id sid tid token lemma pos cord-284810-fs5rx07q 1 1 key key JJ cord-284810-fs5rx07q 1 2 : : : cord-284810-fs5rx07q 1 3 cord-284810-fs5rx07q cord-284810-fs5rx07q ADD cord-284810-fs5rx07q 1 4 authors author NNS cord-284810-fs5rx07q 1 5 : : : cord-284810-fs5rx07q 1 6 Blasius Blasius NNP cord-284810-fs5rx07q 1 7 , , , cord-284810-fs5rx07q 1 8 Bernd Bernd NNP cord-284810-fs5rx07q 1 9 title title NN cord-284810-fs5rx07q 1 10 : : : cord-284810-fs5rx07q 1 11 Power power NN cord-284810-fs5rx07q 1 12 - - HYPH cord-284810-fs5rx07q 1 13 law law NN cord-284810-fs5rx07q 1 14 distribution distribution NN cord-284810-fs5rx07q 1 15 in in IN cord-284810-fs5rx07q 1 16 the the DT cord-284810-fs5rx07q 1 17 number number NN cord-284810-fs5rx07q 1 18 of of IN cord-284810-fs5rx07q 1 19 confirmed confirm VBN cord-284810-fs5rx07q 1 20 COVID-19 covid-19 CD cord-284810-fs5rx07q 1 21 cases case NNS cord-284810-fs5rx07q 1 22 date date NN cord-284810-fs5rx07q 1 23 : : : cord-284810-fs5rx07q 1 24 2020 2020 CD cord-284810-fs5rx07q 1 25 - - HYPH cord-284810-fs5rx07q 1 26 09 09 CD cord-284810-fs5rx07q 1 27 - - SYM cord-284810-fs5rx07q 1 28 17 17 CD cord-284810-fs5rx07q 1 29 journal journal NN cord-284810-fs5rx07q 1 30 : : : cord-284810-fs5rx07q 1 31 Chaos chaos NN cord-284810-fs5rx07q 1 32 DOI DOI NNP cord-284810-fs5rx07q 1 33 : : : cord-284810-fs5rx07q 1 34 10.1063/5.0013031 10.1063/5.0013031 CD cord-284810-fs5rx07q 1 35 sha sha NNP cord-284810-fs5rx07q 1 36 : : : cord-284810-fs5rx07q 1 37 a4680f7f4b03941d0410881b58e724cebfad6356 a4680f7f4b03941d0410881b58e724cebfad6356 ADD cord-284810-fs5rx07q 1 38 doc_id doc_id CD cord-284810-fs5rx07q 1 39 : : : cord-284810-fs5rx07q 1 40 284810 284810 CD cord-284810-fs5rx07q 1 41 cord_uid cord_uid NNS cord-284810-fs5rx07q 1 42 : : : cord-284810-fs5rx07q 2 1 fs5rx07q fs5rx07q NNS cord-284810-fs5rx07q 3 1 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 3 2 is be VBZ cord-284810-fs5rx07q 3 3 an an DT cord-284810-fs5rx07q 3 4 emerging emerge VBG cord-284810-fs5rx07q 3 5 respiratory respiratory JJ cord-284810-fs5rx07q 3 6 infectious infectious JJ cord-284810-fs5rx07q 3 7 disease disease NN cord-284810-fs5rx07q 3 8 caused cause VBN cord-284810-fs5rx07q 3 9 by by IN cord-284810-fs5rx07q 3 10 the the DT cord-284810-fs5rx07q 3 11 coronavirus coronavirus NN cord-284810-fs5rx07q 3 12 SARS SARS NNP cord-284810-fs5rx07q 3 13 - - HYPH cord-284810-fs5rx07q 3 14 CoV-2 CoV-2 NNP cord-284810-fs5rx07q 3 15 . . . cord-284810-fs5rx07q 4 1 It -PRON- PRP cord-284810-fs5rx07q 4 2 was be VBD cord-284810-fs5rx07q 4 3 first first RB cord-284810-fs5rx07q 4 4 reported report VBN cord-284810-fs5rx07q 4 5 on on RB cord-284810-fs5rx07q 4 6 in in IN cord-284810-fs5rx07q 4 7 early early JJ cord-284810-fs5rx07q 4 8 December December NNP cord-284810-fs5rx07q 4 9 2019 2019 CD cord-284810-fs5rx07q 4 10 in in IN cord-284810-fs5rx07q 4 11 Wuhan Wuhan NNP cord-284810-fs5rx07q 4 12 , , , cord-284810-fs5rx07q 4 13 China China NNP cord-284810-fs5rx07q 4 14 and and CC cord-284810-fs5rx07q 4 15 within within IN cord-284810-fs5rx07q 4 16 three three CD cord-284810-fs5rx07q 4 17 months month NNS cord-284810-fs5rx07q 4 18 spread spread VBN cord-284810-fs5rx07q 4 19 as as IN cord-284810-fs5rx07q 4 20 a a DT cord-284810-fs5rx07q 4 21 pandemic pandemic NN cord-284810-fs5rx07q 4 22 around around IN cord-284810-fs5rx07q 4 23 the the DT cord-284810-fs5rx07q 4 24 whole whole JJ cord-284810-fs5rx07q 4 25 globe globe NN cord-284810-fs5rx07q 4 26 . . . cord-284810-fs5rx07q 5 1 Here here RB cord-284810-fs5rx07q 5 2 , , , cord-284810-fs5rx07q 5 3 we -PRON- PRP cord-284810-fs5rx07q 5 4 study study VBP cord-284810-fs5rx07q 5 5 macro macro JJ cord-284810-fs5rx07q 5 6 - - HYPH cord-284810-fs5rx07q 5 7 epidemiological epidemiological JJ cord-284810-fs5rx07q 5 8 patterns pattern NNS cord-284810-fs5rx07q 5 9 along along IN cord-284810-fs5rx07q 5 10 the the DT cord-284810-fs5rx07q 5 11 time time NN cord-284810-fs5rx07q 5 12 course course NN cord-284810-fs5rx07q 5 13 of of IN cord-284810-fs5rx07q 5 14 the the DT cord-284810-fs5rx07q 5 15 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 5 16 pandemic pandemic NN cord-284810-fs5rx07q 5 17 . . . cord-284810-fs5rx07q 6 1 We -PRON- PRP cord-284810-fs5rx07q 6 2 compute compute VBP cord-284810-fs5rx07q 6 3 the the DT cord-284810-fs5rx07q 6 4 distribution distribution NN cord-284810-fs5rx07q 6 5 of of IN cord-284810-fs5rx07q 6 6 confirmed confirm VBN cord-284810-fs5rx07q 6 7 COVID-19 covid-19 CD cord-284810-fs5rx07q 6 8 cases case NNS cord-284810-fs5rx07q 6 9 and and CC cord-284810-fs5rx07q 6 10 deaths death NNS cord-284810-fs5rx07q 6 11 for for IN cord-284810-fs5rx07q 6 12 countries country NNS cord-284810-fs5rx07q 6 13 worldwide worldwide RB cord-284810-fs5rx07q 6 14 and and CC cord-284810-fs5rx07q 6 15 for for IN cord-284810-fs5rx07q 6 16 counties county NNS cord-284810-fs5rx07q 6 17 in in IN cord-284810-fs5rx07q 6 18 the the DT cord-284810-fs5rx07q 6 19 US US NNP cord-284810-fs5rx07q 6 20 and and CC cord-284810-fs5rx07q 6 21 show show VBP cord-284810-fs5rx07q 6 22 that that IN cord-284810-fs5rx07q 6 23 both both DT cord-284810-fs5rx07q 6 24 distributions distribution NNS cord-284810-fs5rx07q 6 25 follow follow VBP cord-284810-fs5rx07q 6 26 a a DT cord-284810-fs5rx07q 6 27 truncated truncated JJ cord-284810-fs5rx07q 6 28 power power NN cord-284810-fs5rx07q 6 29 - - HYPH cord-284810-fs5rx07q 6 30 law law NN cord-284810-fs5rx07q 6 31 over over IN cord-284810-fs5rx07q 6 32 five five CD cord-284810-fs5rx07q 6 33 orders order NNS cord-284810-fs5rx07q 6 34 of of IN cord-284810-fs5rx07q 6 35 magnitude magnitude NN cord-284810-fs5rx07q 6 36 . . . cord-284810-fs5rx07q 7 1 We -PRON- PRP cord-284810-fs5rx07q 7 2 are be VBP cord-284810-fs5rx07q 7 3 able able JJ cord-284810-fs5rx07q 7 4 to to TO cord-284810-fs5rx07q 7 5 explain explain VB cord-284810-fs5rx07q 7 6 the the DT cord-284810-fs5rx07q 7 7 origin origin NN cord-284810-fs5rx07q 7 8 of of IN cord-284810-fs5rx07q 7 9 this this DT cord-284810-fs5rx07q 7 10 scaling scale VBG cord-284810-fs5rx07q 7 11 behavior behavior NN cord-284810-fs5rx07q 7 12 as as IN cord-284810-fs5rx07q 7 13 a a DT cord-284810-fs5rx07q 7 14 dual dual JJ cord-284810-fs5rx07q 7 15 - - HYPH cord-284810-fs5rx07q 7 16 scale scale NN cord-284810-fs5rx07q 7 17 process process NN cord-284810-fs5rx07q 7 18 : : : cord-284810-fs5rx07q 7 19 the the DT cord-284810-fs5rx07q 7 20 large large JJ cord-284810-fs5rx07q 7 21 - - HYPH cord-284810-fs5rx07q 7 22 scale scale NN cord-284810-fs5rx07q 7 23 spread spread NN cord-284810-fs5rx07q 7 24 of of IN cord-284810-fs5rx07q 7 25 the the DT cord-284810-fs5rx07q 7 26 virus virus NN cord-284810-fs5rx07q 7 27 between between IN cord-284810-fs5rx07q 7 28 countries country NNS cord-284810-fs5rx07q 7 29 and and CC cord-284810-fs5rx07q 7 30 the the DT cord-284810-fs5rx07q 7 31 small small JJ cord-284810-fs5rx07q 7 32 - - HYPH cord-284810-fs5rx07q 7 33 scale scale NN cord-284810-fs5rx07q 7 34 accumulation accumulation NN cord-284810-fs5rx07q 7 35 of of IN cord-284810-fs5rx07q 7 36 case case NN cord-284810-fs5rx07q 7 37 numbers number NNS cord-284810-fs5rx07q 7 38 within within IN cord-284810-fs5rx07q 7 39 each each DT cord-284810-fs5rx07q 7 40 country country NN cord-284810-fs5rx07q 7 41 . . . cord-284810-fs5rx07q 8 1 Assuming assume VBG cord-284810-fs5rx07q 8 2 exponential exponential JJ cord-284810-fs5rx07q 8 3 growth growth NN cord-284810-fs5rx07q 8 4 on on IN cord-284810-fs5rx07q 8 5 both both DT cord-284810-fs5rx07q 8 6 scales scale NNS cord-284810-fs5rx07q 8 7 , , , cord-284810-fs5rx07q 8 8 the the DT cord-284810-fs5rx07q 8 9 critical critical JJ cord-284810-fs5rx07q 8 10 exponent exponent NN cord-284810-fs5rx07q 8 11 of of IN cord-284810-fs5rx07q 8 12 the the DT cord-284810-fs5rx07q 8 13 power power NN cord-284810-fs5rx07q 8 14 - - HYPH cord-284810-fs5rx07q 8 15 law law NN cord-284810-fs5rx07q 8 16 is be VBZ cord-284810-fs5rx07q 8 17 determined determine VBN cord-284810-fs5rx07q 8 18 by by IN cord-284810-fs5rx07q 8 19 the the DT cord-284810-fs5rx07q 8 20 ratio ratio NN cord-284810-fs5rx07q 8 21 of of IN cord-284810-fs5rx07q 8 22 large large JJ cord-284810-fs5rx07q 8 23 - - HYPH cord-284810-fs5rx07q 8 24 scale scale NN cord-284810-fs5rx07q 8 25 to to IN cord-284810-fs5rx07q 8 26 small small JJ cord-284810-fs5rx07q 8 27 - - HYPH cord-284810-fs5rx07q 8 28 scale scale NN cord-284810-fs5rx07q 8 29 growth growth NN cord-284810-fs5rx07q 8 30 rates rate NNS cord-284810-fs5rx07q 8 31 . . . cord-284810-fs5rx07q 9 1 We -PRON- PRP cord-284810-fs5rx07q 9 2 confirm confirm VBP cord-284810-fs5rx07q 9 3 this this DT cord-284810-fs5rx07q 9 4 theory theory NN cord-284810-fs5rx07q 9 5 in in IN cord-284810-fs5rx07q 9 6 numerical numerical JJ cord-284810-fs5rx07q 9 7 simulations simulation NNS cord-284810-fs5rx07q 9 8 in in IN cord-284810-fs5rx07q 9 9 a a DT cord-284810-fs5rx07q 9 10 simple simple JJ cord-284810-fs5rx07q 9 11 meta meta JJ cord-284810-fs5rx07q 9 12 - - HYPH cord-284810-fs5rx07q 9 13 population population NN cord-284810-fs5rx07q 9 14 model model NN cord-284810-fs5rx07q 9 15 , , , cord-284810-fs5rx07q 9 16 describing describe VBG cord-284810-fs5rx07q 9 17 the the DT cord-284810-fs5rx07q 9 18 epidemic epidemic NN cord-284810-fs5rx07q 9 19 spread spread VBN cord-284810-fs5rx07q 9 20 in in IN cord-284810-fs5rx07q 9 21 a a DT cord-284810-fs5rx07q 9 22 network network NN cord-284810-fs5rx07q 9 23 of of IN cord-284810-fs5rx07q 9 24 interconnected interconnected JJ cord-284810-fs5rx07q 9 25 countries country NNS cord-284810-fs5rx07q 9 26 . . . cord-284810-fs5rx07q 10 1 Our -PRON- PRP$ cord-284810-fs5rx07q 10 2 theory theory NN cord-284810-fs5rx07q 10 3 gives give VBZ cord-284810-fs5rx07q 10 4 a a DT cord-284810-fs5rx07q 10 5 mechanistic mechanistic JJ cord-284810-fs5rx07q 10 6 explanation explanation NN cord-284810-fs5rx07q 10 7 why why WRB cord-284810-fs5rx07q 10 8 most most JJS cord-284810-fs5rx07q 10 9 COVID-19 covid-19 CD cord-284810-fs5rx07q 10 10 cases case NNS cord-284810-fs5rx07q 10 11 occurred occur VBD cord-284810-fs5rx07q 10 12 within within IN cord-284810-fs5rx07q 10 13 a a DT cord-284810-fs5rx07q 10 14 few few JJ cord-284810-fs5rx07q 10 15 epicenters epicenter NNS cord-284810-fs5rx07q 10 16 , , , cord-284810-fs5rx07q 10 17 at at IN cord-284810-fs5rx07q 10 18 least least JJS cord-284810-fs5rx07q 10 19 in in IN cord-284810-fs5rx07q 10 20 the the DT cord-284810-fs5rx07q 10 21 initial initial JJ cord-284810-fs5rx07q 10 22 phase phase NN cord-284810-fs5rx07q 10 23 of of IN cord-284810-fs5rx07q 10 24 the the DT cord-284810-fs5rx07q 10 25 outbreak outbreak NN cord-284810-fs5rx07q 10 26 . . . cord-284810-fs5rx07q 11 1 By by IN cord-284810-fs5rx07q 11 2 combining combine VBG cord-284810-fs5rx07q 11 3 real real JJ cord-284810-fs5rx07q 11 4 world world NN cord-284810-fs5rx07q 11 5 data datum NNS cord-284810-fs5rx07q 11 6 , , , cord-284810-fs5rx07q 11 7 modeling modeling NN cord-284810-fs5rx07q 11 8 , , , cord-284810-fs5rx07q 11 9 and and CC cord-284810-fs5rx07q 11 10 numerical numerical JJ cord-284810-fs5rx07q 11 11 simulations simulation NNS cord-284810-fs5rx07q 11 12 , , , cord-284810-fs5rx07q 11 13 we -PRON- PRP cord-284810-fs5rx07q 11 14 make make VBP cord-284810-fs5rx07q 11 15 the the DT cord-284810-fs5rx07q 11 16 case case NN cord-284810-fs5rx07q 11 17 that that IN cord-284810-fs5rx07q 11 18 the the DT cord-284810-fs5rx07q 11 19 distribution distribution NN cord-284810-fs5rx07q 11 20 of of IN cord-284810-fs5rx07q 11 21 epidemic epidemic NN cord-284810-fs5rx07q 11 22 prevalence prevalence NN cord-284810-fs5rx07q 11 23 might may MD cord-284810-fs5rx07q 11 24 follow follow VB cord-284810-fs5rx07q 11 25 universal universal JJ cord-284810-fs5rx07q 11 26 rules rule NNS cord-284810-fs5rx07q 11 27 . . . cord-284810-fs5rx07q 12 1 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 12 2 is be VBZ cord-284810-fs5rx07q 12 3 an an DT cord-284810-fs5rx07q 12 4 emerging emerge VBG cord-284810-fs5rx07q 12 5 infectious infectious JJ cord-284810-fs5rx07q 12 6 disease disease NN cord-284810-fs5rx07q 12 7 caused cause VBN cord-284810-fs5rx07q 12 8 by by IN cord-284810-fs5rx07q 12 9 the the DT cord-284810-fs5rx07q 12 10 coronavirus coronavirus NN cord-284810-fs5rx07q 12 11 SARS SARS NNP cord-284810-fs5rx07q 12 12 - - HYPH cord-284810-fs5rx07q 12 13 CoV-2 CoV-2 NNP cord-284810-fs5rx07q 12 14 . . . cord-284810-fs5rx07q 13 1 It -PRON- PRP cord-284810-fs5rx07q 13 2 was be VBD cord-284810-fs5rx07q 13 3 first first RB cord-284810-fs5rx07q 13 4 reported report VBN cord-284810-fs5rx07q 13 5 on on IN cord-284810-fs5rx07q 13 6 in in IN cord-284810-fs5rx07q 13 7 Hubei Hubei NNP cord-284810-fs5rx07q 13 8 , , , cord-284810-fs5rx07q 13 9 mainland mainland NN cord-284810-fs5rx07q 13 10 China China NNP cord-284810-fs5rx07q 13 11 on on IN cord-284810-fs5rx07q 13 12 December December NNP cord-284810-fs5rx07q 13 13 31 31 CD cord-284810-fs5rx07q 13 14 , , , cord-284810-fs5rx07q 13 15 2019 2019 CD cord-284810-fs5rx07q 13 16 and and CC cord-284810-fs5rx07q 13 17 has have VBZ cord-284810-fs5rx07q 13 18 spread spread VBN cord-284810-fs5rx07q 13 19 well well RB cord-284810-fs5rx07q 13 20 outside outside IN cord-284810-fs5rx07q 13 21 China China NNP cord-284810-fs5rx07q 13 22 in in IN cord-284810-fs5rx07q 13 23 a a DT cord-284810-fs5rx07q 13 24 matter matter NN cord-284810-fs5rx07q 13 25 of of IN cord-284810-fs5rx07q 13 26 a a DT cord-284810-fs5rx07q 13 27 few few JJ cord-284810-fs5rx07q 13 28 weeks week NNS cord-284810-fs5rx07q 13 29 , , , cord-284810-fs5rx07q 13 30 reaching reach VBG cord-284810-fs5rx07q 13 31 countries country NNS cord-284810-fs5rx07q 13 32 in in IN cord-284810-fs5rx07q 13 33 all all DT cord-284810-fs5rx07q 13 34 parts part NNS cord-284810-fs5rx07q 13 35 of of IN cord-284810-fs5rx07q 13 36 the the DT cord-284810-fs5rx07q 13 37 globe globe NN cord-284810-fs5rx07q 13 38 within within IN cord-284810-fs5rx07q 13 39 a a DT cord-284810-fs5rx07q 13 40 time time NN cord-284810-fs5rx07q 13 41 span span NN cord-284810-fs5rx07q 13 42 of of IN cord-284810-fs5rx07q 13 43 three three CD cord-284810-fs5rx07q 13 44 month month NN cord-284810-fs5rx07q 13 45 . . . cord-284810-fs5rx07q 14 1 As as IN cord-284810-fs5rx07q 14 2 of of IN cord-284810-fs5rx07q 14 3 29 29 CD cord-284810-fs5rx07q 14 4 March March NNP cord-284810-fs5rx07q 14 5 2020 2020 CD cord-284810-fs5rx07q 14 6 , , , cord-284810-fs5rx07q 14 7 the the DT cord-284810-fs5rx07q 14 8 disease disease NN cord-284810-fs5rx07q 14 9 has have VBZ cord-284810-fs5rx07q 14 10 arrived arrive VBN cord-284810-fs5rx07q 14 11 in in IN cord-284810-fs5rx07q 14 12 177 177 CD cord-284810-fs5rx07q 14 13 countries country NNS cord-284810-fs5rx07q 14 14 , , , cord-284810-fs5rx07q 14 15 with with IN cord-284810-fs5rx07q 14 16 more more JJR cord-284810-fs5rx07q 14 17 than than IN cord-284810-fs5rx07q 14 18 700 700 CD cord-284810-fs5rx07q 14 19 000 000 CD cord-284810-fs5rx07q 14 20 confirmed confirm VBN cord-284810-fs5rx07q 14 21 cases case NNS cord-284810-fs5rx07q 14 22 and and CC cord-284810-fs5rx07q 14 23 30 30 CD cord-284810-fs5rx07q 14 24 000 000 CD cord-284810-fs5rx07q 14 25 deaths death NNS cord-284810-fs5rx07q 14 26 worldwide worldwide RB cord-284810-fs5rx07q 14 27 . . . cord-284810-fs5rx07q 15 1 42 42 CD cord-284810-fs5rx07q 16 1 Despite despite IN cord-284810-fs5rx07q 16 2 the the DT cord-284810-fs5rx07q 16 3 drastic drastic JJ cord-284810-fs5rx07q 16 4 , , , cord-284810-fs5rx07q 16 5 large large JJ cord-284810-fs5rx07q 16 6 - - HYPH cord-284810-fs5rx07q 16 7 scale scale NN cord-284810-fs5rx07q 16 8 containment containment NN cord-284810-fs5rx07q 16 9 measures measure NNS cord-284810-fs5rx07q 16 10 implemented implement VBN cord-284810-fs5rx07q 16 11 in in IN cord-284810-fs5rx07q 16 12 most most JJS cord-284810-fs5rx07q 16 13 countries country NNS cord-284810-fs5rx07q 16 14 , , , cord-284810-fs5rx07q 16 15 Chaos Chaos NNP cord-284810-fs5rx07q 16 16 ARTICLE article NN cord-284810-fs5rx07q 16 17 scitation.org/journal/cha scitation.org/journal/cha NFP cord-284810-fs5rx07q 16 18 these these DT cord-284810-fs5rx07q 16 19 numbers number NNS cord-284810-fs5rx07q 16 20 are be VBP cord-284810-fs5rx07q 16 21 rapidly rapidly RB cord-284810-fs5rx07q 16 22 growing grow VBG cord-284810-fs5rx07q 16 23 every every DT cord-284810-fs5rx07q 16 24 day day NN cord-284810-fs5rx07q 16 25 - - HYPH cord-284810-fs5rx07q 16 26 posing pose VBG cord-284810-fs5rx07q 16 27 an an DT cord-284810-fs5rx07q 16 28 unprecedented unprecedented JJ cord-284810-fs5rx07q 16 29 threat threat NN cord-284810-fs5rx07q 16 30 to to IN cord-284810-fs5rx07q 16 31 the the DT cord-284810-fs5rx07q 16 32 global global JJ cord-284810-fs5rx07q 16 33 health health NN cord-284810-fs5rx07q 16 34 and and CC cord-284810-fs5rx07q 16 35 economy economy NN cord-284810-fs5rx07q 16 36 of of IN cord-284810-fs5rx07q 16 37 interconnected interconnected JJ cord-284810-fs5rx07q 16 38 human human JJ cord-284810-fs5rx07q 16 39 societies society NNS cord-284810-fs5rx07q 16 40 . . . cord-284810-fs5rx07q 17 1 One one CD cord-284810-fs5rx07q 17 2 of of IN cord-284810-fs5rx07q 17 3 the the DT cord-284810-fs5rx07q 17 4 most most RBS cord-284810-fs5rx07q 17 5 powerful powerful JJ cord-284810-fs5rx07q 17 6 tools tool NNS cord-284810-fs5rx07q 17 7 to to TO cord-284810-fs5rx07q 17 8 understand understand VB cord-284810-fs5rx07q 17 9 the the DT cord-284810-fs5rx07q 17 10 laws law NNS cord-284810-fs5rx07q 17 11 of of IN cord-284810-fs5rx07q 17 12 epidemic epidemic NN cord-284810-fs5rx07q 17 13 growth growth NN cord-284810-fs5rx07q 17 14 is be VBZ cord-284810-fs5rx07q 17 15 mathematical mathematical JJ cord-284810-fs5rx07q 17 16 modeling modeling NN cord-284810-fs5rx07q 17 17 , , , cord-284810-fs5rx07q 17 18 going go VBG cord-284810-fs5rx07q 17 19 back back RB cord-284810-fs5rx07q 17 20 to to IN cord-284810-fs5rx07q 17 21 Bernoulli Bernoulli NNP cord-284810-fs5rx07q 17 22 's 's POS cord-284810-fs5rx07q 17 23 work work NN cord-284810-fs5rx07q 17 24 5 5 CD cord-284810-fs5rx07q 17 25 on on IN cord-284810-fs5rx07q 17 26 the the DT cord-284810-fs5rx07q 17 27 spread spread NN cord-284810-fs5rx07q 17 28 of of IN cord-284810-fs5rx07q 17 29 smallpox smallpox NN cord-284810-fs5rx07q 17 30 in in IN cord-284810-fs5rx07q 17 31 1760 1760 CD cord-284810-fs5rx07q 17 32 . . . cord-284810-fs5rx07q 18 1 Epidemiological epidemiological JJ cord-284810-fs5rx07q 18 2 models model NNS cord-284810-fs5rx07q 18 3 can can MD cord-284810-fs5rx07q 18 4 be be VB cord-284810-fs5rx07q 18 5 roughly roughly RB cord-284810-fs5rx07q 18 6 divided divide VBN cord-284810-fs5rx07q 18 7 into into IN cord-284810-fs5rx07q 18 8 two two CD cord-284810-fs5rx07q 18 9 classes class NNS cord-284810-fs5rx07q 18 10 . . . cord-284810-fs5rx07q 19 1 The the DT cord-284810-fs5rx07q 19 2 first first JJ cord-284810-fs5rx07q 19 3 class class NN cord-284810-fs5rx07q 19 4 of of IN cord-284810-fs5rx07q 19 5 models model NNS cord-284810-fs5rx07q 19 6 is be VBZ cord-284810-fs5rx07q 19 7 focused focus VBN cord-284810-fs5rx07q 19 8 on on IN cord-284810-fs5rx07q 19 9 describing describe VBG cord-284810-fs5rx07q 19 10 the the DT cord-284810-fs5rx07q 19 11 temporal temporal JJ cord-284810-fs5rx07q 19 12 development development NN cord-284810-fs5rx07q 19 13 of of IN cord-284810-fs5rx07q 19 14 the the DT cord-284810-fs5rx07q 19 15 epidemic epidemic NN cord-284810-fs5rx07q 19 16 within within IN cord-284810-fs5rx07q 19 17 a a DT cord-284810-fs5rx07q 19 18 localized localized JJ cord-284810-fs5rx07q 19 19 region region NN cord-284810-fs5rx07q 19 20 or or CC cord-284810-fs5rx07q 19 21 country country NN cord-284810-fs5rx07q 19 22 . . . cord-284810-fs5rx07q 20 1 These these DT cord-284810-fs5rx07q 20 2 models model NNS cord-284810-fs5rx07q 20 3 are be VBP cord-284810-fs5rx07q 20 4 often often RB cord-284810-fs5rx07q 20 5 variants variant NNS cord-284810-fs5rx07q 20 6 of of IN cord-284810-fs5rx07q 20 7 the the DT cord-284810-fs5rx07q 20 8 well well RB cord-284810-fs5rx07q 20 9 - - HYPH cord-284810-fs5rx07q 20 10 known know VBN cord-284810-fs5rx07q 20 11 susceptible susceptible JJ cord-284810-fs5rx07q 20 12 - - HYPH cord-284810-fs5rx07q 20 13 infected infected JJ cord-284810-fs5rx07q 20 14 - - HYPH cord-284810-fs5rx07q 20 15 recovered recovered JJ cord-284810-fs5rx07q 20 16 ( ( -LRB- cord-284810-fs5rx07q 20 17 SIR SIR NNP cord-284810-fs5rx07q 20 18 ) ) -RRB- cord-284810-fs5rx07q 20 19 model model NN cord-284810-fs5rx07q 20 20 22 22 CD cord-284810-fs5rx07q 20 21 , , , cord-284810-fs5rx07q 20 22 23 23 CD cord-284810-fs5rx07q 20 23 and and CC cord-284810-fs5rx07q 20 24 have have VBP cord-284810-fs5rx07q 20 25 recently recently RB cord-284810-fs5rx07q 20 26 been be VBN cord-284810-fs5rx07q 20 27 adapted adapt VBN cord-284810-fs5rx07q 20 28 to to IN cord-284810-fs5rx07q 20 29 the the DT cord-284810-fs5rx07q 20 30 situation situation NN cord-284810-fs5rx07q 20 31 of of IN cord-284810-fs5rx07q 20 32 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 20 33 , , , cord-284810-fs5rx07q 20 34 taking take VBG cord-284810-fs5rx07q 20 35 into into IN cord-284810-fs5rx07q 20 36 account account NN cord-284810-fs5rx07q 20 37 non non JJ cord-284810-fs5rx07q 20 38 - - JJ cord-284810-fs5rx07q 20 39 pharmaceutical pharmaceutical JJ cord-284810-fs5rx07q 20 40 interventions intervention NNS cord-284810-fs5rx07q 20 41 ( ( -LRB- cord-284810-fs5rx07q 20 42 e.g. e.g. RB cord-284810-fs5rx07q 20 43 , , , cord-284810-fs5rx07q 20 44 quarantine quarantine NN cord-284810-fs5rx07q 20 45 , , , cord-284810-fs5rx07q 20 46 hospitalization hospitalization NN cord-284810-fs5rx07q 20 47 , , , cord-284810-fs5rx07q 20 48 and and CC cord-284810-fs5rx07q 20 49 containment containment NN cord-284810-fs5rx07q 20 50 policies policy NNS cord-284810-fs5rx07q 20 51 ) ) -RRB- cord-284810-fs5rx07q 20 52 and and CC cord-284810-fs5rx07q 20 53 allowing allow VBG cord-284810-fs5rx07q 20 54 first first JJ cord-284810-fs5rx07q 20 55 predictions prediction NNS cord-284810-fs5rx07q 20 56 of of IN cord-284810-fs5rx07q 20 57 healthcare healthcare NN cord-284810-fs5rx07q 20 58 demand demand NN cord-284810-fs5rx07q 20 59 . . . cord-284810-fs5rx07q 21 1 15 15 CD cord-284810-fs5rx07q 21 2 , , , cord-284810-fs5rx07q 21 3 25 25 CD cord-284810-fs5rx07q 21 4 , , , cord-284810-fs5rx07q 21 5 26 26 CD cord-284810-fs5rx07q 21 6 , , , cord-284810-fs5rx07q 21 7 40 40 CD cord-284810-fs5rx07q 22 1 The the DT cord-284810-fs5rx07q 22 2 second second JJ cord-284810-fs5rx07q 22 3 class class NN cord-284810-fs5rx07q 22 4 of of IN cord-284810-fs5rx07q 22 5 models model NNS cord-284810-fs5rx07q 22 6 is be VBZ cord-284810-fs5rx07q 22 7 concerned concern VBN cord-284810-fs5rx07q 22 8 with with IN cord-284810-fs5rx07q 22 9 the the DT cord-284810-fs5rx07q 22 10 geographic geographic JJ cord-284810-fs5rx07q 22 11 spread spread NN cord-284810-fs5rx07q 22 12 of of IN cord-284810-fs5rx07q 22 13 the the DT cord-284810-fs5rx07q 22 14 epidemic epidemic NN cord-284810-fs5rx07q 22 15 around around IN cord-284810-fs5rx07q 22 16 the the DT cord-284810-fs5rx07q 22 17 globe globe NN cord-284810-fs5rx07q 22 18 . . . cord-284810-fs5rx07q 23 1 For for IN cord-284810-fs5rx07q 23 2 these these DT cord-284810-fs5rx07q 23 3 aims aim NNS cord-284810-fs5rx07q 23 4 , , , cord-284810-fs5rx07q 23 5 spatially spatially RB cord-284810-fs5rx07q 23 6 explicit explicit JJ cord-284810-fs5rx07q 23 7 models model NNS cord-284810-fs5rx07q 23 8 have have VBP cord-284810-fs5rx07q 23 9 been be VBN cord-284810-fs5rx07q 23 10 developed develop VBN cord-284810-fs5rx07q 23 11 that that DT cord-284810-fs5rx07q 23 12 leverage leverage NN cord-284810-fs5rx07q 23 13 information information NN cord-284810-fs5rx07q 23 14 on on IN cord-284810-fs5rx07q 23 15 the the DT cord-284810-fs5rx07q 23 16 topology topology NN cord-284810-fs5rx07q 23 17 of of IN cord-284810-fs5rx07q 23 18 transport transport NN cord-284810-fs5rx07q 23 19 networks network NNS cord-284810-fs5rx07q 23 20 . . . cord-284810-fs5rx07q 24 1 For for IN cord-284810-fs5rx07q 24 2 example example NN cord-284810-fs5rx07q 24 3 , , , cord-284810-fs5rx07q 24 4 the the DT cord-284810-fs5rx07q 24 5 global global JJ cord-284810-fs5rx07q 24 6 network network NN cord-284810-fs5rx07q 24 7 of of IN cord-284810-fs5rx07q 24 8 cargo cargo NN cord-284810-fs5rx07q 24 9 ship ship NN cord-284810-fs5rx07q 24 10 movements movement NNS cord-284810-fs5rx07q 24 11 21 21 CD cord-284810-fs5rx07q 24 12 was be VBD cord-284810-fs5rx07q 24 13 used use VBN cord-284810-fs5rx07q 24 14 to to TO cord-284810-fs5rx07q 24 15 model model VB cord-284810-fs5rx07q 24 16 the the DT cord-284810-fs5rx07q 24 17 dispersal dispersal NN cord-284810-fs5rx07q 24 18 of of IN cord-284810-fs5rx07q 24 19 invasive invasive JJ cord-284810-fs5rx07q 24 20 species specie NNS cord-284810-fs5rx07q 24 21 . . . cord-284810-fs5rx07q 25 1 37 37 CD cord-284810-fs5rx07q 25 2 Similarly similarly RB cord-284810-fs5rx07q 25 3 , , , cord-284810-fs5rx07q 25 4 for for IN cord-284810-fs5rx07q 25 5 infectious infectious JJ cord-284810-fs5rx07q 25 6 diseases disease NNS cord-284810-fs5rx07q 25 7 , , , cord-284810-fs5rx07q 25 8 in in IN cord-284810-fs5rx07q 25 9 a a DT cord-284810-fs5rx07q 25 10 pioneering pioneering JJ cord-284810-fs5rx07q 25 11 study study NN cord-284810-fs5rx07q 25 12 , , , cord-284810-fs5rx07q 25 13 the the DT cord-284810-fs5rx07q 25 14 2003 2003 CD cord-284810-fs5rx07q 25 15 spread spread NN cord-284810-fs5rx07q 25 16 of of IN cord-284810-fs5rx07q 25 17 SARS SARS NNP cord-284810-fs5rx07q 25 18 in in IN cord-284810-fs5rx07q 25 19 the the DT cord-284810-fs5rx07q 25 20 global global JJ cord-284810-fs5rx07q 25 21 aviation aviation NN cord-284810-fs5rx07q 25 22 network network NN cord-284810-fs5rx07q 25 23 41 41 CD cord-284810-fs5rx07q 25 24 was be VBD cord-284810-fs5rx07q 25 25 modeled model VBN cord-284810-fs5rx07q 25 26 . . . cord-284810-fs5rx07q 26 1 19 19 CD cord-284810-fs5rx07q 27 1 Based base VBN cord-284810-fs5rx07q 27 2 on on IN cord-284810-fs5rx07q 27 3 these these DT cord-284810-fs5rx07q 27 4 approaches approach NNS cord-284810-fs5rx07q 27 5 , , , cord-284810-fs5rx07q 27 6 conceptual conceptual JJ cord-284810-fs5rx07q 27 7 frameworks framework NNS cord-284810-fs5rx07q 27 8 have have VBP cord-284810-fs5rx07q 27 9 been be VBN cord-284810-fs5rx07q 27 10 developed develop VBN cord-284810-fs5rx07q 27 11 to to TO cord-284810-fs5rx07q 27 12 estimate estimate VB cord-284810-fs5rx07q 27 13 epidemic epidemic JJ cord-284810-fs5rx07q 27 14 arrival arrival NN cord-284810-fs5rx07q 27 15 times time NNS cord-284810-fs5rx07q 27 16 as as IN cord-284810-fs5rx07q 27 17 effective effective JJ cord-284810-fs5rx07q 27 18 distances distance NNS cord-284810-fs5rx07q 27 19 . . . cord-284810-fs5rx07q 28 1 8 8 CD cord-284810-fs5rx07q 28 2 , , , cord-284810-fs5rx07q 28 3 20 20 CD cord-284810-fs5rx07q 28 4 At at IN cord-284810-fs5rx07q 28 5 the the DT cord-284810-fs5rx07q 28 6 same same JJ cord-284810-fs5rx07q 28 7 time time NN cord-284810-fs5rx07q 28 8 , , , cord-284810-fs5rx07q 28 9 these these DT cord-284810-fs5rx07q 28 10 models model NNS cord-284810-fs5rx07q 28 11 have have VBP cord-284810-fs5rx07q 28 12 been be VBN cord-284810-fs5rx07q 28 13 refined refine VBN cord-284810-fs5rx07q 28 14 to to IN cord-284810-fs5rx07q 28 15 highly highly RB cord-284810-fs5rx07q 28 16 detailed detailed JJ cord-284810-fs5rx07q 28 17 simulation simulation NN cord-284810-fs5rx07q 28 18 frameworks framework NNS cord-284810-fs5rx07q 28 19 for for IN cord-284810-fs5rx07q 28 20 predicting predict VBG cord-284810-fs5rx07q 28 21 the the DT cord-284810-fs5rx07q 28 22 spread spread NN cord-284810-fs5rx07q 28 23 of of IN cord-284810-fs5rx07q 28 24 disease disease NN cord-284810-fs5rx07q 28 25 and and CC cord-284810-fs5rx07q 28 26 are be VBP cord-284810-fs5rx07q 28 27 able able JJ cord-284810-fs5rx07q 28 28 to to TO cord-284810-fs5rx07q 28 29 include include VB cord-284810-fs5rx07q 28 30 factors factor NNS cord-284810-fs5rx07q 28 31 such such JJ cord-284810-fs5rx07q 28 32 as as IN cord-284810-fs5rx07q 28 33 vaccination vaccination NN cord-284810-fs5rx07q 28 34 , , , cord-284810-fs5rx07q 28 35 multiple multiple JJ cord-284810-fs5rx07q 28 36 susceptibility susceptibility NN cord-284810-fs5rx07q 28 37 classes class NNS cord-284810-fs5rx07q 28 38 , , , cord-284810-fs5rx07q 28 39 seasonal seasonal JJ cord-284810-fs5rx07q 28 40 forcing forcing NN cord-284810-fs5rx07q 28 41 , , , cord-284810-fs5rx07q 28 42 and and CC cord-284810-fs5rx07q 28 43 the the DT cord-284810-fs5rx07q 28 44 stochastic stochastic JJ cord-284810-fs5rx07q 28 45 movement movement NN cord-284810-fs5rx07q 28 46 of of IN cord-284810-fs5rx07q 28 47 individual individual JJ cord-284810-fs5rx07q 28 48 agents agent NNS cord-284810-fs5rx07q 28 49 . . . cord-284810-fs5rx07q 29 1 12 12 CD cord-284810-fs5rx07q 29 2 , , , cord-284810-fs5rx07q 29 3 43 43 CD cord-284810-fs5rx07q 29 4 Reacting react VBG cord-284810-fs5rx07q 29 5 rapidly rapidly RB cord-284810-fs5rx07q 29 6 to to IN cord-284810-fs5rx07q 29 7 the the DT cord-284810-fs5rx07q 29 8 emergent emergent JJ cord-284810-fs5rx07q 29 9 pandemic pandemic NN cord-284810-fs5rx07q 29 10 , , , cord-284810-fs5rx07q 29 11 spatial spatial JJ cord-284810-fs5rx07q 29 12 epidemiological epidemiological JJ cord-284810-fs5rx07q 29 13 models model NNS cord-284810-fs5rx07q 29 14 have have VBP cord-284810-fs5rx07q 29 15 been be VBN cord-284810-fs5rx07q 29 16 developed develop VBN cord-284810-fs5rx07q 29 17 to to TO cord-284810-fs5rx07q 29 18 describe describe VB cord-284810-fs5rx07q 29 19 and and CC cord-284810-fs5rx07q 29 20 anticipate anticipate VB cord-284810-fs5rx07q 29 21 the the DT cord-284810-fs5rx07q 29 22 spread spread NN cord-284810-fs5rx07q 29 23 of of IN cord-284810-fs5rx07q 29 24 COVID-19 covid-19 NN cord-284810-fs5rx07q 29 25 . . . cord-284810-fs5rx07q 30 1 2 2 CD cord-284810-fs5rx07q 30 2 , , , cord-284810-fs5rx07q 30 3 10 10 CD cord-284810-fs5rx07q 30 4 , , , cord-284810-fs5rx07q 30 5 16 16 CD cord-284810-fs5rx07q 30 6 , , , cord-284810-fs5rx07q 30 7 33 33 CD cord-284810-fs5rx07q 30 8 These these DT cord-284810-fs5rx07q 30 9 models model NNS cord-284810-fs5rx07q 30 10 allow allow VBP cord-284810-fs5rx07q 30 11 us -PRON- PRP cord-284810-fs5rx07q 30 12 to to TO cord-284810-fs5rx07q 30 13 predict predict VB cord-284810-fs5rx07q 30 14 the the DT cord-284810-fs5rx07q 30 15 incidence incidence NN cord-284810-fs5rx07q 30 16 of of IN cord-284810-fs5rx07q 30 17 the the DT cord-284810-fs5rx07q 30 18 epidemics epidemic NNS cord-284810-fs5rx07q 30 19 in in IN cord-284810-fs5rx07q 30 20 a a DT cord-284810-fs5rx07q 30 21 spatial spatial JJ cord-284810-fs5rx07q 30 22 population population NN cord-284810-fs5rx07q 30 23 through through IN cord-284810-fs5rx07q 30 24 time time NN cord-284810-fs5rx07q 30 25 , , , cord-284810-fs5rx07q 30 26 permitting permit VBG cord-284810-fs5rx07q 30 27 to to TO cord-284810-fs5rx07q 30 28 study study VB cord-284810-fs5rx07q 30 29 the the DT cord-284810-fs5rx07q 30 30 impact impact NN cord-284810-fs5rx07q 30 31 of of IN cord-284810-fs5rx07q 30 32 travel travel NN cord-284810-fs5rx07q 30 33 restrictions restriction NNS cord-284810-fs5rx07q 30 34 and and CC cord-284810-fs5rx07q 30 35 other other JJ cord-284810-fs5rx07q 30 36 control control NN cord-284810-fs5rx07q 30 37 measures measure NNS cord-284810-fs5rx07q 30 38 . . . cord-284810-fs5rx07q 31 1 Despite despite IN cord-284810-fs5rx07q 31 2 this this DT cord-284810-fs5rx07q 31 3 theoretical theoretical JJ cord-284810-fs5rx07q 31 4 progress progress NN cord-284810-fs5rx07q 31 5 , , , cord-284810-fs5rx07q 31 6 not not RB cord-284810-fs5rx07q 31 7 much much JJ cord-284810-fs5rx07q 31 8 is be VBZ cord-284810-fs5rx07q 31 9 known know VBN cord-284810-fs5rx07q 31 10 about about IN cord-284810-fs5rx07q 31 11 the the DT cord-284810-fs5rx07q 31 12 biogeography biogeography NN cord-284810-fs5rx07q 31 13 of of IN cord-284810-fs5rx07q 31 14 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 31 15 , , , cord-284810-fs5rx07q 31 16 neither neither CC cord-284810-fs5rx07q 31 17 from from IN cord-284810-fs5rx07q 31 18 empirical empirical JJ cord-284810-fs5rx07q 31 19 studies study NNS cord-284810-fs5rx07q 31 20 nor nor CC cord-284810-fs5rx07q 31 21 from from IN cord-284810-fs5rx07q 31 22 mathematical mathematical JJ cord-284810-fs5rx07q 31 23 models model NNS cord-284810-fs5rx07q 31 24 . . . cord-284810-fs5rx07q 32 1 This this DT cord-284810-fs5rx07q 32 2 is be VBZ cord-284810-fs5rx07q 32 3 astonishing astonishing JJ cord-284810-fs5rx07q 32 4 , , , cord-284810-fs5rx07q 32 5 as as IN cord-284810-fs5rx07q 32 6 one one CD cord-284810-fs5rx07q 32 7 prominent prominent JJ cord-284810-fs5rx07q 32 8 characteristic characteristic NN cord-284810-fs5rx07q 32 9 of of IN cord-284810-fs5rx07q 32 10 the the DT cord-284810-fs5rx07q 32 11 pandemic pandemic NN cord-284810-fs5rx07q 32 12 is be VBZ cord-284810-fs5rx07q 32 13 the the DT cord-284810-fs5rx07q 32 14 huge huge JJ cord-284810-fs5rx07q 32 15 variation variation NN cord-284810-fs5rx07q 32 16 in in IN cord-284810-fs5rx07q 32 17 the the DT cord-284810-fs5rx07q 32 18 number number NN cord-284810-fs5rx07q 32 19 of of IN cord-284810-fs5rx07q 32 20 cases case NNS cord-284810-fs5rx07q 32 21 that that WDT cord-284810-fs5rx07q 32 22 have have VBP cord-284810-fs5rx07q 32 23 been be VBN cord-284810-fs5rx07q 32 24 reported report VBN cord-284810-fs5rx07q 32 25 from from IN cord-284810-fs5rx07q 32 26 different different JJ cord-284810-fs5rx07q 32 27 countries country NNS cord-284810-fs5rx07q 32 28 of of IN cord-284810-fs5rx07q 32 29 the the DT cord-284810-fs5rx07q 32 30 world world NN cord-284810-fs5rx07q 32 31 . . . cord-284810-fs5rx07q 33 1 As as IN cord-284810-fs5rx07q 33 2 of of IN cord-284810-fs5rx07q 33 3 April April NNP cord-284810-fs5rx07q 33 4 2020 2020 CD cord-284810-fs5rx07q 33 5 , , , cord-284810-fs5rx07q 33 6 some some DT cord-284810-fs5rx07q 33 7 countries country NNS cord-284810-fs5rx07q 33 8 - - : cord-284810-fs5rx07q 33 9 the the DT cord-284810-fs5rx07q 33 10 epicenters epicenter NNS cord-284810-fs5rx07q 33 11 of of IN cord-284810-fs5rx07q 33 12 the the DT cord-284810-fs5rx07q 33 13 pandemic pandemic NN cord-284810-fs5rx07q 33 14 - - , cord-284810-fs5rx07q 33 15 were be VBD cord-284810-fs5rx07q 33 16 already already RB cord-284810-fs5rx07q 33 17 badly badly RB cord-284810-fs5rx07q 33 18 affected affect VBN cord-284810-fs5rx07q 33 19 by by IN cord-284810-fs5rx07q 33 20 the the DT cord-284810-fs5rx07q 33 21 pandemic pandemic NN cord-284810-fs5rx07q 33 22 , , , cord-284810-fs5rx07q 33 23 while while IN cord-284810-fs5rx07q 33 24 others other NNS cord-284810-fs5rx07q 33 25 at at IN cord-284810-fs5rx07q 33 26 the the DT cord-284810-fs5rx07q 33 27 same same JJ cord-284810-fs5rx07q 33 28 time time NN cord-284810-fs5rx07q 33 29 had have VBD cord-284810-fs5rx07q 33 30 just just RB cord-284810-fs5rx07q 33 31 confirmed confirm VBN cord-284810-fs5rx07q 33 32 the the DT cord-284810-fs5rx07q 33 33 first first JJ cord-284810-fs5rx07q 33 34 few few JJ cord-284810-fs5rx07q 33 35 cases case NNS cord-284810-fs5rx07q 33 36 . . . cord-284810-fs5rx07q 34 1 This this DT cord-284810-fs5rx07q 34 2 geographic geographic JJ cord-284810-fs5rx07q 34 3 variation variation NN cord-284810-fs5rx07q 34 4 in in IN cord-284810-fs5rx07q 34 5 COVID-19 covid-19 JJ cord-284810-fs5rx07q 34 6 prevalence prevalence NN cord-284810-fs5rx07q 34 7 might may MD cord-284810-fs5rx07q 34 8 be be VB cord-284810-fs5rx07q 34 9 explained explain VBN cord-284810-fs5rx07q 34 10 by by IN cord-284810-fs5rx07q 34 11 several several JJ cord-284810-fs5rx07q 34 12 arguments argument NNS cord-284810-fs5rx07q 34 13 : : : cord-284810-fs5rx07q 34 14 a a DT cord-284810-fs5rx07q 34 15 first first JJ cord-284810-fs5rx07q 34 16 obvious obvious JJ cord-284810-fs5rx07q 34 17 possibility possibility NN cord-284810-fs5rx07q 34 18 would would MD cord-284810-fs5rx07q 34 19 be be VB cord-284810-fs5rx07q 34 20 that that IN cord-284810-fs5rx07q 34 21 the the DT cord-284810-fs5rx07q 34 22 variation variation NN cord-284810-fs5rx07q 34 23 is be VBZ cord-284810-fs5rx07q 34 24 caused cause VBN cord-284810-fs5rx07q 34 25 by by IN cord-284810-fs5rx07q 34 26 the the DT cord-284810-fs5rx07q 34 27 idiosyncratic idiosyncratic JJ cord-284810-fs5rx07q 34 28 circumstances circumstance NNS cord-284810-fs5rx07q 34 29 of of IN cord-284810-fs5rx07q 34 30 the the DT cord-284810-fs5rx07q 34 31 individual individual JJ cord-284810-fs5rx07q 34 32 countries country NNS cord-284810-fs5rx07q 34 33 which which WDT cord-284810-fs5rx07q 34 34 differ differ VBP cord-284810-fs5rx07q 34 35 largely largely RB cord-284810-fs5rx07q 34 36 in in IN cord-284810-fs5rx07q 34 37 their -PRON- PRP$ cord-284810-fs5rx07q 34 38 geography geography NN cord-284810-fs5rx07q 34 39 and and CC cord-284810-fs5rx07q 34 40 population population NN cord-284810-fs5rx07q 34 41 size size NN cord-284810-fs5rx07q 34 42 , , , cord-284810-fs5rx07q 34 43 but but CC cord-284810-fs5rx07q 34 44 also also RB cord-284810-fs5rx07q 34 45 in in IN cord-284810-fs5rx07q 34 46 the the DT cord-284810-fs5rx07q 34 47 way way NN cord-284810-fs5rx07q 34 48 they -PRON- PRP cord-284810-fs5rx07q 34 49 are be VBP cord-284810-fs5rx07q 34 50 combatting combat VBG cord-284810-fs5rx07q 34 51 the the DT cord-284810-fs5rx07q 34 52 disease disease NN cord-284810-fs5rx07q 34 53 . . . cord-284810-fs5rx07q 35 1 Alternatively alternatively RB cord-284810-fs5rx07q 35 2 , , , cord-284810-fs5rx07q 35 3 parts part NNS cord-284810-fs5rx07q 35 4 of of IN cord-284810-fs5rx07q 35 5 the the DT cord-284810-fs5rx07q 35 6 variation variation NN cord-284810-fs5rx07q 35 7 could could MD cord-284810-fs5rx07q 35 8 simply simply RB cord-284810-fs5rx07q 35 9 be be VB cord-284810-fs5rx07q 35 10 due due JJ cord-284810-fs5rx07q 35 11 to to IN cord-284810-fs5rx07q 35 12 reporting reporting NN cord-284810-fs5rx07q 35 13 errors error NNS cord-284810-fs5rx07q 35 14 , , , cord-284810-fs5rx07q 35 15 reflecting reflect VBG cord-284810-fs5rx07q 35 16 disparate disparate JJ cord-284810-fs5rx07q 35 17 national national JJ cord-284810-fs5rx07q 35 18 testing testing NN cord-284810-fs5rx07q 35 19 regimes regime NNS cord-284810-fs5rx07q 35 20 , , , cord-284810-fs5rx07q 35 21 with with IN cord-284810-fs5rx07q 35 22 countries country NNS cord-284810-fs5rx07q 35 23 such such JJ cord-284810-fs5rx07q 35 24 as as IN cord-284810-fs5rx07q 35 25 China China NNP cord-284810-fs5rx07q 35 26 , , , cord-284810-fs5rx07q 35 27 Japan Japan NNP cord-284810-fs5rx07q 35 28 , , , cord-284810-fs5rx07q 35 29 South South NNP cord-284810-fs5rx07q 35 30 Korea Korea NNP cord-284810-fs5rx07q 35 31 , , , cord-284810-fs5rx07q 35 32 or or CC cord-284810-fs5rx07q 35 33 Germany Germany NNP cord-284810-fs5rx07q 35 34 having have VBG cord-284810-fs5rx07q 35 35 high high JJ cord-284810-fs5rx07q 35 36 testing testing NN cord-284810-fs5rx07q 35 37 rates rate NNS cord-284810-fs5rx07q 35 38 , , , cord-284810-fs5rx07q 35 39 in in IN cord-284810-fs5rx07q 35 40 contrast contrast NN cord-284810-fs5rx07q 35 41 to to IN cord-284810-fs5rx07q 35 42 other other JJ cord-284810-fs5rx07q 35 43 countries country NNS cord-284810-fs5rx07q 35 44 with with IN cord-284810-fs5rx07q 35 45 much much RB cord-284810-fs5rx07q 35 46 poorer poor JJR cord-284810-fs5rx07q 35 47 testing testing NN cord-284810-fs5rx07q 35 48 . . . cord-284810-fs5rx07q 36 1 Here here RB cord-284810-fs5rx07q 36 2 , , , cord-284810-fs5rx07q 36 3 we -PRON- PRP cord-284810-fs5rx07q 36 4 argue argue VBP cord-284810-fs5rx07q 36 5 , , , cord-284810-fs5rx07q 36 6 however however RB cord-284810-fs5rx07q 36 7 , , , cord-284810-fs5rx07q 36 8 that that IN cord-284810-fs5rx07q 36 9 a a DT cord-284810-fs5rx07q 36 10 dominant dominant JJ cord-284810-fs5rx07q 36 11 part part NN cord-284810-fs5rx07q 36 12 of of IN cord-284810-fs5rx07q 36 13 this this DT cord-284810-fs5rx07q 36 14 variation variation NN cord-284810-fs5rx07q 36 15 may may MD cord-284810-fs5rx07q 36 16 be be VB cord-284810-fs5rx07q 36 17 a a DT cord-284810-fs5rx07q 36 18 direct direct JJ cord-284810-fs5rx07q 36 19 consequence consequence NN cord-284810-fs5rx07q 36 20 of of IN cord-284810-fs5rx07q 36 21 the the DT cord-284810-fs5rx07q 36 22 dynamics dynamic NNS cord-284810-fs5rx07q 36 23 of of IN cord-284810-fs5rx07q 36 24 the the DT cord-284810-fs5rx07q 36 25 spreading spreading NN cord-284810-fs5rx07q 36 26 process process NN cord-284810-fs5rx07q 36 27 itself -PRON- PRP cord-284810-fs5rx07q 36 28 . . . cord-284810-fs5rx07q 37 1 Thereby thereby RB cord-284810-fs5rx07q 37 2 , , , cord-284810-fs5rx07q 37 3 the the DT cord-284810-fs5rx07q 37 4 epidemic epidemic NN cord-284810-fs5rx07q 37 5 prevalence prevalence NN cord-284810-fs5rx07q 37 6 in in IN cord-284810-fs5rx07q 37 7 a a DT cord-284810-fs5rx07q 37 8 country country NN cord-284810-fs5rx07q 37 9 should should MD cord-284810-fs5rx07q 37 10 be be VB cord-284810-fs5rx07q 37 11 directly directly RB cord-284810-fs5rx07q 37 12 correlated correlate VBN cord-284810-fs5rx07q 37 13 to to IN cord-284810-fs5rx07q 37 14 the the DT cord-284810-fs5rx07q 37 15 arrival arrival NN cord-284810-fs5rx07q 37 16 time time NN cord-284810-fs5rx07q 37 17 of of IN cord-284810-fs5rx07q 37 18 the the DT cord-284810-fs5rx07q 37 19 disease disease NN cord-284810-fs5rx07q 37 20 : : : cord-284810-fs5rx07q 37 21 countries country NNS cord-284810-fs5rx07q 37 22 that that WDT cord-284810-fs5rx07q 37 23 were be VBD cord-284810-fs5rx07q 37 24 invaded invade VBN cord-284810-fs5rx07q 37 25 very very RB cord-284810-fs5rx07q 37 26 early early RB cord-284810-fs5rx07q 37 27 by by IN cord-284810-fs5rx07q 37 28 the the DT cord-284810-fs5rx07q 37 29 virus virus NN cord-284810-fs5rx07q 37 30 have have VBP cord-284810-fs5rx07q 37 31 accumulated accumulate VBN cord-284810-fs5rx07q 37 32 many many JJ cord-284810-fs5rx07q 37 33 cases case NNS cord-284810-fs5rx07q 37 34 in in IN cord-284810-fs5rx07q 37 35 time time NN cord-284810-fs5rx07q 37 36 , , , cord-284810-fs5rx07q 37 37 while while IN cord-284810-fs5rx07q 37 38 countries country NNS cord-284810-fs5rx07q 37 39 with with IN cord-284810-fs5rx07q 37 40 a a DT cord-284810-fs5rx07q 37 41 late late JJ cord-284810-fs5rx07q 37 42 invasion invasion NN cord-284810-fs5rx07q 37 43 naturally naturally RB cord-284810-fs5rx07q 37 44 still still RB cord-284810-fs5rx07q 37 45 have have VBP cord-284810-fs5rx07q 37 46 smaller small JJR cord-284810-fs5rx07q 37 47 prevalence prevalence NN cord-284810-fs5rx07q 37 48 . . . cord-284810-fs5rx07q 38 1 To to TO cord-284810-fs5rx07q 38 2 test test VB cord-284810-fs5rx07q 38 3 this this DT cord-284810-fs5rx07q 38 4 hypothesis hypothesis NN cord-284810-fs5rx07q 38 5 , , , cord-284810-fs5rx07q 38 6 we -PRON- PRP cord-284810-fs5rx07q 38 7 use use VBP cord-284810-fs5rx07q 38 8 empirical empirical JJ cord-284810-fs5rx07q 38 9 data datum NNS cord-284810-fs5rx07q 38 10 14 14 CD cord-284810-fs5rx07q 38 11 to to TO cord-284810-fs5rx07q 38 12 compute compute VB cord-284810-fs5rx07q 38 13 the the DT cord-284810-fs5rx07q 38 14 country country NN cord-284810-fs5rx07q 38 15 - - HYPH cord-284810-fs5rx07q 38 16 level level NN cord-284810-fs5rx07q 38 17 distribution distribution NN cord-284810-fs5rx07q 38 18 , , , cord-284810-fs5rx07q 38 19 P p NN cord-284810-fs5rx07q 38 20 , , , cord-284810-fs5rx07q 38 21 of of IN cord-284810-fs5rx07q 38 22 confirmed confirm VBN cord-284810-fs5rx07q 38 23 COVID-19 covid-19 CD cord-284810-fs5rx07q 38 24 cases case NNS cord-284810-fs5rx07q 38 25 , , , cord-284810-fs5rx07q 38 26 n n NNP cord-284810-fs5rx07q 38 27 , , , cord-284810-fs5rx07q 38 28 at at IN cord-284810-fs5rx07q 38 29 the the DT cord-284810-fs5rx07q 38 30 end end NN cord-284810-fs5rx07q 38 31 of of IN cord-284810-fs5rx07q 38 32 March March NNP cord-284810-fs5rx07q 38 33 2020 2020 CD cord-284810-fs5rx07q 38 34 worldwide worldwide RB cord-284810-fs5rx07q 38 35 and and CC cord-284810-fs5rx07q 38 36 find find VB cord-284810-fs5rx07q 38 37 that that IN cord-284810-fs5rx07q 38 38 it -PRON- PRP cord-284810-fs5rx07q 38 39 is be VBZ cord-284810-fs5rx07q 38 40 closely closely RB cord-284810-fs5rx07q 38 41 approximated approximate VBN cord-284810-fs5rx07q 38 42 by by IN cord-284810-fs5rx07q 38 43 a a DT cord-284810-fs5rx07q 38 44 truncated truncated JJ cord-284810-fs5rx07q 38 45 power power NN cord-284810-fs5rx07q 38 46 - - HYPH cord-284810-fs5rx07q 38 47 law law NN cord-284810-fs5rx07q 38 48 , , , cord-284810-fs5rx07q 38 49 over over IN cord-284810-fs5rx07q 38 50 five five CD cord-284810-fs5rx07q 38 51 orders order NNS cord-284810-fs5rx07q 38 52 of of IN cord-284810-fs5rx07q 38 53 magnitude magnitude NN cord-284810-fs5rx07q 38 54 . . . cord-284810-fs5rx07q 39 1 Power power NN cord-284810-fs5rx07q 39 2 - - HYPH cord-284810-fs5rx07q 39 3 law law NN cord-284810-fs5rx07q 39 4 distributions distribution NNS cord-284810-fs5rx07q 39 5 characterize characterize VBP cord-284810-fs5rx07q 39 6 a a DT cord-284810-fs5rx07q 39 7 large large JJ cord-284810-fs5rx07q 39 8 range range NN cord-284810-fs5rx07q 39 9 of of IN cord-284810-fs5rx07q 39 10 phenomena phenomenon NNS cord-284810-fs5rx07q 39 11 in in IN cord-284810-fs5rx07q 39 12 natural natural JJ cord-284810-fs5rx07q 39 13 , , , cord-284810-fs5rx07q 39 14 economic economic JJ cord-284810-fs5rx07q 39 15 , , , cord-284810-fs5rx07q 39 16 and and CC cord-284810-fs5rx07q 39 17 social social JJ cord-284810-fs5rx07q 39 18 systems system NNS cord-284810-fs5rx07q 39 19 , , , cord-284810-fs5rx07q 39 20 which which WDT cord-284810-fs5rx07q 39 21 is be VBZ cord-284810-fs5rx07q 39 22 known know VBN cord-284810-fs5rx07q 39 23 as as IN cord-284810-fs5rx07q 39 24 Zipf Zipf NNP cord-284810-fs5rx07q 39 25 - - : cord-284810-fs5rx07q 39 26 or or CC cord-284810-fs5rx07q 39 27 Pareto Pareto NNP cord-284810-fs5rx07q 39 28 law law NN cord-284810-fs5rx07q 39 29 . . . cord-284810-fs5rx07q 40 1 11 11 CD cord-284810-fs5rx07q 40 2 , , , cord-284810-fs5rx07q 40 3 27 27 CD cord-284810-fs5rx07q 40 4 , , , cord-284810-fs5rx07q 40 5 29 29 CD cord-284810-fs5rx07q 40 6 , , , cord-284810-fs5rx07q 40 7 39 39 CD cord-284810-fs5rx07q 40 8 Examples example NNS cord-284810-fs5rx07q 40 9 range range VBP cord-284810-fs5rx07q 40 10 from from IN cord-284810-fs5rx07q 40 11 the the DT cord-284810-fs5rx07q 40 12 number number NN cord-284810-fs5rx07q 40 13 of of IN cord-284810-fs5rx07q 40 14 species specie NNS cord-284810-fs5rx07q 40 15 in in IN cord-284810-fs5rx07q 40 16 biological biological JJ cord-284810-fs5rx07q 40 17 taxa taxon NNS cord-284810-fs5rx07q 40 18 , , , cord-284810-fs5rx07q 40 19 46 46 CD cord-284810-fs5rx07q 41 1 the the DT cord-284810-fs5rx07q 41 2 number number NN cord-284810-fs5rx07q 41 3 of of IN cord-284810-fs5rx07q 41 4 cities city NNS cord-284810-fs5rx07q 41 5 with with IN cord-284810-fs5rx07q 41 6 a a DT cord-284810-fs5rx07q 41 7 given give VBN cord-284810-fs5rx07q 41 8 size size NN cord-284810-fs5rx07q 41 9 , , , cord-284810-fs5rx07q 41 10 47 47 CD cord-284810-fs5rx07q 41 11 the the DT cord-284810-fs5rx07q 41 12 number number NN cord-284810-fs5rx07q 41 13 of of IN cord-284810-fs5rx07q 41 14 different different JJ cord-284810-fs5rx07q 41 15 words word NNS cord-284810-fs5rx07q 41 16 in in IN cord-284810-fs5rx07q 41 17 human human JJ cord-284810-fs5rx07q 41 18 language language NN cord-284810-fs5rx07q 41 19 , , , cord-284810-fs5rx07q 41 20 47 47 CD cord-284810-fs5rx07q 41 21 the the DT cord-284810-fs5rx07q 41 22 frequency frequency NN cord-284810-fs5rx07q 41 23 of of IN cord-284810-fs5rx07q 41 24 earthquakes earthquake NNS cord-284810-fs5rx07q 41 25 , , , cord-284810-fs5rx07q 41 26 18 18 CD cord-284810-fs5rx07q 41 27 the the DT cord-284810-fs5rx07q 41 28 distribution distribution NN cord-284810-fs5rx07q 41 29 of of IN cord-284810-fs5rx07q 41 30 wealth wealth NN cord-284810-fs5rx07q 41 31 , , , cord-284810-fs5rx07q 41 32 32 32 CD cord-284810-fs5rx07q 41 33 the the DT cord-284810-fs5rx07q 41 34 number number NN cord-284810-fs5rx07q 41 35 of of IN cord-284810-fs5rx07q 41 36 scientific scientific JJ cord-284810-fs5rx07q 41 37 citations citation NNS cord-284810-fs5rx07q 41 38 , , , cord-284810-fs5rx07q 41 39 34,36 34,36 CD cord-284810-fs5rx07q 41 40 the the DT cord-284810-fs5rx07q 41 41 step step NN cord-284810-fs5rx07q 41 42 length length NN cord-284810-fs5rx07q 41 43 in in IN cord-284810-fs5rx07q 41 44 animal animal NN cord-284810-fs5rx07q 41 45 search search NN cord-284810-fs5rx07q 41 46 patterns pattern NNS cord-284810-fs5rx07q 41 47 , , , cord-284810-fs5rx07q 41 48 44 44 CD cord-284810-fs5rx07q 41 49 and and CC cord-284810-fs5rx07q 41 50 the the DT cord-284810-fs5rx07q 41 51 popularity popularity NN cord-284810-fs5rx07q 41 52 of of IN cord-284810-fs5rx07q 41 53 chess chess NN cord-284810-fs5rx07q 41 54 openings opening NNS cord-284810-fs5rx07q 41 55 . . . cord-284810-fs5rx07q 42 1 7 7 CD cord-284810-fs5rx07q 43 1 Our -PRON- PRP$ cord-284810-fs5rx07q 43 2 study study NN cord-284810-fs5rx07q 43 3 shows show VBZ cord-284810-fs5rx07q 43 4 that that IN cord-284810-fs5rx07q 43 5 epidemic epidemic NN cord-284810-fs5rx07q 43 6 prevalence prevalence NN cord-284810-fs5rx07q 43 7 , , , cord-284810-fs5rx07q 43 8 at at IN cord-284810-fs5rx07q 43 9 least least JJS cord-284810-fs5rx07q 43 10 in in IN cord-284810-fs5rx07q 43 11 the the DT cord-284810-fs5rx07q 43 12 emerging emerge VBG cord-284810-fs5rx07q 43 13 stage stage NN cord-284810-fs5rx07q 43 14 of of IN cord-284810-fs5rx07q 43 15 a a DT cord-284810-fs5rx07q 43 16 pandemic pandemic NN cord-284810-fs5rx07q 43 17 , , , cord-284810-fs5rx07q 43 18 is be VBZ cord-284810-fs5rx07q 43 19 another another DT cord-284810-fs5rx07q 43 20 system system NN cord-284810-fs5rx07q 43 21 that that WDT cord-284810-fs5rx07q 43 22 falls fall VBZ cord-284810-fs5rx07q 43 23 into into IN cord-284810-fs5rx07q 43 24 this this DT cord-284810-fs5rx07q 43 25 class class NN cord-284810-fs5rx07q 43 26 , , , cord-284810-fs5rx07q 43 27 suggesting suggest VBG cord-284810-fs5rx07q 43 28 that that IN cord-284810-fs5rx07q 43 29 the the DT cord-284810-fs5rx07q 43 30 spatial spatial JJ cord-284810-fs5rx07q 43 31 distribution distribution NN cord-284810-fs5rx07q 43 32 of of IN cord-284810-fs5rx07q 43 33 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 43 34 case case NN cord-284810-fs5rx07q 43 35 numbers number NNS cord-284810-fs5rx07q 43 36 is be VBZ cord-284810-fs5rx07q 43 37 a a DT cord-284810-fs5rx07q 43 38 fractal fractal NN cord-284810-fs5rx07q 43 39 . . . cord-284810-fs5rx07q 44 1 9 9 CD cord-284810-fs5rx07q 45 1 The the DT cord-284810-fs5rx07q 45 2 appearance appearance NN cord-284810-fs5rx07q 45 3 of of IN cord-284810-fs5rx07q 45 4 a a DT cord-284810-fs5rx07q 45 5 power power NN cord-284810-fs5rx07q 45 6 - - HYPH cord-284810-fs5rx07q 45 7 law law NN cord-284810-fs5rx07q 45 8 distribution distribution NN cord-284810-fs5rx07q 45 9 often often RB cord-284810-fs5rx07q 45 10 points point VBZ cord-284810-fs5rx07q 45 11 to to IN cord-284810-fs5rx07q 45 12 the the DT cord-284810-fs5rx07q 45 13 nature nature NN cord-284810-fs5rx07q 45 14 of of IN cord-284810-fs5rx07q 45 15 the the DT cord-284810-fs5rx07q 45 16 underlying underlie VBG cord-284810-fs5rx07q 45 17 processes process NNS cord-284810-fs5rx07q 45 18 . . . cord-284810-fs5rx07q 46 1 It -PRON- PRP cord-284810-fs5rx07q 46 2 might may MD cord-284810-fs5rx07q 46 3 , , , cord-284810-fs5rx07q 46 4 for for IN cord-284810-fs5rx07q 46 5 example example NN cord-284810-fs5rx07q 46 6 , , , cord-284810-fs5rx07q 46 7 be be VB cord-284810-fs5rx07q 46 8 an an DT cord-284810-fs5rx07q 46 9 indication indication NN cord-284810-fs5rx07q 46 10 that that IN cord-284810-fs5rx07q 46 11 the the DT cord-284810-fs5rx07q 46 12 system system NN cord-284810-fs5rx07q 46 13 operates operate VBZ cord-284810-fs5rx07q 46 14 close close RB cord-284810-fs5rx07q 46 15 to to IN cord-284810-fs5rx07q 46 16 criticality criticality NN cord-284810-fs5rx07q 46 17 , , , cord-284810-fs5rx07q 46 18 3 3 CD cord-284810-fs5rx07q 46 19 , , , cord-284810-fs5rx07q 46 20 29 29 CD cord-284810-fs5rx07q 46 21 and and CC cord-284810-fs5rx07q 46 22 it -PRON- PRP cord-284810-fs5rx07q 46 23 might may MD cord-284810-fs5rx07q 46 24 hint hint VB cord-284810-fs5rx07q 46 25 at at IN cord-284810-fs5rx07q 46 26 the the DT cord-284810-fs5rx07q 46 27 presence presence NN cord-284810-fs5rx07q 46 28 of of IN cord-284810-fs5rx07q 46 29 a a DT cord-284810-fs5rx07q 46 30 multiplicative multiplicative JJ cord-284810-fs5rx07q 46 31 stochastic stochastic JJ cord-284810-fs5rx07q 46 32 process process NN cord-284810-fs5rx07q 46 33 with with IN cord-284810-fs5rx07q 46 34 certain certain JJ cord-284810-fs5rx07q 46 35 boundaries boundary NNS cord-284810-fs5rx07q 46 36 7,39 7,39 NN cord-284810-fs5rx07q 46 37 or or CC cord-284810-fs5rx07q 46 38 a a DT cord-284810-fs5rx07q 46 39 rich rich JJ cord-284810-fs5rx07q 46 40 - - HYPH cord-284810-fs5rx07q 46 41 get get NN cord-284810-fs5rx07q 46 42 - - HYPH cord-284810-fs5rx07q 46 43 richer rich JJR cord-284810-fs5rx07q 46 44 process process NN cord-284810-fs5rx07q 46 45 . . . cord-284810-fs5rx07q 47 1 4 4 LS cord-284810-fs5rx07q 47 2 , , , cord-284810-fs5rx07q 47 3 38 38 CD cord-284810-fs5rx07q 48 1 Here here RB cord-284810-fs5rx07q 48 2 , , , cord-284810-fs5rx07q 48 3 we -PRON- PRP cord-284810-fs5rx07q 48 4 provide provide VBP cord-284810-fs5rx07q 48 5 a a DT cord-284810-fs5rx07q 48 6 conceptual conceptual JJ cord-284810-fs5rx07q 48 7 dual dual JJ cord-284810-fs5rx07q 48 8 - - HYPH cord-284810-fs5rx07q 48 9 scale scale NN cord-284810-fs5rx07q 48 10 model model NN cord-284810-fs5rx07q 48 11 that that WDT cord-284810-fs5rx07q 48 12 explains explain VBZ cord-284810-fs5rx07q 48 13 the the DT cord-284810-fs5rx07q 48 14 emergence emergence NN cord-284810-fs5rx07q 48 15 of of IN cord-284810-fs5rx07q 48 16 the the DT cord-284810-fs5rx07q 48 17 power power NN cord-284810-fs5rx07q 48 18 - - HYPH cord-284810-fs5rx07q 48 19 law law NN cord-284810-fs5rx07q 48 20 distribution distribution NN cord-284810-fs5rx07q 48 21 by by IN cord-284810-fs5rx07q 48 22 the the DT cord-284810-fs5rx07q 48 23 " " `` cord-284810-fs5rx07q 48 24 superposition superposition NN cord-284810-fs5rx07q 48 25 " " '' cord-284810-fs5rx07q 48 26 of of IN cord-284810-fs5rx07q 48 27 two two CD cord-284810-fs5rx07q 48 28 concurrent concurrent JJ cord-284810-fs5rx07q 48 29 processes process NNS cord-284810-fs5rx07q 48 30 : : : cord-284810-fs5rx07q 48 31 large large JJ cord-284810-fs5rx07q 48 32 - - HYPH cord-284810-fs5rx07q 48 33 scale scale NN cord-284810-fs5rx07q 48 34 spread spread NN cord-284810-fs5rx07q 48 35 of of IN cord-284810-fs5rx07q 48 36 the the DT cord-284810-fs5rx07q 48 37 virus virus NN cord-284810-fs5rx07q 48 38 between between IN cord-284810-fs5rx07q 48 39 countries country NNS cord-284810-fs5rx07q 48 40 and and CC cord-284810-fs5rx07q 48 41 small small JJ cord-284810-fs5rx07q 48 42 - - HYPH cord-284810-fs5rx07q 48 43 scale scale NN cord-284810-fs5rx07q 48 44 snowballing snowballing NN cord-284810-fs5rx07q 48 45 of of IN cord-284810-fs5rx07q 48 46 case case NN cord-284810-fs5rx07q 48 47 numbers number NNS cord-284810-fs5rx07q 48 48 within within IN cord-284810-fs5rx07q 48 49 each each DT cord-284810-fs5rx07q 48 50 country country NN cord-284810-fs5rx07q 48 51 . . . cord-284810-fs5rx07q 49 1 Assuming assume VBG cord-284810-fs5rx07q 49 2 exponential exponential JJ cord-284810-fs5rx07q 49 3 growth growth NN cord-284810-fs5rx07q 49 4 on on IN cord-284810-fs5rx07q 49 5 both both DT cord-284810-fs5rx07q 49 6 scales scale NNS cord-284810-fs5rx07q 49 7 , , , cord-284810-fs5rx07q 49 8 the the DT cord-284810-fs5rx07q 49 9 critical critical JJ cord-284810-fs5rx07q 49 10 exponent exponent NN cord-284810-fs5rx07q 49 11 is be VBZ cord-284810-fs5rx07q 49 12 simply simply RB cord-284810-fs5rx07q 49 13 determined determine VBN cord-284810-fs5rx07q 49 14 by by IN cord-284810-fs5rx07q 49 15 the the DT cord-284810-fs5rx07q 49 16 ratio ratio NN cord-284810-fs5rx07q 49 17 of of IN cord-284810-fs5rx07q 49 18 large large JJ cord-284810-fs5rx07q 49 19 - - HYPH cord-284810-fs5rx07q 49 20 scale scale NN cord-284810-fs5rx07q 49 21 to to IN cord-284810-fs5rx07q 49 22 small small JJ cord-284810-fs5rx07q 49 23 - - HYPH cord-284810-fs5rx07q 49 24 scale scale NN cord-284810-fs5rx07q 49 25 growth growth NN cord-284810-fs5rx07q 49 26 rates rate NNS cord-284810-fs5rx07q 49 27 . . . cord-284810-fs5rx07q 50 1 We -PRON- PRP cord-284810-fs5rx07q 50 2 confirm confirm VBP cord-284810-fs5rx07q 50 3 this this DT cord-284810-fs5rx07q 50 4 theory theory NN cord-284810-fs5rx07q 50 5 in in IN cord-284810-fs5rx07q 50 6 numerical numerical JJ cord-284810-fs5rx07q 50 7 simulations simulation NNS cord-284810-fs5rx07q 50 8 in in IN cord-284810-fs5rx07q 50 9 a a DT cord-284810-fs5rx07q 50 10 simple simple JJ cord-284810-fs5rx07q 50 11 meta meta JJ cord-284810-fs5rx07q 50 12 - - HYPH cord-284810-fs5rx07q 50 13 population population NN cord-284810-fs5rx07q 50 14 model model NN cord-284810-fs5rx07q 50 15 , , , cord-284810-fs5rx07q 50 16 describing describe VBG cord-284810-fs5rx07q 50 17 the the DT cord-284810-fs5rx07q 50 18 epidemic epidemic NN cord-284810-fs5rx07q 50 19 spread spread VBN cord-284810-fs5rx07q 50 20 in in IN cord-284810-fs5rx07q 50 21 a a DT cord-284810-fs5rx07q 50 22 network network NN cord-284810-fs5rx07q 50 23 of of IN cord-284810-fs5rx07q 50 24 interconnected interconnected JJ cord-284810-fs5rx07q 50 25 countries country NNS cord-284810-fs5rx07q 50 26 . . . cord-284810-fs5rx07q 51 1 By by IN cord-284810-fs5rx07q 51 2 combining combine VBG cord-284810-fs5rx07q 51 3 real real JJ cord-284810-fs5rx07q 51 4 world world NN cord-284810-fs5rx07q 51 5 data datum NNS cord-284810-fs5rx07q 51 6 , , , cord-284810-fs5rx07q 51 7 modeling modeling NN cord-284810-fs5rx07q 51 8 , , , cord-284810-fs5rx07q 51 9 and and CC cord-284810-fs5rx07q 51 10 numerical numerical JJ cord-284810-fs5rx07q 51 11 simulations simulation NNS cord-284810-fs5rx07q 51 12 , , , cord-284810-fs5rx07q 51 13 we -PRON- PRP cord-284810-fs5rx07q 51 14 make make VBP cord-284810-fs5rx07q 51 15 the the DT cord-284810-fs5rx07q 51 16 case case NN cord-284810-fs5rx07q 51 17 that that IN cord-284810-fs5rx07q 51 18 the the DT cord-284810-fs5rx07q 51 19 distribution distribution NN cord-284810-fs5rx07q 51 20 of of IN cord-284810-fs5rx07q 51 21 epidemic epidemic NN cord-284810-fs5rx07q 51 22 prevalence prevalence NN cord-284810-fs5rx07q 51 23 , , , cord-284810-fs5rx07q 51 24 and and CC cord-284810-fs5rx07q 51 25 possibly possibly RB cord-284810-fs5rx07q 51 26 that that DT cord-284810-fs5rx07q 51 27 of of IN cord-284810-fs5rx07q 51 28 spreading spread VBG cord-284810-fs5rx07q 51 29 processes process NNS cord-284810-fs5rx07q 51 30 in in IN cord-284810-fs5rx07q 51 31 general general JJ cord-284810-fs5rx07q 51 32 , , , cord-284810-fs5rx07q 51 33 might may MD cord-284810-fs5rx07q 51 34 follow follow VB cord-284810-fs5rx07q 51 35 universal universal JJ cord-284810-fs5rx07q 51 36 rules rule NNS cord-284810-fs5rx07q 51 37 . . . cord-284810-fs5rx07q 52 1 Our -PRON- PRP$ cord-284810-fs5rx07q 52 2 research research NN cord-284810-fs5rx07q 52 3 builds build VBZ cord-284810-fs5rx07q 52 4 on on IN cord-284810-fs5rx07q 52 5 the the DT cord-284810-fs5rx07q 52 6 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 52 7 data data NN cord-284810-fs5rx07q 52 8 repository repository NN cord-284810-fs5rx07q 52 9 operated operate VBN cord-284810-fs5rx07q 52 10 by by IN cord-284810-fs5rx07q 52 11 the the DT cord-284810-fs5rx07q 52 12 Johns Johns NNP cord-284810-fs5rx07q 52 13 Hopkins Hopkins NNP cord-284810-fs5rx07q 52 14 University University NNP cord-284810-fs5rx07q 52 15 Center Center NNP cord-284810-fs5rx07q 52 16 for for IN cord-284810-fs5rx07q 52 17 Systems Systems NNP cord-284810-fs5rx07q 52 18 Science Science NNP cord-284810-fs5rx07q 52 19 and and CC cord-284810-fs5rx07q 52 20 Engineering Engineering NNP cord-284810-fs5rx07q 52 21 ( ( -LRB- cord-284810-fs5rx07q 52 22 JHU JHU NNP cord-284810-fs5rx07q 52 23 CSSE CSSE NNP cord-284810-fs5rx07q 52 24 ) ) -RRB- cord-284810-fs5rx07q 52 25 . . . cord-284810-fs5rx07q 53 1 14 14 CD cord-284810-fs5rx07q 54 1 The the DT cord-284810-fs5rx07q 54 2 database database NN cord-284810-fs5rx07q 54 3 contains contain VBZ cord-284810-fs5rx07q 54 4 information information NN cord-284810-fs5rx07q 54 5 about about IN cord-284810-fs5rx07q 54 6 the the DT cord-284810-fs5rx07q 54 7 daily daily JJ cord-284810-fs5rx07q 54 8 number number NN cord-284810-fs5rx07q 54 9 of of IN cord-284810-fs5rx07q 54 10 confirmed confirm VBN cord-284810-fs5rx07q 54 11 COVID-19 covid-19 CD cord-284810-fs5rx07q 54 12 cases case NNS cord-284810-fs5rx07q 54 13 and and CC cord-284810-fs5rx07q 54 14 confirmed confirm VBD cord-284810-fs5rx07q 54 15 deaths death NNS cord-284810-fs5rx07q 54 16 in in IN cord-284810-fs5rx07q 54 17 various various JJ cord-284810-fs5rx07q 54 18 countries country NNS cord-284810-fs5rx07q 54 19 worldwide worldwide RB cord-284810-fs5rx07q 54 20 . . . cord-284810-fs5rx07q 55 1 Using use VBG cord-284810-fs5rx07q 55 2 these these DT cord-284810-fs5rx07q 55 3 data datum NNS cord-284810-fs5rx07q 55 4 , , , cord-284810-fs5rx07q 55 5 we -PRON- PRP cord-284810-fs5rx07q 55 6 computed compute VBD cord-284810-fs5rx07q 55 7 the the DT cord-284810-fs5rx07q 55 8 distribution distribution NN cord-284810-fs5rx07q 55 9 P p NN cord-284810-fs5rx07q 55 10 C C NNP cord-284810-fs5rx07q 55 11 ( ( -LRB- cord-284810-fs5rx07q 55 12 n n NNP cord-284810-fs5rx07q 55 13 ) ) -RRB- cord-284810-fs5rx07q 55 14 of of IN cord-284810-fs5rx07q 55 15 confirmed confirm VBN cord-284810-fs5rx07q 55 16 cases case NNS cord-284810-fs5rx07q 55 17 and and CC cord-284810-fs5rx07q 55 18 the the DT cord-284810-fs5rx07q 55 19 distribution distribution NN cord-284810-fs5rx07q 55 20 P p NN cord-284810-fs5rx07q 55 21 D d NN cord-284810-fs5rx07q 55 22 ( ( -LRB- cord-284810-fs5rx07q 55 23 n n NN cord-284810-fs5rx07q 55 24 ) ) -RRB- cord-284810-fs5rx07q 55 25 of of IN cord-284810-fs5rx07q 55 26 confirmed confirm VBN cord-284810-fs5rx07q 55 27 deaths death NNS cord-284810-fs5rx07q 55 28 at at IN cord-284810-fs5rx07q 55 29 a a DT cord-284810-fs5rx07q 55 30 given give VBN cord-284810-fs5rx07q 55 31 date date NN cord-284810-fs5rx07q 55 32 ( ( -LRB- cord-284810-fs5rx07q 55 33 see see VB cord-284810-fs5rx07q 55 34 Appendix Appendix NNP cord-284810-fs5rx07q 55 35 A A NNP cord-284810-fs5rx07q 55 36 ) ) -RRB- cord-284810-fs5rx07q 55 37 . . . cord-284810-fs5rx07q 56 1 The the DT cord-284810-fs5rx07q 56 2 country country NN cord-284810-fs5rx07q 56 3 - - HYPH cord-284810-fs5rx07q 56 4 level level NN cord-284810-fs5rx07q 56 5 prevalence prevalence NN cord-284810-fs5rx07q 56 6 distribution distribution NN cord-284810-fs5rx07q 56 7 on on IN cord-284810-fs5rx07q 56 8 March March NNP cord-284810-fs5rx07q 56 9 22 22 CD cord-284810-fs5rx07q 56 10 , , , cord-284810-fs5rx07q 56 11 2020 2020 CD cord-284810-fs5rx07q 56 12 is be VBZ cord-284810-fs5rx07q 56 13 shown show VBN cord-284810-fs5rx07q 56 14 in in IN cord-284810-fs5rx07q 56 15 Figs Figs NNPS cord-284810-fs5rx07q 56 16 . . . cord-284810-fs5rx07q 57 1 1(a 1(a LS cord-284810-fs5rx07q 57 2 ) ) -RRB- cord-284810-fs5rx07q 57 3 and and CC cord-284810-fs5rx07q 57 4 1(b 1(b CD cord-284810-fs5rx07q 57 5 ) ) -RRB- cord-284810-fs5rx07q 57 6 . . . cord-284810-fs5rx07q 58 1 On on IN cord-284810-fs5rx07q 58 2 that that DT cord-284810-fs5rx07q 58 3 day day NN cord-284810-fs5rx07q 58 4 , , , cord-284810-fs5rx07q 58 5 168 168 CD cord-284810-fs5rx07q 58 6 countries country NNS cord-284810-fs5rx07q 58 7 were be VBD cord-284810-fs5rx07q 58 8 invaded invade VBN cord-284810-fs5rx07q 58 9 by by IN cord-284810-fs5rx07q 58 10 the the DT cord-284810-fs5rx07q 58 11 coronavirus coronavirus NN cord-284810-fs5rx07q 58 12 and and CC cord-284810-fs5rx07q 58 13 86 86 CD cord-284810-fs5rx07q 58 14 countries country NNS cord-284810-fs5rx07q 58 15 already already RB cord-284810-fs5rx07q 58 16 had have VBD cord-284810-fs5rx07q 58 17 reported report VBN cord-284810-fs5rx07q 58 18 fatalities fatality NNS cord-284810-fs5rx07q 58 19 . . . cord-284810-fs5rx07q 59 1 The the DT cord-284810-fs5rx07q 59 2 number number NN cord-284810-fs5rx07q 59 3 of of IN cord-284810-fs5rx07q 59 4 confirmed confirm VBN cord-284810-fs5rx07q 59 5 cases case NNS cord-284810-fs5rx07q 59 6 varied vary VBN cord-284810-fs5rx07q 59 7 between between IN cord-284810-fs5rx07q 59 8 81 81 CD cord-284810-fs5rx07q 59 9 435 435 CD cord-284810-fs5rx07q 59 10 cases case NNS cord-284810-fs5rx07q 59 11 in in IN cord-284810-fs5rx07q 59 12 China China NNP cord-284810-fs5rx07q 59 13 ( ( -LRB- cord-284810-fs5rx07q 59 14 followed follow VBN cord-284810-fs5rx07q 59 15 by by IN cord-284810-fs5rx07q 59 16 59 59 CD cord-284810-fs5rx07q 59 17 138 138 CD cord-284810-fs5rx07q 59 18 cases case NNS cord-284810-fs5rx07q 59 19 in in IN cord-284810-fs5rx07q 59 20 Italy Italy NNP cord-284810-fs5rx07q 59 21 ) ) -RRB- cord-284810-fs5rx07q 59 22 and and CC cord-284810-fs5rx07q 59 23 1 1 CD cord-284810-fs5rx07q 59 24 case case NN cord-284810-fs5rx07q 59 25 in in IN cord-284810-fs5rx07q 59 26 16 16 CD cord-284810-fs5rx07q 59 27 countries country NNS cord-284810-fs5rx07q 59 28 . . . cord-284810-fs5rx07q 60 1 The the DT cord-284810-fs5rx07q 60 2 number number NN cord-284810-fs5rx07q 60 3 of of IN cord-284810-fs5rx07q 60 4 confirmed confirm VBN cord-284810-fs5rx07q 60 5 deaths death NNS cord-284810-fs5rx07q 60 6 varied vary VBN cord-284810-fs5rx07q 60 7 between between IN cord-284810-fs5rx07q 60 8 5476 5476 CD cord-284810-fs5rx07q 60 9 in in IN cord-284810-fs5rx07q 60 10 Italy Italy NNP cord-284810-fs5rx07q 60 11 ( ( -LRB- cord-284810-fs5rx07q 60 12 followed follow VBN cord-284810-fs5rx07q 60 13 by by IN cord-284810-fs5rx07q 60 14 3274 3274 CD cord-284810-fs5rx07q 60 15 in in IN cord-284810-fs5rx07q 60 16 China China NNP cord-284810-fs5rx07q 60 17 ) ) -RRB- cord-284810-fs5rx07q 60 18 and and CC cord-284810-fs5rx07q 60 19 one one CD cord-284810-fs5rx07q 60 20 or or CC cord-284810-fs5rx07q 60 21 zero zero CD cord-284810-fs5rx07q 60 22 deaths death NNS cord-284810-fs5rx07q 60 23 in in IN cord-284810-fs5rx07q 60 24 many many JJ cord-284810-fs5rx07q 60 25 countries country NNS cord-284810-fs5rx07q 60 26 . . . cord-284810-fs5rx07q 61 1 a a DT cord-284810-fs5rx07q 61 2 broad broad JJ cord-284810-fs5rx07q 61 3 , , , cord-284810-fs5rx07q 61 4 long long JJ cord-284810-fs5rx07q 61 5 - - HYPH cord-284810-fs5rx07q 61 6 tailed tailed JJ cord-284810-fs5rx07q 61 7 distribution distribution NN cord-284810-fs5rx07q 61 8 that that WDT cord-284810-fs5rx07q 61 9 in in IN cord-284810-fs5rx07q 61 10 very very RB cord-284810-fs5rx07q 61 11 good good JJ cord-284810-fs5rx07q 61 12 approximation approximation NN cord-284810-fs5rx07q 61 13 can can MD cord-284810-fs5rx07q 61 14 be be VB cord-284810-fs5rx07q 61 15 described describe VBN cord-284810-fs5rx07q 61 16 by by IN cord-284810-fs5rx07q 61 17 a a DT cord-284810-fs5rx07q 61 18 power power NN cord-284810-fs5rx07q 61 19 - - HYPH cord-284810-fs5rx07q 61 20 law law NN cord-284810-fs5rx07q 61 21 , , , cord-284810-fs5rx07q 61 22 spanning span VBG cord-284810-fs5rx07q 61 23 five five CD cord-284810-fs5rx07q 61 24 orders order NNS cord-284810-fs5rx07q 61 25 of of IN cord-284810-fs5rx07q 61 26 magnitude magnitude NN cord-284810-fs5rx07q 61 27 for for IN cord-284810-fs5rx07q 61 28 the the DT cord-284810-fs5rx07q 61 29 confirmed confirm VBN cord-284810-fs5rx07q 61 30 number number NN cord-284810-fs5rx07q 61 31 of of IN cord-284810-fs5rx07q 61 32 cases case NNS cord-284810-fs5rx07q 61 33 and and CC cord-284810-fs5rx07q 61 34 four four CD cord-284810-fs5rx07q 61 35 orders order NNS cord-284810-fs5rx07q 61 36 of of IN cord-284810-fs5rx07q 61 37 magnitude magnitude NN cord-284810-fs5rx07q 61 38 for for IN cord-284810-fs5rx07q 61 39 the the DT cord-284810-fs5rx07q 61 40 confirmed confirm VBN cord-284810-fs5rx07q 61 41 number number NN cord-284810-fs5rx07q 61 42 of of IN cord-284810-fs5rx07q 61 43 deaths death NNS cord-284810-fs5rx07q 61 44 . . . cord-284810-fs5rx07q 62 1 To to TO cord-284810-fs5rx07q 62 2 illustrate illustrate VB cord-284810-fs5rx07q 62 3 the the DT cord-284810-fs5rx07q 62 4 robustness robustness NN cord-284810-fs5rx07q 62 5 of of IN cord-284810-fs5rx07q 62 6 our -PRON- PRP$ cord-284810-fs5rx07q 62 7 hypothesis hypothesis NN cord-284810-fs5rx07q 62 8 to to IN cord-284810-fs5rx07q 62 9 spatial spatial JJ cord-284810-fs5rx07q 62 10 scale scale NN cord-284810-fs5rx07q 62 11 , , , cord-284810-fs5rx07q 62 12 in in IN cord-284810-fs5rx07q 62 13 Figs fig NNS cord-284810-fs5rx07q 62 14 . . . cord-284810-fs5rx07q 63 1 1(c 1(c LS cord-284810-fs5rx07q 63 2 ) ) -RRB- cord-284810-fs5rx07q 64 1 and and CC cord-284810-fs5rx07q 64 2 1(d 1(d LS cord-284810-fs5rx07q 64 3 ) ) -RRB- cord-284810-fs5rx07q 64 4 , , , cord-284810-fs5rx07q 64 5 we -PRON- PRP cord-284810-fs5rx07q 64 6 depict depict VBP cord-284810-fs5rx07q 64 7 the the DT cord-284810-fs5rx07q 64 8 same same JJ cord-284810-fs5rx07q 64 9 analysis analysis NN cord-284810-fs5rx07q 64 10 for for IN cord-284810-fs5rx07q 64 11 the the DT cord-284810-fs5rx07q 64 12 distribution distribution NN cord-284810-fs5rx07q 64 13 of of IN cord-284810-fs5rx07q 64 14 confirmed confirm VBN cord-284810-fs5rx07q 64 15 COVID-19 covid-19 CD cord-284810-fs5rx07q 64 16 cases case NNS cord-284810-fs5rx07q 64 17 in in IN cord-284810-fs5rx07q 64 18 US US NNP cord-284810-fs5rx07q 64 19 counties county NNS cord-284810-fs5rx07q 64 20 on on IN cord-284810-fs5rx07q 64 21 March March NNP cord-284810-fs5rx07q 64 22 31 31 CD cord-284810-fs5rx07q 64 23 , , , cord-284810-fs5rx07q 64 24 2020 2020 CD cord-284810-fs5rx07q 64 25 . . . cord-284810-fs5rx07q 65 1 On on IN cord-284810-fs5rx07q 65 2 this this DT cord-284810-fs5rx07q 65 3 day day NN cord-284810-fs5rx07q 65 4 , , , cord-284810-fs5rx07q 65 5 2160 2160 CD cord-284810-fs5rx07q 65 6 counties county NNS cord-284810-fs5rx07q 65 7 were be VBD cord-284810-fs5rx07q 65 8 invaded invade VBN cord-284810-fs5rx07q 65 9 by by IN cord-284810-fs5rx07q 65 10 the the DT cord-284810-fs5rx07q 65 11 virus virus NN cord-284810-fs5rx07q 65 12 and and CC cord-284810-fs5rx07q 65 13 514 514 CD cord-284810-fs5rx07q 65 14 counties county NNS cord-284810-fs5rx07q 65 15 reported report VBN cord-284810-fs5rx07q 65 16 at at IN cord-284810-fs5rx07q 65 17 least least JJS cord-284810-fs5rx07q 65 18 on on IN cord-284810-fs5rx07q 65 19 death death NN cord-284810-fs5rx07q 65 20 . . . cord-284810-fs5rx07q 66 1 Epidemic epidemic NN cord-284810-fs5rx07q 66 2 prevalence prevalence NN cord-284810-fs5rx07q 66 3 varied varied JJ cord-284810-fs5rx07q 66 4 between between IN cord-284810-fs5rx07q 66 5 43 43 CD cord-284810-fs5rx07q 66 6 119 119 CD cord-284810-fs5rx07q 66 7 confirmed confirm VBN cord-284810-fs5rx07q 66 8 cases case NNS cord-284810-fs5rx07q 66 9 and and CC cord-284810-fs5rx07q 66 10 922 922 CD cord-284810-fs5rx07q 66 11 confirmed confirm VBD cord-284810-fs5rx07q 66 12 deaths death NNS cord-284810-fs5rx07q 66 13 in in IN cord-284810-fs5rx07q 66 14 New New NNP cord-284810-fs5rx07q 66 15 York York NNP cord-284810-fs5rx07q 66 16 City City NNP cord-284810-fs5rx07q 66 17 and and CC cord-284810-fs5rx07q 66 18 one one CD cord-284810-fs5rx07q 66 19 confirmed confirm VBD cord-284810-fs5rx07q 66 20 case case NN cord-284810-fs5rx07q 66 21 in in IN cord-284810-fs5rx07q 66 22 455 455 CD cord-284810-fs5rx07q 66 23 counties county NNS cord-284810-fs5rx07q 66 24 and and CC cord-284810-fs5rx07q 66 25 one one CD cord-284810-fs5rx07q 66 26 confirmed confirm VBD cord-284810-fs5rx07q 66 27 death death NN cord-284810-fs5rx07q 66 28 in in IN cord-284810-fs5rx07q 66 29 253 253 CD cord-284810-fs5rx07q 66 30 counties county NNS cord-284810-fs5rx07q 66 31 . . . cord-284810-fs5rx07q 67 1 Again again RB cord-284810-fs5rx07q 67 2 , , , cord-284810-fs5rx07q 67 3 we -PRON- PRP cord-284810-fs5rx07q 67 4 find find VBP cord-284810-fs5rx07q 67 5 that that IN cord-284810-fs5rx07q 67 6 the the DT cord-284810-fs5rx07q 67 7 distribution distribution NN cord-284810-fs5rx07q 67 8 of of IN cord-284810-fs5rx07q 67 9 confirmed confirm VBN cord-284810-fs5rx07q 67 10 cases case NNS cord-284810-fs5rx07q 67 11 follows follow VBZ cord-284810-fs5rx07q 67 12 a a DT cord-284810-fs5rx07q 67 13 power power NN cord-284810-fs5rx07q 67 14 - - HYPH cord-284810-fs5rx07q 67 15 law law NN cord-284810-fs5rx07q 67 16 over over IN cord-284810-fs5rx07q 67 17 several several JJ cord-284810-fs5rx07q 67 18 orders order NNS cord-284810-fs5rx07q 67 19 of of IN cord-284810-fs5rx07q 67 20 magnitude magnitude NN cord-284810-fs5rx07q 67 21 . . . cord-284810-fs5rx07q 68 1 Thus thus RB cord-284810-fs5rx07q 68 2 , , , cord-284810-fs5rx07q 68 3 although although IN cord-284810-fs5rx07q 68 4 the the DT cord-284810-fs5rx07q 68 5 two two CD cord-284810-fs5rx07q 68 6 datasets dataset NNS cord-284810-fs5rx07q 68 7 differ differ VBP cord-284810-fs5rx07q 68 8 greatly greatly RB cord-284810-fs5rx07q 68 9 in in IN cord-284810-fs5rx07q 68 10 spatial spatial JJ cord-284810-fs5rx07q 68 11 scale scale NN cord-284810-fs5rx07q 68 12 and and CC cord-284810-fs5rx07q 68 13 resolution resolution NN cord-284810-fs5rx07q 68 14 [ [ -LRB- cord-284810-fs5rx07q 68 15 168 168 CD cord-284810-fs5rx07q 68 16 invaded invade VBD cord-284810-fs5rx07q 68 17 countries country NNS cord-284810-fs5rx07q 68 18 in in IN cord-284810-fs5rx07q 68 19 Figs Figs NNP cord-284810-fs5rx07q 68 20 , , , cord-284810-fs5rx07q 68 21 we -PRON- PRP cord-284810-fs5rx07q 68 22 obtain obtain VBP cord-284810-fs5rx07q 68 23 somewhat somewhat RB cord-284810-fs5rx07q 68 24 larger large JJR cord-284810-fs5rx07q 68 25 slopes slope NNS cord-284810-fs5rx07q 68 26 of of IN cord-284810-fs5rx07q 68 27 µ µ NN cord-284810-fs5rx07q 68 28 C c NN cord-284810-fs5rx07q 68 29 = = SYM cord-284810-fs5rx07q 68 30 1.58 1.58 CD cord-284810-fs5rx07q 68 31 and and CC cord-284810-fs5rx07q 68 32 µ µ NN cord-284810-fs5rx07q 68 33 D d NN cord-284810-fs5rx07q 68 34 = = NN cord-284810-fs5rx07q 68 35 1.83 1.83 CD cord-284810-fs5rx07q 68 36 . . . cord-284810-fs5rx07q 69 1 A a DT cord-284810-fs5rx07q 69 2 more more RBR cord-284810-fs5rx07q 69 3 accurate accurate JJ cord-284810-fs5rx07q 69 4 estimation estimation NN cord-284810-fs5rx07q 69 5 of of IN cord-284810-fs5rx07q 69 6 the the DT cord-284810-fs5rx07q 69 7 critical critical JJ cord-284810-fs5rx07q 69 8 exponent exponent NN cord-284810-fs5rx07q 69 9 is be VBZ cord-284810-fs5rx07q 69 10 provided provide VBN cord-284810-fs5rx07q 69 11 by by IN cord-284810-fs5rx07q 69 12 a a DT cord-284810-fs5rx07q 69 13 maximum maximum JJ cord-284810-fs5rx07q 69 14 likelihood likelihood NN cord-284810-fs5rx07q 69 15 estimation estimation NN cord-284810-fs5rx07q 69 16 ( ( -LRB- cord-284810-fs5rx07q 69 17 see see VB cord-284810-fs5rx07q 69 18 Appendix Appendix NNP cord-284810-fs5rx07q 69 19 A A NNP cord-284810-fs5rx07q 69 20 ) ) -RRB- cord-284810-fs5rx07q 69 21 . . . cord-284810-fs5rx07q 70 1 Applying apply VBG cord-284810-fs5rx07q 70 2 this this DT cord-284810-fs5rx07q 70 3 approach approach NN cord-284810-fs5rx07q 70 4 to to IN cord-284810-fs5rx07q 70 5 the the DT cord-284810-fs5rx07q 70 6 country country NN cord-284810-fs5rx07q 70 7 - - HYPH cord-284810-fs5rx07q 70 8 level level NN cord-284810-fs5rx07q 70 9 COVID-19 covid-19 JJ cord-284810-fs5rx07q 70 10 distribution distribution NN cord-284810-fs5rx07q 70 11 yields yield NNS cord-284810-fs5rx07q 70 12 critical critical JJ cord-284810-fs5rx07q 70 13 exponents exponent NNS cord-284810-fs5rx07q 70 14 ofμ ofμ IN cord-284810-fs5rx07q 70 15 C c NN cord-284810-fs5rx07q 70 16 = = SYM cord-284810-fs5rx07q 70 17 1.14 1.14 CD cord-284810-fs5rx07q 71 1 ± ± NNP cord-284810-fs5rx07q 71 2 0.01 0.01 CD cord-284810-fs5rx07q 71 3 andμ andμ NNP cord-284810-fs5rx07q 71 4 D D NNP cord-284810-fs5rx07q 71 5 = = SYM cord-284810-fs5rx07q 71 6 1.50 1.50 CD cord-284810-fs5rx07q 71 7 ± ± CD cord-284810-fs5rx07q 71 8 0.05 0.05 CD cord-284810-fs5rx07q 71 9 . . . cord-284810-fs5rx07q 72 1 For for IN cord-284810-fs5rx07q 72 2 the the DT cord-284810-fs5rx07q 72 3 US US NNP cord-284810-fs5rx07q 72 4 - - HYPH cord-284810-fs5rx07q 72 5 county county NN cord-284810-fs5rx07q 72 6 distribution distribution NN cord-284810-fs5rx07q 72 7 , , , cord-284810-fs5rx07q 72 8 we -PRON- PRP cord-284810-fs5rx07q 72 9 obtain obtain VBP cord-284810-fs5rx07q 72 10 the the DT cord-284810-fs5rx07q 72 11 valueμ valueμ NNS cord-284810-fs5rx07q 72 12 C c NN cord-284810-fs5rx07q 72 13 = = NFP cord-284810-fs5rx07q 73 1 1.49 1.49 CD cord-284810-fs5rx07q 74 1 ± ± NNP cord-284810-fs5rx07q 74 2 0.01 0.01 CD cord-284810-fs5rx07q 74 3 andμ andμ NNP cord-284810-fs5rx07q 74 4 D D NNP cord-284810-fs5rx07q 74 5 = = NNP cord-284810-fs5rx07q 75 1 2.31 2.31 CD cord-284810-fs5rx07q 75 2 ± ± CD cord-284810-fs5rx07q 75 3 0.06 0.06 CD cord-284810-fs5rx07q 75 4 . . . cord-284810-fs5rx07q 76 1 These these DT cord-284810-fs5rx07q 76 2 exponents exponent NNS cord-284810-fs5rx07q 76 3 slightly slightly RB cord-284810-fs5rx07q 76 4 deviate deviate VBP cord-284810-fs5rx07q 76 5 from from IN cord-284810-fs5rx07q 76 6 those those DT cord-284810-fs5rx07q 76 7 obtained obtain VBN cord-284810-fs5rx07q 76 8 from from IN cord-284810-fs5rx07q 76 9 the the DT cord-284810-fs5rx07q 76 10 regression regression NN cord-284810-fs5rx07q 76 11 analysis analysis NN cord-284810-fs5rx07q 76 12 , , , cord-284810-fs5rx07q 76 13 but but CC cord-284810-fs5rx07q 76 14 are be VBP cord-284810-fs5rx07q 76 15 still still RB cord-284810-fs5rx07q 76 16 in in IN cord-284810-fs5rx07q 76 17 the the DT cord-284810-fs5rx07q 76 18 same same JJ cord-284810-fs5rx07q 76 19 ballpark ballpark NN cord-284810-fs5rx07q 76 20 . . . cord-284810-fs5rx07q 77 1 Given give VBN cord-284810-fs5rx07q 77 2 an an DT cord-284810-fs5rx07q 77 3 unbounded unbounded JJ cord-284810-fs5rx07q 77 4 power power NN cord-284810-fs5rx07q 77 5 - - HYPH cord-284810-fs5rx07q 77 6 law law NN cord-284810-fs5rx07q 77 7 distribution distribution NN cord-284810-fs5rx07q 77 8 P(n p(n NN cord-284810-fs5rx07q 77 9 ) ) -RRB- cord-284810-fs5rx07q 77 10 , , , cord-284810-fs5rx07q 77 11 the the DT cord-284810-fs5rx07q 77 12 cumulative cumulative JJ cord-284810-fs5rx07q 77 13 distribution distribution NN cord-284810-fs5rx07q 77 14 function function NN cord-284810-fs5rx07q 77 15 C(n C(n NNP cord-284810-fs5rx07q 77 16 ) ) -RRB- cord-284810-fs5rx07q 77 17 = = NFP cord-284810-fs5rx07q 78 1 ∞ ∞ NNP cord-284810-fs5rx07q 78 2 n n NNP cord-284810-fs5rx07q 78 3 P(n P(n NNP cord-284810-fs5rx07q 78 4 ) ) -RRB- cord-284810-fs5rx07q 79 1 dn dn NNP cord-284810-fs5rx07q 79 2 should should MD cord-284810-fs5rx07q 79 3 also also RB cord-284810-fs5rx07q 79 4 follow follow VB cord-284810-fs5rx07q 79 5 a a DT cord-284810-fs5rx07q 79 6 power power NN cord-284810-fs5rx07q 79 7 - - HYPH cord-284810-fs5rx07q 79 8 law law NN cord-284810-fs5rx07q 79 9 C(n C(n NNP cord-284810-fs5rx07q 79 10 ) ) -RRB- cord-284810-fs5rx07q 79 11 ∼ ∼ CC cord-284810-fs5rx07q 79 12 n n NN cord-284810-fs5rx07q 79 13 1−µ 1−µ CD cord-284810-fs5rx07q 79 14 . . . cord-284810-fs5rx07q 80 1 As as IN cord-284810-fs5rx07q 80 2 shown show VBN cord-284810-fs5rx07q 80 3 in in IN cord-284810-fs5rx07q 80 4 the the DT cord-284810-fs5rx07q 80 5 insets inset NNS cord-284810-fs5rx07q 80 6 in in IN cord-284810-fs5rx07q 80 7 Fig Fig NNP cord-284810-fs5rx07q 80 8 . . . cord-284810-fs5rx07q 81 1 1 1 LS cord-284810-fs5rx07q 81 2 , , , cord-284810-fs5rx07q 81 3 this this DT cord-284810-fs5rx07q 81 4 is be VBZ cord-284810-fs5rx07q 81 5 not not RB cord-284810-fs5rx07q 81 6 the the DT cord-284810-fs5rx07q 81 7 case case NN cord-284810-fs5rx07q 81 8 for for IN cord-284810-fs5rx07q 81 9 the the DT cord-284810-fs5rx07q 81 10 distribution distribution NN cord-284810-fs5rx07q 81 11 of of IN cord-284810-fs5rx07q 81 12 COVID-19 covid-19 JJ cord-284810-fs5rx07q 81 13 cases case NNS cord-284810-fs5rx07q 81 14 , , , cord-284810-fs5rx07q 81 15 for for IN cord-284810-fs5rx07q 81 16 which which WDT cord-284810-fs5rx07q 81 17 the the DT cord-284810-fs5rx07q 81 18 cumulative cumulative JJ cord-284810-fs5rx07q 81 19 fraction fraction NN cord-284810-fs5rx07q 81 20 C(n C(n NNP cord-284810-fs5rx07q 81 21 ) ) -RRB- cord-284810-fs5rx07q 81 22 = = NFP cord-284810-fs5rx07q 82 1 N n NN cord-284810-fs5rx07q 82 2 m m NN cord-284810-fs5rx07q 82 3 = = SYM cord-284810-fs5rx07q 82 4 n+1 n+1 NN cord-284810-fs5rx07q 82 5 P(m P(m NNP cord-284810-fs5rx07q 82 6 ) ) -RRB- cord-284810-fs5rx07q 82 7 of of IN cord-284810-fs5rx07q 82 8 countries country NNS cord-284810-fs5rx07q 82 9 , , , cord-284810-fs5rx07q 82 10 or or CC cord-284810-fs5rx07q 82 11 counties county NNS cord-284810-fs5rx07q 82 12 , , , cord-284810-fs5rx07q 82 13 with with IN cord-284810-fs5rx07q 82 14 case case NN cord-284810-fs5rx07q 82 15 number number NN cord-284810-fs5rx07q 82 16 m m NN cord-284810-fs5rx07q 82 17 > > XX cord-284810-fs5rx07q 82 18 n n NN cord-284810-fs5rx07q 82 19 do do VBP cord-284810-fs5rx07q 82 20 not not RB cord-284810-fs5rx07q 82 21 really really RB cord-284810-fs5rx07q 82 22 follow follow VB cord-284810-fs5rx07q 82 23 a a DT cord-284810-fs5rx07q 82 24 straight straight JJ cord-284810-fs5rx07q 82 25 line line NN cord-284810-fs5rx07q 82 26 in in IN cord-284810-fs5rx07q 82 27 a a DT cord-284810-fs5rx07q 82 28 double double JJ cord-284810-fs5rx07q 82 29 logarithmic logarithmic JJ cord-284810-fs5rx07q 82 30 plot plot NN cord-284810-fs5rx07q 82 31 . . . cord-284810-fs5rx07q 83 1 Instead instead RB cord-284810-fs5rx07q 83 2 , , , cord-284810-fs5rx07q 83 3 they -PRON- PRP cord-284810-fs5rx07q 83 4 are be VBP cord-284810-fs5rx07q 83 5 better well RBR cord-284810-fs5rx07q 83 6 described describe VBN cord-284810-fs5rx07q 83 7 by by IN cord-284810-fs5rx07q 83 8 the the DT cord-284810-fs5rx07q 83 9 cumulative cumulative JJ cord-284810-fs5rx07q 83 10 distribution distribution NN cord-284810-fs5rx07q 83 11 function function NN cord-284810-fs5rx07q 83 12 Eq Eq NNP cord-284810-fs5rx07q 83 13 . . . cord-284810-fs5rx07q 84 1 ( ( -LRB- cord-284810-fs5rx07q 84 2 A2 A2 NNP cord-284810-fs5rx07q 84 3 ) ) -RRB- cord-284810-fs5rx07q 84 4 of of IN cord-284810-fs5rx07q 84 5 a a DT cord-284810-fs5rx07q 84 6 truncated truncated JJ cord-284810-fs5rx07q 84 7 power power NN cord-284810-fs5rx07q 84 8 - - HYPH cord-284810-fs5rx07q 84 9 law law NN cord-284810-fs5rx07q 84 10 , , , cord-284810-fs5rx07q 84 11 that that RB cord-284810-fs5rx07q 84 12 is is RB cord-284810-fs5rx07q 84 13 , , , cord-284810-fs5rx07q 84 14 a a DT cord-284810-fs5rx07q 84 15 power power NN cord-284810-fs5rx07q 84 16 - - HYPH cord-284810-fs5rx07q 84 17 law law NN cord-284810-fs5rx07q 84 18 distribution distribution NN cord-284810-fs5rx07q 84 19 with with IN cord-284810-fs5rx07q 84 20 an an DT cord-284810-fs5rx07q 84 21 upper upper JJ cord-284810-fs5rx07q 84 22 bound bind VBN cord-284810-fs5rx07q 84 23 n n NN cord-284810-fs5rx07q 84 24 max max NN cord-284810-fs5rx07q 84 25 for for IN cord-284810-fs5rx07q 84 26 the the DT cord-284810-fs5rx07q 84 27 number number NN cord-284810-fs5rx07q 84 28 of of IN cord-284810-fs5rx07q 84 29 cases case NNS cord-284810-fs5rx07q 84 30 , , , cord-284810-fs5rx07q 84 31 Eq Eq NNP cord-284810-fs5rx07q 84 32 . . . cord-284810-fs5rx07q 85 1 ( ( -LRB- cord-284810-fs5rx07q 85 2 1 1 LS cord-284810-fs5rx07q 85 3 ) ) -RRB- cord-284810-fs5rx07q 85 4 ( ( -LRB- cord-284810-fs5rx07q 85 5 see see VB cord-284810-fs5rx07q 85 6 Appendix Appendix NNP cord-284810-fs5rx07q 85 7 A A NNP cord-284810-fs5rx07q 85 8 and and CC cord-284810-fs5rx07q 85 9 Fig Fig NNP cord-284810-fs5rx07q 85 10 . . NNP cord-284810-fs5rx07q 85 11 5 5 CD cord-284810-fs5rx07q 85 12 ) ) -RRB- cord-284810-fs5rx07q 85 13 . . . cord-284810-fs5rx07q 86 1 This this DT cord-284810-fs5rx07q 86 2 indication indication NN cord-284810-fs5rx07q 86 3 for for IN cord-284810-fs5rx07q 86 4 the the DT cord-284810-fs5rx07q 86 5 presence presence NN cord-284810-fs5rx07q 86 6 of of IN cord-284810-fs5rx07q 86 7 a a DT cord-284810-fs5rx07q 86 8 truncated truncated JJ cord-284810-fs5rx07q 86 9 power power NN cord-284810-fs5rx07q 86 10 - - HYPH cord-284810-fs5rx07q 86 11 law law NN cord-284810-fs5rx07q 86 12 distribution distribution NN cord-284810-fs5rx07q 86 13 also also RB cord-284810-fs5rx07q 86 14 conforms conform VBZ cord-284810-fs5rx07q 86 15 with with IN cord-284810-fs5rx07q 86 16 our -PRON- PRP$ cord-284810-fs5rx07q 86 17 theoretical theoretical JJ cord-284810-fs5rx07q 86 18 analysis analysis NN cord-284810-fs5rx07q 86 19 below below RB cord-284810-fs5rx07q 86 20 . . . cord-284810-fs5rx07q 87 1 However however RB cord-284810-fs5rx07q 87 2 , , , cord-284810-fs5rx07q 87 3 we -PRON- PRP cord-284810-fs5rx07q 87 4 note note VBP cord-284810-fs5rx07q 87 5 that that IN cord-284810-fs5rx07q 87 6 although although IN cord-284810-fs5rx07q 87 7 the the DT cord-284810-fs5rx07q 87 8 shape shape NN cord-284810-fs5rx07q 87 9 of of IN cord-284810-fs5rx07q 87 10 the the DT cord-284810-fs5rx07q 87 11 empirically empirically RB cord-284810-fs5rx07q 87 12 obtained obtain VBN cord-284810-fs5rx07q 87 13 C(n c(n CD cord-284810-fs5rx07q 87 14 ) ) -RRB- cord-284810-fs5rx07q 87 15 overall overall NN cord-284810-fs5rx07q 87 16 follows follow VBZ cord-284810-fs5rx07q 87 17 the the DT cord-284810-fs5rx07q 87 18 curve curve NN cord-284810-fs5rx07q 87 19 of of IN cord-284810-fs5rx07q 87 20 a a DT cord-284810-fs5rx07q 87 21 truncated truncated JJ cord-284810-fs5rx07q 87 22 power power NN cord-284810-fs5rx07q 87 23 - - HYPH cord-284810-fs5rx07q 87 24 law law NN cord-284810-fs5rx07q 87 25 distribution distribution NN cord-284810-fs5rx07q 87 26 , , , cord-284810-fs5rx07q 87 27 there there EX cord-284810-fs5rx07q 87 28 is be VBZ cord-284810-fs5rx07q 87 29 a a DT cord-284810-fs5rx07q 87 30 considerable considerable JJ cord-284810-fs5rx07q 87 31 wavering wavering NN cord-284810-fs5rx07q 87 32 around around IN cord-284810-fs5rx07q 87 33 the the DT cord-284810-fs5rx07q 87 34 theoretical theoretical JJ cord-284810-fs5rx07q 87 35 curve curve NN cord-284810-fs5rx07q 87 36 ( ( -LRB- cord-284810-fs5rx07q 87 37 compare compare VB cord-284810-fs5rx07q 87 38 blue blue JJ cord-284810-fs5rx07q 87 39 circles circle NNS cord-284810-fs5rx07q 87 40 and and CC cord-284810-fs5rx07q 87 41 black black JJ cord-284810-fs5rx07q 87 42 lines line NNS cord-284810-fs5rx07q 87 43 in in IN cord-284810-fs5rx07q 87 44 Fig Fig NNP cord-284810-fs5rx07q 87 45 . . . cord-284810-fs5rx07q 87 46 1 1 CD cord-284810-fs5rx07q 87 47 insets inset NNS cord-284810-fs5rx07q 87 48 ) ) -RRB- cord-284810-fs5rx07q 87 49 . . . cord-284810-fs5rx07q 88 1 Thus thus RB cord-284810-fs5rx07q 88 2 , , , cord-284810-fs5rx07q 88 3 a a DT cord-284810-fs5rx07q 88 4 rigorous rigorous JJ cord-284810-fs5rx07q 88 5 hypothesis hypothesis NN cord-284810-fs5rx07q 88 6 testing testing NN cord-284810-fs5rx07q 88 7 with with IN cord-284810-fs5rx07q 88 8 Monte Monte NNP cord-284810-fs5rx07q 88 9 Carlo Carlo NNP cord-284810-fs5rx07q 88 10 simulations simulation NNS cord-284810-fs5rx07q 88 11 , , , cord-284810-fs5rx07q 88 12 11,13 11,13 CD cord-284810-fs5rx07q 88 13 which which WDT cord-284810-fs5rx07q 88 14 does do VBZ cord-284810-fs5rx07q 88 15 not not RB cord-284810-fs5rx07q 88 16 take take VB cord-284810-fs5rx07q 88 17 disturbances disturbance NNS cord-284810-fs5rx07q 88 18 due due JJ cord-284810-fs5rx07q 88 19 to to IN cord-284810-fs5rx07q 88 20 additional additional JJ cord-284810-fs5rx07q 88 21 irregularities irregularity NNS cord-284810-fs5rx07q 88 22 ( ( -LRB- cord-284810-fs5rx07q 88 23 e.g. e.g. RB cord-284810-fs5rx07q 88 24 , , , cord-284810-fs5rx07q 88 25 heterogeneities heterogeneity NNS cord-284810-fs5rx07q 88 26 in in IN cord-284810-fs5rx07q 88 27 country country NN cord-284810-fs5rx07q 88 28 sizes size NNS cord-284810-fs5rx07q 88 29 or or CC cord-284810-fs5rx07q 88 30 containment containment NN cord-284810-fs5rx07q 88 31 measures measure NNS cord-284810-fs5rx07q 88 32 ) ) -RRB- cord-284810-fs5rx07q 88 33 fully fully RB cord-284810-fs5rx07q 88 34 into into IN cord-284810-fs5rx07q 88 35 account account NN cord-284810-fs5rx07q 88 36 , , , cord-284810-fs5rx07q 88 37 will will MD cord-284810-fs5rx07q 88 38 always always RB cord-284810-fs5rx07q 88 39 reject reject VB cord-284810-fs5rx07q 88 40 the the DT cord-284810-fs5rx07q 88 41 hypothesis hypothesis NN cord-284810-fs5rx07q 88 42 of of IN cord-284810-fs5rx07q 88 43 a a DT cord-284810-fs5rx07q 88 44 perfect perfect JJ cord-284810-fs5rx07q 88 45 truncated truncated JJ cord-284810-fs5rx07q 88 46 power power NN cord-284810-fs5rx07q 88 47 - - HYPH cord-284810-fs5rx07q 88 48 law law NN cord-284810-fs5rx07q 88 49 as as IN cord-284810-fs5rx07q 88 50 the the DT cord-284810-fs5rx07q 88 51 true true JJ cord-284810-fs5rx07q 88 52 underlying underlying JJ cord-284810-fs5rx07q 88 53 distribution distribution NN cord-284810-fs5rx07q 88 54 . . . cord-284810-fs5rx07q 89 1 The the DT cord-284810-fs5rx07q 89 2 presence presence NN cord-284810-fs5rx07q 89 3 of of IN cord-284810-fs5rx07q 89 4 a a DT cord-284810-fs5rx07q 89 5 power power NN cord-284810-fs5rx07q 89 6 - - HYPH cord-284810-fs5rx07q 89 7 law law NN cord-284810-fs5rx07q 89 8 distribution distribution NN cord-284810-fs5rx07q 89 9 means mean VBZ cord-284810-fs5rx07q 89 10 that that IN cord-284810-fs5rx07q 89 11 global global JJ cord-284810-fs5rx07q 89 12 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 89 13 prevalence prevalence NN cord-284810-fs5rx07q 89 14 patterns pattern NNS cord-284810-fs5rx07q 89 15 are be VBP cord-284810-fs5rx07q 89 16 characterized characterize VBN cord-284810-fs5rx07q 89 17 by by IN cord-284810-fs5rx07q 89 18 a a DT cord-284810-fs5rx07q 89 19 small small JJ cord-284810-fs5rx07q 89 20 number number NN cord-284810-fs5rx07q 89 21 of of IN cord-284810-fs5rx07q 89 22 countries country NNS cord-284810-fs5rx07q 89 23 with with IN cord-284810-fs5rx07q 89 24 huge huge JJ cord-284810-fs5rx07q 89 25 epidemic epidemic NN cord-284810-fs5rx07q 89 26 prevalence prevalence NN cord-284810-fs5rx07q 89 27 ( ( -LRB- cord-284810-fs5rx07q 89 28 the the DT cord-284810-fs5rx07q 89 29 long long JJ cord-284810-fs5rx07q 89 30 tail tail NN cord-284810-fs5rx07q 89 31 of of IN cord-284810-fs5rx07q 89 32 the the DT cord-284810-fs5rx07q 89 33 distribution distribution NN cord-284810-fs5rx07q 89 34 ) ) -RRB- cord-284810-fs5rx07q 89 35 and and CC cord-284810-fs5rx07q 89 36 a a DT cord-284810-fs5rx07q 89 37 large large JJ cord-284810-fs5rx07q 89 38 number number NN cord-284810-fs5rx07q 89 39 of of IN cord-284810-fs5rx07q 89 40 countries country NNS cord-284810-fs5rx07q 89 41 that that WDT cord-284810-fs5rx07q 89 42 are be VBP cord-284810-fs5rx07q 89 43 ( ( -LRB- cord-284810-fs5rx07q 89 44 yet yet RB cord-284810-fs5rx07q 89 45 ) ) -RRB- cord-284810-fs5rx07q 89 46 barely barely RB cord-284810-fs5rx07q 89 47 affected affect VBN cord-284810-fs5rx07q 89 48 by by IN cord-284810-fs5rx07q 89 49 the the DT cord-284810-fs5rx07q 89 50 disease disease NN cord-284810-fs5rx07q 89 51 . . . cord-284810-fs5rx07q 90 1 In in IN cord-284810-fs5rx07q 90 2 between between IN cord-284810-fs5rx07q 90 3 these these DT cord-284810-fs5rx07q 90 4 two two CD cord-284810-fs5rx07q 90 5 extremes extreme NNS cord-284810-fs5rx07q 90 6 , , , cord-284810-fs5rx07q 90 7 there there EX cord-284810-fs5rx07q 90 8 is be VBZ cord-284810-fs5rx07q 90 9 a a DT cord-284810-fs5rx07q 90 10 smooth smooth JJ cord-284810-fs5rx07q 90 11 transition transition NN cord-284810-fs5rx07q 90 12 and and CC cord-284810-fs5rx07q 90 13 this this DT cord-284810-fs5rx07q 90 14 transition transition NN cord-284810-fs5rx07q 90 15 is be VBZ cord-284810-fs5rx07q 90 16 scale scale NN cord-284810-fs5rx07q 90 17 - - HYPH cord-284810-fs5rx07q 90 18 free free JJ cord-284810-fs5rx07q 90 19 , , , cord-284810-fs5rx07q 90 20 that that RB cord-284810-fs5rx07q 90 21 is is RB cord-284810-fs5rx07q 90 22 , , , cord-284810-fs5rx07q 90 23 the the DT cord-284810-fs5rx07q 90 24 amplification amplification NN cord-284810-fs5rx07q 90 25 in in IN cord-284810-fs5rx07q 90 26 the the DT cord-284810-fs5rx07q 90 27 number number NN cord-284810-fs5rx07q 90 28 of of IN cord-284810-fs5rx07q 90 29 countries country NNS cord-284810-fs5rx07q 90 30 ( ( -LRB- cord-284810-fs5rx07q 90 31 or or CC cord-284810-fs5rx07q 90 32 counties county NNS cord-284810-fs5rx07q 90 33 ) ) -RRB- cord-284810-fs5rx07q 90 34 with with IN cord-284810-fs5rx07q 90 35 decreasing decrease VBG cord-284810-fs5rx07q 90 36 number number NN cord-284810-fs5rx07q 90 37 of of IN cord-284810-fs5rx07q 90 38 cases case NNS cord-284810-fs5rx07q 90 39 is be VBZ cord-284810-fs5rx07q 90 40 the the DT cord-284810-fs5rx07q 90 41 same same JJ cord-284810-fs5rx07q 90 42 at at IN cord-284810-fs5rx07q 90 43 all all DT cord-284810-fs5rx07q 90 44 scales scale NNS cord-284810-fs5rx07q 90 45 . . . cord-284810-fs5rx07q 91 1 In in IN cord-284810-fs5rx07q 91 2 general general JJ cord-284810-fs5rx07q 91 3 , , , cord-284810-fs5rx07q 91 4 the the DT cord-284810-fs5rx07q 91 5 obtained obtain VBN cord-284810-fs5rx07q 91 6 critical critical JJ cord-284810-fs5rx07q 91 7 exponents exponent NNS cord-284810-fs5rx07q 91 8 are be VBP cord-284810-fs5rx07q 91 9 rather rather RB cord-284810-fs5rx07q 91 10 small small JJ cord-284810-fs5rx07q 91 11 . . . cord-284810-fs5rx07q 92 1 While while IN cord-284810-fs5rx07q 92 2 for for IN cord-284810-fs5rx07q 92 3 most most JJS cord-284810-fs5rx07q 92 4 natural natural JJ cord-284810-fs5rx07q 92 5 power power NN cord-284810-fs5rx07q 92 6 - - HYPH cord-284810-fs5rx07q 92 7 law law NN cord-284810-fs5rx07q 92 8 distributions distribution NNS cord-284810-fs5rx07q 92 9 critical critical JJ cord-284810-fs5rx07q 92 10 exponents exponent NNS cord-284810-fs5rx07q 92 11 are be VBP cord-284810-fs5rx07q 92 12 around around IN cord-284810-fs5rx07q 92 13 µ µ NN cord-284810-fs5rx07q 92 14 ≈ ≈ NNP cord-284810-fs5rx07q 92 15 2 2 CD cord-284810-fs5rx07q 92 16 , , , cord-284810-fs5rx07q 92 17 here here RB cord-284810-fs5rx07q 92 18 we -PRON- PRP cord-284810-fs5rx07q 92 19 estimate estimate VBP cord-284810-fs5rx07q 92 20 exponents exponent NNS cord-284810-fs5rx07q 92 21 that that WDT cord-284810-fs5rx07q 92 22 are be VBP cord-284810-fs5rx07q 92 23 clearly clearly RB cord-284810-fs5rx07q 92 24 below below IN cord-284810-fs5rx07q 92 25 two two CD cord-284810-fs5rx07q 92 26 , , , cord-284810-fs5rx07q 92 27 µ µ NN cord-284810-fs5rx07q 92 28 < < XX cord-284810-fs5rx07q 92 29 2 2 CD cord-284810-fs5rx07q 92 30 , , , cord-284810-fs5rx07q 92 31 indicating indicate VBG cord-284810-fs5rx07q 92 32 a a DT cord-284810-fs5rx07q 92 33 very very RB cord-284810-fs5rx07q 92 34 broad broad JJ cord-284810-fs5rx07q 92 35 distribution distribution NN cord-284810-fs5rx07q 92 36 for for IN cord-284810-fs5rx07q 92 37 which which WDT cord-284810-fs5rx07q 92 38 in in IN cord-284810-fs5rx07q 92 39 the the DT cord-284810-fs5rx07q 92 40 absence absence NN cord-284810-fs5rx07q 92 41 of of IN cord-284810-fs5rx07q 92 42 an an DT cord-284810-fs5rx07q 92 43 upper upper JJ cord-284810-fs5rx07q 92 44 bound bind VBN cord-284810-fs5rx07q 92 45 , , , cord-284810-fs5rx07q 92 46 the the DT cord-284810-fs5rx07q 92 47 mean mean JJ cord-284810-fs5rx07q 92 48 value value NN cord-284810-fs5rx07q 92 49 diverges diverge VBZ cord-284810-fs5rx07q 92 50 . . . cord-284810-fs5rx07q 93 1 While while IN cord-284810-fs5rx07q 93 2 the the DT cord-284810-fs5rx07q 93 3 present present JJ cord-284810-fs5rx07q 93 4 analysis analysis NN cord-284810-fs5rx07q 93 5 considers consider VBZ cord-284810-fs5rx07q 93 6 the the DT cord-284810-fs5rx07q 93 7 distribution distribution NN cord-284810-fs5rx07q 93 8 of of IN cord-284810-fs5rx07q 93 9 case case NN cord-284810-fs5rx07q 93 10 numbers number NNS cord-284810-fs5rx07q 93 11 at at IN cord-284810-fs5rx07q 93 12 a a DT cord-284810-fs5rx07q 93 13 temporal temporal JJ cord-284810-fs5rx07q 93 14 snapshot snapshot NN cord-284810-fs5rx07q 93 15 , , , cord-284810-fs5rx07q 93 16 in in IN cord-284810-fs5rx07q 93 17 reality reality NN cord-284810-fs5rx07q 93 18 the the DT cord-284810-fs5rx07q 93 19 pandemic pandemic NN cord-284810-fs5rx07q 93 20 is be VBZ cord-284810-fs5rx07q 93 21 a a DT cord-284810-fs5rx07q 93 22 dynamic dynamic JJ cord-284810-fs5rx07q 93 23 process process NN cord-284810-fs5rx07q 93 24 successively successively RB cord-284810-fs5rx07q 93 25 invading invade VBG cord-284810-fs5rx07q 93 26 countries country NNS cord-284810-fs5rx07q 93 27 worldwide worldwide RB cord-284810-fs5rx07q 93 28 . . . cord-284810-fs5rx07q 94 1 In in IN cord-284810-fs5rx07q 94 2 Fig Fig NNP cord-284810-fs5rx07q 94 3 . . . cord-284810-fs5rx07q 95 1 2 2 LS cord-284810-fs5rx07q 95 2 , , , cord-284810-fs5rx07q 95 3 we -PRON- PRP cord-284810-fs5rx07q 95 4 investigate investigate VBP cord-284810-fs5rx07q 95 5 the the DT cord-284810-fs5rx07q 95 6 temporal temporal JJ cord-284810-fs5rx07q 95 7 development development NN cord-284810-fs5rx07q 95 8 of of IN cord-284810-fs5rx07q 95 9 the the DT cord-284810-fs5rx07q 95 10 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 95 11 distribution distribution NN cord-284810-fs5rx07q 95 12 . . . cord-284810-fs5rx07q 96 1 The the DT cord-284810-fs5rx07q 96 2 figure figure NN cord-284810-fs5rx07q 96 3 shows show VBZ cord-284810-fs5rx07q 96 4 that that IN cord-284810-fs5rx07q 96 5 the the DT cord-284810-fs5rx07q 96 6 country country NN cord-284810-fs5rx07q 96 7 - - HYPH cord-284810-fs5rx07q 96 8 level level NN cord-284810-fs5rx07q 96 9 distribution distribution NN cord-284810-fs5rx07q 96 10 of of IN cord-284810-fs5rx07q 96 11 confirmed confirm VBN cord-284810-fs5rx07q 96 12 cases case NNS cord-284810-fs5rx07q 96 13 is be VBZ cord-284810-fs5rx07q 96 14 formed form VBN cord-284810-fs5rx07q 96 15 already already RB cord-284810-fs5rx07q 96 16 within within IN cord-284810-fs5rx07q 96 17 a a DT cord-284810-fs5rx07q 96 18 few few JJ cord-284810-fs5rx07q 96 19 weeks week NNS cord-284810-fs5rx07q 96 20 from from IN cord-284810-fs5rx07q 96 21 the the DT cord-284810-fs5rx07q 96 22 start start NN cord-284810-fs5rx07q 96 23 of of IN cord-284810-fs5rx07q 96 24 the the DT cord-284810-fs5rx07q 96 25 outbreak outbreak NN cord-284810-fs5rx07q 96 26 and and CC cord-284810-fs5rx07q 96 27 remains remain VBZ cord-284810-fs5rx07q 96 28 roughly roughly RB cord-284810-fs5rx07q 96 29 stationary stationary JJ cord-284810-fs5rx07q 96 30 over over IN cord-284810-fs5rx07q 96 31 the the DT cord-284810-fs5rx07q 96 32 considered consider VBN cord-284810-fs5rx07q 96 33 time time NN cord-284810-fs5rx07q 96 34 interval interval NN cord-284810-fs5rx07q 96 35 of of IN cord-284810-fs5rx07q 96 36 75 75 CD cord-284810-fs5rx07q 96 37 days day NNS cord-284810-fs5rx07q 96 38 . . . cord-284810-fs5rx07q 97 1 A a DT cord-284810-fs5rx07q 97 2 closer close JJR cord-284810-fs5rx07q 97 3 inspection inspection NN cord-284810-fs5rx07q 97 4 ( ( -LRB- cord-284810-fs5rx07q 97 5 see see VB cord-284810-fs5rx07q 97 6 inset inset NN cord-284810-fs5rx07q 97 7 in in IN cord-284810-fs5rx07q 97 8 Fig Fig NNP cord-284810-fs5rx07q 97 9 reveals reveal VBZ cord-284810-fs5rx07q 97 10 that that IN cord-284810-fs5rx07q 97 11 the the DT cord-284810-fs5rx07q 97 12 critical critical JJ cord-284810-fs5rx07q 97 13 exponents exponent NNS cord-284810-fs5rx07q 97 14 in in IN cord-284810-fs5rx07q 97 15 fact fact NN cord-284810-fs5rx07q 97 16 are be VBP cord-284810-fs5rx07q 97 17 not not RB cord-284810-fs5rx07q 97 18 constant constant JJ cord-284810-fs5rx07q 97 19 , , , cord-284810-fs5rx07q 97 20 but but CC cord-284810-fs5rx07q 97 21 in in IN cord-284810-fs5rx07q 97 22 general general JJ cord-284810-fs5rx07q 97 23 are be VBP cord-284810-fs5rx07q 97 24 decreasing decrease VBG cord-284810-fs5rx07q 97 25 functions function NNS cord-284810-fs5rx07q 97 26 of of IN cord-284810-fs5rx07q 97 27 time time NN cord-284810-fs5rx07q 97 28 , , , cord-284810-fs5rx07q 97 29 indicating indicate VBG cord-284810-fs5rx07q 97 30 that that IN cord-284810-fs5rx07q 97 31 the the DT cord-284810-fs5rx07q 97 32 case case NN cord-284810-fs5rx07q 97 33 distributions distribution NNS cord-284810-fs5rx07q 97 34 tend tend VBP cord-284810-fs5rx07q 97 35 to to TO cord-284810-fs5rx07q 97 36 broaden broaden VB cord-284810-fs5rx07q 97 37 over over IN cord-284810-fs5rx07q 97 38 the the DT cord-284810-fs5rx07q 97 39 course course NN cord-284810-fs5rx07q 97 40 of of IN cord-284810-fs5rx07q 97 41 the the DT cord-284810-fs5rx07q 97 42 pandemic pandemic NN cord-284810-fs5rx07q 97 43 . . . cord-284810-fs5rx07q 98 1 Figure figure NN cord-284810-fs5rx07q 98 2 2 2 CD cord-284810-fs5rx07q 99 1 ( ( -LRB- cord-284810-fs5rx07q 99 2 b b LS cord-284810-fs5rx07q 99 3 ) ) -RRB- cord-284810-fs5rx07q 99 4 further further RB cord-284810-fs5rx07q 99 5 investigates investigate VBZ cord-284810-fs5rx07q 99 6 the the DT cord-284810-fs5rx07q 99 7 spatial spatial JJ cord-284810-fs5rx07q 99 8 spread spread NN cord-284810-fs5rx07q 99 9 of of IN cord-284810-fs5rx07q 99 10 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 99 11 across across IN cord-284810-fs5rx07q 99 12 countries country NNS cord-284810-fs5rx07q 99 13 worldwide worldwide RB cord-284810-fs5rx07q 99 14 more more RBR cord-284810-fs5rx07q 99 15 systematically systematically RB cord-284810-fs5rx07q 99 16 . . . cord-284810-fs5rx07q 100 1 The the DT cord-284810-fs5rx07q 100 2 figure figure NN cord-284810-fs5rx07q 100 3 plots plot VBZ cord-284810-fs5rx07q 100 4 the the DT cord-284810-fs5rx07q 100 5 number number NN cord-284810-fs5rx07q 100 6 of of IN cord-284810-fs5rx07q 100 7 countries country NNS cord-284810-fs5rx07q 100 8 that that WDT cord-284810-fs5rx07q 100 9 were be VBD cord-284810-fs5rx07q 100 10 invaded invade VBN cord-284810-fs5rx07q 100 11 by by IN cord-284810-fs5rx07q 100 12 the the DT cord-284810-fs5rx07q 100 13 coronavirus coronavirus NN cord-284810-fs5rx07q 100 14 ( ( -LRB- cord-284810-fs5rx07q 100 15 i.e. i.e. FW cord-284810-fs5rx07q 100 16 , , , cord-284810-fs5rx07q 100 17 having have VBG cord-284810-fs5rx07q 100 18 the the DT cord-284810-fs5rx07q 100 19 first first JJ cord-284810-fs5rx07q 100 20 confirmed confirm VBN cord-284810-fs5rx07q 100 21 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 100 22 case case NN cord-284810-fs5rx07q 100 23 ) ) -RRB- cord-284810-fs5rx07q 100 24 at at IN cord-284810-fs5rx07q 100 25 a a DT cord-284810-fs5rx07q 100 26 particular particular JJ cord-284810-fs5rx07q 100 27 day day NN cord-284810-fs5rx07q 100 28 in in IN cord-284810-fs5rx07q 100 29 the the DT cord-284810-fs5rx07q 100 30 time time NN cord-284810-fs5rx07q 100 31 span span NN cord-284810-fs5rx07q 100 32 from from IN cord-284810-fs5rx07q 100 33 January January NNP cord-284810-fs5rx07q 100 34 22 22 CD cord-284810-fs5rx07q 100 35 to to IN cord-284810-fs5rx07q 100 36 April April NNP cord-284810-fs5rx07q 100 37 5 5 CD cord-284810-fs5rx07q 100 38 , , , cord-284810-fs5rx07q 100 39 2020 2020 CD cord-284810-fs5rx07q 100 40 . . . cord-284810-fs5rx07q 101 1 On on IN cord-284810-fs5rx07q 101 2 January January NNP cord-284810-fs5rx07q 101 3 22 22 CD cord-284810-fs5rx07q 101 4 , , , cord-284810-fs5rx07q 101 5 the the DT cord-284810-fs5rx07q 101 6 first first JJ cord-284810-fs5rx07q 101 7 entry entry NN cord-284810-fs5rx07q 101 8 in in IN cord-284810-fs5rx07q 101 9 the the DT cord-284810-fs5rx07q 101 10 database database NN cord-284810-fs5rx07q 101 11 , , , cord-284810-fs5rx07q 101 12 six six CD cord-284810-fs5rx07q 101 13 countries country NNS cord-284810-fs5rx07q 101 14 ( ( -LRB- cord-284810-fs5rx07q 101 15 China China NNP cord-284810-fs5rx07q 101 16 , , , cord-284810-fs5rx07q 101 17 Japan Japan NNP cord-284810-fs5rx07q 101 18 , , , cord-284810-fs5rx07q 101 19 South South NNP cord-284810-fs5rx07q 101 20 Korea Korea NNP cord-284810-fs5rx07q 101 21 , , , cord-284810-fs5rx07q 101 22 Taiwan Taiwan NNP cord-284810-fs5rx07q 101 23 , , , cord-284810-fs5rx07q 101 24 Thailand Thailand NNP cord-284810-fs5rx07q 101 25 , , , cord-284810-fs5rx07q 101 26 US US NNP cord-284810-fs5rx07q 101 27 ) ) -RRB- cord-284810-fs5rx07q 101 28 were be VBD cord-284810-fs5rx07q 101 29 already already RB cord-284810-fs5rx07q 101 30 invaded invade VBN cord-284810-fs5rx07q 101 31 by by IN cord-284810-fs5rx07q 101 32 the the DT cord-284810-fs5rx07q 101 33 virus virus NN cord-284810-fs5rx07q 101 34 . . . cord-284810-fs5rx07q 102 1 From from IN cord-284810-fs5rx07q 102 2 this this DT cord-284810-fs5rx07q 102 3 day day NN cord-284810-fs5rx07q 102 4 , , , cord-284810-fs5rx07q 102 5 within within IN cord-284810-fs5rx07q 102 6 roughly roughly RB cord-284810-fs5rx07q 102 7 two two CD cord-284810-fs5rx07q 102 8 months month NNS cord-284810-fs5rx07q 102 9 , , , cord-284810-fs5rx07q 102 10 the the DT cord-284810-fs5rx07q 102 11 pandemic pandemic NN cord-284810-fs5rx07q 102 12 spread spread VBD cord-284810-fs5rx07q 102 13 to to IN cord-284810-fs5rx07q 102 14 nearly nearly RB cord-284810-fs5rx07q 102 15 every every DT cord-284810-fs5rx07q 102 16 country country NN cord-284810-fs5rx07q 102 17 in in IN cord-284810-fs5rx07q 102 18 the the DT cord-284810-fs5rx07q 102 19 world world NN cord-284810-fs5rx07q 102 20 . . . cord-284810-fs5rx07q 103 1 Interestingly interestingly RB cord-284810-fs5rx07q 103 2 , , , cord-284810-fs5rx07q 103 3 the the DT cord-284810-fs5rx07q 103 4 invasion invasion NN cord-284810-fs5rx07q 103 5 speed speed NN cord-284810-fs5rx07q 103 6 was be VBD cord-284810-fs5rx07q 103 7 not not RB cord-284810-fs5rx07q 103 8 constant constant JJ cord-284810-fs5rx07q 103 9 . . . cord-284810-fs5rx07q 104 1 Instead instead RB cord-284810-fs5rx07q 104 2 , , , cord-284810-fs5rx07q 104 3 Fig Fig NNP cord-284810-fs5rx07q 104 4 . . NNP cord-284810-fs5rx07q 104 5 2 2 CD cord-284810-fs5rx07q 104 6 _SP cord-284810-fs5rx07q 104 7 scitation.org/journal/cha scitation.org/journal/cha NN cord-284810-fs5rx07q 104 8 distribution distribution NN cord-284810-fs5rx07q 104 9 . . . cord-284810-fs5rx07q 105 1 A a DT cord-284810-fs5rx07q 105 2 first first JJ cord-284810-fs5rx07q 105 3 group group NN cord-284810-fs5rx07q 105 4 of of IN cord-284810-fs5rx07q 105 5 countries country NNS cord-284810-fs5rx07q 105 6 was be VBD cord-284810-fs5rx07q 105 7 invaded invade VBN cord-284810-fs5rx07q 105 8 by by IN cord-284810-fs5rx07q 105 9 the the DT cord-284810-fs5rx07q 105 10 disease disease NN cord-284810-fs5rx07q 105 11 in in IN cord-284810-fs5rx07q 105 12 the the DT cord-284810-fs5rx07q 105 13 end end NN cord-284810-fs5rx07q 105 14 of of IN cord-284810-fs5rx07q 105 15 January January NNP cord-284810-fs5rx07q 105 16 . . . cord-284810-fs5rx07q 106 1 In in IN cord-284810-fs5rx07q 106 2 the the DT cord-284810-fs5rx07q 106 3 first first JJ cord-284810-fs5rx07q 106 4 three three CD cord-284810-fs5rx07q 106 5 weeks week NNS cord-284810-fs5rx07q 106 6 of of IN cord-284810-fs5rx07q 106 7 February February NNP cord-284810-fs5rx07q 106 8 nearly nearly RB cord-284810-fs5rx07q 106 9 no no DT cord-284810-fs5rx07q 106 10 new new JJ cord-284810-fs5rx07q 106 11 arrivals arrival NNS cord-284810-fs5rx07q 106 12 were be VBD cord-284810-fs5rx07q 106 13 reported report VBN cord-284810-fs5rx07q 106 14 . . . cord-284810-fs5rx07q 107 1 Starting start VBG cord-284810-fs5rx07q 107 2 from from IN cord-284810-fs5rx07q 107 3 February February NNP cord-284810-fs5rx07q 107 4 24 24 CD cord-284810-fs5rx07q 107 5 , , , cord-284810-fs5rx07q 107 6 a a DT cord-284810-fs5rx07q 107 7 second second JJ cord-284810-fs5rx07q 107 8 wave wave NN cord-284810-fs5rx07q 107 9 of of IN cord-284810-fs5rx07q 107 10 invasions invasion NNS cord-284810-fs5rx07q 107 11 appeared appear VBD cord-284810-fs5rx07q 107 12 which which WDT cord-284810-fs5rx07q 107 13 lasted last VBD cord-284810-fs5rx07q 107 14 until until IN cord-284810-fs5rx07q 107 15 the the DT cord-284810-fs5rx07q 107 16 end end NN cord-284810-fs5rx07q 107 17 of of IN cord-284810-fs5rx07q 107 18 March March NNP cord-284810-fs5rx07q 107 19 , , , cord-284810-fs5rx07q 107 20 after after IN cord-284810-fs5rx07q 107 21 which which WDT cord-284810-fs5rx07q 107 22 the the DT cord-284810-fs5rx07q 107 23 number number NN cord-284810-fs5rx07q 107 24 of of IN cord-284810-fs5rx07q 107 25 new new JJ cord-284810-fs5rx07q 107 26 arrivals arrival NNS cord-284810-fs5rx07q 107 27 began begin VBD cord-284810-fs5rx07q 107 28 to to TO cord-284810-fs5rx07q 107 29 fall fall VB cord-284810-fs5rx07q 107 30 again again RB cord-284810-fs5rx07q 107 31 , , , cord-284810-fs5rx07q 107 32 probably probably RB cord-284810-fs5rx07q 107 33 reflecting reflect VBG cord-284810-fs5rx07q 107 34 the the DT cord-284810-fs5rx07q 107 35 fact fact NN cord-284810-fs5rx07q 107 36 that that IN cord-284810-fs5rx07q 107 37 the the DT cord-284810-fs5rx07q 107 38 pandemic pandemic NN cord-284810-fs5rx07q 107 39 had have VBD cord-284810-fs5rx07q 107 40 reached reach VBN cord-284810-fs5rx07q 107 41 basically basically RB cord-284810-fs5rx07q 107 42 all all DT cord-284810-fs5rx07q 107 43 countries country NNS cord-284810-fs5rx07q 107 44 of of IN cord-284810-fs5rx07q 107 45 the the DT cord-284810-fs5rx07q 107 46 world world NN cord-284810-fs5rx07q 107 47 . . . cord-284810-fs5rx07q 108 1 As as IN cord-284810-fs5rx07q 108 2 of of IN cord-284810-fs5rx07q 108 3 April April NNP cord-284810-fs5rx07q 108 4 5 5 CD cord-284810-fs5rx07q 108 5 , , , cord-284810-fs5rx07q 108 6 a a DT cord-284810-fs5rx07q 108 7 total total JJ cord-284810-fs5rx07q 108 8 185 185 CD cord-284810-fs5rx07q 108 9 countries country NNS cord-284810-fs5rx07q 108 10 were be VBD cord-284810-fs5rx07q 108 11 invaded invade VBN cord-284810-fs5rx07q 108 12 by by IN cord-284810-fs5rx07q 108 13 the the DT cord-284810-fs5rx07q 108 14 coronavirus coronavirus NN cord-284810-fs5rx07q 108 15 . . . cord-284810-fs5rx07q 109 1 There there EX cord-284810-fs5rx07q 109 2 are be VBP cord-284810-fs5rx07q 109 3 several several JJ cord-284810-fs5rx07q 109 4 possible possible JJ cord-284810-fs5rx07q 109 5 reasons reason NNS cord-284810-fs5rx07q 109 6 why why WRB cord-284810-fs5rx07q 109 7 the the DT cord-284810-fs5rx07q 109 8 disease disease NN cord-284810-fs5rx07q 109 9 arrival arrival NN cord-284810-fs5rx07q 109 10 is be VBZ cord-284810-fs5rx07q 109 11 not not RB cord-284810-fs5rx07q 109 12 more more RBR cord-284810-fs5rx07q 109 13 evenly evenly RB cord-284810-fs5rx07q 109 14 distributed distribute VBN cord-284810-fs5rx07q 109 15 . . . cord-284810-fs5rx07q 110 1 One one CD cord-284810-fs5rx07q 110 2 explanation explanation NN cord-284810-fs5rx07q 110 3 for for IN cord-284810-fs5rx07q 110 4 the the DT cord-284810-fs5rx07q 110 5 bimodal bimodal JJ cord-284810-fs5rx07q 110 6 shape shape NN cord-284810-fs5rx07q 110 7 is be VBZ cord-284810-fs5rx07q 110 8 related relate VBN cord-284810-fs5rx07q 110 9 to to IN cord-284810-fs5rx07q 110 10 the the DT cord-284810-fs5rx07q 110 11 lockdown lockdown NN cord-284810-fs5rx07q 110 12 of of IN cord-284810-fs5rx07q 110 13 airline airline NN cord-284810-fs5rx07q 110 14 transportation transportation NN cord-284810-fs5rx07q 110 15 in in IN cord-284810-fs5rx07q 110 16 China China NNP cord-284810-fs5rx07q 110 17 in in IN cord-284810-fs5rx07q 110 18 the the DT cord-284810-fs5rx07q 110 19 end end NN cord-284810-fs5rx07q 110 20 of of IN cord-284810-fs5rx07q 110 21 January January NNP cord-284810-fs5rx07q 110 22 2020 2020 CD cord-284810-fs5rx07q 110 23 . . . cord-284810-fs5rx07q 111 1 According accord VBG cord-284810-fs5rx07q 111 2 to to IN cord-284810-fs5rx07q 111 3 this this DT cord-284810-fs5rx07q 111 4 hypothesis hypothesis NN cord-284810-fs5rx07q 111 5 , , , cord-284810-fs5rx07q 111 6 after after IN cord-284810-fs5rx07q 111 7 the the DT cord-284810-fs5rx07q 111 8 first first JJ cord-284810-fs5rx07q 111 9 pandemic pandemic JJ cord-284810-fs5rx07q 111 10 bubble bubble NN cord-284810-fs5rx07q 111 11 in in IN cord-284810-fs5rx07q 111 12 January January NNP cord-284810-fs5rx07q 111 13 , , , cord-284810-fs5rx07q 111 14 the the DT cord-284810-fs5rx07q 111 15 further further JJ cord-284810-fs5rx07q 111 16 spread spread NN cord-284810-fs5rx07q 111 17 of of IN cord-284810-fs5rx07q 111 18 the the DT cord-284810-fs5rx07q 111 19 pandemic pandemic NN cord-284810-fs5rx07q 111 20 came come VBD cord-284810-fs5rx07q 111 21 to to IN cord-284810-fs5rx07q 111 22 a a DT cord-284810-fs5rx07q 111 23 temporary temporary JJ cord-284810-fs5rx07q 111 24 standstill standstill NN cord-284810-fs5rx07q 111 25 with with IN cord-284810-fs5rx07q 111 26 the the DT cord-284810-fs5rx07q 111 27 onset onset NN cord-284810-fs5rx07q 111 28 of of IN cord-284810-fs5rx07q 111 29 travel travel NN cord-284810-fs5rx07q 111 30 restrictions restriction NNS cord-284810-fs5rx07q 111 31 , , , cord-284810-fs5rx07q 111 32 only only RB cord-284810-fs5rx07q 111 33 to to TO cord-284810-fs5rx07q 111 34 resurface resurface VB cord-284810-fs5rx07q 111 35 in in IN cord-284810-fs5rx07q 111 36 a a DT cord-284810-fs5rx07q 111 37 second second JJ cord-284810-fs5rx07q 111 38 wave wave NN cord-284810-fs5rx07q 111 39 , , , cord-284810-fs5rx07q 111 40 starting start VBG cord-284810-fs5rx07q 111 41 end end NN cord-284810-fs5rx07q 111 42 of of IN cord-284810-fs5rx07q 111 43 February February NNP cord-284810-fs5rx07q 111 44 . . . cord-284810-fs5rx07q 112 1 Alternatively alternatively RB cord-284810-fs5rx07q 112 2 , , , cord-284810-fs5rx07q 112 3 it -PRON- PRP cord-284810-fs5rx07q 112 4 may may MD cord-284810-fs5rx07q 112 5 be be VB cord-284810-fs5rx07q 112 6 that that IN cord-284810-fs5rx07q 112 7 many many JJ cord-284810-fs5rx07q 112 8 arrivals arrival NNS cord-284810-fs5rx07q 112 9 of of IN cord-284810-fs5rx07q 112 10 the the DT cord-284810-fs5rx07q 112 11 virus virus NN cord-284810-fs5rx07q 112 12 in in IN cord-284810-fs5rx07q 112 13 countries country NNS cord-284810-fs5rx07q 112 14 all all RB cord-284810-fs5rx07q 112 15 over over IN cord-284810-fs5rx07q 112 16 the the DT cord-284810-fs5rx07q 112 17 world world NN cord-284810-fs5rx07q 112 18 simply simply RB cord-284810-fs5rx07q 112 19 went go VBD cord-284810-fs5rx07q 112 20 undetected undetected JJ cord-284810-fs5rx07q 112 21 during during IN cord-284810-fs5rx07q 112 22 the the DT cord-284810-fs5rx07q 112 23 first first JJ cord-284810-fs5rx07q 112 24 weeks week NNS cord-284810-fs5rx07q 112 25 of of IN cord-284810-fs5rx07q 112 26 February February NNP cord-284810-fs5rx07q 112 27 and and CC cord-284810-fs5rx07q 112 28 were be VBD cord-284810-fs5rx07q 112 29 detected detect VBN cord-284810-fs5rx07q 112 30 only only RB cord-284810-fs5rx07q 112 31 later later RB cord-284810-fs5rx07q 112 32 with with IN cord-284810-fs5rx07q 112 33 the the DT cord-284810-fs5rx07q 112 34 increasing increase VBG cord-284810-fs5rx07q 112 35 awareness awareness NN cord-284810-fs5rx07q 112 36 and and CC cord-284810-fs5rx07q 112 37 increased increase VBN cord-284810-fs5rx07q 112 38 testing testing NN cord-284810-fs5rx07q 112 39 . . . cord-284810-fs5rx07q 113 1 This this DT cord-284810-fs5rx07q 113 2 hypothesis hypothesis NN cord-284810-fs5rx07q 113 3 is be VBZ cord-284810-fs5rx07q 113 4 corroborated corroborate VBN cord-284810-fs5rx07q 113 5 by by IN cord-284810-fs5rx07q 113 6 the the DT cord-284810-fs5rx07q 113 7 observation observation NN cord-284810-fs5rx07q 113 8 that that WDT cord-284810-fs5rx07q 113 9 end end NN cord-284810-fs5rx07q 113 10 of of IN cord-284810-fs5rx07q 113 11 February February NNP cord-284810-fs5rx07q 113 12 is be VBZ cord-284810-fs5rx07q 113 13 also also RB cord-284810-fs5rx07q 113 14 the the DT cord-284810-fs5rx07q 113 15 time time NN cord-284810-fs5rx07q 113 16 when when WRB cord-284810-fs5rx07q 113 17 the the DT cord-284810-fs5rx07q 113 18 first first JJ cord-284810-fs5rx07q 113 19 PCR PCR NNP cord-284810-fs5rx07q 113 20 based base VBN cord-284810-fs5rx07q 113 21 tests test NNS cord-284810-fs5rx07q 113 22 became become VBD cord-284810-fs5rx07q 113 23 available available JJ cord-284810-fs5rx07q 113 24 . . . cord-284810-fs5rx07q 114 1 In in IN cord-284810-fs5rx07q 114 2 general general JJ cord-284810-fs5rx07q 114 3 , , , cord-284810-fs5rx07q 114 4 the the DT cord-284810-fs5rx07q 114 5 strong strong JJ cord-284810-fs5rx07q 114 6 irregularity irregularity NN cord-284810-fs5rx07q 114 7 in in IN cord-284810-fs5rx07q 114 8 the the DT cord-284810-fs5rx07q 114 9 arrival arrival NN cord-284810-fs5rx07q 114 10 time time NN cord-284810-fs5rx07q 114 11 distribution distribution NN cord-284810-fs5rx07q 114 12 points point NNS cord-284810-fs5rx07q 114 13 to to IN cord-284810-fs5rx07q 114 14 the the DT cord-284810-fs5rx07q 114 15 high high JJ cord-284810-fs5rx07q 114 16 level level NN cord-284810-fs5rx07q 114 17 of of IN cord-284810-fs5rx07q 114 18 stochasticity stochasticity NN cord-284810-fs5rx07q 114 19 of of IN cord-284810-fs5rx07q 114 20 the the DT cord-284810-fs5rx07q 114 21 worldwide worldwide JJ cord-284810-fs5rx07q 114 22 spreading spread VBG cord-284810-fs5rx07q 114 23 process process NN cord-284810-fs5rx07q 114 24 . . . cord-284810-fs5rx07q 115 1 C. C. NNP cord-284810-fs5rx07q 115 2 Mechanistic mechanistic JJ cord-284810-fs5rx07q 115 3 explanation explanation NN cord-284810-fs5rx07q 115 4 of of IN cord-284810-fs5rx07q 115 5 the the DT cord-284810-fs5rx07q 115 6 power power NN cord-284810-fs5rx07q 115 7 - - HYPH cord-284810-fs5rx07q 115 8 law law NN cord-284810-fs5rx07q 115 9 distribution distribution NN cord-284810-fs5rx07q 115 10 Figure figure NN cord-284810-fs5rx07q 115 11 2 2 CD cord-284810-fs5rx07q 115 12 would would MD cord-284810-fs5rx07q 115 13 suggest suggest VB cord-284810-fs5rx07q 115 14 that that IN cord-284810-fs5rx07q 115 15 the the DT cord-284810-fs5rx07q 115 16 temporal temporal JJ cord-284810-fs5rx07q 115 17 development development NN cord-284810-fs5rx07q 115 18 of of IN cord-284810-fs5rx07q 115 19 the the DT cord-284810-fs5rx07q 115 20 pandemic pandemic NN cord-284810-fs5rx07q 115 21 is be VBZ cord-284810-fs5rx07q 115 22 characterized characterize VBN cord-284810-fs5rx07q 115 23 by by IN cord-284810-fs5rx07q 115 24 two two CD cord-284810-fs5rx07q 115 25 complementary complementary JJ cord-284810-fs5rx07q 115 26 processes process NNS cord-284810-fs5rx07q 115 27 : : : cord-284810-fs5rx07q 115 28 the the DT cord-284810-fs5rx07q 115 29 successive successive JJ cord-284810-fs5rx07q 115 30 invasion invasion NN cord-284810-fs5rx07q 115 31 of of IN cord-284810-fs5rx07q 115 32 more more JJR cord-284810-fs5rx07q 115 33 and and CC cord-284810-fs5rx07q 115 34 more more JJR cord-284810-fs5rx07q 115 35 countries country NNS cord-284810-fs5rx07q 115 36 and and CC cord-284810-fs5rx07q 115 37 the the DT cord-284810-fs5rx07q 115 38 increasing increase VBG cord-284810-fs5rx07q 115 39 number number NN cord-284810-fs5rx07q 115 40 of of IN cord-284810-fs5rx07q 115 41 cases case NNS cord-284810-fs5rx07q 115 42 within within IN cord-284810-fs5rx07q 115 43 each each DT cord-284810-fs5rx07q 115 44 affected affect VBN cord-284810-fs5rx07q 115 45 country country NN cord-284810-fs5rx07q 115 46 . . . cord-284810-fs5rx07q 116 1 Here here RB cord-284810-fs5rx07q 116 2 , , , cord-284810-fs5rx07q 116 3 we -PRON- PRP cord-284810-fs5rx07q 116 4 argue argue VBP cord-284810-fs5rx07q 116 5 that that IN cord-284810-fs5rx07q 116 6 the the DT cord-284810-fs5rx07q 116 7 emergence emergence NN cord-284810-fs5rx07q 116 8 of of IN cord-284810-fs5rx07q 116 9 the the DT cord-284810-fs5rx07q 116 10 power power NN cord-284810-fs5rx07q 116 11 - - HYPH cord-284810-fs5rx07q 116 12 law law NN cord-284810-fs5rx07q 116 13 distribution distribution NN cord-284810-fs5rx07q 116 14 could could MD cord-284810-fs5rx07q 116 15 be be VB cord-284810-fs5rx07q 116 16 related relate VBN cord-284810-fs5rx07q 116 17 to to IN cord-284810-fs5rx07q 116 18 the the DT cord-284810-fs5rx07q 116 19 concurrent concurrent JJ cord-284810-fs5rx07q 116 20 " " `` cord-284810-fs5rx07q 116 21 superposition superposition NN cord-284810-fs5rx07q 116 22 " " '' cord-284810-fs5rx07q 116 23 of of IN cord-284810-fs5rx07q 116 24 these these DT cord-284810-fs5rx07q 116 25 two two CD cord-284810-fs5rx07q 116 26 processes process NNS cord-284810-fs5rx07q 116 27 . . . cord-284810-fs5rx07q 117 1 Thereby thereby RB cord-284810-fs5rx07q 117 2 , , , cord-284810-fs5rx07q 117 3 on on IN cord-284810-fs5rx07q 117 4 a a DT cord-284810-fs5rx07q 117 5 large large JJ cord-284810-fs5rx07q 117 6 geographic geographic JJ cord-284810-fs5rx07q 117 7 scale scale NN cord-284810-fs5rx07q 117 8 , , , cord-284810-fs5rx07q 117 9 the the DT cord-284810-fs5rx07q 117 10 pandemic pandemic NN cord-284810-fs5rx07q 117 11 is be VBZ cord-284810-fs5rx07q 117 12 driven drive VBN cord-284810-fs5rx07q 117 13 by by IN cord-284810-fs5rx07q 117 14 the the DT cord-284810-fs5rx07q 117 15 spread spread NN cord-284810-fs5rx07q 117 16 of of IN cord-284810-fs5rx07q 117 17 the the DT cord-284810-fs5rx07q 117 18 virus virus NN cord-284810-fs5rx07q 117 19 in in IN cord-284810-fs5rx07q 117 20 the the DT cord-284810-fs5rx07q 117 21 network network NN cord-284810-fs5rx07q 117 22 of of IN cord-284810-fs5rx07q 117 23 interconnected interconnected JJ cord-284810-fs5rx07q 117 24 countries country NNS cord-284810-fs5rx07q 117 25 . . . cord-284810-fs5rx07q 118 1 On on IN cord-284810-fs5rx07q 118 2 a a DT cord-284810-fs5rx07q 118 3 small small JJ cord-284810-fs5rx07q 118 4 scale scale NN cord-284810-fs5rx07q 118 5 , , , cord-284810-fs5rx07q 118 6 case case NN cord-284810-fs5rx07q 118 7 numbers number NNS cord-284810-fs5rx07q 118 8 are be VBP cord-284810-fs5rx07q 118 9 snowballing snowball VBG cord-284810-fs5rx07q 118 10 within within IN cord-284810-fs5rx07q 118 11 each each DT cord-284810-fs5rx07q 118 12 country country NN cord-284810-fs5rx07q 118 13 , , , cord-284810-fs5rx07q 118 14 once once IN cord-284810-fs5rx07q 118 15 it -PRON- PRP cord-284810-fs5rx07q 118 16 has have VBZ cord-284810-fs5rx07q 118 17 been be VBN cord-284810-fs5rx07q 118 18 invaded invade VBN cord-284810-fs5rx07q 118 19 , , , cord-284810-fs5rx07q 118 20 thereby thereby RB cord-284810-fs5rx07q 118 21 further further RB cord-284810-fs5rx07q 118 22 increasing increase VBG cord-284810-fs5rx07q 118 23 the the DT cord-284810-fs5rx07q 118 24 epidemic epidemic NN cord-284810-fs5rx07q 118 25 imbalance imbalance NN cord-284810-fs5rx07q 118 26 due due IN cord-284810-fs5rx07q 118 27 to to IN cord-284810-fs5rx07q 118 28 different different JJ cord-284810-fs5rx07q 118 29 arrival arrival NN cord-284810-fs5rx07q 118 30 times time NNS cord-284810-fs5rx07q 118 31 between between IN cord-284810-fs5rx07q 118 32 countries country NNS cord-284810-fs5rx07q 118 33 . . . cord-284810-fs5rx07q 119 1 In in IN cord-284810-fs5rx07q 119 2 the the DT cord-284810-fs5rx07q 119 3 simplest simple JJS cord-284810-fs5rx07q 119 4 approximation approximation NN cord-284810-fs5rx07q 119 5 , , , cord-284810-fs5rx07q 119 6 at at IN cord-284810-fs5rx07q 119 7 the the DT cord-284810-fs5rx07q 119 8 begin begin NN cord-284810-fs5rx07q 119 9 of of IN cord-284810-fs5rx07q 119 10 the the DT cord-284810-fs5rx07q 119 11 pandemic pandemic NN cord-284810-fs5rx07q 119 12 both both DT cord-284810-fs5rx07q 119 13 of of IN cord-284810-fs5rx07q 119 14 these these DT cord-284810-fs5rx07q 119 15 processes process NNS cord-284810-fs5rx07q 119 16 developed develop VBN cord-284810-fs5rx07q 119 17 exponentially exponentially RB cord-284810-fs5rx07q 119 18 in in IN cord-284810-fs5rx07q 119 19 time time NN cord-284810-fs5rx07q 119 20 . . . cord-284810-fs5rx07q 120 1 A a DT cord-284810-fs5rx07q 120 2 straightforward straightforward JJ cord-284810-fs5rx07q 120 3 calculation calculation NN cord-284810-fs5rx07q 120 4 shows show VBZ cord-284810-fs5rx07q 120 5 that that IN cord-284810-fs5rx07q 120 6 the the DT cord-284810-fs5rx07q 120 7 combination combination NN cord-284810-fs5rx07q 120 8 of of IN cord-284810-fs5rx07q 120 9 the the DT cord-284810-fs5rx07q 120 10 two two CD cord-284810-fs5rx07q 120 11 exponential exponential JJ cord-284810-fs5rx07q 120 12 processes process NNS cord-284810-fs5rx07q 120 13 generically generically RB cord-284810-fs5rx07q 120 14 yields yield VBZ cord-284810-fs5rx07q 120 15 a a DT cord-284810-fs5rx07q 120 16 truncated truncated JJ cord-284810-fs5rx07q 120 17 power power NN cord-284810-fs5rx07q 120 18 - - HYPH cord-284810-fs5rx07q 120 19 law law NN cord-284810-fs5rx07q 120 20 distribution distribution NN cord-284810-fs5rx07q 120 21 in in IN cord-284810-fs5rx07q 120 22 the the DT cord-284810-fs5rx07q 120 23 number number NN cord-284810-fs5rx07q 120 24 of of IN cord-284810-fs5rx07q 120 25 cases case NNS cord-284810-fs5rx07q 120 26 in in IN cord-284810-fs5rx07q 120 27 countries country NNS cord-284810-fs5rx07q 120 28 : : : cord-284810-fs5rx07q 121 1 Consider consider VB cord-284810-fs5rx07q 121 2 an an DT cord-284810-fs5rx07q 121 3 epidemic epidemic NN cord-284810-fs5rx07q 121 4 outbreak outbreak NN cord-284810-fs5rx07q 121 5 that that WDT cord-284810-fs5rx07q 121 6 started start VBD cord-284810-fs5rx07q 121 7 ( ( -LRB- cord-284810-fs5rx07q 121 8 the the DT cord-284810-fs5rx07q 121 9 first first JJ cord-284810-fs5rx07q 121 10 case case NN cord-284810-fs5rx07q 121 11 reported report VBN cord-284810-fs5rx07q 121 12 in in IN cord-284810-fs5rx07q 121 13 a a DT cord-284810-fs5rx07q 121 14 country country NN cord-284810-fs5rx07q 121 15 ) ) -RRB- cord-284810-fs5rx07q 121 16 at at IN cord-284810-fs5rx07q 121 17 time time NN cord-284810-fs5rx07q 121 18 t t NN cord-284810-fs5rx07q 121 19 = = SYM cord-284810-fs5rx07q 121 20 0 0 CD cord-284810-fs5rx07q 121 21 . . . cord-284810-fs5rx07q 122 1 We -PRON- PRP cord-284810-fs5rx07q 122 2 are be VBP cord-284810-fs5rx07q 122 3 interested interested JJ cord-284810-fs5rx07q 122 4 in in IN cord-284810-fs5rx07q 122 5 the the DT cord-284810-fs5rx07q 122 6 case case NN cord-284810-fs5rx07q 122 7 distribution distribution NN cord-284810-fs5rx07q 122 8 at at IN cord-284810-fs5rx07q 122 9 time time NN cord-284810-fs5rx07q 122 10 t t NN cord-284810-fs5rx07q 122 11 > > XX cord-284810-fs5rx07q 122 12 0 0 NFP cord-284810-fs5rx07q 122 13 . . . cord-284810-fs5rx07q 123 1 Let let VB cord-284810-fs5rx07q 123 2 us -PRON- PRP cord-284810-fs5rx07q 123 3 first first RB cord-284810-fs5rx07q 123 4 assume assume VB cord-284810-fs5rx07q 123 5 that that IN cord-284810-fs5rx07q 123 6 at at IN cord-284810-fs5rx07q 123 7 this this DT cord-284810-fs5rx07q 123 8 day day NN cord-284810-fs5rx07q 123 9 , , , cord-284810-fs5rx07q 123 10 the the DT cord-284810-fs5rx07q 123 11 probability probability NN cord-284810-fs5rx07q 123 12 distribution distribution NN cord-284810-fs5rx07q 123 13 for for IN cord-284810-fs5rx07q 123 14 a a DT cord-284810-fs5rx07q 123 15 country country NN cord-284810-fs5rx07q 123 16 to to TO cord-284810-fs5rx07q 123 17 have have VB cord-284810-fs5rx07q 123 18 been be VBN cord-284810-fs5rx07q 123 19 invaded invade VBN cord-284810-fs5rx07q 123 20 by by IN cord-284810-fs5rx07q 123 21 the the DT cord-284810-fs5rx07q 123 22 virus virus NN cord-284810-fs5rx07q 123 23 at at IN cord-284810-fs5rx07q 124 1 some some DT cord-284810-fs5rx07q 124 2 former former JJ cord-284810-fs5rx07q 124 3 time time NN cord-284810-fs5rx07q 124 4 τ τ NN cord-284810-fs5rx07q 124 5 grows grow VBZ cord-284810-fs5rx07q 124 6 exponential exponential JJ cord-284810-fs5rx07q 124 7 in in IN cord-284810-fs5rx07q 124 8 τ τ NN cord-284810-fs5rx07q 124 9 with with IN cord-284810-fs5rx07q 124 10 spreading spread VBG cord-284810-fs5rx07q 124 11 rate rate NN cord-284810-fs5rx07q 124 12 s s NN cord-284810-fs5rx07q 124 13 , , , cord-284810-fs5rx07q 124 14 This this DT cord-284810-fs5rx07q 124 15 exponential exponential JJ cord-284810-fs5rx07q 124 16 growth growth NN cord-284810-fs5rx07q 124 17 in in IN cord-284810-fs5rx07q 124 18 the the DT cord-284810-fs5rx07q 124 19 geographic geographic JJ cord-284810-fs5rx07q 124 20 distribution distribution NN cord-284810-fs5rx07q 124 21 of of IN cord-284810-fs5rx07q 124 22 the the DT cord-284810-fs5rx07q 124 23 pandemic pandemic NN cord-284810-fs5rx07q 124 24 would would MD cord-284810-fs5rx07q 124 25 be be VB cord-284810-fs5rx07q 124 26 the the DT cord-284810-fs5rx07q 124 27 expectation expectation NN cord-284810-fs5rx07q 124 28 if if IN cord-284810-fs5rx07q 124 29 one one CD cord-284810-fs5rx07q 124 30 modeled model VBD cord-284810-fs5rx07q 124 31 the the DT cord-284810-fs5rx07q 124 32 spread spread NN cord-284810-fs5rx07q 124 33 in in IN cord-284810-fs5rx07q 124 34 a a DT cord-284810-fs5rx07q 124 35 network network NN cord-284810-fs5rx07q 124 36 where where WRB cord-284810-fs5rx07q 124 37 nodes node NNS cord-284810-fs5rx07q 124 38 are be VBP cord-284810-fs5rx07q 124 39 countries country NNS cord-284810-fs5rx07q 124 40 ( ( -LRB- cord-284810-fs5rx07q 124 41 neglecting neglect VBG cord-284810-fs5rx07q 124 42 saturation saturation NN cord-284810-fs5rx07q 124 43 when when WRB cord-284810-fs5rx07q 124 44 the the DT cord-284810-fs5rx07q 124 45 pandemic pandemic NN cord-284810-fs5rx07q 124 46 has have VBZ cord-284810-fs5rx07q 124 47 reached reach VBN cord-284810-fs5rx07q 124 48 most most JJS cord-284810-fs5rx07q 124 49 countries country NNS cord-284810-fs5rx07q 124 50 ) ) -RRB- cord-284810-fs5rx07q 124 51 . . . cord-284810-fs5rx07q 125 1 Note note VB cord-284810-fs5rx07q 125 2 that that IN cord-284810-fs5rx07q 125 3 the the DT cord-284810-fs5rx07q 125 4 distribution distribution NN cord-284810-fs5rx07q 125 5 is be VBZ cord-284810-fs5rx07q 125 6 truncated truncate VBN cord-284810-fs5rx07q 125 7 from from IN cord-284810-fs5rx07q 125 8 two two CD cord-284810-fs5rx07q 125 9 sides side NNS cord-284810-fs5rx07q 125 10 because because IN cord-284810-fs5rx07q 125 11 arrivals arrival NNS cord-284810-fs5rx07q 125 12 of of IN cord-284810-fs5rx07q 125 13 the the DT cord-284810-fs5rx07q 125 14 disease disease NN cord-284810-fs5rx07q 125 15 can can MD cord-284810-fs5rx07q 125 16 only only RB cord-284810-fs5rx07q 125 17 have have VB cord-284810-fs5rx07q 125 18 occurred occur VBN cord-284810-fs5rx07q 125 19 after after IN cord-284810-fs5rx07q 125 20 the the DT cord-284810-fs5rx07q 125 21 start start NN cord-284810-fs5rx07q 125 22 of of IN cord-284810-fs5rx07q 125 23 the the DT cord-284810-fs5rx07q 125 24 pandemic pandemic NN cord-284810-fs5rx07q 125 25 , , , cord-284810-fs5rx07q 125 26 τ τ NN cord-284810-fs5rx07q 125 27 ≥ ≥ CD cord-284810-fs5rx07q 125 28 0 0 CD cord-284810-fs5rx07q 125 29 , , , cord-284810-fs5rx07q 125 30 and and CC cord-284810-fs5rx07q 125 31 in in IN cord-284810-fs5rx07q 125 32 the the DT cord-284810-fs5rx07q 125 33 past past NN cord-284810-fs5rx07q 125 34 , , , cord-284810-fs5rx07q 125 35 τ τ NN cord-284810-fs5rx07q 125 36 ≤ ≤ NN cord-284810-fs5rx07q 125 37 t. t. NNP cord-284810-fs5rx07q 125 38 Second Second NNP cord-284810-fs5rx07q 125 39 , , , cord-284810-fs5rx07q 125 40 we -PRON- PRP cord-284810-fs5rx07q 125 41 assume assume VBP cord-284810-fs5rx07q 125 42 that that IN cord-284810-fs5rx07q 125 43 in in IN cord-284810-fs5rx07q 125 44 each each DT cord-284810-fs5rx07q 125 45 country country NN cord-284810-fs5rx07q 125 46 , , , cord-284810-fs5rx07q 125 47 the the DT cord-284810-fs5rx07q 125 48 number number NN cord-284810-fs5rx07q 125 49 of of IN cord-284810-fs5rx07q 125 50 confirmed confirm VBN cord-284810-fs5rx07q 125 51 cases case NNS cord-284810-fs5rx07q 125 52 has have VBZ cord-284810-fs5rx07q 125 53 grown grow VBN cord-284810-fs5rx07q 125 54 exponentially exponentially RB cord-284810-fs5rx07q 125 55 with with IN cord-284810-fs5rx07q 125 56 the the DT cord-284810-fs5rx07q 125 57 time time NN cord-284810-fs5rx07q 125 58 since since IN cord-284810-fs5rx07q 125 59 invasion invasion NN cord-284810-fs5rx07q 125 60 t t NNP cord-284810-fs5rx07q 125 61 − − NNP cord-284810-fs5rx07q 125 62 τ τ NN cord-284810-fs5rx07q 125 63 with with IN cord-284810-fs5rx07q 125 64 growth growth NN cord-284810-fs5rx07q 125 65 rate rate NN cord-284810-fs5rx07q 125 66 r r NN cord-284810-fs5rx07q 125 67 ( ( -LRB- cord-284810-fs5rx07q 125 68 neglecting neglect VBG cord-284810-fs5rx07q 125 69 containment containment NN cord-284810-fs5rx07q 125 70 measures measure NNS cord-284810-fs5rx07q 125 71 and and CC cord-284810-fs5rx07q 125 72 saturation saturation NN cord-284810-fs5rx07q 125 73 after after IN cord-284810-fs5rx07q 125 74 the the DT cord-284810-fs5rx07q 125 75 epidemic epidemic NN cord-284810-fs5rx07q 125 76 peak peak NN cord-284810-fs5rx07q 125 77 ) ) -RRB- cord-284810-fs5rx07q 125 78 , , , cord-284810-fs5rx07q 125 79 Combining combine VBG cord-284810-fs5rx07q 125 80 these these DT cord-284810-fs5rx07q 125 81 two two CD cord-284810-fs5rx07q 125 82 equations equation NNS cord-284810-fs5rx07q 125 83 , , , cord-284810-fs5rx07q 125 84 the the DT cord-284810-fs5rx07q 125 85 probability probability NN cord-284810-fs5rx07q 125 86 distribution distribution NN cord-284810-fs5rx07q 125 87 of of IN cord-284810-fs5rx07q 125 88 confirmed confirm VBN cord-284810-fs5rx07q 125 89 cases case NNS cord-284810-fs5rx07q 125 90 P(n P(n NNP cord-284810-fs5rx07q 125 91 ) ) -RRB- cord-284810-fs5rx07q 125 92 can can MD cord-284810-fs5rx07q 125 93 be be VB cord-284810-fs5rx07q 125 94 calculated calculate VBN cord-284810-fs5rx07q 125 95 as as IN cord-284810-fs5rx07q 125 96 29 29 CD cord-284810-fs5rx07q 125 97 which which WDT cord-284810-fs5rx07q 125 98 is be VBZ cord-284810-fs5rx07q 125 99 a a DT cord-284810-fs5rx07q 125 100 truncated truncated JJ cord-284810-fs5rx07q 125 101 power power NN cord-284810-fs5rx07q 125 102 - - HYPH cord-284810-fs5rx07q 125 103 law law NN cord-284810-fs5rx07q 125 104 with with IN cord-284810-fs5rx07q 125 105 critical critical JJ cord-284810-fs5rx07q 125 106 exponent exponent NN cord-284810-fs5rx07q 125 107 , , , cord-284810-fs5rx07q 125 108 Thus thus RB cord-284810-fs5rx07q 125 109 , , , cord-284810-fs5rx07q 125 110 the the DT cord-284810-fs5rx07q 125 111 critical critical JJ cord-284810-fs5rx07q 125 112 exponent exponent NN cord-284810-fs5rx07q 125 113 is be VBZ cord-284810-fs5rx07q 125 114 simply simply RB cord-284810-fs5rx07q 125 115 determined determine VBN cord-284810-fs5rx07q 125 116 by by IN cord-284810-fs5rx07q 125 117 the the DT cord-284810-fs5rx07q 125 118 ratio ratio NN cord-284810-fs5rx07q 125 119 of of IN cord-284810-fs5rx07q 125 120 large large JJ cord-284810-fs5rx07q 125 121 - - HYPH cord-284810-fs5rx07q 125 122 scale scale NN cord-284810-fs5rx07q 125 123 to to IN cord-284810-fs5rx07q 125 124 small small JJ cord-284810-fs5rx07q 125 125 - - HYPH cord-284810-fs5rx07q 125 126 scale scale NN cord-284810-fs5rx07q 125 127 growth growth NN cord-284810-fs5rx07q 125 128 rates rate NNS cord-284810-fs5rx07q 125 129 . . . cord-284810-fs5rx07q 126 1 In in IN cord-284810-fs5rx07q 126 2 the the DT cord-284810-fs5rx07q 126 3 symmetric symmetric JJ cord-284810-fs5rx07q 126 4 case case NN cord-284810-fs5rx07q 126 5 that that IN cord-284810-fs5rx07q 126 6 both both DT cord-284810-fs5rx07q 126 7 growth growth NN cord-284810-fs5rx07q 126 8 rates rate NNS cord-284810-fs5rx07q 126 9 are be VBP cord-284810-fs5rx07q 126 10 identical identical JJ cord-284810-fs5rx07q 126 11 , , , cord-284810-fs5rx07q 126 12 s s XX cord-284810-fs5rx07q 127 1 = = NFP cord-284810-fs5rx07q 127 2 r r NN cord-284810-fs5rx07q 127 3 , , , cord-284810-fs5rx07q 127 4 we -PRON- PRP cord-284810-fs5rx07q 127 5 would would MD cord-284810-fs5rx07q 127 6 expect expect VB cord-284810-fs5rx07q 127 7 a a DT cord-284810-fs5rx07q 127 8 powerlaw powerlaw NN cord-284810-fs5rx07q 127 9 with with IN cord-284810-fs5rx07q 127 10 µ µ NN cord-284810-fs5rx07q 127 11 = = SYM cord-284810-fs5rx07q 127 12 2 2 CD cord-284810-fs5rx07q 127 13 . . . cord-284810-fs5rx07q 128 1 In in IN cord-284810-fs5rx07q 128 2 the the DT cord-284810-fs5rx07q 128 3 limiting limit VBG cord-284810-fs5rx07q 128 4 case case NN cord-284810-fs5rx07q 128 5 that that IN cord-284810-fs5rx07q 128 6 the the DT cord-284810-fs5rx07q 128 7 large large RB cord-284810-fs5rx07q 128 8 - - HYPH cord-284810-fs5rx07q 128 9 scaling scale VBG cord-284810-fs5rx07q 128 10 spreading spreading NN cord-284810-fs5rx07q 128 11 process process NN cord-284810-fs5rx07q 128 12 is be VBZ cord-284810-fs5rx07q 128 13 linear linear JJ cord-284810-fs5rx07q 128 14 in in IN cord-284810-fs5rx07q 128 15 time time NN cord-284810-fs5rx07q 128 16 , , , cord-284810-fs5rx07q 128 17 s s NN cord-284810-fs5rx07q 128 18 = = SYM cord-284810-fs5rx07q 128 19 0 0 NFP cord-284810-fs5rx07q 128 20 , , , cord-284810-fs5rx07q 128 21 we -PRON- PRP cord-284810-fs5rx07q 128 22 obtain obtain VBP cord-284810-fs5rx07q 128 23 a a DT cord-284810-fs5rx07q 128 24 border border NN cord-284810-fs5rx07q 128 25 - - HYPH cord-284810-fs5rx07q 128 26 line line NN cord-284810-fs5rx07q 128 27 distribution distribution NN cord-284810-fs5rx07q 128 28 with with IN cord-284810-fs5rx07q 128 29 critical critical JJ cord-284810-fs5rx07q 128 30 exponent exponent NN cord-284810-fs5rx07q 128 31 µ µ NN cord-284810-fs5rx07q 128 32 = = SYM cord-284810-fs5rx07q 128 33 1 1 CD cord-284810-fs5rx07q 128 34 . . . cord-284810-fs5rx07q 129 1 Note note VB cord-284810-fs5rx07q 129 2 that that IN cord-284810-fs5rx07q 129 3 from from IN cord-284810-fs5rx07q 129 4 the the DT cord-284810-fs5rx07q 129 5 truncation truncation NN cord-284810-fs5rx07q 129 6 of of IN cord-284810-fs5rx07q 129 7 τ τ NN cord-284810-fs5rx07q 129 8 in in IN cord-284810-fs5rx07q 129 9 the the DT cord-284810-fs5rx07q 129 10 arrival arrival NN cord-284810-fs5rx07q 129 11 time time NN cord-284810-fs5rx07q 129 12 distribution distribution NN cord-284810-fs5rx07q 129 13 , , , cord-284810-fs5rx07q 129 14 Eq Eq NNP cord-284810-fs5rx07q 129 15 . . . cord-284810-fs5rx07q 130 1 ( ( -LRB- cord-284810-fs5rx07q 130 2 2 2 LS cord-284810-fs5rx07q 130 3 ) ) -RRB- cord-284810-fs5rx07q 130 4 , , , cord-284810-fs5rx07q 130 5 the the DT cord-284810-fs5rx07q 130 6 admissible admissible JJ cord-284810-fs5rx07q 130 7 range range NN cord-284810-fs5rx07q 130 8 of of IN cord-284810-fs5rx07q 130 9 case case NN cord-284810-fs5rx07q 130 10 numbers number NNS cord-284810-fs5rx07q 130 11 in in IN cord-284810-fs5rx07q 130 12 the the DT cord-284810-fs5rx07q 130 13 power power NN cord-284810-fs5rx07q 130 14 - - HYPH cord-284810-fs5rx07q 130 15 law law NN cord-284810-fs5rx07q 130 16 distribution distribution NN cord-284810-fs5rx07q 130 17 Eq eq NN cord-284810-fs5rx07q 130 18 . . . cord-284810-fs5rx07q 131 1 ( ( -LRB- cord-284810-fs5rx07q 131 2 4 4 LS cord-284810-fs5rx07q 131 3 ) ) -RRB- cord-284810-fs5rx07q 131 4 necessarily necessarily RB cord-284810-fs5rx07q 131 5 is be VBZ cord-284810-fs5rx07q 131 6 restricted restrict VBN cord-284810-fs5rx07q 131 7 between between IN cord-284810-fs5rx07q 131 8 the the DT cord-284810-fs5rx07q 131 9 lower lower RBR cord-284810-fs5rx07q 131 10 bound bind VBN cord-284810-fs5rx07q 131 11 n n NN cord-284810-fs5rx07q 131 12 = = SYM cord-284810-fs5rx07q 131 13 1 1 CD cord-284810-fs5rx07q 131 14 ( ( -LRB- cord-284810-fs5rx07q 131 15 the the DT cord-284810-fs5rx07q 131 16 epidemic epidemic NN cord-284810-fs5rx07q 131 17 prevalence prevalence NN cord-284810-fs5rx07q 131 18 in in IN cord-284810-fs5rx07q 131 19 a a DT cord-284810-fs5rx07q 131 20 newly newly RB cord-284810-fs5rx07q 131 21 invaded invade VBN cord-284810-fs5rx07q 131 22 country country NN cord-284810-fs5rx07q 131 23 ) ) -RRB- cord-284810-fs5rx07q 131 24 and and CC cord-284810-fs5rx07q 131 25 the the DT cord-284810-fs5rx07q 131 26 cut cut VB cord-284810-fs5rx07q 131 27 - - HYPH cord-284810-fs5rx07q 131 28 off off RP cord-284810-fs5rx07q 131 29 value value NN cord-284810-fs5rx07q 131 30 n n CC cord-284810-fs5rx07q 131 31 max max NNP cord-284810-fs5rx07q 131 32 ∼ ∼ NNP cord-284810-fs5rx07q 131 33 e e NNP cord-284810-fs5rx07q 131 34 rt rt NNP cord-284810-fs5rx07q 131 35 ( ( -LRB- cord-284810-fs5rx07q 131 36 the the DT cord-284810-fs5rx07q 131 37 epidemic epidemic NN cord-284810-fs5rx07q 131 38 prevalence prevalence NN cord-284810-fs5rx07q 131 39 at at IN cord-284810-fs5rx07q 131 40 time time NN cord-284810-fs5rx07q 131 41 t t NN cord-284810-fs5rx07q 131 42 in in IN cord-284810-fs5rx07q 131 43 the the DT cord-284810-fs5rx07q 131 44 country country NN cord-284810-fs5rx07q 131 45 with with IN cord-284810-fs5rx07q 132 1 the the DT cord-284810-fs5rx07q 132 2 first first RB cord-284810-fs5rx07q 132 3 confirmed confirm VBD cord-284810-fs5rx07q 132 4 case)-justifying case)-justifye VBG cord-284810-fs5rx07q 132 5 the the DT cord-284810-fs5rx07q 132 6 observation observation NN cord-284810-fs5rx07q 132 7 of of IN cord-284810-fs5rx07q 132 8 a a DT cord-284810-fs5rx07q 132 9 truncated truncated JJ cord-284810-fs5rx07q 132 10 power power NN cord-284810-fs5rx07q 132 11 - - HYPH cord-284810-fs5rx07q 132 12 law law NN cord-284810-fs5rx07q 132 13 in in IN cord-284810-fs5rx07q 132 14 the the DT cord-284810-fs5rx07q 132 15 empirical empirical JJ cord-284810-fs5rx07q 132 16 data datum NNS cord-284810-fs5rx07q 132 17 as as IN cord-284810-fs5rx07q 132 18 shown show VBN cord-284810-fs5rx07q 132 19 in in IN cord-284810-fs5rx07q 132 20 Fig Fig NNP cord-284810-fs5rx07q 132 21 . . . cord-284810-fs5rx07q 133 1 1 1 LS cord-284810-fs5rx07q 133 2 . . . cord-284810-fs5rx07q 134 1 Obviously obviously RB cord-284810-fs5rx07q 134 2 , , , cord-284810-fs5rx07q 134 3 this this DT cord-284810-fs5rx07q 134 4 simple simple JJ cord-284810-fs5rx07q 134 5 theory theory NN cord-284810-fs5rx07q 134 6 far far RB cord-284810-fs5rx07q 134 7 from from IN cord-284810-fs5rx07q 134 8 accurately accurately RB cord-284810-fs5rx07q 134 9 describes describe VBZ cord-284810-fs5rx07q 134 10 a a DT cord-284810-fs5rx07q 134 11 real real JJ cord-284810-fs5rx07q 134 12 - - HYPH cord-284810-fs5rx07q 134 13 word word NN cord-284810-fs5rx07q 134 14 pandemic pandemic NN cord-284810-fs5rx07q 134 15 . . . cord-284810-fs5rx07q 135 1 First first RB cord-284810-fs5rx07q 135 2 of of IN cord-284810-fs5rx07q 135 3 all all DT cord-284810-fs5rx07q 135 4 , , , cord-284810-fs5rx07q 135 5 the the DT cord-284810-fs5rx07q 135 6 theory theory NN cord-284810-fs5rx07q 135 7 is be VBZ cord-284810-fs5rx07q 135 8 valid valid JJ cord-284810-fs5rx07q 135 9 only only RB cord-284810-fs5rx07q 135 10 in in IN cord-284810-fs5rx07q 135 11 the the DT cord-284810-fs5rx07q 135 12 initial initial JJ cord-284810-fs5rx07q 135 13 phase phase NN cord-284810-fs5rx07q 135 14 of of IN cord-284810-fs5rx07q 135 15 the the DT cord-284810-fs5rx07q 135 16 pandemic pandemic NN cord-284810-fs5rx07q 135 17 , , , cord-284810-fs5rx07q 135 18 while while IN cord-284810-fs5rx07q 135 19 both both DT cord-284810-fs5rx07q 135 20 geographical geographical JJ cord-284810-fs5rx07q 135 21 spread spread NN cord-284810-fs5rx07q 135 22 and and CC cord-284810-fs5rx07q 135 23 within within IN cord-284810-fs5rx07q 135 24 - - HYPH cord-284810-fs5rx07q 135 25 country country NN cord-284810-fs5rx07q 135 26 epidemic epidemic NN cord-284810-fs5rx07q 135 27 growth growth NN cord-284810-fs5rx07q 135 28 are be VBP cord-284810-fs5rx07q 135 29 still still RB cord-284810-fs5rx07q 135 30 exponential exponential JJ cord-284810-fs5rx07q 135 31 . . . cord-284810-fs5rx07q 136 1 As as RB cord-284810-fs5rx07q 136 2 soon soon RB cord-284810-fs5rx07q 136 3 as as IN cord-284810-fs5rx07q 136 4 saturation saturation NN cord-284810-fs5rx07q 136 5 processes process NNS cord-284810-fs5rx07q 136 6 set set VBN cord-284810-fs5rx07q 136 7 in in RP cord-284810-fs5rx07q 136 8 , , , cord-284810-fs5rx07q 136 9 the the DT cord-284810-fs5rx07q 136 10 derivation derivation NN cord-284810-fs5rx07q 136 11 of of IN cord-284810-fs5rx07q 136 12 the the DT cord-284810-fs5rx07q 136 13 power power NN cord-284810-fs5rx07q 136 14 - - HYPH cord-284810-fs5rx07q 136 15 law law NN cord-284810-fs5rx07q 136 16 breaks break VBZ cord-284810-fs5rx07q 136 17 down down RP cord-284810-fs5rx07q 136 18 . . . cord-284810-fs5rx07q 137 1 Next next RB cord-284810-fs5rx07q 137 2 , , , cord-284810-fs5rx07q 137 3 as as IN cord-284810-fs5rx07q 137 4 shown show VBN cord-284810-fs5rx07q 137 5 in in IN cord-284810-fs5rx07q 137 6 Fig Fig NNP cord-284810-fs5rx07q 137 7 . . . cord-284810-fs5rx07q 137 8 2(b 2(b CD cord-284810-fs5rx07q 137 9 ) ) -RRB- cord-284810-fs5rx07q 137 10 , , , cord-284810-fs5rx07q 137 11 the the DT cord-284810-fs5rx07q 137 12 arrival arrival NN cord-284810-fs5rx07q 137 13 time time NN cord-284810-fs5rx07q 137 14 distribution distribution NN cord-284810-fs5rx07q 137 15 during during IN cord-284810-fs5rx07q 137 16 the the DT cord-284810-fs5rx07q 137 17 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 137 18 pandemic pandemic NN cord-284810-fs5rx07q 137 19 is be VBZ cord-284810-fs5rx07q 137 20 not not RB cord-284810-fs5rx07q 137 21 exponential exponential JJ cord-284810-fs5rx07q 137 22 , , , cord-284810-fs5rx07q 137 23 as as IN cord-284810-fs5rx07q 137 24 discussed discuss VBN cord-284810-fs5rx07q 137 25 above above RB cord-284810-fs5rx07q 137 26 . . . cord-284810-fs5rx07q 138 1 In in IN cord-284810-fs5rx07q 138 2 gross gross JJ cord-284810-fs5rx07q 138 3 oversimplification oversimplification NN cord-284810-fs5rx07q 138 4 , , , cord-284810-fs5rx07q 138 5 we -PRON- PRP cord-284810-fs5rx07q 138 6 may may MD cord-284810-fs5rx07q 138 7 nevertheless nevertheless RB cord-284810-fs5rx07q 138 8 fit fit VB cord-284810-fs5rx07q 138 9 an an DT cord-284810-fs5rx07q 138 10 exponential exponential JJ cord-284810-fs5rx07q 138 11 function function NN cord-284810-fs5rx07q 138 12 P(t p(t NN cord-284810-fs5rx07q 138 13 ) ) -RRB- cord-284810-fs5rx07q 138 14 ∼ ∼ NNP cord-284810-fs5rx07q 138 15 e e NNP cord-284810-fs5rx07q 138 16 st st NNP cord-284810-fs5rx07q 138 17 through through IN cord-284810-fs5rx07q 138 18 the the DT cord-284810-fs5rx07q 138 19 data datum NNS cord-284810-fs5rx07q 138 20 , , , cord-284810-fs5rx07q 138 21 yielding yield VBG cord-284810-fs5rx07q 138 22 an an DT cord-284810-fs5rx07q 138 23 " " `` cord-284810-fs5rx07q 138 24 average average JJ cord-284810-fs5rx07q 138 25 " " '' cord-284810-fs5rx07q 138 26 spreading spread VBG cord-284810-fs5rx07q 138 27 rate rate NN cord-284810-fs5rx07q 138 28 of of IN cord-284810-fs5rx07q 138 29 s s NN cord-284810-fs5rx07q 138 30 = = NN cord-284810-fs5rx07q 139 1 0.03 0.03 CD cord-284810-fs5rx07q 139 2 d d NNP cord-284810-fs5rx07q 139 3 −1 −1 NNP cord-284810-fs5rx07q 140 1 [ [ -LRB- cord-284810-fs5rx07q 140 2 black black JJ cord-284810-fs5rx07q 140 3 dashed dash VBD cord-284810-fs5rx07q 140 4 line line NN cord-284810-fs5rx07q 140 5 in in IN cord-284810-fs5rx07q 140 6 Fig Fig NNP cord-284810-fs5rx07q 140 7 . . . cord-284810-fs5rx07q 140 8 2(b 2(b CD cord-284810-fs5rx07q 140 9 ) ) -RRB- cord-284810-fs5rx07q 140 10 ] ] -RRB- cord-284810-fs5rx07q 140 11 . . . cord-284810-fs5rx07q 141 1 Finally finally RB cord-284810-fs5rx07q 141 2 , , , cord-284810-fs5rx07q 141 3 epidemic epidemic JJ cord-284810-fs5rx07q 141 4 growth growth NN cord-284810-fs5rx07q 141 5 rates rate NNS cord-284810-fs5rx07q 141 6 during during IN cord-284810-fs5rx07q 141 7 the the DT cord-284810-fs5rx07q 141 8 COVID-19 covid-19 JJ cord-284810-fs5rx07q 141 9 pandemic pandemic NN cord-284810-fs5rx07q 141 10 have have VBP cord-284810-fs5rx07q 141 11 not not RB cord-284810-fs5rx07q 141 12 been be VBN cord-284810-fs5rx07q 141 13 identical identical JJ cord-284810-fs5rx07q 141 14 in in IN cord-284810-fs5rx07q 141 15 all all DT cord-284810-fs5rx07q 141 16 countries country NNS cord-284810-fs5rx07q 141 17 ( ( -LRB- cord-284810-fs5rx07q 141 18 even even RB cord-284810-fs5rx07q 141 19 in in IN cord-284810-fs5rx07q 141 20 the the DT cord-284810-fs5rx07q 141 21 initial initial JJ cord-284810-fs5rx07q 141 22 stages stage NNS cord-284810-fs5rx07q 141 23 ) ) -RRB- cord-284810-fs5rx07q 141 24 . . . cord-284810-fs5rx07q 142 1 They -PRON- PRP cord-284810-fs5rx07q 142 2 have have VBP cord-284810-fs5rx07q 142 3 also also RB cord-284810-fs5rx07q 142 4 not not RB cord-284810-fs5rx07q 142 5 remained remain VBN cord-284810-fs5rx07q 142 6 constant constant JJ cord-284810-fs5rx07q 142 7 in in IN cord-284810-fs5rx07q 142 8 time time NN cord-284810-fs5rx07q 142 9 , , , cord-284810-fs5rx07q 142 10 but but CC cord-284810-fs5rx07q 142 11 in in IN cord-284810-fs5rx07q 142 12 most most JJS cord-284810-fs5rx07q 142 13 countries country NNS cord-284810-fs5rx07q 142 14 have have VBP cord-284810-fs5rx07q 142 15 fallen fall VBN cord-284810-fs5rx07q 142 16 in in IN cord-284810-fs5rx07q 142 17 the the DT cord-284810-fs5rx07q 142 18 course course NN cord-284810-fs5rx07q 142 19 of of IN cord-284810-fs5rx07q 142 20 the the DT cord-284810-fs5rx07q 142 21 epidemic epidemic NN cord-284810-fs5rx07q 142 22 . . . cord-284810-fs5rx07q 143 1 Furthermore furthermore RB cord-284810-fs5rx07q 143 2 , , , cord-284810-fs5rx07q 143 3 most most JJS cord-284810-fs5rx07q 143 4 countries country NNS cord-284810-fs5rx07q 143 5 were be VBD cord-284810-fs5rx07q 143 6 invaded invade VBN cord-284810-fs5rx07q 143 7 multiple multiple JJ cord-284810-fs5rx07q 143 8 times time NNS cord-284810-fs5rx07q 143 9 , , , cord-284810-fs5rx07q 143 10 leading lead VBG cord-284810-fs5rx07q 143 11 to to IN cord-284810-fs5rx07q 143 12 different different JJ cord-284810-fs5rx07q 143 13 epidemic epidemic NN cord-284810-fs5rx07q 143 14 foci foci NN cord-284810-fs5rx07q 143 15 within within IN cord-284810-fs5rx07q 143 16 countries country NNS cord-284810-fs5rx07q 143 17 . . . cord-284810-fs5rx07q 144 1 Neglecting neglect VBG cord-284810-fs5rx07q 144 2 all all PDT cord-284810-fs5rx07q 144 3 these these DT cord-284810-fs5rx07q 144 4 observations observation NNS cord-284810-fs5rx07q 144 5 , , , cord-284810-fs5rx07q 144 6 for for IN cord-284810-fs5rx07q 144 7 the the DT cord-284810-fs5rx07q 144 8 sake sake NN cord-284810-fs5rx07q 144 9 of of IN cord-284810-fs5rx07q 144 10 argument argument NN cord-284810-fs5rx07q 144 11 , , , cord-284810-fs5rx07q 144 12 let let VB cord-284810-fs5rx07q 144 13 us -PRON- PRP cord-284810-fs5rx07q 144 14 assume assume VB cord-284810-fs5rx07q 144 15 an an DT cord-284810-fs5rx07q 144 16 average average JJ cord-284810-fs5rx07q 144 17 doubling double VBG cord-284810-fs5rx07q 144 18 time time NN cord-284810-fs5rx07q 144 19 of of IN cord-284810-fs5rx07q 144 20 case case NN cord-284810-fs5rx07q 144 21 numbers number NNS cord-284810-fs5rx07q 144 22 of of IN cord-284810-fs5rx07q 144 23 T T NNP cord-284810-fs5rx07q 144 24 1/2 1/2 CD cord-284810-fs5rx07q 144 25 = = NFP cord-284810-fs5rx07q 145 1 3.5 3.5 CD cord-284810-fs5rx07q 145 2 d d NN cord-284810-fs5rx07q 145 3 in in IN cord-284810-fs5rx07q 145 4 all all DT cord-284810-fs5rx07q 145 5 countries country NNS cord-284810-fs5rx07q 145 6 , , , cord-284810-fs5rx07q 145 7 yielding yield VBG cord-284810-fs5rx07q 145 8 an an DT cord-284810-fs5rx07q 145 9 exponential exponential JJ cord-284810-fs5rx07q 145 10 growth growth NN cord-284810-fs5rx07q 145 11 rate rate NN cord-284810-fs5rx07q 145 12 of of IN cord-284810-fs5rx07q 145 13 r r NN cord-284810-fs5rx07q 145 14 = = SYM cord-284810-fs5rx07q 145 15 log(2)/T log(2)/t CD cord-284810-fs5rx07q 145 16 1/2 1/2 CD cord-284810-fs5rx07q 145 17 = = SYM cord-284810-fs5rx07q 145 18 0.2 0.2 CD cord-284810-fs5rx07q 145 19 d d NNP cord-284810-fs5rx07q 145 20 −1 −1 NNP cord-284810-fs5rx07q 145 21 and and CC cord-284810-fs5rx07q 145 22 a a DT cord-284810-fs5rx07q 145 23 maximal maximal JJ cord-284810-fs5rx07q 145 24 case case NN cord-284810-fs5rx07q 145 25 number number NN cord-284810-fs5rx07q 145 26 of of IN cord-284810-fs5rx07q 145 27 n n NN cord-284810-fs5rx07q 145 28 max max NN cord-284810-fs5rx07q 145 29 = = NN cord-284810-fs5rx07q 146 1 e e LS cord-284810-fs5rx07q 146 2 0.2 0.2 CD cord-284810-fs5rx07q 147 1 * * NFP cord-284810-fs5rx07q 147 2 60 60 CD cord-284810-fs5rx07q 147 3 = = SYM cord-284810-fs5rx07q 147 4 1.6 1.6 CD cord-284810-fs5rx07q 147 5 × × NN cord-284810-fs5rx07q 147 6 10 10 CD cord-284810-fs5rx07q 147 7 5 5 CD cord-284810-fs5rx07q 147 8 after after IN cord-284810-fs5rx07q 147 9 60 60 CD cord-284810-fs5rx07q 147 10 days day NNS cord-284810-fs5rx07q 147 11 . . . cord-284810-fs5rx07q 148 1 Then then RB cord-284810-fs5rx07q 148 2 , , , cord-284810-fs5rx07q 148 3 according accord VBG cord-284810-fs5rx07q 148 4 to to IN cord-284810-fs5rx07q 148 5 our -PRON- PRP$ cord-284810-fs5rx07q 148 6 simple simple JJ cord-284810-fs5rx07q 148 7 theory theory NN cord-284810-fs5rx07q 148 8 equation equation NN cord-284810-fs5rx07q 148 9 ( ( -LRB- cord-284810-fs5rx07q 148 10 5 5 CD cord-284810-fs5rx07q 148 11 ) ) -RRB- cord-284810-fs5rx07q 148 12 , , , cord-284810-fs5rx07q 148 13 we -PRON- PRP cord-284810-fs5rx07q 148 14 would would MD cord-284810-fs5rx07q 148 15 expect expect VB cord-284810-fs5rx07q 148 16 a a DT cord-284810-fs5rx07q 148 17 critical critical JJ cord-284810-fs5rx07q 148 18 exponent exponent NN cord-284810-fs5rx07q 148 19 of of IN cord-284810-fs5rx07q 148 20 µ µ NN cord-284810-fs5rx07q 148 21 = = SYM cord-284810-fs5rx07q 148 22 1 1 CD cord-284810-fs5rx07q 148 23 + + SYM cord-284810-fs5rx07q 148 24 0.03/0.2 0.03/0.2 CD cord-284810-fs5rx07q 149 1 ≈ ≈ NNP cord-284810-fs5rx07q 149 2 1.15 1.15 CD cord-284810-fs5rx07q 149 3 , , , cord-284810-fs5rx07q 149 4 in in IN cord-284810-fs5rx07q 149 5 rather rather RB cord-284810-fs5rx07q 149 6 good good JJ cord-284810-fs5rx07q 149 7 agreement agreement NN cord-284810-fs5rx07q 149 8 to to IN cord-284810-fs5rx07q 149 9 the the DT cord-284810-fs5rx07q 149 10 fitted fit VBN cord-284810-fs5rx07q 149 11 exponents exponent NNS cord-284810-fs5rx07q 149 12 in in IN cord-284810-fs5rx07q 149 13 Fig Fig NNP cord-284810-fs5rx07q 149 14 . . . cord-284810-fs5rx07q 150 1 1 1 LS cord-284810-fs5rx07q 150 2 . . . cord-284810-fs5rx07q 151 1 To to TO cord-284810-fs5rx07q 151 2 test test VB cord-284810-fs5rx07q 151 3 the the DT cord-284810-fs5rx07q 151 4 theory theory NN cord-284810-fs5rx07q 151 5 of of IN cord-284810-fs5rx07q 151 6 Sec Sec NNP cord-284810-fs5rx07q 151 7 . . . cord-284810-fs5rx07q 152 1 II II NNP cord-284810-fs5rx07q 152 2 C C NNP cord-284810-fs5rx07q 152 3 , , , cord-284810-fs5rx07q 152 4 we -PRON- PRP cord-284810-fs5rx07q 152 5 developed develop VBD cord-284810-fs5rx07q 152 6 a a DT cord-284810-fs5rx07q 152 7 dual dual JJ cord-284810-fs5rx07q 152 8 - - HYPH cord-284810-fs5rx07q 152 9 scale scale NN cord-284810-fs5rx07q 152 10 metapopulation metapopulation NN cord-284810-fs5rx07q 152 11 model model NN cord-284810-fs5rx07q 152 12 ( ( -LRB- cord-284810-fs5rx07q 152 13 see see VB cord-284810-fs5rx07q 152 14 Appendix Appendix NNP cord-284810-fs5rx07q 152 15 B B NNP cord-284810-fs5rx07q 152 16 ) ) -RRB- cord-284810-fs5rx07q 152 17 . . . cord-284810-fs5rx07q 153 1 The the DT cord-284810-fs5rx07q 153 2 first first JJ cord-284810-fs5rx07q 153 3 level level NN cord-284810-fs5rx07q 153 4 describes describe VBZ cord-284810-fs5rx07q 153 5 the the DT cord-284810-fs5rx07q 153 6 Chaos Chaos NNP cord-284810-fs5rx07q 153 7 ARTICLE article NN cord-284810-fs5rx07q 153 8 scitation.org/journal/cha scitation.org/journal/cha `` cord-284810-fs5rx07q 153 9 large large JJ cord-284810-fs5rx07q 153 10 - - HYPH cord-284810-fs5rx07q 153 11 scale scale NN cord-284810-fs5rx07q 153 12 stochastic stochastic JJ cord-284810-fs5rx07q 153 13 spread spread NN cord-284810-fs5rx07q 153 14 of of IN cord-284810-fs5rx07q 153 15 the the DT cord-284810-fs5rx07q 153 16 virus virus NN cord-284810-fs5rx07q 153 17 in in IN cord-284810-fs5rx07q 153 18 a a DT cord-284810-fs5rx07q 153 19 network network NN cord-284810-fs5rx07q 153 20 of of IN cord-284810-fs5rx07q 153 21 N n CD cord-284810-fs5rx07q 153 22 interconnected interconnect VBN cord-284810-fs5rx07q 153 23 countries country NNS cord-284810-fs5rx07q 153 24 . . . cord-284810-fs5rx07q 154 1 The the DT cord-284810-fs5rx07q 154 2 second second JJ cord-284810-fs5rx07q 154 3 level level NN cord-284810-fs5rx07q 154 4 describes describe VBZ cord-284810-fs5rx07q 154 5 the the DT cord-284810-fs5rx07q 154 6 small small JJ cord-284810-fs5rx07q 154 7 - - HYPH cord-284810-fs5rx07q 154 8 scale scale NN cord-284810-fs5rx07q 154 9 increase increase NN cord-284810-fs5rx07q 154 10 in in IN cord-284810-fs5rx07q 154 11 case case NN cord-284810-fs5rx07q 154 12 numbers number NNS cord-284810-fs5rx07q 154 13 within within IN cord-284810-fs5rx07q 154 14 a a DT cord-284810-fs5rx07q 154 15 country country NN cord-284810-fs5rx07q 154 16 ; ; : cord-284810-fs5rx07q 154 17 it -PRON- PRP cord-284810-fs5rx07q 154 18 is be VBZ cord-284810-fs5rx07q 154 19 started start VBN cord-284810-fs5rx07q 154 20 in in IN cord-284810-fs5rx07q 154 21 each each DT cord-284810-fs5rx07q 154 22 country country NN cord-284810-fs5rx07q 154 23 from from IN cord-284810-fs5rx07q 154 24 the the DT cord-284810-fs5rx07q 154 25 time time NN cord-284810-fs5rx07q 154 26 point point NN cord-284810-fs5rx07q 154 27 of of IN cord-284810-fs5rx07q 154 28 invasion invasion NN cord-284810-fs5rx07q 154 29 by by IN cord-284810-fs5rx07q 154 30 the the DT cord-284810-fs5rx07q 154 31 virus virus NN cord-284810-fs5rx07q 154 32 and and CC cord-284810-fs5rx07q 154 33 follows follow VBZ cord-284810-fs5rx07q 154 34 a a DT cord-284810-fs5rx07q 154 35 simple simple JJ cord-284810-fs5rx07q 154 36 deterministic deterministic JJ cord-284810-fs5rx07q 154 37 SIR sir NN cord-284810-fs5rx07q 154 38 - - HYPH cord-284810-fs5rx07q 154 39 dynamics dynamic NNS cord-284810-fs5rx07q 154 40 . . . cord-284810-fs5rx07q 155 1 The the DT cord-284810-fs5rx07q 155 2 motivation motivation NN cord-284810-fs5rx07q 155 3 for for IN cord-284810-fs5rx07q 155 4 this this DT cord-284810-fs5rx07q 155 5 model model NN cord-284810-fs5rx07q 155 6 design design NN cord-284810-fs5rx07q 155 7 was be VBD cord-284810-fs5rx07q 155 8 not not RB cord-284810-fs5rx07q 155 9 to to TO cord-284810-fs5rx07q 155 10 predict predict VB cord-284810-fs5rx07q 155 11 the the DT cord-284810-fs5rx07q 155 12 worldwide worldwide JJ cord-284810-fs5rx07q 155 13 spread spread NN cord-284810-fs5rx07q 155 14 of of IN cord-284810-fs5rx07q 155 15 COVID-19 covid-19 NN cord-284810-fs5rx07q 155 16 , , , cord-284810-fs5rx07q 155 17 but but CC cord-284810-fs5rx07q 155 18 rather rather RB cord-284810-fs5rx07q 155 19 to to TO cord-284810-fs5rx07q 155 20 quantitatively quantitatively RB cord-284810-fs5rx07q 155 21 test test VB cord-284810-fs5rx07q 155 22 the the DT cord-284810-fs5rx07q 155 23 emergence emergence NN cord-284810-fs5rx07q 155 24 of of IN cord-284810-fs5rx07q 155 25 heterogeneous heterogeneous JJ cord-284810-fs5rx07q 155 26 case case NN cord-284810-fs5rx07q 155 27 distributions distribution NNS cord-284810-fs5rx07q 155 28 in in IN cord-284810-fs5rx07q 155 29 a a DT cord-284810-fs5rx07q 155 30 conceptual conceptual JJ cord-284810-fs5rx07q 155 31 model model NN cord-284810-fs5rx07q 155 32 framework framework NN cord-284810-fs5rx07q 155 33 that that WDT cord-284810-fs5rx07q 155 34 incorporates incorporate VBZ cord-284810-fs5rx07q 155 35 the the DT cord-284810-fs5rx07q 155 36 ideas idea NNS cord-284810-fs5rx07q 155 37 from from IN cord-284810-fs5rx07q 155 38 Sec Sec NNP cord-284810-fs5rx07q 155 39 . . . cord-284810-fs5rx07q 156 1 II II NNP cord-284810-fs5rx07q 156 2 C. C. NNP cord-284810-fs5rx07q 156 3 Figure Figure NNP cord-284810-fs5rx07q 156 4 3 3 CD cord-284810-fs5rx07q 156 5 shows show VBZ cord-284810-fs5rx07q 156 6 a a DT cord-284810-fs5rx07q 156 7 typical typical JJ cord-284810-fs5rx07q 156 8 model model NN cord-284810-fs5rx07q 156 9 outcome outcome NN cord-284810-fs5rx07q 156 10 . . . cord-284810-fs5rx07q 157 1 The the DT cord-284810-fs5rx07q 157 2 large large JJ cord-284810-fs5rx07q 157 3 - - HYPH cord-284810-fs5rx07q 157 4 scale scale NN cord-284810-fs5rx07q 157 5 spreading spreading NN cord-284810-fs5rx07q 157 6 process process NN cord-284810-fs5rx07q 157 7 is be VBZ cord-284810-fs5rx07q 157 8 captured capture VBN cord-284810-fs5rx07q 157 9 in in IN cord-284810-fs5rx07q 157 10 the the DT cord-284810-fs5rx07q 157 11 arrival arrival NN cord-284810-fs5rx07q 157 12 time time NN cord-284810-fs5rx07q 157 13 distribution distribution NN cord-284810-fs5rx07q 157 14 , , , cord-284810-fs5rx07q 157 15 which which WDT cord-284810-fs5rx07q 157 16 exhibits exhibit VBZ cord-284810-fs5rx07q 157 17 a a DT cord-284810-fs5rx07q 157 18 unimodal unimodal JJ cord-284810-fs5rx07q 157 19 dependency dependency NN cord-284810-fs5rx07q 157 20 on on IN cord-284810-fs5rx07q 157 21 time time NN cord-284810-fs5rx07q 157 22 [ [ -LRB- cord-284810-fs5rx07q 157 23 Fig Fig NNP cord-284810-fs5rx07q 157 24 . . . cord-284810-fs5rx07q 157 25 3(d 3(d CD cord-284810-fs5rx07q 157 26 ) ) -RRB- cord-284810-fs5rx07q 157 27 ] ] -RRB- cord-284810-fs5rx07q 157 28 . . . cord-284810-fs5rx07q 158 1 Correspondingly correspondingly RB cord-284810-fs5rx07q 158 2 , , , cord-284810-fs5rx07q 158 3 the the DT cord-284810-fs5rx07q 158 4 number number NN cord-284810-fs5rx07q 158 5 of of IN cord-284810-fs5rx07q 158 6 invaded invade VBN cord-284810-fs5rx07q 158 7 countries country NNS cord-284810-fs5rx07q 158 8 grows grow VBZ cord-284810-fs5rx07q 158 9 stochastically stochastically RB cord-284810-fs5rx07q 158 10 and and CC cord-284810-fs5rx07q 158 11 roughly roughly RB cord-284810-fs5rx07q 158 12 follows follow VBZ cord-284810-fs5rx07q 158 13 a a DT cord-284810-fs5rx07q 158 14 sigmoidal sigmoidal JJ cord-284810-fs5rx07q 158 15 shape shape NN cord-284810-fs5rx07q 158 16 . . . cord-284810-fs5rx07q 159 1 In in IN cord-284810-fs5rx07q 159 2 accord accord NN cord-284810-fs5rx07q 159 3 to to IN cord-284810-fs5rx07q 159 4 our -PRON- PRP$ cord-284810-fs5rx07q 159 5 theory theory NN cord-284810-fs5rx07q 159 6 , , , cord-284810-fs5rx07q 159 7 Eq Eq NNP cord-284810-fs5rx07q 159 8 . . . cord-284810-fs5rx07q 160 1 ( ( -LRB- cord-284810-fs5rx07q 160 2 2 2 LS cord-284810-fs5rx07q 160 3 ) ) -RRB- cord-284810-fs5rx07q 160 4 , , , cord-284810-fs5rx07q 160 5 this this DT cord-284810-fs5rx07q 160 6 arrival arrival NN cord-284810-fs5rx07q 160 7 time time NN cord-284810-fs5rx07q 160 8 distribution distribution NN cord-284810-fs5rx07q 160 9 starts start VBZ cord-284810-fs5rx07q 160 10 to to TO cord-284810-fs5rx07q 160 11 grow grow VB cord-284810-fs5rx07q 160 12 exponentially exponentially RB cord-284810-fs5rx07q 160 13 in in IN cord-284810-fs5rx07q 160 14 the the DT cord-284810-fs5rx07q 160 15 build build VB cord-284810-fs5rx07q 160 16 - - HYPH cord-284810-fs5rx07q 160 17 up up RP cord-284810-fs5rx07q 160 18 phase phase NN cord-284810-fs5rx07q 160 19 of of IN cord-284810-fs5rx07q 160 20 the the DT cord-284810-fs5rx07q 160 21 pandemic pandemic NN cord-284810-fs5rx07q 160 22 . . . cord-284810-fs5rx07q 161 1 The the DT cord-284810-fs5rx07q 161 2 highest high JJS cord-284810-fs5rx07q 161 3 invasion invasion NN cord-284810-fs5rx07q 161 4 rates rate NNS cord-284810-fs5rx07q 161 5 occur occur VBP cord-284810-fs5rx07q 161 6 after after IN cord-284810-fs5rx07q 161 7 about about RB cord-284810-fs5rx07q 161 8 50 50 CD cord-284810-fs5rx07q 161 9 days day NNS cord-284810-fs5rx07q 161 10 , , , cord-284810-fs5rx07q 161 11 while while IN cord-284810-fs5rx07q 161 12 after after IN cord-284810-fs5rx07q 161 13 a a DT cord-284810-fs5rx07q 161 14 simulation simulation NN cord-284810-fs5rx07q 161 15 time time NN cord-284810-fs5rx07q 161 16 of of IN cord-284810-fs5rx07q 161 17 80 80 CD cord-284810-fs5rx07q 161 18 days day NNS cord-284810-fs5rx07q 161 19 , , , cord-284810-fs5rx07q 161 20 196 196 CD cord-284810-fs5rx07q 161 21 out out IN cord-284810-fs5rx07q 161 22 of of IN cord-284810-fs5rx07q 161 23 the the DT cord-284810-fs5rx07q 161 24 N n NN cord-284810-fs5rx07q 161 25 = = SYM cord-284810-fs5rx07q 161 26 200 200 CD cord-284810-fs5rx07q 161 27 countries country NNS cord-284810-fs5rx07q 161 28 are be VBP cord-284810-fs5rx07q 161 29 already already RB cord-284810-fs5rx07q 161 30 invaded invade VBN cord-284810-fs5rx07q 161 31 by by IN cord-284810-fs5rx07q 161 32 the the DT cord-284810-fs5rx07q 161 33 virus virus NN cord-284810-fs5rx07q 161 34 . . . cord-284810-fs5rx07q 161 35 _SP cord-284810-fs5rx07q 162 1 Combining combine VBG cord-284810-fs5rx07q 162 2 the the DT cord-284810-fs5rx07q 162 3 large large JJ cord-284810-fs5rx07q 162 4 - - HYPH cord-284810-fs5rx07q 162 5 scale scale NN cord-284810-fs5rx07q 162 6 and and CC cord-284810-fs5rx07q 162 7 small small JJ cord-284810-fs5rx07q 162 8 - - HYPH cord-284810-fs5rx07q 162 9 scale scale NN cord-284810-fs5rx07q 162 10 model model NN cord-284810-fs5rx07q 162 11 components component NNS cord-284810-fs5rx07q 162 12 allows allow VBZ cord-284810-fs5rx07q 162 13 us -PRON- PRP cord-284810-fs5rx07q 162 14 to to TO cord-284810-fs5rx07q 162 15 simulate simulate VB cord-284810-fs5rx07q 162 16 the the DT cord-284810-fs5rx07q 162 17 epidemic epidemic NN cord-284810-fs5rx07q 162 18 prevalence prevalence NN cord-284810-fs5rx07q 162 19 in in IN cord-284810-fs5rx07q 162 20 each each DT cord-284810-fs5rx07q 162 21 country country NN cord-284810-fs5rx07q 162 22 as as IN cord-284810-fs5rx07q 162 23 a a DT cord-284810-fs5rx07q 162 24 function function NN cord-284810-fs5rx07q 162 25 of of IN cord-284810-fs5rx07q 162 26 time time NN cord-284810-fs5rx07q 162 27 . . . cord-284810-fs5rx07q 163 1 Figures figure NNS cord-284810-fs5rx07q 163 2 3(a 3(a CD cord-284810-fs5rx07q 163 3 ) ) -RRB- cord-284810-fs5rx07q 163 4 and and CC cord-284810-fs5rx07q 163 5 3(b 3(b LS cord-284810-fs5rx07q 163 6 ) ) -RRB- cord-284810-fs5rx07q 163 7 show show VBP cord-284810-fs5rx07q 163 8 the the DT cord-284810-fs5rx07q 163 9 resulting result VBG cord-284810-fs5rx07q 163 10 distribution distribution NN cord-284810-fs5rx07q 163 11 of of IN cord-284810-fs5rx07q 163 12 cases case NNS cord-284810-fs5rx07q 163 13 and and CC cord-284810-fs5rx07q 163 14 deaths death NNS cord-284810-fs5rx07q 163 15 after after IN cord-284810-fs5rx07q 163 16 a a DT cord-284810-fs5rx07q 163 17 simulation simulation NN cord-284810-fs5rx07q 163 18 time time NN cord-284810-fs5rx07q 163 19 of of IN cord-284810-fs5rx07q 163 20 62 62 CD cord-284810-fs5rx07q 163 21 days day NNS cord-284810-fs5rx07q 163 22 [ [ -LRB- cord-284810-fs5rx07q 163 23 vertical vertical JJ cord-284810-fs5rx07q 163 24 red red JJ cord-284810-fs5rx07q 163 25 line line NN cord-284810-fs5rx07q 163 26 in in IN cord-284810-fs5rx07q 163 27 Fig Fig NNP cord-284810-fs5rx07q 163 28 . . . cord-284810-fs5rx07q 163 29 3(d 3(d CD cord-284810-fs5rx07q 163 30 ) ) -RRB- cord-284810-fs5rx07q 163 31 ] ] -RRB- cord-284810-fs5rx07q 163 32 . . . cord-284810-fs5rx07q 164 1 Again again RB cord-284810-fs5rx07q 164 2 , , , cord-284810-fs5rx07q 164 3 the the DT cord-284810-fs5rx07q 164 4 distributions distribution NNS cord-284810-fs5rx07q 164 5 are be VBP cord-284810-fs5rx07q 164 6 well well RB cord-284810-fs5rx07q 164 7 characterized characterize VBN cord-284810-fs5rx07q 164 8 by by IN cord-284810-fs5rx07q 164 9 a a DT cord-284810-fs5rx07q 164 10 truncated truncated JJ cord-284810-fs5rx07q 164 11 power power NN cord-284810-fs5rx07q 164 12 - - HYPH cord-284810-fs5rx07q 164 13 law law NN cord-284810-fs5rx07q 164 14 . . . cord-284810-fs5rx07q 165 1 Comparison comparison NN cord-284810-fs5rx07q 165 2 with with IN cord-284810-fs5rx07q 165 3 Fig Fig NNP cord-284810-fs5rx07q 165 4 . . . cord-284810-fs5rx07q 166 1 1 1 CD cord-284810-fs5rx07q 166 2 shows show VBZ cord-284810-fs5rx07q 166 3 that that IN cord-284810-fs5rx07q 166 4 the the DT cord-284810-fs5rx07q 166 5 model model NN cord-284810-fs5rx07q 166 6 is be VBZ cord-284810-fs5rx07q 166 7 able able JJ cord-284810-fs5rx07q 166 8 to to TO cord-284810-fs5rx07q 166 9 describe describe VB cord-284810-fs5rx07q 166 10 the the DT cord-284810-fs5rx07q 166 11 characteristics characteristic NNS cord-284810-fs5rx07q 166 12 of of IN cord-284810-fs5rx07q 166 13 the the DT cord-284810-fs5rx07q 166 14 empirical empirical JJ cord-284810-fs5rx07q 166 15 distribution distribution NN cord-284810-fs5rx07q 166 16 of of IN cord-284810-fs5rx07q 166 17 COVID-19 covid-19 JJ cord-284810-fs5rx07q 166 18 cases case NNS cord-284810-fs5rx07q 166 19 rather rather RB cord-284810-fs5rx07q 166 20 well well RB cord-284810-fs5rx07q 166 21 . . . cord-284810-fs5rx07q 167 1 The the DT cord-284810-fs5rx07q 167 2 log log NN cord-284810-fs5rx07q 167 3 - - HYPH cord-284810-fs5rx07q 167 4 likelihood likelihood NN cord-284810-fs5rx07q 167 5 estimation estimation NN cord-284810-fs5rx07q 167 6 of of IN cord-284810-fs5rx07q 167 7 the the DT cord-284810-fs5rx07q 167 8 critical critical JJ cord-284810-fs5rx07q 167 9 exponents exponent NNS cord-284810-fs5rx07q 167 10 yields yield VBZ cord-284810-fs5rx07q 167 11 values value NNS cord-284810-fs5rx07q 167 12 ofμ ofμ IN cord-284810-fs5rx07q 167 13 C c NN cord-284810-fs5rx07q 167 14 = = NFP cord-284810-fs5rx07q 168 1 1.18 1.18 CD cord-284810-fs5rx07q 169 1 ± ± NNP cord-284810-fs5rx07q 169 2 0.01 0.01 CD cord-284810-fs5rx07q 169 3 andμ andμ NNP cord-284810-fs5rx07q 169 4 D D NNP cord-284810-fs5rx07q 169 5 = = SYM cord-284810-fs5rx07q 169 6 1.40 1.40 CD cord-284810-fs5rx07q 169 7 ± ± CD cord-284810-fs5rx07q 169 8 0.06 0.06 CD cord-284810-fs5rx07q 169 9 . . . cord-284810-fs5rx07q 170 1 These these DT cord-284810-fs5rx07q 170 2 exponents exponent NNS cord-284810-fs5rx07q 170 3 can can MD cord-284810-fs5rx07q 170 4 be be VB cord-284810-fs5rx07q 170 5 compared compare VBN cord-284810-fs5rx07q 170 6 to to IN cord-284810-fs5rx07q 170 7 our -PRON- PRP$ cord-284810-fs5rx07q 170 8 theory theory NN cord-284810-fs5rx07q 170 9 equation equation NN cord-284810-fs5rx07q 170 10 ( ( -LRB- cord-284810-fs5rx07q 170 11 5 5 CD cord-284810-fs5rx07q 170 12 ) ) -RRB- cord-284810-fs5rx07q 170 13 . . . cord-284810-fs5rx07q 171 1 From from IN cord-284810-fs5rx07q 171 2 Fig Fig NNP cord-284810-fs5rx07q 171 3 . . . cord-284810-fs5rx07q 171 4 3(d 3(d CD cord-284810-fs5rx07q 171 5 ) ) -RRB- cord-284810-fs5rx07q 171 6 , , , cord-284810-fs5rx07q 171 7 we -PRON- PRP cord-284810-fs5rx07q 171 8 estimate estimate VBP cord-284810-fs5rx07q 171 9 a a DT cord-284810-fs5rx07q 171 10 spatial spatial JJ cord-284810-fs5rx07q 171 11 spreading spreading NN cord-284810-fs5rx07q 171 12 rate rate NN cord-284810-fs5rx07q 171 13 of of IN cord-284810-fs5rx07q 171 14 s s NN cord-284810-fs5rx07q 171 15 = = SYM cord-284810-fs5rx07q 171 16 0.037 0.037 CD cord-284810-fs5rx07q 171 17 d d NNP cord-284810-fs5rx07q 171 18 −1 −1 NNP cord-284810-fs5rx07q 171 19 in in IN cord-284810-fs5rx07q 171 20 the the DT cord-284810-fs5rx07q 171 21 build build VB cord-284810-fs5rx07q 171 22 - - HYPH cord-284810-fs5rx07q 171 23 up up RP cord-284810-fs5rx07q 171 24 phase phase NN cord-284810-fs5rx07q 171 25 of of IN cord-284810-fs5rx07q 171 26 the the DT cord-284810-fs5rx07q 171 27 pandemic pandemic NN cord-284810-fs5rx07q 171 28 . . . cord-284810-fs5rx07q 172 1 The the DT cord-284810-fs5rx07q 172 2 initial initial JJ cord-284810-fs5rx07q 172 3 growth growth NN cord-284810-fs5rx07q 172 4 rate rate NN cord-284810-fs5rx07q 172 5 of of IN cord-284810-fs5rx07q 172 6 infected infect VBN cord-284810-fs5rx07q 172 7 in in IN cord-284810-fs5rx07q 172 8 the the DT cord-284810-fs5rx07q 172 9 SIR SIR NNP cord-284810-fs5rx07q 172 10 - - HYPH cord-284810-fs5rx07q 172 11 model model NN cord-284810-fs5rx07q 172 12 equals equal VBZ cord-284810-fs5rx07q 172 13 r r NN cord-284810-fs5rx07q 172 14 = = SYM cord-284810-fs5rx07q 172 15 0.23 0.23 CD cord-284810-fs5rx07q 172 16 d d NNP cord-284810-fs5rx07q 172 17 −1 −1 NNP cord-284810-fs5rx07q 172 18 ( ( -LRB- cord-284810-fs5rx07q 172 19 see see VB cord-284810-fs5rx07q 172 20 Appendix Appendix NNP cord-284810-fs5rx07q 172 21 B B NNP cord-284810-fs5rx07q 172 22 ) ) -RRB- cord-284810-fs5rx07q 172 23 . . . cord-284810-fs5rx07q 173 1 Thus thus RB cord-284810-fs5rx07q 173 2 , , , cord-284810-fs5rx07q 173 3 according accord VBG cord-284810-fs5rx07q 173 4 to to IN cord-284810-fs5rx07q 173 5 Eq Eq NNP cord-284810-fs5rx07q 173 6 . . . cord-284810-fs5rx07q 174 1 ( ( -LRB- cord-284810-fs5rx07q 174 2 5 5 LS cord-284810-fs5rx07q 174 3 ) ) -RRB- cord-284810-fs5rx07q 174 4 , , , cord-284810-fs5rx07q 174 5 we -PRON- PRP cord-284810-fs5rx07q 174 6 would would MD cord-284810-fs5rx07q 174 7 expect expect VB cord-284810-fs5rx07q 174 8 a a DT cord-284810-fs5rx07q 174 9 critical critical JJ cord-284810-fs5rx07q 174 10 exponent exponent NN cord-284810-fs5rx07q 174 11 of of IN cord-284810-fs5rx07q 175 1 µ µ NN cord-284810-fs5rx07q 175 2 = = SYM cord-284810-fs5rx07q 175 3 1 1 CD cord-284810-fs5rx07q 175 4 + + SYM cord-284810-fs5rx07q 175 5 0.037/0.23 0.037/0.23 CD cord-284810-fs5rx07q 175 6 = = SYM cord-284810-fs5rx07q 175 7 0.16 0.16 CD cord-284810-fs5rx07q 175 8 , , , cord-284810-fs5rx07q 175 9 in in IN cord-284810-fs5rx07q 175 10 good good JJ cord-284810-fs5rx07q 175 11 agreement agreement NN cord-284810-fs5rx07q 175 12 to to IN cord-284810-fs5rx07q 175 13 the the DT cord-284810-fs5rx07q 175 14 estimated estimate VBN cord-284810-fs5rx07q 175 15 value value NN cord-284810-fs5rx07q 175 16 from from IN cord-284810-fs5rx07q 175 17 the the DT cord-284810-fs5rx07q 175 18 numerical numerical JJ cord-284810-fs5rx07q 175 19 simulation simulation NN cord-284810-fs5rx07q 175 20 . . . cord-284810-fs5rx07q 176 1 We -PRON- PRP cord-284810-fs5rx07q 176 2 want want VBP cord-284810-fs5rx07q 176 3 to to TO cord-284810-fs5rx07q 176 4 note note VB cord-284810-fs5rx07q 176 5 that that IN cord-284810-fs5rx07q 176 6 the the DT cord-284810-fs5rx07q 176 7 nearly nearly RB cord-284810-fs5rx07q 176 8 ideal ideal JJ cord-284810-fs5rx07q 176 9 power power NN cord-284810-fs5rx07q 176 10 - - HYPH cord-284810-fs5rx07q 176 11 law law NN cord-284810-fs5rx07q 176 12 scaling scaling NN cord-284810-fs5rx07q 176 13 in in IN cord-284810-fs5rx07q 176 14 the the DT cord-284810-fs5rx07q 176 15 case case NN cord-284810-fs5rx07q 176 16 distribution distribution NN cord-284810-fs5rx07q 176 17 holds hold VBZ cord-284810-fs5rx07q 176 18 only only RB cord-284810-fs5rx07q 176 19 in in IN cord-284810-fs5rx07q 176 20 the the DT cord-284810-fs5rx07q 176 21 initial initial JJ cord-284810-fs5rx07q 176 22 phase phase NN cord-284810-fs5rx07q 176 23 of of IN cord-284810-fs5rx07q 176 24 the the DT cord-284810-fs5rx07q 176 25 pandemic pandemic NN cord-284810-fs5rx07q 176 26 and and CC cord-284810-fs5rx07q 176 27 is be VBZ cord-284810-fs5rx07q 176 28 lost lose VBN cord-284810-fs5rx07q 176 29 when when WRB cord-284810-fs5rx07q 176 30 the the DT cord-284810-fs5rx07q 176 31 spatial spatial JJ cord-284810-fs5rx07q 176 32 spreading spreading NN cord-284810-fs5rx07q 176 33 starts start VBZ cord-284810-fs5rx07q 176 34 to to TO cord-284810-fs5rx07q 176 35 saturate saturate VB cord-284810-fs5rx07q 176 36 . . . cord-284810-fs5rx07q 177 1 This this DT cord-284810-fs5rx07q 177 2 can can MD cord-284810-fs5rx07q 177 3 be be VB cord-284810-fs5rx07q 177 4 seen see VBN cord-284810-fs5rx07q 177 5 in in IN cord-284810-fs5rx07q 177 6 the the DT cord-284810-fs5rx07q 177 7 simulated simulated JJ cord-284810-fs5rx07q 177 8 case case NN cord-284810-fs5rx07q 177 9 distribution distribution NN cord-284810-fs5rx07q 177 10 P(n p(n NN cord-284810-fs5rx07q 177 11 ) ) -RRB- cord-284810-fs5rx07q 177 12 for for IN cord-284810-fs5rx07q 177 13 different different JJ cord-284810-fs5rx07q 177 14 time time NN cord-284810-fs5rx07q 177 15 instances instance NNS cord-284810-fs5rx07q 177 16 [ [ -LRB- cord-284810-fs5rx07q 177 17 Fig Fig NNP cord-284810-fs5rx07q 177 18 . . . cord-284810-fs5rx07q 177 19 3(c 3(c CD cord-284810-fs5rx07q 177 20 ) ) -RRB- cord-284810-fs5rx07q 177 21 ] ] -RRB- cord-284810-fs5rx07q 177 22 . . . cord-284810-fs5rx07q 178 1 While while IN cord-284810-fs5rx07q 178 2 P(n P(n NNP cord-284810-fs5rx07q 178 3 ) ) -RRB- cord-284810-fs5rx07q 178 4 remains remain VBZ cord-284810-fs5rx07q 178 5 roughly roughly RB cord-284810-fs5rx07q 178 6 stationary stationary JJ cord-284810-fs5rx07q 178 7 for for IN cord-284810-fs5rx07q 178 8 the the DT cord-284810-fs5rx07q 178 9 first first JJ cord-284810-fs5rx07q 178 10 50 50 CD cord-284810-fs5rx07q 178 11 - - SYM cord-284810-fs5rx07q 178 12 60 60 CD cord-284810-fs5rx07q 178 13 days day NNS cord-284810-fs5rx07q 178 14 of of IN cord-284810-fs5rx07q 178 15 the the DT cord-284810-fs5rx07q 178 16 simulation simulation NN cord-284810-fs5rx07q 178 17 , , , cord-284810-fs5rx07q 178 18 a a DT cord-284810-fs5rx07q 178 19 first first JJ cord-284810-fs5rx07q 178 20 plateau plateau NN cord-284810-fs5rx07q 178 21 begins begin VBZ cord-284810-fs5rx07q 178 22 to to TO cord-284810-fs5rx07q 178 23 emerge emerge VB cord-284810-fs5rx07q 178 24 at at IN cord-284810-fs5rx07q 178 25 the the DT cord-284810-fs5rx07q 178 26 left left JJ cord-284810-fs5rx07q 178 27 end end NN cord-284810-fs5rx07q 178 28 of of IN cord-284810-fs5rx07q 178 29 the the DT cord-284810-fs5rx07q 178 30 distribution distribution NN cord-284810-fs5rx07q 178 31 for for IN cord-284810-fs5rx07q 178 32 larger large JJR cord-284810-fs5rx07q 178 33 times time NNS cord-284810-fs5rx07q 178 34 . . . cord-284810-fs5rx07q 179 1 This this DT cord-284810-fs5rx07q 179 2 plateau plateau NN cord-284810-fs5rx07q 179 3 reflects reflect VBZ cord-284810-fs5rx07q 179 4 the the DT cord-284810-fs5rx07q 179 5 fact fact NN cord-284810-fs5rx07q 179 6 that that IN cord-284810-fs5rx07q 179 7 when when WRB cord-284810-fs5rx07q 179 8 the the DT cord-284810-fs5rx07q 179 9 number number NN cord-284810-fs5rx07q 179 10 of of IN cord-284810-fs5rx07q 179 11 newly newly RB cord-284810-fs5rx07q 179 12 invaded invade VBN cord-284810-fs5rx07q 179 13 countries country NNS cord-284810-fs5rx07q 179 14 is be VBZ cord-284810-fs5rx07q 179 15 reduced reduce VBN cord-284810-fs5rx07q 179 16 , , , cord-284810-fs5rx07q 179 17 these these DT cord-284810-fs5rx07q 179 18 countries country NNS cord-284810-fs5rx07q 179 19 with with IN cord-284810-fs5rx07q 179 20 just just RB cord-284810-fs5rx07q 179 21 a a DT cord-284810-fs5rx07q 179 22 few few JJ cord-284810-fs5rx07q 179 23 cases case NNS cord-284810-fs5rx07q 179 24 are be VBP cord-284810-fs5rx07q 179 25 missing miss VBG cord-284810-fs5rx07q 179 26 in in IN cord-284810-fs5rx07q 179 27 the the DT cord-284810-fs5rx07q 179 28 left left JJ cord-284810-fs5rx07q 179 29 end end NN cord-284810-fs5rx07q 179 30 of of IN cord-284810-fs5rx07q 179 31 the the DT cord-284810-fs5rx07q 179 32 case case NN cord-284810-fs5rx07q 179 33 distribution distribution NN cord-284810-fs5rx07q 179 34 [ [ -LRB- cord-284810-fs5rx07q 179 35 reminiscent reminiscent JJ cord-284810-fs5rx07q 179 36 to to IN cord-284810-fs5rx07q 179 37 the the DT cord-284810-fs5rx07q 179 38 behavior behavior NN cord-284810-fs5rx07q 179 39 exhibited exhibit VBN cord-284810-fs5rx07q 179 40 in in IN cord-284810-fs5rx07q 179 41 the the DT cord-284810-fs5rx07q 179 42 empirical empirical JJ cord-284810-fs5rx07q 179 43 case case NN cord-284810-fs5rx07q 179 44 distribution distribution NN cord-284810-fs5rx07q 179 45 , , , cord-284810-fs5rx07q 179 46 Fig Fig NNP cord-284810-fs5rx07q 179 47 . . NNP cord-284810-fs5rx07q 179 48 2(a 2(a CD cord-284810-fs5rx07q 179 49 ) ) -RRB- cord-284810-fs5rx07q 179 50 ] ] -RRB- cord-284810-fs5rx07q 179 51 . . . cord-284810-fs5rx07q 180 1 Additionally additionally RB cord-284810-fs5rx07q 180 2 , , , cord-284810-fs5rx07q 180 3 the the DT cord-284810-fs5rx07q 180 4 estimated estimate VBN cord-284810-fs5rx07q 180 5 critical critical JJ cord-284810-fs5rx07q 180 6 exponents exponent NNS cord-284810-fs5rx07q 180 7 are be VBP cord-284810-fs5rx07q 180 8 decaying decay VBG cord-284810-fs5rx07q 180 9 in in IN cord-284810-fs5rx07q 180 10 time time NN cord-284810-fs5rx07q 180 11 [ [ -LRB- cord-284810-fs5rx07q 180 12 inset inset NN cord-284810-fs5rx07q 180 13 of of IN cord-284810-fs5rx07q 180 14 Fig Fig NNP cord-284810-fs5rx07q 180 15 . . . cord-284810-fs5rx07q 181 1 3(d 3(d LS cord-284810-fs5rx07q 181 2 ) ) -RRB- cord-284810-fs5rx07q 181 3 ] ] -RRB- cord-284810-fs5rx07q 181 4 , , , cord-284810-fs5rx07q 181 5 similar similar JJ cord-284810-fs5rx07q 181 6 to to IN cord-284810-fs5rx07q 181 7 that that DT cord-284810-fs5rx07q 181 8 of of IN cord-284810-fs5rx07q 181 9 the the DT cord-284810-fs5rx07q 181 10 empirical empirical JJ cord-284810-fs5rx07q 181 11 data datum NNS cord-284810-fs5rx07q 181 12 [ [ -LRB- cord-284810-fs5rx07q 181 13 inset inset NN cord-284810-fs5rx07q 181 14 of of IN cord-284810-fs5rx07q 181 15 Fig Fig NNP cord-284810-fs5rx07q 181 16 . . . cord-284810-fs5rx07q 181 17 2(b 2(b CD cord-284810-fs5rx07q 181 18 ) ) -RRB- cord-284810-fs5rx07q 181 19 ] ] -RRB- cord-284810-fs5rx07q 181 20 . . . cord-284810-fs5rx07q 182 1 Thus thus RB cord-284810-fs5rx07q 182 2 , , , cord-284810-fs5rx07q 182 3 the the DT cord-284810-fs5rx07q 182 4 first first JJ cord-284810-fs5rx07q 182 5 sign sign NN cord-284810-fs5rx07q 182 6 that that IN cord-284810-fs5rx07q 182 7 the the DT cord-284810-fs5rx07q 182 8 outbreak outbreak NN cord-284810-fs5rx07q 182 9 has have VBZ cord-284810-fs5rx07q 182 10 reached reach VBN cord-284810-fs5rx07q 182 11 most most JJS cord-284810-fs5rx07q 182 12 countries country NNS cord-284810-fs5rx07q 182 13 in in IN cord-284810-fs5rx07q 182 14 the the DT cord-284810-fs5rx07q 182 15 network network NN cord-284810-fs5rx07q 182 16 is be VBZ cord-284810-fs5rx07q 182 17 the the DT cord-284810-fs5rx07q 182 18 reduction reduction NN cord-284810-fs5rx07q 182 19 in in IN cord-284810-fs5rx07q 182 20 the the DT cord-284810-fs5rx07q 182 21 scaling scale VBG cord-284810-fs5rx07q 182 22 range range NN cord-284810-fs5rx07q 182 23 and and CC cord-284810-fs5rx07q 182 24 a a DT cord-284810-fs5rx07q 182 25 simultaneous simultaneous JJ cord-284810-fs5rx07q 182 26 broadening broadening NN cord-284810-fs5rx07q 182 27 of of IN cord-284810-fs5rx07q 182 28 the the DT cord-284810-fs5rx07q 182 29 case case NN cord-284810-fs5rx07q 182 30 distribution distribution NN cord-284810-fs5rx07q 182 31 . . . cord-284810-fs5rx07q 183 1 Eventually eventually RB cord-284810-fs5rx07q 183 2 , , , cord-284810-fs5rx07q 183 3 in in IN cord-284810-fs5rx07q 183 4 the the DT cord-284810-fs5rx07q 183 5 limit limit NN cord-284810-fs5rx07q 183 6 of of IN cord-284810-fs5rx07q 183 7 large large JJ cord-284810-fs5rx07q 183 8 time time NN cord-284810-fs5rx07q 183 9 , , , cord-284810-fs5rx07q 183 10 when when WRB cord-284810-fs5rx07q 183 11 the the DT cord-284810-fs5rx07q 183 12 epidemic epidemic NN cord-284810-fs5rx07q 183 13 has have VBZ cord-284810-fs5rx07q 183 14 come come VBN cord-284810-fs5rx07q 183 15 to to IN cord-284810-fs5rx07q 183 16 an an DT cord-284810-fs5rx07q 183 17 end end NN cord-284810-fs5rx07q 183 18 in in IN cord-284810-fs5rx07q 183 19 every every DT cord-284810-fs5rx07q 183 20 country country NN cord-284810-fs5rx07q 183 21 , , , cord-284810-fs5rx07q 183 22 scaling scale VBG cord-284810-fs5rx07q 183 23 is be VBZ cord-284810-fs5rx07q 183 24 lost lose VBN cord-284810-fs5rx07q 183 25 and and CC cord-284810-fs5rx07q 183 26 the the DT cord-284810-fs5rx07q 183 27 distribution distribution NN cord-284810-fs5rx07q 183 28 of of IN cord-284810-fs5rx07q 183 29 cases case NNS cord-284810-fs5rx07q 183 30 must must MD cord-284810-fs5rx07q 183 31 converge converge VB cord-284810-fs5rx07q 183 32 toward toward IN cord-284810-fs5rx07q 183 33 a a DT cord-284810-fs5rx07q 183 34 delta delta NN cord-284810-fs5rx07q 183 35 function function NN cord-284810-fs5rx07q 183 36 P(n p(n NN cord-284810-fs5rx07q 183 37 ) ) -RRB- cord-284810-fs5rx07q 183 38 = = NFP cord-284810-fs5rx07q 184 1 δ(n δ(n NNP cord-284810-fs5rx07q 184 2 − − NNP cord-284810-fs5rx07q 185 1 fN fN NFP cord-284810-fs5rx07q 185 2 pop pop NNP cord-284810-fs5rx07q 185 3 ) ) -RRB- cord-284810-fs5rx07q 185 4 , , , cord-284810-fs5rx07q 185 5 with with IN cord-284810-fs5rx07q 185 6 f f NNP cord-284810-fs5rx07q 185 7 the the DT cord-284810-fs5rx07q 185 8 fraction fraction NN cord-284810-fs5rx07q 185 9 of of IN cord-284810-fs5rx07q 185 10 susceptible susceptible JJ cord-284810-fs5rx07q 185 11 out out IN cord-284810-fs5rx07q 185 12 of of IN cord-284810-fs5rx07q 185 13 a a DT cord-284810-fs5rx07q 185 14 population population NN cord-284810-fs5rx07q 185 15 of of IN cord-284810-fs5rx07q 185 16 N n CD cord-284810-fs5rx07q 185 17 pop pop NN cord-284810-fs5rx07q 185 18 individuals individual NNS cord-284810-fs5rx07q 185 19 in in IN cord-284810-fs5rx07q 185 20 a a DT cord-284810-fs5rx07q 185 21 country country NN cord-284810-fs5rx07q 185 22 that that WDT cord-284810-fs5rx07q 185 23 will will MD cord-284810-fs5rx07q 185 24 be be VB cord-284810-fs5rx07q 185 25 infected infect VBN cord-284810-fs5rx07q 185 26 ( ( -LRB- cord-284810-fs5rx07q 185 27 or or CC cord-284810-fs5rx07q 185 28 it -PRON- PRP cord-284810-fs5rx07q 185 29 would would MD cord-284810-fs5rx07q 185 30 approach approach VB cord-284810-fs5rx07q 185 31 the the DT cord-284810-fs5rx07q 185 32 country country NN cord-284810-fs5rx07q 185 33 size size NN cord-284810-fs5rx07q 185 34 distribution distribution NN cord-284810-fs5rx07q 185 35 in in IN cord-284810-fs5rx07q 185 36 a a DT cord-284810-fs5rx07q 185 37 meta meta NN cord-284810-fs5rx07q 185 38 - - HYPH cord-284810-fs5rx07q 185 39 population population NN cord-284810-fs5rx07q 185 40 with with IN cord-284810-fs5rx07q 185 41 heterogeneously heterogeneously NNP cord-284810-fs5rx07q 185 42 distributed distribute VBN cord-284810-fs5rx07q 185 43 country country NN cord-284810-fs5rx07q 185 44 sizes size NNS cord-284810-fs5rx07q 185 45 ) ) -RRB- cord-284810-fs5rx07q 185 46 . . . cord-284810-fs5rx07q 186 1 Interestingly interestingly RB cord-284810-fs5rx07q 186 2 , , , cord-284810-fs5rx07q 186 3 in in IN cord-284810-fs5rx07q 186 4 our -PRON- PRP$ cord-284810-fs5rx07q 186 5 numerical numerical JJ cord-284810-fs5rx07q 186 6 simulations simulation NNS cord-284810-fs5rx07q 186 7 , , , cord-284810-fs5rx07q 186 8 we -PRON- PRP cord-284810-fs5rx07q 186 9 still still RB cord-284810-fs5rx07q 186 10 obtained obtain VBD cord-284810-fs5rx07q 186 11 power power NN cord-284810-fs5rx07q 186 12 - - HYPH cord-284810-fs5rx07q 186 13 law law NN cord-284810-fs5rx07q 186 14 distribution distribution NN cord-284810-fs5rx07q 186 15 when when WRB cord-284810-fs5rx07q 186 16 the the DT cord-284810-fs5rx07q 186 17 contact contact NN cord-284810-fs5rx07q 186 18 rate rate NN cord-284810-fs5rx07q 186 19 β β NNP cord-284810-fs5rx07q 186 20 was be VBD cord-284810-fs5rx07q 186 21 set set VBN cord-284810-fs5rx07q 186 22 to to IN cord-284810-fs5rx07q 186 23 a a DT cord-284810-fs5rx07q 186 24 large large JJ cord-284810-fs5rx07q 186 25 value value NN cord-284810-fs5rx07q 186 26 , , , cord-284810-fs5rx07q 186 27 so so IN cord-284810-fs5rx07q 186 28 that that IN cord-284810-fs5rx07q 186 29 the the DT cord-284810-fs5rx07q 186 30 dynamics dynamic NNS cord-284810-fs5rx07q 186 31 within within IN cord-284810-fs5rx07q 186 32 a a DT cord-284810-fs5rx07q 186 33 country country NN cord-284810-fs5rx07q 186 34 rapidly rapidly RB cord-284810-fs5rx07q 186 35 reach reach VBP cord-284810-fs5rx07q 186 36 a a DT cord-284810-fs5rx07q 186 37 stationary stationary JJ cord-284810-fs5rx07q 186 38 state state NN cord-284810-fs5rx07q 186 39 . . . cord-284810-fs5rx07q 187 1 In in IN cord-284810-fs5rx07q 187 2 this this DT cord-284810-fs5rx07q 187 3 case case NN cord-284810-fs5rx07q 187 4 , , , cord-284810-fs5rx07q 187 5 with with IN cord-284810-fs5rx07q 187 6 increasing increase VBG cord-284810-fs5rx07q 187 7 β β NN cord-284810-fs5rx07q 187 8 ( ( -LRB- cord-284810-fs5rx07q 187 9 and and CC cord-284810-fs5rx07q 187 10 thus thus RB cord-284810-fs5rx07q 187 11 increasing increase VBG cord-284810-fs5rx07q 187 12 initial initial JJ cord-284810-fs5rx07q 187 13 epidemic epidemic NN cord-284810-fs5rx07q 187 14 growth growth NN cord-284810-fs5rx07q 187 15 rates rate NNS cord-284810-fs5rx07q 187 16 r r NNP cord-284810-fs5rx07q 187 17 ) ) -RRB- cord-284810-fs5rx07q 187 18 , , , cord-284810-fs5rx07q 187 19 the the DT cord-284810-fs5rx07q 187 20 critical critical JJ cord-284810-fs5rx07q 187 21 exponents exponent NNS cord-284810-fs5rx07q 187 22 tended tend VBD cord-284810-fs5rx07q 187 23 to to IN cord-284810-fs5rx07q 187 24 µ µ VB cord-284810-fs5rx07q 187 25 → → SYM cord-284810-fs5rx07q 187 26 1 1 CD cord-284810-fs5rx07q 187 27 . . . cord-284810-fs5rx07q 188 1 It -PRON- PRP cord-284810-fs5rx07q 188 2 is be VBZ cord-284810-fs5rx07q 188 3 well well RB cord-284810-fs5rx07q 188 4 known know VBN cord-284810-fs5rx07q 188 5 from from IN cord-284810-fs5rx07q 188 6 the the DT cord-284810-fs5rx07q 188 7 literature literature NN cord-284810-fs5rx07q 188 8 11,29 11,29 CD cord-284810-fs5rx07q 188 9 that that WDT cord-284810-fs5rx07q 188 10 caution caution NN cord-284810-fs5rx07q 188 11 is be VBZ cord-284810-fs5rx07q 188 12 in in IN cord-284810-fs5rx07q 188 13 order order NN cord-284810-fs5rx07q 188 14 when when WRB cord-284810-fs5rx07q 188 15 trying try VBG cord-284810-fs5rx07q 188 16 to to TO cord-284810-fs5rx07q 188 17 identify identify VB cord-284810-fs5rx07q 188 18 power power NN cord-284810-fs5rx07q 188 19 - - HYPH cord-284810-fs5rx07q 188 20 law law NN cord-284810-fs5rx07q 188 21 distributions distribution NNS cord-284810-fs5rx07q 188 22 in in IN cord-284810-fs5rx07q 188 23 real real JJ cord-284810-fs5rx07q 188 24 data datum NNS cord-284810-fs5rx07q 188 25 and and CC cord-284810-fs5rx07q 188 26 , , , cord-284810-fs5rx07q 188 27 in in IN cord-284810-fs5rx07q 188 28 particular particular JJ cord-284810-fs5rx07q 188 29 , , , cord-284810-fs5rx07q 188 30 that that IN cord-284810-fs5rx07q 188 31 a a DT cord-284810-fs5rx07q 188 32 straight straight JJ cord-284810-fs5rx07q 188 33 line line NN cord-284810-fs5rx07q 188 34 in in IN cord-284810-fs5rx07q 188 35 a a DT cord-284810-fs5rx07q 188 36 double double JJ cord-284810-fs5rx07q 188 37 - - HYPH cord-284810-fs5rx07q 188 38 logarithmic logarithmic JJ cord-284810-fs5rx07q 188 39 plot plot NN cord-284810-fs5rx07q 188 40 does do VBZ cord-284810-fs5rx07q 188 41 not not RB cord-284810-fs5rx07q 188 42 suffice suffice VB cord-284810-fs5rx07q 188 43 to to TO cord-284810-fs5rx07q 188 44 prove prove VB cord-284810-fs5rx07q 188 45 the the DT cord-284810-fs5rx07q 188 46 existence existence NN cord-284810-fs5rx07q 188 47 of of IN cord-284810-fs5rx07q 188 48 a a DT cord-284810-fs5rx07q 188 49 power power NN cord-284810-fs5rx07q 188 50 - - HYPH cord-284810-fs5rx07q 188 51 law law NN cord-284810-fs5rx07q 188 52 distribution distribution NN cord-284810-fs5rx07q 188 53 . . . cord-284810-fs5rx07q 189 1 For for IN cord-284810-fs5rx07q 189 2 this this DT cord-284810-fs5rx07q 189 3 reason reason NN cord-284810-fs5rx07q 189 4 , , , cord-284810-fs5rx07q 189 5 the the DT cord-284810-fs5rx07q 189 6 aim aim NN cord-284810-fs5rx07q 189 7 of of IN cord-284810-fs5rx07q 189 8 this this DT cord-284810-fs5rx07q 189 9 study study NN cord-284810-fs5rx07q 189 10 is be VBZ cord-284810-fs5rx07q 189 11 not not RB cord-284810-fs5rx07q 189 12 to to TO cord-284810-fs5rx07q 189 13 prove prove VB cord-284810-fs5rx07q 189 14 that that IN cord-284810-fs5rx07q 189 15 the the DT cord-284810-fs5rx07q 189 16 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 189 17 case case NN cord-284810-fs5rx07q 189 18 distribution distribution NN cord-284810-fs5rx07q 189 19 is be VBZ cord-284810-fs5rx07q 189 20 a a DT cord-284810-fs5rx07q 189 21 perfect perfect JJ cord-284810-fs5rx07q 189 22 power power NN cord-284810-fs5rx07q 189 23 - - HYPH cord-284810-fs5rx07q 189 24 law law NN cord-284810-fs5rx07q 189 25 , , , cord-284810-fs5rx07q 189 26 an an DT cord-284810-fs5rx07q 189 27 undertaking undertaking NN cord-284810-fs5rx07q 189 28 that that WDT cord-284810-fs5rx07q 189 29 would would MD cord-284810-fs5rx07q 189 30 require require VB cord-284810-fs5rx07q 189 31 sophisticated sophisticated JJ cord-284810-fs5rx07q 189 32 statistical statistical JJ cord-284810-fs5rx07q 189 33 analysis analysis NN cord-284810-fs5rx07q 189 34 and and CC cord-284810-fs5rx07q 189 35 a a DT cord-284810-fs5rx07q 189 36 much much RB cord-284810-fs5rx07q 189 37 larger large JJR cord-284810-fs5rx07q 189 38 sample sample NN cord-284810-fs5rx07q 189 39 size size NN cord-284810-fs5rx07q 189 40 . . . cord-284810-fs5rx07q 190 1 11 11 CD cord-284810-fs5rx07q 191 1 We -PRON- PRP cord-284810-fs5rx07q 191 2 also also RB cord-284810-fs5rx07q 191 3 do do VBP cord-284810-fs5rx07q 191 4 not not RB cord-284810-fs5rx07q 191 5 intend intend VB cord-284810-fs5rx07q 191 6 to to TO cord-284810-fs5rx07q 191 7 rule rule VB cord-284810-fs5rx07q 191 8 out out RP cord-284810-fs5rx07q 191 9 other other JJ cord-284810-fs5rx07q 191 10 likely likely JJ cord-284810-fs5rx07q 191 11 candidate candidate NN cord-284810-fs5rx07q 191 12 distributions distribution NNS cord-284810-fs5rx07q 191 13 ( ( -LRB- cord-284810-fs5rx07q 191 14 e.g. e.g. RB cord-284810-fs5rx07q 191 15 , , , cord-284810-fs5rx07q 191 16 log log NN cord-284810-fs5rx07q 191 17 - - HYPH cord-284810-fs5rx07q 191 18 normal normal JJ cord-284810-fs5rx07q 191 19 or or CC cord-284810-fs5rx07q 191 20 stretched stretched JJ cord-284810-fs5rx07q 191 21 exponential exponential JJ cord-284810-fs5rx07q 191 22 distributions distribution NNS cord-284810-fs5rx07q 191 23 ) ) -RRB- cord-284810-fs5rx07q 191 24 . . . cord-284810-fs5rx07q 192 1 Instead instead RB cord-284810-fs5rx07q 192 2 , , , cord-284810-fs5rx07q 192 3 our -PRON- PRP$ cord-284810-fs5rx07q 192 4 claim claim NN cord-284810-fs5rx07q 192 5 is be VBZ cord-284810-fs5rx07q 192 6 merely merely RB cord-284810-fs5rx07q 192 7 to to TO cord-284810-fs5rx07q 192 8 demonstrate demonstrate VB cord-284810-fs5rx07q 192 9 that that IN cord-284810-fs5rx07q 192 10 the the DT cord-284810-fs5rx07q 192 11 empirical empirical JJ cord-284810-fs5rx07q 192 12 data datum NNS cord-284810-fs5rx07q 192 13 are be VBP cord-284810-fs5rx07q 192 14 highly highly RB cord-284810-fs5rx07q 192 15 consistent consistent JJ cord-284810-fs5rx07q 192 16 with with IN cord-284810-fs5rx07q 192 17 the the DT cord-284810-fs5rx07q 192 18 hypothesis hypothesis NN cord-284810-fs5rx07q 192 19 that that IN cord-284810-fs5rx07q 192 20 the the DT cord-284810-fs5rx07q 192 21 number number NN cord-284810-fs5rx07q 192 22 of of IN cord-284810-fs5rx07q 192 23 reported report VBN cord-284810-fs5rx07q 192 24 cases case NNS cord-284810-fs5rx07q 192 25 are be VBP cord-284810-fs5rx07q 192 26 taken take VBN cord-284810-fs5rx07q 192 27 from from IN cord-284810-fs5rx07q 192 28 a a DT cord-284810-fs5rx07q 192 29 truncated truncated JJ cord-284810-fs5rx07q 192 30 power power NN cord-284810-fs5rx07q 192 31 - - HYPH cord-284810-fs5rx07q 192 32 law law NN cord-284810-fs5rx07q 192 33 distribution distribution NN cord-284810-fs5rx07q 192 34 of of IN cord-284810-fs5rx07q 192 35 the the DT cord-284810-fs5rx07q 192 36 form form NN cord-284810-fs5rx07q 192 37 equation equation NN cord-284810-fs5rx07q 192 38 ( ( -LRB- cord-284810-fs5rx07q 192 39 1 1 CD cord-284810-fs5rx07q 192 40 ) ) -RRB- cord-284810-fs5rx07q 192 41 . . . cord-284810-fs5rx07q 193 1 Nevertheless nevertheless RB cord-284810-fs5rx07q 193 2 , , , cord-284810-fs5rx07q 193 3 the the DT cord-284810-fs5rx07q 193 4 scaling scale VBG cord-284810-fs5rx07q 193 5 relations relation NNS cord-284810-fs5rx07q 193 6 in in IN cord-284810-fs5rx07q 193 7 the the DT cord-284810-fs5rx07q 193 8 distributions distribution NNS cord-284810-fs5rx07q 193 9 shown show VBN cord-284810-fs5rx07q 193 10 in in IN cord-284810-fs5rx07q 193 11 Fig Fig NNP cord-284810-fs5rx07q 193 12 . . . cord-284810-fs5rx07q 194 1 1 1 CD cord-284810-fs5rx07q 194 2 are be VBP cord-284810-fs5rx07q 194 3 remarkably remarkably RB cord-284810-fs5rx07q 194 4 constant constant JJ cord-284810-fs5rx07q 194 5 over over IN cord-284810-fs5rx07q 194 6 the the DT cord-284810-fs5rx07q 194 7 whole whole JJ cord-284810-fs5rx07q 194 8 range range NN cord-284810-fs5rx07q 194 9 of of IN cord-284810-fs5rx07q 194 10 case case NN cord-284810-fs5rx07q 194 11 numbers number NNS cord-284810-fs5rx07q 194 12 , , , cord-284810-fs5rx07q 194 13 stretching stretch VBG cord-284810-fs5rx07q 194 14 several several JJ cord-284810-fs5rx07q 194 15 orders order NNS cord-284810-fs5rx07q 194 16 of of IN cord-284810-fs5rx07q 194 17 magnitude magnitude NN cord-284810-fs5rx07q 194 18 with with IN cord-284810-fs5rx07q 194 19 no no DT cord-284810-fs5rx07q 194 20 obvious obvious JJ cord-284810-fs5rx07q 194 21 signs sign NNS cord-284810-fs5rx07q 194 22 of of IN cord-284810-fs5rx07q 194 23 saturation saturation NN cord-284810-fs5rx07q 194 24 for for IN cord-284810-fs5rx07q 194 25 either either CC cord-284810-fs5rx07q 194 26 the the DT cord-284810-fs5rx07q 194 27 range range NN cord-284810-fs5rx07q 194 28 of of IN cord-284810-fs5rx07q 194 29 small small JJ cord-284810-fs5rx07q 194 30 or or CC cord-284810-fs5rx07q 194 31 large large JJ cord-284810-fs5rx07q 194 32 case case NN cord-284810-fs5rx07q 194 33 numbers number NNS cord-284810-fs5rx07q 194 34 . . . cord-284810-fs5rx07q 195 1 One one PRP cord-284810-fs5rx07q 195 2 might may MD cord-284810-fs5rx07q 195 3 argue argue VB cord-284810-fs5rx07q 195 4 that that IN cord-284810-fs5rx07q 195 5 the the DT cord-284810-fs5rx07q 195 6 bend bend NN cord-284810-fs5rx07q 195 7 in in IN cord-284810-fs5rx07q 195 8 the the DT cord-284810-fs5rx07q 195 9 cumulative cumulative JJ cord-284810-fs5rx07q 195 10 distribution distribution NN cord-284810-fs5rx07q 195 11 function function NN cord-284810-fs5rx07q 195 12 is be VBZ cord-284810-fs5rx07q 195 13 a a DT cord-284810-fs5rx07q 195 14 sign sign NN cord-284810-fs5rx07q 195 15 that that IN cord-284810-fs5rx07q 195 16 the the DT cord-284810-fs5rx07q 195 17 growth growth NN cord-284810-fs5rx07q 195 18 in in IN cord-284810-fs5rx07q 195 19 some some DT cord-284810-fs5rx07q 195 20 countries country NNS cord-284810-fs5rx07q 195 21 ( ( -LRB- cord-284810-fs5rx07q 195 22 e.g. e.g. RB cord-284810-fs5rx07q 195 23 , , , cord-284810-fs5rx07q 195 24 China China NNP cord-284810-fs5rx07q 195 25 , , , cord-284810-fs5rx07q 195 26 Korea Korea NNP cord-284810-fs5rx07q 195 27 ) ) -RRB- cord-284810-fs5rx07q 195 28 had have VBD cord-284810-fs5rx07q 195 29 already already RB cord-284810-fs5rx07q 195 30 become become VBN cord-284810-fs5rx07q 195 31 sub sub NN cord-284810-fs5rx07q 195 32 - - JJ cord-284810-fs5rx07q 195 33 exponential exponential JJ cord-284810-fs5rx07q 195 34 . . . cord-284810-fs5rx07q 196 1 However however RB cord-284810-fs5rx07q 196 2 , , , cord-284810-fs5rx07q 196 3 this this DT cord-284810-fs5rx07q 196 4 is be VBZ cord-284810-fs5rx07q 196 5 contradicted contradict VBN cord-284810-fs5rx07q 196 6 by by IN cord-284810-fs5rx07q 196 7 the the DT cord-284810-fs5rx07q 196 8 observation observation NN cord-284810-fs5rx07q 196 9 that that IN cord-284810-fs5rx07q 196 10 a a DT cord-284810-fs5rx07q 196 11 similar similar JJ cord-284810-fs5rx07q 196 12 bend bend NN cord-284810-fs5rx07q 196 13 is be VBZ cord-284810-fs5rx07q 196 14 also also RB cord-284810-fs5rx07q 196 15 exhibited exhibit VBN cord-284810-fs5rx07q 196 16 by by IN cord-284810-fs5rx07q 196 17 the the DT cord-284810-fs5rx07q 196 18 cumulative cumulative JJ cord-284810-fs5rx07q 196 19 distribution distribution NN cord-284810-fs5rx07q 196 20 function function NN cord-284810-fs5rx07q 196 21 obtained obtain VBN cord-284810-fs5rx07q 196 22 from from IN cord-284810-fs5rx07q 196 23 the the DT cord-284810-fs5rx07q 196 24 meta meta JJ cord-284810-fs5rx07q 196 25 - - HYPH cord-284810-fs5rx07q 196 26 population population NN cord-284810-fs5rx07q 196 27 model model NN cord-284810-fs5rx07q 196 28 ( ( -LRB- cord-284810-fs5rx07q 196 29 Fig Fig NNP cord-284810-fs5rx07q 196 30 . . . cord-284810-fs5rx07q 196 31 3 3 CD cord-284810-fs5rx07q 196 32 ) ) -RRB- cord-284810-fs5rx07q 196 33 . . . cord-284810-fs5rx07q 197 1 Thus thus RB cord-284810-fs5rx07q 197 2 , , , cord-284810-fs5rx07q 197 3 the the DT cord-284810-fs5rx07q 197 4 most most RBS cord-284810-fs5rx07q 197 5 likely likely JJ cord-284810-fs5rx07q 197 6 explanation explanation NN cord-284810-fs5rx07q 197 7 is be VBZ cord-284810-fs5rx07q 197 8 that that IN cord-284810-fs5rx07q 197 9 the the DT cord-284810-fs5rx07q 197 10 case case NN cord-284810-fs5rx07q 197 11 distribution distribution NN cord-284810-fs5rx07q 197 12 follows follow VBZ cord-284810-fs5rx07q 197 13 a a DT cord-284810-fs5rx07q 197 14 truncated truncated JJ cord-284810-fs5rx07q 197 15 powerlaw powerlaw NN cord-284810-fs5rx07q 197 16 ( ( -LRB- cord-284810-fs5rx07q 197 17 see see VB cord-284810-fs5rx07q 197 18 also also RB cord-284810-fs5rx07q 197 19 Fig Fig NNP cord-284810-fs5rx07q 197 20 . . NNP cord-284810-fs5rx07q 197 21 5 5 CD cord-284810-fs5rx07q 197 22 ) ) -RRB- cord-284810-fs5rx07q 197 23 , , , cord-284810-fs5rx07q 197 24 suggesting suggest VBG cord-284810-fs5rx07q 197 25 the the DT cord-284810-fs5rx07q 197 26 hypothesis hypothesis NN cord-284810-fs5rx07q 197 27 that that IN cord-284810-fs5rx07q 197 28 the the DT cord-284810-fs5rx07q 197 29 spatial spatial JJ cord-284810-fs5rx07q 197 30 distribution distribution NN cord-284810-fs5rx07q 197 31 of of IN cord-284810-fs5rx07q 197 32 COVID-19 covid-19 JJ cord-284810-fs5rx07q 197 33 cases case NNS cord-284810-fs5rx07q 197 34 is be VBZ cord-284810-fs5rx07q 197 35 a a DT cord-284810-fs5rx07q 197 36 fractal fractal NN cord-284810-fs5rx07q 197 37 . . . cord-284810-fs5rx07q 198 1 9 9 CD cord-284810-fs5rx07q 199 1 This this DT cord-284810-fs5rx07q 199 2 is be VBZ cord-284810-fs5rx07q 199 3 further further RB cord-284810-fs5rx07q 199 4 corroborated corroborate VBN cord-284810-fs5rx07q 199 5 by by IN cord-284810-fs5rx07q 199 6 our -PRON- PRP$ cord-284810-fs5rx07q 199 7 simple simple JJ cord-284810-fs5rx07q 199 8 theory theory NN cord-284810-fs5rx07q 199 9 , , , cord-284810-fs5rx07q 199 10 which which WDT cord-284810-fs5rx07q 199 11 provides provide VBZ cord-284810-fs5rx07q 199 12 a a DT cord-284810-fs5rx07q 199 13 mechanistic mechanistic JJ cord-284810-fs5rx07q 199 14 explanation explanation NN cord-284810-fs5rx07q 199 15 for for IN cord-284810-fs5rx07q 199 16 why why WRB cord-284810-fs5rx07q 199 17 we -PRON- PRP cord-284810-fs5rx07q 199 18 would would MD cord-284810-fs5rx07q 199 19 expect expect VB cord-284810-fs5rx07q 199 20 a a DT cord-284810-fs5rx07q 199 21 truncated truncated JJ cord-284810-fs5rx07q 199 22 power power NN cord-284810-fs5rx07q 199 23 - - HYPH cord-284810-fs5rx07q 199 24 law law NN cord-284810-fs5rx07q 199 25 in in IN cord-284810-fs5rx07q 199 26 the the DT cord-284810-fs5rx07q 199 27 first first JJ cord-284810-fs5rx07q 199 28 place place NN cord-284810-fs5rx07q 199 29 . . . cord-284810-fs5rx07q 200 1 Our -PRON- PRP$ cord-284810-fs5rx07q 200 2 finding finding NN cord-284810-fs5rx07q 200 3 of of IN cord-284810-fs5rx07q 200 4 power power NN cord-284810-fs5rx07q 200 5 - - HYPH cord-284810-fs5rx07q 200 6 law law NN cord-284810-fs5rx07q 200 7 distributions distribution NNS cord-284810-fs5rx07q 200 8 in in IN cord-284810-fs5rx07q 200 9 the the DT cord-284810-fs5rx07q 200 10 number number NN cord-284810-fs5rx07q 200 11 of of IN cord-284810-fs5rx07q 200 12 reported report VBN cord-284810-fs5rx07q 200 13 cases case NNS cord-284810-fs5rx07q 200 14 has have VBZ cord-284810-fs5rx07q 200 15 important important JJ cord-284810-fs5rx07q 200 16 consequences consequence NNS cord-284810-fs5rx07q 200 17 for for IN cord-284810-fs5rx07q 200 18 epidemiology epidemiology NN cord-284810-fs5rx07q 200 19 . . . cord-284810-fs5rx07q 201 1 Most most RBS cord-284810-fs5rx07q 201 2 notably notably RB cord-284810-fs5rx07q 201 3 , , , cord-284810-fs5rx07q 201 4 the the DT cord-284810-fs5rx07q 201 5 small small JJ cord-284810-fs5rx07q 201 6 values value NNS cord-284810-fs5rx07q 201 7 of of IN cord-284810-fs5rx07q 201 8 the the DT cord-284810-fs5rx07q 201 9 estimated estimate VBN cord-284810-fs5rx07q 201 10 critical critical JJ cord-284810-fs5rx07q 201 11 power power NN cord-284810-fs5rx07q 201 12 - - HYPH cord-284810-fs5rx07q 201 13 law law NN cord-284810-fs5rx07q 201 14 exponents exponent NNS cord-284810-fs5rx07q 201 15 are be VBP cord-284810-fs5rx07q 201 16 related relate VBN cord-284810-fs5rx07q 201 17 to to IN cord-284810-fs5rx07q 201 18 the the DT cord-284810-fs5rx07q 201 19 strong strong JJ cord-284810-fs5rx07q 201 20 inequality inequality NN cord-284810-fs5rx07q 201 21 of of IN cord-284810-fs5rx07q 201 22 case case NN cord-284810-fs5rx07q 201 23 numbers number NNS cord-284810-fs5rx07q 201 24 that that WDT cord-284810-fs5rx07q 201 25 was be VBD cord-284810-fs5rx07q 201 26 frequently frequently RB cord-284810-fs5rx07q 201 27 observed observe VBN cord-284810-fs5rx07q 201 28 all all RB cord-284810-fs5rx07q 201 29 over over IN cord-284810-fs5rx07q 201 30 the the DT cord-284810-fs5rx07q 201 31 world world NN cord-284810-fs5rx07q 201 32 in in IN cord-284810-fs5rx07q 201 33 the the DT cord-284810-fs5rx07q 201 34 initial initial JJ cord-284810-fs5rx07q 201 35 phase phase NN cord-284810-fs5rx07q 201 36 of of IN cord-284810-fs5rx07q 201 37 the the DT cord-284810-fs5rx07q 201 38 COVID-19 covid-19 JJ cord-284810-fs5rx07q 201 39 outbreak outbreak NN cord-284810-fs5rx07q 201 40 . . . cord-284810-fs5rx07q 202 1 Following follow VBG cord-284810-fs5rx07q 202 2 a a DT cord-284810-fs5rx07q 202 3 power power NN cord-284810-fs5rx07q 202 4 - - HYPH cord-284810-fs5rx07q 202 5 law law NN cord-284810-fs5rx07q 202 6 distribution distribution NN cord-284810-fs5rx07q 202 7 means mean VBZ cord-284810-fs5rx07q 202 8 that that IN cord-284810-fs5rx07q 202 9 this this DT cord-284810-fs5rx07q 202 10 pattern pattern NN cord-284810-fs5rx07q 202 11 prevails prevail VBZ cord-284810-fs5rx07q 202 12 even even RB cord-284810-fs5rx07q 202 13 as as IN cord-284810-fs5rx07q 202 14 numbers number NNS cord-284810-fs5rx07q 202 15 grew grow VBD cord-284810-fs5rx07q 202 16 and and CC cord-284810-fs5rx07q 202 17 the the DT cord-284810-fs5rx07q 202 18 scale scale NN cord-284810-fs5rx07q 202 19 of of IN cord-284810-fs5rx07q 202 20 infection infection NN cord-284810-fs5rx07q 202 21 expanded expand VBN cord-284810-fs5rx07q 202 22 globally globally RB cord-284810-fs5rx07q 202 23 . . . cord-284810-fs5rx07q 203 1 In in IN cord-284810-fs5rx07q 203 2 particular particular JJ cord-284810-fs5rx07q 203 3 , , , cord-284810-fs5rx07q 203 4 during during IN cord-284810-fs5rx07q 203 5 the the DT cord-284810-fs5rx07q 203 6 course course NN cord-284810-fs5rx07q 203 7 of of IN cord-284810-fs5rx07q 203 8 the the DT cord-284810-fs5rx07q 203 9 pandemic pandemic NN cord-284810-fs5rx07q 203 10 , , , cord-284810-fs5rx07q 203 11 most most JJS cord-284810-fs5rx07q 203 12 cases case NNS cord-284810-fs5rx07q 203 13 were be VBD cord-284810-fs5rx07q 203 14 reported report VBN cord-284810-fs5rx07q 203 15 to to TO cord-284810-fs5rx07q 203 16 have have VB cord-284810-fs5rx07q 203 17 occurred occur VBN cord-284810-fs5rx07q 203 18 in in IN cord-284810-fs5rx07q 203 19 a a DT cord-284810-fs5rx07q 203 20 few few JJ cord-284810-fs5rx07q 203 21 countries country NNS cord-284810-fs5rx07q 203 22 , , , cord-284810-fs5rx07q 203 23 sometimes sometimes RB cord-284810-fs5rx07q 203 24 even even RB cord-284810-fs5rx07q 203 25 a a DT cord-284810-fs5rx07q 203 26 single single JJ cord-284810-fs5rx07q 203 27 country country NN cord-284810-fs5rx07q 203 28 - - , cord-284810-fs5rx07q 203 29 the the DT cord-284810-fs5rx07q 203 30 so so RB cord-284810-fs5rx07q 203 31 - - HYPH cord-284810-fs5rx07q 203 32 called call VBN cord-284810-fs5rx07q 203 33 epicenters epicenter NNS cord-284810-fs5rx07q 203 34 of of IN cord-284810-fs5rx07q 203 35 the the DT cord-284810-fs5rx07q 203 36 pandemic pandemic NN cord-284810-fs5rx07q 203 37 . . . cord-284810-fs5rx07q 204 1 The the DT cord-284810-fs5rx07q 204 2 distribution distribution NN cord-284810-fs5rx07q 204 3 of of IN cord-284810-fs5rx07q 204 4 cases case NNS cord-284810-fs5rx07q 204 5 within within IN cord-284810-fs5rx07q 204 6 countries country NNS cord-284810-fs5rx07q 204 7 followed follow VBD cord-284810-fs5rx07q 204 8 a a DT cord-284810-fs5rx07q 204 9 similar similar JJ cord-284810-fs5rx07q 204 10 pattern pattern NN cord-284810-fs5rx07q 204 11 . . . cord-284810-fs5rx07q 205 1 Often often RB cord-284810-fs5rx07q 205 2 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 205 3 was be VBD cord-284810-fs5rx07q 205 4 peaking peak VBG cord-284810-fs5rx07q 205 5 in in IN cord-284810-fs5rx07q 205 6 a a DT cord-284810-fs5rx07q 205 7 few few JJ cord-284810-fs5rx07q 205 8 localized localize VBN cord-284810-fs5rx07q 205 9 foci foci NN cord-284810-fs5rx07q 205 10 ( ( -LRB- cord-284810-fs5rx07q 205 11 local local JJ cord-284810-fs5rx07q 205 12 regions region NNS cord-284810-fs5rx07q 205 13 or or CC cord-284810-fs5rx07q 205 14 cities city NNS cord-284810-fs5rx07q 205 15 ) ) -RRB- cord-284810-fs5rx07q 205 16 , , , cord-284810-fs5rx07q 205 17 while while IN cord-284810-fs5rx07q 205 18 other other JJ cord-284810-fs5rx07q 205 19 parts part NNS cord-284810-fs5rx07q 205 20 of of IN cord-284810-fs5rx07q 205 21 the the DT cord-284810-fs5rx07q 205 22 country country NN cord-284810-fs5rx07q 205 23 at at IN cord-284810-fs5rx07q 205 24 the the DT cord-284810-fs5rx07q 205 25 same same JJ cord-284810-fs5rx07q 205 26 time time NN cord-284810-fs5rx07q 205 27 had have VBD cord-284810-fs5rx07q 205 28 experienced experience VBN cord-284810-fs5rx07q 205 29 only only RB cord-284810-fs5rx07q 205 30 a a DT cord-284810-fs5rx07q 205 31 moderate moderate JJ cord-284810-fs5rx07q 205 32 number number NN cord-284810-fs5rx07q 205 33 of of IN cord-284810-fs5rx07q 205 34 cases case NNS cord-284810-fs5rx07q 205 35 . . . cord-284810-fs5rx07q 206 1 Our -PRON- PRP$ cord-284810-fs5rx07q 206 2 theory theory NN cord-284810-fs5rx07q 206 3 provides provide VBZ cord-284810-fs5rx07q 206 4 a a DT cord-284810-fs5rx07q 206 5 mechanistic mechanistic JJ cord-284810-fs5rx07q 206 6 explanation explanation NN cord-284810-fs5rx07q 206 7 why why WRB cord-284810-fs5rx07q 206 8 this this DT cord-284810-fs5rx07q 206 9 might may MD cord-284810-fs5rx07q 206 10 have have VB cord-284810-fs5rx07q 206 11 been be VBN cord-284810-fs5rx07q 206 12 the the DT cord-284810-fs5rx07q 206 13 case case NN cord-284810-fs5rx07q 206 14 . . . cord-284810-fs5rx07q 207 1 A a DT cord-284810-fs5rx07q 207 2 graphical graphical JJ cord-284810-fs5rx07q 207 3 representation representation NN cord-284810-fs5rx07q 207 4 for for IN cord-284810-fs5rx07q 207 5 the the DT cord-284810-fs5rx07q 207 6 inequality inequality NN cord-284810-fs5rx07q 207 7 of of IN cord-284810-fs5rx07q 207 8 a a DT cord-284810-fs5rx07q 207 9 distribution distribution NN cord-284810-fs5rx07q 207 10 is be VBZ cord-284810-fs5rx07q 207 11 given give VBN cord-284810-fs5rx07q 207 12 by by IN cord-284810-fs5rx07q 207 13 the the DT cord-284810-fs5rx07q 207 14 Lorenz Lorenz NNP cord-284810-fs5rx07q 207 15 curve curve NN cord-284810-fs5rx07q 207 16 , , , cord-284810-fs5rx07q 207 17 29 29 CD cord-284810-fs5rx07q 207 18 which which WDT cord-284810-fs5rx07q 207 19 in in IN cord-284810-fs5rx07q 207 20 the the DT cord-284810-fs5rx07q 207 21 case case NN cord-284810-fs5rx07q 207 22 of of IN cord-284810-fs5rx07q 207 23 the the DT cord-284810-fs5rx07q 207 24 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 207 25 case case NN cord-284810-fs5rx07q 207 26 distribution distribution NN cord-284810-fs5rx07q 207 27 is be VBZ cord-284810-fs5rx07q 207 28 a a DT cord-284810-fs5rx07q 207 29 plot plot NN cord-284810-fs5rx07q 207 30 of of IN cord-284810-fs5rx07q 207 31 the the DT cord-284810-fs5rx07q 207 32 fraction fraction NN cord-284810-fs5rx07q 207 33 of of IN cord-284810-fs5rx07q 207 34 the the DT cord-284810-fs5rx07q 207 35 total total JJ cord-284810-fs5rx07q 207 36 number number NN cord-284810-fs5rx07q 207 37 of of IN cord-284810-fs5rx07q 207 38 confirmed confirm VBN cord-284810-fs5rx07q 207 39 cases case NNS cord-284810-fs5rx07q 207 40 in in IN cord-284810-fs5rx07q 207 41 dependence dependence NN cord-284810-fs5rx07q 207 42 of of IN cord-284810-fs5rx07q 207 43 the the DT cord-284810-fs5rx07q 207 44 fraction fraction NN cord-284810-fs5rx07q 207 45 of of IN cord-284810-fs5rx07q 207 46 the the DT cord-284810-fs5rx07q 207 47 most most RBS cord-284810-fs5rx07q 207 48 affected affected JJ cord-284810-fs5rx07q 207 49 countries country NNS cord-284810-fs5rx07q 207 50 . . . cord-284810-fs5rx07q 208 1 This this DT cord-284810-fs5rx07q 208 2 is be VBZ cord-284810-fs5rx07q 208 3 shown show VBN cord-284810-fs5rx07q 208 4 in in IN cord-284810-fs5rx07q 208 5 Fig Fig NNP cord-284810-fs5rx07q 208 6 . . . cord-284810-fs5rx07q 209 1 4 4 CD cord-284810-fs5rx07q 209 2 for for IN cord-284810-fs5rx07q 209 3 the the DT cord-284810-fs5rx07q 209 4 number number NN cord-284810-fs5rx07q 209 5 of of IN cord-284810-fs5rx07q 209 6 confirmed confirm VBN cord-284810-fs5rx07q 209 7 COVID-19 covid-19 CD cord-284810-fs5rx07q 209 8 cases case NNS cord-284810-fs5rx07q 209 9 and and CC cord-284810-fs5rx07q 209 10 confirmed confirm VBD cord-284810-fs5rx07q 209 11 deaths death NNS cord-284810-fs5rx07q 209 12 on on IN cord-284810-fs5rx07q 209 13 March March NNP cord-284810-fs5rx07q 209 14 22 22 CD cord-284810-fs5rx07q 209 15 , , , cord-284810-fs5rx07q 209 16 2020 2020 CD cord-284810-fs5rx07q 209 17 . . . cord-284810-fs5rx07q 210 1 The the DT cord-284810-fs5rx07q 210 2 Lorenz Lorenz NNP cord-284810-fs5rx07q 210 3 curve curve NN cord-284810-fs5rx07q 210 4 shows show VBZ cord-284810-fs5rx07q 210 5 that that IN cord-284810-fs5rx07q 210 6 on on IN cord-284810-fs5rx07q 210 7 this this DT cord-284810-fs5rx07q 210 8 day day NN cord-284810-fs5rx07q 210 9 , , , cord-284810-fs5rx07q 210 10 95.7 95.7 CD cord-284810-fs5rx07q 210 11 % % NN cord-284810-fs5rx07q 210 12 of of IN cord-284810-fs5rx07q 210 13 confirmed confirm VBN cord-284810-fs5rx07q 210 14 cases case NNS cord-284810-fs5rx07q 210 15 and and CC cord-284810-fs5rx07q 210 16 97.6 97.6 CD cord-284810-fs5rx07q 210 17 % % NN cord-284810-fs5rx07q 210 18 of of IN cord-284810-fs5rx07q 210 19 the the DT cord-284810-fs5rx07q 210 20 confirmed confirm VBN cord-284810-fs5rx07q 210 21 deaths death NNS cord-284810-fs5rx07q 210 22 had have VBD cord-284810-fs5rx07q 210 23 been be VBN cord-284810-fs5rx07q 210 24 reported report VBN cord-284810-fs5rx07q 210 25 in in IN cord-284810-fs5rx07q 210 26 the the DT cord-284810-fs5rx07q 210 27 20 20 CD cord-284810-fs5rx07q 210 28 % % NN cord-284810-fs5rx07q 210 29 most most RBS cord-284810-fs5rx07q 210 30 affected affected JJ cord-284810-fs5rx07q 210 31 countries country NNS cord-284810-fs5rx07q 210 32 ( ( -LRB- cord-284810-fs5rx07q 210 33 while while IN cord-284810-fs5rx07q 210 34 the the DT cord-284810-fs5rx07q 210 35 top top JJ cord-284810-fs5rx07q 210 36 5 5 CD cord-284810-fs5rx07q 210 37 % % NN cord-284810-fs5rx07q 210 38 most most RBS cord-284810-fs5rx07q 210 39 affected affected JJ cord-284810-fs5rx07q 210 40 countries country NNS cord-284810-fs5rx07q 210 41 had have VBD cord-284810-fs5rx07q 210 42 accumulated accumulate VBN cord-284810-fs5rx07q 210 43 82.3 82.3 CD cord-284810-fs5rx07q 210 44 % % NN cord-284810-fs5rx07q 210 45 of of IN cord-284810-fs5rx07q 210 46 all all DT cord-284810-fs5rx07q 210 47 confirmed confirm VBN cord-284810-fs5rx07q 210 48 cases case NNS cord-284810-fs5rx07q 210 49 and and CC cord-284810-fs5rx07q 210 50 84.4 84.4 CD cord-284810-fs5rx07q 210 51 % % NN cord-284810-fs5rx07q 210 52 of of IN cord-284810-fs5rx07q 210 53 all all DT cord-284810-fs5rx07q 210 54 confirmed confirm VBN cord-284810-fs5rx07q 210 55 deaths death NNS cord-284810-fs5rx07q 210 56 ) ) -RRB- cord-284810-fs5rx07q 210 57 . . . cord-284810-fs5rx07q 211 1 With with IN cord-284810-fs5rx07q 211 2 81 81 CD cord-284810-fs5rx07q 211 3 435 435 CD cord-284810-fs5rx07q 211 4 out out IN cord-284810-fs5rx07q 211 5 of of IN cord-284810-fs5rx07q 211 6 336 336 CD cord-284810-fs5rx07q 211 7 953 953 CD cord-284810-fs5rx07q 211 8 confirmed confirm VBD cord-284810-fs5rx07q 211 9 cases case NNS cord-284810-fs5rx07q 211 10 on on IN cord-284810-fs5rx07q 211 11 that that DT cord-284810-fs5rx07q 211 12 day day NN cord-284810-fs5rx07q 211 13 , , , cord-284810-fs5rx07q 211 14 China China NNP cord-284810-fs5rx07q 211 15 alone alone RB cord-284810-fs5rx07q 211 16 had have VBD cord-284810-fs5rx07q 211 17 accumulated accumulate VBN cord-284810-fs5rx07q 211 18 a a DT cord-284810-fs5rx07q 211 19 fraction fraction NN cord-284810-fs5rx07q 211 20 of of IN cord-284810-fs5rx07q 211 21 24 24 CD cord-284810-fs5rx07q 211 22 % % NN cord-284810-fs5rx07q 211 23 of of IN cord-284810-fs5rx07q 211 24 all all DT cord-284810-fs5rx07q 211 25 cases case NNS cord-284810-fs5rx07q 211 26 . . . cord-284810-fs5rx07q 212 1 The the DT cord-284810-fs5rx07q 212 2 two two CD cord-284810-fs5rx07q 212 3 most most RBS cord-284810-fs5rx07q 212 4 affected affect VBN cord-284810-fs5rx07q 212 5 countries country NNS cord-284810-fs5rx07q 212 6 , , , cord-284810-fs5rx07q 212 7 China China NNP cord-284810-fs5rx07q 212 8 and and CC cord-284810-fs5rx07q 212 9 Italy Italy NNP cord-284810-fs5rx07q 212 10 , , , cord-284810-fs5rx07q 212 11 together together RB cord-284810-fs5rx07q 212 12 had have VBD cord-284810-fs5rx07q 212 13 accumulated accumulate VBN cord-284810-fs5rx07q 212 14 a a DT cord-284810-fs5rx07q 212 15 fraction fraction NN cord-284810-fs5rx07q 212 16 of of IN cord-284810-fs5rx07q 212 17 41 41 CD cord-284810-fs5rx07q 212 18 % % NN cord-284810-fs5rx07q 212 19 of of IN cord-284810-fs5rx07q 212 20 the the DT cord-284810-fs5rx07q 212 21 worldwide worldwide RB cord-284810-fs5rx07q 212 22 reported report VBN cord-284810-fs5rx07q 212 23 cases case NNS cord-284810-fs5rx07q 212 24 . . . cord-284810-fs5rx07q 213 1 This this DT cord-284810-fs5rx07q 213 2 inequality inequality NN cord-284810-fs5rx07q 213 3 can can MD cord-284810-fs5rx07q 213 4 also also RB cord-284810-fs5rx07q 213 5 be be VB cord-284810-fs5rx07q 213 6 measured measure VBN cord-284810-fs5rx07q 213 7 by by IN cord-284810-fs5rx07q 213 8 the the DT cord-284810-fs5rx07q 213 9 Gini Gini NNP cord-284810-fs5rx07q 213 10 - - HYPH cord-284810-fs5rx07q 213 11 coefficient coefficient NN cord-284810-fs5rx07q 213 12 G g NN cord-284810-fs5rx07q 213 13 , , , cord-284810-fs5rx07q 213 14 17 17 CD cord-284810-fs5rx07q 213 15 power power NN cord-284810-fs5rx07q 213 16 - - HYPH cord-284810-fs5rx07q 213 17 law law NN cord-284810-fs5rx07q 213 18 distribution distribution NN cord-284810-fs5rx07q 213 19 with with IN cord-284810-fs5rx07q 213 20 µ µ NN cord-284810-fs5rx07q 213 21 < < XX cord-284810-fs5rx07q 213 22 2 2 CD cord-284810-fs5rx07q 213 23 , , , cord-284810-fs5rx07q 213 24 one one PRP cord-284810-fs5rx07q 213 25 would would MD cord-284810-fs5rx07q 213 26 theoretically theoretically RB cord-284810-fs5rx07q 213 27 expect expect VB cord-284810-fs5rx07q 213 28 a a DT cord-284810-fs5rx07q 213 29 Gini Gini NNP cord-284810-fs5rx07q 213 30 - - HYPH cord-284810-fs5rx07q 213 31 coefficient coefficient NN cord-284810-fs5rx07q 213 32 of of IN cord-284810-fs5rx07q 213 33 G g NN cord-284810-fs5rx07q 213 34 = = SYM cord-284810-fs5rx07q 213 35 1 1 CD cord-284810-fs5rx07q 213 36 . . . cord-284810-fs5rx07q 213 37 29 29 CD cord-284810-fs5rx07q 214 1 The the DT cord-284810-fs5rx07q 214 2 emergence emergence NN cord-284810-fs5rx07q 214 3 of of IN cord-284810-fs5rx07q 214 4 power power NN cord-284810-fs5rx07q 214 5 - - HYPH cord-284810-fs5rx07q 214 6 law law NN cord-284810-fs5rx07q 214 7 distributions distribution NNS cord-284810-fs5rx07q 214 8 with with IN cord-284810-fs5rx07q 214 9 a a DT cord-284810-fs5rx07q 214 10 small small JJ cord-284810-fs5rx07q 214 11 critical critical JJ cord-284810-fs5rx07q 214 12 exponent exponent NN cord-284810-fs5rx07q 214 13 and and CC cord-284810-fs5rx07q 214 14 the the DT cord-284810-fs5rx07q 214 15 associated associated JJ cord-284810-fs5rx07q 214 16 inequality inequality NN cord-284810-fs5rx07q 214 17 of of IN cord-284810-fs5rx07q 214 18 the the DT cord-284810-fs5rx07q 214 19 distribution distribution NN cord-284810-fs5rx07q 214 20 , , , cord-284810-fs5rx07q 214 21 with with IN cord-284810-fs5rx07q 214 22 Gini Gini NNP cord-284810-fs5rx07q 214 23 coefficients coefficient NNS cord-284810-fs5rx07q 214 24 close close JJ cord-284810-fs5rx07q 214 25 to to IN cord-284810-fs5rx07q 214 26 one one CD cord-284810-fs5rx07q 214 27 is be VBZ cord-284810-fs5rx07q 214 28 also also RB cord-284810-fs5rx07q 214 29 observed observe VBN cord-284810-fs5rx07q 214 30 in in IN cord-284810-fs5rx07q 214 31 the the DT cord-284810-fs5rx07q 214 32 developed develop VBN cord-284810-fs5rx07q 214 33 meta meta JJ cord-284810-fs5rx07q 214 34 - - HYPH cord-284810-fs5rx07q 214 35 population population NN cord-284810-fs5rx07q 214 36 model model NN cord-284810-fs5rx07q 214 37 . . . cord-284810-fs5rx07q 215 1 Consequently consequently RB cord-284810-fs5rx07q 215 2 , , , cord-284810-fs5rx07q 215 3 also also RB cord-284810-fs5rx07q 215 4 in in IN cord-284810-fs5rx07q 215 5 the the DT cord-284810-fs5rx07q 215 6 model model NN cord-284810-fs5rx07q 215 7 case case NN cord-284810-fs5rx07q 215 8 numbers number NNS cord-284810-fs5rx07q 215 9 are be VBP cord-284810-fs5rx07q 215 10 mostly mostly RB cord-284810-fs5rx07q 215 11 concentrated concentrated JJ cord-284810-fs5rx07q 215 12 in in IN cord-284810-fs5rx07q 215 13 a a DT cord-284810-fs5rx07q 215 14 few few JJ cord-284810-fs5rx07q 215 15 countries country NNS cord-284810-fs5rx07q 215 16 . . . cord-284810-fs5rx07q 216 1 In in IN cord-284810-fs5rx07q 216 2 the the DT cord-284810-fs5rx07q 216 3 simulations simulation NNS cord-284810-fs5rx07q 216 4 , , , cord-284810-fs5rx07q 216 5 these these DT cord-284810-fs5rx07q 216 6 epicenters epicenter NNS cord-284810-fs5rx07q 216 7 of of IN cord-284810-fs5rx07q 216 8 the the DT cord-284810-fs5rx07q 216 9 pandemic pandemic NN cord-284810-fs5rx07q 216 10 , , , cord-284810-fs5rx07q 216 11 i.e. i.e. FW cord-284810-fs5rx07q 216 12 , , , cord-284810-fs5rx07q 216 13 the the DT cord-284810-fs5rx07q 216 14 countries country NNS cord-284810-fs5rx07q 216 15 with with IN cord-284810-fs5rx07q 216 16 most most JJS cord-284810-fs5rx07q 216 17 cases case NNS cord-284810-fs5rx07q 216 18 , , , cord-284810-fs5rx07q 216 19 are be VBP cord-284810-fs5rx07q 216 20 always always RB cord-284810-fs5rx07q 216 21 the the DT cord-284810-fs5rx07q 216 22 countries country NNS cord-284810-fs5rx07q 216 23 in in IN cord-284810-fs5rx07q 216 24 which which WDT cord-284810-fs5rx07q 216 25 the the DT cord-284810-fs5rx07q 216 26 diseases disease NNS cord-284810-fs5rx07q 216 27 originated originate VBD cord-284810-fs5rx07q 216 28 or or CC cord-284810-fs5rx07q 216 29 which which WDT cord-284810-fs5rx07q 216 30 were be VBD cord-284810-fs5rx07q 216 31 first first RB cord-284810-fs5rx07q 216 32 invaded invade VBN cord-284810-fs5rx07q 216 33 by by IN cord-284810-fs5rx07q 216 34 the the DT cord-284810-fs5rx07q 216 35 virus virus NN cord-284810-fs5rx07q 216 36 . . . cord-284810-fs5rx07q 217 1 In in IN cord-284810-fs5rx07q 217 2 other other JJ cord-284810-fs5rx07q 217 3 words word NNS cord-284810-fs5rx07q 217 4 , , , cord-284810-fs5rx07q 217 5 the the DT cord-284810-fs5rx07q 217 6 prevalence prevalence NN cord-284810-fs5rx07q 217 7 rank rank NN cord-284810-fs5rx07q 217 8 order order NN cord-284810-fs5rx07q 217 9 among among IN cord-284810-fs5rx07q 217 10 countries country NNS cord-284810-fs5rx07q 217 11 remains remain VBZ cord-284810-fs5rx07q 217 12 unchanged unchanged JJ cord-284810-fs5rx07q 217 13 during during IN cord-284810-fs5rx07q 217 14 the the DT cord-284810-fs5rx07q 217 15 course course NN cord-284810-fs5rx07q 217 16 of of IN cord-284810-fs5rx07q 217 17 the the DT cord-284810-fs5rx07q 217 18 pandemic pandemic NN cord-284810-fs5rx07q 217 19 . . . cord-284810-fs5rx07q 218 1 This this DT cord-284810-fs5rx07q 218 2 is be VBZ cord-284810-fs5rx07q 218 3 akin akin JJ cord-284810-fs5rx07q 218 4 to to IN cord-284810-fs5rx07q 218 5 the the DT cord-284810-fs5rx07q 218 6 " " `` cord-284810-fs5rx07q 218 7 rich rich JJ cord-284810-fs5rx07q 218 8 - - HYPH cord-284810-fs5rx07q 218 9 get get NN cord-284810-fs5rx07q 218 10 - - HYPH cord-284810-fs5rx07q 218 11 richer rich JJR cord-284810-fs5rx07q 218 12 process process NN cord-284810-fs5rx07q 218 13 " " '' cord-284810-fs5rx07q 218 14 or or CC cord-284810-fs5rx07q 218 15 " " `` cord-284810-fs5rx07q 218 16 firstmover firstmover NN cord-284810-fs5rx07q 218 17 - - HYPH cord-284810-fs5rx07q 218 18 advantage advantage NN cord-284810-fs5rx07q 218 19 , , , cord-284810-fs5rx07q 218 20 " " '' cord-284810-fs5rx07q 218 21 30,38 30,38 CD cord-284810-fs5rx07q 218 22 a a DT cord-284810-fs5rx07q 218 23 well well RB cord-284810-fs5rx07q 218 24 - - HYPH cord-284810-fs5rx07q 218 25 studied study VBN cord-284810-fs5rx07q 218 26 process process NN cord-284810-fs5rx07q 218 27 to to TO cord-284810-fs5rx07q 218 28 generate generate VB cord-284810-fs5rx07q 218 29 power power NN cord-284810-fs5rx07q 218 30 - - HYPH cord-284810-fs5rx07q 218 31 law law NN cord-284810-fs5rx07q 218 32 distributions distribution NNS cord-284810-fs5rx07q 218 33 . . . cord-284810-fs5rx07q 219 1 In in IN cord-284810-fs5rx07q 219 2 the the DT cord-284810-fs5rx07q 219 3 real real JJ cord-284810-fs5rx07q 219 4 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 219 5 pandemic pandemic NN cord-284810-fs5rx07q 219 6 , , , cord-284810-fs5rx07q 219 7 this this DT cord-284810-fs5rx07q 219 8 was be VBD cord-284810-fs5rx07q 219 9 not not RB cord-284810-fs5rx07q 219 10 the the DT cord-284810-fs5rx07q 219 11 case case NN cord-284810-fs5rx07q 219 12 . . . cord-284810-fs5rx07q 220 1 During during IN cord-284810-fs5rx07q 220 2 the the DT cord-284810-fs5rx07q 220 3 beginning beginning NN cord-284810-fs5rx07q 220 4 of of IN cord-284810-fs5rx07q 220 5 the the DT cord-284810-fs5rx07q 220 6 pandemic pandemic NN cord-284810-fs5rx07q 220 7 , , , cord-284810-fs5rx07q 220 8 most most JJS cord-284810-fs5rx07q 220 9 cases case NNS cord-284810-fs5rx07q 220 10 were be VBD cord-284810-fs5rx07q 220 11 observed observe VBN cord-284810-fs5rx07q 220 12 in in IN cord-284810-fs5rx07q 220 13 China China NNP cord-284810-fs5rx07q 220 14 , , , cord-284810-fs5rx07q 220 15 later later RB cord-284810-fs5rx07q 220 16 the the DT cord-284810-fs5rx07q 220 17 " " `` cord-284810-fs5rx07q 220 18 leading leading JJ cord-284810-fs5rx07q 220 19 role role NN cord-284810-fs5rx07q 220 20 " " '' cord-284810-fs5rx07q 220 21 changed change VBD cord-284810-fs5rx07q 220 22 next next RB cord-284810-fs5rx07q 220 23 to to IN cord-284810-fs5rx07q 220 24 Italy Italy NNP cord-284810-fs5rx07q 220 25 and and CC cord-284810-fs5rx07q 220 26 finally finally RB cord-284810-fs5rx07q 220 27 to to IN cord-284810-fs5rx07q 220 28 the the DT cord-284810-fs5rx07q 220 29 USA USA NNP cord-284810-fs5rx07q 220 30 . . . cord-284810-fs5rx07q 221 1 This this DT cord-284810-fs5rx07q 221 2 reflects reflect VBZ cord-284810-fs5rx07q 221 3 different different JJ cord-284810-fs5rx07q 221 4 mitigation mitigation NN cord-284810-fs5rx07q 221 5 strategies strategy NNS cord-284810-fs5rx07q 221 6 and and CC cord-284810-fs5rx07q 221 7 circumstances circumstance NNS cord-284810-fs5rx07q 221 8 in in IN cord-284810-fs5rx07q 221 9 different different JJ cord-284810-fs5rx07q 221 10 countries country NNS cord-284810-fs5rx07q 221 11 , , , cord-284810-fs5rx07q 221 12 a a DT cord-284810-fs5rx07q 221 13 factor factor NN cord-284810-fs5rx07q 221 14 that that WDT cord-284810-fs5rx07q 221 15 is be VBZ cord-284810-fs5rx07q 221 16 not not RB cord-284810-fs5rx07q 221 17 considered consider VBN cord-284810-fs5rx07q 221 18 in in IN cord-284810-fs5rx07q 221 19 the the DT cord-284810-fs5rx07q 221 20 simple simple JJ cord-284810-fs5rx07q 221 21 model model NN cord-284810-fs5rx07q 221 22 . . . cord-284810-fs5rx07q 222 1 Nevertheless nevertheless RB cord-284810-fs5rx07q 222 2 , , , cord-284810-fs5rx07q 222 3 despite despite IN cord-284810-fs5rx07q 222 4 these these DT cord-284810-fs5rx07q 222 5 changes change NNS cord-284810-fs5rx07q 222 6 in in IN cord-284810-fs5rx07q 222 7 the the DT cord-284810-fs5rx07q 222 8 rank rank NN cord-284810-fs5rx07q 222 9 order order NN cord-284810-fs5rx07q 222 10 , , , cord-284810-fs5rx07q 222 11 the the DT cord-284810-fs5rx07q 222 12 distribution distribution NN cord-284810-fs5rx07q 222 13 of of IN cord-284810-fs5rx07q 222 14 cases case NNS cord-284810-fs5rx07q 222 15 in in IN cord-284810-fs5rx07q 222 16 the the DT cord-284810-fs5rx07q 222 17 empirical empirical JJ cord-284810-fs5rx07q 222 18 data datum NNS cord-284810-fs5rx07q 222 19 was be VBD cord-284810-fs5rx07q 222 20 always always RB cord-284810-fs5rx07q 222 21 closely closely RB cord-284810-fs5rx07q 222 22 represented represent VBN cord-284810-fs5rx07q 222 23 by by IN cord-284810-fs5rx07q 222 24 a a DT cord-284810-fs5rx07q 222 25 power power NN cord-284810-fs5rx07q 222 26 - - HYPH cord-284810-fs5rx07q 222 27 law law NN cord-284810-fs5rx07q 222 28 . . . cord-284810-fs5rx07q 223 1 We -PRON- PRP cord-284810-fs5rx07q 223 2 would would MD cord-284810-fs5rx07q 223 3 like like VB cord-284810-fs5rx07q 223 4 to to TO cord-284810-fs5rx07q 223 5 remark remark VB cord-284810-fs5rx07q 223 6 that that IN cord-284810-fs5rx07q 223 7 the the DT cord-284810-fs5rx07q 223 8 available available JJ cord-284810-fs5rx07q 223 9 database database NN cord-284810-fs5rx07q 223 10 only only RB cord-284810-fs5rx07q 223 11 provides provide VBZ cord-284810-fs5rx07q 223 12 information information NN cord-284810-fs5rx07q 223 13 on on IN cord-284810-fs5rx07q 223 14 the the DT cord-284810-fs5rx07q 223 15 reported report VBN cord-284810-fs5rx07q 223 16 COVID-19 covid-19 CD cord-284810-fs5rx07q 223 17 cases case NNS cord-284810-fs5rx07q 223 18 in in IN cord-284810-fs5rx07q 223 19 each each DT cord-284810-fs5rx07q 223 20 country country NN cord-284810-fs5rx07q 223 21 . . . cord-284810-fs5rx07q 224 1 In in IN cord-284810-fs5rx07q 224 2 all all DT cord-284810-fs5rx07q 224 3 likelihood likelihood NN cord-284810-fs5rx07q 224 4 , , , cord-284810-fs5rx07q 224 5 the the DT cord-284810-fs5rx07q 224 6 real real JJ cord-284810-fs5rx07q 224 7 number number NN cord-284810-fs5rx07q 224 8 of of IN cord-284810-fs5rx07q 224 9 cases case NNS cord-284810-fs5rx07q 224 10 will will MD cord-284810-fs5rx07q 224 11 be be VB cord-284810-fs5rx07q 224 12 much much RB cord-284810-fs5rx07q 224 13 larger large JJR cord-284810-fs5rx07q 224 14 . . . cord-284810-fs5rx07q 225 1 Not not RB cord-284810-fs5rx07q 225 2 much much JJ cord-284810-fs5rx07q 225 3 is be VBZ cord-284810-fs5rx07q 225 4 known know VBN cord-284810-fs5rx07q 225 5 about about IN cord-284810-fs5rx07q 225 6 the the DT cord-284810-fs5rx07q 225 7 reporting reporting NN cord-284810-fs5rx07q 225 8 rates rate NNS cord-284810-fs5rx07q 225 9 , , , cord-284810-fs5rx07q 225 10 but but CC cord-284810-fs5rx07q 225 11 first first JJ cord-284810-fs5rx07q 225 12 estimates estimate NNS cord-284810-fs5rx07q 225 13 indicate indicate VBP cord-284810-fs5rx07q 225 14 that that IN cord-284810-fs5rx07q 225 15 a a DT cord-284810-fs5rx07q 225 16 substantial substantial JJ cord-284810-fs5rx07q 225 17 fraction fraction NN cord-284810-fs5rx07q 225 18 ( ( -LRB- cord-284810-fs5rx07q 225 19 possible possible JJ cord-284810-fs5rx07q 225 20 86 86 CD cord-284810-fs5rx07q 225 21 % % NN cord-284810-fs5rx07q 225 22 ) ) -RRB- cord-284810-fs5rx07q 225 23 of of IN cord-284810-fs5rx07q 225 24 infections infection NNS cord-284810-fs5rx07q 225 25 might may MD cord-284810-fs5rx07q 225 26 go go VB cord-284810-fs5rx07q 225 27 undetected undetected JJ cord-284810-fs5rx07q 225 28 . . . cord-284810-fs5rx07q 226 1 24 24 CD cord-284810-fs5rx07q 226 2 Reporting reporting NN cord-284810-fs5rx07q 226 3 rates rate NNS cord-284810-fs5rx07q 226 4 probably probably RB cord-284810-fs5rx07q 226 5 vary vary VBP cord-284810-fs5rx07q 226 6 strongly strongly RB cord-284810-fs5rx07q 226 7 between between IN cord-284810-fs5rx07q 226 8 countries country NNS cord-284810-fs5rx07q 226 9 and and CC cord-284810-fs5rx07q 226 10 may may MD cord-284810-fs5rx07q 226 11 change change VB cord-284810-fs5rx07q 226 12 in in IN cord-284810-fs5rx07q 226 13 time time NN cord-284810-fs5rx07q 226 14 with with IN cord-284810-fs5rx07q 226 15 the the DT cord-284810-fs5rx07q 226 16 awareness awareness NN cord-284810-fs5rx07q 226 17 of of IN cord-284810-fs5rx07q 226 18 national national JJ cord-284810-fs5rx07q 226 19 health health NN cord-284810-fs5rx07q 226 20 institutions institution NNS cord-284810-fs5rx07q 226 21 and and CC cord-284810-fs5rx07q 226 22 available available JJ cord-284810-fs5rx07q 226 23 testing testing NN cord-284810-fs5rx07q 226 24 capabilities capability NNS cord-284810-fs5rx07q 226 25 . . . cord-284810-fs5rx07q 227 1 Further further JJ cord-284810-fs5rx07q 227 2 uncertainties uncertainty NNS cord-284810-fs5rx07q 227 3 arise arise VBP cord-284810-fs5rx07q 227 4 because because IN cord-284810-fs5rx07q 227 5 the the DT cord-284810-fs5rx07q 227 6 criteria criterion NNS cord-284810-fs5rx07q 227 7 by by IN cord-284810-fs5rx07q 227 8 which which WDT cord-284810-fs5rx07q 227 9 a a DT cord-284810-fs5rx07q 227 10 person person NN cord-284810-fs5rx07q 227 11 is be VBZ cord-284810-fs5rx07q 227 12 classified classify VBN cord-284810-fs5rx07q 227 13 as as IN cord-284810-fs5rx07q 227 14 active active JJ cord-284810-fs5rx07q 227 15 case case NN cord-284810-fs5rx07q 227 16 ( ( -LRB- cord-284810-fs5rx07q 227 17 and and CC cord-284810-fs5rx07q 227 18 even even RB cord-284810-fs5rx07q 227 19 more more RBR cord-284810-fs5rx07q 227 20 so so RB cord-284810-fs5rx07q 227 21 for for IN cord-284810-fs5rx07q 227 22 being be VBG cord-284810-fs5rx07q 227 23 classified classify VBN cord-284810-fs5rx07q 227 24 as as IN cord-284810-fs5rx07q 227 25 recovered recover VBN cord-284810-fs5rx07q 227 26 ) ) -RRB- cord-284810-fs5rx07q 227 27 vary vary VBP cord-284810-fs5rx07q 227 28 between between IN cord-284810-fs5rx07q 227 29 countries country NNS cord-284810-fs5rx07q 227 30 and and CC cord-284810-fs5rx07q 227 31 not not RB cord-284810-fs5rx07q 227 32 uncommonly uncommonly RB cord-284810-fs5rx07q 227 33 have have VBP cord-284810-fs5rx07q 227 34 been be VBN cord-284810-fs5rx07q 227 35 modified modify VBN cord-284810-fs5rx07q 227 36 during during IN cord-284810-fs5rx07q 227 37 the the DT cord-284810-fs5rx07q 227 38 course course NN cord-284810-fs5rx07q 227 39 of of IN cord-284810-fs5rx07q 227 40 the the DT cord-284810-fs5rx07q 227 41 pandemic pandemic NN cord-284810-fs5rx07q 227 42 within within IN cord-284810-fs5rx07q 227 43 a a DT cord-284810-fs5rx07q 227 44 country country NN cord-284810-fs5rx07q 227 45 . . . cord-284810-fs5rx07q 228 1 Remarkably remarkably RB cord-284810-fs5rx07q 228 2 , , , cord-284810-fs5rx07q 228 3 we -PRON- PRP cord-284810-fs5rx07q 228 4 obtained obtain VBD cord-284810-fs5rx07q 228 5 power power NN cord-284810-fs5rx07q 228 6 - - HYPH cord-284810-fs5rx07q 228 7 law law NN cord-284810-fs5rx07q 228 8 distributions distribution NNS cord-284810-fs5rx07q 228 9 in in IN cord-284810-fs5rx07q 228 10 the the DT cord-284810-fs5rx07q 228 11 absolute absolute JJ cord-284810-fs5rx07q 228 12 number number NN cord-284810-fs5rx07q 228 13 of of IN cord-284810-fs5rx07q 228 14 cases case NNS cord-284810-fs5rx07q 228 15 in in IN cord-284810-fs5rx07q 228 16 each each DT cord-284810-fs5rx07q 228 17 country country NN cord-284810-fs5rx07q 228 18 . . . cord-284810-fs5rx07q 229 1 At at IN cord-284810-fs5rx07q 229 2 first first JJ cord-284810-fs5rx07q 229 3 guess guess NN cord-284810-fs5rx07q 229 4 , , , cord-284810-fs5rx07q 229 5 one one PRP cord-284810-fs5rx07q 229 6 might may MD cord-284810-fs5rx07q 229 7 have have VB cord-284810-fs5rx07q 229 8 expected expect VBN cord-284810-fs5rx07q 229 9 such such JJ cord-284810-fs5rx07q 229 10 scaling scaling NN cord-284810-fs5rx07q 229 11 only only RB cord-284810-fs5rx07q 229 12 after after IN cord-284810-fs5rx07q 229 13 case case NN cord-284810-fs5rx07q 229 14 numbers number NNS cord-284810-fs5rx07q 229 15 have have VBP cord-284810-fs5rx07q 229 16 been be VBN cord-284810-fs5rx07q 229 17 normalized normalize VBN cord-284810-fs5rx07q 229 18 by by IN cord-284810-fs5rx07q 229 19 population population NN cord-284810-fs5rx07q 229 20 sizes size NNS cord-284810-fs5rx07q 229 21 . . . cord-284810-fs5rx07q 230 1 Our -PRON- PRP$ cord-284810-fs5rx07q 230 2 preliminary preliminary JJ cord-284810-fs5rx07q 230 3 investigations investigation NNS cord-284810-fs5rx07q 230 4 show show VBP cord-284810-fs5rx07q 230 5 that that IN cord-284810-fs5rx07q 230 6 such such JJ cord-284810-fs5rx07q 230 7 normalized normalize VBN cord-284810-fs5rx07q 230 8 case case NN cord-284810-fs5rx07q 230 9 numbers number NNS cord-284810-fs5rx07q 230 10 become become VBP cord-284810-fs5rx07q 230 11 even even RB cord-284810-fs5rx07q 230 12 more more RBR cord-284810-fs5rx07q 230 13 unequally unequally RB cord-284810-fs5rx07q 230 14 distributed distribute VBN cord-284810-fs5rx07q 230 15 , , , cord-284810-fs5rx07q 230 16 Robustness robustness NN cord-284810-fs5rx07q 230 17 of of IN cord-284810-fs5rx07q 230 18 the the DT cord-284810-fs5rx07q 230 19 algorithm algorithm NN cord-284810-fs5rx07q 230 20 for for IN cord-284810-fs5rx07q 230 21 estimating estimate VBG cord-284810-fs5rx07q 230 22 parameters parameter NNS cord-284810-fs5rx07q 230 23 of of IN cord-284810-fs5rx07q 230 24 a a DT cord-284810-fs5rx07q 230 25 truncated truncated JJ cord-284810-fs5rx07q 230 26 power power NN cord-284810-fs5rx07q 230 27 - - HYPH cord-284810-fs5rx07q 230 28 law law NN cord-284810-fs5rx07q 230 29 . . . cord-284810-fs5rx07q 231 1 The the DT cord-284810-fs5rx07q 231 2 same same JJ cord-284810-fs5rx07q 231 3 as as IN cord-284810-fs5rx07q 231 4 Fig Fig NNP cord-284810-fs5rx07q 231 5 . . . cord-284810-fs5rx07q 232 1 1 1 LS cord-284810-fs5rx07q 233 1 but but CC cord-284810-fs5rx07q 233 2 for for IN cord-284810-fs5rx07q 233 3 200 200 CD cord-284810-fs5rx07q 233 4 random random JJ cord-284810-fs5rx07q 233 5 numbers number NNS cord-284810-fs5rx07q 234 1 n n NNP cord-284810-fs5rx07q 235 1 i i PRP cord-284810-fs5rx07q 235 2 that that WDT cord-284810-fs5rx07q 235 3 were be VBD cord-284810-fs5rx07q 235 4 generated generate VBN cord-284810-fs5rx07q 235 5 from from IN cord-284810-fs5rx07q 235 6 a a DT cord-284810-fs5rx07q 235 7 truncated truncated JJ cord-284810-fs5rx07q 235 8 power power NN cord-284810-fs5rx07q 235 9 - - HYPH cord-284810-fs5rx07q 235 10 law law NN cord-284810-fs5rx07q 235 11 distribution distribution NN cord-284810-fs5rx07q 235 12 with with IN cord-284810-fs5rx07q 235 13 µ µ NN cord-284810-fs5rx07q 235 14 = = SYM cord-284810-fs5rx07q 235 15 1.2 1.2 CD cord-284810-fs5rx07q 235 16 and and CC cord-284810-fs5rx07q 235 17 cut cut VBN cord-284810-fs5rx07q 235 18 - - HYPH cord-284810-fs5rx07q 235 19 off off RP cord-284810-fs5rx07q 235 20 value value NN cord-284810-fs5rx07q 235 21 n n CC cord-284810-fs5rx07q 235 22 max max NN cord-284810-fs5rx07q 235 23 = = SYM cord-284810-fs5rx07q 235 24 1 1 CD cord-284810-fs5rx07q 235 25 × × NNP cord-284810-fs5rx07q 235 26 10 10 CD cord-284810-fs5rx07q 235 27 5 5 CD cord-284810-fs5rx07q 235 28 . . . cord-284810-fs5rx07q 236 1 The the DT cord-284810-fs5rx07q 236 2 estimated estimate VBN cord-284810-fs5rx07q 236 3 distribution distribution NN cord-284810-fs5rx07q 236 4 roughly roughly RB cord-284810-fs5rx07q 236 5 follows follow VBZ cord-284810-fs5rx07q 236 6 a a DT cord-284810-fs5rx07q 236 7 straight straight JJ cord-284810-fs5rx07q 236 8 line line NN cord-284810-fs5rx07q 236 9 on on IN cord-284810-fs5rx07q 236 10 the the DT cord-284810-fs5rx07q 236 11 double double JJ cord-284810-fs5rx07q 236 12 - - HYPH cord-284810-fs5rx07q 236 13 logarithmic logarithmic JJ cord-284810-fs5rx07q 236 14 plot plot NN cord-284810-fs5rx07q 236 15 with with IN cord-284810-fs5rx07q 236 16 equally equally RB cord-284810-fs5rx07q 236 17 spaced space VBN cord-284810-fs5rx07q 236 18 bins bin NNS cord-284810-fs5rx07q 236 19 . . . cord-284810-fs5rx07q 237 1 Note note VB cord-284810-fs5rx07q 237 2 that that IN cord-284810-fs5rx07q 237 3 even even RB cord-284810-fs5rx07q 237 4 though though IN cord-284810-fs5rx07q 237 5 only only RB cord-284810-fs5rx07q 237 6 200 200 CD cord-284810-fs5rx07q 237 7 random random JJ cord-284810-fs5rx07q 237 8 numbers number NNS cord-284810-fs5rx07q 237 9 were be VBD cord-284810-fs5rx07q 237 10 drawn draw VBN cord-284810-fs5rx07q 237 11 , , , cord-284810-fs5rx07q 237 12 the the DT cord-284810-fs5rx07q 237 13 estimated estimate VBN cord-284810-fs5rx07q 237 14 probabilities probability NNS cord-284810-fs5rx07q 237 15 vary vary VBP cord-284810-fs5rx07q 237 16 over over IN cord-284810-fs5rx07q 237 17 many many JJ cord-284810-fs5rx07q 237 18 orders order NNS cord-284810-fs5rx07q 237 19 of of IN cord-284810-fs5rx07q 237 20 magnitude magnitude NN cord-284810-fs5rx07q 237 21 ( ( -LRB- cord-284810-fs5rx07q 237 22 which which WDT cord-284810-fs5rx07q 237 23 is be VBZ cord-284810-fs5rx07q 237 24 numerically numerically RB cord-284810-fs5rx07q 237 25 possible possible JJ cord-284810-fs5rx07q 237 26 since since IN cord-284810-fs5rx07q 237 27 in in IN cord-284810-fs5rx07q 237 28 order order NN cord-284810-fs5rx07q 237 29 to to TO cord-284810-fs5rx07q 237 30 compute compute VB cord-284810-fs5rx07q 237 31 the the DT cord-284810-fs5rx07q 237 32 probability probability NN cord-284810-fs5rx07q 237 33 distribution distribution NN cord-284810-fs5rx07q 237 34 , , , cord-284810-fs5rx07q 237 35 the the DT cord-284810-fs5rx07q 237 36 histogram histogram NN cord-284810-fs5rx07q 237 37 counts count NNS cord-284810-fs5rx07q 237 38 are be VBP cord-284810-fs5rx07q 237 39 divided divide VBN cord-284810-fs5rx07q 237 40 by by IN cord-284810-fs5rx07q 237 41 the the DT cord-284810-fs5rx07q 237 42 variable variable JJ cord-284810-fs5rx07q 237 43 bin bin NNP cord-284810-fs5rx07q 237 44 sizes size NNS cord-284810-fs5rx07q 237 45 ) ) -RRB- cord-284810-fs5rx07q 237 46 . . . cord-284810-fs5rx07q 238 1 Log log JJ cord-284810-fs5rx07q 238 2 - - HYPH cord-284810-fs5rx07q 238 3 likelihood likelihood NN cord-284810-fs5rx07q 238 4 estimation estimation NN cord-284810-fs5rx07q 238 5 of of IN cord-284810-fs5rx07q 238 6 critical critical JJ cord-284810-fs5rx07q 238 7 exponent exponent NN cord-284810-fs5rx07q 238 8 ( ( -LRB- cord-284810-fs5rx07q 238 9 Appendix Appendix NNP cord-284810-fs5rx07q 238 10 A A NNP cord-284810-fs5rx07q 238 11 ) ) -RRB- cord-284810-fs5rx07q 238 12 yieldsμ yieldsμ NN cord-284810-fs5rx07q 238 13 = = SYM cord-284810-fs5rx07q 238 14 1.21 1.21 CD cord-284810-fs5rx07q 238 15 ± ± CD cord-284810-fs5rx07q 238 16 0.01 0.01 CD cord-284810-fs5rx07q 238 17 in in IN cord-284810-fs5rx07q 238 18 good good JJ cord-284810-fs5rx07q 238 19 agreement agreement NN cord-284810-fs5rx07q 238 20 with with IN cord-284810-fs5rx07q 238 21 the the DT cord-284810-fs5rx07q 238 22 actually actually RB cord-284810-fs5rx07q 238 23 used use VBN cord-284810-fs5rx07q 238 24 exponent exponent NN cord-284810-fs5rx07q 238 25 . . . cord-284810-fs5rx07q 239 1 In in IN cord-284810-fs5rx07q 239 2 contrast contrast NN cord-284810-fs5rx07q 239 3 , , , cord-284810-fs5rx07q 239 4 the the DT cord-284810-fs5rx07q 239 5 estimator estimator NN cord-284810-fs5rx07q 239 6 for for IN cord-284810-fs5rx07q 239 7 an an DT cord-284810-fs5rx07q 239 8 unbound unbound JJ cord-284810-fs5rx07q 239 9 power power NN cord-284810-fs5rx07q 239 10 - - HYPH cord-284810-fs5rx07q 239 11 law law NN cord-284810-fs5rx07q 239 12 , , , cord-284810-fs5rx07q 239 13 Eq Eq NNP cord-284810-fs5rx07q 239 14 . . . cord-284810-fs5rx07q 240 1 ( ( -LRB- cord-284810-fs5rx07q 240 2 A6 A6 NNP cord-284810-fs5rx07q 240 3 ) ) -RRB- cord-284810-fs5rx07q 240 4 , , , cord-284810-fs5rx07q 240 5 yieldsμ yieldsμ NNP cord-284810-fs5rx07q 240 6 = = NFP cord-284810-fs5rx07q 241 1 1.28 1.28 CD cord-284810-fs5rx07q 241 2 ± ± CD cord-284810-fs5rx07q 241 3 0.01 0.01 CD cord-284810-fs5rx07q 241 4 , , , cord-284810-fs5rx07q 241 5 strongly strongly RB cord-284810-fs5rx07q 241 6 overestimating overestimate VBG cord-284810-fs5rx07q 241 7 the the DT cord-284810-fs5rx07q 241 8 true true JJ cord-284810-fs5rx07q 241 9 exponent exponent NN cord-284810-fs5rx07q 241 10 . . . cord-284810-fs5rx07q 242 1 The the DT cord-284810-fs5rx07q 242 2 estimation estimation NN cord-284810-fs5rx07q 242 3 by by IN cord-284810-fs5rx07q 242 4 a a DT cord-284810-fs5rx07q 242 5 regression regression NN cord-284810-fs5rx07q 242 6 line line NN cord-284810-fs5rx07q 242 7 , , , cord-284810-fs5rx07q 242 8 yielding yield VBG cord-284810-fs5rx07q 242 9 µ µ NN cord-284810-fs5rx07q 242 10 = = SYM cord-284810-fs5rx07q 242 11 1.24 1.24 CD cord-284810-fs5rx07q 242 12 , , , cord-284810-fs5rx07q 242 13 also also RB cord-284810-fs5rx07q 242 14 is be VBZ cord-284810-fs5rx07q 242 15 slightly slightly RB cord-284810-fs5rx07q 242 16 too too RB cord-284810-fs5rx07q 242 17 large large JJ cord-284810-fs5rx07q 242 18 . . . cord-284810-fs5rx07q 243 1 The the DT cord-284810-fs5rx07q 243 2 inset inset NN cord-284810-fs5rx07q 243 3 shows show VBZ cord-284810-fs5rx07q 243 4 that that IN cord-284810-fs5rx07q 243 5 the the DT cord-284810-fs5rx07q 243 6 cumulative cumulative JJ cord-284810-fs5rx07q 243 7 fraction fraction NN cord-284810-fs5rx07q 243 8 is be VBZ cord-284810-fs5rx07q 243 9 well well RB cord-284810-fs5rx07q 243 10 described describe VBN cord-284810-fs5rx07q 243 11 by by IN cord-284810-fs5rx07q 243 12 the the DT cord-284810-fs5rx07q 243 13 cumulative cumulative JJ cord-284810-fs5rx07q 243 14 distribution distribution NN cord-284810-fs5rx07q 243 15 function function NN cord-284810-fs5rx07q 243 16 C(n C(n NNP cord-284810-fs5rx07q 243 17 ) ) -RRB- cord-284810-fs5rx07q 243 18 of of IN cord-284810-fs5rx07q 243 19 a a DT cord-284810-fs5rx07q 243 20 truncated truncated JJ cord-284810-fs5rx07q 243 21 power power NN cord-284810-fs5rx07q 243 22 - - HYPH cord-284810-fs5rx07q 243 23 law law NN cord-284810-fs5rx07q 243 24 with with IN cord-284810-fs5rx07q 243 25 critical critical JJ cord-284810-fs5rx07q 243 26 exponentμ exponentμ NN cord-284810-fs5rx07q 243 27 and and CC cord-284810-fs5rx07q 243 28 n n NN cord-284810-fs5rx07q 243 29 max max NN cord-284810-fs5rx07q 244 1 = = SYM cord-284810-fs5rx07q 244 2 8.4 8.4 CD cord-284810-fs5rx07q 244 3 × × NN cord-284810-fs5rx07q 244 4 10 10 CD cord-284810-fs5rx07q 244 5 4 4 CD cord-284810-fs5rx07q 244 6 , , , cord-284810-fs5rx07q 244 7 the the DT cord-284810-fs5rx07q 244 8 maximal maximal JJ cord-284810-fs5rx07q 244 9 n n NN cord-284810-fs5rx07q 244 10 i i PRP cord-284810-fs5rx07q 244 11 value value NN cord-284810-fs5rx07q 244 12 of of IN cord-284810-fs5rx07q 244 13 the the DT cord-284810-fs5rx07q 244 14 sample sample NN cord-284810-fs5rx07q 244 15 . . . cord-284810-fs5rx07q 245 1 with with IN cord-284810-fs5rx07q 245 2 even even RB cord-284810-fs5rx07q 245 3 smaller small JJR cord-284810-fs5rx07q 245 4 estimated estimate VBN cord-284810-fs5rx07q 245 5 values value NNS cord-284810-fs5rx07q 245 6 of of IN cord-284810-fs5rx07q 245 7 the the DT cord-284810-fs5rx07q 245 8 critical critical JJ cord-284810-fs5rx07q 245 9 exponent exponent NN cord-284810-fs5rx07q 245 10 , , , cord-284810-fs5rx07q 245 11 and and CC cord-284810-fs5rx07q 245 12 the the DT cord-284810-fs5rx07q 245 13 distributed distribute VBN cord-284810-fs5rx07q 245 14 values value NNS cord-284810-fs5rx07q 245 15 do do VBP cord-284810-fs5rx07q 245 16 not not RB cord-284810-fs5rx07q 245 17 line line VB cord-284810-fs5rx07q 245 18 up up RP cord-284810-fs5rx07q 245 19 any any DT cord-284810-fs5rx07q 245 20 more more RBR cord-284810-fs5rx07q 245 21 so so RB cord-284810-fs5rx07q 245 22 well well RB cord-284810-fs5rx07q 245 23 on on IN cord-284810-fs5rx07q 245 24 a a DT cord-284810-fs5rx07q 245 25 straight straight JJ cord-284810-fs5rx07q 245 26 line line NN cord-284810-fs5rx07q 245 27 on on IN cord-284810-fs5rx07q 245 28 a a DT cord-284810-fs5rx07q 245 29 double double JJ cord-284810-fs5rx07q 245 30 - - HYPH cord-284810-fs5rx07q 245 31 logarithmic logarithmic JJ cord-284810-fs5rx07q 245 32 plot plot NN cord-284810-fs5rx07q 245 33 . . . cord-284810-fs5rx07q 246 1 Thus thus RB cord-284810-fs5rx07q 246 2 , , , cord-284810-fs5rx07q 246 3 " " `` cord-284810-fs5rx07q 246 4 folding fold VBG cord-284810-fs5rx07q 246 5 " " '' cord-284810-fs5rx07q 246 6 the the DT cord-284810-fs5rx07q 246 7 distribution distribution NN cord-284810-fs5rx07q 246 8 of of IN cord-284810-fs5rx07q 246 9 population population NN cord-284810-fs5rx07q 246 10 sizes size NNS cord-284810-fs5rx07q 246 11 over over IN cord-284810-fs5rx07q 246 12 the the DT cord-284810-fs5rx07q 246 13 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 246 14 case case NN cord-284810-fs5rx07q 246 15 distribution distribution NN cord-284810-fs5rx07q 246 16 does do VBZ cord-284810-fs5rx07q 246 17 not not RB cord-284810-fs5rx07q 246 18 flatten flatten VB cord-284810-fs5rx07q 246 19 , , , cord-284810-fs5rx07q 246 20 but but CC cord-284810-fs5rx07q 246 21 rather rather RB cord-284810-fs5rx07q 246 22 tends tend VBZ cord-284810-fs5rx07q 246 23 to to TO cord-284810-fs5rx07q 246 24 further further RB cord-284810-fs5rx07q 246 25 increase increase VB cord-284810-fs5rx07q 246 26 , , , cord-284810-fs5rx07q 246 27 the the DT cord-284810-fs5rx07q 246 28 inequality inequality NN cord-284810-fs5rx07q 246 29 of of IN cord-284810-fs5rx07q 246 30 the the DT cord-284810-fs5rx07q 246 31 resulting result VBG cord-284810-fs5rx07q 246 32 distribution distribution NN cord-284810-fs5rx07q 246 33 . . . cord-284810-fs5rx07q 247 1 This this DT cord-284810-fs5rx07q 247 2 indicates indicate VBZ cord-284810-fs5rx07q 247 3 that that DT cord-284810-fs5rx07q 247 4 absolute absolute JJ cord-284810-fs5rx07q 247 5 ( ( -LRB- cord-284810-fs5rx07q 247 6 non non JJ cord-284810-fs5rx07q 247 7 - - JJ cord-284810-fs5rx07q 247 8 normalized normalized JJ cord-284810-fs5rx07q 247 9 ) ) -RRB- cord-284810-fs5rx07q 247 10 case case NN cord-284810-fs5rx07q 247 11 numbers number NNS cord-284810-fs5rx07q 247 12 may may MD cord-284810-fs5rx07q 247 13 be be VB cord-284810-fs5rx07q 247 14 the the DT cord-284810-fs5rx07q 247 15 natural natural JJ cord-284810-fs5rx07q 247 16 variables variable NNS cord-284810-fs5rx07q 247 17 to to TO cord-284810-fs5rx07q 247 18 describe describe VB cord-284810-fs5rx07q 247 19 the the DT cord-284810-fs5rx07q 247 20 patterns pattern NNS cord-284810-fs5rx07q 247 21 of of IN cord-284810-fs5rx07q 247 22 the the DT cord-284810-fs5rx07q 247 23 pandemic pandemic NN cord-284810-fs5rx07q 247 24 in in IN cord-284810-fs5rx07q 247 25 its -PRON- PRP$ cord-284810-fs5rx07q 247 26 initial initial JJ cord-284810-fs5rx07q 247 27 stage stage NN cord-284810-fs5rx07q 247 28 . . . cord-284810-fs5rx07q 248 1 In in IN cord-284810-fs5rx07q 248 2 all all DT cord-284810-fs5rx07q 248 3 likelihood likelihood NN cord-284810-fs5rx07q 248 4 , , , cord-284810-fs5rx07q 248 5 the the DT cord-284810-fs5rx07q 248 6 role role NN cord-284810-fs5rx07q 248 7 of of IN cord-284810-fs5rx07q 248 8 country country NN cord-284810-fs5rx07q 248 9 sizes size NNS cord-284810-fs5rx07q 248 10 and and CC cord-284810-fs5rx07q 248 11 population population NN cord-284810-fs5rx07q 248 12 numbers number NNS cord-284810-fs5rx07q 248 13 will will MD cord-284810-fs5rx07q 248 14 become become VB cord-284810-fs5rx07q 248 15 increasingly increasingly RB cord-284810-fs5rx07q 248 16 important important JJ cord-284810-fs5rx07q 248 17 with with IN cord-284810-fs5rx07q 248 18 the the DT cord-284810-fs5rx07q 248 19 further further JJ cord-284810-fs5rx07q 248 20 spread spread NN cord-284810-fs5rx07q 248 21 of of IN cord-284810-fs5rx07q 248 22 the the DT cord-284810-fs5rx07q 248 23 pandemic pandemic NN cord-284810-fs5rx07q 248 24 . . . cord-284810-fs5rx07q 249 1 We -PRON- PRP cord-284810-fs5rx07q 249 2 have have VBP cord-284810-fs5rx07q 249 3 shown show VBN cord-284810-fs5rx07q 249 4 that that IN cord-284810-fs5rx07q 249 5 a a DT cord-284810-fs5rx07q 249 6 simple simple JJ cord-284810-fs5rx07q 249 7 conceptual conceptual JJ cord-284810-fs5rx07q 249 8 model model NN cord-284810-fs5rx07q 249 9 yields yield VBZ cord-284810-fs5rx07q 249 10 an an DT cord-284810-fs5rx07q 249 11 accurate accurate JJ cord-284810-fs5rx07q 249 12 description description NN cord-284810-fs5rx07q 249 13 of of IN cord-284810-fs5rx07q 249 14 the the DT cord-284810-fs5rx07q 249 15 COVID-19 covid-19 JJ cord-284810-fs5rx07q 249 16 prevalence prevalence NN cord-284810-fs5rx07q 249 17 distribution distribution NN cord-284810-fs5rx07q 249 18 in in IN cord-284810-fs5rx07q 249 19 the the DT cord-284810-fs5rx07q 249 20 initial initial JJ cord-284810-fs5rx07q 249 21 phase phase NN cord-284810-fs5rx07q 249 22 of of IN cord-284810-fs5rx07q 249 23 the the DT cord-284810-fs5rx07q 249 24 pandemic pandemic NN cord-284810-fs5rx07q 249 25 . . . cord-284810-fs5rx07q 250 1 This this DT cord-284810-fs5rx07q 250 2 is be VBZ cord-284810-fs5rx07q 250 3 remarkable remarkable JJ cord-284810-fs5rx07q 250 4 because because IN cord-284810-fs5rx07q 250 5 many many JJ cord-284810-fs5rx07q 250 6 important important JJ cord-284810-fs5rx07q 250 7 epidemiological epidemiological JJ cord-284810-fs5rx07q 250 8 aspects aspect NNS cord-284810-fs5rx07q 250 9 of of IN cord-284810-fs5rx07q 250 10 the the DT cord-284810-fs5rx07q 250 11 spreading spreading NN cord-284810-fs5rx07q 250 12 process process NN cord-284810-fs5rx07q 250 13 are be VBP cord-284810-fs5rx07q 250 14 not not RB cord-284810-fs5rx07q 250 15 captured capture VBN cord-284810-fs5rx07q 250 16 by by IN cord-284810-fs5rx07q 250 17 the the DT cord-284810-fs5rx07q 250 18 model model NN cord-284810-fs5rx07q 250 19 . . . cord-284810-fs5rx07q 251 1 Most most RBS cord-284810-fs5rx07q 251 2 notably notably RB cord-284810-fs5rx07q 251 3 , , , cord-284810-fs5rx07q 251 4 the the DT cord-284810-fs5rx07q 251 5 model model NN cord-284810-fs5rx07q 251 6 takes take VBZ cord-284810-fs5rx07q 251 7 into into IN cord-284810-fs5rx07q 251 8 account account NN cord-284810-fs5rx07q 251 9 neither neither DT cord-284810-fs5rx07q 251 10 variability variability NN cord-284810-fs5rx07q 251 11 in in IN cord-284810-fs5rx07q 251 12 country country NN cord-284810-fs5rx07q 251 13 sizes size NNS cord-284810-fs5rx07q 251 14 , , , cord-284810-fs5rx07q 251 15 population population NN cord-284810-fs5rx07q 251 16 numbers number NNS cord-284810-fs5rx07q 251 17 , , , cord-284810-fs5rx07q 251 18 testing test VBG cord-284810-fs5rx07q 251 19 rates rate NNS cord-284810-fs5rx07q 251 20 , , , cord-284810-fs5rx07q 251 21 heterogeneity heterogeneity NN cord-284810-fs5rx07q 251 22 of of IN cord-284810-fs5rx07q 251 23 intra intra JJ cord-284810-fs5rx07q 251 24 - - : cord-284810-fs5rx07q 251 25 and and CC cord-284810-fs5rx07q 251 26 inter inter JJ cord-284810-fs5rx07q 251 27 - - JJ cord-284810-fs5rx07q 251 28 country country JJ cord-284810-fs5rx07q 251 29 connectivity connectivity NN cord-284810-fs5rx07q 251 30 , , , cord-284810-fs5rx07q 251 31 nor nor CC cord-284810-fs5rx07q 251 32 the the DT cord-284810-fs5rx07q 251 33 corresponding correspond VBG cord-284810-fs5rx07q 251 34 changes change NNS cord-284810-fs5rx07q 251 35 due due JJ cord-284810-fs5rx07q 251 36 to to IN cord-284810-fs5rx07q 251 37 social social JJ cord-284810-fs5rx07q 251 38 distancing distancing NN cord-284810-fs5rx07q 251 39 , , , cord-284810-fs5rx07q 251 40 lock lock VB cord-284810-fs5rx07q 251 41 - - HYPH cord-284810-fs5rx07q 251 42 down down RP cord-284810-fs5rx07q 251 43 measures measure NNS cord-284810-fs5rx07q 251 44 , , , cord-284810-fs5rx07q 251 45 closing closing NN cord-284810-fs5rx07q 251 46 of of IN cord-284810-fs5rx07q 251 47 airline airline NN cord-284810-fs5rx07q 251 48 connections connection NNS cord-284810-fs5rx07q 251 49 and and CC cord-284810-fs5rx07q 251 50 shut shut VBN cord-284810-fs5rx07q 251 51 - - HYPH cord-284810-fs5rx07q 251 52 down down NN cord-284810-fs5rx07q 251 53 of of IN cord-284810-fs5rx07q 251 54 borders border NNS cord-284810-fs5rx07q 251 55 . . . cord-284810-fs5rx07q 252 1 These these DT cord-284810-fs5rx07q 252 2 simplifications simplification NNS cord-284810-fs5rx07q 252 3 leave leave VBP cord-284810-fs5rx07q 252 4 much much JJ cord-284810-fs5rx07q 252 5 room room NN cord-284810-fs5rx07q 252 6 for for IN cord-284810-fs5rx07q 252 7 future future JJ cord-284810-fs5rx07q 252 8 investigations investigation NNS cord-284810-fs5rx07q 252 9 and and CC cord-284810-fs5rx07q 252 10 model model NN cord-284810-fs5rx07q 252 11 improvements improvement NNS cord-284810-fs5rx07q 252 12 . . . cord-284810-fs5rx07q 253 1 Obvious obvious JJ cord-284810-fs5rx07q 253 2 model model NN cord-284810-fs5rx07q 253 3 improvements improvement NNS cord-284810-fs5rx07q 253 4 would would MD cord-284810-fs5rx07q 253 5 be be VB cord-284810-fs5rx07q 253 6 to to TO cord-284810-fs5rx07q 253 7 consider consider VB cord-284810-fs5rx07q 253 8 a a DT cord-284810-fs5rx07q 253 9 meta meta NN cord-284810-fs5rx07q 253 10 - - HYPH cord-284810-fs5rx07q 253 11 population population NN cord-284810-fs5rx07q 253 12 with with IN cord-284810-fs5rx07q 253 13 heterogeneously heterogeneously NNP cord-284810-fs5rx07q 253 14 distributed distribute VBN cord-284810-fs5rx07q 253 15 country country NN cord-284810-fs5rx07q 253 16 sizes size NNS cord-284810-fs5rx07q 253 17 or or CC cord-284810-fs5rx07q 253 18 to to TO cord-284810-fs5rx07q 253 19 make make VB cord-284810-fs5rx07q 253 20 the the DT cord-284810-fs5rx07q 253 21 initial initial JJ cord-284810-fs5rx07q 253 22 number number NN cord-284810-fs5rx07q 253 23 of of IN cord-284810-fs5rx07q 253 24 infected infected JJ cord-284810-fs5rx07q 253 25 individuals individual NNS cord-284810-fs5rx07q 253 26 a a DT cord-284810-fs5rx07q 253 27 random random JJ cord-284810-fs5rx07q 253 28 number number NN cord-284810-fs5rx07q 253 29 , , , cord-284810-fs5rx07q 253 30 as as IN cord-284810-fs5rx07q 253 31 would would MD cord-284810-fs5rx07q 253 32 be be VB cord-284810-fs5rx07q 253 33 a a DT cord-284810-fs5rx07q 253 34 better well JJR cord-284810-fs5rx07q 253 35 description description NN cord-284810-fs5rx07q 253 36 of of IN cord-284810-fs5rx07q 253 37 what what WP cord-284810-fs5rx07q 253 38 happened happen VBD cord-284810-fs5rx07q 253 39 in in IN cord-284810-fs5rx07q 253 40 many many JJ cord-284810-fs5rx07q 253 41 countries country NNS cord-284810-fs5rx07q 253 42 . . . cord-284810-fs5rx07q 254 1 One one CD cord-284810-fs5rx07q 254 2 basic basic JJ cord-284810-fs5rx07q 254 3 assumption assumption NN cord-284810-fs5rx07q 254 4 of of IN cord-284810-fs5rx07q 254 5 the the DT cord-284810-fs5rx07q 254 6 developed develop VBN cord-284810-fs5rx07q 254 7 model model NN cord-284810-fs5rx07q 254 8 is be VBZ cord-284810-fs5rx07q 254 9 the the DT cord-284810-fs5rx07q 254 10 separation separation NN cord-284810-fs5rx07q 254 11 of of IN cord-284810-fs5rx07q 254 12 the the DT cord-284810-fs5rx07q 254 13 pandemic pandemic NN cord-284810-fs5rx07q 254 14 into into IN cord-284810-fs5rx07q 254 15 two two CD cord-284810-fs5rx07q 254 16 spatial spatial JJ cord-284810-fs5rx07q 254 17 scales scale NNS cord-284810-fs5rx07q 254 18 , , , cord-284810-fs5rx07q 254 19 the the DT cord-284810-fs5rx07q 254 20 large large JJ cord-284810-fs5rx07q 254 21 - - HYPH cord-284810-fs5rx07q 254 22 spatial spatial JJ cord-284810-fs5rx07q 254 23 spread spread NN cord-284810-fs5rx07q 254 24 over over IN cord-284810-fs5rx07q 254 25 a a DT cord-284810-fs5rx07q 254 26 rather rather RB cord-284810-fs5rx07q 254 27 small small JJ cord-284810-fs5rx07q 254 28 number number NN cord-284810-fs5rx07q 254 29 ( ( -LRB- cord-284810-fs5rx07q 254 30 N n NN cord-284810-fs5rx07q 254 31 < < XX cord-284810-fs5rx07q 254 32 200 200 CD cord-284810-fs5rx07q 254 33 ) ) -RRB- cord-284810-fs5rx07q 254 34 of of IN cord-284810-fs5rx07q 254 35 interconnected interconnected JJ cord-284810-fs5rx07q 254 36 countries country NNS cord-284810-fs5rx07q 254 37 and and CC cord-284810-fs5rx07q 254 38 the the DT cord-284810-fs5rx07q 254 39 small small JJ cord-284810-fs5rx07q 254 40 - - HYPH cord-284810-fs5rx07q 254 41 scale scale NN cord-284810-fs5rx07q 254 42 growth growth NN cord-284810-fs5rx07q 254 43 within within IN cord-284810-fs5rx07q 254 44 a a DT cord-284810-fs5rx07q 254 45 population population NN cord-284810-fs5rx07q 254 46 of of IN cord-284810-fs5rx07q 254 47 much much RB cord-284810-fs5rx07q 254 48 larger large JJR cord-284810-fs5rx07q 254 49 size size NN cord-284810-fs5rx07q 254 50 ( ( -LRB- cord-284810-fs5rx07q 254 51 N n NN cord-284810-fs5rx07q 254 52 = = SYM cord-284810-fs5rx07q 254 53 5 5 CD cord-284810-fs5rx07q 254 54 × × NNP cord-284810-fs5rx07q 254 55 10 10 CD cord-284810-fs5rx07q 254 56 7 7 CD cord-284810-fs5rx07q 254 57 ) ) -RRB- cord-284810-fs5rx07q 254 58 . . . cord-284810-fs5rx07q 255 1 This this DT cord-284810-fs5rx07q 255 2 separation separation NN cord-284810-fs5rx07q 255 3 obviously obviously RB cord-284810-fs5rx07q 255 4 is be VBZ cord-284810-fs5rx07q 255 5 somewhat somewhat RB cord-284810-fs5rx07q 255 6 arbitrary arbitrary JJ cord-284810-fs5rx07q 255 7 . . . cord-284810-fs5rx07q 256 1 For for IN cord-284810-fs5rx07q 256 2 the the DT cord-284810-fs5rx07q 256 3 virus virus NN cord-284810-fs5rx07q 256 4 , , , cord-284810-fs5rx07q 256 5 countries country NNS cord-284810-fs5rx07q 256 6 are be VBP cord-284810-fs5rx07q 256 7 , , , cord-284810-fs5rx07q 256 8 of of IN cord-284810-fs5rx07q 256 9 course course NN cord-284810-fs5rx07q 256 10 , , , cord-284810-fs5rx07q 256 11 quasi quasi JJ cord-284810-fs5rx07q 256 12 - - JJ cord-284810-fs5rx07q 256 13 arbitrary arbitrary JJ cord-284810-fs5rx07q 256 14 entities entity NNS cord-284810-fs5rx07q 256 15 . . . cord-284810-fs5rx07q 257 1 Therefore therefore RB cord-284810-fs5rx07q 257 2 , , , cord-284810-fs5rx07q 257 3 it -PRON- PRP cord-284810-fs5rx07q 257 4 would would MD cord-284810-fs5rx07q 257 5 be be VB cord-284810-fs5rx07q 257 6 important important JJ cord-284810-fs5rx07q 257 7 to to TO cord-284810-fs5rx07q 257 8 check check VB cord-284810-fs5rx07q 257 9 whether whether IN cord-284810-fs5rx07q 257 10 both both CC cord-284810-fs5rx07q 257 11 the the DT cord-284810-fs5rx07q 257 12 data data NN cord-284810-fs5rx07q 257 13 analysis analysis NN cord-284810-fs5rx07q 258 1 ( ( -LRB- cord-284810-fs5rx07q 258 2 Fig Fig NNP cord-284810-fs5rx07q 258 3 . . NNP cord-284810-fs5rx07q 258 4 1 1 CD cord-284810-fs5rx07q 258 5 ) ) -RRB- cord-284810-fs5rx07q 258 6 and and CC cord-284810-fs5rx07q 258 7 the the DT cord-284810-fs5rx07q 258 8 mathematical mathematical JJ cord-284810-fs5rx07q 258 9 model model NN cord-284810-fs5rx07q 258 10 are be VBP cord-284810-fs5rx07q 258 11 robust robust JJ cord-284810-fs5rx07q 258 12 to to IN cord-284810-fs5rx07q 258 13 arbitrarily arbitrarily RB cord-284810-fs5rx07q 258 14 subdividing subdivide VBG cord-284810-fs5rx07q 258 15 or or CC cord-284810-fs5rx07q 258 16 lumping lump VBG cord-284810-fs5rx07q 258 17 countries country NNS cord-284810-fs5rx07q 258 18 . . . cord-284810-fs5rx07q 259 1 The the DT cord-284810-fs5rx07q 259 2 very very RB cord-284810-fs5rx07q 259 3 similar similar JJ cord-284810-fs5rx07q 259 4 scaling scaling NN cord-284810-fs5rx07q 259 5 observed observe VBD cord-284810-fs5rx07q 259 6 among among IN cord-284810-fs5rx07q 259 7 US US NNP cord-284810-fs5rx07q 259 8 counties county NNS cord-284810-fs5rx07q 259 9 [ [ -LRB- cord-284810-fs5rx07q 259 10 Figs fig NNS cord-284810-fs5rx07q 259 11 . . . cord-284810-fs5rx07q 259 12 1(c 1(c CD cord-284810-fs5rx07q 259 13 ) ) -RRB- cord-284810-fs5rx07q 260 1 and and CC cord-284810-fs5rx07q 260 2 ( ( -LRB- cord-284810-fs5rx07q 260 3 d d NN cord-284810-fs5rx07q 260 4 ) ) -RRB- cord-284810-fs5rx07q 260 5 ] ] -RRB- cord-284810-fs5rx07q 260 6 lends lend VBZ cord-284810-fs5rx07q 260 7 credence credence NN cord-284810-fs5rx07q 260 8 to to IN cord-284810-fs5rx07q 260 9 the the DT cord-284810-fs5rx07q 260 10 model model NN cord-284810-fs5rx07q 260 11 's 's POS cord-284810-fs5rx07q 260 12 generality generality NN cord-284810-fs5rx07q 260 13 . . . cord-284810-fs5rx07q 261 1 Similarly similarly RB cord-284810-fs5rx07q 261 2 , , , cord-284810-fs5rx07q 261 3 one one PRP cord-284810-fs5rx07q 261 4 can can MD cord-284810-fs5rx07q 261 5 readily readily RB cord-284810-fs5rx07q 261 6 ascertain ascertain VB cord-284810-fs5rx07q 261 7 that that IN cord-284810-fs5rx07q 261 8 the the DT cord-284810-fs5rx07q 261 9 model model NN cord-284810-fs5rx07q 261 10 result result NN cord-284810-fs5rx07q 261 11 is be VBZ cord-284810-fs5rx07q 261 12 not not RB cord-284810-fs5rx07q 261 13 an an DT cord-284810-fs5rx07q 261 14 artifact artifact NN cord-284810-fs5rx07q 261 15 of of IN cord-284810-fs5rx07q 261 16 artificial artificial JJ cord-284810-fs5rx07q 261 17 lumping lumping NN cord-284810-fs5rx07q 261 18 . . . cord-284810-fs5rx07q 262 1 Suppose suppose VB cord-284810-fs5rx07q 262 2 a a DT cord-284810-fs5rx07q 262 3 virus virus NN cord-284810-fs5rx07q 262 4 that that WDT cord-284810-fs5rx07q 262 5 is be VBZ cord-284810-fs5rx07q 262 6 spreading spread VBG cord-284810-fs5rx07q 262 7 in in IN cord-284810-fs5rx07q 262 8 an an DT cord-284810-fs5rx07q 262 9 all all RB cord-284810-fs5rx07q 262 10 - - HYPH cord-284810-fs5rx07q 262 11 to to IN cord-284810-fs5rx07q 262 12 - - HYPH cord-284810-fs5rx07q 262 13 all all DT cord-284810-fs5rx07q 262 14 , , , cord-284810-fs5rx07q 262 15 or or CC cord-284810-fs5rx07q 262 16 randomly randomly RB cord-284810-fs5rx07q 262 17 coupled couple VBN cord-284810-fs5rx07q 262 18 , , , cord-284810-fs5rx07q 262 19 network network NN cord-284810-fs5rx07q 262 20 of of IN cord-284810-fs5rx07q 262 21 a a DT cord-284810-fs5rx07q 262 22 number number NN cord-284810-fs5rx07q 262 23 of of IN cord-284810-fs5rx07q 262 24 N n NN cord-284810-fs5rx07q 262 25 · · NN cord-284810-fs5rx07q 262 26 N n CD cord-284810-fs5rx07q 262 27 pop pop NN cord-284810-fs5rx07q 262 28 individuals individual NNS cord-284810-fs5rx07q 262 29 . . . cord-284810-fs5rx07q 263 1 If if IN cord-284810-fs5rx07q 263 2 we -PRON- PRP cord-284810-fs5rx07q 263 3 would would MD cord-284810-fs5rx07q 263 4 artificially artificially RB cord-284810-fs5rx07q 263 5 subdivide subdivide VB cord-284810-fs5rx07q 263 6 individuals individual NNS cord-284810-fs5rx07q 263 7 into into IN cord-284810-fs5rx07q 263 8 a a DT cord-284810-fs5rx07q 263 9 small small JJ cord-284810-fs5rx07q 263 10 number number NN cord-284810-fs5rx07q 263 11 N n CD cord-284810-fs5rx07q 263 12 of of IN cord-284810-fs5rx07q 263 13 classes class NNS cord-284810-fs5rx07q 263 14 ( ( -LRB- cord-284810-fs5rx07q 263 15 or or CC cord-284810-fs5rx07q 263 16 countries country NNS cord-284810-fs5rx07q 263 17 ) ) -RRB- cord-284810-fs5rx07q 263 18 , , , cord-284810-fs5rx07q 263 19 at at IN cord-284810-fs5rx07q 263 20 the the DT cord-284810-fs5rx07q 263 21 time time NN cord-284810-fs5rx07q 263 22 point point NN cord-284810-fs5rx07q 263 23 when when WRB cord-284810-fs5rx07q 263 24 the the DT cord-284810-fs5rx07q 263 25 disease disease NN cord-284810-fs5rx07q 263 26 has have VBZ cord-284810-fs5rx07q 263 27 spread spread VBN cord-284810-fs5rx07q 263 28 to to IN cord-284810-fs5rx07q 263 29 all all DT cord-284810-fs5rx07q 263 30 countries country NNS cord-284810-fs5rx07q 263 31 , , , cord-284810-fs5rx07q 263 32 within within IN cord-284810-fs5rx07q 263 33 each each DT cord-284810-fs5rx07q 263 34 country country NN cord-284810-fs5rx07q 263 35 , , , cord-284810-fs5rx07q 263 36 we -PRON- PRP cord-284810-fs5rx07q 263 37 would would MD cord-284810-fs5rx07q 263 38 still still RB cord-284810-fs5rx07q 263 39 have have VB cord-284810-fs5rx07q 263 40 only only RB cord-284810-fs5rx07q 263 41 a a DT cord-284810-fs5rx07q 263 42 few few JJ cord-284810-fs5rx07q 263 43 cases case NNS cord-284810-fs5rx07q 263 44 ( ( -LRB- cord-284810-fs5rx07q 263 45 of of IN cord-284810-fs5rx07q 263 46 the the DT cord-284810-fs5rx07q 263 47 order order NN cord-284810-fs5rx07q 263 48 of of IN cord-284810-fs5rx07q 263 49 N N NNP cord-284810-fs5rx07q 263 50 N N NNP cord-284810-fs5rx07q 263 51 pop pop NN cord-284810-fs5rx07q 263 52 ) ) -RRB- cord-284810-fs5rx07q 263 53 . . . cord-284810-fs5rx07q 264 1 Thus thus RB cord-284810-fs5rx07q 264 2 , , , cord-284810-fs5rx07q 264 3 the the DT cord-284810-fs5rx07q 264 4 assumed assume VBN cord-284810-fs5rx07q 264 5 simultaneous simultaneous JJ cord-284810-fs5rx07q 264 6 spread spread NN cord-284810-fs5rx07q 264 7 on on IN cord-284810-fs5rx07q 264 8 both both DT cord-284810-fs5rx07q 264 9 spatial spatial JJ cord-284810-fs5rx07q 264 10 scales scale NNS cord-284810-fs5rx07q 264 11 requires require VBZ cord-284810-fs5rx07q 264 12 a a DT cord-284810-fs5rx07q 264 13 real real JJ cord-284810-fs5rx07q 264 14 physical physical JJ cord-284810-fs5rx07q 264 15 separation separation NN cord-284810-fs5rx07q 264 16 in in IN cord-284810-fs5rx07q 264 17 the the DT cord-284810-fs5rx07q 264 18 network network NN cord-284810-fs5rx07q 264 19 structure structure NN cord-284810-fs5rx07q 264 20 . . . cord-284810-fs5rx07q 265 1 It -PRON- PRP cord-284810-fs5rx07q 265 2 would would MD cord-284810-fs5rx07q 265 3 be be VB cord-284810-fs5rx07q 265 4 an an DT cord-284810-fs5rx07q 265 5 interesting interesting JJ cord-284810-fs5rx07q 265 6 perspective perspective NN cord-284810-fs5rx07q 265 7 for for IN cord-284810-fs5rx07q 265 8 future future JJ cord-284810-fs5rx07q 265 9 research research NN cord-284810-fs5rx07q 265 10 to to TO cord-284810-fs5rx07q 265 11 study study VB cord-284810-fs5rx07q 265 12 the the DT cord-284810-fs5rx07q 265 13 spread spread NN cord-284810-fs5rx07q 265 14 in in IN cord-284810-fs5rx07q 265 15 multi multi JJ cord-284810-fs5rx07q 265 16 - - JJ cord-284810-fs5rx07q 265 17 scale scale JJ cord-284810-fs5rx07q 265 18 hierarchies hierarchy NNS cord-284810-fs5rx07q 265 19 or or CC cord-284810-fs5rx07q 265 20 in in IN cord-284810-fs5rx07q 265 21 more more RBR cord-284810-fs5rx07q 265 22 realistic realistic JJ cord-284810-fs5rx07q 265 23 models model NNS cord-284810-fs5rx07q 265 24 of of IN cord-284810-fs5rx07q 265 25 interconnected interconnected JJ cord-284810-fs5rx07q 265 26 societies society NNS cord-284810-fs5rx07q 265 27 . . . cord-284810-fs5rx07q 266 1 One one CD cord-284810-fs5rx07q 266 2 important important JJ cord-284810-fs5rx07q 266 3 model model NN cord-284810-fs5rx07q 266 4 application application NN cord-284810-fs5rx07q 266 5 would would MD cord-284810-fs5rx07q 266 6 be be VB cord-284810-fs5rx07q 266 7 the the DT cord-284810-fs5rx07q 266 8 simulation simulation NN cord-284810-fs5rx07q 266 9 of of IN cord-284810-fs5rx07q 266 10 interim interim JJ cord-284810-fs5rx07q 266 11 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 266 12 lockdown lockdown NN cord-284810-fs5rx07q 266 13 or or CC cord-284810-fs5rx07q 266 14 containment containment NN cord-284810-fs5rx07q 266 15 measures measure NNS cord-284810-fs5rx07q 266 16 , , , cord-284810-fs5rx07q 266 17 as as IN cord-284810-fs5rx07q 266 18 were be VBD cord-284810-fs5rx07q 266 19 introduced introduce VBN cord-284810-fs5rx07q 266 20 in in IN cord-284810-fs5rx07q 266 21 many many JJ cord-284810-fs5rx07q 266 22 countries country NNS cord-284810-fs5rx07q 266 23 in in IN cord-284810-fs5rx07q 266 24 the the DT cord-284810-fs5rx07q 266 25 world world NN cord-284810-fs5rx07q 266 26 in in IN cord-284810-fs5rx07q 266 27 March March NNP cord-284810-fs5rx07q 266 28 and and CC cord-284810-fs5rx07q 266 29 April April NNP cord-284810-fs5rx07q 266 30 2020 2020 CD cord-284810-fs5rx07q 266 31 . . . cord-284810-fs5rx07q 267 1 Such such JJ cord-284810-fs5rx07q 267 2 measures measure NNS cord-284810-fs5rx07q 267 3 might may MD cord-284810-fs5rx07q 267 4 inhibit inhibit VB cord-284810-fs5rx07q 267 5 the the DT cord-284810-fs5rx07q 267 6 increase increase NN cord-284810-fs5rx07q 267 7 of of IN cord-284810-fs5rx07q 267 8 case case NN cord-284810-fs5rx07q 267 9 numbers number NNS cord-284810-fs5rx07q 267 10 within within IN cord-284810-fs5rx07q 267 11 local local JJ cord-284810-fs5rx07q 267 12 regions region NNS cord-284810-fs5rx07q 267 13 ( ( -LRB- cord-284810-fs5rx07q 267 14 the the DT cord-284810-fs5rx07q 267 15 small small JJ cord-284810-fs5rx07q 267 16 - - HYPH cord-284810-fs5rx07q 267 17 scale scale NN cord-284810-fs5rx07q 267 18 part part NN cord-284810-fs5rx07q 267 19 of of IN cord-284810-fs5rx07q 267 20 our -PRON- PRP$ cord-284810-fs5rx07q 267 21 theory theory NN cord-284810-fs5rx07q 267 22 ) ) -RRB- cord-284810-fs5rx07q 267 23 but but CC cord-284810-fs5rx07q 267 24 they -PRON- PRP cord-284810-fs5rx07q 267 25 would would MD cord-284810-fs5rx07q 267 26 not not RB cord-284810-fs5rx07q 267 27 necessarily necessarily RB cord-284810-fs5rx07q 267 28 suppress suppress VB cord-284810-fs5rx07q 267 29 also also RB cord-284810-fs5rx07q 267 30 the the DT cord-284810-fs5rx07q 267 31 large large JJ cord-284810-fs5rx07q 267 32 - - HYPH cord-284810-fs5rx07q 267 33 scale scale NN cord-284810-fs5rx07q 267 34 diffusion diffusion NN cord-284810-fs5rx07q 267 35 of of IN cord-284810-fs5rx07q 267 36 infections infection NNS cord-284810-fs5rx07q 267 37 across across IN cord-284810-fs5rx07q 267 38 regions region NNS cord-284810-fs5rx07q 267 39 . . . cord-284810-fs5rx07q 268 1 Thus thus RB cord-284810-fs5rx07q 268 2 , , , cord-284810-fs5rx07q 268 3 under under IN cord-284810-fs5rx07q 268 4 the the DT cord-284810-fs5rx07q 268 5 guise guise NN cord-284810-fs5rx07q 268 6 of of IN cord-284810-fs5rx07q 268 7 suppressed suppress VBN cord-284810-fs5rx07q 268 8 case case NN cord-284810-fs5rx07q 268 9 numbers number NNS cord-284810-fs5rx07q 268 10 during during IN cord-284810-fs5rx07q 268 11 the the DT cord-284810-fs5rx07q 268 12 mitigation mitigation NN cord-284810-fs5rx07q 268 13 period period NN cord-284810-fs5rx07q 268 14 , , , cord-284810-fs5rx07q 268 15 there there EX cord-284810-fs5rx07q 268 16 could could MD cord-284810-fs5rx07q 268 17 be be VB cord-284810-fs5rx07q 268 18 a a DT cord-284810-fs5rx07q 268 19 dangerous dangerous JJ cord-284810-fs5rx07q 268 20 " " `` cord-284810-fs5rx07q 268 21 invisible invisible JJ cord-284810-fs5rx07q 268 22 " " '' cord-284810-fs5rx07q 268 23 homogenization homogenization NN cord-284810-fs5rx07q 268 24 in in IN cord-284810-fs5rx07q 268 25 the the DT cord-284810-fs5rx07q 268 26 spatial spatial JJ cord-284810-fs5rx07q 268 27 distribution distribution NN cord-284810-fs5rx07q 268 28 of of IN cord-284810-fs5rx07q 268 29 the the DT cord-284810-fs5rx07q 268 30 virus virus NN cord-284810-fs5rx07q 268 31 . . . cord-284810-fs5rx07q 269 1 This this DT cord-284810-fs5rx07q 269 2 would would MD cord-284810-fs5rx07q 269 3 have have VB cord-284810-fs5rx07q 269 4 tremendous tremendous JJ cord-284810-fs5rx07q 269 5 implications implication NNS cord-284810-fs5rx07q 269 6 in in IN cord-284810-fs5rx07q 269 7 a a DT cord-284810-fs5rx07q 269 8 scenario scenario NN cord-284810-fs5rx07q 269 9 where where WRB cord-284810-fs5rx07q 269 10 the the DT cord-284810-fs5rx07q 269 11 measures measure NNS cord-284810-fs5rx07q 269 12 are be VBP cord-284810-fs5rx07q 269 13 suddenly suddenly RB cord-284810-fs5rx07q 269 14 lifted lift VBN cord-284810-fs5rx07q 269 15 in in IN cord-284810-fs5rx07q 269 16 many many JJ cord-284810-fs5rx07q 269 17 places place NNS cord-284810-fs5rx07q 269 18 . . . cord-284810-fs5rx07q 270 1 In in IN cord-284810-fs5rx07q 270 2 this this DT cord-284810-fs5rx07q 270 3 case case NN cord-284810-fs5rx07q 270 4 , , , cord-284810-fs5rx07q 270 5 our -PRON- PRP$ cord-284810-fs5rx07q 270 6 theory theory NN cord-284810-fs5rx07q 270 7 would would MD cord-284810-fs5rx07q 270 8 predict predict VB cord-284810-fs5rx07q 270 9 the the DT cord-284810-fs5rx07q 270 10 emergence emergence NN cord-284810-fs5rx07q 270 11 of of IN cord-284810-fs5rx07q 270 12 a a DT cord-284810-fs5rx07q 270 13 very very RB cord-284810-fs5rx07q 270 14 different different JJ cord-284810-fs5rx07q 270 15 case case NN cord-284810-fs5rx07q 270 16 number number NN cord-284810-fs5rx07q 270 17 distribution distribution NN cord-284810-fs5rx07q 270 18 than than IN cord-284810-fs5rx07q 270 19 shown show VBN cord-284810-fs5rx07q 270 20 in in IN cord-284810-fs5rx07q 270 21 Fig Fig NNP cord-284810-fs5rx07q 270 22 . . . cord-284810-fs5rx07q 271 1 1 1 LS cord-284810-fs5rx07q 271 2 . . . cord-284810-fs5rx07q 272 1 Instead instead RB cord-284810-fs5rx07q 272 2 of of IN cord-284810-fs5rx07q 272 3 the the DT cord-284810-fs5rx07q 272 4 previous previous JJ cord-284810-fs5rx07q 272 5 power power NN cord-284810-fs5rx07q 272 6 - - HYPH cord-284810-fs5rx07q 272 7 law law NN cord-284810-fs5rx07q 272 8 distribution distribution NN cord-284810-fs5rx07q 272 9 resurfacing resurfacing NN cord-284810-fs5rx07q 272 10 , , , cord-284810-fs5rx07q 272 11 the the DT cord-284810-fs5rx07q 272 12 most most RBS cord-284810-fs5rx07q 272 13 likely likely JJ cord-284810-fs5rx07q 272 14 situation situation NN cord-284810-fs5rx07q 272 15 would would MD cord-284810-fs5rx07q 272 16 be be VB cord-284810-fs5rx07q 272 17 the the DT cord-284810-fs5rx07q 272 18 synchronous synchronous JJ cord-284810-fs5rx07q 272 19 initiation initiation NN cord-284810-fs5rx07q 272 20 of of IN cord-284810-fs5rx07q 272 21 increasing increase VBG cord-284810-fs5rx07q 272 22 in in IN cord-284810-fs5rx07q 272 23 case case NN cord-284810-fs5rx07q 272 24 numbers number NNS cord-284810-fs5rx07q 272 25 everywhere everywhere RB cord-284810-fs5rx07q 272 26 . . . cord-284810-fs5rx07q 273 1 Thus thus RB cord-284810-fs5rx07q 273 2 , , , cord-284810-fs5rx07q 273 3 situations situation NNS cord-284810-fs5rx07q 273 4 as as IN cord-284810-fs5rx07q 273 5 they -PRON- PRP cord-284810-fs5rx07q 273 6 appeared appear VBD cord-284810-fs5rx07q 273 7 only only RB cord-284810-fs5rx07q 273 8 in in IN cord-284810-fs5rx07q 273 9 the the DT cord-284810-fs5rx07q 273 10 epicenters epicenter NNS cord-284810-fs5rx07q 273 11 during during IN cord-284810-fs5rx07q 273 12 the the DT cord-284810-fs5rx07q 273 13 beginning beginning NN cord-284810-fs5rx07q 273 14 phase phase NN cord-284810-fs5rx07q 273 15 of of IN cord-284810-fs5rx07q 273 16 the the DT cord-284810-fs5rx07q 273 17 pandemic pandemic NN cord-284810-fs5rx07q 273 18 could could MD cord-284810-fs5rx07q 273 19 be be VB cord-284810-fs5rx07q 273 20 the the DT cord-284810-fs5rx07q 273 21 rule rule NN cord-284810-fs5rx07q 273 22 in in IN cord-284810-fs5rx07q 273 23 most most JJS cord-284810-fs5rx07q 273 24 parts part NNS cord-284810-fs5rx07q 273 25 where where WRB cord-284810-fs5rx07q 273 26 mitigation mitigation NN cord-284810-fs5rx07q 273 27 measures measure NNS cord-284810-fs5rx07q 273 28 are be VBP cord-284810-fs5rx07q 273 29 lifted lift VBN cord-284810-fs5rx07q 273 30 . . . cord-284810-fs5rx07q 274 1 In in IN cord-284810-fs5rx07q 274 2 this this DT cord-284810-fs5rx07q 274 3 sense sense NN cord-284810-fs5rx07q 274 4 , , , cord-284810-fs5rx07q 274 5 the the DT cord-284810-fs5rx07q 274 6 long long JJ cord-284810-fs5rx07q 274 7 tail tail NN cord-284810-fs5rx07q 274 8 of of IN cord-284810-fs5rx07q 274 9 the the DT cord-284810-fs5rx07q 274 10 case case NN cord-284810-fs5rx07q 274 11 distribution distribution NN cord-284810-fs5rx07q 274 12 , , , cord-284810-fs5rx07q 274 13 characterized characterize VBN cord-284810-fs5rx07q 274 14 by by IN cord-284810-fs5rx07q 274 15 the the DT cord-284810-fs5rx07q 274 16 many many JJ cord-284810-fs5rx07q 274 17 regions region NNS cord-284810-fs5rx07q 274 18 with with IN cord-284810-fs5rx07q 274 19 only only JJ cord-284810-fs5rx07q 274 20 mild mild JJ cord-284810-fs5rx07q 274 21 epidemic epidemic NN cord-284810-fs5rx07q 274 22 prevalence prevalence NN cord-284810-fs5rx07q 274 23 , , , cord-284810-fs5rx07q 274 24 that that WDT cord-284810-fs5rx07q 274 25 was be VBD cord-284810-fs5rx07q 274 26 observed observe VBN cord-284810-fs5rx07q 274 27 in in IN cord-284810-fs5rx07q 274 28 the the DT cord-284810-fs5rx07q 274 29 initial initial JJ cord-284810-fs5rx07q 274 30 phase phase NN cord-284810-fs5rx07q 274 31 of of IN cord-284810-fs5rx07q 274 32 the the DT cord-284810-fs5rx07q 274 33 pandemic pandemic NN cord-284810-fs5rx07q 274 34 , , , cord-284810-fs5rx07q 274 35 could could MD cord-284810-fs5rx07q 274 36 create create VB cord-284810-fs5rx07q 274 37 a a DT cord-284810-fs5rx07q 274 38 false false JJ cord-284810-fs5rx07q 274 39 sense sense NN cord-284810-fs5rx07q 274 40 of of IN cord-284810-fs5rx07q 274 41 security security NN cord-284810-fs5rx07q 274 42 . . . cord-284810-fs5rx07q 275 1 Finally finally RB cord-284810-fs5rx07q 275 2 , , , cord-284810-fs5rx07q 275 3 we -PRON- PRP cord-284810-fs5rx07q 275 4 would would MD cord-284810-fs5rx07q 275 5 like like VB cord-284810-fs5rx07q 275 6 to to TO cord-284810-fs5rx07q 275 7 remark remark VB cord-284810-fs5rx07q 275 8 that that IN cord-284810-fs5rx07q 275 9 the the DT cord-284810-fs5rx07q 275 10 model model NN cord-284810-fs5rx07q 275 11 's 's POS cord-284810-fs5rx07q 275 12 strong strong JJ cord-284810-fs5rx07q 275 13 simplicity simplicity NN cord-284810-fs5rx07q 275 14 is be VBZ cord-284810-fs5rx07q 275 15 at at IN cord-284810-fs5rx07q 275 16 the the DT cord-284810-fs5rx07q 275 17 same same JJ cord-284810-fs5rx07q 275 18 time time NN cord-284810-fs5rx07q 275 19 a a DT cord-284810-fs5rx07q 275 20 strength strength NN cord-284810-fs5rx07q 275 21 : : : cord-284810-fs5rx07q 275 22 being be VBG cord-284810-fs5rx07q 275 23 rather rather RB cord-284810-fs5rx07q 275 24 generic generic JJ cord-284810-fs5rx07q 275 25 , , , cord-284810-fs5rx07q 275 26 it -PRON- PRP cord-284810-fs5rx07q 275 27 should should MD cord-284810-fs5rx07q 275 28 be be VB cord-284810-fs5rx07q 275 29 applicable applicable JJ cord-284810-fs5rx07q 275 30 to to IN cord-284810-fs5rx07q 275 31 very very RB cord-284810-fs5rx07q 275 32 different different JJ cord-284810-fs5rx07q 275 33 systems system NNS cord-284810-fs5rx07q 275 34 , , , cord-284810-fs5rx07q 275 35 to to TO cord-284810-fs5rx07q 275 36 describe describe VB cord-284810-fs5rx07q 275 37 the the DT cord-284810-fs5rx07q 275 38 spread spread NN cord-284810-fs5rx07q 275 39 of of IN cord-284810-fs5rx07q 275 40 commodities commodity NNS cord-284810-fs5rx07q 275 41 as as IN cord-284810-fs5rx07q 275 42 a a DT cord-284810-fs5rx07q 275 43 process process NN cord-284810-fs5rx07q 275 44 with with IN cord-284810-fs5rx07q 275 45 two two CD cord-284810-fs5rx07q 275 46 spatial spatial JJ cord-284810-fs5rx07q 275 47 scales scale NNS cord-284810-fs5rx07q 275 48 . . . cord-284810-fs5rx07q 276 1 The the DT cord-284810-fs5rx07q 276 2 fact fact NN cord-284810-fs5rx07q 276 3 that that IN cord-284810-fs5rx07q 276 4 the the DT cord-284810-fs5rx07q 276 5 distribution distribution NN cord-284810-fs5rx07q 276 6 of of IN cord-284810-fs5rx07q 276 7 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 276 8 resembles resemble VBZ cord-284810-fs5rx07q 276 9 a a DT cord-284810-fs5rx07q 276 10 model model NN cord-284810-fs5rx07q 276 11 where where WRB cord-284810-fs5rx07q 276 12 only only RB cord-284810-fs5rx07q 276 13 the the DT cord-284810-fs5rx07q 276 14 initial initial JJ cord-284810-fs5rx07q 276 15 infection infection NN cord-284810-fs5rx07q 276 16 " " `` cord-284810-fs5rx07q 276 17 counts count NNS cord-284810-fs5rx07q 276 18 " " '' cord-284810-fs5rx07q 276 19 reflects reflect VBZ cord-284810-fs5rx07q 276 20 the the DT cord-284810-fs5rx07q 276 21 intrinsic intrinsic JJ cord-284810-fs5rx07q 276 22 difficulty difficulty NN cord-284810-fs5rx07q 276 23 in in IN cord-284810-fs5rx07q 276 24 containing contain VBG cord-284810-fs5rx07q 276 25 epidemics epidemic NNS cord-284810-fs5rx07q 276 26 at at IN cord-284810-fs5rx07q 276 27 global global JJ cord-284810-fs5rx07q 276 28 and and CC cord-284810-fs5rx07q 276 29 local local JJ cord-284810-fs5rx07q 276 30 scales scale NNS cord-284810-fs5rx07q 276 31 when when WRB cord-284810-fs5rx07q 276 32 unilateral unilateral JJ cord-284810-fs5rx07q 276 33 measures measure NNS cord-284810-fs5rx07q 276 34 ( ( -LRB- cord-284810-fs5rx07q 276 35 e.g. e.g. RB cord-284810-fs5rx07q 276 36 , , , cord-284810-fs5rx07q 276 37 travel travel NN cord-284810-fs5rx07q 276 38 bans ban NNS cord-284810-fs5rx07q 276 39 and and CC cord-284810-fs5rx07q 276 40 lockdowns lockdown NNS cord-284810-fs5rx07q 276 41 ) ) -RRB- cord-284810-fs5rx07q 276 42 are be VBP cord-284810-fs5rx07q 276 43 impractical impractical JJ cord-284810-fs5rx07q 276 44 or or CC cord-284810-fs5rx07q 276 45 non non JJ cord-284810-fs5rx07q 276 46 - - JJ cord-284810-fs5rx07q 276 47 enforceable enforceable JJ cord-284810-fs5rx07q 276 48 , , , cord-284810-fs5rx07q 276 49 i.e. i.e. FW cord-284810-fs5rx07q 276 50 , , , cord-284810-fs5rx07q 276 51 where where WRB cord-284810-fs5rx07q 276 52 other other JJ cord-284810-fs5rx07q 276 53 countries country NNS cord-284810-fs5rx07q 276 54 or or CC cord-284810-fs5rx07q 276 55 regions region NNS cord-284810-fs5rx07q 276 56 will will MD cord-284810-fs5rx07q 276 57 step step VB cord-284810-fs5rx07q 276 58 up up RP cord-284810-fs5rx07q 276 59 and and CC cord-284810-fs5rx07q 276 60 continue continue VB cord-284810-fs5rx07q 276 61 the the DT cord-284810-fs5rx07q 276 62 spread spread NN cord-284810-fs5rx07q 276 63 . . . cord-284810-fs5rx07q 277 1 Thus thus RB cord-284810-fs5rx07q 277 2 , , , cord-284810-fs5rx07q 277 3 assessing assess VBG cord-284810-fs5rx07q 277 4 how how WRB cord-284810-fs5rx07q 277 5 a a DT cord-284810-fs5rx07q 277 6 well well RB cord-284810-fs5rx07q 277 7 simple simple JJ cord-284810-fs5rx07q 277 8 dualscale dualscale NN cord-284810-fs5rx07q 277 9 model model NN cord-284810-fs5rx07q 277 10 predicts predict VBZ cord-284810-fs5rx07q 277 11 the the DT cord-284810-fs5rx07q 277 12 early early JJ cord-284810-fs5rx07q 277 13 spread spread NN cord-284810-fs5rx07q 277 14 of of IN cord-284810-fs5rx07q 277 15 epidemics epidemic NNS cord-284810-fs5rx07q 277 16 , , , cord-284810-fs5rx07q 277 17 despite despite IN cord-284810-fs5rx07q 277 18 the the DT cord-284810-fs5rx07q 277 19 huge huge JJ cord-284810-fs5rx07q 277 20 contrasts contrast NNS cord-284810-fs5rx07q 277 21 between between IN cord-284810-fs5rx07q 277 22 countries country NNS cord-284810-fs5rx07q 277 23 , , , cord-284810-fs5rx07q 277 24 could could MD cord-284810-fs5rx07q 277 25 help help VB cord-284810-fs5rx07q 277 26 identify identify VB cord-284810-fs5rx07q 277 27 critical critical JJ cord-284810-fs5rx07q 277 28 temporal temporal JJ cord-284810-fs5rx07q 277 29 and and CC cord-284810-fs5rx07q 277 30 spatial spatial JJ cord-284810-fs5rx07q 277 31 scales scale NNS cord-284810-fs5rx07q 277 32 of of IN cord-284810-fs5rx07q 277 33 response response NN cord-284810-fs5rx07q 277 34 in in IN cord-284810-fs5rx07q 277 35 which which WDT cord-284810-fs5rx07q 277 36 to to TO cord-284810-fs5rx07q 277 37 mitigate mitigate VB cord-284810-fs5rx07q 277 38 future future JJ cord-284810-fs5rx07q 277 39 epidemic epidemic NN cord-284810-fs5rx07q 277 40 threats threat NNS cord-284810-fs5rx07q 277 41 . . . cord-284810-fs5rx07q 278 1 The the DT cord-284810-fs5rx07q 278 2 author author NN cord-284810-fs5rx07q 278 3 would would MD cord-284810-fs5rx07q 278 4 like like VB cord-284810-fs5rx07q 278 5 to to TO cord-284810-fs5rx07q 278 6 thank thank VB cord-284810-fs5rx07q 278 7 Christoph Christoph NNP cord-284810-fs5rx07q 278 8 Feenders Feenders NNP cord-284810-fs5rx07q 278 9 , , , cord-284810-fs5rx07q 278 10 Thilo Thilo NNP cord-284810-fs5rx07q 278 11 Gross Gross NNP cord-284810-fs5rx07q 278 12 , , , cord-284810-fs5rx07q 278 13 Alastair Alastair NNP cord-284810-fs5rx07q 278 14 Jamieson Jamieson NNP cord-284810-fs5rx07q 278 15 - - HYPH cord-284810-fs5rx07q 278 16 Lane Lane NNP cord-284810-fs5rx07q 278 17 , , , cord-284810-fs5rx07q 278 18 Cora Cora NNP cord-284810-fs5rx07q 278 19 Kohlmeier Kohlmeier NNP cord-284810-fs5rx07q 278 20 , , , cord-284810-fs5rx07q 278 21 James James NNP cord-284810-fs5rx07q 278 22 McLaren McLaren NNP cord-284810-fs5rx07q 278 23 , , , cord-284810-fs5rx07q 278 24 and and CC cord-284810-fs5rx07q 278 25 Alexey Alexey NNP cord-284810-fs5rx07q 278 26 Ryabov Ryabov NNP cord-284810-fs5rx07q 278 27 for for IN cord-284810-fs5rx07q 278 28 helpful helpful JJ cord-284810-fs5rx07q 278 29 comments comment NNS cord-284810-fs5rx07q 278 30 regarding regard VBG cord-284810-fs5rx07q 278 31 the the DT cord-284810-fs5rx07q 278 32 article article NN cord-284810-fs5rx07q 278 33 . . . cord-284810-fs5rx07q 279 1 Assume assume VB cord-284810-fs5rx07q 279 2 a a DT cord-284810-fs5rx07q 279 3 truncated truncated JJ cord-284810-fs5rx07q 279 4 power power NN cord-284810-fs5rx07q 279 5 - - HYPH cord-284810-fs5rx07q 279 6 law law NN cord-284810-fs5rx07q 279 7 ( ( -LRB- cord-284810-fs5rx07q 279 8 or or CC cord-284810-fs5rx07q 279 9 Pareto Pareto NNP cord-284810-fs5rx07q 279 10 ) ) -RRB- cord-284810-fs5rx07q 279 11 distribution distribution NN cord-284810-fs5rx07q 279 12 of of IN cord-284810-fs5rx07q 279 13 the the DT cord-284810-fs5rx07q 279 14 random random JJ cord-284810-fs5rx07q 279 15 variable variable NN cord-284810-fs5rx07q 279 16 n n CC cord-284810-fs5rx07q 279 17 with with IN cord-284810-fs5rx07q 279 18 upper upper JJ cord-284810-fs5rx07q 279 19 bound bind VBN cord-284810-fs5rx07q 279 20 n n CC cord-284810-fs5rx07q 279 21 max max NN cord-284810-fs5rx07q 279 22 . . . cord-284810-fs5rx07q 280 1 Normalization normalization NN cord-284810-fs5rx07q 280 2 P(n)dn p(n)dn NN cord-284810-fs5rx07q 280 3 = = SYM cord-284810-fs5rx07q 280 4 1 1 CD cord-284810-fs5rx07q 280 5 yields yield NNS cord-284810-fs5rx07q 280 6 . . . cord-284810-fs5rx07q 281 1 The the DT cord-284810-fs5rx07q 281 2 cumulative cumulative JJ cord-284810-fs5rx07q 281 3 distribution distribution NN cord-284810-fs5rx07q 281 4 function function NN cord-284810-fs5rx07q 281 5 reads read VBZ cord-284810-fs5rx07q 281 6 In in IN cord-284810-fs5rx07q 281 7 the the DT cord-284810-fs5rx07q 281 8 limit limit NN cord-284810-fs5rx07q 282 1 n n NNP cord-284810-fs5rx07q 282 2 max max NNP cord-284810-fs5rx07q 282 3 → → NNP cord-284810-fs5rx07q 282 4 ∞ ∞ NNP cord-284810-fs5rx07q 282 5 ( ( -LRB- cord-284810-fs5rx07q 282 6 a a DT cord-284810-fs5rx07q 282 7 power power NN cord-284810-fs5rx07q 282 8 - - HYPH cord-284810-fs5rx07q 282 9 law law NN cord-284810-fs5rx07q 282 10 distribution distribution NN cord-284810-fs5rx07q 282 11 without without IN cord-284810-fs5rx07q 282 12 upper upper JJ cord-284810-fs5rx07q 282 13 bound bind VBN cord-284810-fs5rx07q 282 14 ) ) -RRB- cord-284810-fs5rx07q 282 15 , , , cord-284810-fs5rx07q 282 16 the the DT cord-284810-fs5rx07q 282 17 cumulative cumulative JJ cord-284810-fs5rx07q 282 18 distribution distribution NN cord-284810-fs5rx07q 282 19 function function NN cord-284810-fs5rx07q 282 20 also also RB cord-284810-fs5rx07q 282 21 follows follow VBZ cord-284810-fs5rx07q 282 22 a a DT cord-284810-fs5rx07q 282 23 power power NN cord-284810-fs5rx07q 282 24 - - HYPH cord-284810-fs5rx07q 282 25 law law NN cord-284810-fs5rx07q 282 26 C(n C(n NNP cord-284810-fs5rx07q 282 27 ) ) -RRB- cord-284810-fs5rx07q 282 28 ∼ ∼ CC cord-284810-fs5rx07q 282 29 n n NN cord-284810-fs5rx07q 282 30 1−µ 1−µ CD cord-284810-fs5rx07q 282 31 . . . cord-284810-fs5rx07q 283 1 A a DT cord-284810-fs5rx07q 283 2 synthetic synthetic JJ cord-284810-fs5rx07q 283 3 sample sample NN cord-284810-fs5rx07q 283 4 of of IN cord-284810-fs5rx07q 283 5 the the DT cord-284810-fs5rx07q 283 6 distribution distribution NN cord-284810-fs5rx07q 283 7 ( ( -LRB- cord-284810-fs5rx07q 283 8 A1 a1 NN cord-284810-fs5rx07q 283 9 ) ) -RRB- cord-284810-fs5rx07q 283 10 can can MD cord-284810-fs5rx07q 283 11 be be VB cord-284810-fs5rx07q 283 12 obtained obtain VBN cord-284810-fs5rx07q 283 13 by by IN cord-284810-fs5rx07q 283 14 the the DT cord-284810-fs5rx07q 283 15 formula formula NN cord-284810-fs5rx07q 283 16 where where WRB cord-284810-fs5rx07q 283 17 u u NNP cord-284810-fs5rx07q 283 18 i i PRP cord-284810-fs5rx07q 283 19 are be VBP cord-284810-fs5rx07q 283 20 random random JJ cord-284810-fs5rx07q 283 21 numbers number NNS cord-284810-fs5rx07q 283 22 taken take VBN cord-284810-fs5rx07q 283 23 from from IN cord-284810-fs5rx07q 283 24 a a DT cord-284810-fs5rx07q 283 25 uniform uniform JJ cord-284810-fs5rx07q 283 26 distribution distribution NN cord-284810-fs5rx07q 283 27 in in IN cord-284810-fs5rx07q 283 28 the the DT cord-284810-fs5rx07q 283 29 range range NN cord-284810-fs5rx07q 283 30 [ [ -LRB- cord-284810-fs5rx07q 283 31 0 0 CD cord-284810-fs5rx07q 283 32 , , , cord-284810-fs5rx07q 283 33 1 1 CD cord-284810-fs5rx07q 283 34 ] ] -RRB- cord-284810-fs5rx07q 283 35 . . . cord-284810-fs5rx07q 284 1 The the DT cord-284810-fs5rx07q 284 2 inverse inverse JJ cord-284810-fs5rx07q 284 3 problem problem NN cord-284810-fs5rx07q 284 4 is be VBZ cord-284810-fs5rx07q 284 5 to to TO cord-284810-fs5rx07q 284 6 estimate estimate VB cord-284810-fs5rx07q 284 7 the the DT cord-284810-fs5rx07q 284 8 parameters parameter NNS cord-284810-fs5rx07q 284 9 of of IN cord-284810-fs5rx07q 284 10 the the DT cord-284810-fs5rx07q 284 11 distribution distribution NN cord-284810-fs5rx07q 284 12 given give VBN cord-284810-fs5rx07q 284 13 a a DT cord-284810-fs5rx07q 284 14 random random JJ cord-284810-fs5rx07q 284 15 sample sample NN cord-284810-fs5rx07q 284 16 n n NN cord-284810-fs5rx07q 284 17 ( ( -LRB- cord-284810-fs5rx07q 284 18 1 1 CD cord-284810-fs5rx07q 284 19 , , , cord-284810-fs5rx07q 284 20 n n NN cord-284810-fs5rx07q 284 21 2 2 CD cord-284810-fs5rx07q 284 22 , , , cord-284810-fs5rx07q 284 23 . . . cord-284810-fs5rx07q 284 24 . . . cord-284810-fs5rx07q 284 25 . . . cord-284810-fs5rx07q 285 1 , , , cord-284810-fs5rx07q 285 2 n n NNP cord-284810-fs5rx07q 285 3 N N NNP cord-284810-fs5rx07q 285 4 ) ) -RRB- cord-284810-fs5rx07q 285 5 of of IN cord-284810-fs5rx07q 285 6 N n CD cord-284810-fs5rx07q 285 7 data data NN cord-284810-fs5rx07q 285 8 points point NNS cord-284810-fs5rx07q 285 9 . . . cord-284810-fs5rx07q 286 1 The the DT cord-284810-fs5rx07q 286 2 log log NN cord-284810-fs5rx07q 286 3 - - HYPH cord-284810-fs5rx07q 286 4 likelihood likelihood NN cord-284810-fs5rx07q 286 5 for for IN cord-284810-fs5rx07q 286 6 the the DT cord-284810-fs5rx07q 286 7 distribution distribution NN cord-284810-fs5rx07q 286 8 Eq eq NN cord-284810-fs5rx07q 286 9 . . . cord-284810-fs5rx07q 287 1 ( ( -LRB- cord-284810-fs5rx07q 287 2 A1 a1 NN cord-284810-fs5rx07q 287 3 ) ) -RRB- cord-284810-fs5rx07q 287 4 can can MD cord-284810-fs5rx07q 287 5 be be VB cord-284810-fs5rx07q 287 6 defined define VBN cord-284810-fs5rx07q 287 7 as as IN cord-284810-fs5rx07q 287 8 1 1 CD cord-284810-fs5rx07q 287 9 , , , cord-284810-fs5rx07q 287 10 13 13 CD cord-284810-fs5rx07q 287 11 , , , cord-284810-fs5rx07q 287 12 45 45 CD cord-284810-fs5rx07q 287 13 _SP cord-284810-fs5rx07q 288 1 Then then RB cord-284810-fs5rx07q 288 2 , , , cord-284810-fs5rx07q 288 3 an an DT cord-284810-fs5rx07q 288 4 estimator estimator NN cord-284810-fs5rx07q 288 5 for for IN cord-284810-fs5rx07q 288 6 the the DT cord-284810-fs5rx07q 288 7 cut cut VB cord-284810-fs5rx07q 288 8 - - HYPH cord-284810-fs5rx07q 288 9 off off RP cord-284810-fs5rx07q 288 10 value value NN cord-284810-fs5rx07q 288 11 is be VBZ cord-284810-fs5rx07q 288 12 obtained obtain VBN cord-284810-fs5rx07q 288 13 byn byn NNP cord-284810-fs5rx07q 288 14 max max NNP cord-284810-fs5rx07q 288 15 = = SYM cord-284810-fs5rx07q 288 16 max(n max(n NN cord-284810-fs5rx07q 288 17 i i NN cord-284810-fs5rx07q 288 18 ) ) -RRB- cord-284810-fs5rx07q 288 19 1 1 CD cord-284810-fs5rx07q 288 20 and and CC cord-284810-fs5rx07q 288 21 an an DT cord-284810-fs5rx07q 288 22 estimatorμ estimatorμ NN cord-284810-fs5rx07q 288 23 for for IN cord-284810-fs5rx07q 288 24 the the DT cord-284810-fs5rx07q 288 25 critical critical JJ cord-284810-fs5rx07q 288 26 exponent exponent NN cord-284810-fs5rx07q 288 27 is be VBZ cord-284810-fs5rx07q 288 28 obtained obtain VBN cord-284810-fs5rx07q 288 29 by by IN cord-284810-fs5rx07q 288 30 maximizing maximize VBG cord-284810-fs5rx07q 288 31 L(µ L(µ NNP cord-284810-fs5rx07q 288 32 ) ) -RRB- cord-284810-fs5rx07q 288 33 , , , cord-284810-fs5rx07q 288 34 yielding yield VBG cord-284810-fs5rx07q 288 35 a a DT cord-284810-fs5rx07q 288 36 standard standard JJ cord-284810-fs5rx07q 288 37 error error NN cord-284810-fs5rx07q 288 38 13 13 CD cord-284810-fs5rx07q 289 1 In in IN cord-284810-fs5rx07q 289 2 these these DT cord-284810-fs5rx07q 289 3 expressions expression NNS cord-284810-fs5rx07q 289 4 , , , cord-284810-fs5rx07q 289 5 the the DT cord-284810-fs5rx07q 289 6 " " `` cord-284810-fs5rx07q 289 7 hat hat NN cord-284810-fs5rx07q 289 8 " " '' cord-284810-fs5rx07q 289 9 means mean VBZ cord-284810-fs5rx07q 289 10 that that IN cord-284810-fs5rx07q 289 11 we -PRON- PRP cord-284810-fs5rx07q 289 12 refer refer VBP cord-284810-fs5rx07q 289 13 to to IN cord-284810-fs5rx07q 289 14 an an DT cord-284810-fs5rx07q 289 15 estimated estimate VBN cord-284810-fs5rx07q 289 16 value value NN cord-284810-fs5rx07q 289 17 . . . cord-284810-fs5rx07q 290 1 The the DT cord-284810-fs5rx07q 290 2 maximization maximization NN cord-284810-fs5rx07q 290 3 of of IN cord-284810-fs5rx07q 290 4 L(µ L(µ NNP cord-284810-fs5rx07q 290 5 ) ) -RRB- cord-284810-fs5rx07q 290 6 must must MD cord-284810-fs5rx07q 290 7 be be VB cord-284810-fs5rx07q 290 8 computed compute VBN cord-284810-fs5rx07q 290 9 numerically numerically RB cord-284810-fs5rx07q 290 10 ( ( -LRB- cord-284810-fs5rx07q 290 11 here here RB cord-284810-fs5rx07q 290 12 , , , cord-284810-fs5rx07q 290 13 we -PRON- PRP cord-284810-fs5rx07q 290 14 use use VBP cord-284810-fs5rx07q 290 15 Brent Brent NNP cord-284810-fs5rx07q 290 16 's 's POS cord-284810-fs5rx07q 290 17 method method NN cord-284810-fs5rx07q 290 18 from from IN cord-284810-fs5rx07q 290 19 the the DT cord-284810-fs5rx07q 290 20 Julia Julia NNP cord-284810-fs5rx07q 290 21 package package NN cord-284810-fs5rx07q 290 22 Optim.jl Optim.jl NNP cord-284810-fs5rx07q 290 23 28 28 CD cord-284810-fs5rx07q 290 24 ) ) -RRB- cord-284810-fs5rx07q 290 25 . . . cord-284810-fs5rx07q 291 1 In in IN cord-284810-fs5rx07q 291 2 the the DT cord-284810-fs5rx07q 291 3 limit limit NN cord-284810-fs5rx07q 291 4 of of IN cord-284810-fs5rx07q 291 5 an an DT cord-284810-fs5rx07q 291 6 unbounded unbounded JJ cord-284810-fs5rx07q 291 7 power power NN cord-284810-fs5rx07q 291 8 - - HYPH cord-284810-fs5rx07q 291 9 law law NN cord-284810-fs5rx07q 291 10 distribution distribution NN cord-284810-fs5rx07q 292 1 n n NNP cord-284810-fs5rx07q 292 2 max max NNP cord-284810-fs5rx07q 292 3 → → NNP cord-284810-fs5rx07q 292 4 ∞ ∞ NNP cord-284810-fs5rx07q 292 5 , , , cord-284810-fs5rx07q 292 6 the the DT cord-284810-fs5rx07q 292 7 maximization maximization NN cord-284810-fs5rx07q 292 8 can can MD cord-284810-fs5rx07q 292 9 be be VB cord-284810-fs5rx07q 292 10 calculated calculate VBN cord-284810-fs5rx07q 292 11 analytically analytically RB cord-284810-fs5rx07q 292 12 , , , cord-284810-fs5rx07q 292 13 yielding yield VBG cord-284810-fs5rx07q 292 14 29μ 29μ NNS cord-284810-fs5rx07q 292 15 ( ( -LRB- cord-284810-fs5rx07q 292 16 A6 A6 NNP cord-284810-fs5rx07q 292 17 ) ) -RRB- cord-284810-fs5rx07q 293 1 To to TO cord-284810-fs5rx07q 293 2 estimate estimate VB cord-284810-fs5rx07q 293 3 the the DT cord-284810-fs5rx07q 293 4 distribution distribution NN cord-284810-fs5rx07q 293 5 P(n p(n NN cord-284810-fs5rx07q 293 6 ) ) -RRB- cord-284810-fs5rx07q 293 7 of of IN cord-284810-fs5rx07q 293 8 case case NN cord-284810-fs5rx07q 293 9 numbers number NNS cord-284810-fs5rx07q 293 10 that that WDT cord-284810-fs5rx07q 293 11 vary vary VBP cord-284810-fs5rx07q 293 12 over over IN cord-284810-fs5rx07q 293 13 many many JJ cord-284810-fs5rx07q 293 14 orders order NNS cord-284810-fs5rx07q 293 15 of of IN cord-284810-fs5rx07q 293 16 magnitude magnitude NN cord-284810-fs5rx07q 293 17 , , , cord-284810-fs5rx07q 293 18 we -PRON- PRP cord-284810-fs5rx07q 293 19 used use VBD cord-284810-fs5rx07q 293 20 a a DT cord-284810-fs5rx07q 293 21 histogram histogram NN cord-284810-fs5rx07q 293 22 with with IN cord-284810-fs5rx07q 293 23 logarithmic logarithmic JJ cord-284810-fs5rx07q 293 24 binning binning NN cord-284810-fs5rx07q 293 25 . . . cord-284810-fs5rx07q 294 1 That that RB cord-284810-fs5rx07q 294 2 is is RB cord-284810-fs5rx07q 294 3 , , , cord-284810-fs5rx07q 294 4 we -PRON- PRP cord-284810-fs5rx07q 294 5 placed place VBD cord-284810-fs5rx07q 294 6 a a DT cord-284810-fs5rx07q 294 7 discrete discrete JJ cord-284810-fs5rx07q 294 8 number number NN cord-284810-fs5rx07q 294 9 of of IN cord-284810-fs5rx07q 294 10 bins bin NNS cord-284810-fs5rx07q 294 11 , , , cord-284810-fs5rx07q 294 12 k k NNP cord-284810-fs5rx07q 294 13 , , , cord-284810-fs5rx07q 294 14 at at IN cord-284810-fs5rx07q 294 15 positions position NNS cord-284810-fs5rx07q 294 16 of of IN cord-284810-fs5rx07q 294 17 integer integer NN cord-284810-fs5rx07q 294 18 powers power NNS cord-284810-fs5rx07q 294 19 of of IN cord-284810-fs5rx07q 294 20 two two CD cord-284810-fs5rx07q 294 21 n n NN cord-284810-fs5rx07q 294 22 k k NN cord-284810-fs5rx07q 294 23 = = SYM cord-284810-fs5rx07q 294 24 2 2 CD cord-284810-fs5rx07q 294 25 k k NNP cord-284810-fs5rx07q 294 26 ( ( -LRB- cord-284810-fs5rx07q 294 27 i.e. i.e. FW cord-284810-fs5rx07q 294 28 , , , cord-284810-fs5rx07q 294 29 1 1 CD cord-284810-fs5rx07q 294 30 , , , cord-284810-fs5rx07q 294 31 2 2 CD cord-284810-fs5rx07q 294 32 , , , cord-284810-fs5rx07q 294 33 4 4 CD cord-284810-fs5rx07q 294 34 , , , cord-284810-fs5rx07q 294 35 8 8 CD cord-284810-fs5rx07q 294 36 , , , cord-284810-fs5rx07q 294 37 16 16 CD cord-284810-fs5rx07q 294 38 , , , cord-284810-fs5rx07q 294 39 etc etc FW cord-284810-fs5rx07q 294 40 . . . cord-284810-fs5rx07q 294 41 ) ) -RRB- cord-284810-fs5rx07q 295 1 Chaos Chaos NNP cord-284810-fs5rx07q 295 2 ARTICLE article NN cord-284810-fs5rx07q 295 3 scitation.org/journal/cha scitation.org/journal/cha , cord-284810-fs5rx07q 295 4 and and CC cord-284810-fs5rx07q 295 5 for for IN cord-284810-fs5rx07q 295 6 each each DT cord-284810-fs5rx07q 295 7 bin bin NN cord-284810-fs5rx07q 295 8 counted count VBD cord-284810-fs5rx07q 295 9 the the DT cord-284810-fs5rx07q 295 10 number number NN cord-284810-fs5rx07q 295 11 H h NN cord-284810-fs5rx07q 295 12 k k NN cord-284810-fs5rx07q 295 13 of of IN cord-284810-fs5rx07q 295 14 countries country NNS cord-284810-fs5rx07q 295 15 ( ( -LRB- cord-284810-fs5rx07q 295 16 or or CC cord-284810-fs5rx07q 295 17 US US NNP cord-284810-fs5rx07q 295 18 counties county NNS cord-284810-fs5rx07q 295 19 ) ) -RRB- cord-284810-fs5rx07q 296 1 that that IN cord-284810-fs5rx07q 296 2 under under IN cord-284810-fs5rx07q 296 3 the the DT cord-284810-fs5rx07q 296 4 day day NN cord-284810-fs5rx07q 296 5 of of IN cord-284810-fs5rx07q 296 6 investigation investigation NN cord-284810-fs5rx07q 296 7 reported report VBD cord-284810-fs5rx07q 296 8 a a DT cord-284810-fs5rx07q 296 9 number number NN cord-284810-fs5rx07q 296 10 n n NN cord-284810-fs5rx07q 296 11 of of IN cord-284810-fs5rx07q 296 12 cases case NNS cord-284810-fs5rx07q 296 13 that that WDT cord-284810-fs5rx07q 296 14 was be VBD cord-284810-fs5rx07q 296 15 falling fall VBG cord-284810-fs5rx07q 296 16 into into IN cord-284810-fs5rx07q 296 17 this this DT cord-284810-fs5rx07q 296 18 bin bin NN cord-284810-fs5rx07q 296 19 ( ( -LRB- cord-284810-fs5rx07q 296 20 n n NNP cord-284810-fs5rx07q 296 21 k k NNP cord-284810-fs5rx07q 296 22 ≤ ≤ NNP cord-284810-fs5rx07q 296 23 n n NNP cord-284810-fs5rx07q 296 24 < < XX cord-284810-fs5rx07q 296 25 n n XX cord-284810-fs5rx07q 296 26 k+1 k+1 NNP cord-284810-fs5rx07q 296 27 ) ) -RRB- cord-284810-fs5rx07q 296 28 . . . cord-284810-fs5rx07q 297 1 To to TO cord-284810-fs5rx07q 297 2 obtain obtain VB cord-284810-fs5rx07q 297 3 the the DT cord-284810-fs5rx07q 297 4 probability probability NN cord-284810-fs5rx07q 297 5 distribution distribution NN cord-284810-fs5rx07q 297 6 , , , cord-284810-fs5rx07q 297 7 the the DT cord-284810-fs5rx07q 297 8 resulting result VBG cord-284810-fs5rx07q 297 9 histogram histogram NN cord-284810-fs5rx07q 297 10 counts count NNS cord-284810-fs5rx07q 297 11 were be VBD cord-284810-fs5rx07q 297 12 divided divide VBN cord-284810-fs5rx07q 297 13 by by IN cord-284810-fs5rx07q 297 14 the the DT cord-284810-fs5rx07q 297 15 varying vary VBG cord-284810-fs5rx07q 297 16 bin bin NNP cord-284810-fs5rx07q 297 17 sizes size NNS cord-284810-fs5rx07q 297 18 P(n P(n NNP cord-284810-fs5rx07q 297 19 k k NN cord-284810-fs5rx07q 297 20 ) ) -RRB- cord-284810-fs5rx07q 298 1 = = NFP cord-284810-fs5rx07q 299 1 cH cH NNP cord-284810-fs5rx07q 300 1 k k NNP cord-284810-fs5rx07q 300 2 /(n /(n NNP cord-284810-fs5rx07q 301 1 k+1 k+1 NNP cord-284810-fs5rx07q 301 2 − − NN cord-284810-fs5rx07q 301 3 n n CC cord-284810-fs5rx07q 301 4 k k NN cord-284810-fs5rx07q 301 5 ) ) -RRB- cord-284810-fs5rx07q 302 1 and and CC cord-284810-fs5rx07q 302 2 the the DT cord-284810-fs5rx07q 302 3 normalization normalization NN cord-284810-fs5rx07q 302 4 constant constant JJ cord-284810-fs5rx07q 302 5 c c NN cord-284810-fs5rx07q 302 6 fixed fix VBN cord-284810-fs5rx07q 303 1 so so IN cord-284810-fs5rx07q 303 2 that that IN cord-284810-fs5rx07q 303 3 k k XX cord-284810-fs5rx07q 303 4 P(n p(n NN cord-284810-fs5rx07q 303 5 k k NNP cord-284810-fs5rx07q 303 6 ) ) -RRB- cord-284810-fs5rx07q 303 7 = = SYM cord-284810-fs5rx07q 303 8 1 1 CD cord-284810-fs5rx07q 303 9 . . . cord-284810-fs5rx07q 304 1 For for IN cord-284810-fs5rx07q 304 2 visualization visualization NN cord-284810-fs5rx07q 304 3 , , , cord-284810-fs5rx07q 304 4 we -PRON- PRP cord-284810-fs5rx07q 304 5 plotted plot VBD cord-284810-fs5rx07q 304 6 the the DT cord-284810-fs5rx07q 304 7 distribution distribution NN cord-284810-fs5rx07q 304 8 on on IN cord-284810-fs5rx07q 304 9 double double JJ cord-284810-fs5rx07q 304 10 - - HYPH cord-284810-fs5rx07q 304 11 logarithmic logarithmic NN cord-284810-fs5rx07q 304 12 axes axis NNS cord-284810-fs5rx07q 304 13 , , , cord-284810-fs5rx07q 304 14 excluding exclude VBG cord-284810-fs5rx07q 304 15 bins bin NNS cord-284810-fs5rx07q 304 16 without without IN cord-284810-fs5rx07q 304 17 entries entry NNS cord-284810-fs5rx07q 304 18 . . . cord-284810-fs5rx07q 305 1 To to TO cord-284810-fs5rx07q 305 2 confirm confirm VB cord-284810-fs5rx07q 305 3 the the DT cord-284810-fs5rx07q 305 4 robustness robustness NN cord-284810-fs5rx07q 305 5 of of IN cord-284810-fs5rx07q 305 6 the the DT cord-284810-fs5rx07q 305 7 histogram histogram NN cord-284810-fs5rx07q 305 8 estimation estimation NN cord-284810-fs5rx07q 305 9 , , , cord-284810-fs5rx07q 305 10 we -PRON- PRP cord-284810-fs5rx07q 305 11 also also RB cord-284810-fs5rx07q 305 12 used use VBD cord-284810-fs5rx07q 305 13 an an DT cord-284810-fs5rx07q 305 14 alternative alternative JJ cord-284810-fs5rx07q 305 15 algorithm algorithm NN cord-284810-fs5rx07q 305 16 , , , cord-284810-fs5rx07q 305 17 where where WRB cord-284810-fs5rx07q 305 18 we -PRON- PRP cord-284810-fs5rx07q 305 19 first first RB cord-284810-fs5rx07q 305 20 computed compute VBD cord-284810-fs5rx07q 305 21 the the DT cord-284810-fs5rx07q 305 22 histogram histogram NN cord-284810-fs5rx07q 305 23 of of IN cord-284810-fs5rx07q 305 24 log log NN cord-284810-fs5rx07q 305 25 - - HYPH cord-284810-fs5rx07q 305 26 transformed transform VBN cord-284810-fs5rx07q 305 27 case case NN cord-284810-fs5rx07q 305 28 numbers number NNS cord-284810-fs5rx07q 305 29 ν ν NNP cord-284810-fs5rx07q 305 30 = = SYM cord-284810-fs5rx07q 305 31 log(n log(n FW cord-284810-fs5rx07q 305 32 ) ) -RRB- cord-284810-fs5rx07q 305 33 using use VBG cord-284810-fs5rx07q 305 34 equally equally RB cord-284810-fs5rx07q 305 35 spaced space VBN cord-284810-fs5rx07q 305 36 bins bin NNS cord-284810-fs5rx07q 305 37 , , , cord-284810-fs5rx07q 305 38 which which WDT cord-284810-fs5rx07q 305 39 , , , cord-284810-fs5rx07q 305 40 after after IN cord-284810-fs5rx07q 305 41 normalization normalization NN cord-284810-fs5rx07q 305 42 , , , cord-284810-fs5rx07q 305 43 yielded yield VBD cord-284810-fs5rx07q 305 44 the the DT cord-284810-fs5rx07q 305 45 distributioñ distributioñ NNP cord-284810-fs5rx07q 305 46 P(ν P(ν NNP cord-284810-fs5rx07q 305 47 ) ) -RRB- cord-284810-fs5rx07q 305 48 . . . cord-284810-fs5rx07q 306 1 Next next RB cord-284810-fs5rx07q 306 2 , , , cord-284810-fs5rx07q 306 3 we -PRON- PRP cord-284810-fs5rx07q 306 4 used use VBD cord-284810-fs5rx07q 306 5 the the DT cord-284810-fs5rx07q 306 6 back back RB cord-284810-fs5rx07q 306 7 - - HYPH cord-284810-fs5rx07q 306 8 transform transform NN cord-284810-fs5rx07q 306 9 P(n p(n NN cord-284810-fs5rx07q 306 10 ) ) -RRB- cord-284810-fs5rx07q 306 11 = = NFP cord-284810-fs5rx07q 307 1 P(ν)/n P(ν)/n NNP cord-284810-fs5rx07q 308 1 to to TO cord-284810-fs5rx07q 308 2 obtain obtain VB cord-284810-fs5rx07q 308 3 the the DT cord-284810-fs5rx07q 308 4 probability probability NN cord-284810-fs5rx07q 308 5 distribution distribution NN cord-284810-fs5rx07q 308 6 P(n P(n NNP cord-284810-fs5rx07q 308 7 ) ) -RRB- cord-284810-fs5rx07q 308 8 of of IN cord-284810-fs5rx07q 308 9 non non JJ cord-284810-fs5rx07q 308 10 - - JJ cord-284810-fs5rx07q 308 11 logarithmic logarithmic JJ cord-284810-fs5rx07q 308 12 case case NN cord-284810-fs5rx07q 308 13 numbers number NNS cord-284810-fs5rx07q 308 14 . . . cord-284810-fs5rx07q 309 1 This this DT cord-284810-fs5rx07q 309 2 procedure procedure NN cord-284810-fs5rx07q 309 3 also also RB cord-284810-fs5rx07q 309 4 yields yield VBZ cord-284810-fs5rx07q 309 5 a a DT cord-284810-fs5rx07q 309 6 distribution distribution NN cord-284810-fs5rx07q 309 7 with with IN cord-284810-fs5rx07q 309 8 bins bin NNS cord-284810-fs5rx07q 309 9 that that WDT cord-284810-fs5rx07q 309 10 are be VBP cord-284810-fs5rx07q 309 11 equally equally RB cord-284810-fs5rx07q 309 12 spaced spaced JJ cord-284810-fs5rx07q 309 13 on on IN cord-284810-fs5rx07q 309 14 a a DT cord-284810-fs5rx07q 309 15 logarithmic logarithmic JJ cord-284810-fs5rx07q 309 16 scale scale NN cord-284810-fs5rx07q 309 17 and and CC cord-284810-fs5rx07q 309 18 the the DT cord-284810-fs5rx07q 309 19 resulting result VBG cord-284810-fs5rx07q 309 20 distributions distribution NNS cord-284810-fs5rx07q 309 21 , , , cord-284810-fs5rx07q 309 22 shown show VBN cord-284810-fs5rx07q 309 23 in in IN cord-284810-fs5rx07q 309 24 Fig Fig NNP cord-284810-fs5rx07q 309 25 . . NNP cord-284810-fs5rx07q 309 26 7 7 CD cord-284810-fs5rx07q 309 27 in in IN cord-284810-fs5rx07q 309 28 Appendix Appendix NNP cord-284810-fs5rx07q 309 29 C C NNP cord-284810-fs5rx07q 309 30 , , , cord-284810-fs5rx07q 309 31 are be VBP cord-284810-fs5rx07q 309 32 very very RB cord-284810-fs5rx07q 309 33 similar similar JJ cord-284810-fs5rx07q 309 34 to to IN cord-284810-fs5rx07q 309 35 that that DT cord-284810-fs5rx07q 309 36 from from IN cord-284810-fs5rx07q 309 37 the the DT cord-284810-fs5rx07q 309 38 logarithmic logarithmic JJ cord-284810-fs5rx07q 309 39 binning binning NN cord-284810-fs5rx07q 309 40 method method NN cord-284810-fs5rx07q 309 41 described describe VBN cord-284810-fs5rx07q 309 42 above above RB cord-284810-fs5rx07q 309 43 . . . cord-284810-fs5rx07q 310 1 We -PRON- PRP cord-284810-fs5rx07q 310 2 have have VBP cord-284810-fs5rx07q 310 3 checked check VBN cord-284810-fs5rx07q 310 4 that that IN cord-284810-fs5rx07q 310 5 the the DT cord-284810-fs5rx07q 310 6 resulting result VBG cord-284810-fs5rx07q 310 7 distribution distribution NN cord-284810-fs5rx07q 310 8 is be VBZ cord-284810-fs5rx07q 310 9 largely largely RB cord-284810-fs5rx07q 310 10 independent independent JJ cord-284810-fs5rx07q 310 11 to to IN cord-284810-fs5rx07q 310 12 the the DT cord-284810-fs5rx07q 310 13 choice choice NN cord-284810-fs5rx07q 310 14 and and CC cord-284810-fs5rx07q 310 15 number number NN cord-284810-fs5rx07q 310 16 of of IN cord-284810-fs5rx07q 310 17 used use VBN cord-284810-fs5rx07q 310 18 histogram histogram NN cord-284810-fs5rx07q 310 19 bins bin NNS cord-284810-fs5rx07q 310 20 and and CC cord-284810-fs5rx07q 310 21 other other JJ cord-284810-fs5rx07q 310 22 numerical numerical JJ cord-284810-fs5rx07q 310 23 parameters parameter NNS cord-284810-fs5rx07q 310 24 . . . cord-284810-fs5rx07q 311 1 We -PRON- PRP cord-284810-fs5rx07q 311 2 also also RB cord-284810-fs5rx07q 311 3 computed compute VBD cord-284810-fs5rx07q 311 4 the the DT cord-284810-fs5rx07q 311 5 cumulative cumulative JJ cord-284810-fs5rx07q 311 6 fraction fraction NN cord-284810-fs5rx07q 311 7 C(n C(n NNP cord-284810-fs5rx07q 311 8 ) ) -RRB- cord-284810-fs5rx07q 311 9 = = NFP cord-284810-fs5rx07q 312 1 N n NN cord-284810-fs5rx07q 312 2 m m NN cord-284810-fs5rx07q 312 3 = = SYM cord-284810-fs5rx07q 312 4 n+1 n+1 NN cord-284810-fs5rx07q 312 5 P(m P(m NNP cord-284810-fs5rx07q 312 6 ) ) -RRB- cord-284810-fs5rx07q 312 7 of of IN cord-284810-fs5rx07q 312 8 countries country NNS cord-284810-fs5rx07q 312 9 with with IN cord-284810-fs5rx07q 312 10 case case NN cord-284810-fs5rx07q 313 1 number number NN cord-284810-fs5rx07q 313 2 m m NNP cord-284810-fs5rx07q 314 1 > > XX cord-284810-fs5rx07q 315 1 n. n. NNP cord-284810-fs5rx07q 316 1 This this DT cord-284810-fs5rx07q 316 2 was be VBD cord-284810-fs5rx07q 316 3 obtained obtain VBN cord-284810-fs5rx07q 316 4 by by IN cord-284810-fs5rx07q 316 5 taking take VBG cord-284810-fs5rx07q 316 6 a a DT cord-284810-fs5rx07q 316 7 rank rank NN cord-284810-fs5rx07q 316 8 - - HYPH cord-284810-fs5rx07q 316 9 plot plot NN cord-284810-fs5rx07q 316 10 of of IN cord-284810-fs5rx07q 316 11 case case NN cord-284810-fs5rx07q 316 12 numbers number NNS cord-284810-fs5rx07q 316 13 and and CC cord-284810-fs5rx07q 316 14 inverting invert VBG cord-284810-fs5rx07q 316 15 axes axis NNS cord-284810-fs5rx07q 316 16 , , , cord-284810-fs5rx07q 316 17 i.e. i.e. FW cord-284810-fs5rx07q 316 18 , , , cord-284810-fs5rx07q 316 19 sorting sort VBG cord-284810-fs5rx07q 316 20 the the DT cord-284810-fs5rx07q 316 21 array array NN cord-284810-fs5rx07q 316 22 of of IN cord-284810-fs5rx07q 316 23 case case NN cord-284810-fs5rx07q 316 24 numbers number NNS cord-284810-fs5rx07q 316 25 in in IN cord-284810-fs5rx07q 316 26 descending descend VBG cord-284810-fs5rx07q 316 27 order order NN cord-284810-fs5rx07q 316 28 and and CC cord-284810-fs5rx07q 316 29 plotting plot VBG cord-284810-fs5rx07q 316 30 for for IN cord-284810-fs5rx07q 316 31 each each DT cord-284810-fs5rx07q 316 32 country country NN cord-284810-fs5rx07q 316 33 the the DT cord-284810-fs5rx07q 316 34 rank rank NN cord-284810-fs5rx07q 316 35 as as IN cord-284810-fs5rx07q 316 36 a a DT cord-284810-fs5rx07q 316 37 function function NN cord-284810-fs5rx07q 316 38 of of IN cord-284810-fs5rx07q 316 39 the the DT cord-284810-fs5rx07q 316 40 sorted sort VBN cord-284810-fs5rx07q 316 41 case case NN cord-284810-fs5rx07q 316 42 number number NN cord-284810-fs5rx07q 316 43 on on IN cord-284810-fs5rx07q 316 44 double double JJ cord-284810-fs5rx07q 316 45 - - HYPH cord-284810-fs5rx07q 316 46 logarithmic logarithmic JJ cord-284810-fs5rx07q 316 47 axes axis NNS cord-284810-fs5rx07q 316 48 . . . cord-284810-fs5rx07q 317 1 29 29 CD cord-284810-fs5rx07q 318 1 To to TO cord-284810-fs5rx07q 318 2 describe describe VB cord-284810-fs5rx07q 318 3 the the DT cord-284810-fs5rx07q 318 4 spatiotemporal spatiotemporal JJ cord-284810-fs5rx07q 318 5 evolution evolution NN cord-284810-fs5rx07q 318 6 of of IN cord-284810-fs5rx07q 318 7 epidemic epidemic NN cord-284810-fs5rx07q 318 8 prevalence prevalence NN cord-284810-fs5rx07q 318 9 during during IN cord-284810-fs5rx07q 318 10 the the DT cord-284810-fs5rx07q 318 11 course course NN cord-284810-fs5rx07q 318 12 of of IN cord-284810-fs5rx07q 318 13 a a DT cord-284810-fs5rx07q 318 14 pandemic pandemic NN cord-284810-fs5rx07q 318 15 , , , cord-284810-fs5rx07q 318 16 we -PRON- PRP cord-284810-fs5rx07q 318 17 developed develop VBD cord-284810-fs5rx07q 318 18 a a DT cord-284810-fs5rx07q 318 19 conceptual conceptual JJ cord-284810-fs5rx07q 318 20 dual dual JJ cord-284810-fs5rx07q 318 21 - - HYPH cord-284810-fs5rx07q 318 22 scale scale NN cord-284810-fs5rx07q 318 23 meta meta NN cord-284810-fs5rx07q 318 24 - - HYPH cord-284810-fs5rx07q 318 25 population population NN cord-284810-fs5rx07q 318 26 model model NN cord-284810-fs5rx07q 318 27 . . . cord-284810-fs5rx07q 319 1 The the DT cord-284810-fs5rx07q 319 2 large large JJ cord-284810-fs5rx07q 319 3 - - HYPH cord-284810-fs5rx07q 319 4 scale scale NN cord-284810-fs5rx07q 319 5 model model NN cord-284810-fs5rx07q 319 6 component component NN cord-284810-fs5rx07q 319 7 allows allow VBZ cord-284810-fs5rx07q 319 8 us -PRON- PRP cord-284810-fs5rx07q 319 9 to to TO cord-284810-fs5rx07q 319 10 simulate simulate VB cord-284810-fs5rx07q 319 11 the the DT cord-284810-fs5rx07q 319 12 spread spread NN cord-284810-fs5rx07q 319 13 of of IN cord-284810-fs5rx07q 319 14 the the DT cord-284810-fs5rx07q 319 15 virus virus NN cord-284810-fs5rx07q 319 16 in in IN cord-284810-fs5rx07q 319 17 a a DT cord-284810-fs5rx07q 319 18 network network NN cord-284810-fs5rx07q 319 19 of of IN cord-284810-fs5rx07q 319 20 N n CD cord-284810-fs5rx07q 319 21 interconnected interconnect VBN cord-284810-fs5rx07q 319 22 countries country NNS cord-284810-fs5rx07q 319 23 ( ( -LRB- cord-284810-fs5rx07q 319 24 with with IN cord-284810-fs5rx07q 319 25 average average JJ cord-284810-fs5rx07q 319 26 network network NN cord-284810-fs5rx07q 319 27 degree degree NN cord-284810-fs5rx07q 319 28 k k NNP cord-284810-fs5rx07q 319 29 ) ) -RRB- cord-284810-fs5rx07q 319 30 . . . cord-284810-fs5rx07q 320 1 The the DT cord-284810-fs5rx07q 320 2 state state NN cord-284810-fs5rx07q 320 3 of of IN cord-284810-fs5rx07q 320 4 a a DT cord-284810-fs5rx07q 320 5 country country NN cord-284810-fs5rx07q 320 6 is be VBZ cord-284810-fs5rx07q 320 7 given give VBN cord-284810-fs5rx07q 320 8 as as IN cord-284810-fs5rx07q 320 9 a a DT cord-284810-fs5rx07q 320 10 Boolean boolean JJ cord-284810-fs5rx07q 320 11 value value NN cord-284810-fs5rx07q 320 12 , , , cord-284810-fs5rx07q 320 13 being be VBG cord-284810-fs5rx07q 320 14 either either CC cord-284810-fs5rx07q 320 15 invaded invade VBN cord-284810-fs5rx07q 320 16 by by IN cord-284810-fs5rx07q 320 17 the the DT cord-284810-fs5rx07q 320 18 virus virus NN cord-284810-fs5rx07q 320 19 or or CC cord-284810-fs5rx07q 320 20 non non JJ cord-284810-fs5rx07q 320 21 - - JJ cord-284810-fs5rx07q 320 22 invaded invaded JJ cord-284810-fs5rx07q 320 23 . . . cord-284810-fs5rx07q 321 1 The the DT cord-284810-fs5rx07q 321 2 model model NN cord-284810-fs5rx07q 321 3 starts start VBZ cord-284810-fs5rx07q 321 4 with with IN cord-284810-fs5rx07q 321 5 a a DT cord-284810-fs5rx07q 321 6 single single JJ cord-284810-fs5rx07q 321 7 invaded invaded JJ cord-284810-fs5rx07q 321 8 country country NN cord-284810-fs5rx07q 321 9 . . . cord-284810-fs5rx07q 322 1 The the DT cord-284810-fs5rx07q 322 2 geographic geographic JJ cord-284810-fs5rx07q 322 3 spread spread NN cord-284810-fs5rx07q 322 4 runs run VBZ cord-284810-fs5rx07q 322 5 in in IN cord-284810-fs5rx07q 322 6 discrete discrete JJ cord-284810-fs5rx07q 322 7 time time NN cord-284810-fs5rx07q 322 8 , , , cord-284810-fs5rx07q 322 9 each each DT cord-284810-fs5rx07q 322 10 step step NN cord-284810-fs5rx07q 322 11 corresponding correspond VBG cord-284810-fs5rx07q 322 12 to to IN cord-284810-fs5rx07q 322 13 one one CD cord-284810-fs5rx07q 322 14 day day NN cord-284810-fs5rx07q 322 15 of of IN cord-284810-fs5rx07q 322 16 the the DT cord-284810-fs5rx07q 322 17 time time NN cord-284810-fs5rx07q 322 18 - - HYPH cord-284810-fs5rx07q 322 19 continuous continuous JJ cord-284810-fs5rx07q 322 20 small small JJ cord-284810-fs5rx07q 322 21 - - HYPH cord-284810-fs5rx07q 322 22 scale scale NN cord-284810-fs5rx07q 322 23 model model NN cord-284810-fs5rx07q 322 24 . . . cord-284810-fs5rx07q 323 1 In in IN cord-284810-fs5rx07q 323 2 each each DT cord-284810-fs5rx07q 323 3 time time NN cord-284810-fs5rx07q 323 4 step step NN cord-284810-fs5rx07q 323 5 , , , cord-284810-fs5rx07q 323 6 a a DT cord-284810-fs5rx07q 323 7 non non JJ cord-284810-fs5rx07q 323 8 - - JJ cord-284810-fs5rx07q 323 9 invaded invaded JJ cord-284810-fs5rx07q 323 10 country country NN cord-284810-fs5rx07q 323 11 becomes become VBZ cord-284810-fs5rx07q 323 12 infected infect VBN cord-284810-fs5rx07q 323 13 by by IN cord-284810-fs5rx07q 323 14 neighboring neighbor VBG cord-284810-fs5rx07q 323 15 invaded invade VBN cord-284810-fs5rx07q 323 16 countries country NNS cord-284810-fs5rx07q 323 17 in in IN cord-284810-fs5rx07q 323 18 the the DT cord-284810-fs5rx07q 323 19 network network NN cord-284810-fs5rx07q 323 20 with with IN cord-284810-fs5rx07q 323 21 the the DT cord-284810-fs5rx07q 323 22 transmission transmission NN cord-284810-fs5rx07q 323 23 probability probability NN cord-284810-fs5rx07q 323 24 p. p. NN cord-284810-fs5rx07q 324 1 As as RB cord-284810-fs5rx07q 324 2 soon soon RB cord-284810-fs5rx07q 324 3 as as IN cord-284810-fs5rx07q 324 4 a a DT cord-284810-fs5rx07q 324 5 country country NN cord-284810-fs5rx07q 324 6 has have VBZ cord-284810-fs5rx07q 324 7 been be VBN cord-284810-fs5rx07q 324 8 invaded invade VBN cord-284810-fs5rx07q 324 9 by by IN cord-284810-fs5rx07q 324 10 the the DT cord-284810-fs5rx07q 324 11 virus virus NN cord-284810-fs5rx07q 324 12 in in IN cord-284810-fs5rx07q 324 13 this this DT cord-284810-fs5rx07q 324 14 process process NN cord-284810-fs5rx07q 324 15 , , , cord-284810-fs5rx07q 324 16 the the DT cord-284810-fs5rx07q 324 17 small small JJ cord-284810-fs5rx07q 324 18 - - HYPH cord-284810-fs5rx07q 324 19 scale scale NN cord-284810-fs5rx07q 324 20 model model NN cord-284810-fs5rx07q 324 21 for for IN cord-284810-fs5rx07q 324 22 this this DT cord-284810-fs5rx07q 324 23 country country NN cord-284810-fs5rx07q 324 24 is be VBZ cord-284810-fs5rx07q 324 25 initiated initiate VBN cord-284810-fs5rx07q 324 26 . . . cord-284810-fs5rx07q 325 1 This this DT cord-284810-fs5rx07q 325 2 large large JJ cord-284810-fs5rx07q 325 3 - - HYPH cord-284810-fs5rx07q 325 4 scale scale NN cord-284810-fs5rx07q 325 5 model model NN cord-284810-fs5rx07q 325 6 corresponds correspond VBZ cord-284810-fs5rx07q 325 7 to to IN cord-284810-fs5rx07q 325 8 the the DT cord-284810-fs5rx07q 325 9 well well RB cord-284810-fs5rx07q 325 10 - - HYPH cord-284810-fs5rx07q 325 11 known know VBN cord-284810-fs5rx07q 325 12 SIepidemic SIepidemic NNP cord-284810-fs5rx07q 325 13 spread spread NN cord-284810-fs5rx07q 325 14 on on IN cord-284810-fs5rx07q 325 15 a a DT cord-284810-fs5rx07q 325 16 network network NN cord-284810-fs5rx07q 325 17 . . . cord-284810-fs5rx07q 326 1 31 31 CD cord-284810-fs5rx07q 327 1 The the DT cord-284810-fs5rx07q 327 2 number number NN cord-284810-fs5rx07q 327 3 of of IN cord-284810-fs5rx07q 327 4 invaded invade VBN cord-284810-fs5rx07q 327 5 countries country NNS cord-284810-fs5rx07q 327 6 grows grow VBZ cord-284810-fs5rx07q 327 7 stochastically stochastically RB cord-284810-fs5rx07q 327 8 and and CC cord-284810-fs5rx07q 327 9 roughly roughly RB cord-284810-fs5rx07q 327 10 follows follow VBZ cord-284810-fs5rx07q 327 11 a a DT cord-284810-fs5rx07q 327 12 sigmoidal sigmoidal JJ cord-284810-fs5rx07q 327 13 shape shape NN cord-284810-fs5rx07q 327 14 . . . cord-284810-fs5rx07q 328 1 Neglecting neglect VBG cord-284810-fs5rx07q 328 2 saturation saturation NN cord-284810-fs5rx07q 328 3 effects effect NNS cord-284810-fs5rx07q 328 4 ( ( -LRB- cord-284810-fs5rx07q 328 5 that that RB cord-284810-fs5rx07q 328 6 is is RB cord-284810-fs5rx07q 328 7 , , , cord-284810-fs5rx07q 328 8 in in IN cord-284810-fs5rx07q 328 9 the the DT cord-284810-fs5rx07q 328 10 initial initial JJ cord-284810-fs5rx07q 328 11 phase phase NN cord-284810-fs5rx07q 328 12 of of IN cord-284810-fs5rx07q 328 13 the the DT cord-284810-fs5rx07q 328 14 pandemic pandemic NN cord-284810-fs5rx07q 328 15 ) ) -RRB- cord-284810-fs5rx07q 328 16 and and CC cord-284810-fs5rx07q 328 17 assuming assume VBG cord-284810-fs5rx07q 328 18 a a DT cord-284810-fs5rx07q 328 19 homogeneous homogeneous JJ cord-284810-fs5rx07q 328 20 degree degree NN cord-284810-fs5rx07q 328 21 distribution distribution NN cord-284810-fs5rx07q 328 22 , , , cord-284810-fs5rx07q 328 23 the the DT cord-284810-fs5rx07q 328 24 expected expect VBN cord-284810-fs5rx07q 328 25 number number NN cord-284810-fs5rx07q 328 26 of of IN cord-284810-fs5rx07q 328 27 invaded invade VBN cord-284810-fs5rx07q 328 28 countries country NNS cord-284810-fs5rx07q 328 29 X(t X(t NNP cord-284810-fs5rx07q 328 30 ) ) -RRB- cord-284810-fs5rx07q 328 31 grows grow VBZ cord-284810-fs5rx07q 328 32 exponentially exponentially RB cord-284810-fs5rx07q 328 33 in in IN cord-284810-fs5rx07q 328 34 time time NN cord-284810-fs5rx07q 328 35 , , , cord-284810-fs5rx07q 328 36 X(t x(t ADD cord-284810-fs5rx07q 328 37 ) ) -RRB- cord-284810-fs5rx07q 329 1 = = NFP cord-284810-fs5rx07q 330 1 X x NN cord-284810-fs5rx07q 330 2 0 0 CD cord-284810-fs5rx07q 330 3 exp(st exp(st NNP cord-284810-fs5rx07q 330 4 ) ) -RRB- cord-284810-fs5rx07q 330 5 , , , cord-284810-fs5rx07q 330 6 with with IN cord-284810-fs5rx07q 330 7 X x NN cord-284810-fs5rx07q 330 8 0 0 CD cord-284810-fs5rx07q 330 9 = = SYM cord-284810-fs5rx07q 330 10 1 1 CD cord-284810-fs5rx07q 330 11 and and CC cord-284810-fs5rx07q 330 12 exponent exponent NN cord-284810-fs5rx07q 330 13 s s NNP cord-284810-fs5rx07q 330 14 = = SYM cord-284810-fs5rx07q 330 15 kp kp NN cord-284810-fs5rx07q 330 16 . . . cord-284810-fs5rx07q 331 1 Then then RB cord-284810-fs5rx07q 331 2 , , , cord-284810-fs5rx07q 331 3 the the DT cord-284810-fs5rx07q 331 4 rate rate NN cord-284810-fs5rx07q 331 5 of of IN cord-284810-fs5rx07q 331 6 newly newly RB cord-284810-fs5rx07q 331 7 invaded invade VBN cord-284810-fs5rx07q 331 8 countries country NNS cord-284810-fs5rx07q 331 9 is be VBZ cord-284810-fs5rx07q 331 10 given give VBN cord-284810-fs5rx07q 332 1 byẊ byẊ NNP cord-284810-fs5rx07q 332 2 = = SYM cord-284810-fs5rx07q 332 3 s s NN cord-284810-fs5rx07q 333 1 exp(st exp(st NNP cord-284810-fs5rx07q 333 2 ) ) -RRB- cord-284810-fs5rx07q 334 1 and and CC cord-284810-fs5rx07q 334 2 thus thus RB cord-284810-fs5rx07q 334 3 also also RB cord-284810-fs5rx07q 334 4 the the DT cord-284810-fs5rx07q 334 5 probability probability NN cord-284810-fs5rx07q 334 6 distribution distribution NN cord-284810-fs5rx07q 334 7 P(τ P(τ NNP cord-284810-fs5rx07q 334 8 ) ) -RRB- cord-284810-fs5rx07q 334 9 for for IN cord-284810-fs5rx07q 334 10 a a DT cord-284810-fs5rx07q 334 11 country country NN cord-284810-fs5rx07q 334 12 to to TO cord-284810-fs5rx07q 334 13 have have VB cord-284810-fs5rx07q 334 14 been be VBN cord-284810-fs5rx07q 334 15 invaded invade VBN cord-284810-fs5rx07q 334 16 at at IN cord-284810-fs5rx07q 334 17 some some DT cord-284810-fs5rx07q 334 18 former former JJ cord-284810-fs5rx07q 334 19 time time NN cord-284810-fs5rx07q 334 20 τ τ NN cord-284810-fs5rx07q 334 21 ≤ ≤ NN cord-284810-fs5rx07q 334 22 t t NN cord-284810-fs5rx07q 334 23 , , , cord-284810-fs5rx07q 334 24 Eq Eq NNP cord-284810-fs5rx07q 334 25 . . . cord-284810-fs5rx07q 335 1 ( ( -LRB- cord-284810-fs5rx07q 335 2 2 2 LS cord-284810-fs5rx07q 335 3 ) ) -RRB- cord-284810-fs5rx07q 335 4 , , , cord-284810-fs5rx07q 335 5 grows grow VBZ cord-284810-fs5rx07q 335 6 exponentially exponentially RB cord-284810-fs5rx07q 335 7 , , , cord-284810-fs5rx07q 335 8 P(τ P(τ NNP cord-284810-fs5rx07q 335 9 ) ) -RRB- cord-284810-fs5rx07q 335 10 = = NFP cord-284810-fs5rx07q 336 1 c c NNP cord-284810-fs5rx07q 336 2 exp(st exp(st NNP cord-284810-fs5rx07q 336 3 ) ) -RRB- cord-284810-fs5rx07q 336 4 . . . cord-284810-fs5rx07q 337 1 Here here RB cord-284810-fs5rx07q 337 2 , , , cord-284810-fs5rx07q 337 3 the the DT cord-284810-fs5rx07q 337 4 normalization normalization NN cord-284810-fs5rx07q 337 5 factor factor NN cord-284810-fs5rx07q 337 6 is be VBZ cord-284810-fs5rx07q 337 7 given give VBN cord-284810-fs5rx07q 337 8 by by IN cord-284810-fs5rx07q 338 1 c c NN cord-284810-fs5rx07q 338 2 = = SYM cord-284810-fs5rx07q 338 3 s s NN cord-284810-fs5rx07q 339 1 N N NNP cord-284810-fs5rx07q 339 2 exp(st)/(exp exp(st)/(exp NN cord-284810-fs5rx07q 340 1 ( ( -LRB- cord-284810-fs5rx07q 340 2 st st NNP cord-284810-fs5rx07q 340 3 ) ) -RRB- cord-284810-fs5rx07q 340 4 − − NNP cord-284810-fs5rx07q 340 5 1 1 CD cord-284810-fs5rx07q 340 6 ) ) -RRB- cord-284810-fs5rx07q 340 7 , , , cord-284810-fs5rx07q 340 8 which which WDT cord-284810-fs5rx07q 340 9 is be VBZ cord-284810-fs5rx07q 340 10 determined determine VBN cord-284810-fs5rx07q 340 11 by by IN cord-284810-fs5rx07q 340 12 the the DT cord-284810-fs5rx07q 340 13 condition condition NN cord-284810-fs5rx07q 340 14 that that IN cord-284810-fs5rx07q 340 15 the the DT cord-284810-fs5rx07q 340 16 time time NN cord-284810-fs5rx07q 340 17 integral integral JJ cord-284810-fs5rx07q 340 18 t t NN cord-284810-fs5rx07q 340 19 0 0 CD cord-284810-fs5rx07q 340 20 P(τ P(τ NNP cord-284810-fs5rx07q 340 21 ) ) -RRB- cord-284810-fs5rx07q 340 22 dτ dτ . cord-284810-fs5rx07q 341 1 = = NFP cord-284810-fs5rx07q 342 1 X(t)/N. X(t)/N. NNP cord-284810-fs5rx07q 343 1 In in IN cord-284810-fs5rx07q 343 2 our -PRON- PRP$ cord-284810-fs5rx07q 343 3 simulation simulation NN cord-284810-fs5rx07q 343 4 , , , cord-284810-fs5rx07q 343 5 parameter parameter NN cord-284810-fs5rx07q 343 6 values value NNS cord-284810-fs5rx07q 343 7 were be VBD cord-284810-fs5rx07q 343 8 taken take VBN cord-284810-fs5rx07q 343 9 as as IN cord-284810-fs5rx07q 343 10 follows follow VBZ cord-284810-fs5rx07q 343 11 : : : cord-284810-fs5rx07q 343 12 number number NN cord-284810-fs5rx07q 343 13 of of IN cord-284810-fs5rx07q 343 14 countries country NNS cord-284810-fs5rx07q 343 15 N n CD cord-284810-fs5rx07q 343 16 = = SYM cord-284810-fs5rx07q 343 17 200 200 CD cord-284810-fs5rx07q 343 18 , , , cord-284810-fs5rx07q 343 19 degree degree NN cord-284810-fs5rx07q 343 20 k k NN cord-284810-fs5rx07q 343 21 = = SYM cord-284810-fs5rx07q 343 22 199 199 CD cord-284810-fs5rx07q 343 23 ( ( -LRB- cord-284810-fs5rx07q 343 24 fully fully RB cord-284810-fs5rx07q 343 25 connected connect VBN cord-284810-fs5rx07q 343 26 network network NN cord-284810-fs5rx07q 343 27 ) ) -RRB- cord-284810-fs5rx07q 343 28 , , , cord-284810-fs5rx07q 343 29 and and CC cord-284810-fs5rx07q 343 30 invasion invasion NN cord-284810-fs5rx07q 343 31 probability probability NN cord-284810-fs5rx07q 343 32 p p NN cord-284810-fs5rx07q 343 33 = = SYM cord-284810-fs5rx07q 343 34 6 6 CD cord-284810-fs5rx07q 343 35 × × NN cord-284810-fs5rx07q 343 36 10 10 CD cord-284810-fs5rx07q 343 37 −4 −4 CD cord-284810-fs5rx07q 343 38 . . . cord-284810-fs5rx07q 344 1 The the DT cord-284810-fs5rx07q 344 2 small small JJ cord-284810-fs5rx07q 344 3 - - HYPH cord-284810-fs5rx07q 344 4 scale scale NN cord-284810-fs5rx07q 344 5 model model NN cord-284810-fs5rx07q 344 6 is be VBZ cord-284810-fs5rx07q 344 7 time time NN cord-284810-fs5rx07q 344 8 - - HYPH cord-284810-fs5rx07q 344 9 continuous continuous JJ cord-284810-fs5rx07q 344 10 and and CC cord-284810-fs5rx07q 344 11 deterministically deterministically RB cord-284810-fs5rx07q 344 12 describes describe VBZ cord-284810-fs5rx07q 344 13 the the DT cord-284810-fs5rx07q 344 14 epidemic epidemic NN cord-284810-fs5rx07q 344 15 dynamics dynamic NNS cord-284810-fs5rx07q 344 16 within within IN cord-284810-fs5rx07q 344 17 a a DT cord-284810-fs5rx07q 344 18 country country NN cord-284810-fs5rx07q 344 19 . . . cord-284810-fs5rx07q 345 1 The the DT cord-284810-fs5rx07q 345 2 model model NN cord-284810-fs5rx07q 345 3 determines determine VBZ cord-284810-fs5rx07q 345 4 the the DT cord-284810-fs5rx07q 345 5 time time NN cord-284810-fs5rx07q 345 6 course course NN cord-284810-fs5rx07q 345 7 of of IN cord-284810-fs5rx07q 345 8 susceptible susceptible JJ cord-284810-fs5rx07q 345 9 S S NNP cord-284810-fs5rx07q 345 10 , , , cord-284810-fs5rx07q 345 11 infected infect VBN cord-284810-fs5rx07q 345 12 I -PRON- PRP cord-284810-fs5rx07q 345 13 , , , cord-284810-fs5rx07q 345 14 recovered recover VBD cord-284810-fs5rx07q 345 15 R r NN cord-284810-fs5rx07q 345 16 , , , cord-284810-fs5rx07q 345 17 and and CC cord-284810-fs5rx07q 345 18 dead dead JJ cord-284810-fs5rx07q 345 19 D d NN cord-284810-fs5rx07q 345 20 from from IN cord-284810-fs5rx07q 345 21 a a DT cord-284810-fs5rx07q 345 22 standard standard JJ cord-284810-fs5rx07q 345 23 SIR SIR NNP cord-284810-fs5rx07q 345 24 - - HYPH cord-284810-fs5rx07q 345 25 model model NN cord-284810-fs5rx07q 345 26 , , , cord-284810-fs5rx07q 345 27 22 22 CD cord-284810-fs5rx07q 346 1 Here here RB cord-284810-fs5rx07q 346 2 , , , cord-284810-fs5rx07q 346 3 N n CD cord-284810-fs5rx07q 346 4 pop pop NN cord-284810-fs5rx07q 346 5 is be VBZ cord-284810-fs5rx07q 346 6 the the DT cord-284810-fs5rx07q 346 7 constant constant JJ cord-284810-fs5rx07q 346 8 population population NN cord-284810-fs5rx07q 346 9 size size NN cord-284810-fs5rx07q 346 10 in in IN cord-284810-fs5rx07q 346 11 the the DT cord-284810-fs5rx07q 346 12 country country NN cord-284810-fs5rx07q 346 13 , , , cord-284810-fs5rx07q 346 14 β β NN cord-284810-fs5rx07q 346 15 is be VBZ cord-284810-fs5rx07q 346 16 the the DT cord-284810-fs5rx07q 346 17 contact contact NN cord-284810-fs5rx07q 346 18 rate rate NN cord-284810-fs5rx07q 346 19 , , , cord-284810-fs5rx07q 346 20 1 1 CD cord-284810-fs5rx07q 346 21 / / SYM cord-284810-fs5rx07q 346 22 γ γ NN cord-284810-fs5rx07q 346 23 the the DT cord-284810-fs5rx07q 346 24 infectious infectious JJ cord-284810-fs5rx07q 346 25 period period NN cord-284810-fs5rx07q 346 26 , , , cord-284810-fs5rx07q 346 27 and and CC cord-284810-fs5rx07q 346 28 m m LS cord-284810-fs5rx07q 346 29 the the DT cord-284810-fs5rx07q 346 30 case case NN cord-284810-fs5rx07q 346 31 fatality fatality NN cord-284810-fs5rx07q 346 32 rate rate NN cord-284810-fs5rx07q 346 33 . . . cord-284810-fs5rx07q 347 1 The the DT cord-284810-fs5rx07q 347 2 total total JJ cord-284810-fs5rx07q 347 3 number number NN cord-284810-fs5rx07q 347 4 of of IN cord-284810-fs5rx07q 347 5 cases case NNS cord-284810-fs5rx07q 347 6 is be VBZ cord-284810-fs5rx07q 347 7 determined determine VBN cord-284810-fs5rx07q 347 8 as as IN cord-284810-fs5rx07q 347 9 C c NN cord-284810-fs5rx07q 347 10 = = NFP cord-284810-fs5rx07q 348 1 I -PRON- PRP cord-284810-fs5rx07q 348 2 + + CC cord-284810-fs5rx07q 348 3 R r NN cord-284810-fs5rx07q 348 4 + + CC cord-284810-fs5rx07q 348 5 D. D. NNP cord-284810-fs5rx07q 349 1 In in IN cord-284810-fs5rx07q 349 2 the the DT cord-284810-fs5rx07q 349 3 small small JJ cord-284810-fs5rx07q 349 4 - - HYPH cord-284810-fs5rx07q 349 5 scale scale NN cord-284810-fs5rx07q 349 6 model model NN cord-284810-fs5rx07q 349 7 , , , cord-284810-fs5rx07q 349 8 countries country NNS cord-284810-fs5rx07q 349 9 are be VBP cord-284810-fs5rx07q 349 10 simulated simulate VBN cord-284810-fs5rx07q 349 11 independently independently RB cord-284810-fs5rx07q 349 12 from from IN cord-284810-fs5rx07q 349 13 each each DT cord-284810-fs5rx07q 349 14 other other JJ cord-284810-fs5rx07q 349 15 and and CC cord-284810-fs5rx07q 349 16 are be VBP cord-284810-fs5rx07q 349 17 only only RB cord-284810-fs5rx07q 349 18 coupled couple VBN cord-284810-fs5rx07q 349 19 by by IN cord-284810-fs5rx07q 349 20 the the DT cord-284810-fs5rx07q 349 21 unique unique JJ cord-284810-fs5rx07q 349 22 invasion invasion NN cord-284810-fs5rx07q 349 23 event event NN cord-284810-fs5rx07q 349 24 for for IN cord-284810-fs5rx07q 349 25 each each DT cord-284810-fs5rx07q 349 26 country country NN cord-284810-fs5rx07q 349 27 , , , cord-284810-fs5rx07q 349 28 which which WDT cord-284810-fs5rx07q 349 29 starts start VBZ cord-284810-fs5rx07q 349 30 the the DT cord-284810-fs5rx07q 349 31 epidemic epidemic NN cord-284810-fs5rx07q 349 32 growth growth NN cord-284810-fs5rx07q 349 33 in in IN cord-284810-fs5rx07q 349 34 that that DT cord-284810-fs5rx07q 349 35 country country NN cord-284810-fs5rx07q 349 36 with with IN cord-284810-fs5rx07q 349 37 initial initial JJ cord-284810-fs5rx07q 349 38 values value NNS cord-284810-fs5rx07q 349 39 S(0 S(0 NNS cord-284810-fs5rx07q 349 40 ) ) -RRB- cord-284810-fs5rx07q 350 1 = = NFP cord-284810-fs5rx07q 351 1 5 5 CD cord-284810-fs5rx07q 351 2 × × CD cord-284810-fs5rx07q 351 3 10 10 CD cord-284810-fs5rx07q 351 4 7 7 CD cord-284810-fs5rx07q 351 5 , , , cord-284810-fs5rx07q 351 6 I(0 I(0 NNP cord-284810-fs5rx07q 351 7 ) ) -RRB- cord-284810-fs5rx07q 352 1 = = NFP cord-284810-fs5rx07q 353 1 1 1 CD cord-284810-fs5rx07q 353 2 and and CC cord-284810-fs5rx07q 353 3 R(0 R(0 NNP cord-284810-fs5rx07q 353 4 ) ) -RRB- cord-284810-fs5rx07q 354 1 = = NFP cord-284810-fs5rx07q 355 1 D(0 D(0 NNP cord-284810-fs5rx07q 355 2 ) ) -RRB- cord-284810-fs5rx07q 355 3 = = SYM cord-284810-fs5rx07q 355 4 0 0 CD cord-284810-fs5rx07q 355 5 . . . cord-284810-fs5rx07q 356 1 All all DT cord-284810-fs5rx07q 356 2 infection infection NN cord-284810-fs5rx07q 356 3 state state NN cord-284810-fs5rx07q 356 4 variables variable NNS cord-284810-fs5rx07q 356 5 in in IN cord-284810-fs5rx07q 356 6 a a DT cord-284810-fs5rx07q 356 7 country country NN cord-284810-fs5rx07q 356 8 are be VBP cord-284810-fs5rx07q 356 9 zero zero CD cord-284810-fs5rx07q 356 10 before before IN cord-284810-fs5rx07q 356 11 invasion invasion NN cord-284810-fs5rx07q 356 12 by by IN cord-284810-fs5rx07q 356 13 the the DT cord-284810-fs5rx07q 356 14 virus virus NN cord-284810-fs5rx07q 356 15 , , , cord-284810-fs5rx07q 356 16 I i NN cord-284810-fs5rx07q 356 17 = = SYM cord-284810-fs5rx07q 356 18 R r NN cord-284810-fs5rx07q 356 19 = = SYM cord-284810-fs5rx07q 356 20 D d NN cord-284810-fs5rx07q 356 21 = = SYM cord-284810-fs5rx07q 356 22 0 0 CD cord-284810-fs5rx07q 356 23 . . . cord-284810-fs5rx07q 357 1 The the DT cord-284810-fs5rx07q 357 2 resulting result VBG cord-284810-fs5rx07q 357 3 well well RB cord-284810-fs5rx07q 357 4 - - HYPH cord-284810-fs5rx07q 357 5 known know VBN cord-284810-fs5rx07q 357 6 SIR SIR NNP cord-284810-fs5rx07q 357 7 - - HYPH cord-284810-fs5rx07q 357 8 dynamics dynamic NNS cord-284810-fs5rx07q 357 9 in in IN cord-284810-fs5rx07q 357 10 a a DT cord-284810-fs5rx07q 357 11 single single JJ cord-284810-fs5rx07q 357 12 country country NN cord-284810-fs5rx07q 357 13 is be VBZ cord-284810-fs5rx07q 357 14 shown show VBN cord-284810-fs5rx07q 357 15 in in IN cord-284810-fs5rx07q 357 16 Fig Fig NNP cord-284810-fs5rx07q 357 17 . . . cord-284810-fs5rx07q 358 1 6 6 LS cord-284810-fs5rx07q 358 2 . . . cord-284810-fs5rx07q 359 1 With with IN cord-284810-fs5rx07q 359 2 the the DT cord-284810-fs5rx07q 359 3 chosen choose VBN cord-284810-fs5rx07q 359 4 parameterization parameterization NN cord-284810-fs5rx07q 359 5 , , , cord-284810-fs5rx07q 359 6 it -PRON- PRP cord-284810-fs5rx07q 359 7 takes take VBZ cord-284810-fs5rx07q 359 8 roughly roughly RB cord-284810-fs5rx07q 359 9 80 80 CD cord-284810-fs5rx07q 359 10 days day NNS cord-284810-fs5rx07q 359 11 until until IN cord-284810-fs5rx07q 359 12 the the DT cord-284810-fs5rx07q 359 13 epidemic epidemic NN cord-284810-fs5rx07q 359 14 peak peak NN cord-284810-fs5rx07q 359 15 is be VBZ cord-284810-fs5rx07q 359 16 reached reach VBN cord-284810-fs5rx07q 359 17 . . . cord-284810-fs5rx07q 360 1 After after IN cord-284810-fs5rx07q 360 2 this this DT cord-284810-fs5rx07q 360 3 time time NN cord-284810-fs5rx07q 360 4 , , , cord-284810-fs5rx07q 360 5 the the DT cord-284810-fs5rx07q 360 6 assumption assumption NN cord-284810-fs5rx07q 360 7 of of IN cord-284810-fs5rx07q 360 8 an an DT cord-284810-fs5rx07q 360 9 exponential exponential JJ cord-284810-fs5rx07q 360 10 increase increase NN cord-284810-fs5rx07q 360 11 , , , cord-284810-fs5rx07q 360 12 Eq Eq NNP cord-284810-fs5rx07q 360 13 . . . cord-284810-fs5rx07q 361 1 ( ( -LRB- cord-284810-fs5rx07q 361 2 3 3 LS cord-284810-fs5rx07q 361 3 ) ) -RRB- cord-284810-fs5rx07q 361 4 , , , cord-284810-fs5rx07q 361 5 breaks break VBZ cord-284810-fs5rx07q 361 6 down down RP cord-284810-fs5rx07q 361 7 . . . cord-284810-fs5rx07q 362 1 Parameter parameter NN cord-284810-fs5rx07q 362 2 values value NNS cord-284810-fs5rx07q 362 3 were be VBD cord-284810-fs5rx07q 362 4 taken take VBN cord-284810-fs5rx07q 362 5 as as IN cord-284810-fs5rx07q 362 6 follows follow VBZ cord-284810-fs5rx07q 362 7 : : : cord-284810-fs5rx07q 362 8 country country NN cord-284810-fs5rx07q 362 9 population population NN cord-284810-fs5rx07q 362 10 size size NN cord-284810-fs5rx07q 362 11 N n CD cord-284810-fs5rx07q 363 1 pop pop NN cord-284810-fs5rx07q 363 2 = = NFP cord-284810-fs5rx07q 364 1 5 5 CD cord-284810-fs5rx07q 364 2 × × CD cord-284810-fs5rx07q 364 3 10 10 CD cord-284810-fs5rx07q 364 4 7 7 CD cord-284810-fs5rx07q 364 5 , , , cord-284810-fs5rx07q 364 6 case case NN cord-284810-fs5rx07q 364 7 fatality fatality NN cord-284810-fs5rx07q 364 8 rate rate NN cord-284810-fs5rx07q 364 9 m m NN cord-284810-fs5rx07q 365 1 = = SYM cord-284810-fs5rx07q 365 2 0.01 0.01 CD cord-284810-fs5rx07q 366 1 , , , cord-284810-fs5rx07q 366 2 infectious infectious JJ cord-284810-fs5rx07q 366 3 period period NN cord-284810-fs5rx07q 366 4 1 1 CD cord-284810-fs5rx07q 366 5 / / SYM cord-284810-fs5rx07q 366 6 γ γ NN cord-284810-fs5rx07q 366 7 = = SYM cord-284810-fs5rx07q 366 8 6d 6d NNP cord-284810-fs5rx07q 366 9 , , , cord-284810-fs5rx07q 366 10 and and CC cord-284810-fs5rx07q 366 11 contact contact NN cord-284810-fs5rx07q 366 12 rate rate NN cord-284810-fs5rx07q 366 13 β β NN cord-284810-fs5rx07q 366 14 = = SYM cord-284810-fs5rx07q 366 15 0.4d 0.4d CD cord-284810-fs5rx07q 367 1 −1 −1 NNP cord-284810-fs5rx07q 367 2 . . . cord-284810-fs5rx07q 368 1 This this DT cord-284810-fs5rx07q 368 2 yields yield VBZ cord-284810-fs5rx07q 368 3 a a DT cord-284810-fs5rx07q 368 4 growth growth NN cord-284810-fs5rx07q 368 5 rate rate NN cord-284810-fs5rx07q 368 6 r r NN cord-284810-fs5rx07q 368 7 = = SYM cord-284810-fs5rx07q 368 8 β β NN cord-284810-fs5rx07q 368 9 − − NN cord-284810-fs5rx07q 368 10 γ γ NN cord-284810-fs5rx07q 368 11 = = SYM cord-284810-fs5rx07q 368 12 0.23d 0.23d CD cord-284810-fs5rx07q 368 13 −1 −1 NNP cord-284810-fs5rx07q 368 14 , , , cord-284810-fs5rx07q 368 15 corresponding correspond VBG cord-284810-fs5rx07q 368 16 to to IN cord-284810-fs5rx07q 368 17 a a DT cord-284810-fs5rx07q 368 18 doubling double VBG cord-284810-fs5rx07q 368 19 time time NN cord-284810-fs5rx07q 368 20 of of IN cord-284810-fs5rx07q 368 21 T t NN cord-284810-fs5rx07q 368 22 1,2 1,2 CD cord-284810-fs5rx07q 368 23 = = SYM cord-284810-fs5rx07q 368 24 log(2)/r log(2)/r NNP cord-284810-fs5rx07q 368 25 = = SYM cord-284810-fs5rx07q 368 26 3d 3d NNP cord-284810-fs5rx07q 368 27 and and CC cord-284810-fs5rx07q 368 28 a a DT cord-284810-fs5rx07q 368 29 basic basic JJ cord-284810-fs5rx07q 368 30 reproduction reproduction NN cord-284810-fs5rx07q 368 31 number number NN cord-284810-fs5rx07q 368 32 R r NN cord-284810-fs5rx07q 368 33 0 0 CD cord-284810-fs5rx07q 368 34 = = NFP cord-284810-fs5rx07q 369 1 β β NNP cord-284810-fs5rx07q 369 2 / / SYM cord-284810-fs5rx07q 369 3 γ γ NN cord-284810-fs5rx07q 369 4 = = SYM cord-284810-fs5rx07q 369 5 2.4 2.4 CD cord-284810-fs5rx07q 369 6 . . . cord-284810-fs5rx07q 370 1 Alternative alternative JJ cord-284810-fs5rx07q 370 2 calculation calculation NN cord-284810-fs5rx07q 370 3 of of IN cord-284810-fs5rx07q 370 4 the the DT cord-284810-fs5rx07q 370 5 distribution distribution NN cord-284810-fs5rx07q 370 6 of of IN cord-284810-fs5rx07q 370 7 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 370 8 case case NN cord-284810-fs5rx07q 370 9 numbers number NNS cord-284810-fs5rx07q 370 10 in in IN cord-284810-fs5rx07q 370 11 countries country NNS cord-284810-fs5rx07q 370 12 worldwide worldwide RB cord-284810-fs5rx07q 370 13 and and CC cord-284810-fs5rx07q 370 14 counties county NNS cord-284810-fs5rx07q 370 15 in in IN cord-284810-fs5rx07q 370 16 the the DT cord-284810-fs5rx07q 370 17 US US NNP cord-284810-fs5rx07q 370 18 . . . cord-284810-fs5rx07q 370 19 _SP cord-284810-fs5rx07q 371 1 Code code NN cord-284810-fs5rx07q 371 2 for for IN cord-284810-fs5rx07q 371 3 data datum NNS cord-284810-fs5rx07q 371 4 analysis analysis NN cord-284810-fs5rx07q 371 5 and and CC cord-284810-fs5rx07q 371 6 numerical numerical JJ cord-284810-fs5rx07q 371 7 simulations simulation NNS cord-284810-fs5rx07q 371 8 was be VBD cord-284810-fs5rx07q 371 9 written write VBN cord-284810-fs5rx07q 371 10 in in IN cord-284810-fs5rx07q 371 11 Julia Julia NNP cord-284810-fs5rx07q 371 12 , , , cord-284810-fs5rx07q 371 13 Ref Ref NNP cord-284810-fs5rx07q 371 14 . . . cord-284810-fs5rx07q 371 15 6 6 CD cord-284810-fs5rx07q 371 16 _SP cord-284810-fs5rx07q 372 1 Parameter parameter NN cord-284810-fs5rx07q 372 2 estimation estimation NN cord-284810-fs5rx07q 372 3 for for IN cord-284810-fs5rx07q 372 4 the the DT cord-284810-fs5rx07q 372 5 truncated truncated JJ cord-284810-fs5rx07q 372 6 Pareto Pareto NNP cord-284810-fs5rx07q 372 7 distribution distribution NN cord-284810-fs5rx07q 373 1 A a DT cord-284810-fs5rx07q 373 2 mathematical mathematical JJ cord-284810-fs5rx07q 373 3 model model NN cord-284810-fs5rx07q 373 4 for for IN cord-284810-fs5rx07q 373 5 the the DT cord-284810-fs5rx07q 373 6 spatiotemporal spatiotemporal JJ cord-284810-fs5rx07q 373 7 epidemic epidemic NN cord-284810-fs5rx07q 373 8 spreading spread VBG cord-284810-fs5rx07q 373 9 of of IN cord-284810-fs5rx07q 373 10 COVID19 COVID19 NNP cord-284810-fs5rx07q 373 11 Self self NN cord-284810-fs5rx07q 373 12 - - HYPH cord-284810-fs5rx07q 373 13 organized organize VBN cord-284810-fs5rx07q 373 14 criticality criticality NN cord-284810-fs5rx07q 373 15 : : : cord-284810-fs5rx07q 374 1 An an DT cord-284810-fs5rx07q 374 2 explanation explanation NN cord-284810-fs5rx07q 374 3 of of IN cord-284810-fs5rx07q 374 4 the the DT cord-284810-fs5rx07q 374 5 1 1 CD cord-284810-fs5rx07q 374 6 / / SYM cord-284810-fs5rx07q 374 7 f f NN cord-284810-fs5rx07q 374 8 noise noise NN cord-284810-fs5rx07q 374 9 Emergence emergence NN cord-284810-fs5rx07q 374 10 of of IN cord-284810-fs5rx07q 374 11 scaling scale VBG cord-284810-fs5rx07q 374 12 in in IN cord-284810-fs5rx07q 374 13 random random JJ cord-284810-fs5rx07q 374 14 networks network NNS cord-284810-fs5rx07q 375 1 Réflexions réflexion NNS cord-284810-fs5rx07q 376 1 sur sur NNP cord-284810-fs5rx07q 376 2 les les FW cord-284810-fs5rx07q 376 3 avantages avantages NNP cord-284810-fs5rx07q 376 4 de de IN cord-284810-fs5rx07q 376 5 l'inoculation l'inoculation NNP cord-284810-fs5rx07q 376 6 Julia Julia NNP cord-284810-fs5rx07q 376 7 : : : cord-284810-fs5rx07q 377 1 A a DT cord-284810-fs5rx07q 377 2 fresh fresh JJ cord-284810-fs5rx07q 377 3 approach approach NN cord-284810-fs5rx07q 377 4 to to IN cord-284810-fs5rx07q 377 5 numerical numerical JJ cord-284810-fs5rx07q 377 6 computing computing NN cord-284810-fs5rx07q 377 7 Zipf Zipf NNP cord-284810-fs5rx07q 377 8 's 's POS cord-284810-fs5rx07q 377 9 law law NN cord-284810-fs5rx07q 377 10 in in IN cord-284810-fs5rx07q 377 11 the the DT cord-284810-fs5rx07q 377 12 popularity popularity NN cord-284810-fs5rx07q 377 13 distribution distribution NN cord-284810-fs5rx07q 377 14 of of IN cord-284810-fs5rx07q 377 15 chess chess NN cord-284810-fs5rx07q 377 16 openings opening NNS cord-284810-fs5rx07q 378 1 The the DT cord-284810-fs5rx07q 378 2 hidden hidden JJ cord-284810-fs5rx07q 378 3 geometry geometry NN cord-284810-fs5rx07q 378 4 of of IN cord-284810-fs5rx07q 378 5 complex complex NN cord-284810-fs5rx07q 378 6 , , , cord-284810-fs5rx07q 378 7 networkdriven networkdriven NNP cord-284810-fs5rx07q 378 8 contagion contagion NN cord-284810-fs5rx07q 378 9 phenomena phenomena VBP cord-284810-fs5rx07q 378 10 Fractals Fractals NNPS cord-284810-fs5rx07q 378 11 and and CC cord-284810-fs5rx07q 378 12 Disordered Disordered NNP cord-284810-fs5rx07q 378 13 Systems Systems NNPS cord-284810-fs5rx07q 379 1 The the DT cord-284810-fs5rx07q 379 2 effect effect NN cord-284810-fs5rx07q 379 3 of of IN cord-284810-fs5rx07q 379 4 travel travel NN cord-284810-fs5rx07q 379 5 restrictions restriction NNS cord-284810-fs5rx07q 379 6 on on IN cord-284810-fs5rx07q 379 7 the the DT cord-284810-fs5rx07q 379 8 spread spread NN cord-284810-fs5rx07q 379 9 of of IN cord-284810-fs5rx07q 379 10 the the DT cord-284810-fs5rx07q 379 11 2019 2019 CD cord-284810-fs5rx07q 379 12 novel novel NN cord-284810-fs5rx07q 379 13 coronavirus coronavirus NN cord-284810-fs5rx07q 379 14 ( ( -LRB- cord-284810-fs5rx07q 379 15 2019-nCoV 2019-ncov CD cord-284810-fs5rx07q 379 16 ) ) -RRB- cord-284810-fs5rx07q 379 17 outbreak outbreak NN cord-284810-fs5rx07q 379 18 Power power NN cord-284810-fs5rx07q 379 19 - - HYPH cord-284810-fs5rx07q 379 20 law law NN cord-284810-fs5rx07q 379 21 distributions distribution NNS cord-284810-fs5rx07q 379 22 in in IN cord-284810-fs5rx07q 379 23 empirical empirical JJ cord-284810-fs5rx07q 379 24 data datum NNS cord-284810-fs5rx07q 380 1 The the DT cord-284810-fs5rx07q 380 2 role role NN cord-284810-fs5rx07q 380 3 of of IN cord-284810-fs5rx07q 380 4 the the DT cord-284810-fs5rx07q 380 5 airline airline NN cord-284810-fs5rx07q 380 6 transportation transportation NN cord-284810-fs5rx07q 380 7 network network NN cord-284810-fs5rx07q 380 8 in in IN cord-284810-fs5rx07q 380 9 the the DT cord-284810-fs5rx07q 380 10 prediction prediction NN cord-284810-fs5rx07q 380 11 and and CC cord-284810-fs5rx07q 380 12 predictability predictability NN cord-284810-fs5rx07q 380 13 of of IN cord-284810-fs5rx07q 380 14 global global JJ cord-284810-fs5rx07q 380 15 epidemics epidemic NNS cord-284810-fs5rx07q 380 16 Fitting Fitting NNP cord-284810-fs5rx07q 380 17 and and CC cord-284810-fs5rx07q 380 18 goodness goodness NN cord-284810-fs5rx07q 380 19 - - HYPH cord-284810-fs5rx07q 380 20 of of IN cord-284810-fs5rx07q 380 21 - - HYPH cord-284810-fs5rx07q 380 22 fit fit JJ cord-284810-fs5rx07q 380 23 test test NN cord-284810-fs5rx07q 380 24 of of IN cord-284810-fs5rx07q 380 25 non non JJ cord-284810-fs5rx07q 380 26 - - JJ cord-284810-fs5rx07q 380 27 truncated truncated JJ cord-284810-fs5rx07q 380 28 and and CC cord-284810-fs5rx07q 380 29 truncated truncated JJ cord-284810-fs5rx07q 380 30 power power NN cord-284810-fs5rx07q 380 31 - - HYPH cord-284810-fs5rx07q 380 32 law law NN cord-284810-fs5rx07q 380 33 distributions distribution NNS cord-284810-fs5rx07q 381 1 An an DT cord-284810-fs5rx07q 381 2 interactive interactive JJ cord-284810-fs5rx07q 381 3 web web NN cord-284810-fs5rx07q 381 4 - - HYPH cord-284810-fs5rx07q 381 5 based base VBN cord-284810-fs5rx07q 381 6 dashboard dashboard NN cord-284810-fs5rx07q 381 7 to to TO cord-284810-fs5rx07q 381 8 track track VB cord-284810-fs5rx07q 381 9 COVID-19 COVID-19 NNP cord-284810-fs5rx07q 381 10 in in IN cord-284810-fs5rx07q 381 11 real real JJ cord-284810-fs5rx07q 381 12 time time NN cord-284810-fs5rx07q 381 13 Impact impact NN cord-284810-fs5rx07q 381 14 of of IN cord-284810-fs5rx07q 381 15 non non JJ cord-284810-fs5rx07q 381 16 - - JJ cord-284810-fs5rx07q 381 17 pharmaceutical pharmaceutical JJ cord-284810-fs5rx07q 381 18 interventions intervention NNS cord-284810-fs5rx07q 381 19 ( ( -LRB- cord-284810-fs5rx07q 381 20 NPIs NPIs NNP cord-284810-fs5rx07q 381 21 ) ) -RRB- cord-284810-fs5rx07q 381 22 to to TO cord-284810-fs5rx07q 381 23 reduce reduce VB cord-284810-fs5rx07q 381 24 COVID-19 covid-19 JJ cord-284810-fs5rx07q 381 25 mortality mortality NN cord-284810-fs5rx07q 381 26 and and CC cord-284810-fs5rx07q 381 27 healthcare healthcare NN cord-284810-fs5rx07q 381 28 demand demand NN cord-284810-fs5rx07q 381 29 Preparedness preparedness NN cord-284810-fs5rx07q 381 30 and and CC cord-284810-fs5rx07q 381 31 vulnerability vulnerability NN cord-284810-fs5rx07q 381 32 of of IN cord-284810-fs5rx07q 381 33 African african JJ cord-284810-fs5rx07q 381 34 countries country NNS cord-284810-fs5rx07q 381 35 against against IN cord-284810-fs5rx07q 381 36 importations importation NNS cord-284810-fs5rx07q 381 37 of of IN cord-284810-fs5rx07q 381 38 COVID-19 covid-19 NN cord-284810-fs5rx07q 382 1 : : : cord-284810-fs5rx07q 382 2 A a DT cord-284810-fs5rx07q 382 3 modelling modelling NN cord-284810-fs5rx07q 382 4 study study NN cord-284810-fs5rx07q 382 5 Variabilita Variabilita NNP cord-284810-fs5rx07q 382 6 e e NN cord-284810-fs5rx07q 382 7 mutabilita mutabilita NNP cord-284810-fs5rx07q 382 8 Frequency frequency NN cord-284810-fs5rx07q 382 9 of of IN cord-284810-fs5rx07q 382 10 earthquakes earthquake NNS cord-284810-fs5rx07q 382 11 in in IN cord-284810-fs5rx07q 382 12 California California NNP cord-284810-fs5rx07q 382 13 Forecast Forecast NNP cord-284810-fs5rx07q 382 14 and and CC cord-284810-fs5rx07q 382 15 control control NN cord-284810-fs5rx07q 382 16 of of IN cord-284810-fs5rx07q 382 17 epidemics epidemic NNS cord-284810-fs5rx07q 382 18 in in IN cord-284810-fs5rx07q 382 19 a a DT cord-284810-fs5rx07q 382 20 globalized globalized JJ cord-284810-fs5rx07q 382 21 world world NN cord-284810-fs5rx07q 382 22 Calculation calculation NN cord-284810-fs5rx07q 382 23 of of IN cord-284810-fs5rx07q 382 24 epidemic epidemic JJ cord-284810-fs5rx07q 382 25 arrival arrival NN cord-284810-fs5rx07q 382 26 time time NN cord-284810-fs5rx07q 382 27 distributions distribution NNS cord-284810-fs5rx07q 382 28 using use VBG cord-284810-fs5rx07q 382 29 branching branch VBG cord-284810-fs5rx07q 382 30 processes process NNS cord-284810-fs5rx07q 382 31 The the DT cord-284810-fs5rx07q 382 32 complex complex JJ cord-284810-fs5rx07q 382 33 network network NN cord-284810-fs5rx07q 382 34 of of IN cord-284810-fs5rx07q 382 35 global global JJ cord-284810-fs5rx07q 382 36 cargo cargo NN cord-284810-fs5rx07q 382 37 ship ship NN cord-284810-fs5rx07q 382 38 movements movement NNS cord-284810-fs5rx07q 382 39 Modeling model VBG cord-284810-fs5rx07q 382 40 Infectious infectious JJ cord-284810-fs5rx07q 382 41 Diseases Diseases NNPS cord-284810-fs5rx07q 382 42 in in IN cord-284810-fs5rx07q 382 43 Humans Humans NNPS cord-284810-fs5rx07q 382 44 and and CC cord-284810-fs5rx07q 383 1 Animals animal NNS cord-284810-fs5rx07q 383 2 A a DT cord-284810-fs5rx07q 383 3 contribution contribution NN cord-284810-fs5rx07q 383 4 to to IN cord-284810-fs5rx07q 383 5 the the DT cord-284810-fs5rx07q 383 6 mathematical mathematical JJ cord-284810-fs5rx07q 383 7 theory theory NN cord-284810-fs5rx07q 383 8 of of IN cord-284810-fs5rx07q 383 9 epidemics epidemic NNS cord-284810-fs5rx07q 384 1 Substantial substantial JJ cord-284810-fs5rx07q 384 2 undocumented undocumented JJ cord-284810-fs5rx07q 384 3 infection infection NN cord-284810-fs5rx07q 384 4 facilitates facilitate VBZ cord-284810-fs5rx07q 384 5 the the DT cord-284810-fs5rx07q 384 6 rapid rapid JJ cord-284810-fs5rx07q 384 7 dissemination dissemination NN cord-284810-fs5rx07q 384 8 of of IN cord-284810-fs5rx07q 384 9 novel novel JJ cord-284810-fs5rx07q 384 10 coronavirus coronavirus NN cord-284810-fs5rx07q 384 11 ( ( -LRB- cord-284810-fs5rx07q 384 12 SARS SARS NNP cord-284810-fs5rx07q 384 13 - - HYPH cord-284810-fs5rx07q 384 14 CoV2 CoV2 NNP cord-284810-fs5rx07q 384 15 ) ) -RRB- cord-284810-fs5rx07q 385 1 Effective effective JJ cord-284810-fs5rx07q 385 2 containment containment NN cord-284810-fs5rx07q 385 3 explains explain VBZ cord-284810-fs5rx07q 385 4 subexponential subexponential JJ cord-284810-fs5rx07q 385 5 growth growth NN cord-284810-fs5rx07q 385 6 in in IN cord-284810-fs5rx07q 385 7 recent recent JJ cord-284810-fs5rx07q 385 8 confirmed confirm VBD cord-284810-fs5rx07q 385 9 COVID-19 covid-19 CD cord-284810-fs5rx07q 385 10 cases case NNS cord-284810-fs5rx07q 385 11 in in IN cord-284810-fs5rx07q 385 12 China China NNP cord-284810-fs5rx07q 385 13 Strong strong JJ cord-284810-fs5rx07q 385 14 correlations correlation NNS cord-284810-fs5rx07q 385 15 between between IN cord-284810-fs5rx07q 385 16 power power NN cord-284810-fs5rx07q 385 17 - - HYPH cord-284810-fs5rx07q 385 18 law law NN cord-284810-fs5rx07q 385 19 growth growth NN cord-284810-fs5rx07q 385 20 of of IN cord-284810-fs5rx07q 385 21 COVID-19 covid-19 CD cord-284810-fs5rx07q 385 22 in in IN cord-284810-fs5rx07q 385 23 four four CD cord-284810-fs5rx07q 385 24 continents continent NNS cord-284810-fs5rx07q 385 25 and and CC cord-284810-fs5rx07q 385 26 the the DT cord-284810-fs5rx07q 385 27 inefficiency inefficiency NN cord-284810-fs5rx07q 385 28 of of IN cord-284810-fs5rx07q 385 29 soft soft JJ cord-284810-fs5rx07q 385 30 quarantine quarantine NN cord-284810-fs5rx07q 385 31 strategies strategy NNS cord-284810-fs5rx07q 386 1 A a DT cord-284810-fs5rx07q 386 2 brief brief JJ cord-284810-fs5rx07q 386 3 history history NN cord-284810-fs5rx07q 386 4 of of IN cord-284810-fs5rx07q 386 5 generative generative JJ cord-284810-fs5rx07q 386 6 models model NNS cord-284810-fs5rx07q 386 7 for for IN cord-284810-fs5rx07q 386 8 power power NN cord-284810-fs5rx07q 386 9 law law NN cord-284810-fs5rx07q 386 10 and and CC cord-284810-fs5rx07q 386 11 lognormal lognormal JJ cord-284810-fs5rx07q 386 12 distributions distribution NNS cord-284810-fs5rx07q 386 13 Optim Optim NNP cord-284810-fs5rx07q 386 14 : : : cord-284810-fs5rx07q 387 1 A a DT cord-284810-fs5rx07q 387 2 mathematical mathematical JJ cord-284810-fs5rx07q 387 3 optimization optimization NN cord-284810-fs5rx07q 387 4 package package NN cord-284810-fs5rx07q 387 5 for for IN cord-284810-fs5rx07q 387 6 Julia Julia NNP cord-284810-fs5rx07q 387 7 Power Power NNP cord-284810-fs5rx07q 387 8 laws law NNS cord-284810-fs5rx07q 387 9 , , , cord-284810-fs5rx07q 387 10 Pareto Pareto NNP cord-284810-fs5rx07q 387 11 distributions distribution NNS cord-284810-fs5rx07q 387 12 and and CC cord-284810-fs5rx07q 387 13 Zipf Zipf NNP cord-284810-fs5rx07q 387 14 's 's POS cord-284810-fs5rx07q 387 15 law law NN cord-284810-fs5rx07q 388 1 The the DT cord-284810-fs5rx07q 388 2 first first JJ cord-284810-fs5rx07q 388 3 - - HYPH cord-284810-fs5rx07q 388 4 mover mover NN cord-284810-fs5rx07q 388 5 advantage advantage NN cord-284810-fs5rx07q 388 6 in in IN cord-284810-fs5rx07q 388 7 scientific scientific JJ cord-284810-fs5rx07q 388 8 publication publication NN cord-284810-fs5rx07q 388 9 Networks network NNS cord-284810-fs5rx07q 388 10 : : : cord-284810-fs5rx07q 389 1 An an DT cord-284810-fs5rx07q 389 2 Introduction Introduction NNP cord-284810-fs5rx07q 389 3 Cours Cours NNP cord-284810-fs5rx07q 389 4 d'economie d'economie NNP cord-284810-fs5rx07q 390 1 Politique Politique NNP cord-284810-fs5rx07q 390 2 Novel Novel NNP cord-284810-fs5rx07q 390 3 coronavirus coronavirus NN cord-284810-fs5rx07q 390 4 ( ( -LRB- cord-284810-fs5rx07q 390 5 2019-nCoV 2019-ncov CD cord-284810-fs5rx07q 390 6 ) ) -RRB- cord-284810-fs5rx07q 390 7 early early JJ cord-284810-fs5rx07q 390 8 - - HYPH cord-284810-fs5rx07q 390 9 stage stage NN cord-284810-fs5rx07q 390 10 importation importation NN cord-284810-fs5rx07q 390 11 risk risk NN cord-284810-fs5rx07q 390 12 to to IN cord-284810-fs5rx07q 390 13 Europe Europe NNP cord-284810-fs5rx07q 390 14 Networks Networks NNP cord-284810-fs5rx07q 390 15 of of IN cord-284810-fs5rx07q 390 16 scientific scientific JJ cord-284810-fs5rx07q 390 17 papers paper NNS cord-284810-fs5rx07q 391 1 Differential differential JJ cord-284810-fs5rx07q 391 2 equations.jl equations.jl FW cord-284810-fs5rx07q 391 3 - - HYPH cord-284810-fs5rx07q 391 4 A a DT cord-284810-fs5rx07q 391 5 performant performant JJ cord-284810-fs5rx07q 391 6 and and CC cord-284810-fs5rx07q 391 7 featurerich featurerich JJ cord-284810-fs5rx07q 391 8 ecosystem ecosystem NN cord-284810-fs5rx07q 391 9 for for IN cord-284810-fs5rx07q 391 10 solving solve VBG cord-284810-fs5rx07q 391 11 differential differential JJ cord-284810-fs5rx07q 391 12 equations equation NNS cord-284810-fs5rx07q 391 13 in in IN cord-284810-fs5rx07q 391 14 Julia Julia NNP cord-284810-fs5rx07q 392 1 How how WRB cord-284810-fs5rx07q 392 2 popular popular JJ cord-284810-fs5rx07q 392 3 is be VBZ cord-284810-fs5rx07q 392 4 your -PRON- PRP$ cord-284810-fs5rx07q 392 5 paper paper NN cord-284810-fs5rx07q 392 6 ? ? . cord-284810-fs5rx07q 393 1 An an DT cord-284810-fs5rx07q 393 2 empirical empirical JJ cord-284810-fs5rx07q 393 3 study study NN cord-284810-fs5rx07q 393 4 of of IN cord-284810-fs5rx07q 393 5 the the DT cord-284810-fs5rx07q 393 6 citation citation NN cord-284810-fs5rx07q 393 7 distribution distribution NN cord-284810-fs5rx07q 394 1 The the DT cord-284810-fs5rx07q 394 2 risk risk NN cord-284810-fs5rx07q 394 3 of of IN cord-284810-fs5rx07q 394 4 marine marine JJ cord-284810-fs5rx07q 394 5 bioinvasion bioinvasion NN cord-284810-fs5rx07q 394 6 caused cause VBN cord-284810-fs5rx07q 394 7 by by IN cord-284810-fs5rx07q 394 8 global global JJ cord-284810-fs5rx07q 394 9 shipping shipping NN cord-284810-fs5rx07q 394 10 On on IN cord-284810-fs5rx07q 394 11 a a DT cord-284810-fs5rx07q 394 12 class class NN cord-284810-fs5rx07q 394 13 of of IN cord-284810-fs5rx07q 394 14 skew skew NN cord-284810-fs5rx07q 394 15 distribution distribution NN cord-284810-fs5rx07q 394 16 functions function NNS cord-284810-fs5rx07q 394 17 Critical Critical NNP cord-284810-fs5rx07q 394 18 Phenomena Phenomena NNP cord-284810-fs5rx07q 394 19 in in IN cord-284810-fs5rx07q 394 20 Natural Natural NNP cord-284810-fs5rx07q 394 21 Sciences Sciences NNPS cord-284810-fs5rx07q 394 22 Evolving evolve VBG cord-284810-fs5rx07q 394 23 epidemiology epidemiology NN cord-284810-fs5rx07q 394 24 and and CC cord-284810-fs5rx07q 394 25 impact impact NN cord-284810-fs5rx07q 394 26 of of IN cord-284810-fs5rx07q 394 27 non non JJ cord-284810-fs5rx07q 394 28 - - JJ cord-284810-fs5rx07q 394 29 pharmaceutical pharmaceutical JJ cord-284810-fs5rx07q 394 30 interventions intervention NNS cord-284810-fs5rx07q 394 31 on on IN cord-284810-fs5rx07q 394 32 the the DT cord-284810-fs5rx07q 394 33 outbreak outbreak NN cord-284810-fs5rx07q 394 34 of of IN cord-284810-fs5rx07q 394 35 coronavirus coronavirus NN cord-284810-fs5rx07q 394 36 disease disease NN cord-284810-fs5rx07q 394 37 Complexity complexity NN cord-284810-fs5rx07q 394 38 in in IN cord-284810-fs5rx07q 394 39 human human JJ cord-284810-fs5rx07q 394 40 transportation transportation NN cord-284810-fs5rx07q 394 41 networks network NNS cord-284810-fs5rx07q 394 42 : : : cord-284810-fs5rx07q 394 43 A a DT cord-284810-fs5rx07q 394 44 comparative comparative JJ cord-284810-fs5rx07q 394 45 analysis analysis NN cord-284810-fs5rx07q 394 46 of of IN cord-284810-fs5rx07q 395 1 worldwide worldwide RB cord-284810-fs5rx07q 395 2 air air NNP cord-284810-fs5rx07q 395 3 transportation transportation NN cord-284810-fs5rx07q 395 4 and and CC cord-284810-fs5rx07q 395 5 global global JJ cord-284810-fs5rx07q 395 6 cargo cargo NN cord-284810-fs5rx07q 395 7 - - HYPH cord-284810-fs5rx07q 395 8 ship ship NN cord-284810-fs5rx07q 395 9 movements movement NNS cord-284810-fs5rx07q 395 10 Coronavirus Coronavirus NNP cord-284810-fs5rx07q 395 11 disease disease NN cord-284810-fs5rx07q 395 12 ( ( -LRB- cord-284810-fs5rx07q 395 13 COVID-2019 COVID-2019 NNP cord-284810-fs5rx07q 395 14 ) ) -RRB- cord-284810-fs5rx07q 395 15 situation situation NN cord-284810-fs5rx07q 395 16 reports report VBZ cord-284810-fs5rx07q 395 17 The the DT cord-284810-fs5rx07q 395 18 GLEaMviz GLEaMviz NNP cord-284810-fs5rx07q 395 19 computational computational JJ cord-284810-fs5rx07q 395 20 tool tool NN cord-284810-fs5rx07q 395 21 , , , cord-284810-fs5rx07q 395 22 a a DT cord-284810-fs5rx07q 395 23 publicly publicly RB cord-284810-fs5rx07q 395 24 available available JJ cord-284810-fs5rx07q 395 25 software software NN cord-284810-fs5rx07q 395 26 to to TO cord-284810-fs5rx07q 395 27 explore explore VB cord-284810-fs5rx07q 395 28 realistic realistic JJ cord-284810-fs5rx07q 395 29 epidemic epidemic NN cord-284810-fs5rx07q 395 30 spreading spread VBG cord-284810-fs5rx07q 395 31 scenarios scenario NNS cord-284810-fs5rx07q 395 32 at at IN cord-284810-fs5rx07q 395 33 the the DT cord-284810-fs5rx07q 395 34 global global JJ cord-284810-fs5rx07q 395 35 scale scale NN cord-284810-fs5rx07q 395 36 Levy Levy NNP cord-284810-fs5rx07q 395 37 flight flight NN cord-284810-fs5rx07q 395 38 search search NN cord-284810-fs5rx07q 395 39 patterns pattern NNS cord-284810-fs5rx07q 395 40 of of IN cord-284810-fs5rx07q 395 41 wandering wander VBG cord-284810-fs5rx07q 395 42 albatrosses albatross NNS cord-284810-fs5rx07q 395 43 On on IN cord-284810-fs5rx07q 395 44 estimating estimate VBG cord-284810-fs5rx07q 395 45 the the DT cord-284810-fs5rx07q 395 46 exponent exponent NN cord-284810-fs5rx07q 395 47 of of IN cord-284810-fs5rx07q 395 48 power power NN cord-284810-fs5rx07q 395 49 ? ? . cord-284810-fs5rx07q 396 1 Law law NN cord-284810-fs5rx07q 396 2 frequency frequency NN cord-284810-fs5rx07q 396 3 distributions distribution NNS cord-284810-fs5rx07q 397 1 A a DT cord-284810-fs5rx07q 397 2 mathematical mathematical JJ cord-284810-fs5rx07q 397 3 theory theory NN cord-284810-fs5rx07q 397 4 of of IN cord-284810-fs5rx07q 397 5 evolution evolution NN cord-284810-fs5rx07q 397 6 based base VBN cord-284810-fs5rx07q 397 7 on on IN cord-284810-fs5rx07q 397 8 the the DT cord-284810-fs5rx07q 397 9 conclusions conclusion NNS cord-284810-fs5rx07q 397 10 of of IN cord-284810-fs5rx07q 397 11 Human Human NNP cord-284810-fs5rx07q 397 12 Behavior Behavior NNP cord-284810-fs5rx07q 397 13 and and CC cord-284810-fs5rx07q 397 14 The the DT cord-284810-fs5rx07q 397 15 Principle Principle NNP cord-284810-fs5rx07q 397 16 of of IN cord-284810-fs5rx07q 397 17 Least Least JJS cord-284810-fs5rx07q 397 18 Effort Effort NNP