cord-335886-m0d72ntg 48 22 general general JJ cord-335886-m0d72ntg 48 23 epidemic epidemic NN cord-335886-m0d72ntg 48 24 . . . cord-335886-m0d72ntg 49 1 Figure figure NN cord-335886-m0d72ntg 49 2 3 3 CD cord-335886-m0d72ntg 49 3 shows show VBZ cord-335886-m0d72ntg 49 4 the the DT cord-335886-m0d72ntg 49 5 influenza influenza NN cord-335886-m0d72ntg 49 6 epidemic epidemic NN cord-335886-m0d72ntg 49 7 in in IN cord-335886-m0d72ntg 49 8 Japan Japan NNP cord-335886-m0d72ntg 49 9 over over IN cord-335886-m0d72ntg 49 10 the the DT cord-335886-m0d72ntg 49 11 past past JJ cord-335886-m0d72ntg 49 12 decade decade NN cord-335886-m0d72ntg 49 13 ( ( -LRB- cord-335886-m0d72ntg 49 14 ref ref NN cord-335886-m0d72ntg 49 15 . . . cord-335886-m0d72ntg 50 1 the the DT cord-335886-m0d72ntg 50 2 author author NN cord-335886-m0d72ntg 50 3 / / SYM cord-335886-m0d72ntg 50 4 funder funder NN cord-335886-m0d72ntg 50 5 , , , cord-335886-m0d72ntg 50 6 who who WP cord-335886-m0d72ntg 50 7 has have VBZ cord-335886-m0d72ntg 50 8 granted grant VBN cord-335886-m0d72ntg 50 9 medRxiv medRxiv NNS cord-335886-m0d72ntg 50 10 a a DT cord-335886-m0d72ntg 50 11 license license NN cord-335886-m0d72ntg 50 12 to to TO cord-335886-m0d72ntg 50 13 display display VB cord-335886-m0d72ntg 50 14 the the DT cord-335886-m0d72ntg 50 15 preprint preprint NN cord-335886-m0d72ntg 50 16 in in IN cord-335886-m0d72ntg 50 17 perpetuity perpetuity NN cord-335886-m0d72ntg 50 18 . . . cord-335886-m0d72ntg 51 1 The the DT cord-335886-m0d72ntg 51 2 copyright copyright NN cord-335886-m0d72ntg 51 3 holder holder NN cord-335886-m0d72ntg 51 4 for for IN cord-335886-m0d72ntg 51 5 this this DT cord-335886-m0d72ntg 51 6 preprint preprint NN cord-335886-m0d72ntg 51 7 ( ( -LRB- cord-335886-m0d72ntg 51 8 which which WDT cord-335886-m0d72ntg 51 9 was be VBD cord-335886-m0d72ntg 51 10 not not RB cord-335886-m0d72ntg 51 11 peer peer NN cord-335886-m0d72ntg 51 12 - - HYPH cord-335886-m0d72ntg 51 13 reviewed review VBN cord-335886-m0d72ntg 51 14 ) ) -RRB- cord-335886-m0d72ntg 51 15 is be VBZ cord-335886-m0d72ntg 51 16 from from IN cord-335886-m0d72ntg 51 17 0.52 0.52 CD cord-335886-m0d72ntg 51 18 weeks week NNS cord-335886-m0d72ntg 51 19 , , , cord-335886-m0d72ntg 51 20 the the DT cord-335886-m0d72ntg 51 21 time time NN cord-335886-m0d72ntg 51 22 constant constant JJ cord-335886-m0d72ntg 51 23 of of IN cord-335886-m0d72ntg 51 24 the the DT cord-335886-m0d72ntg 51 25 rising rise VBG cord-335886-m0d72ntg 51 26 of of IN cord-335886-m0d72ntg 51 27 the the DT cord-335886-m0d72ntg 51 28 epidemic epidemic NN cord-335886-m0d72ntg 51 29 can can MD cord-335886-m0d72ntg 51 30 be be VB cord-335886-m0d72ntg 51 31 increased increase VBN cord-335886-m0d72ntg 51 32 to to IN cord-335886-m0d72ntg 51 33 1.5 1.5 CD cord-335886-m0d72ntg 51 34 weeks week NNS cord-335886-m0d72ntg 51 35 in in IN cord-335886-m0d72ntg 51 36 the the DT cord-335886-m0d72ntg 51 37 model model NN cord-335886-m0d72ntg 51 38 calculation calculation NN cord-335886-m0d72ntg 51 39 , , , cord-335886-m0d72ntg 51 40 but but CC cord-335886-m0d72ntg 51 41 the the DT cord-335886-m0d72ntg 51 42 width width NN cord-335886-m0d72ntg 51 43 of of IN cord-335886-m0d72ntg 51 44 the the DT cord-335886-m0d72ntg 51 45 epidemic epidemic NN cord-335886-m0d72ntg 51 46 in in IN cord-335886-m0d72ntg 51 47 the the DT cord-335886-m0d72ntg 51 48 model model NN cord-335886-m0d72ntg 51 49 calculation calculation NN cord-335886-m0d72ntg 51 50 was be VBD cord-335886-m0d72ntg 51 51 too too RB cord-335886-m0d72ntg 51 52 wider wide JJR cord-335886-m0d72ntg 51 53 than than IN cord-335886-m0d72ntg 51 54 the the DT cord-335886-m0d72ntg 51 55 real real JJ cord-335886-m0d72ntg 51 56 one one NN cord-335886-m0d72ntg 51 57 as as IN cord-335886-m0d72ntg 51 58 shown show VBN cord-335886-m0d72ntg 51 59 in in IN cord-335886-m0d72ntg 51 60 Fig.6 fig.6 NN cord-335886-m0d72ntg 51 61 . . . cord-335886-m0d72ntg 52 1 In in IN cord-335886-m0d72ntg 52 2 all all PDT cord-335886-m0d72ntg 52 3 the the DT cord-335886-m0d72ntg 52 4 cases case NNS cord-335886-m0d72ntg 52 5 of of IN cord-335886-m0d72ntg 52 6 the the DT cord-335886-m0d72ntg 52 7 epidemic epidemic NN cord-335886-m0d72ntg 52 8 , , , cord-335886-m0d72ntg 52 9 there there EX cord-335886-m0d72ntg 52 10 should should MD cord-335886-m0d72ntg 52 11 be be VB cord-335886-m0d72ntg 52 12 a a DT cord-335886-m0d72ntg 52 13 difference difference NN cord-335886-m0d72ntg 52 14 between between IN cord-335886-m0d72ntg 52 15 the the DT cord-335886-m0d72ntg 52 16 reported report VBN cord-335886-m0d72ntg 52 17 number number NN cord-335886-m0d72ntg 52 18 of of IN cord-335886-m0d72ntg 52 19 patients patient NNS cord-335886-m0d72ntg 52 20 and and CC cord-335886-m0d72ntg 52 21 the the DT cord-335886-m0d72ntg 52 22 real real JJ cord-335886-m0d72ntg 52 23 number number NN cord-335886-m0d72ntg 52 24 of of IN cord-335886-m0d72ntg 52 25 infected infected JJ cord-335886-m0d72ntg 52 26 people people NNS cord-335886-m0d72ntg 52 27 . . . cord-335886-m0d72ntg 53 1 Not not RB cord-335886-m0d72ntg 53 2 all all DT cord-335886-m0d72ntg 53 3 infected infected JJ cord-335886-m0d72ntg 53 4 people people NNS cord-335886-m0d72ntg 53 5 will will MD cord-335886-m0d72ntg 53 6 go go VB cord-335886-m0d72ntg 53 7 to to IN cord-335886-m0d72ntg 53 8 a a DT cord-335886-m0d72ntg 53 9 hospital hospital NN cord-335886-m0d72ntg 53 10 and and CC cord-335886-m0d72ntg 53 11 not not RB cord-335886-m0d72ntg 53 12 all all DT cord-335886-m0d72ntg 53 13 patients patient NNS cord-335886-m0d72ntg 53 14 are be VBP cord-335886-m0d72ntg 53 15 not not RB cord-335886-m0d72ntg 53 16 inspected inspect VBN cord-335886-m0d72ntg 53 17 by by IN cord-335886-m0d72ntg 53 18 medical medical JJ cord-335886-m0d72ntg 53 19 institutes institute NNS cord-335886-m0d72ntg 53 20 . . . cord-335886-m0d72ntg 54 1 In in IN cord-335886-m0d72ntg 54 2 analyzing analyze VBG cord-335886-m0d72ntg 54 3 statistics statistic NNS cord-335886-m0d72ntg 54 4 , , , cord-335886-m0d72ntg 54 5 we -PRON- PRP cord-335886-m0d72ntg 54 6 assume assume VBP cord-335886-m0d72ntg 54 7 the the DT cord-335886-m0d72ntg 54 8 ratio ratio NN cord-335886-m0d72ntg 54 9 of of IN cord-335886-m0d72ntg 54 10 the the DT cord-335886-m0d72ntg 54 11 reported report VBN cord-335886-m0d72ntg 54 12 number number NN cord-335886-m0d72ntg 54 13 to to IN cord-335886-m0d72ntg 54 14 the the DT cord-335886-m0d72ntg 54 15 real real JJ cord-335886-m0d72ntg 54 16 number number NN cord-335886-m0d72ntg 54 17 is be VBZ cord-335886-m0d72ntg 54 18 constant constant JJ cord-335886-m0d72ntg 54 19 during during IN cord-335886-m0d72ntg 54 20 the the DT cord-335886-m0d72ntg 54 21 epidemic epidemic NN cord-335886-m0d72ntg 54 22 , , , cord-335886-m0d72ntg 54 23 but but CC cord-335886-m0d72ntg 54 24 often often RB cord-335886-m0d72ntg 54 25 the the DT cord-335886-m0d72ntg 54 26 assumption assumption NN cord-335886-m0d72ntg 54 27 can can MD cord-335886-m0d72ntg 54 28 be be VB cord-335886-m0d72ntg 54 29 wrong wrong JJ cord-335886-m0d72ntg 54 30 . . . cord-335886-m0d72ntg 55 1 We -PRON- PRP cord-335886-m0d72ntg 55 2 expect expect VBP cord-335886-m0d72ntg 55 3 the the DT cord-335886-m0d72ntg 55 4 ratio ratio NN cord-335886-m0d72ntg 55 5 is be VBZ cord-335886-m0d72ntg 55 6 smaller small JJR cord-335886-m0d72ntg 55 7 in in IN cord-335886-m0d72ntg 55 8 the the DT cord-335886-m0d72ntg 55 9 beginning beginning NN cord-335886-m0d72ntg 55 10 and and CC cord-335886-m0d72ntg 55 11 at at IN cord-335886-m0d72ntg 55 12 the the DT cord-335886-m0d72ntg 55 13 ending ending NN cord-335886-m0d72ntg 55 14 of of IN cord-335886-m0d72ntg 55 15 an an DT cord-335886-m0d72ntg 55 16 epidemic epidemic NN cord-335886-m0d72ntg 55 17 . . . cord-335886-m0d72ntg 56 1 Then then RB cord-335886-m0d72ntg 56 2 , , , cord-335886-m0d72ntg 56 3 the the DT cord-335886-m0d72ntg 56 4 time time NN cord-335886-m0d72ntg 56 5 constant constant JJ cord-335886-m0d72ntg 56 6 of of IN cord-335886-m0d72ntg 56 7 the the DT cord-335886-m0d72ntg 56 8 " " `` cord-335886-m0d72ntg 56 9 apparent apparent JJ cord-335886-m0d72ntg 56 10 rise rise NN cord-335886-m0d72ntg 56 11 " " '' cord-335886-m0d72ntg 56 12 and and CC cord-335886-m0d72ntg 56 13 " " `` cord-335886-m0d72ntg 56 14 apparent apparent JJ cord-335886-m0d72ntg 56 15 ending ending NN cord-335886-m0d72ntg 56 16 " " '' cord-335886-m0d72ntg 56 17 will will MD cord-335886-m0d72ntg 56 18 be be VB cord-335886-m0d72ntg 56 19 shorter short JJR cord-335886-m0d72ntg 56 20 than than IN cord-335886-m0d72ntg 56 21 the the DT cord-335886-m0d72ntg 56 22 real real JJ cord-335886-m0d72ntg 56 23 ones one NNS cord-335886-m0d72ntg 56 24 . . . cord-335886-m0d72ntg 57 1 However however RB cord-335886-m0d72ntg 57 2 , , , cord-335886-m0d72ntg 57 3 this this DT cord-335886-m0d72ntg 57 4 expectation expectation NN cord-335886-m0d72ntg 57 5 was be VBD cord-335886-m0d72ntg 57 6 the the DT cord-335886-m0d72ntg 57 7 opposite opposite NN cord-335886-m0d72ntg 57 8 in in IN cord-335886-m0d72ntg 57 9 Fig.5 Fig.5 NNP cord-335886-m0d72ntg 57 10 . . . cord-335886-m0d72ntg 58 1 The the DT cord-335886-m0d72ntg 58 2 slower slow JJR cord-335886-m0d72ntg 58 3 increase increase NN cord-335886-m0d72ntg 58 4 and and CC cord-335886-m0d72ntg 58 5 the the DT cord-335886-m0d72ntg 58 6 slower slow JJR cord-335886-m0d72ntg 58 7 decrease decrease NN cord-335886-m0d72ntg 58 8 at at IN cord-335886-m0d72ntg 58 9 the the DT cord-335886-m0d72ntg 58 10 skirt skirt NN cord-335886-m0d72ntg 58 11 of of IN cord-335886-m0d72ntg 58 12 the the DT cord-335886-m0d72ntg 58 13 epidemic epidemic NN cord-335886-m0d72ntg 58 14 could could MD cord-335886-m0d72ntg 58 15 suggest suggest VB cord-335886-m0d72ntg 58 16 the the DT cord-335886-m0d72ntg 58 17 transmission transmission NN cord-335886-m0d72ntg 58 18 power power NN cord-335886-m0d72ntg 58 19 β β XX cord-335886-m0d72ntg 58 20 of of IN cord-335886-m0d72ntg 58 21 the the DT cord-335886-m0d72ntg 58 22 virus virus NN cord-335886-m0d72ntg 58 23 may may MD cord-335886-m0d72ntg 58 24 change change VB cord-335886-m0d72ntg 58 25 in in IN cord-335886-m0d72ntg 58 26 time time NN cord-335886-m0d72ntg 58 27 , , , cord-335886-m0d72ntg 58 28 which which WDT cord-335886-m0d72ntg 58 29 , , , cord-335886-m0d72ntg 58 30 we -PRON- PRP cord-335886-m0d72ntg 58 31 think think VBP cord-335886-m0d72ntg 58 32 , , , cord-335886-m0d72ntg 58 33 is be VBZ cord-335886-m0d72ntg 58 34 not not RB cord-335886-m0d72ntg 58 35 plausible plausible JJ cord-335886-m0d72ntg 58 36 . . . cord-335886-m0d72ntg 59 1 At at IN cord-335886-m0d72ntg 59 2 present present NN cord-335886-m0d72ntg 59 3 , , , cord-335886-m0d72ntg 59 4 we -PRON- PRP cord-335886-m0d72ntg 59 5 do do VBP cord-335886-m0d72ntg 59 6 not not RB cord-335886-m0d72ntg 59 7 know know VB cord-335886-m0d72ntg 59 8 the the DT cord-335886-m0d72ntg 59 9 reason reason NN cord-335886-m0d72ntg 59 10 why why WRB cord-335886-m0d72ntg 59 11 the the DT cord-335886-m0d72ntg 59 12 simple simple JJ cord-335886-m0d72ntg 59 13 Kermack Kermack NNP cord-335886-m0d72ntg 59 14 - - HYPH cord-335886-m0d72ntg 59 15 McKendrick McKendrick NNP cord-335886-m0d72ntg 59 16 can can MD cord-335886-m0d72ntg 59 17 not not RB cord-335886-m0d72ntg 59 18 reproduce reproduce VB cord-335886-m0d72ntg 59 19 the the DT cord-335886-m0d72ntg 59 20 whole whole JJ cord-335886-m0d72ntg 59 21 epidemic epidemic NN cord-335886-m0d72ntg 59 22 including include VBG cord-335886-m0d72ntg 59 23 the the DT cord-335886-m0d72ntg 59 24 skirt skirt NN cord-335886-m0d72ntg 59 25 parts part NNS cord-335886-m0d72ntg 59 26 . . . cord-335886-m0d72ntg 60 1 Thus thus RB cord-335886-m0d72ntg 60 2 , , , cord-335886-m0d72ntg 60 3 from from IN cord-335886-m0d72ntg 60 4 the the DT cord-335886-m0d72ntg 60 5 analysis analysis NN cord-335886-m0d72ntg 60 6 of of IN cord-335886-m0d72ntg 60 7 JpnInf2019 jpninf2019 NN cord-335886-m0d72ntg 60 8 by by IN cord-335886-m0d72ntg 60 9 the the DT cord-335886-m0d72ntg 60 10 model model NN cord-335886-m0d72ntg 60 11 described describe VBN cord-335886-m0d72ntg 60 12 above above RB cord-335886-m0d72ntg 60 13 , , , cord-335886-m0d72ntg 60 14 we -PRON- PRP cord-335886-m0d72ntg 60 15 learn learn VBP cord-335886-m0d72ntg 60 16 that that IN cord-335886-m0d72ntg 60 17 it -PRON- PRP cord-335886-m0d72ntg 60 18 is be VBZ cord-335886-m0d72ntg 60 19 important important JJ cord-335886-m0d72ntg 60 20 to to TO cord-335886-m0d72ntg 60 21 remember remember VB cord-335886-m0d72ntg 60 22 that that IN cord-335886-m0d72ntg 60 23 the the DT cord-335886-m0d72ntg 60 24 time time NN cord-335886-m0d72ntg 60 25 constant constant JJ cord-335886-m0d72ntg 60 26 of of IN cord-335886-m0d72ntg 60 27 the the DT cord-335886-m0d72ntg 60 28 " " `` cord-335886-m0d72ntg 60 29 apparent apparent JJ cord-335886-m0d72ntg 60 30 " " '' cord-335886-m0d72ntg 60 31 increase increase NN cord-335886-m0d72ntg 60 32 of of IN cord-335886-m0d72ntg 60 33 the the DT cord-335886-m0d72ntg 60 34 epidemic epidemic NN cord-335886-m0d72ntg 60 35 in in IN cord-335886-m0d72ntg 60 36 the the DT cord-335886-m0d72ntg 60 37 early early JJ cord-335886-m0d72ntg 60 38 stage stage NN cord-335886-m0d72ntg 60 39 does do VBZ cord-335886-m0d72ntg 60 40 not not RB cord-335886-m0d72ntg 60 41 re re VB cord-335886-m0d72ntg 60 42 - - VB cord-335886-m0d72ntg 60 43 produce produce VB cord-335886-m0d72ntg 60 44 the the DT cord-335886-m0d72ntg 60 45 whole whole JJ cord-335886-m0d72ntg 60 46 epidemic epidemic NN cord-335886-m0d72ntg 60 47 . . . cord-335886-m0d72ntg 61 1 The the DT cord-335886-m0d72ntg 61 2 above above JJ cord-335886-m0d72ntg 61 3 information information NN cord-335886-m0d72ntg 61 4 helps help VBZ cord-335886-m0d72ntg 61 5 greatly greatly RB cord-335886-m0d72ntg 61 6 to to TO cord-335886-m0d72ntg 61 7 understand understand VB cord-335886-m0d72ntg 61 8 the the DT cord-335886-m0d72ntg 61 9 to to TO cord-335886-m0d72ntg 61 10 - - HYPH cord-335886-m0d72ntg 61 11 be be VB cord-335886-m0d72ntg 61 12 - - HYPH cord-335886-m0d72ntg 61 13 planned plan VBN cord-335886-m0d72ntg 61 14 analysis analysis NN cord-335886-m0d72ntg 61 15 of of IN cord-335886-m0d72ntg 61 16 COVID-19 COVID-19 NNP cord-335886-m0d72ntg 61 17 . . . cord-335886-m0d72ntg 62 1 Useful useful JJ cord-335886-m0d72ntg 63 1 By by IN cord-335886-m0d72ntg 63 2 applying apply VBG cord-335886-m0d72ntg 63 3 the the DT cord-335886-m0d72ntg 63 4 model model NN cord-335886-m0d72ntg 63 5 , , , cord-335886-m0d72ntg 63 6 we -PRON- PRP cord-335886-m0d72ntg 63 7 found find VBD cord-335886-m0d72ntg 63 8 that that IN cord-335886-m0d72ntg 63 9 the the DT cord-335886-m0d72ntg 63 10 epidemic epidemic NN cord-335886-m0d72ntg 63 11 of of IN cord-335886-m0d72ntg 63 12 influenza influenza NN cord-335886-m0d72ntg 63 13 in in IN cord-335886-m0d72ntg 63 14 Japan Japan NNP cord-335886-m0d72ntg 63 15 in in IN cord-335886-m0d72ntg 63 16 2019 2019 CD cord-335886-m0d72ntg 63 17 was be VBD cord-335886-m0d72ntg 63 18 re re VBN cord-335886-m0d72ntg 63 19 - - VBN cord-335886-m0d72ntg 63 20 produced produce VBN cord-335886-m0d72ntg 63 21 by by IN cord-335886-m0d72ntg 63 22 the the DT cord-335886-m0d72ntg 63 23 parameters;τ parameters;τ NNP cord-335886-m0d72ntg 63 24 trans trans NNP cord-335886-m0d72ntg 63 25 = = SYM cord-335886-m0d72ntg 63 26 0.52 0.52 CD cord-335886-m0d72ntg 63 27 week week NN cord-335886-m0d72ntg 63 28 and and CC cord-335886-m0d72ntg 63 29 τ τ NN cord-335886-m0d72ntg 63 30 inf inf NNP cord-335886-m0d72ntg 63 31 = = SYM cord-335886-m0d72ntg 63 32 1 1 CD cord-335886-m0d72ntg 63 33 week week NN cord-335886-m0d72ntg 63 34 and and CC cord-335886-m0d72ntg 63 35 that that DT cord-335886-m0d72ntg 63 36 τ τ NN cord-335886-m0d72ntg 63 37 grow grow VB cord-335886-m0d72ntg 63 38 observed observe VBN cord-335886-m0d72ntg 63 39 in in IN cord-335886-m0d72ntg 63 40 the the DT cord-335886-m0d72ntg 63 41 early early JJ cord-335886-m0d72ntg 63 42 stage stage NN cord-335886-m0d72ntg 63 43 can can MD cord-335886-m0d72ntg 63 44 be be VB cord-335886-m0d72ntg 63 45 different different JJ cord-335886-m0d72ntg 63 46 from from IN cord-335886-m0d72ntg 63 47 τ τ NN cord-335886-m0d72ntg 63 48 grow grow VB cord-335886-m0d72ntg 63 49 for for IN cord-335886-m0d72ntg 63 50 re re NN cord-335886-m0d72ntg 63 51 - - JJ cord-335886-m0d72ntg 63 52 producing produce VBG cord-335886-m0d72ntg 63 53 the the DT cord-335886-m0d72ntg 63 54 overall overall JJ cord-335886-m0d72ntg 63 55 epidemic epidemic NN cord-335886-m0d72ntg 63 56 . . . cord-335886-m0d72ntg 64 1 Understanding understand VBG cord-335886-m0d72ntg 64 2 the the DT cord-335886-m0d72ntg 64 3 present present JJ cord-335886-m0d72ntg 64 4 status status NN cord-335886-m0d72ntg 64 5 and and CC cord-335886-m0d72ntg 64 6 forecasting forecasting NN cord-335886-m0d72ntg 64 7 of of IN cord-335886-m0d72ntg 64 8 COVID-19 COVID-19 NNP cord-335886-m0d72ntg 64 9 in in IN cord-335886-m0d72ntg 64 10 Wuhan Wuhan NNP cord-335886-m0d72ntg 65 1 A a DT cord-335886-m0d72ntg 65 2 contribution contribution NN cord-335886-m0d72ntg 65 3 to to IN cord-335886-m0d72ntg 65 4 the the DT cord-335886-m0d72ntg 65 5 mathematical mathematical JJ cord-335886-m0d72ntg 65 6 theory theory NN cord-335886-m0d72ntg 65 7 of of IN cord-335886-m0d72ntg 65 8 epidemics epidemic NNS cord-335886-m0d72ntg 65 9 National National NNP cord-335886-m0d72ntg 65 10 Health Health NNP cord-335886-m0d72ntg 65 11 Commission Commission NNP cord-335886-m0d72ntg 65 12 of of IN cord-335886-m0d72ntg 65 13 the the DT cord-335886-m0d72ntg 65 14 People People NNPS cord-335886-m0d72ntg 65 15 's 's POS cord-335886-m0d72ntg 65 16 Republic Republic NNP cord-335886-m0d72ntg 65 17 of of IN cord-335886-m0d72ntg 65 18 China China NNP cord-335886-m0d72ntg 65 19 , , , cord-335886-m0d72ntg 65 20 Prevention Prevention NNP cord-335886-m0d72ntg 65 21 of of IN cord-335886-m0d72ntg 65 22 Epidemics Epidemics NNP cord-335886-m0d72ntg 65 23 Health Health NNP cord-335886-m0d72ntg 65 24 Commission Commission NNP cord-335886-m0d72ntg 65 25 of of IN cord-335886-m0d72ntg 65 26 Hubei Hubei NNP cord-335886-m0d72ntg 65 27 Province Province NNP cord-335886-m0d72ntg 65 28 , , , cord-335886-m0d72ntg 65 29 Anti Anti NNP cord-335886-m0d72ntg 65 30 - - NNP cord-335886-m0d72ntg 65 31 Prevention Prevention NNP cord-335886-m0d72ntg 65 32 New New NNP cord-335886-m0d72ntg 65 33 Coronary Coronary NNP cord-335886-m0d72ntg 65 34 Disease Disease NNP cord-335886-m0d72ntg 65 35 Infection infection NN cord-335886-m0d72ntg 65 36 , , , cord-335886-m0d72ntg 66 1 Information information NN cord-335886-m0d72ntg 66 2 Number number NN cord-335886-m0d72ntg 66 3 of of IN cord-335886-m0d72ntg 66 4 reports report NNS cord-335886-m0d72ntg 66 5 at at IN cord-335886-m0d72ntg 66 6 fixed fix VBN cord-335886-m0d72ntg 66 7 disease disease NN cord-335886-m0d72ntg 66 8 points point NNS cord-335886-m0d72ntg 67 1 -Comparison -Comparison NNP cord-335886-m0d72ntg 67 2 with with IN cord-335886-m0d72ntg 67 3 the the DT cord-335886-m0d72ntg 67 4 past past JJ cord-335886-m0d72ntg 67 5 10 10 CD cord-335886-m0d72ntg 67 6 years year NNS cord-335886-m0d72ntg 67 7 National National NNP cord-335886-m0d72ntg 67 8 Institute Institute NNP cord-335886-m0d72ntg 67 9 of of IN cord-335886-m0d72ntg 67 10 Infectious Infectious NNP cord-335886-m0d72ntg 67 11 Diseases Diseases NNPS cord-335886-m0d72ntg 67 12 and and CC cord-335886-m0d72ntg 67 13 Ministry Ministry NNP cord-335886-m0d72ntg 67 14 of of IN cord-335886-m0d72ntg 67 15 Health Health NNP cord-335886-m0d72ntg 67 16 , , , cord-335886-m0d72ntg 67 17 Labor Labor NNP cord-335886-m0d72ntg 67 18 and and CC cord-335886-m0d72ntg 67 19 Welfare Welfare NNP cord-335886-m0d72ntg 67 20 Tuberculosis Tuberculosis NNP cord-335886-m0d72ntg 67 21 Infectious Infectious NNP cord-335886-m0d72ntg 67 22 Disease Disease NNP cord-335886-m0d72ntg 67 23 Division Division NNP