id sid tid token lemma pos cord-222193-0b4o0ccp 1 1 key key JJ cord-222193-0b4o0ccp 1 2 : : : cord-222193-0b4o0ccp 1 3 cord-222193 cord-222193 NNP cord-222193-0b4o0ccp 1 4 - - HYPH cord-222193-0b4o0ccp 1 5 0b4o0ccp 0b4o0ccp CD cord-222193-0b4o0ccp 1 6 authors author NNS cord-222193-0b4o0ccp 1 7 : : : cord-222193-0b4o0ccp 1 8 Saakian Saakian NNP cord-222193-0b4o0ccp 1 9 , , , cord-222193-0b4o0ccp 1 10 David David NNP cord-222193-0b4o0ccp 1 11 B. B. NNP cord-222193-0b4o0ccp 1 12 title title NN cord-222193-0b4o0ccp 1 13 : : : cord-222193-0b4o0ccp 1 14 A a DT cord-222193-0b4o0ccp 1 15 simple simple JJ cord-222193-0b4o0ccp 1 16 statistical statistical JJ cord-222193-0b4o0ccp 1 17 physics physics NN cord-222193-0b4o0ccp 1 18 model model NN cord-222193-0b4o0ccp 1 19 for for IN cord-222193-0b4o0ccp 1 20 the the DT cord-222193-0b4o0ccp 1 21 epidemic epidemic NN cord-222193-0b4o0ccp 1 22 with with IN cord-222193-0b4o0ccp 1 23 incubation incubation NN cord-222193-0b4o0ccp 1 24 period period NN cord-222193-0b4o0ccp 1 25 date date NN cord-222193-0b4o0ccp 1 26 : : : cord-222193-0b4o0ccp 1 27 2020 2020 CD cord-222193-0b4o0ccp 1 28 - - HYPH cord-222193-0b4o0ccp 1 29 04 04 CD cord-222193-0b4o0ccp 1 30 - - SYM cord-222193-0b4o0ccp 1 31 13 13 CD cord-222193-0b4o0ccp 1 32 journal journal NN cord-222193-0b4o0ccp 1 33 : : : cord-222193-0b4o0ccp 1 34 nan nan NNP cord-222193-0b4o0ccp 1 35 DOI DOI NNP cord-222193-0b4o0ccp 1 36 : : : cord-222193-0b4o0ccp 1 37 nan nan NNP cord-222193-0b4o0ccp 1 38 sha sha NNP cord-222193-0b4o0ccp 1 39 : : : cord-222193-0b4o0ccp 1 40 2c55a747d7e3d676fbedaaa5794c4d7b2923996f 2c55a747d7e3d676fbedaaa5794c4d7b2923996f CD cord-222193-0b4o0ccp 1 41 doc_id doc_id CD cord-222193-0b4o0ccp 1 42 : : : cord-222193-0b4o0ccp 1 43 222193 222193 CD cord-222193-0b4o0ccp 1 44 cord_uid cord_uid NNS cord-222193-0b4o0ccp 1 45 : : : cord-222193-0b4o0ccp 1 46 0b4o0ccp 0b4o0ccp CD cord-222193-0b4o0ccp 2 1 Based base VBN cord-222193-0b4o0ccp 2 2 on on IN cord-222193-0b4o0ccp 2 3 the the DT cord-222193-0b4o0ccp 2 4 classical classical JJ cord-222193-0b4o0ccp 2 5 SIR SIR NNP cord-222193-0b4o0ccp 2 6 model model NN cord-222193-0b4o0ccp 2 7 , , , cord-222193-0b4o0ccp 2 8 we -PRON- PRP cord-222193-0b4o0ccp 2 9 derive derive VBP cord-222193-0b4o0ccp 2 10 a a DT cord-222193-0b4o0ccp 2 11 simple simple JJ cord-222193-0b4o0ccp 2 12 modification modification NN cord-222193-0b4o0ccp 2 13 for for IN cord-222193-0b4o0ccp 2 14 the the DT cord-222193-0b4o0ccp 2 15 dynamics dynamic NNS cord-222193-0b4o0ccp 2 16 of of IN cord-222193-0b4o0ccp 2 17 epidemics epidemic NNS cord-222193-0b4o0ccp 2 18 with with IN cord-222193-0b4o0ccp 2 19 a a DT cord-222193-0b4o0ccp 2 20 known know VBN cord-222193-0b4o0ccp 2 21 incubation incubation NN cord-222193-0b4o0ccp 2 22 period period NN cord-222193-0b4o0ccp 2 23 of of IN cord-222193-0b4o0ccp 2 24 infection infection NN cord-222193-0b4o0ccp 2 25 . . . cord-222193-0b4o0ccp 3 1 The the DT cord-222193-0b4o0ccp 3 2 model model NN cord-222193-0b4o0ccp 3 3 is be VBZ cord-222193-0b4o0ccp 3 4 described describe VBN cord-222193-0b4o0ccp 3 5 by by IN cord-222193-0b4o0ccp 3 6 a a DT cord-222193-0b4o0ccp 3 7 system system NN cord-222193-0b4o0ccp 3 8 of of IN cord-222193-0b4o0ccp 3 9 integro integro JJ cord-222193-0b4o0ccp 3 10 - - HYPH cord-222193-0b4o0ccp 3 11 differential differential JJ cord-222193-0b4o0ccp 3 12 equations equation NNS cord-222193-0b4o0ccp 3 13 . . . cord-222193-0b4o0ccp 4 1 Parameters parameter NNS cord-222193-0b4o0ccp 4 2 of of IN cord-222193-0b4o0ccp 4 3 our -PRON- PRP$ cord-222193-0b4o0ccp 4 4 model model NN cord-222193-0b4o0ccp 4 5 directly directly RB cord-222193-0b4o0ccp 4 6 related relate VBN cord-222193-0b4o0ccp 4 7 to to IN cord-222193-0b4o0ccp 4 8 epidemiological epidemiological JJ cord-222193-0b4o0ccp 4 9 data datum NNS cord-222193-0b4o0ccp 4 10 . . . cord-222193-0b4o0ccp 5 1 We -PRON- PRP cord-222193-0b4o0ccp 5 2 derive derive VBP cord-222193-0b4o0ccp 5 3 some some DT cord-222193-0b4o0ccp 5 4 analytical analytical JJ cord-222193-0b4o0ccp 5 5 results result NNS cord-222193-0b4o0ccp 5 6 , , , cord-222193-0b4o0ccp 5 7 as as RB cord-222193-0b4o0ccp 5 8 well well RB cord-222193-0b4o0ccp 5 9 as as IN cord-222193-0b4o0ccp 5 10 perform perform VB cord-222193-0b4o0ccp 5 11 numerical numerical JJ cord-222193-0b4o0ccp 5 12 simulations simulation NNS cord-222193-0b4o0ccp 5 13 . . . cord-222193-0b4o0ccp 6 1 We -PRON- PRP cord-222193-0b4o0ccp 6 2 use use VBP cord-222193-0b4o0ccp 6 3 the the DT cord-222193-0b4o0ccp 6 4 proposed propose VBN cord-222193-0b4o0ccp 6 5 model model NN cord-222193-0b4o0ccp 6 6 to to TO cord-222193-0b4o0ccp 6 7 analyze analyze VB cord-222193-0b4o0ccp 6 8 COVID-19 COVID-19 NNP cord-222193-0b4o0ccp 6 9 epidemic epidemic JJ cord-222193-0b4o0ccp 6 10 data datum NNS cord-222193-0b4o0ccp 6 11 in in IN cord-222193-0b4o0ccp 6 12 Armenia Armenia NNP cord-222193-0b4o0ccp 6 13 . . . cord-222193-0b4o0ccp 7 1 We -PRON- PRP cord-222193-0b4o0ccp 7 2 propose propose VBP cord-222193-0b4o0ccp 7 3 a a DT cord-222193-0b4o0ccp 7 4 strategy strategy NN cord-222193-0b4o0ccp 7 5 : : : cord-222193-0b4o0ccp 7 6 organize organize VB cord-222193-0b4o0ccp 7 7 a a DT cord-222193-0b4o0ccp 7 8 quarantine quarantine NN cord-222193-0b4o0ccp 7 9 , , , cord-222193-0b4o0ccp 7 10 and and CC cord-222193-0b4o0ccp 7 11 then then RB cord-222193-0b4o0ccp 7 12 conduct conduct VB cord-222193-0b4o0ccp 7 13 extensive extensive JJ cord-222193-0b4o0ccp 7 14 testing testing NN cord-222193-0b4o0ccp 7 15 of of IN cord-222193-0b4o0ccp 7 16 risk risk NN cord-222193-0b4o0ccp 7 17 groups group NNS cord-222193-0b4o0ccp 7 18 during during IN cord-222193-0b4o0ccp 7 19 the the DT cord-222193-0b4o0ccp 7 20 quarantine quarantine NN cord-222193-0b4o0ccp 7 21 , , , cord-222193-0b4o0ccp 7 22 evaluating evaluate VBG cord-222193-0b4o0ccp 7 23 the the DT cord-222193-0b4o0ccp 7 24 percentage percentage NN cord-222193-0b4o0ccp 7 25 of of IN cord-222193-0b4o0ccp 7 26 the the DT cord-222193-0b4o0ccp 7 27 population population NN cord-222193-0b4o0ccp 7 28 among among IN cord-222193-0b4o0ccp 7 29 risk risk NN cord-222193-0b4o0ccp 7 30 groups group NNS cord-222193-0b4o0ccp 7 31 and and CC cord-222193-0b4o0ccp 7 32 people people NNS cord-222193-0b4o0ccp 7 33 with with IN cord-222193-0b4o0ccp 7 34 symptoms symptom NNS cord-222193-0b4o0ccp 7 35 . . . cord-222193-0b4o0ccp 8 1 Mathematical mathematical JJ cord-222193-0b4o0ccp 8 2 modeling modeling NN cord-222193-0b4o0ccp 8 3 for for IN cord-222193-0b4o0ccp 8 4 epidemiology epidemiology NN cord-222193-0b4o0ccp 8 5 has have VBZ cord-222193-0b4o0ccp 8 6 a a DT cord-222193-0b4o0ccp 8 7 rather rather RB cord-222193-0b4o0ccp 8 8 long long JJ cord-222193-0b4o0ccp 8 9 history history NN cord-222193-0b4o0ccp 8 10 , , , cord-222193-0b4o0ccp 8 11 dating date VBG cord-222193-0b4o0ccp 8 12 back back RB cord-222193-0b4o0ccp 8 13 to to IN cord-222193-0b4o0ccp 8 14 the the DT cord-222193-0b4o0ccp 8 15 studies study NNS cord-222193-0b4o0ccp 8 16 by by IN cord-222193-0b4o0ccp 8 17 D. D. NNP cord-222193-0b4o0ccp 8 18 Bernoulli Bernoulli NNP cord-222193-0b4o0ccp 8 19 [ [ -LRB- cord-222193-0b4o0ccp 8 20 1 1 CD cord-222193-0b4o0ccp 8 21 ] ] -RRB- cord-222193-0b4o0ccp 8 22 . . . cord-222193-0b4o0ccp 9 1 Later later RBR cord-222193-0b4o0ccp 9 2 , , , cord-222193-0b4o0ccp 9 3 Kermack Kermack NNP cord-222193-0b4o0ccp 9 4 and and CC cord-222193-0b4o0ccp 9 5 McKendrick McKendrick NNP cord-222193-0b4o0ccp 9 6 [ [ -LRB- cord-222193-0b4o0ccp 9 7 2 2 CD cord-222193-0b4o0ccp 9 8 ] ] -RRB- cord-222193-0b4o0ccp 9 9 proposed propose VBN cord-222193-0b4o0ccp 9 10 their -PRON- PRP$ cord-222193-0b4o0ccp 9 11 prominent prominent JJ cord-222193-0b4o0ccp 9 12 theory theory NN cord-222193-0b4o0ccp 9 13 for for IN cord-222193-0b4o0ccp 9 14 infectious infectious JJ cord-222193-0b4o0ccp 9 15 disease disease NN cord-222193-0b4o0ccp 9 16 dynamics dynamic NNS cord-222193-0b4o0ccp 9 17 , , , cord-222193-0b4o0ccp 9 18 which which WDT cord-222193-0b4o0ccp 9 19 influenced influence VBD cord-222193-0b4o0ccp 9 20 the the DT cord-222193-0b4o0ccp 9 21 following follow VBG cord-222193-0b4o0ccp 9 22 SIR SIR NNP cord-222193-0b4o0ccp 9 23 and and CC cord-222193-0b4o0ccp 9 24 related related JJ cord-222193-0b4o0ccp 9 25 models model NNS cord-222193-0b4o0ccp 9 26 . . . cord-222193-0b4o0ccp 10 1 By by IN cord-222193-0b4o0ccp 10 2 the the DT cord-222193-0b4o0ccp 10 3 end end NN cord-222193-0b4o0ccp 10 4 of of IN cord-222193-0b4o0ccp 10 5 the the DT cord-222193-0b4o0ccp 10 6 last last JJ cord-222193-0b4o0ccp 10 7 century century NN cord-222193-0b4o0ccp 10 8 , , , cord-222193-0b4o0ccp 10 9 significant significant JJ cord-222193-0b4o0ccp 10 10 progress progress NN cord-222193-0b4o0ccp 10 11 in in IN cord-222193-0b4o0ccp 10 12 the the DT cord-222193-0b4o0ccp 10 13 field field NN cord-222193-0b4o0ccp 10 14 was be VBD cord-222193-0b4o0ccp 10 15 made make VBN cord-222193-0b4o0ccp 10 16 ( ( -LRB- cord-222193-0b4o0ccp 10 17 a a DT cord-222193-0b4o0ccp 10 18 systematic systematic JJ cord-222193-0b4o0ccp 10 19 literature literature NN cord-222193-0b4o0ccp 10 20 review review NN cord-222193-0b4o0ccp 10 21 for for IN cord-222193-0b4o0ccp 10 22 this this DT cord-222193-0b4o0ccp 10 23 period period NN cord-222193-0b4o0ccp 10 24 is be VBZ cord-222193-0b4o0ccp 10 25 presented present VBN cord-222193-0b4o0ccp 10 26 in in IN cord-222193-0b4o0ccp 10 27 Anderson Anderson NNP cord-222193-0b4o0ccp 10 28 and and CC cord-222193-0b4o0ccp 10 29 May May NNP cord-222193-0b4o0ccp 10 30 's 's POS cord-222193-0b4o0ccp 10 31 book book NN cord-222193-0b4o0ccp 10 32 [ [ -LRB- cord-222193-0b4o0ccp 10 33 3 3 CD cord-222193-0b4o0ccp 10 34 ] ] -RRB- cord-222193-0b4o0ccp 10 35 ) ) -RRB- cord-222193-0b4o0ccp 10 36 . . . cord-222193-0b4o0ccp 11 1 The the DT cord-222193-0b4o0ccp 11 2 COVID-19 COVID-19 NNP cord-222193-0b4o0ccp 11 3 pandemic pandemic NN cord-222193-0b4o0ccp 11 4 has have VBZ cord-222193-0b4o0ccp 11 5 drawn draw VBN cord-222193-0b4o0ccp 11 6 the the DT cord-222193-0b4o0ccp 11 7 attention attention NN cord-222193-0b4o0ccp 11 8 of of IN cord-222193-0b4o0ccp 11 9 researchers researcher NNS cord-222193-0b4o0ccp 11 10 from from IN cord-222193-0b4o0ccp 11 11 all all RB cord-222193-0b4o0ccp 11 12 over over IN cord-222193-0b4o0ccp 11 13 the the DT cord-222193-0b4o0ccp 11 14 world world NN cord-222193-0b4o0ccp 11 15 and and CC cord-222193-0b4o0ccp 11 16 different different JJ cord-222193-0b4o0ccp 11 17 areas area NNS cord-222193-0b4o0ccp 11 18 to to IN cord-222193-0b4o0ccp 11 19 epidemic epidemic NN cord-222193-0b4o0ccp 11 20 modeling modeling NN cord-222193-0b4o0ccp 11 21 . . . cord-222193-0b4o0ccp 12 1 One one CD cord-222193-0b4o0ccp 12 2 of of IN cord-222193-0b4o0ccp 12 3 the the DT cord-222193-0b4o0ccp 12 4 simplest simple JJS cord-222193-0b4o0ccp 12 5 SIR SIR NNP cord-222193-0b4o0ccp 12 6 models model NNS cord-222193-0b4o0ccp 12 7 for for IN cord-222193-0b4o0ccp 12 8 the the DT cord-222193-0b4o0ccp 12 9 virus virus NN cord-222193-0b4o0ccp 12 10 spread spread VBN cord-222193-0b4o0ccp 12 11 in in IN cord-222193-0b4o0ccp 12 12 Northern Northern NNP cord-222193-0b4o0ccp 12 13 Italy Italy NNP cord-222193-0b4o0ccp 12 14 was be VBD cord-222193-0b4o0ccp 12 15 introduced introduce VBN cord-222193-0b4o0ccp 12 16 in in IN cord-222193-0b4o0ccp 12 17 [ [ -LRB- cord-222193-0b4o0ccp 12 18 4 4 CD cord-222193-0b4o0ccp 12 19 ] ] -RRB- cord-222193-0b4o0ccp 12 20 . . . cord-222193-0b4o0ccp 13 1 Another another DT cord-222193-0b4o0ccp 13 2 research research NN cord-222193-0b4o0ccp 13 3 group group NN cord-222193-0b4o0ccp 13 4 used use VBD cord-222193-0b4o0ccp 13 5 the the DT cord-222193-0b4o0ccp 13 6 logistic logistic JJ cord-222193-0b4o0ccp 13 7 equation equation NN cord-222193-0b4o0ccp 13 8 to to TO cord-222193-0b4o0ccp 13 9 analyze analyze VB cord-222193-0b4o0ccp 13 10 empirical empirical JJ cord-222193-0b4o0ccp 13 11 data datum NNS cord-222193-0b4o0ccp 13 12 on on IN cord-222193-0b4o0ccp 13 13 the the DT cord-222193-0b4o0ccp 13 14 epidemic epidemic NN cord-222193-0b4o0ccp 13 15 in in IN cord-222193-0b4o0ccp 13 16 different different JJ cord-222193-0b4o0ccp 13 17 states state NNS cord-222193-0b4o0ccp 13 18 [ [ -LRB- cord-222193-0b4o0ccp 13 19 11 11 CD cord-222193-0b4o0ccp 13 20 ] ] -RRB- cord-222193-0b4o0ccp 13 21 . . . cord-222193-0b4o0ccp 14 1 Here here RB cord-222193-0b4o0ccp 14 2 , , , cord-222193-0b4o0ccp 14 3 we -PRON- PRP cord-222193-0b4o0ccp 14 4 mainly mainly RB cord-222193-0b4o0ccp 14 5 focus focus VBP cord-222193-0b4o0ccp 14 6 on on IN cord-222193-0b4o0ccp 14 7 mean mean JJ cord-222193-0b4o0ccp 14 8 - - HYPH cord-222193-0b4o0ccp 14 9 field field NN cord-222193-0b4o0ccp 14 10 models model NNS cord-222193-0b4o0ccp 14 11 that that WDT cord-222193-0b4o0ccp 14 12 discard discard VBP cord-222193-0b4o0ccp 14 13 the the DT cord-222193-0b4o0ccp 14 14 spatial spatial JJ cord-222193-0b4o0ccp 14 15 dependence dependence NN cord-222193-0b4o0ccp 14 16 of of IN cord-222193-0b4o0ccp 14 17 the the DT cord-222193-0b4o0ccp 14 18 epidemic epidemic NN cord-222193-0b4o0ccp 14 19 process process NN cord-222193-0b4o0ccp 14 20 . . . cord-222193-0b4o0ccp 15 1 Therefore therefore RB cord-222193-0b4o0ccp 15 2 , , , cord-222193-0b4o0ccp 15 3 we -PRON- PRP cord-222193-0b4o0ccp 15 4 avoid avoid VBP cord-222193-0b4o0ccp 15 5 network network NN cord-222193-0b4o0ccp 15 6 models model NNS cord-222193-0b4o0ccp 15 7 of of IN cord-222193-0b4o0ccp 15 8 epidemics epidemic NNS cord-222193-0b4o0ccp 15 9 . . . cord-222193-0b4o0ccp 16 1 Moreover moreover RB cord-222193-0b4o0ccp 16 2 , , , cord-222193-0b4o0ccp 16 3 it -PRON- PRP cord-222193-0b4o0ccp 16 4 is be VBZ cord-222193-0b4o0ccp 16 5 crucial crucial JJ cord-222193-0b4o0ccp 16 6 to to TO cord-222193-0b4o0ccp 16 7 consider consider VB cord-222193-0b4o0ccp 16 8 the the DT cord-222193-0b4o0ccp 16 9 final final JJ cord-222193-0b4o0ccp 16 10 incubation incubation NN cord-222193-0b4o0ccp 16 11 period period NN cord-222193-0b4o0ccp 16 12 of of IN cord-222193-0b4o0ccp 16 13 the the DT cord-222193-0b4o0ccp 16 14 disease disease NN cord-222193-0b4o0ccp 16 15 to to TO cord-222193-0b4o0ccp 16 16 construct construct VB cord-222193-0b4o0ccp 16 17 a a DT cord-222193-0b4o0ccp 16 18 correct correct JJ cord-222193-0b4o0ccp 16 19 model model NN cord-222193-0b4o0ccp 16 20 for for IN cord-222193-0b4o0ccp 16 21 the the DT cord-222193-0b4o0ccp 16 22 COVID-19 COVID-19 NNP cord-222193-0b4o0ccp 16 23 case case NN cord-222193-0b4o0ccp 16 24 . . . cord-222193-0b4o0ccp 17 1 Taking take VBG cord-222193-0b4o0ccp 17 2 into into IN cord-222193-0b4o0ccp 17 3 account account NN cord-222193-0b4o0ccp 17 4 this this DT cord-222193-0b4o0ccp 17 5 distinctive distinctive JJ cord-222193-0b4o0ccp 17 6 feature feature NN cord-222193-0b4o0ccp 17 7 , , , cord-222193-0b4o0ccp 17 8 we -PRON- PRP cord-222193-0b4o0ccp 17 9 consider consider VBP cord-222193-0b4o0ccp 17 10 the the DT cord-222193-0b4o0ccp 17 11 dynamics dynamic NNS cord-222193-0b4o0ccp 17 12 of of IN cord-222193-0b4o0ccp 17 13 the the DT cord-222193-0b4o0ccp 17 14 aged age VBN cord-222193-0b4o0ccp 17 15 - - HYPH cord-222193-0b4o0ccp 17 16 structured structured JJ cord-222193-0b4o0ccp 17 17 population population NN cord-222193-0b4o0ccp 17 18 , , , cord-222193-0b4o0ccp 17 19 which which WDT cord-222193-0b4o0ccp 17 20 a a DT cord-222193-0b4o0ccp 17 21 well well RB cord-222193-0b4o0ccp 17 22 - - HYPH cord-222193-0b4o0ccp 17 23 known know VBN cord-222193-0b4o0ccp 17 24 problem problem NN cord-222193-0b4o0ccp 17 25 in in IN cord-222193-0b4o0ccp 17 26 evolutionary evolutionary JJ cord-222193-0b4o0ccp 17 27 research research NN cord-222193-0b4o0ccp 17 28 [ [ -LRB- cord-222193-0b4o0ccp 17 29 5 5 CD cord-222193-0b4o0ccp 17 30 ] ] -RRB- cord-222193-0b4o0ccp 17 31 - - : cord-222193-0b4o0ccp 18 1 [ [ -LRB- cord-222193-0b4o0ccp 18 2 10 10 CD cord-222193-0b4o0ccp 18 3 ] ] -RRB- cord-222193-0b4o0ccp 18 4 . . . cord-222193-0b4o0ccp 19 1 Generally generally RB cord-222193-0b4o0ccp 19 2 , , , cord-222193-0b4o0ccp 19 3 epidemic epidemic NN cord-222193-0b4o0ccp 19 4 models model NNS cord-222193-0b4o0ccp 19 5 have have VBP cord-222193-0b4o0ccp 19 6 a a DT cord-222193-0b4o0ccp 19 7 higher high JJR cord-222193-0b4o0ccp 19 8 order order NN cord-222193-0b4o0ccp 19 9 of of IN cord-222193-0b4o0ccp 19 10 non non JJ cord-222193-0b4o0ccp 19 11 - - JJ cord-222193-0b4o0ccp 19 12 linearity linearity NN cord-222193-0b4o0ccp 19 13 than than IN cord-222193-0b4o0ccp 19 14 evolutionary evolutionary JJ cord-222193-0b4o0ccp 19 15 models model NNS cord-222193-0b4o0ccp 19 16 , , , cord-222193-0b4o0ccp 19 17 although although IN cord-222193-0b4o0ccp 19 18 there there EX cord-222193-0b4o0ccp 19 19 are be VBP cord-222193-0b4o0ccp 19 20 some some DT cord-222193-0b4o0ccp 19 21 similarities similarity NNS cord-222193-0b4o0ccp 19 22 between between IN cord-222193-0b4o0ccp 19 23 these these DT cord-222193-0b4o0ccp 19 24 two two CD cord-222193-0b4o0ccp 19 25 classes class NNS cord-222193-0b4o0ccp 19 26 . . . cord-222193-0b4o0ccp 20 1 In in IN cord-222193-0b4o0ccp 20 2 this this DT cord-222193-0b4o0ccp 20 3 study study NN cord-222193-0b4o0ccp 20 4 , , , cord-222193-0b4o0ccp 20 5 we -PRON- PRP cord-222193-0b4o0ccp 20 6 derive derive VBP cord-222193-0b4o0ccp 20 7 a a DT cord-222193-0b4o0ccp 20 8 system system NN cord-222193-0b4o0ccp 20 9 of of IN cord-222193-0b4o0ccp 20 10 integro integro JJ cord-222193-0b4o0ccp 20 11 - - HYPH cord-222193-0b4o0ccp 20 12 differential differential JJ cord-222193-0b4o0ccp 20 13 equations equation NNS cord-222193-0b4o0ccp 20 14 based base VBN cord-222193-0b4o0ccp 20 15 on on IN cord-222193-0b4o0ccp 20 16 the the DT cord-222193-0b4o0ccp 20 17 rigorous rigorous JJ cord-222193-0b4o0ccp 20 18 master master NN cord-222193-0b4o0ccp 20 19 equation equation NN cord-222193-0b4o0ccp 20 20 that that WDT cord-222193-0b4o0ccp 20 21 adequately adequately RB cord-222193-0b4o0ccp 20 22 describes describe VBZ cord-222193-0b4o0ccp 20 23 infection infection NN cord-222193-0b4o0ccp 20 24 dynamics dynamic NNS cord-222193-0b4o0ccp 20 25 with with IN cord-222193-0b4o0ccp 20 26 an an DT cord-222193-0b4o0ccp 20 27 incubation incubation NN cord-222193-0b4o0ccp 20 28 period period NN cord-222193-0b4o0ccp 20 29 , , , cord-222193-0b4o0ccp 20 30 e.g. e.g. RB cord-222193-0b4o0ccp 20 31 , , , cord-222193-0b4o0ccp 20 32 COVID-19 COVID-19 NNP cord-222193-0b4o0ccp 20 33 . . . cord-222193-0b4o0ccp 21 1 First first RB cord-222193-0b4o0ccp 21 2 , , , cord-222193-0b4o0ccp 21 3 we -PRON- PRP cord-222193-0b4o0ccp 21 4 discuss discuss VBP cord-222193-0b4o0ccp 21 5 the the DT cord-222193-0b4o0ccp 21 6 SIR SIR NNP cord-222193-0b4o0ccp 21 7 model model NN cord-222193-0b4o0ccp 21 8 . . . cord-222193-0b4o0ccp 22 1 Then then RB cord-222193-0b4o0ccp 22 2 , , , cord-222193-0b4o0ccp 22 3 we -PRON- PRP cord-222193-0b4o0ccp 22 4 move move VBP cord-222193-0b4o0ccp 22 5 on on IN cord-222193-0b4o0ccp 22 6 to to IN cord-222193-0b4o0ccp 22 7 its -PRON- PRP$ cord-222193-0b4o0ccp 22 8 modification modification NN cord-222193-0b4o0ccp 22 9 and and CC cord-222193-0b4o0ccp 22 10 apply apply VB cord-222193-0b4o0ccp 22 11 it -PRON- PRP cord-222193-0b4o0ccp 22 12 to to IN cord-222193-0b4o0ccp 22 13 the the DT cord-222193-0b4o0ccp 22 14 data datum NNS cord-222193-0b4o0ccp 22 15 on on IN cord-222193-0b4o0ccp 22 16 the the DT cord-222193-0b4o0ccp 22 17 COVID-19 covid-19 JJ cord-222193-0b4o0ccp 22 18 epidemic epidemic NN cord-222193-0b4o0ccp 22 19 in in IN cord-222193-0b4o0ccp 22 20 Armenia Armenia NNP cord-222193-0b4o0ccp 22 21 . . . cord-222193-0b4o0ccp 23 1 Consider consider VB cord-222193-0b4o0ccp 23 2 the the DT cord-222193-0b4o0ccp 23 3 SIR SIR NNP cord-222193-0b4o0ccp 23 4 model model NN cord-222193-0b4o0ccp 23 5 where where WRB cord-222193-0b4o0ccp 23 6 the the DT cord-222193-0b4o0ccp 23 7 parameter parameter NN cord-222193-0b4o0ccp 23 8 S S NNP cord-222193-0b4o0ccp 23 9 stands stand VBZ cord-222193-0b4o0ccp 23 10 for for IN cord-222193-0b4o0ccp 23 11 the the DT cord-222193-0b4o0ccp 23 12 number number NN cord-222193-0b4o0ccp 23 13 of of IN cord-222193-0b4o0ccp 23 14 susceptible susceptible JJ cord-222193-0b4o0ccp 23 15 people people NNS cord-222193-0b4o0ccp 23 16 , , , cord-222193-0b4o0ccp 23 17 I -PRON- PRP cord-222193-0b4o0ccp 23 18 for for IN cord-222193-0b4o0ccp 23 19 the the DT cord-222193-0b4o0ccp 23 20 number number NN cord-222193-0b4o0ccp 23 21 of of IN cord-222193-0b4o0ccp 23 22 infected infected JJ cord-222193-0b4o0ccp 23 23 people people NNS cord-222193-0b4o0ccp 23 24 , , , cord-222193-0b4o0ccp 23 25 and and CC cord-222193-0b4o0ccp 23 26 R r NN cord-222193-0b4o0ccp 23 27 for for IN cord-222193-0b4o0ccp 23 28 the the DT cord-222193-0b4o0ccp 23 29 number number NN cord-222193-0b4o0ccp 23 30 of of IN cord-222193-0b4o0ccp 23 31 people people NNS cord-222193-0b4o0ccp 23 32 who who WP cord-222193-0b4o0ccp 23 33 have have VBP cord-222193-0b4o0ccp 23 34 recovered recover VBN cord-222193-0b4o0ccp 23 35 and and CC cord-222193-0b4o0ccp 23 36 developed develop VBN cord-222193-0b4o0ccp 23 37 immunity immunity NN cord-222193-0b4o0ccp 23 38 to to IN cord-222193-0b4o0ccp 23 39 the the DT cord-222193-0b4o0ccp 23 40 infection infection NN cord-222193-0b4o0ccp 23 41 . . . cord-222193-0b4o0ccp 24 1 We -PRON- PRP cord-222193-0b4o0ccp 24 2 assume assume VBP cord-222193-0b4o0ccp 24 3 that that IN cord-222193-0b4o0ccp 24 4 S S NNP cord-222193-0b4o0ccp 24 5 , , , cord-222193-0b4o0ccp 24 6 I -PRON- PRP cord-222193-0b4o0ccp 24 7 , , , cord-222193-0b4o0ccp 24 8 R R NNS cord-222193-0b4o0ccp 24 9 satisfy satisfy VBP cord-222193-0b4o0ccp 24 10 the the DT cord-222193-0b4o0ccp 24 11 constraint constraint NN cord-222193-0b4o0ccp 24 12 S s NN cord-222193-0b4o0ccp 25 1 + + CC cord-222193-0b4o0ccp 26 1 I -PRON- PRP cord-222193-0b4o0ccp 26 2 + + CC cord-222193-0b4o0ccp 26 3 R r NN cord-222193-0b4o0ccp 26 4 = = SYM cord-222193-0b4o0ccp 26 5 N n NN cord-222193-0b4o0ccp 26 6 . . . cord-222193-0b4o0ccp 27 1 where where WRB cord-222193-0b4o0ccp 27 2 1 1 CD cord-222193-0b4o0ccp 27 3 / / SYM cord-222193-0b4o0ccp 27 4 b b NN cord-222193-0b4o0ccp 27 5 is be VBZ cord-222193-0b4o0ccp 27 6 the the DT cord-222193-0b4o0ccp 27 7 period period NN cord-222193-0b4o0ccp 27 8 when when WRB cord-222193-0b4o0ccp 27 9 the the DT cord-222193-0b4o0ccp 27 10 infected infected JJ cord-222193-0b4o0ccp 27 11 people people NNS cord-222193-0b4o0ccp 27 12 are be VBP cord-222193-0b4o0ccp 27 13 contagious contagious JJ cord-222193-0b4o0ccp 27 14 . . . cord-222193-0b4o0ccp 28 1 The the DT cord-222193-0b4o0ccp 28 2 parameter parameter NN cord-222193-0b4o0ccp 28 3 a a DT cord-222193-0b4o0ccp 28 4 can can MD cord-222193-0b4o0ccp 28 5 be be VB cord-222193-0b4o0ccp 28 6 obtained obtain VBN cord-222193-0b4o0ccp 28 7 from from IN cord-222193-0b4o0ccp 28 8 the the DT cord-222193-0b4o0ccp 28 9 empirical empirical JJ cord-222193-0b4o0ccp 28 10 data datum NNS cord-222193-0b4o0ccp 28 11 on on IN cord-222193-0b4o0ccp 28 12 infection infection NN cord-222193-0b4o0ccp 28 13 rate rate NN cord-222193-0b4o0ccp 28 14 : : : cord-222193-0b4o0ccp 29 1 Thus thus RB cord-222193-0b4o0ccp 29 2 , , , cord-222193-0b4o0ccp 29 3 we -PRON- PRP cord-222193-0b4o0ccp 29 4 assume assume VBP cord-222193-0b4o0ccp 29 5 that that IN cord-222193-0b4o0ccp 29 6 a a DT cord-222193-0b4o0ccp 29 7 healthy healthy JJ cord-222193-0b4o0ccp 29 8 person person NN cord-222193-0b4o0ccp 29 9 is be VBZ cord-222193-0b4o0ccp 29 10 infected infect VBN cord-222193-0b4o0ccp 29 11 with with IN cord-222193-0b4o0ccp 29 12 a a DT cord-222193-0b4o0ccp 29 13 probability probability NN cord-222193-0b4o0ccp 29 14 proportional proportional JJ cord-222193-0b4o0ccp 29 15 to to IN cord-222193-0b4o0ccp 29 16 the the DT cord-222193-0b4o0ccp 29 17 fraction fraction NN cord-222193-0b4o0ccp 29 18 of of IN cord-222193-0b4o0ccp 29 19 infection infection NN cord-222193-0b4o0ccp 29 20 in in IN cord-222193-0b4o0ccp 29 21 the the DT cord-222193-0b4o0ccp 29 22 population population NN cord-222193-0b4o0ccp 29 23 . . . cord-222193-0b4o0ccp 30 1 Probability probability NN cord-222193-0b4o0ccp 30 2 is be VBZ cord-222193-0b4o0ccp 30 3 also also RB cord-222193-0b4o0ccp 30 4 proportional proportional JJ cord-222193-0b4o0ccp 30 5 to to IN cord-222193-0b4o0ccp 30 6 the the DT cord-222193-0b4o0ccp 30 7 population population NN cord-222193-0b4o0ccp 30 8 density density NN cord-222193-0b4o0ccp 30 9 . . . cord-222193-0b4o0ccp 31 1 One one CD cord-222193-0b4o0ccp 31 2 of of IN cord-222193-0b4o0ccp 31 3 the the DT cord-222193-0b4o0ccp 31 4 most most RBS cord-222193-0b4o0ccp 31 5 widely widely RB cord-222193-0b4o0ccp 31 6 discussed discuss VBN cord-222193-0b4o0ccp 31 7 and and CC cord-222193-0b4o0ccp 31 8 crucial crucial JJ cord-222193-0b4o0ccp 31 9 parameters parameter NNS cord-222193-0b4o0ccp 31 10 in in IN cord-222193-0b4o0ccp 31 11 epidemiological epidemiological JJ cord-222193-0b4o0ccp 31 12 data data NN cord-222193-0b4o0ccp 31 13 is be VBZ cord-222193-0b4o0ccp 31 14 the the DT cord-222193-0b4o0ccp 31 15 basic basic JJ cord-222193-0b4o0ccp 31 16 reproduction reproduction NN cord-222193-0b4o0ccp 31 17 number number NN cord-222193-0b4o0ccp 31 18 of of IN cord-222193-0b4o0ccp 31 19 the the DT cord-222193-0b4o0ccp 31 20 infection infection NN cord-222193-0b4o0ccp 31 21 : : : cord-222193-0b4o0ccp 31 22 For for IN cord-222193-0b4o0ccp 31 23 the the DT cord-222193-0b4o0ccp 31 24 COVID-19 COVID-19 NNP cord-222193-0b4o0ccp 31 25 , , , cord-222193-0b4o0ccp 31 26 it -PRON- PRP cord-222193-0b4o0ccp 31 27 has have VBZ cord-222193-0b4o0ccp 31 28 been be VBN cord-222193-0b4o0ccp 31 29 estimated estimate VBN cord-222193-0b4o0ccp 31 30 as as IN cord-222193-0b4o0ccp 31 31 [ [ -LRB- cord-222193-0b4o0ccp 31 32 4 4 CD cord-222193-0b4o0ccp 31 33 ] ] -RRB- cord-222193-0b4o0ccp 31 34 : : : cord-222193-0b4o0ccp 32 1 In in IN cord-222193-0b4o0ccp 32 2 fact fact NN cord-222193-0b4o0ccp 32 3 , , , cord-222193-0b4o0ccp 32 4 the the DT cord-222193-0b4o0ccp 32 5 real real JJ cord-222193-0b4o0ccp 32 6 data data NN cord-222193-0b4o0ccp 32 7 allows allow VBZ cord-222193-0b4o0ccp 32 8 us -PRON- PRP cord-222193-0b4o0ccp 32 9 to to TO cord-222193-0b4o0ccp 32 10 measure measure VB cord-222193-0b4o0ccp 32 11 three three CD cord-222193-0b4o0ccp 32 12 main main JJ cord-222193-0b4o0ccp 32 13 parameters parameter NNS cord-222193-0b4o0ccp 32 14 : : : cord-222193-0b4o0ccp 32 15 the the DT cord-222193-0b4o0ccp 32 16 exponential exponential JJ cord-222193-0b4o0ccp 32 17 growth growth NN cord-222193-0b4o0ccp 32 18 coefficient coefficient NN cord-222193-0b4o0ccp 32 19 at at IN cord-222193-0b4o0ccp 32 20 the the DT cord-222193-0b4o0ccp 32 21 beginning beginning NN cord-222193-0b4o0ccp 32 22 of of IN cord-222193-0b4o0ccp 32 23 the the DT cord-222193-0b4o0ccp 32 24 epidemic epidemic NN cord-222193-0b4o0ccp 32 25 ; ; : cord-222193-0b4o0ccp 32 26 the the DT cord-222193-0b4o0ccp 32 27 minimum minimum JJ cord-222193-0b4o0ccp 32 28 period period NN cord-222193-0b4o0ccp 32 29 of of IN cord-222193-0b4o0ccp 32 30 time time NN cord-222193-0b4o0ccp 32 31 , , , cord-222193-0b4o0ccp 32 32 in in IN cord-222193-0b4o0ccp 32 33 which which WDT cord-222193-0b4o0ccp 32 34 an an DT cord-222193-0b4o0ccp 32 35 infected infected JJ cord-222193-0b4o0ccp 32 36 person person NN cord-222193-0b4o0ccp 32 37 can can MD cord-222193-0b4o0ccp 32 38 transmit transmit VB cord-222193-0b4o0ccp 32 39 the the DT cord-222193-0b4o0ccp 32 40 infection infection NN cord-222193-0b4o0ccp 32 41 ; ; : cord-222193-0b4o0ccp 32 42 and and CC cord-222193-0b4o0ccp 32 43 the the DT cord-222193-0b4o0ccp 32 44 maximum maximum JJ cord-222193-0b4o0ccp 32 45 period period NN cord-222193-0b4o0ccp 32 46 , , , cord-222193-0b4o0ccp 32 47 when when WRB cord-222193-0b4o0ccp 32 48 an an DT cord-222193-0b4o0ccp 32 49 infected infected JJ cord-222193-0b4o0ccp 32 50 person person NN cord-222193-0b4o0ccp 32 51 ceases cease VBZ cord-222193-0b4o0ccp 32 52 to to TO cord-222193-0b4o0ccp 32 53 transmit transmit VB cord-222193-0b4o0ccp 32 54 the the DT cord-222193-0b4o0ccp 32 55 infection infection NN cord-222193-0b4o0ccp 32 56 . . . cord-222193-0b4o0ccp 33 1 The the DT cord-222193-0b4o0ccp 33 2 most most RBS cord-222193-0b4o0ccp 33 3 important important JJ cord-222193-0b4o0ccp 33 4 objectives objective NNS cord-222193-0b4o0ccp 33 5 of of IN cord-222193-0b4o0ccp 33 6 the the DT cord-222193-0b4o0ccp 33 7 investigation investigation NN cord-222193-0b4o0ccp 33 8 are be VBP cord-222193-0b4o0ccp 33 9 the the DT cord-222193-0b4o0ccp 33 10 maximal maximal JJ cord-222193-0b4o0ccp 33 11 possible possible JJ cord-222193-0b4o0ccp 33 12 proportion proportion NN cord-222193-0b4o0ccp 33 13 of of IN cord-222193-0b4o0ccp 33 14 the the DT cord-222193-0b4o0ccp 33 15 infected infected JJ cord-222193-0b4o0ccp 33 16 population population NN cord-222193-0b4o0ccp 33 17 , , , cord-222193-0b4o0ccp 33 18 and and CC cord-222193-0b4o0ccp 33 19 then then RB cord-222193-0b4o0ccp 33 20 the the DT cord-222193-0b4o0ccp 33 21 period period NN cord-222193-0b4o0ccp 33 22 before before IN cord-222193-0b4o0ccp 33 23 the the DT cord-222193-0b4o0ccp 33 24 peak peak NN cord-222193-0b4o0ccp 33 25 of of IN cord-222193-0b4o0ccp 33 26 the the DT cord-222193-0b4o0ccp 33 27 epidemic epidemic NN cord-222193-0b4o0ccp 33 28 . . . cord-222193-0b4o0ccp 34 1 Consider consider VB cord-222193-0b4o0ccp 34 2 the the DT cord-222193-0b4o0ccp 34 3 spread spread NN cord-222193-0b4o0ccp 34 4 of of IN cord-222193-0b4o0ccp 34 5 infectious infectious JJ cord-222193-0b4o0ccp 34 6 diseases disease NNS cord-222193-0b4o0ccp 34 7 with with IN cord-222193-0b4o0ccp 34 8 a a DT cord-222193-0b4o0ccp 34 9 recovery recovery NN cord-222193-0b4o0ccp 34 10 period period NN cord-222193-0b4o0ccp 34 11 up up IN cord-222193-0b4o0ccp 34 12 to to IN cord-222193-0b4o0ccp 34 13 T T NNP cord-222193-0b4o0ccp 34 14 days day NNS cord-222193-0b4o0ccp 34 15 . . . cord-222193-0b4o0ccp 35 1 At at IN cord-222193-0b4o0ccp 35 2 the the DT cord-222193-0b4o0ccp 35 3 t t NN cord-222193-0b4o0ccp 35 4 - - HYPH cord-222193-0b4o0ccp 35 5 th th DT cord-222193-0b4o0ccp 35 6 moment moment NN cord-222193-0b4o0ccp 35 7 of of IN cord-222193-0b4o0ccp 35 8 time time NN cord-222193-0b4o0ccp 35 9 , , , cord-222193-0b4o0ccp 35 10 we -PRON- PRP cord-222193-0b4o0ccp 35 11 have have VBP cord-222193-0b4o0ccp 35 12 S(t s(t CD cord-222193-0b4o0ccp 35 13 ) ) -RRB- cord-222193-0b4o0ccp 35 14 for for IN cord-222193-0b4o0ccp 35 15 the the DT cord-222193-0b4o0ccp 35 16 size size NN cord-222193-0b4o0ccp 35 17 of of IN cord-222193-0b4o0ccp 35 18 the the DT cord-222193-0b4o0ccp 35 19 susceptible susceptible JJ cord-222193-0b4o0ccp 35 20 population population NN cord-222193-0b4o0ccp 35 21 , , , cord-222193-0b4o0ccp 35 22 R(t R(t NNP cord-222193-0b4o0ccp 35 23 ) ) -RRB- cord-222193-0b4o0ccp 35 24 for for IN cord-222193-0b4o0ccp 35 25 the the DT cord-222193-0b4o0ccp 35 26 recovered recover VBN cord-222193-0b4o0ccp 35 27 population population NN cord-222193-0b4o0ccp 35 28 . . . cord-222193-0b4o0ccp 36 1 We -PRON- PRP cord-222193-0b4o0ccp 36 2 divide divide VBP cord-222193-0b4o0ccp 36 3 the the DT cord-222193-0b4o0ccp 36 4 infected infected JJ cord-222193-0b4o0ccp 36 5 population population NN cord-222193-0b4o0ccp 36 6 according accord VBG cord-222193-0b4o0ccp 36 7 to to IN cord-222193-0b4o0ccp 36 8 the the DT cord-222193-0b4o0ccp 36 9 age age NN cord-222193-0b4o0ccp 36 10 of of IN cord-222193-0b4o0ccp 36 11 infection infection NN cord-222193-0b4o0ccp 36 12 , , , cord-222193-0b4o0ccp 36 13 looking look VBG cord-222193-0b4o0ccp 36 14 at at IN cord-222193-0b4o0ccp 36 15 time time NN cord-222193-0b4o0ccp 36 16 intervals interval NNS cord-222193-0b4o0ccp 36 17 δ δ NN cord-222193-0b4o0ccp 36 18 and and CC cord-222193-0b4o0ccp 36 19 defining define VBG cord-222193-0b4o0ccp 36 20 I -PRON- PRP cord-222193-0b4o0ccp 36 21 l l NN cord-222193-0b4o0ccp 36 22 ( ( -LRB- cord-222193-0b4o0ccp 36 23 t t NN cord-222193-0b4o0ccp 36 24 ) ) -RRB- cord-222193-0b4o0ccp 36 25 as as IN cord-222193-0b4o0ccp 36 26 the the DT cord-222193-0b4o0ccp 36 27 number number NN cord-222193-0b4o0ccp 36 28 of of IN cord-222193-0b4o0ccp 36 29 infected infected JJ cord-222193-0b4o0ccp 36 30 people people NNS cord-222193-0b4o0ccp 36 31 with with IN cord-222193-0b4o0ccp 36 32 the the DT cord-222193-0b4o0ccp 36 33 age age NN cord-222193-0b4o0ccp 36 34 of of IN cord-222193-0b4o0ccp 36 35 infection infection NN cord-222193-0b4o0ccp 36 36 in in IN cord-222193-0b4o0ccp 36 37 ( ( -LRB- cord-222193-0b4o0ccp 36 38 lδ lδ NN cord-222193-0b4o0ccp 36 39 , , , cord-222193-0b4o0ccp 36 40 ( ( -LRB- cord-222193-0b4o0ccp 36 41 l+1)δ l+1)δ NN cord-222193-0b4o0ccp 36 42 ) ) -RRB- cord-222193-0b4o0ccp 36 43 . . . cord-222193-0b4o0ccp 37 1 We -PRON- PRP cord-222193-0b4o0ccp 37 2 assume assume VBP cord-222193-0b4o0ccp 37 3 that that IN cord-222193-0b4o0ccp 37 4 the the DT cord-222193-0b4o0ccp 37 5 incubation incubation NN cord-222193-0b4o0ccp 37 6 period period NN cord-222193-0b4o0ccp 37 7 for for IN cord-222193-0b4o0ccp 37 8 a a DT cord-222193-0b4o0ccp 37 9 random random JJ cord-222193-0b4o0ccp 37 10 infected infected JJ cord-222193-0b4o0ccp 37 11 person person NN cord-222193-0b4o0ccp 37 12 is be VBZ cord-222193-0b4o0ccp 37 13 L l NN cord-222193-0b4o0ccp 37 14 and and CC cord-222193-0b4o0ccp 37 15 the the DT cord-222193-0b4o0ccp 37 16 infection infection NN cord-222193-0b4o0ccp 37 17 spreads spread VBZ cord-222193-0b4o0ccp 37 18 from from IN cord-222193-0b4o0ccp 37 19 L L NNP cord-222193-0b4o0ccp 37 20 to to IN cord-222193-0b4o0ccp 37 21 T t NN cord-222193-0b4o0ccp 37 22 days day NNS cord-222193-0b4o0ccp 37 23 . . . cord-222193-0b4o0ccp 38 1 Below below RB cord-222193-0b4o0ccp 38 2 , , , cord-222193-0b4o0ccp 38 3 we -PRON- PRP cord-222193-0b4o0ccp 38 4 take take VBP cord-222193-0b4o0ccp 38 5 δ δ NN cord-222193-0b4o0ccp 38 6 → → SYM cord-222193-0b4o0ccp 38 7 0 0 CD cord-222193-0b4o0ccp 38 8 for for IN cord-222193-0b4o0ccp 38 9 the the DT cord-222193-0b4o0ccp 38 10 continuous continuous JJ cord-222193-0b4o0ccp 38 11 mode mode NN cord-222193-0b4o0ccp 38 12 of of IN cord-222193-0b4o0ccp 38 13 time time NN cord-222193-0b4o0ccp 38 14 limit limit NN cord-222193-0b4o0ccp 38 15 . . . cord-222193-0b4o0ccp 39 1 Assuming assume VBG cord-222193-0b4o0ccp 39 2 that that IN cord-222193-0b4o0ccp 39 3 the the DT cord-222193-0b4o0ccp 39 4 spread spread NN cord-222193-0b4o0ccp 39 5 of of IN cord-222193-0b4o0ccp 39 6 infection infection NN cord-222193-0b4o0ccp 39 7 has have VBZ cord-222193-0b4o0ccp 39 8 a a DT cord-222193-0b4o0ccp 39 9 rate rate NN cord-222193-0b4o0ccp 39 10 a a NN cord-222193-0b4o0ccp 39 11 , , , cord-222193-0b4o0ccp 39 12 we -PRON- PRP cord-222193-0b4o0ccp 39 13 obtain obtain VBP cord-222193-0b4o0ccp 39 14 the the DT cord-222193-0b4o0ccp 39 15 following follow VBG cord-222193-0b4o0ccp 39 16 system system NN cord-222193-0b4o0ccp 39 17 of of IN cord-222193-0b4o0ccp 39 18 equations equation NNS cord-222193-0b4o0ccp 39 19 : : : cord-222193-0b4o0ccp 39 20 where where WRB cord-222193-0b4o0ccp 39 21 the the DT cord-222193-0b4o0ccp 39 22 coefficient coefficient NN cord-222193-0b4o0ccp 39 23 a a NN cord-222193-0b4o0ccp 39 24 is be VBZ cord-222193-0b4o0ccp 39 25 expressed express VBN cord-222193-0b4o0ccp 39 26 via via IN cord-222193-0b4o0ccp 39 27 the the DT cord-222193-0b4o0ccp 39 28 infection infection NN cord-222193-0b4o0ccp 39 29 rate rate NN cord-222193-0b4o0ccp 40 1 We -PRON- PRP cord-222193-0b4o0ccp 40 2 suggested suggest VBD cord-222193-0b4o0ccp 40 3 that that IN cord-222193-0b4o0ccp 40 4 after after IN cord-222193-0b4o0ccp 40 5 T T NNP cord-222193-0b4o0ccp 40 6 days day NNS cord-222193-0b4o0ccp 40 7 a a DT cord-222193-0b4o0ccp 40 8 person person NN cord-222193-0b4o0ccp 40 9 recovers recover VBZ cord-222193-0b4o0ccp 40 10 and and CC cord-222193-0b4o0ccp 40 11 the the DT cord-222193-0b4o0ccp 40 12 patients patient NNS cord-222193-0b4o0ccp 40 13 are be VBP cord-222193-0b4o0ccp 40 14 not not RB cord-222193-0b4o0ccp 40 15 isolated isolate VBN cord-222193-0b4o0ccp 40 16 from from IN cord-222193-0b4o0ccp 40 17 the the DT cord-222193-0b4o0ccp 40 18 rest rest NN cord-222193-0b4o0ccp 40 19 of of IN cord-222193-0b4o0ccp 40 20 the the DT cord-222193-0b4o0ccp 40 21 population population NN cord-222193-0b4o0ccp 40 22 between between IN cord-222193-0b4o0ccp 40 23 days day NNS cord-222193-0b4o0ccp 40 24 L L NNP cord-222193-0b4o0ccp 40 25 and and CC cord-222193-0b4o0ccp 40 26 T T NNP cord-222193-0b4o0ccp 40 27 . . . cord-222193-0b4o0ccp 41 1 Eq Eq NNP cord-222193-0b4o0ccp 41 2 . . . cord-222193-0b4o0ccp 42 1 ( ( -LRB- cord-222193-0b4o0ccp 42 2 4 4 LS cord-222193-0b4o0ccp 42 3 ) ) -RRB- cord-222193-0b4o0ccp 42 4 describes describe VBZ cord-222193-0b4o0ccp 42 5 the the DT cord-222193-0b4o0ccp 42 6 dynamics dynamic NNS cord-222193-0b4o0ccp 42 7 of of IN cord-222193-0b4o0ccp 42 8 the the DT cord-222193-0b4o0ccp 42 9 population population NN cord-222193-0b4o0ccp 42 10 over over IN cord-222193-0b4o0ccp 42 11 discrete discrete JJ cord-222193-0b4o0ccp 42 12 time time NN cord-222193-0b4o0ccp 42 13 , , , cord-222193-0b4o0ccp 42 14 which which WDT cord-222193-0b4o0ccp 42 15 is be VBZ cord-222193-0b4o0ccp 42 16 the the DT cord-222193-0b4o0ccp 42 17 right right JJ cord-222193-0b4o0ccp 42 18 choice choice NN cord-222193-0b4o0ccp 42 19 for for IN cord-222193-0b4o0ccp 42 20 numerical numerical JJ cord-222193-0b4o0ccp 42 21 simulation simulation NN cord-222193-0b4o0ccp 42 22 . . . cord-222193-0b4o0ccp 43 1 Consider consider VB cord-222193-0b4o0ccp 43 2 now now RB cord-222193-0b4o0ccp 43 3 the the DT cord-222193-0b4o0ccp 43 4 continuous continuous JJ cord-222193-0b4o0ccp 43 5 - - HYPH cord-222193-0b4o0ccp 43 6 time time NN cord-222193-0b4o0ccp 43 7 version version NN cord-222193-0b4o0ccp 43 8 of of IN cord-222193-0b4o0ccp 43 9 the the DT cord-222193-0b4o0ccp 43 10 model model NN cord-222193-0b4o0ccp 43 11 . . . cord-222193-0b4o0ccp 44 1 In in IN cord-222193-0b4o0ccp 44 2 the the DT cord-222193-0b4o0ccp 44 3 limit limit NN cord-222193-0b4o0ccp 44 4 of of IN cord-222193-0b4o0ccp 44 5 small small JJ cord-222193-0b4o0ccp 44 6 δ δ NN cord-222193-0b4o0ccp 44 7 , , , cord-222193-0b4o0ccp 44 8 we -PRON- PRP cord-222193-0b4o0ccp 44 9 introduce introduce VBP cord-222193-0b4o0ccp 44 10 the the DT cord-222193-0b4o0ccp 44 11 continuous continuous JJ cord-222193-0b4o0ccp 44 12 function function NN cord-222193-0b4o0ccp 44 13 I -PRON- PRP cord-222193-0b4o0ccp 44 14 l l NN cord-222193-0b4o0ccp 44 15 ( ( -LRB- cord-222193-0b4o0ccp 44 16 t t NN cord-222193-0b4o0ccp 44 17 ) ) -RRB- cord-222193-0b4o0ccp 44 18 = = NFP cord-222193-0b4o0ccp 45 1 I(x I(x NNP cord-222193-0b4o0ccp 45 2 , , , cord-222193-0b4o0ccp 45 3 t t NNP cord-222193-0b4o0ccp 45 4 ) ) -RRB- cord-222193-0b4o0ccp 45 5 , , , cord-222193-0b4o0ccp 45 6 where where WRB cord-222193-0b4o0ccp 45 7 δI(x δI(x NNP cord-222193-0b4o0ccp 45 8 , , , cord-222193-0b4o0ccp 45 9 t t NN cord-222193-0b4o0ccp 45 10 ) ) -RRB- cord-222193-0b4o0ccp 45 11 is be VBZ cord-222193-0b4o0ccp 45 12 the the DT cord-222193-0b4o0ccp 45 13 size size NN cord-222193-0b4o0ccp 45 14 of of IN cord-222193-0b4o0ccp 45 15 the the DT cord-222193-0b4o0ccp 45 16 infected infected JJ cord-222193-0b4o0ccp 45 17 population population NN cord-222193-0b4o0ccp 45 18 with with IN cord-222193-0b4o0ccp 46 1 age age NN cord-222193-0b4o0ccp 46 2 x x NN cord-222193-0b4o0ccp 46 3 , , , cord-222193-0b4o0ccp 47 1 x x LS cord-222193-0b4o0ccp 47 2 + + CC cord-222193-0b4o0ccp 47 3 δ δ NN cord-222193-0b4o0ccp 47 4 . . . cord-222193-0b4o0ccp 48 1 The the DT cord-222193-0b4o0ccp 48 2 continuous continuous JJ cord-222193-0b4o0ccp 48 3 time time NN cord-222193-0b4o0ccp 48 4 versions version NNS cord-222193-0b4o0ccp 48 5 for for IN cord-222193-0b4o0ccp 48 6 the the DT cord-222193-0b4o0ccp 48 7 first first JJ cord-222193-0b4o0ccp 48 8 three three CD cord-222193-0b4o0ccp 48 9 equations equation NNS cord-222193-0b4o0ccp 48 10 are be VBP cord-222193-0b4o0ccp 48 11 : : : cord-222193-0b4o0ccp 48 12 The the DT cord-222193-0b4o0ccp 48 13 solution solution NN cord-222193-0b4o0ccp 48 14 of of IN cord-222193-0b4o0ccp 48 15 the the DT cord-222193-0b4o0ccp 48 16 second second JJ cord-222193-0b4o0ccp 48 17 equation equation NN cord-222193-0b4o0ccp 48 18 in in IN cord-222193-0b4o0ccp 48 19 Eq Eq NNP cord-222193-0b4o0ccp 48 20 . . . cord-222193-0b4o0ccp 49 1 ( ( -LRB- cord-222193-0b4o0ccp 49 2 1 1 LS cord-222193-0b4o0ccp 49 3 ) ) -RRB- cord-222193-0b4o0ccp 49 4 is be VBZ cord-222193-0b4o0ccp 49 5 where where WRB cord-222193-0b4o0ccp 49 6 we -PRON- PRP cord-222193-0b4o0ccp 49 7 denote denote VBP cord-222193-0b4o0ccp 49 8 J(x j(x NN cord-222193-0b4o0ccp 49 9 ) ) -RRB- cord-222193-0b4o0ccp 49 10 = = NFP cord-222193-0b4o0ccp 50 1 I(0 I(0 NNP cord-222193-0b4o0ccp 51 1 , , , cord-222193-0b4o0ccp 51 2 t t LS cord-222193-0b4o0ccp 51 3 ) ) -RRB- cord-222193-0b4o0ccp 51 4 Let let VB cord-222193-0b4o0ccp 51 5 us -PRON- PRP cord-222193-0b4o0ccp 51 6 look look VB cord-222193-0b4o0ccp 51 7 at at IN cord-222193-0b4o0ccp 51 8 the the DT cord-222193-0b4o0ccp 51 9 difference difference NN cord-222193-0b4o0ccp 51 10 Using use VBG cord-222193-0b4o0ccp 51 11 the the DT cord-222193-0b4o0ccp 51 12 latter latter JJ cord-222193-0b4o0ccp 51 13 expressions expression NNS cord-222193-0b4o0ccp 51 14 , , , cord-222193-0b4o0ccp 51 15 we -PRON- PRP cord-222193-0b4o0ccp 51 16 get get VBP cord-222193-0b4o0ccp 51 17 the the DT cord-222193-0b4o0ccp 51 18 following follow VBG cord-222193-0b4o0ccp 51 19 full full JJ cord-222193-0b4o0ccp 51 20 system system NN cord-222193-0b4o0ccp 51 21 of of IN cord-222193-0b4o0ccp 51 22 equations equation NNS cord-222193-0b4o0ccp 51 23 : : : cord-222193-0b4o0ccp 51 24 At at IN cord-222193-0b4o0ccp 51 25 the the DT cord-222193-0b4o0ccp 51 26 start start NN cord-222193-0b4o0ccp 51 27 , , , cord-222193-0b4o0ccp 51 28 when when WRB cord-222193-0b4o0ccp 51 29 Substituting substitute VBG cord-222193-0b4o0ccp 51 30 an an DT cord-222193-0b4o0ccp 51 31 ansatz ansatz NN cord-222193-0b4o0ccp 51 32 J(t J(t NNP cord-222193-0b4o0ccp 51 33 ) ) -RRB- cord-222193-0b4o0ccp 51 34 = = NFP cord-222193-0b4o0ccp 52 1 e e LS cord-222193-0b4o0ccp 52 2 kt kt NNP cord-222193-0b4o0ccp 52 3 , , , cord-222193-0b4o0ccp 52 4 we -PRON- PRP cord-222193-0b4o0ccp 52 5 get get VBP cord-222193-0b4o0ccp 52 6 : : : cord-222193-0b4o0ccp 53 1 At at IN cord-222193-0b4o0ccp 53 2 k k NNP cord-222193-0b4o0ccp 53 3 → → SYM cord-222193-0b4o0ccp 53 4 0 0 NFP cord-222193-0b4o0ccp 53 5 , , , cord-222193-0b4o0ccp 53 6 we -PRON- PRP cord-222193-0b4o0ccp 53 7 get get VBP cord-222193-0b4o0ccp 53 8 : : : cord-222193-0b4o0ccp 54 1 For for IN cord-222193-0b4o0ccp 54 2 increasing increase VBG cord-222193-0b4o0ccp 54 3 α α NN cord-222193-0b4o0ccp 54 4 , , , cord-222193-0b4o0ccp 54 5 we -PRON- PRP cord-222193-0b4o0ccp 54 6 get get VBP cord-222193-0b4o0ccp 54 7 an an DT cord-222193-0b4o0ccp 54 8 increasing increase VBG cord-222193-0b4o0ccp 54 9 value value NN cord-222193-0b4o0ccp 54 10 of of IN cord-222193-0b4o0ccp 54 11 k k NN cord-222193-0b4o0ccp 54 12 as as RB cord-222193-0b4o0ccp 54 13 well well RB cord-222193-0b4o0ccp 54 14 . . . cord-222193-0b4o0ccp 55 1 In in IN cord-222193-0b4o0ccp 55 2 the the DT cord-222193-0b4o0ccp 55 3 SIR SIR NNP cord-222193-0b4o0ccp 55 4 model model VB cord-222193-0b4o0ccp 55 5 the the DT cord-222193-0b4o0ccp 55 6 epidemic epidemic NN cord-222193-0b4o0ccp 55 7 threshold threshold NN cord-222193-0b4o0ccp 55 8 is be VBZ cord-222193-0b4o0ccp 55 9 at at IN cord-222193-0b4o0ccp 55 10 R r NN cord-222193-0b4o0ccp 55 11 = = SYM cord-222193-0b4o0ccp 55 12 1 1 CD cord-222193-0b4o0ccp 55 13 or or CC cord-222193-0b4o0ccp 55 14 a a DT cord-222193-0b4o0ccp 55 15 = = NN cord-222193-0b4o0ccp 55 16 b b NN cord-222193-0b4o0ccp 55 17 , , , cord-222193-0b4o0ccp 55 18 so so RB cord-222193-0b4o0ccp 55 19 our -PRON- PRP$ cord-222193-0b4o0ccp 55 20 model model NN cord-222193-0b4o0ccp 55 21 is be VBZ cord-222193-0b4o0ccp 55 22 similar similar JJ cord-222193-0b4o0ccp 55 23 to to IN cord-222193-0b4o0ccp 55 24 SIR SIR NNP cord-222193-0b4o0ccp 55 25 with with IN cord-222193-0b4o0ccp 55 26 b b NN cord-222193-0b4o0ccp 55 27 = = SYM cord-222193-0b4o0ccp 55 28 1/(T 1/(t CD cord-222193-0b4o0ccp 55 29 − − NNP cord-222193-0b4o0ccp 55 30 L l NN cord-222193-0b4o0ccp 55 31 ) ) -RRB- cord-222193-0b4o0ccp 55 32 . . . cord-222193-0b4o0ccp 56 1 In in IN cord-222193-0b4o0ccp 56 2 Fig Fig NNP cord-222193-0b4o0ccp 56 3 1 1 CD cord-222193-0b4o0ccp 56 4 . . . cord-222193-0b4o0ccp 56 5 , , , cord-222193-0b4o0ccp 56 6 we -PRON- PRP cord-222193-0b4o0ccp 56 7 analyze analyze VBP cord-222193-0b4o0ccp 56 8 the the DT cord-222193-0b4o0ccp 56 9 epidemiological epidemiological JJ cord-222193-0b4o0ccp 56 10 data datum NNS cord-222193-0b4o0ccp 56 11 for for IN cord-222193-0b4o0ccp 56 12 COVID-19 COVID-19 NNP cord-222193-0b4o0ccp 56 13 in in IN cord-222193-0b4o0ccp 56 14 Armenia Armenia NNP cord-222193-0b4o0ccp 56 15 using use VBG cord-222193-0b4o0ccp 56 16 our -PRON- PRP$ cord-222193-0b4o0ccp 56 17 model model NN cord-222193-0b4o0ccp 56 18 . . . cord-222193-0b4o0ccp 57 1 We -PRON- PRP cord-222193-0b4o0ccp 57 2 examine examine VBP cord-222193-0b4o0ccp 57 3 the the DT cord-222193-0b4o0ccp 57 4 dynamics dynamic NNS cord-222193-0b4o0ccp 57 5 of of IN cord-222193-0b4o0ccp 57 6 infected infected JJ cord-222193-0b4o0ccp 57 7 population population NN cord-222193-0b4o0ccp 57 8 in in IN cord-222193-0b4o0ccp 57 9 Armenia Armenia NNP cord-222193-0b4o0ccp 57 10 from from IN cord-222193-0b4o0ccp 57 11 March March NNP cord-222193-0b4o0ccp 57 12 25 25 CD cord-222193-0b4o0ccp 57 13 , , , cord-222193-0b4o0ccp 57 14 when when WRB cord-222193-0b4o0ccp 57 15 the the DT cord-222193-0b4o0ccp 57 16 quarantine quarantine NN cord-222193-0b4o0ccp 57 17 in in IN cord-222193-0b4o0ccp 57 18 the the DT cord-222193-0b4o0ccp 57 19 country country NN cord-222193-0b4o0ccp 57 20 has have VBZ cord-222193-0b4o0ccp 57 21 been be VBN cord-222193-0b4o0ccp 57 22 introduced introduce VBN cord-222193-0b4o0ccp 57 23 by by IN cord-222193-0b4o0ccp 57 24 the the DT cord-222193-0b4o0ccp 57 25 government government NN cord-222193-0b4o0ccp 57 26 , , , cord-222193-0b4o0ccp 57 27 until until IN cord-222193-0b4o0ccp 57 28 April April NNP cord-222193-0b4o0ccp 57 29 5 5 CD cord-222193-0b4o0ccp 57 30 . . . cord-222193-0b4o0ccp 57 31 _SP cord-222193-0b4o0ccp 58 1 Let let VB cord-222193-0b4o0ccp 58 2 us -PRON- PRP cord-222193-0b4o0ccp 58 3 consider consider VB cord-222193-0b4o0ccp 58 4 the the DT cord-222193-0b4o0ccp 58 5 case case NN cord-222193-0b4o0ccp 58 6 , , , cord-222193-0b4o0ccp 58 7 when when WRB cord-222193-0b4o0ccp 58 8 the the DT cord-222193-0b4o0ccp 58 9 infectivity infectivity NN cord-222193-0b4o0ccp 58 10 ( ( -LRB- cord-222193-0b4o0ccp 58 11 the the DT cord-222193-0b4o0ccp 58 12 ability ability NN cord-222193-0b4o0ccp 58 13 to to TO cord-222193-0b4o0ccp 58 14 transfer transfer VB cord-222193-0b4o0ccp 58 15 the the DT cord-222193-0b4o0ccp 58 16 infection infection NN cord-222193-0b4o0ccp 58 17 to to IN cord-222193-0b4o0ccp 58 18 susceptible susceptible JJ cord-222193-0b4o0ccp 58 19 individuals individual NNS cord-222193-0b4o0ccp 58 20 ) ) -RRB- cord-222193-0b4o0ccp 58 21 of of IN cord-222193-0b4o0ccp 58 22 infected infected JJ cord-222193-0b4o0ccp 58 23 individuals individual NNS cord-222193-0b4o0ccp 58 24 depends depend VBZ cord-222193-0b4o0ccp 58 25 on on IN cord-222193-0b4o0ccp 58 26 the the DT cord-222193-0b4o0ccp 58 27 age age NN cord-222193-0b4o0ccp 58 28 of of IN cord-222193-0b4o0ccp 58 29 infection infection NN cord-222193-0b4o0ccp 58 30 ( ( -LRB- cord-222193-0b4o0ccp 58 31 via via IN cord-222193-0b4o0ccp 58 32 a a DT cord-222193-0b4o0ccp 58 33 kernel kernel NN cord-222193-0b4o0ccp 58 34 f f NN cord-222193-0b4o0ccp 58 35 ( ( -LRB- cord-222193-0b4o0ccp 58 36 x x NN cord-222193-0b4o0ccp 58 37 ) ) -RRB- cord-222193-0b4o0ccp 58 38 ) ) -RRB- cord-222193-0b4o0ccp 58 39 , , , cord-222193-0b4o0ccp 58 40 also also RB cord-222193-0b4o0ccp 58 41 the the DT cord-222193-0b4o0ccp 58 42 population population NN cord-222193-0b4o0ccp 58 43 with with IN cord-222193-0b4o0ccp 58 44 the the DT cord-222193-0b4o0ccp 58 45 age age NN cord-222193-0b4o0ccp 58 46 x x NN cord-222193-0b4o0ccp 58 47 is be VBZ cord-222193-0b4o0ccp 58 48 diluted dilute VBN cord-222193-0b4o0ccp 58 49 with with IN cord-222193-0b4o0ccp 58 50 the the DT cord-222193-0b4o0ccp 58 51 rate rate NN cord-222193-0b4o0ccp 58 52 g(x g(x NNP cord-222193-0b4o0ccp 58 53 ) ) -RRB- cord-222193-0b4o0ccp 58 54 . . . cord-222193-0b4o0ccp 59 1 The the DT cord-222193-0b4o0ccp 59 2 latter latter NN cord-222193-0b4o0ccp 59 3 seems seem VBZ cord-222193-0b4o0ccp 59 4 to to TO cord-222193-0b4o0ccp 59 5 be be VB cord-222193-0b4o0ccp 59 6 a a DT cord-222193-0b4o0ccp 59 7 reasonable reasonable JJ cord-222193-0b4o0ccp 59 8 assumption assumption NN cord-222193-0b4o0ccp 59 9 , , , cord-222193-0b4o0ccp 59 10 since since IN cord-222193-0b4o0ccp 59 11 an an DT cord-222193-0b4o0ccp 59 12 infected infected JJ cord-222193-0b4o0ccp 59 13 individual individual NN cord-222193-0b4o0ccp 59 14 with with IN cord-222193-0b4o0ccp 59 15 a a DT cord-222193-0b4o0ccp 59 16 large large JJ cord-222193-0b4o0ccp 59 17 age age NN cord-222193-0b4o0ccp 59 18 reveals reveal VBZ cord-222193-0b4o0ccp 59 19 some some DT cord-222193-0b4o0ccp 59 20 symptoms symptom NNS cord-222193-0b4o0ccp 59 21 of of IN cord-222193-0b4o0ccp 59 22 infection infection NN cord-222193-0b4o0ccp 59 23 , , , cord-222193-0b4o0ccp 59 24 therefore therefore RB cord-222193-0b4o0ccp 59 25 , , , cord-222193-0b4o0ccp 59 26 has have VBZ cord-222193-0b4o0ccp 59 27 chances chance NNS cord-222193-0b4o0ccp 59 28 to to TO cord-222193-0b4o0ccp 59 29 be be VB cord-222193-0b4o0ccp 59 30 isolated isolate VBN cord-222193-0b4o0ccp 59 31 . . . cord-222193-0b4o0ccp 60 1 Now now RB cord-222193-0b4o0ccp 60 2 Eq Eq NNP cord-222193-0b4o0ccp 60 3 . . . cord-222193-0b4o0ccp 61 1 ( ( -LRB- cord-222193-0b4o0ccp 61 2 4 4 LS cord-222193-0b4o0ccp 61 3 ) ) -RRB- cord-222193-0b4o0ccp 61 4 is be VBZ cord-222193-0b4o0ccp 61 5 modified modify VBN cord-222193-0b4o0ccp 61 6 : : : cord-222193-0b4o0ccp 61 7 The the DT cord-222193-0b4o0ccp 61 8 continuous continuous JJ cord-222193-0b4o0ccp 61 9 time time NN cord-222193-0b4o0ccp 61 10 limit limit NN cord-222193-0b4o0ccp 61 11 gives give VBZ cord-222193-0b4o0ccp 61 12 the the DT cord-222193-0b4o0ccp 61 13 following follow VBG cord-222193-0b4o0ccp 61 14 system system NN cord-222193-0b4o0ccp 61 15 of of IN cord-222193-0b4o0ccp 61 16 equations equation NNS cord-222193-0b4o0ccp 62 1 : : : cord-222193-0b4o0ccp 62 2 Consider consider VB cord-222193-0b4o0ccp 62 3 now now RB cord-222193-0b4o0ccp 62 4 the the DT cord-222193-0b4o0ccp 62 5 asymptotic asymptotic JJ cord-222193-0b4o0ccp 62 6 solution solution NN cord-222193-0b4o0ccp 62 7 : : : cord-222193-0b4o0ccp 62 8 Then then RB cord-222193-0b4o0ccp 62 9 , , , cord-222193-0b4o0ccp 62 10 we -PRON- PRP cord-222193-0b4o0ccp 62 11 get get VBP cord-222193-0b4o0ccp 62 12 the the DT cord-222193-0b4o0ccp 62 13 following follow VBG cord-222193-0b4o0ccp 62 14 equations equation NNS cord-222193-0b4o0ccp 62 15 : : : cord-222193-0b4o0ccp 62 16 and and CC cord-222193-0b4o0ccp 62 17 Thus thus RB cord-222193-0b4o0ccp 62 18 , , , cord-222193-0b4o0ccp 62 19 we -PRON- PRP cord-222193-0b4o0ccp 62 20 derive derive VBP cord-222193-0b4o0ccp 62 21 for for IN cord-222193-0b4o0ccp 62 22 the the DT cord-222193-0b4o0ccp 62 23 epidemics epidemic NNS cord-222193-0b4o0ccp 62 24 threshold threshold NN cord-222193-0b4o0ccp 62 25 : : : cord-222193-0b4o0ccp 63 1 A. A. NNP cord-222193-0b4o0ccp 64 1 The the DT cord-222193-0b4o0ccp 64 2 specific specific JJ cord-222193-0b4o0ccp 64 3 functions function NNS cord-222193-0b4o0ccp 64 4 g(x g(x VBP cord-222193-0b4o0ccp 64 5 ) ) -RRB- cord-222193-0b4o0ccp 64 6 Let let VB cord-222193-0b4o0ccp 64 7 us -PRON- PRP cord-222193-0b4o0ccp 64 8 analyze analyze VB cord-222193-0b4o0ccp 64 9 our -PRON- PRP$ cord-222193-0b4o0ccp 64 10 Eq eq NN cord-222193-0b4o0ccp 64 11 . . . cord-222193-0b4o0ccp 65 1 ( ( -LRB- cord-222193-0b4o0ccp 65 2 16 16 CD cord-222193-0b4o0ccp 65 3 ) ) -RRB- cord-222193-0b4o0ccp 65 4 . . . cord-222193-0b4o0ccp 66 1 If if IN cord-222193-0b4o0ccp 66 2 we -PRON- PRP cord-222193-0b4o0ccp 66 3 are be VBP cord-222193-0b4o0ccp 66 4 trying try VBG cord-222193-0b4o0ccp 66 5 to to TO cord-222193-0b4o0ccp 66 6 reduce reduce VB cord-222193-0b4o0ccp 66 7 the the DT cord-222193-0b4o0ccp 66 8 growth growth NN cord-222193-0b4o0ccp 66 9 rate rate NN cord-222193-0b4o0ccp 67 1 k k NNP cord-222193-0b4o0ccp 67 2 , , , cord-222193-0b4o0ccp 67 3 it -PRON- PRP cord-222193-0b4o0ccp 67 4 can can MD cord-222193-0b4o0ccp 67 5 be be VB cord-222193-0b4o0ccp 67 6 done do VBN cord-222193-0b4o0ccp 67 7 in in IN cord-222193-0b4o0ccp 67 8 two two CD cord-222193-0b4o0ccp 67 9 ways way NNS cord-222193-0b4o0ccp 67 10 : : : cord-222193-0b4o0ccp 67 11 1 1 LS cord-222193-0b4o0ccp 67 12 . . . cord-222193-0b4o0ccp 67 13 reducing reduce VBG cord-222193-0b4o0ccp 67 14 the the DT cord-222193-0b4o0ccp 67 15 number number NN cord-222193-0b4o0ccp 67 16 of of IN cord-222193-0b4o0ccp 67 17 contacts contact NNS cord-222193-0b4o0ccp 67 18 , , , cord-222193-0b4o0ccp 67 19 A A NNP cord-222193-0b4o0ccp 67 20 , , , cord-222193-0b4o0ccp 67 21 Let let VB cord-222193-0b4o0ccp 67 22 us -PRON- PRP cord-222193-0b4o0ccp 67 23 introduce introduce VB cord-222193-0b4o0ccp 67 24 non non JJ cord-222193-0b4o0ccp 67 25 - - JJ cord-222193-0b4o0ccp 67 26 zero zero JJ cord-222193-0b4o0ccp 67 27 reduction reduction NN cord-222193-0b4o0ccp 67 28 , , , cord-222193-0b4o0ccp 67 29 just just RB cord-222193-0b4o0ccp 67 30 after after IN cord-222193-0b4o0ccp 67 31 7 7 CD cord-222193-0b4o0ccp 67 32 days day NNS cord-222193-0b4o0ccp 67 33 , , , cord-222193-0b4o0ccp 67 34 g(x g(x NN cord-222193-0b4o0ccp 67 35 ) ) -RRB- cord-222193-0b4o0ccp 67 36 = = NFP cord-222193-0b4o0ccp 68 1 g. g. NNP cord-222193-0b4o0ccp 69 1 Hence hence RB cord-222193-0b4o0ccp 69 2 , , , cord-222193-0b4o0ccp 69 3 we -PRON- PRP cord-222193-0b4o0ccp 69 4 get get VBP cord-222193-0b4o0ccp 69 5 the the DT cord-222193-0b4o0ccp 69 6 following following JJ cord-222193-0b4o0ccp 69 7 result result NN cord-222193-0b4o0ccp 69 8 : : : cord-222193-0b4o0ccp 69 9 We -PRON- PRP cord-222193-0b4o0ccp 69 10 should should MD cord-222193-0b4o0ccp 69 11 estimate estimate VB cord-222193-0b4o0ccp 69 12 the the DT cord-222193-0b4o0ccp 69 13 value value NN cord-222193-0b4o0ccp 69 14 of of IN cord-222193-0b4o0ccp 69 15 g g NN cord-222193-0b4o0ccp 69 16 that that WDT cord-222193-0b4o0ccp 69 17 stops stop VBZ cord-222193-0b4o0ccp 69 18 the the DT cord-222193-0b4o0ccp 69 19 epidemics epidemic NNS cord-222193-0b4o0ccp 69 20 . . . cord-222193-0b4o0ccp 70 1 We -PRON- PRP cord-222193-0b4o0ccp 70 2 now now RB cord-222193-0b4o0ccp 70 3 apply apply VBP cord-222193-0b4o0ccp 70 4 the the DT cord-222193-0b4o0ccp 70 5 generalized generalized JJ cord-222193-0b4o0ccp 70 6 version version NN cord-222193-0b4o0ccp 70 7 of of IN cord-222193-0b4o0ccp 70 8 the the DT cord-222193-0b4o0ccp 70 9 model model NN cord-222193-0b4o0ccp 70 10 to to IN cord-222193-0b4o0ccp 70 11 the the DT cord-222193-0b4o0ccp 70 12 epidemics epidemic NNS cord-222193-0b4o0ccp 70 13 in in IN cord-222193-0b4o0ccp 70 14 Armenia Armenia NNP cord-222193-0b4o0ccp 70 15 . . . cord-222193-0b4o0ccp 71 1 We -PRON- PRP cord-222193-0b4o0ccp 71 2 look look VBP cord-222193-0b4o0ccp 71 3 at at IN cord-222193-0b4o0ccp 71 4 two two CD cord-222193-0b4o0ccp 71 5 periods period NNS cord-222193-0b4o0ccp 71 6 of of IN cord-222193-0b4o0ccp 71 7 epidemics epidemic NNS cord-222193-0b4o0ccp 71 8 : : : cord-222193-0b4o0ccp 71 9 the the DT cord-222193-0b4o0ccp 71 10 first first JJ cord-222193-0b4o0ccp 71 11 period period NN cord-222193-0b4o0ccp 71 12 from from IN cord-222193-0b4o0ccp 71 13 March March NNP cord-222193-0b4o0ccp 71 14 24 24 CD cord-222193-0b4o0ccp 71 15 to to IN cord-222193-0b4o0ccp 71 16 April April NNP cord-222193-0b4o0ccp 71 17 5 5 CD cord-222193-0b4o0ccp 71 18 and and CC cord-222193-0b4o0ccp 71 19 the the DT cord-222193-0b4o0ccp 71 20 later later JJ cord-222193-0b4o0ccp 71 21 ( ( -LRB- cord-222193-0b4o0ccp 71 22 second second JJ cord-222193-0b4o0ccp 71 23 period period NN cord-222193-0b4o0ccp 71 24 ) ) -RRB- cord-222193-0b4o0ccp 71 25 , , , cord-222193-0b4o0ccp 71 26 when when WRB cord-222193-0b4o0ccp 71 27 quarantine quarantine NN cord-222193-0b4o0ccp 71 28 starts start VBZ cord-222193-0b4o0ccp 71 29 to to TO cord-222193-0b4o0ccp 71 30 work work VB cord-222193-0b4o0ccp 71 31 efficiently efficiently RB cord-222193-0b4o0ccp 71 32 . . . cord-222193-0b4o0ccp 72 1 A. A. NNP cord-222193-0b4o0ccp 73 1 The the DT cord-222193-0b4o0ccp 73 2 choice choice NN cord-222193-0b4o0ccp 73 3 g=0 g=0 NN cord-222193-0b4o0ccp 73 4 in in IN cord-222193-0b4o0ccp 73 5 the the DT cord-222193-0b4o0ccp 73 6 model model NN cord-222193-0b4o0ccp 73 7 . . . cord-222193-0b4o0ccp 74 1 Let let VB cord-222193-0b4o0ccp 74 2 us -PRON- PRP cord-222193-0b4o0ccp 74 3 first first RB cord-222193-0b4o0ccp 74 4 take take VB cord-222193-0b4o0ccp 74 5 g g NN cord-222193-0b4o0ccp 74 6 = = SYM cord-222193-0b4o0ccp 74 7 0 0 CD cord-222193-0b4o0ccp 74 8 for for IN cord-222193-0b4o0ccp 74 9 the the DT cord-222193-0b4o0ccp 74 10 first first JJ cord-222193-0b4o0ccp 74 11 period period NN cord-222193-0b4o0ccp 74 12 , , , cord-222193-0b4o0ccp 74 13 see see VB cord-222193-0b4o0ccp 74 14 Table table NN cord-222193-0b4o0ccp 74 15 1 1 CD cord-222193-0b4o0ccp 74 16 . . . cord-222193-0b4o0ccp 75 1 The the DT cord-222193-0b4o0ccp 75 2 parameter parameter NN cord-222193-0b4o0ccp 75 3 A a NN cord-222193-0b4o0ccp 75 4 in in IN cord-222193-0b4o0ccp 75 5 our -PRON- PRP$ cord-222193-0b4o0ccp 75 6 model model NN cord-222193-0b4o0ccp 75 7 is be VBZ cord-222193-0b4o0ccp 75 8 proportional proportional JJ cord-222193-0b4o0ccp 75 9 to to IN cord-222193-0b4o0ccp 75 10 the the DT cord-222193-0b4o0ccp 75 11 number number NN cord-222193-0b4o0ccp 75 12 of of IN cord-222193-0b4o0ccp 75 13 human human JJ cord-222193-0b4o0ccp 75 14 contacts contact NNS cord-222193-0b4o0ccp 75 15 during during IN cord-222193-0b4o0ccp 75 16 the the DT cord-222193-0b4o0ccp 75 17 day day NN cord-222193-0b4o0ccp 75 18 . . . cord-222193-0b4o0ccp 76 1 In in IN cord-222193-0b4o0ccp 76 2 the the DT cord-222193-0b4o0ccp 76 3 first first JJ cord-222193-0b4o0ccp 76 4 time time NN cord-222193-0b4o0ccp 76 5 period period NN cord-222193-0b4o0ccp 76 6 , , , cord-222193-0b4o0ccp 76 7 we -PRON- PRP cord-222193-0b4o0ccp 76 8 have have VBP cord-222193-0b4o0ccp 76 9 had have VBN cord-222193-0b4o0ccp 76 10 a a DT cord-222193-0b4o0ccp 76 11 = = SYM cord-222193-0b4o0ccp 76 12 0.235 0.235 CD cord-222193-0b4o0ccp 76 13 , , , cord-222193-0b4o0ccp 76 14 k k NN cord-222193-0b4o0ccp 76 15 = = SYM cord-222193-0b4o0ccp 76 16 0.088 0.088 CD cord-222193-0b4o0ccp 76 17 . . . cord-222193-0b4o0ccp 77 1 After after IN cord-222193-0b4o0ccp 77 2 the the DT cord-222193-0b4o0ccp 77 3 quarantine quarantine NN cord-222193-0b4o0ccp 77 4 in in IN cord-222193-0b4o0ccp 77 5 Armenia Armenia NNP cord-222193-0b4o0ccp 77 6 , , , cord-222193-0b4o0ccp 77 7 k k NNP cord-222193-0b4o0ccp 77 8 decreased decrease VBD cord-222193-0b4o0ccp 77 9 from from IN cord-222193-0b4o0ccp 77 10 the the DT cord-222193-0b4o0ccp 77 11 value value NN cord-222193-0b4o0ccp 77 12 0.088 0.088 CD cord-222193-0b4o0ccp 77 13 till till IN cord-222193-0b4o0ccp 77 14 the the DT cord-222193-0b4o0ccp 77 15 value value NN cord-222193-0b4o0ccp 77 16 0.031 0.031 CD cord-222193-0b4o0ccp 77 17 , , , cord-222193-0b4o0ccp 77 18 with with IN cord-222193-0b4o0ccp 77 19 a a DT cord-222193-0b4o0ccp 77 20 = = SYM cord-222193-0b4o0ccp 77 21 0.135 0.135 CD cord-222193-0b4o0ccp 77 22 . . . cord-222193-0b4o0ccp 78 1 The the DT cord-222193-0b4o0ccp 78 2 critical critical JJ cord-222193-0b4o0ccp 78 3 value value NN cord-222193-0b4o0ccp 78 4 of of IN cord-222193-0b4o0ccp 78 5 A a NN cord-222193-0b4o0ccp 78 6 to to TO cord-222193-0b4o0ccp 78 7 eliminate eliminate VB cord-222193-0b4o0ccp 78 8 the the DT cord-222193-0b4o0ccp 78 9 epidemics epidemic NNS cord-222193-0b4o0ccp 78 10 is be VBZ cord-222193-0b4o0ccp 78 11 a a DT cord-222193-0b4o0ccp 78 12 = = SYM cord-222193-0b4o0ccp 78 13 0.1 0.1 CD cord-222193-0b4o0ccp 78 14 . . . cord-222193-0b4o0ccp 79 1 We -PRON- PRP cord-222193-0b4o0ccp 79 2 reduced reduce VBD cord-222193-0b4o0ccp 79 3 43 43 CD cord-222193-0b4o0ccp 79 4 % % NN cord-222193-0b4o0ccp 79 5 of of IN cord-222193-0b4o0ccp 79 6 human human JJ cord-222193-0b4o0ccp 79 7 contacts contact NNS cord-222193-0b4o0ccp 79 8 . . . cord-222193-0b4o0ccp 80 1 The the DT cord-222193-0b4o0ccp 80 2 reducing reduce VBG cord-222193-0b4o0ccp 80 3 further further RB cord-222193-0b4o0ccp 80 4 26 26 CD cord-222193-0b4o0ccp 80 5 % % NN cord-222193-0b4o0ccp 80 6 of of IN cord-222193-0b4o0ccp 80 7 remaining remain VBG cord-222193-0b4o0ccp 80 8 contacts contact NNS cord-222193-0b4o0ccp 80 9 , , , cord-222193-0b4o0ccp 80 10 we -PRON- PRP cord-222193-0b4o0ccp 80 11 can can MD cord-222193-0b4o0ccp 80 12 eliminate eliminate VB cord-222193-0b4o0ccp 80 13 the the DT cord-222193-0b4o0ccp 80 14 epidemics epidemic NNS cord-222193-0b4o0ccp 80 15 . . . cord-222193-0b4o0ccp 81 1 Let let VB cord-222193-0b4o0ccp 81 2 's -PRON- PRP cord-222193-0b4o0ccp 81 3 evaluate evaluate VB cord-222193-0b4o0ccp 81 4 what what WP cord-222193-0b4o0ccp 81 5 degree degree NN cord-222193-0b4o0ccp 81 6 of of IN cord-222193-0b4o0ccp 81 7 g g NN cord-222193-0b4o0ccp 81 8 we -PRON- PRP cord-222193-0b4o0ccp 81 9 need need VBP cord-222193-0b4o0ccp 81 10 to to TO cord-222193-0b4o0ccp 81 11 eliminate eliminate VB cord-222193-0b4o0ccp 81 12 the the DT cord-222193-0b4o0ccp 81 13 epidemic epidemic NN cord-222193-0b4o0ccp 81 14 at at IN cord-222193-0b4o0ccp 81 15 given give VBN cord-222193-0b4o0ccp 81 16 values value NNS cord-222193-0b4o0ccp 82 1 ofA ofa UH cord-222193-0b4o0ccp 82 2 , , , cord-222193-0b4o0ccp 82 3 if if IN cord-222193-0b4o0ccp 82 4 we -PRON- PRP cord-222193-0b4o0ccp 82 5 attribute attribute VBP cord-222193-0b4o0ccp 82 6 the the DT cord-222193-0b4o0ccp 82 7 current current JJ cord-222193-0b4o0ccp 82 8 situation situation NN cord-222193-0b4o0ccp 82 9 to to IN cord-222193-0b4o0ccp 82 10 g g NN cord-222193-0b4o0ccp 82 11 = = SYM cord-222193-0b4o0ccp 82 12 0 0 CD cord-222193-0b4o0ccp 82 13 . . . cord-222193-0b4o0ccp 83 1 For for IN cord-222193-0b4o0ccp 83 2 the the DT cord-222193-0b4o0ccp 83 3 case case NN cord-222193-0b4o0ccp 83 4 of of IN cord-222193-0b4o0ccp 83 5 quarantine quarantine NN cord-222193-0b4o0ccp 83 6 , , , cord-222193-0b4o0ccp 83 7 we -PRON- PRP cord-222193-0b4o0ccp 83 8 take take VBP cord-222193-0b4o0ccp 83 9 the the DT cord-222193-0b4o0ccp 83 10 current current JJ cord-222193-0b4o0ccp 83 11 value value NN cord-222193-0b4o0ccp 84 1 k k NNP cord-222193-0b4o0ccp 84 2 = = SYM cord-222193-0b4o0ccp 84 3 0.031 0.031 CD cord-222193-0b4o0ccp 84 4 , , , cord-222193-0b4o0ccp 84 5 then then RB cord-222193-0b4o0ccp 84 6 we -PRON- PRP cord-222193-0b4o0ccp 84 7 see see VBP cord-222193-0b4o0ccp 84 8 that that IN cord-222193-0b4o0ccp 84 9 g g NN cord-222193-0b4o0ccp 84 10 = = SYM cord-222193-0b4o0ccp 84 11 0.035 0.035 CD cord-222193-0b4o0ccp 84 12 eliminates eliminate VBZ cord-222193-0b4o0ccp 84 13 epidemics epidemic NNS cord-222193-0b4o0ccp 84 14 . . . cord-222193-0b4o0ccp 85 1 The the DT cord-222193-0b4o0ccp 85 2 parameter parameter NN cord-222193-0b4o0ccp 85 3 A a NN cord-222193-0b4o0ccp 85 4 in in IN cord-222193-0b4o0ccp 85 5 our -PRON- PRP$ cord-222193-0b4o0ccp 85 6 model model NN cord-222193-0b4o0ccp 85 7 is be VBZ cord-222193-0b4o0ccp 85 8 proportional proportional JJ cord-222193-0b4o0ccp 85 9 to to IN cord-222193-0b4o0ccp 85 10 the the DT cord-222193-0b4o0ccp 85 11 number number NN cord-222193-0b4o0ccp 85 12 of of IN cord-222193-0b4o0ccp 85 13 human human JJ cord-222193-0b4o0ccp 85 14 contacts contact NNS cord-222193-0b4o0ccp 85 15 during during IN cord-222193-0b4o0ccp 85 16 the the DT cord-222193-0b4o0ccp 85 17 day day NN cord-222193-0b4o0ccp 85 18 . . . cord-222193-0b4o0ccp 86 1 In in IN cord-222193-0b4o0ccp 86 2 the the DT cord-222193-0b4o0ccp 86 3 first first JJ cord-222193-0b4o0ccp 86 4 period period NN cord-222193-0b4o0ccp 86 5 of of IN cord-222193-0b4o0ccp 86 6 epidemics epidemic NNS cord-222193-0b4o0ccp 86 7 , , , cord-222193-0b4o0ccp 86 8 we -PRON- PRP cord-222193-0b4o0ccp 86 9 had have VBD cord-222193-0b4o0ccp 86 10 a a DT cord-222193-0b4o0ccp 86 11 = = SYM cord-222193-0b4o0ccp 86 12 0.235 0.235 CD cord-222193-0b4o0ccp 86 13 , , , cord-222193-0b4o0ccp 86 14 k k NN cord-222193-0b4o0ccp 86 15 = = SYM cord-222193-0b4o0ccp 86 16 0.088 0.088 CD cord-222193-0b4o0ccp 86 17 . . . cord-222193-0b4o0ccp 87 1 After after IN cord-222193-0b4o0ccp 87 2 quarantine quarantine NN cord-222193-0b4o0ccp 87 3 in in IN cord-222193-0b4o0ccp 87 4 Armenia Armenia NNP cord-222193-0b4o0ccp 87 5 , , , cord-222193-0b4o0ccp 87 6 k k NNP cord-222193-0b4o0ccp 87 7 decreased decrease VBD cord-222193-0b4o0ccp 87 8 from from IN cord-222193-0b4o0ccp 87 9 0.088 0.088 CD cord-222193-0b4o0ccp 87 10 to to IN cord-222193-0b4o0ccp 87 11 0.031 0.031 CD cord-222193-0b4o0ccp 87 12 , , , cord-222193-0b4o0ccp 87 13 with with IN cord-222193-0b4o0ccp 87 14 a a DT cord-222193-0b4o0ccp 87 15 = = SYM cord-222193-0b4o0ccp 87 16 0.135 0.135 CD cord-222193-0b4o0ccp 87 17 . . . cord-222193-0b4o0ccp 88 1 The the DT cord-222193-0b4o0ccp 88 2 critical critical JJ cord-222193-0b4o0ccp 88 3 value value NN cord-222193-0b4o0ccp 88 4 of of IN cord-222193-0b4o0ccp 88 5 A a NN cord-222193-0b4o0ccp 88 6 for for IN cord-222193-0b4o0ccp 88 7 the the DT cord-222193-0b4o0ccp 88 8 elimination elimination NN cord-222193-0b4o0ccp 88 9 of of IN cord-222193-0b4o0ccp 88 10 epidemics epidemic NNS cord-222193-0b4o0ccp 88 11 is be VBZ cord-222193-0b4o0ccp 88 12 A a NN cord-222193-0b4o0ccp 88 13 = = SYM cord-222193-0b4o0ccp 88 14 0.1 0.1 CD cord-222193-0b4o0ccp 88 15 . . . cord-222193-0b4o0ccp 89 1 We -PRON- PRP cord-222193-0b4o0ccp 89 2 have have VBP cord-222193-0b4o0ccp 89 3 reduced reduce VBN cord-222193-0b4o0ccp 89 4 43 43 CD cord-222193-0b4o0ccp 89 5 % % NN cord-222193-0b4o0ccp 89 6 of of IN cord-222193-0b4o0ccp 89 7 human human JJ cord-222193-0b4o0ccp 89 8 contacts contact NNS cord-222193-0b4o0ccp 89 9 . . . cord-222193-0b4o0ccp 90 1 A a DT cord-222193-0b4o0ccp 90 2 further further JJ cord-222193-0b4o0ccp 90 3 reduction reduction NN cord-222193-0b4o0ccp 90 4 of of IN cord-222193-0b4o0ccp 90 5 26 26 CD cord-222193-0b4o0ccp 90 6 % % NN cord-222193-0b4o0ccp 90 7 of of IN cord-222193-0b4o0ccp 90 8 the the DT cord-222193-0b4o0ccp 90 9 remaining remain VBG cord-222193-0b4o0ccp 90 10 contacts contact NNS cord-222193-0b4o0ccp 90 11 , , , cord-222193-0b4o0ccp 90 12 we -PRON- PRP cord-222193-0b4o0ccp 90 13 can can MD cord-222193-0b4o0ccp 90 14 eliminate eliminate VB cord-222193-0b4o0ccp 90 15 the the DT cord-222193-0b4o0ccp 90 16 epidemic epidemic NN cord-222193-0b4o0ccp 90 17 . . . cord-222193-0b4o0ccp 91 1 For for IN cord-222193-0b4o0ccp 91 2 the the DT cord-222193-0b4o0ccp 91 3 case case NN cord-222193-0b4o0ccp 91 4 without without IN cord-222193-0b4o0ccp 91 5 quarantine quarantine NN cord-222193-0b4o0ccp 91 6 , , , cord-222193-0b4o0ccp 91 7 k k NN cord-222193-0b4o0ccp 91 8 = = SYM cord-222193-0b4o0ccp 91 9 0.088 0.088 CD cord-222193-0b4o0ccp 91 10 , , , cord-222193-0b4o0ccp 91 11 we -PRON- PRP cord-222193-0b4o0ccp 91 12 need need VBP cord-222193-0b4o0ccp 91 13 g g NN cord-222193-0b4o0ccp 91 14 = = SYM cord-222193-0b4o0ccp 91 15 0.12 0.12 CD cord-222193-0b4o0ccp 91 16 to to TO cord-222193-0b4o0ccp 91 17 eliminate eliminate VB cord-222193-0b4o0ccp 91 18 the the DT cord-222193-0b4o0ccp 91 19 epidemics epidemic NNS cord-222193-0b4o0ccp 91 20 , , , cord-222193-0b4o0ccp 91 21 much much RB cord-222193-0b4o0ccp 91 22 more more JJR cord-222193-0b4o0ccp 91 23 efforts effort NNS cord-222193-0b4o0ccp 91 24 compared compare VBN cord-222193-0b4o0ccp 91 25 to to IN cord-222193-0b4o0ccp 91 26 the the DT cord-222193-0b4o0ccp 91 27 previous previous JJ cord-222193-0b4o0ccp 91 28 considered consider VBN cord-222193-0b4o0ccp 91 29 case case NN cord-222193-0b4o0ccp 91 30 . . . cord-222193-0b4o0ccp 91 31 . . . cord-222193-0b4o0ccp 92 1 Let let VB cord-222193-0b4o0ccp 92 2 us -PRON- PRP cord-222193-0b4o0ccp 92 3 take take VB cord-222193-0b4o0ccp 92 4 g g NN cord-222193-0b4o0ccp 92 5 = = SYM cord-222193-0b4o0ccp 92 6 0.05 0.05 CD cord-222193-0b4o0ccp 92 7 for for IN cord-222193-0b4o0ccp 92 8 the the DT cord-222193-0b4o0ccp 92 9 first first JJ cord-222193-0b4o0ccp 92 10 period period NN cord-222193-0b4o0ccp 93 1 ( ( -LRB- cord-222193-0b4o0ccp 93 2 we -PRON- PRP cord-222193-0b4o0ccp 93 3 identify identify VBP cord-222193-0b4o0ccp 93 4 the the DT cord-222193-0b4o0ccp 93 5 35 35 CD cord-222193-0b4o0ccp 93 6 % % NN cord-222193-0b4o0ccp 93 7 of of IN cord-222193-0b4o0ccp 93 8 infected infected JJ cord-222193-0b4o0ccp 93 9 individuals individual NNS cord-222193-0b4o0ccp 93 10 during during IN cord-222193-0b4o0ccp 93 11 a a DT cord-222193-0b4o0ccp 93 12 week week NN cord-222193-0b4o0ccp 93 13 ) ) -RRB- cord-222193-0b4o0ccp 93 14 , , , cord-222193-0b4o0ccp 93 15 see see VB cord-222193-0b4o0ccp 93 16 Table Table NNP cord-222193-0b4o0ccp 93 17 II II NNP cord-222193-0b4o0ccp 93 18 . . . cord-222193-0b4o0ccp 94 1 Then then RB cord-222193-0b4o0ccp 94 2 , , , cord-222193-0b4o0ccp 94 3 we -PRON- PRP cord-222193-0b4o0ccp 94 4 apply apply VBP cord-222193-0b4o0ccp 94 5 A a DT cord-222193-0b4o0ccp 94 6 = = SYM cord-222193-0b4o0ccp 94 7 0.333 0.333 CD cord-222193-0b4o0ccp 94 8 for for IN cord-222193-0b4o0ccp 94 9 the the DT cord-222193-0b4o0ccp 94 10 first first JJ cord-222193-0b4o0ccp 94 11 period period NN cord-222193-0b4o0ccp 94 12 , , , cord-222193-0b4o0ccp 94 13 A a NN cord-222193-0b4o0ccp 94 14 = = SYM cord-222193-0b4o0ccp 94 15 0.2 0.2 CD cord-222193-0b4o0ccp 94 16 during during IN cord-222193-0b4o0ccp 94 17 the the DT cord-222193-0b4o0ccp 94 18 second second JJ cord-222193-0b4o0ccp 94 19 period period NN cord-222193-0b4o0ccp 95 1 and and CC cord-222193-0b4o0ccp 95 2 we -PRON- PRP cord-222193-0b4o0ccp 95 3 need need VBP cord-222193-0b4o0ccp 95 4 A a NN cord-222193-0b4o0ccp 95 5 = = SYM cord-222193-0b4o0ccp 95 6 0.151 0.151 CD cord-222193-0b4o0ccp 95 7 to to TO cord-222193-0b4o0ccp 95 8 eliminate eliminate VB cord-222193-0b4o0ccp 95 9 the the DT cord-222193-0b4o0ccp 95 10 epidemic epidemic NN cord-222193-0b4o0ccp 95 11 . . . cord-222193-0b4o0ccp 96 1 Due due IN cord-222193-0b4o0ccp 96 2 to to IN cord-222193-0b4o0ccp 96 3 the the DT cord-222193-0b4o0ccp 96 4 quarantine quarantine NN cord-222193-0b4o0ccp 96 5 , , , cord-222193-0b4o0ccp 96 6 we -PRON- PRP cord-222193-0b4o0ccp 96 7 reduced reduce VBD cord-222193-0b4o0ccp 96 8 40 40 CD cord-222193-0b4o0ccp 96 9 % % NN cord-222193-0b4o0ccp 96 10 of of IN cord-222193-0b4o0ccp 96 11 contacts contact NNS cord-222193-0b4o0ccp 96 12 , , , cord-222193-0b4o0ccp 96 13 we -PRON- PRP cord-222193-0b4o0ccp 96 14 now now RB cord-222193-0b4o0ccp 96 15 needs need VBZ cord-222193-0b4o0ccp 96 16 in in IN cord-222193-0b4o0ccp 96 17 reducing reduce VBG cord-222193-0b4o0ccp 96 18 of of IN cord-222193-0b4o0ccp 96 19 25 25 CD cord-222193-0b4o0ccp 96 20 % % NN cord-222193-0b4o0ccp 96 21 of of IN cord-222193-0b4o0ccp 96 22 existing exist VBG cord-222193-0b4o0ccp 96 23 contacts contact NNS cord-222193-0b4o0ccp 96 24 . . . cord-222193-0b4o0ccp 97 1 Holding hold VBG cord-222193-0b4o0ccp 97 2 current current JJ cord-222193-0b4o0ccp 97 3 values value NNS cord-222193-0b4o0ccp 97 4 of of IN cord-222193-0b4o0ccp 97 5 contacts contact NNS cord-222193-0b4o0ccp 97 6 , , , cord-222193-0b4o0ccp 97 7 we -PRON- PRP cord-222193-0b4o0ccp 97 8 need need VBP cord-222193-0b4o0ccp 97 9 rising rise VBG cord-222193-0b4o0ccp 97 10 the the DT cord-222193-0b4o0ccp 97 11 value value NN cord-222193-0b4o0ccp 97 12 of of IN cord-222193-0b4o0ccp 97 13 g g NN cord-222193-0b4o0ccp 97 14 from from IN cord-222193-0b4o0ccp 97 15 0.05 0.05 CD cord-222193-0b4o0ccp 97 16 to to IN cord-222193-0b4o0ccp 97 17 0.09 0.09 CD cord-222193-0b4o0ccp 97 18 . . . cord-222193-0b4o0ccp 98 1 We -PRON- PRP cord-222193-0b4o0ccp 98 2 verified verify VBD cord-222193-0b4o0ccp 98 3 that that IN cord-222193-0b4o0ccp 98 4 taking take VBG cord-222193-0b4o0ccp 98 5 g g NN cord-222193-0b4o0ccp 98 6 = = SYM cord-222193-0b4o0ccp 98 7 0.15 0.15 CD cord-222193-0b4o0ccp 98 8 before before IN cord-222193-0b4o0ccp 98 9 the the DT cord-222193-0b4o0ccp 98 10 quarantine quarantine NN cord-222193-0b4o0ccp 98 11 does do VBZ cord-222193-0b4o0ccp 98 12 not not RB cord-222193-0b4o0ccp 98 13 give give VB cord-222193-0b4o0ccp 98 14 adequate adequate JJ cord-222193-0b4o0ccp 98 15 results result NNS cord-222193-0b4o0ccp 98 16 . . . cord-222193-0b4o0ccp 99 1 How how WRB cord-222193-0b4o0ccp 99 2 can can MD cord-222193-0b4o0ccp 99 3 we -PRON- PRP cord-222193-0b4o0ccp 99 4 increase increase VB cord-222193-0b4o0ccp 99 5 g g NN cord-222193-0b4o0ccp 99 6 in in IN cord-222193-0b4o0ccp 99 7 practice practice NN cord-222193-0b4o0ccp 99 8 ? ? . cord-222193-0b4o0ccp 100 1 Testing test VBG cord-222193-0b4o0ccp 100 2 the the DT cord-222193-0b4o0ccp 100 3 20 20 CD cord-222193-0b4o0ccp 100 4 % % NN cord-222193-0b4o0ccp 100 5 per per IN cord-222193-0b4o0ccp 100 6 week week NN cord-222193-0b4o0ccp 100 7 in in IN cord-222193-0b4o0ccp 100 8 high high JJ cord-222193-0b4o0ccp 100 9 risk risk NN cord-222193-0b4o0ccp 100 10 groups group NNS cord-222193-0b4o0ccp 100 11 of of IN cord-222193-0b4o0ccp 100 12 the the DT cord-222193-0b4o0ccp 100 13 population population NN cord-222193-0b4o0ccp 100 14 , , , cord-222193-0b4o0ccp 100 15 we -PRON- PRP cord-222193-0b4o0ccp 100 16 can can MD cord-222193-0b4o0ccp 100 17 eliminate eliminate VB cord-222193-0b4o0ccp 100 18 the the DT cord-222193-0b4o0ccp 100 19 epidemics epidemic NNS cord-222193-0b4o0ccp 100 20 . . . cord-222193-0b4o0ccp 101 1 In in IN cord-222193-0b4o0ccp 101 2 this this DT cord-222193-0b4o0ccp 101 3 paper paper NN cord-222193-0b4o0ccp 101 4 , , , cord-222193-0b4o0ccp 101 5 we -PRON- PRP cord-222193-0b4o0ccp 101 6 introduced introduce VBD cord-222193-0b4o0ccp 101 7 a a DT cord-222193-0b4o0ccp 101 8 version version NN cord-222193-0b4o0ccp 101 9 of of IN cord-222193-0b4o0ccp 101 10 SIR SIR NNP cord-222193-0b4o0ccp 101 11 model model NN cord-222193-0b4o0ccp 101 12 for for IN cord-222193-0b4o0ccp 101 13 infection infection NN cord-222193-0b4o0ccp 101 14 spreading spread VBG cord-222193-0b4o0ccp 101 15 with with IN cord-222193-0b4o0ccp 101 16 known know VBN cord-222193-0b4o0ccp 101 17 incubation incubation NN cord-222193-0b4o0ccp 101 18 period period NN cord-222193-0b4o0ccp 101 19 . . . cord-222193-0b4o0ccp 102 1 This this DT cord-222193-0b4o0ccp 102 2 model model NN cord-222193-0b4o0ccp 102 3 was be VBD cord-222193-0b4o0ccp 102 4 applied apply VBN cord-222193-0b4o0ccp 102 5 to to TO cord-222193-0b4o0ccp 102 6 analyze analyze VB cord-222193-0b4o0ccp 102 7 the the DT cord-222193-0b4o0ccp 102 8 COVID-19 covid-19 JJ cord-222193-0b4o0ccp 102 9 epidemic epidemic NN cord-222193-0b4o0ccp 102 10 data datum NNS cord-222193-0b4o0ccp 102 11 in in IN cord-222193-0b4o0ccp 102 12 Armenia Armenia NNP cord-222193-0b4o0ccp 102 13 . . . cord-222193-0b4o0ccp 103 1 We -PRON- PRP cord-222193-0b4o0ccp 103 2 constructed construct VBD cord-222193-0b4o0ccp 103 3 the the DT cord-222193-0b4o0ccp 103 4 simplest simple JJS cord-222193-0b4o0ccp 103 5 version version NN cord-222193-0b4o0ccp 103 6 of of IN cord-222193-0b4o0ccp 103 7 population population NN cord-222193-0b4o0ccp 103 8 dynamics dynamic NNS cord-222193-0b4o0ccp 103 9 of of IN cord-222193-0b4o0ccp 103 10 age age NN cord-222193-0b4o0ccp 103 11 - - HYPH cord-222193-0b4o0ccp 103 12 structured structure VBN cord-222193-0b4o0ccp 103 13 population population NN cord-222193-0b4o0ccp 103 14 . . . cord-222193-0b4o0ccp 104 1 Close close JJ cord-222193-0b4o0ccp 104 2 work work NN cord-222193-0b4o0ccp 104 3 has have VBZ cord-222193-0b4o0ccp 104 4 been be VBN cord-222193-0b4o0ccp 104 5 done do VBN cord-222193-0b4o0ccp 104 6 in in IN cord-222193-0b4o0ccp 104 7 [ [ -LRB- cord-222193-0b4o0ccp 104 8 13 13 CD cord-222193-0b4o0ccp 104 9 ] ] -RRB- cord-222193-0b4o0ccp 104 10 , , , cord-222193-0b4o0ccp 104 11 which which WDT cord-222193-0b4o0ccp 104 12 is be VBZ cord-222193-0b4o0ccp 104 13 related relate VBN cord-222193-0b4o0ccp 104 14 to to IN cord-222193-0b4o0ccp 104 15 SIR SIR NNP cord-222193-0b4o0ccp 104 16 model model NN cord-222193-0b4o0ccp 104 17 . . . cord-222193-0b4o0ccp 105 1 In in IN cord-222193-0b4o0ccp 105 2 [ [ -LRB- cord-222193-0b4o0ccp 105 3 13 13 CD cord-222193-0b4o0ccp 105 4 ] ] -RRB- cord-222193-0b4o0ccp 105 5 , , , cord-222193-0b4o0ccp 105 6 a a DT cord-222193-0b4o0ccp 105 7 temporal temporal JJ cord-222193-0b4o0ccp 105 8 kernel kernel NN cord-222193-0b4o0ccp 105 9 F f NN cord-222193-0b4o0ccp 105 10 ( ( -LRB- cord-222193-0b4o0ccp 105 11 t t NN cord-222193-0b4o0ccp 105 12 ) ) -RRB- cord-222193-0b4o0ccp 105 13 has have VBZ cord-222193-0b4o0ccp 105 14 been be VBN cord-222193-0b4o0ccp 105 15 introduced introduce VBN cord-222193-0b4o0ccp 105 16 that that WDT cord-222193-0b4o0ccp 105 17 modulates modulate VBZ cord-222193-0b4o0ccp 105 18 the the DT cord-222193-0b4o0ccp 105 19 infectivity infectivity NN cord-222193-0b4o0ccp 105 20 of of IN cord-222193-0b4o0ccp 105 21 each each DT cord-222193-0b4o0ccp 105 22 infected infect VBN cord-222193-0b4o0ccp 105 23 individual individual NN cord-222193-0b4o0ccp 105 24 . . . cord-222193-0b4o0ccp 106 1 Compared compare VBN cord-222193-0b4o0ccp 106 2 to to IN cord-222193-0b4o0ccp 106 3 such such JJ cord-222193-0b4o0ccp 106 4 model model NN cord-222193-0b4o0ccp 106 5 , , , cord-222193-0b4o0ccp 106 6 we -PRON- PRP cord-222193-0b4o0ccp 106 7 introduced introduce VBD cord-222193-0b4o0ccp 106 8 the the DT cord-222193-0b4o0ccp 106 9 distribution distribution NN cord-222193-0b4o0ccp 106 10 of of IN cord-222193-0b4o0ccp 106 11 infected infected JJ cord-222193-0b4o0ccp 106 12 population population NN cord-222193-0b4o0ccp 106 13 at at IN cord-222193-0b4o0ccp 106 14 given give VBN cord-222193-0b4o0ccp 106 15 moment moment NN cord-222193-0b4o0ccp 106 16 of of IN cord-222193-0b4o0ccp 106 17 time time NN cord-222193-0b4o0ccp 106 18 via via IN cord-222193-0b4o0ccp 106 19 an an DT cord-222193-0b4o0ccp 106 20 age age NN cord-222193-0b4o0ccp 106 21 of of IN cord-222193-0b4o0ccp 106 22 infection infection NN cord-222193-0b4o0ccp 106 23 , , , cord-222193-0b4o0ccp 106 24 instead instead RB cord-222193-0b4o0ccp 106 25 of of IN cord-222193-0b4o0ccp 106 26 looking look VBG cord-222193-0b4o0ccp 106 27 just just RB cord-222193-0b4o0ccp 106 28 long long JJ cord-222193-0b4o0ccp 106 29 history history NN cord-222193-0b4o0ccp 106 30 of of IN cord-222193-0b4o0ccp 106 31 focus focus NN cord-222193-0b4o0ccp 106 32 populations population NNS cord-222193-0b4o0ccp 106 33 . . . cord-222193-0b4o0ccp 107 1 In in IN cord-222193-0b4o0ccp 107 2 other other JJ cord-222193-0b4o0ccp 107 3 works work NNS cord-222193-0b4o0ccp 107 4 related relate VBN cord-222193-0b4o0ccp 107 5 to to IN cord-222193-0b4o0ccp 107 6 the the DT cord-222193-0b4o0ccp 107 7 population population NN cord-222193-0b4o0ccp 107 8 dynamics dynamic NNS cord-222193-0b4o0ccp 107 9 of of IN cord-222193-0b4o0ccp 107 10 age age NN cord-222193-0b4o0ccp 107 11 - - HYPH cord-222193-0b4o0ccp 107 12 structured structure VBN cord-222193-0b4o0ccp 107 13 population population NN cord-222193-0b4o0ccp 107 14 , , , cord-222193-0b4o0ccp 107 15 the the DT cord-222193-0b4o0ccp 107 16 differential differential JJ cord-222193-0b4o0ccp 107 17 equations equation NNS cord-222193-0b4o0ccp 107 18 with with IN cord-222193-0b4o0ccp 107 19 time time NN cord-222193-0b4o0ccp 107 20 delay delay NN cord-222193-0b4o0ccp 107 21 usually usually RB cord-222193-0b4o0ccp 107 22 have have VBP cord-222193-0b4o0ccp 107 23 been be VBN cord-222193-0b4o0ccp 107 24 considered consider VBN cord-222193-0b4o0ccp 107 25 . . . cord-222193-0b4o0ccp 108 1 Instead instead RB cord-222193-0b4o0ccp 108 2 , , , cord-222193-0b4o0ccp 108 3 we -PRON- PRP cord-222193-0b4o0ccp 108 4 use use VBP cord-222193-0b4o0ccp 108 5 integro integro JJ cord-222193-0b4o0ccp 108 6 - - HYPH cord-222193-0b4o0ccp 108 7 differential differential JJ cord-222193-0b4o0ccp 108 8 system system NN cord-222193-0b4o0ccp 108 9 of of IN cord-222193-0b4o0ccp 108 10 equations equation NNS cord-222193-0b4o0ccp 108 11 , , , cord-222193-0b4o0ccp 108 12 which which WDT cord-222193-0b4o0ccp 108 13 seems seem VBZ cord-222193-0b4o0ccp 108 14 to to TO cord-222193-0b4o0ccp 108 15 be be VB cord-222193-0b4o0ccp 108 16 an an DT cord-222193-0b4o0ccp 108 17 adequate adequate JJ cord-222193-0b4o0ccp 108 18 approach approach NN cord-222193-0b4o0ccp 108 19 to to IN cord-222193-0b4o0ccp 108 20 the the DT cord-222193-0b4o0ccp 108 21 current current JJ cord-222193-0b4o0ccp 108 22 situation situation NN cord-222193-0b4o0ccp 108 23 with with IN cord-222193-0b4o0ccp 108 24 COVID-19 covid-19 JJ cord-222193-0b4o0ccp 108 25 epidemic epidemic NN cord-222193-0b4o0ccp 108 26 . . . cord-222193-0b4o0ccp 109 1 From from IN cord-222193-0b4o0ccp 109 2 our -PRON- PRP$ cord-222193-0b4o0ccp 109 3 perspective perspective NN cord-222193-0b4o0ccp 109 4 , , , cord-222193-0b4o0ccp 109 5 the the DT cord-222193-0b4o0ccp 109 6 proposed propose VBN cord-222193-0b4o0ccp 109 7 approach approach NN cord-222193-0b4o0ccp 109 8 significantly significantly RB cord-222193-0b4o0ccp 109 9 changes change VBZ cord-222193-0b4o0ccp 109 10 the the DT cord-222193-0b4o0ccp 109 11 epidemiological epidemiological JJ cord-222193-0b4o0ccp 109 12 picture picture NN cord-222193-0b4o0ccp 109 13 ( ( -LRB- cord-222193-0b4o0ccp 109 14 compare compare VB cord-222193-0b4o0ccp 109 15 to to IN cord-222193-0b4o0ccp 109 16 classical classical JJ cord-222193-0b4o0ccp 109 17 SIR SIR NNP cord-222193-0b4o0ccp 109 18 models model NNS cord-222193-0b4o0ccp 109 19 ) ) -RRB- cord-222193-0b4o0ccp 109 20 , , , cord-222193-0b4o0ccp 109 21 since since IN cord-222193-0b4o0ccp 109 22 the the DT cord-222193-0b4o0ccp 109 23 virus virus NN cord-222193-0b4o0ccp 109 24 is be VBZ cord-222193-0b4o0ccp 109 25 active active JJ cord-222193-0b4o0ccp 109 26 for for IN cord-222193-0b4o0ccp 109 27 about about RB cord-222193-0b4o0ccp 109 28 two two CD cord-222193-0b4o0ccp 109 29 weeks week NNS cord-222193-0b4o0ccp 109 30 . . . cord-222193-0b4o0ccp 110 1 Next next RB cord-222193-0b4o0ccp 110 2 , , , cord-222193-0b4o0ccp 110 3 we -PRON- PRP cord-222193-0b4o0ccp 110 4 introduced introduce VBD cord-222193-0b4o0ccp 110 5 two two CD cord-222193-0b4o0ccp 110 6 functions function NNS cord-222193-0b4o0ccp 110 7 : : : cord-222193-0b4o0ccp 110 8 f f NNP cord-222193-0b4o0ccp 110 9 ( ( -LRB- cord-222193-0b4o0ccp 110 10 x x NNP cord-222193-0b4o0ccp 110 11 ) ) -RRB- cord-222193-0b4o0ccp 110 12 , , , cord-222193-0b4o0ccp 110 13 which which WDT cord-222193-0b4o0ccp 110 14 describes describe VBZ cord-222193-0b4o0ccp 110 15 the the DT cord-222193-0b4o0ccp 110 16 distribution distribution NN cord-222193-0b4o0ccp 110 17 of of IN cord-222193-0b4o0ccp 110 18 infectivity infectivity NN cord-222193-0b4o0ccp 110 19 by by IN cord-222193-0b4o0ccp 110 20 age age NN cord-222193-0b4o0ccp 110 21 , , , cord-222193-0b4o0ccp 110 22 and and CC cord-222193-0b4o0ccp 110 23 g(x g(x NNP cord-222193-0b4o0ccp 110 24 ) ) -RRB- cord-222193-0b4o0ccp 110 25 , , , cord-222193-0b4o0ccp 110 26 which which WDT cord-222193-0b4o0ccp 110 27 describes describe VBZ cord-222193-0b4o0ccp 110 28 the the DT cord-222193-0b4o0ccp 110 29 content content NN cord-222193-0b4o0ccp 110 30 measures measure NNS cord-222193-0b4o0ccp 110 31 . . . cord-222193-0b4o0ccp 111 1 In in IN cord-222193-0b4o0ccp 111 2 the the DT cord-222193-0b4o0ccp 111 3 normal normal JJ cord-222193-0b4o0ccp 111 4 SIR SIR NNP cord-222193-0b4o0ccp 111 5 model model NN cord-222193-0b4o0ccp 111 6 , , , cord-222193-0b4o0ccp 111 7 we -PRON- PRP cord-222193-0b4o0ccp 111 8 have have VBP cord-222193-0b4o0ccp 111 9 two two CD cord-222193-0b4o0ccp 111 10 parameters parameter NNS cord-222193-0b4o0ccp 111 11 for for IN cord-222193-0b4o0ccp 111 12 the the DT cord-222193-0b4o0ccp 111 13 rate rate NN cord-222193-0b4o0ccp 111 14 of of IN cord-222193-0b4o0ccp 111 15 infection infection NN cord-222193-0b4o0ccp 111 16 and and CC cord-222193-0b4o0ccp 111 17 the the DT cord-222193-0b4o0ccp 111 18 removal removal NN cord-222193-0b4o0ccp 111 19 of of IN cord-222193-0b4o0ccp 111 20 infections infection NNS cord-222193-0b4o0ccp 111 21 . . . cord-222193-0b4o0ccp 112 1 In in IN cord-222193-0b4o0ccp 112 2 our -PRON- PRP$ cord-222193-0b4o0ccp 112 3 integrodifferential integrodifferential JJ cord-222193-0b4o0ccp 112 4 model model NN cord-222193-0b4o0ccp 112 5 , , , cord-222193-0b4o0ccp 112 6 mapping mapping NN cord-222193-0b4o0ccp 112 7 to to IN cord-222193-0b4o0ccp 112 8 elementary elementary JJ cord-222193-0b4o0ccp 112 9 processes process NNS cord-222193-0b4o0ccp 112 10 is be VBZ cord-222193-0b4o0ccp 112 11 straightforward straightforward JJ cord-222193-0b4o0ccp 112 12 : : : cord-222193-0b4o0ccp 112 13 we -PRON- PRP cord-222193-0b4o0ccp 112 14 just just RB cord-222193-0b4o0ccp 112 15 need need VBP cord-222193-0b4o0ccp 112 16 the the DT cord-222193-0b4o0ccp 112 17 velocity velocity NN cord-222193-0b4o0ccp 112 18 parameter parameter NN cord-222193-0b4o0ccp 112 19 a a NN cord-222193-0b4o0ccp 112 20 and and CC cord-222193-0b4o0ccp 112 21 two two CD cord-222193-0b4o0ccp 112 22 periods period NNS cord-222193-0b4o0ccp 112 23 : : : cord-222193-0b4o0ccp 112 24 the the DT cord-222193-0b4o0ccp 112 25 incubation incubation NN cord-222193-0b4o0ccp 112 26 period period NN cord-222193-0b4o0ccp 112 27 L l NN cord-222193-0b4o0ccp 112 28 and and CC cord-222193-0b4o0ccp 112 29 recovery recovery NN cord-222193-0b4o0ccp 112 30 period period NN cord-222193-0b4o0ccp 112 31 T t NN cord-222193-0b4o0ccp 112 32 with with IN cord-222193-0b4o0ccp 112 33 symptoms symptom NNS cord-222193-0b4o0ccp 112 34 after after IN cord-222193-0b4o0ccp 112 35 the the DT cord-222193-0b4o0ccp 112 36 carrier carrier NN cord-222193-0b4o0ccp 112 37 is be VBZ cord-222193-0b4o0ccp 112 38 separated separate VBN cord-222193-0b4o0ccp 112 39 from from IN cord-222193-0b4o0ccp 112 40 society society NN cord-222193-0b4o0ccp 112 41 . . . cord-222193-0b4o0ccp 113 1 We -PRON- PRP cord-222193-0b4o0ccp 113 2 derive derive VBP cord-222193-0b4o0ccp 113 3 an an DT cord-222193-0b4o0ccp 113 4 analytical analytical JJ cord-222193-0b4o0ccp 113 5 result result NN cord-222193-0b4o0ccp 113 6 for for IN cord-222193-0b4o0ccp 113 7 exponential exponential JJ cord-222193-0b4o0ccp 113 8 growth growth NN cord-222193-0b4o0ccp 113 9 in in IN cord-222193-0b4o0ccp 113 10 the the DT cord-222193-0b4o0ccp 113 11 early early JJ cord-222193-0b4o0ccp 113 12 stages stage NNS cord-222193-0b4o0ccp 113 13 of of IN cord-222193-0b4o0ccp 113 14 epidemics epidemic NNS cord-222193-0b4o0ccp 113 15 , , , cord-222193-0b4o0ccp 113 16 as as RB cord-222193-0b4o0ccp 113 17 well well RB cord-222193-0b4o0ccp 113 18 as as IN cord-222193-0b4o0ccp 113 19 for for IN cord-222193-0b4o0ccp 113 20 the the DT cord-222193-0b4o0ccp 113 21 epidemic epidemic NN cord-222193-0b4o0ccp 113 22 threshold threshold NN cord-222193-0b4o0ccp 113 23 . . . cord-222193-0b4o0ccp 114 1 It -PRON- PRP cord-222193-0b4o0ccp 114 2 will will MD cord-222193-0b4o0ccp 114 3 be be VB cord-222193-0b4o0ccp 114 4 very very RB cord-222193-0b4o0ccp 114 5 interesting interesting JJ cord-222193-0b4o0ccp 114 6 to to TO cord-222193-0b4o0ccp 114 7 investigate investigate VB cord-222193-0b4o0ccp 114 8 the the DT cord-222193-0b4o0ccp 114 9 transitional transitional JJ cord-222193-0b4o0ccp 114 10 situation situation NN cord-222193-0b4o0ccp 114 11 near near IN cord-222193-0b4o0ccp 114 12 the the DT cord-222193-0b4o0ccp 114 13 threshold threshold NN cord-222193-0b4o0ccp 114 14 . . . cord-222193-0b4o0ccp 115 1 We -PRON- PRP cord-222193-0b4o0ccp 115 2 suggest suggest VBP cord-222193-0b4o0ccp 115 3 simply simply RB cord-222193-0b4o0ccp 115 4 making make VBG cord-222193-0b4o0ccp 115 5 numbers number NNS cord-222193-0b4o0ccp 115 6 and and CC cord-222193-0b4o0ccp 115 7 choosing choose VBG cord-222193-0b4o0ccp 115 8 a a DT cord-222193-0b4o0ccp 115 9 parameter parameter NN cord-222193-0b4o0ccp 115 10 value value NN cord-222193-0b4o0ccp 115 11 to to TO cord-222193-0b4o0ccp 115 12 match match VB cord-222193-0b4o0ccp 115 13 the the DT cord-222193-0b4o0ccp 115 14 correct correct JJ cord-222193-0b4o0ccp 115 15 exponential exponential JJ cord-222193-0b4o0ccp 115 16 growth growth NN cord-222193-0b4o0ccp 115 17 . . . cord-222193-0b4o0ccp 116 1 We -PRON- PRP cord-222193-0b4o0ccp 116 2 applied apply VBD cord-222193-0b4o0ccp 116 3 our -PRON- PRP$ cord-222193-0b4o0ccp 116 4 model model NN cord-222193-0b4o0ccp 116 5 to to TO cord-222193-0b4o0ccp 116 6 understand understand VB cord-222193-0b4o0ccp 116 7 the the DT cord-222193-0b4o0ccp 116 8 situation situation NN cord-222193-0b4o0ccp 116 9 with with IN cord-222193-0b4o0ccp 116 10 epidemics epidemic NNS cord-222193-0b4o0ccp 116 11 in in IN cord-222193-0b4o0ccp 116 12 Armenia Armenia NNP cord-222193-0b4o0ccp 116 13 . . . cord-222193-0b4o0ccp 117 1 What what WP cord-222193-0b4o0ccp 117 2 is be VBZ cord-222193-0b4o0ccp 117 3 advantageous advantageous JJ cord-222193-0b4o0ccp 117 4 in in IN cord-222193-0b4o0ccp 117 5 our -PRON- PRP$ cord-222193-0b4o0ccp 117 6 model model NN cord-222193-0b4o0ccp 117 7 , , , cord-222193-0b4o0ccp 117 8 that that IN cord-222193-0b4o0ccp 117 9 we -PRON- PRP cord-222193-0b4o0ccp 117 10 can can MD cord-222193-0b4o0ccp 117 11 clearly clearly RB cord-222193-0b4o0ccp 117 12 separate separate VB cord-222193-0b4o0ccp 117 13 two two CD cord-222193-0b4o0ccp 117 14 aspects aspect NNS cord-222193-0b4o0ccp 117 15 of of IN cord-222193-0b4o0ccp 117 16 the the DT cord-222193-0b4o0ccp 117 17 epidemic epidemic NN cord-222193-0b4o0ccp 117 18 : : : cord-222193-0b4o0ccp 117 19 contact contact NN cord-222193-0b4o0ccp 117 20 strength strength NN cord-222193-0b4o0ccp 117 21 ( ( -LRB- cord-222193-0b4o0ccp 117 22 through through IN cord-222193-0b4o0ccp 117 23 coefficient coefficient NN cord-222193-0b4o0ccp 117 24 A A NNP cord-222193-0b4o0ccp 117 25 ) ) -RRB- cord-222193-0b4o0ccp 117 26 and and CC cord-222193-0b4o0ccp 117 27 deterrence deterrence NN cord-222193-0b4o0ccp 117 28 measures measure NNS cord-222193-0b4o0ccp 117 29 through through IN cord-222193-0b4o0ccp 117 30 parameter parameter NN cord-222193-0b4o0ccp 118 1 g. g. NNP cord-222193-0b4o0ccp 119 1 We -PRON- PRP cord-222193-0b4o0ccp 119 2 check check VBP cord-222193-0b4o0ccp 119 3 that that IN cord-222193-0b4o0ccp 119 4 in in IN cord-222193-0b4o0ccp 119 5 fact fact NN cord-222193-0b4o0ccp 119 6 we -PRON- PRP cord-222193-0b4o0ccp 119 7 need need VBP cord-222193-0b4o0ccp 119 8 to to TO cord-222193-0b4o0ccp 119 9 make make VB cord-222193-0b4o0ccp 119 10 minimal minimal JJ cord-222193-0b4o0ccp 119 11 efforts effort NNS cord-222193-0b4o0ccp 119 12 to to TO cord-222193-0b4o0ccp 119 13 stop stop VB cord-222193-0b4o0ccp 119 14 the the DT cord-222193-0b4o0ccp 119 15 epidemics epidemic NNS cord-222193-0b4o0ccp 119 16 , , , cord-222193-0b4o0ccp 119 17 and and CC cord-222193-0b4o0ccp 119 18 testing testing NN cord-222193-0b4o0ccp 119 19 is be VBZ cord-222193-0b4o0ccp 119 20 much much RB cord-222193-0b4o0ccp 119 21 cheaper cheap JJR cord-222193-0b4o0ccp 119 22 during during IN cord-222193-0b4o0ccp 119 23 quarantine quarantine NN cord-222193-0b4o0ccp 119 24 . . . cord-222193-0b4o0ccp 120 1 Currently currently RB cord-222193-0b4o0ccp 120 2 , , , cord-222193-0b4o0ccp 120 3 if if IN cord-222193-0b4o0ccp 120 4 we -PRON- PRP cord-222193-0b4o0ccp 120 5 detect detect VBP cord-222193-0b4o0ccp 120 6 only only RB cord-222193-0b4o0ccp 120 7 3.5 3.5 CD cord-222193-0b4o0ccp 120 8 % % NN cord-222193-0b4o0ccp 120 9 of of IN cord-222193-0b4o0ccp 120 10 the the DT cord-222193-0b4o0ccp 120 11 infected infected JJ cord-222193-0b4o0ccp 120 12 population population NN cord-222193-0b4o0ccp 120 13 per per IN cord-222193-0b4o0ccp 120 14 day day NN cord-222193-0b4o0ccp 120 15 , , , cord-222193-0b4o0ccp 120 16 strictly strictly RB cord-222193-0b4o0ccp 120 17 monitoring monitor VBG cord-222193-0b4o0ccp 120 18 the the DT cord-222193-0b4o0ccp 120 19 symptoms symptom NNS cord-222193-0b4o0ccp 120 20 , , , cord-222193-0b4o0ccp 120 21 we -PRON- PRP cord-222193-0b4o0ccp 120 22 can can MD cord-222193-0b4o0ccp 120 23 stop stop VB cord-222193-0b4o0ccp 120 24 the the DT cord-222193-0b4o0ccp 120 25 epidemic epidemic NN cord-222193-0b4o0ccp 120 26 . . . cord-222193-0b4o0ccp 121 1 This this DT cord-222193-0b4o0ccp 121 2 is be VBZ cord-222193-0b4o0ccp 121 3 much much RB cord-222193-0b4o0ccp 121 4 more more RBR cord-222193-0b4o0ccp 121 5 complicated complicated JJ cord-222193-0b4o0ccp 121 6 without without IN cord-222193-0b4o0ccp 121 7 quarantine quarantine NN cord-222193-0b4o0ccp 121 8 . . . cord-222193-0b4o0ccp 122 1 I -PRON- PRP cord-222193-0b4o0ccp 122 2 thank thank VBP cord-222193-0b4o0ccp 122 3 Armen Armen NNP cord-222193-0b4o0ccp 122 4 Allahverdyan Allahverdyan NNP cord-222193-0b4o0ccp 122 5 , , , cord-222193-0b4o0ccp 122 6 Pavel Pavel NNP cord-222193-0b4o0ccp 122 7 Krapivsky Krapivsky NNP cord-222193-0b4o0ccp 122 8 , , , cord-222193-0b4o0ccp 122 9 Ruben Ruben NNP cord-222193-0b4o0ccp 122 10 Poghosyan Poghosyan NNP cord-222193-0b4o0ccp 122 11 , , , cord-222193-0b4o0ccp 122 12 Didier Didier NNP cord-222193-0b4o0ccp 122 13 Sornette Sornette NNP cord-222193-0b4o0ccp 122 14 , , , cord-222193-0b4o0ccp 122 15 and and CC cord-222193-0b4o0ccp 122 16 Tatiana Tatiana NNP cord-222193-0b4o0ccp 122 17 Yakushkina Yakushkina NNP cord-222193-0b4o0ccp 122 18 for for IN cord-222193-0b4o0ccp 122 19 useful useful JJ cord-222193-0b4o0ccp 122 20 discussions discussion NNS cord-222193-0b4o0ccp 122 21 . . . cord-222193-0b4o0ccp 123 1 The the DT cord-222193-0b4o0ccp 123 2 work work NN cord-222193-0b4o0ccp 123 3 is be VBZ cord-222193-0b4o0ccp 123 4 supported support VBN cord-222193-0b4o0ccp 123 5 by by IN cord-222193-0b4o0ccp 123 6 the the DT cord-222193-0b4o0ccp 123 7 Russian Russian NNP cord-222193-0b4o0ccp 123 8 Science Science NNP cord-222193-0b4o0ccp 123 9 Foundation Foundation NNP cord-222193-0b4o0ccp 123 10 under under IN cord-222193-0b4o0ccp 123 11 grant grant NN cord-222193-0b4o0ccp 123 12 19 19 CD cord-222193-0b4o0ccp 123 13 - - SYM cord-222193-0b4o0ccp 123 14 11 11 CD cord-222193-0b4o0ccp 123 15 - - HYPH cord-222193-0b4o0ccp 123 16 00008 00008 CD cord-222193-0b4o0ccp 123 17 from from IN cord-222193-0b4o0ccp 123 18 Russian Russian NNP cord-222193-0b4o0ccp 123 19 University University NNP cord-222193-0b4o0ccp 123 20 of of IN cord-222193-0b4o0ccp 123 21 Transport Transport NNP cord-222193-0b4o0ccp 123 22 Infectious Infectious NNP cord-222193-0b4o0ccp 123 23 Diseases Diseases NNPS cord-222193-0b4o0ccp 123 24 in in IN cord-222193-0b4o0ccp 123 25 Humans Humans NNPS cord-222193-0b4o0ccp 123 26 Data Data NNP cord-222193-0b4o0ccp 123 27 analysis analysis NN cord-222193-0b4o0ccp 123 28 for for IN cord-222193-0b4o0ccp 123 29 the the DT cord-222193-0b4o0ccp 123 30 COVID-19 COVID-19 NNP cord-222193-0b4o0ccp 123 31 early early JJ cord-222193-0b4o0ccp 123 32 dynamics dynamic NNS cord-222193-0b4o0ccp 123 33 in in IN cord-222193-0b4o0ccp 123 34 Northern Northern NNP cord-222193-0b4o0ccp 123 35 Italy Italy NNP cord-222193-0b4o0ccp 123 36 Evolution Evolution NNP cord-222193-0b4o0ccp 123 37 in in IN cord-222193-0b4o0ccp 123 38 Age Age NNP cord-222193-0b4o0ccp 123 39 - - HYPH cord-222193-0b4o0ccp 123 40 Structured Structured NNP cord-222193-0b4o0ccp 123 41 Populations Populations NNPS cord-222193-0b4o0ccp 124 1 rDoes rDoes NNP cord-222193-0b4o0ccp 124 2 Good Good NNP cord-222193-0b4o0ccp 124 3 Mutation Mutation NNP cord-222193-0b4o0ccp 124 4 Help help VB cord-222193-0b4o0ccp 124 5 You -PRON- PRP cord-222193-0b4o0ccp 124 6 Live live VB cord-222193-0b4o0ccp 124 7 Longer long RBR cord-222193-0b4o0ccp 124 8 ? ? . cord-222193-0b4o0ccp 125 1 Different different JJ cord-222193-0b4o0ccp 125 2 fitnesses fitness NNS cord-222193-0b4o0ccp 125 3 for for IN cord-222193-0b4o0ccp 125 4 in in IN cord-222193-0b4o0ccp 125 5 vivo vivo NN cord-222193-0b4o0ccp 125 6 and and CC cord-222193-0b4o0ccp 125 7 in in IN cord-222193-0b4o0ccp 125 8 vitro vitro FW cord-222193-0b4o0ccp 125 9 evolutions evolution NNS cord-222193-0b4o0ccp 125 10 due due JJ cord-222193-0b4o0ccp 125 11 to to IN cord-222193-0b4o0ccp 125 12 the the DT cord-222193-0b4o0ccp 125 13 finite finite JJ cord-222193-0b4o0ccp 125 14 generation generation NN cord-222193-0b4o0ccp 125 15 - - HYPH cord-222193-0b4o0ccp 125 16 time time NN cord-222193-0b4o0ccp 125 17 effect effect NN cord-222193-0b4o0ccp 125 18 DB DB NNP cord-222193-0b4o0ccp 125 19 Saakian Saakian NNP cord-222193-0b4o0ccp 125 20 , , , cord-222193-0b4o0ccp 125 21 AS as IN cord-222193-0b4o0ccp 125 22 Martirosyan Martirosyan NNP cord-222193-0b4o0ccp 125 23 Generalized generalize VBD cord-222193-0b4o0ccp 125 24 logistic logistic JJ cord-222193-0b4o0ccp 125 25 growth growth NN cord-222193-0b4o0ccp 125 26 modeling modeling NN cord-222193-0b4o0ccp 125 27 of of IN cord-222193-0b4o0ccp 125 28 the the DT cord-222193-0b4o0ccp 125 29 COVID-19 covid-19 JJ cord-222193-0b4o0ccp 125 30 outbreak outbreak NN cord-222193-0b4o0ccp 125 31 in in IN cord-222193-0b4o0ccp 125 32 29 29 CD cord-222193-0b4o0ccp 125 33 provinces province NNS cord-222193-0b4o0ccp 125 34 in in IN cord-222193-0b4o0ccp 125 35 China China NNP cord-222193-0b4o0ccp 125 36 and and CC cord-222193-0b4o0ccp 125 37 in in IN cord-222193-0b4o0ccp 125 38 the the DT cord-222193-0b4o0ccp 125 39 rest rest NN cord-222193-0b4o0ccp 125 40 of of IN cord-222193-0b4o0ccp 125 41 the the DT cord-222193-0b4o0ccp 125 42 world world NN cord-222193-0b4o0ccp 126 1 Ke Ke NNP cord-222193-0b4o0ccp 126 2 Wu Wu NNP cord-222193-0b4o0ccp 126 3 , , , cord-222193-0b4o0ccp 126 4 Didier Didier NNP cord-222193-0b4o0ccp 126 5 Darcet Darcet NNP cord-222193-0b4o0ccp 126 6 Epidemic Epidemic NNP cord-222193-0b4o0ccp 126 7 processes process NNS cord-222193-0b4o0ccp 126 8 in in IN cord-222193-0b4o0ccp 126 9 complex complex JJ cord-222193-0b4o0ccp 126 10 networks network NNS cord-222193-0b4o0ccp 126 11 Epidemics epidemic NNS cord-222193-0b4o0ccp 126 12 with with IN cord-222193-0b4o0ccp 126 13 containment containment NN cord-222193-0b4o0ccp 126 14 measures measure NNS