id sid tid token lemma pos cord-229937-fy90oebs 1 1 key key JJ cord-229937-fy90oebs 2 1 : : : cord-229937-fy90oebs 2 2 cord-229937-fy90oebs cord-229937-fy90oebs NN cord-229937-fy90oebs 2 3 authors author NNS cord-229937-fy90oebs 2 4 : : : cord-229937-fy90oebs 3 1 Amaro Amaro NNP cord-229937-fy90oebs 3 2 , , , cord-229937-fy90oebs 3 3 J. J. NNP cord-229937-fy90oebs 3 4 E. E. NNP cord-229937-fy90oebs 3 5 ; ; : cord-229937-fy90oebs 3 6 Dudouet Dudouet NNP cord-229937-fy90oebs 3 7 , , , cord-229937-fy90oebs 3 8 J. J. NNP cord-229937-fy90oebs 3 9 ; ; : cord-229937-fy90oebs 3 10 Orce Orce NNP cord-229937-fy90oebs 3 11 , , , cord-229937-fy90oebs 3 12 J. J. NNP cord-229937-fy90oebs 3 13 N. N. NNP cord-229937-fy90oebs 3 14 title title NN cord-229937-fy90oebs 3 15 : : : cord-229937-fy90oebs 4 1 Global global JJ cord-229937-fy90oebs 4 2 analysis analysis NN cord-229937-fy90oebs 4 3 of of IN cord-229937-fy90oebs 4 4 the the DT cord-229937-fy90oebs 4 5 COVID-19 covid-19 JJ cord-229937-fy90oebs 4 6 pandemic pandemic NN cord-229937-fy90oebs 4 7 using use VBG cord-229937-fy90oebs 4 8 simple simple JJ cord-229937-fy90oebs 4 9 epidemiological epidemiological JJ cord-229937-fy90oebs 4 10 models model NNS cord-229937-fy90oebs 4 11 date date NN cord-229937-fy90oebs 4 12 : : : cord-229937-fy90oebs 4 13 2020 2020 CD cord-229937-fy90oebs 4 14 - - HYPH cord-229937-fy90oebs 4 15 05 05 CD cord-229937-fy90oebs 4 16 - - SYM cord-229937-fy90oebs 4 17 14 14 CD cord-229937-fy90oebs 4 18 journal journal NN cord-229937-fy90oebs 4 19 : : : cord-229937-fy90oebs 5 1 nan nan NNP cord-229937-fy90oebs 5 2 DOI DOI NNP cord-229937-fy90oebs 5 3 : : : cord-229937-fy90oebs 5 4 nan nan NNP cord-229937-fy90oebs 5 5 sha sha NNP cord-229937-fy90oebs 5 6 : : : cord-229937-fy90oebs 5 7 afb462d1840f57be1e7800c3344b53cedd4a5d1c afb462d1840f57be1e7800c3344b53cedd4a5d1c NNP cord-229937-fy90oebs 5 8 doc_id doc_id '' cord-229937-fy90oebs 5 9 : : : cord-229937-fy90oebs 5 10 229937 229937 CD cord-229937-fy90oebs 5 11 cord_uid cord_uid NNS cord-229937-fy90oebs 5 12 : : : cord-229937-fy90oebs 5 13 fy90oebs fy90oebs NNP cord-229937-fy90oebs 6 1 Several several JJ cord-229937-fy90oebs 6 2 analytical analytical JJ cord-229937-fy90oebs 6 3 models model NNS cord-229937-fy90oebs 6 4 have have VBP cord-229937-fy90oebs 6 5 been be VBN cord-229937-fy90oebs 6 6 used use VBN cord-229937-fy90oebs 6 7 in in IN cord-229937-fy90oebs 6 8 this this DT cord-229937-fy90oebs 6 9 work work NN cord-229937-fy90oebs 6 10 to to TO cord-229937-fy90oebs 6 11 describe describe VB cord-229937-fy90oebs 6 12 the the DT cord-229937-fy90oebs 6 13 evolution evolution NN cord-229937-fy90oebs 6 14 of of IN cord-229937-fy90oebs 6 15 death death NN cord-229937-fy90oebs 6 16 cases case NNS cord-229937-fy90oebs 6 17 arising arise VBG cord-229937-fy90oebs 6 18 from from IN cord-229937-fy90oebs 6 19 coronavirus coronavirus NN cord-229937-fy90oebs 6 20 ( ( -LRB- cord-229937-fy90oebs 6 21 COVID-19 COVID-19 NNP cord-229937-fy90oebs 6 22 ) ) -RRB- cord-229937-fy90oebs 6 23 . . . cord-229937-fy90oebs 7 1 The the DT cord-229937-fy90oebs 7 2 Death death NN cord-229937-fy90oebs 7 3 or or CC cord-229937-fy90oebs 7 4 ` ` '' cord-229937-fy90oebs 7 5 D D NNP cord-229937-fy90oebs 7 6 ' ' '' cord-229937-fy90oebs 7 7 model model NN cord-229937-fy90oebs 7 8 is be VBZ cord-229937-fy90oebs 7 9 a a DT cord-229937-fy90oebs 7 10 simplified simplified JJ cord-229937-fy90oebs 7 11 version version NN cord-229937-fy90oebs 7 12 of of IN cord-229937-fy90oebs 7 13 the the DT cord-229937-fy90oebs 7 14 SIR SIR NNP cord-229937-fy90oebs 7 15 ( ( -LRB- cord-229937-fy90oebs 7 16 susceptible susceptible JJ cord-229937-fy90oebs 7 17 - - HYPH cord-229937-fy90oebs 7 18 infected infected JJ cord-229937-fy90oebs 7 19 - - HYPH cord-229937-fy90oebs 7 20 recovered recovered JJ cord-229937-fy90oebs 7 21 ) ) -RRB- cord-229937-fy90oebs 7 22 model model NN cord-229937-fy90oebs 7 23 , , , cord-229937-fy90oebs 7 24 which which WDT cord-229937-fy90oebs 7 25 assumes assume VBZ cord-229937-fy90oebs 7 26 no no DT cord-229937-fy90oebs 7 27 recovery recovery NN cord-229937-fy90oebs 7 28 over over IN cord-229937-fy90oebs 7 29 time time NN cord-229937-fy90oebs 7 30 , , , cord-229937-fy90oebs 7 31 and and CC cord-229937-fy90oebs 7 32 allows allow VBZ cord-229937-fy90oebs 7 33 for for IN cord-229937-fy90oebs 7 34 the the DT cord-229937-fy90oebs 7 35 transmission transmission NN cord-229937-fy90oebs 7 36 - - HYPH cord-229937-fy90oebs 7 37 dynamics dynamic NNS cord-229937-fy90oebs 7 38 equations equation NNS cord-229937-fy90oebs 7 39 to to TO cord-229937-fy90oebs 7 40 be be VB cord-229937-fy90oebs 7 41 solved solve VBN cord-229937-fy90oebs 7 42 analytically analytically RB cord-229937-fy90oebs 7 43 . . . cord-229937-fy90oebs 8 1 The the DT cord-229937-fy90oebs 8 2 D d NN cord-229937-fy90oebs 8 3 - - HYPH cord-229937-fy90oebs 8 4 model model NN cord-229937-fy90oebs 8 5 can can MD cord-229937-fy90oebs 8 6 be be VB cord-229937-fy90oebs 8 7 extended extend VBN cord-229937-fy90oebs 8 8 to to TO cord-229937-fy90oebs 8 9 describe describe VB cord-229937-fy90oebs 8 10 various various JJ cord-229937-fy90oebs 8 11 focuses focus NNS cord-229937-fy90oebs 8 12 of of IN cord-229937-fy90oebs 8 13 infection infection NN cord-229937-fy90oebs 8 14 , , , cord-229937-fy90oebs 8 15 which which WDT cord-229937-fy90oebs 8 16 may may MD cord-229937-fy90oebs 8 17 account account VB cord-229937-fy90oebs 8 18 for for IN cord-229937-fy90oebs 8 19 the the DT cord-229937-fy90oebs 8 20 original original JJ cord-229937-fy90oebs 8 21 pandemic pandemic NN cord-229937-fy90oebs 8 22 ( ( -LRB- cord-229937-fy90oebs 8 23 D1 D1 NNP cord-229937-fy90oebs 8 24 ) ) -RRB- cord-229937-fy90oebs 8 25 , , , cord-229937-fy90oebs 8 26 the the DT cord-229937-fy90oebs 8 27 lockdown lockdown NN cord-229937-fy90oebs 8 28 ( ( -LRB- cord-229937-fy90oebs 8 29 D2 D2 NNP cord-229937-fy90oebs 8 30 ) ) -RRB- cord-229937-fy90oebs 8 31 and and CC cord-229937-fy90oebs 8 32 other other JJ cord-229937-fy90oebs 8 33 effects effect NNS cord-229937-fy90oebs 8 34 ( ( -LRB- cord-229937-fy90oebs 8 35 Dn Dn NNP cord-229937-fy90oebs 8 36 ) ) -RRB- cord-229937-fy90oebs 8 37 . . . cord-229937-fy90oebs 9 1 The the DT cord-229937-fy90oebs 9 2 evolution evolution NN cord-229937-fy90oebs 9 3 of of IN cord-229937-fy90oebs 9 4 the the DT cord-229937-fy90oebs 9 5 COVID-19 covid-19 JJ cord-229937-fy90oebs 9 6 pandemic pandemic NN cord-229937-fy90oebs 9 7 in in IN cord-229937-fy90oebs 9 8 several several JJ cord-229937-fy90oebs 9 9 countries country NNS cord-229937-fy90oebs 9 10 ( ( -LRB- cord-229937-fy90oebs 9 11 China China NNP cord-229937-fy90oebs 9 12 , , , cord-229937-fy90oebs 9 13 Spain Spain NNP cord-229937-fy90oebs 9 14 , , , cord-229937-fy90oebs 9 15 Italy Italy NNP cord-229937-fy90oebs 9 16 , , , cord-229937-fy90oebs 9 17 France France NNP cord-229937-fy90oebs 9 18 , , , cord-229937-fy90oebs 9 19 UK UK NNP cord-229937-fy90oebs 9 20 , , , cord-229937-fy90oebs 9 21 Iran Iran NNP cord-229937-fy90oebs 9 22 , , , cord-229937-fy90oebs 9 23 USA USA NNP cord-229937-fy90oebs 9 24 and and CC cord-229937-fy90oebs 9 25 Germany Germany NNP cord-229937-fy90oebs 9 26 ) ) -RRB- cord-229937-fy90oebs 9 27 shows show VBZ cord-229937-fy90oebs 9 28 a a DT cord-229937-fy90oebs 9 29 similar similar JJ cord-229937-fy90oebs 9 30 behavior behavior NN cord-229937-fy90oebs 9 31 in in IN cord-229937-fy90oebs 9 32 concord concord NNP cord-229937-fy90oebs 9 33 with with IN cord-229937-fy90oebs 9 34 the the DT cord-229937-fy90oebs 9 35 D d NN cord-229937-fy90oebs 9 36 - - HYPH cord-229937-fy90oebs 9 37 model model NN cord-229937-fy90oebs 9 38 trend trend NN cord-229937-fy90oebs 9 39 , , , cord-229937-fy90oebs 9 40 characterized characterize VBN cord-229937-fy90oebs 9 41 by by IN cord-229937-fy90oebs 9 42 a a DT cord-229937-fy90oebs 9 43 rapid rapid JJ cord-229937-fy90oebs 9 44 increase increase NN cord-229937-fy90oebs 9 45 of of IN cord-229937-fy90oebs 9 46 death death NN cord-229937-fy90oebs 9 47 cases case NNS cord-229937-fy90oebs 9 48 followed follow VBN cord-229937-fy90oebs 9 49 by by IN cord-229937-fy90oebs 9 50 a a DT cord-229937-fy90oebs 9 51 slow slow JJ cord-229937-fy90oebs 9 52 decline decline NN cord-229937-fy90oebs 9 53 , , , cord-229937-fy90oebs 9 54 which which WDT cord-229937-fy90oebs 9 55 are be VBP cord-229937-fy90oebs 9 56 affected affect VBN cord-229937-fy90oebs 9 57 by by IN cord-229937-fy90oebs 9 58 the the DT cord-229937-fy90oebs 9 59 earliness earliness NN cord-229937-fy90oebs 9 60 and and CC cord-229937-fy90oebs 9 61 efficiency efficiency NN cord-229937-fy90oebs 9 62 of of IN cord-229937-fy90oebs 9 63 the the DT cord-229937-fy90oebs 9 64 lockdown lockdown NN cord-229937-fy90oebs 9 65 effect effect NN cord-229937-fy90oebs 9 66 . . . cord-229937-fy90oebs 10 1 These these DT cord-229937-fy90oebs 10 2 results result NNS cord-229937-fy90oebs 10 3 are be VBP cord-229937-fy90oebs 10 4 in in IN cord-229937-fy90oebs 10 5 agreement agreement NN cord-229937-fy90oebs 10 6 with with IN cord-229937-fy90oebs 10 7 more more RBR cord-229937-fy90oebs 10 8 accurate accurate JJ cord-229937-fy90oebs 10 9 calculations calculation NNS cord-229937-fy90oebs 10 10 using use VBG cord-229937-fy90oebs 10 11 the the DT cord-229937-fy90oebs 10 12 extended extended JJ cord-229937-fy90oebs 10 13 SIR SIR NNP cord-229937-fy90oebs 10 14 model model NN cord-229937-fy90oebs 10 15 with with IN cord-229937-fy90oebs 10 16 a a DT cord-229937-fy90oebs 10 17 parametrized parametrize VBN cord-229937-fy90oebs 10 18 solution solution NN cord-229937-fy90oebs 10 19 and and CC cord-229937-fy90oebs 10 20 more more RBR cord-229937-fy90oebs 10 21 sophisticated sophisticated JJ cord-229937-fy90oebs 10 22 Monte Monte NNP cord-229937-fy90oebs 10 23 Carlo Carlo NNP cord-229937-fy90oebs 10 24 grid grid NN cord-229937-fy90oebs 10 25 simulations simulation NNS cord-229937-fy90oebs 10 26 , , , cord-229937-fy90oebs 10 27 which which WDT cord-229937-fy90oebs 10 28 predict predict VBP cord-229937-fy90oebs 10 29 similar similar JJ cord-229937-fy90oebs 10 30 trends trend NNS cord-229937-fy90oebs 10 31 and and CC cord-229937-fy90oebs 10 32 indicate indicate VBP cord-229937-fy90oebs 10 33 a a DT cord-229937-fy90oebs 10 34 common common JJ cord-229937-fy90oebs 10 35 evolution evolution NN cord-229937-fy90oebs 10 36 of of IN cord-229937-fy90oebs 10 37 the the DT cord-229937-fy90oebs 10 38 pandemic pandemic NN cord-229937-fy90oebs 10 39 with with IN cord-229937-fy90oebs 10 40 universal universal JJ cord-229937-fy90oebs 10 41 parameters parameter NNS cord-229937-fy90oebs 10 42 . . . cord-229937-fy90oebs 11 1 The the DT cord-229937-fy90oebs 11 2 SIR SIR NNP cord-229937-fy90oebs 11 3 ( ( -LRB- cord-229937-fy90oebs 11 4 susceptible susceptible JJ cord-229937-fy90oebs 11 5 - - HYPH cord-229937-fy90oebs 11 6 infected infected JJ cord-229937-fy90oebs 11 7 - - HYPH cord-229937-fy90oebs 11 8 recovered recovered JJ cord-229937-fy90oebs 11 9 ) ) -RRB- cord-229937-fy90oebs 11 10 model model NN cord-229937-fy90oebs 11 11 is be VBZ cord-229937-fy90oebs 11 12 widely widely RB cord-229937-fy90oebs 11 13 used use VBN cord-229937-fy90oebs 11 14 as as IN cord-229937-fy90oebs 11 15 first first JJ cord-229937-fy90oebs 11 16 - - HYPH cord-229937-fy90oebs 11 17 order order NN cord-229937-fy90oebs 11 18 approximation approximation NN cord-229937-fy90oebs 11 19 to to IN cord-229937-fy90oebs 11 20 viral viral JJ cord-229937-fy90oebs 11 21 spreading spreading NN cord-229937-fy90oebs 11 22 of of IN cord-229937-fy90oebs 11 23 contagious contagious JJ cord-229937-fy90oebs 11 24 epidemics epidemic NNS cord-229937-fy90oebs 11 25 [ [ -LRB- cord-229937-fy90oebs 11 26 1 1 CD cord-229937-fy90oebs 11 27 ] ] -RRB- cord-229937-fy90oebs 11 28 , , , cord-229937-fy90oebs 11 29 mass mass NN cord-229937-fy90oebs 11 30 immunization immunization NN cord-229937-fy90oebs 11 31 planning planning NN cord-229937-fy90oebs 11 32 [ [ -LRB- cord-229937-fy90oebs 11 33 2 2 CD cord-229937-fy90oebs 11 34 , , , cord-229937-fy90oebs 11 35 3 3 CD cord-229937-fy90oebs 11 36 ] ] -RRB- cord-229937-fy90oebs 11 37 , , , cord-229937-fy90oebs 11 38 marketing marketing NN cord-229937-fy90oebs 11 39 , , , cord-229937-fy90oebs 11 40 informatics informatics NN cord-229937-fy90oebs 11 41 and and CC cord-229937-fy90oebs 11 42 social social JJ cord-229937-fy90oebs 11 43 networks network NNS cord-229937-fy90oebs 11 44 [ [ -LRB- cord-229937-fy90oebs 11 45 4 4 CD cord-229937-fy90oebs 11 46 ] ] -RRB- cord-229937-fy90oebs 11 47 . . . cord-229937-fy90oebs 12 1 Its -PRON- PRP$ cord-229937-fy90oebs 12 2 cornerstone cornerstone NN cord-229937-fy90oebs 12 3 is be VBZ cord-229937-fy90oebs 12 4 the the DT cord-229937-fy90oebs 12 5 so so RB cord-229937-fy90oebs 12 6 - - HYPH cord-229937-fy90oebs 12 7 called call VBN cord-229937-fy90oebs 12 8 " " `` cord-229937-fy90oebs 12 9 mass mass JJ cord-229937-fy90oebs 12 10 - - HYPH cord-229937-fy90oebs 12 11 action action NN cord-229937-fy90oebs 12 12 " " '' cord-229937-fy90oebs 12 13 principle principle NN cord-229937-fy90oebs 12 14 introduced introduce VBN cord-229937-fy90oebs 12 15 by by IN cord-229937-fy90oebs 12 16 Hamer Hamer NNP cord-229937-fy90oebs 12 17 , , , cord-229937-fy90oebs 12 18 which which WDT cord-229937-fy90oebs 12 19 assumes assume VBZ cord-229937-fy90oebs 12 20 that that IN cord-229937-fy90oebs 12 21 the the DT cord-229937-fy90oebs 12 22 course course NN cord-229937-fy90oebs 12 23 of of IN cord-229937-fy90oebs 12 24 an an DT cord-229937-fy90oebs 12 25 epidemic epidemic NN cord-229937-fy90oebs 12 26 depends depend VBZ cord-229937-fy90oebs 12 27 on on IN cord-229937-fy90oebs 12 28 the the DT cord-229937-fy90oebs 12 29 rate rate NN cord-229937-fy90oebs 12 30 of of IN cord-229937-fy90oebs 12 31 contact contact NN cord-229937-fy90oebs 12 32 between between IN cord-229937-fy90oebs 12 33 susceptible susceptible JJ cord-229937-fy90oebs 12 34 and and CC cord-229937-fy90oebs 12 35 infected infected JJ cord-229937-fy90oebs 12 36 individuals individual NNS cord-229937-fy90oebs 12 37 [ [ -LRB- cord-229937-fy90oebs 12 38 5 5 CD cord-229937-fy90oebs 12 39 ] ] -RRB- cord-229937-fy90oebs 12 40 . . . cord-229937-fy90oebs 13 1 This this DT cord-229937-fy90oebs 13 2 idea idea NN cord-229937-fy90oebs 13 3 was be VBD cord-229937-fy90oebs 13 4 extended extend VBN cord-229937-fy90oebs 13 5 to to IN cord-229937-fy90oebs 13 6 a a DT cord-229937-fy90oebs 13 7 continuous continuous JJ cord-229937-fy90oebs 13 8 time time NN cord-229937-fy90oebs 13 9 framework framework NN cord-229937-fy90oebs 13 10 by by IN cord-229937-fy90oebs 13 11 Ross Ross NNP cord-229937-fy90oebs 13 12 in in IN cord-229937-fy90oebs 13 13 his -PRON- PRP$ cord-229937-fy90oebs 13 14 pioneering pioneering JJ cord-229937-fy90oebs 13 15 work work NN cord-229937-fy90oebs 13 16 on on IN cord-229937-fy90oebs 13 17 malaria malaria NN cord-229937-fy90oebs 13 18 transmission transmission NN cord-229937-fy90oebs 13 19 dynamics dynamic NNS cord-229937-fy90oebs 13 20 [ [ -LRB- cord-229937-fy90oebs 13 21 6 6 CD cord-229937-fy90oebs 13 22 ] ] -RRB- cord-229937-fy90oebs 13 23 [ [ -LRB- cord-229937-fy90oebs 13 24 7 7 CD cord-229937-fy90oebs 13 25 ] ] -RRB- cord-229937-fy90oebs 13 26 [ [ -LRB- cord-229937-fy90oebs 13 27 8 8 CD cord-229937-fy90oebs 13 28 ] ] -RRB- cord-229937-fy90oebs 13 29 , , , cord-229937-fy90oebs 13 30 and and CC cord-229937-fy90oebs 13 31 finally finally RB cord-229937-fy90oebs 13 32 put put VB cord-229937-fy90oebs 13 33 into into IN cord-229937-fy90oebs 13 34 its -PRON- PRP$ cord-229937-fy90oebs 13 35 classic classic JJ cord-229937-fy90oebs 13 36 mathematical mathematical JJ cord-229937-fy90oebs 13 37 form form NN cord-229937-fy90oebs 13 38 by by IN cord-229937-fy90oebs 13 39 Kermack Kermack NNP cord-229937-fy90oebs 13 40 and and CC cord-229937-fy90oebs 13 41 McKendric McKendric NNP cord-229937-fy90oebs 13 42 [ [ -LRB- cord-229937-fy90oebs 13 43 9 9 CD cord-229937-fy90oebs 13 44 ] ] -RRB- cord-229937-fy90oebs 13 45 . . . cord-229937-fy90oebs 14 1 The the DT cord-229937-fy90oebs 14 2 SIR SIR NNP cord-229937-fy90oebs 14 3 model model NN cord-229937-fy90oebs 14 4 was be VBD cord-229937-fy90oebs 14 5 further further RB cord-229937-fy90oebs 14 6 developed develop VBN cord-229937-fy90oebs 14 7 by by IN cord-229937-fy90oebs 14 8 Kendall Kendall NNP cord-229937-fy90oebs 14 9 , , , cord-229937-fy90oebs 14 10 who who WP cord-229937-fy90oebs 14 11 provided provide VBD cord-229937-fy90oebs 14 12 a a DT cord-229937-fy90oebs 14 13 spatial spatial JJ cord-229937-fy90oebs 14 14 generalization generalization NN cord-229937-fy90oebs 14 15 of of IN cord-229937-fy90oebs 14 16 the the DT cord-229937-fy90oebs 14 17 Kermack Kermack NNP cord-229937-fy90oebs 14 18 and and CC cord-229937-fy90oebs 14 19 McKendrick McKendrick NNP cord-229937-fy90oebs 14 20 model model NN cord-229937-fy90oebs 14 21 in in IN cord-229937-fy90oebs 14 22 a a DT cord-229937-fy90oebs 14 23 closed closed JJ cord-229937-fy90oebs 14 24 population population NN cord-229937-fy90oebs 14 25 [ [ -LRB- cord-229937-fy90oebs 14 26 10 10 CD cord-229937-fy90oebs 14 27 ] ] -RRB- cord-229937-fy90oebs 14 28 ( ( -LRB- cord-229937-fy90oebs 15 1 i.e. i.e. FW cord-229937-fy90oebs 15 2 neglecting neglect VBG cord-229937-fy90oebs 15 3 the the DT cord-229937-fy90oebs 15 4 effects effect NNS cord-229937-fy90oebs 15 5 of of IN cord-229937-fy90oebs 15 6 spatial spatial JJ cord-229937-fy90oebs 15 7 migration migration NN cord-229937-fy90oebs 15 8 ) ) -RRB- cord-229937-fy90oebs 15 9 , , , cord-229937-fy90oebs 15 10 and and CC cord-229937-fy90oebs 15 11 Bartlett Bartlett NNP cord-229937-fy90oebs 15 12 , , , cord-229937-fy90oebs 15 13 who who WP cord-229937-fy90oebs 15 14 -after -after VBP cord-229937-fy90oebs 15 15 investigating investigate VBG cord-229937-fy90oebs 15 16 the the DT cord-229937-fy90oebs 15 17 connection connection NN cord-229937-fy90oebs 15 18 between between IN cord-229937-fy90oebs 15 19 the the DT cord-229937-fy90oebs 15 20 periodicity periodicity NN cord-229937-fy90oebs 15 21 of of IN cord-229937-fy90oebs 15 22 measles measles NN cord-229937-fy90oebs 15 23 epidemics epidemic NNS cord-229937-fy90oebs 15 24 and and CC cord-229937-fy90oebs 15 25 community community NN cord-229937-fy90oebs 15 26 size size NN cord-229937-fy90oebs 15 27 -predicted -predicte VBN cord-229937-fy90oebs 16 1 a a DT cord-229937-fy90oebs 16 2 traveling travel VBG cord-229937-fy90oebs 16 3 wave wave NN cord-229937-fy90oebs 16 4 of of IN cord-229937-fy90oebs 16 5 infection infection NN cord-229937-fy90oebs 16 6 moving move VBG cord-229937-fy90oebs 16 7 out out RP cord-229937-fy90oebs 16 8 from from IN cord-229937-fy90oebs 16 9 the the DT cord-229937-fy90oebs 16 10 initial initial JJ cord-229937-fy90oebs 16 11 source source NN cord-229937-fy90oebs 16 12 of of IN cord-229937-fy90oebs 16 13 infection infection NN cord-229937-fy90oebs 16 14 [ [ -LRB- cord-229937-fy90oebs 16 15 11 11 CD cord-229937-fy90oebs 16 16 , , , cord-229937-fy90oebs 16 17 12 12 CD cord-229937-fy90oebs 16 18 ] ] -RRB- cord-229937-fy90oebs 16 19 . . . cord-229937-fy90oebs 17 1 More More JJR cord-229937-fy90oebs 17 2 recent recent JJ cord-229937-fy90oebs 17 3 implementations implementation NNS cord-229937-fy90oebs 17 4 have have VBP cord-229937-fy90oebs 17 5 considered consider VBN cord-229937-fy90oebs 17 6 the the DT cord-229937-fy90oebs 17 7 typical typical JJ cord-229937-fy90oebs 17 8 incubation incubation NN cord-229937-fy90oebs 17 9 period period NN cord-229937-fy90oebs 17 10 of of IN cord-229937-fy90oebs 17 11 the the DT cord-229937-fy90oebs 17 12 disease disease NN cord-229937-fy90oebs 17 13 and and CC cord-229937-fy90oebs 17 14 the the DT cord-229937-fy90oebs 17 15 spatial spatial JJ cord-229937-fy90oebs 17 16 migration migration NN cord-229937-fy90oebs 17 17 of of IN cord-229937-fy90oebs 17 18 the the DT cord-229937-fy90oebs 17 19 population population NN cord-229937-fy90oebs 17 20 . . . cord-229937-fy90oebs 18 1 The the DT cord-229937-fy90oebs 18 2 pandemic pandemic NN cord-229937-fy90oebs 18 3 has have VBZ cord-229937-fy90oebs 18 4 ignited ignite VBN cord-229937-fy90oebs 18 5 the the DT cord-229937-fy90oebs 18 6 submission submission NN cord-229937-fy90oebs 18 7 of of IN cord-229937-fy90oebs 18 8 multiple multiple JJ cord-229937-fy90oebs 18 9 manuscripts manuscript NNS cord-229937-fy90oebs 18 10 in in IN cord-229937-fy90oebs 18 11 the the DT cord-229937-fy90oebs 18 12 last last JJ cord-229937-fy90oebs 18 13 weeks week NNS cord-229937-fy90oebs 18 14 . . . cord-229937-fy90oebs 19 1 Most Most JJS cord-229937-fy90oebs 19 2 statistical statistical JJ cord-229937-fy90oebs 19 3 distributions distribution NNS cord-229937-fy90oebs 19 4 used use VBN cord-229937-fy90oebs 19 5 to to TO cord-229937-fy90oebs 19 6 estimate estimate VB cord-229937-fy90oebs 19 7 disease disease NN cord-229937-fy90oebs 19 8 occurrence occurrence NN cord-229937-fy90oebs 19 9 are be VBP cord-229937-fy90oebs 19 10 of of IN cord-229937-fy90oebs 19 11 the the DT cord-229937-fy90oebs 19 12 binomial binomial NN cord-229937-fy90oebs 19 13 , , , cord-229937-fy90oebs 19 14 Poisson Poisson NNP cord-229937-fy90oebs 19 15 , , , cord-229937-fy90oebs 19 16 Gaussian Gaussian NNP cord-229937-fy90oebs 19 17 , , , cord-229937-fy90oebs 19 18 Fermi Fermi NNP cord-229937-fy90oebs 19 19 or or CC cord-229937-fy90oebs 19 20 exponential exponential JJ cord-229937-fy90oebs 19 21 types type NNS cord-229937-fy90oebs 19 22 . . . cord-229937-fy90oebs 20 1 Despite despite IN cord-229937-fy90oebs 20 2 their -PRON- PRP$ cord-229937-fy90oebs 20 3 intrinsic intrinsic JJ cord-229937-fy90oebs 20 4 differences difference NNS cord-229937-fy90oebs 20 5 , , , cord-229937-fy90oebs 20 6 these these DT cord-229937-fy90oebs 20 7 distributions distribution NNS cord-229937-fy90oebs 20 8 generally generally RB cord-229937-fy90oebs 20 9 lead lead VBP cord-229937-fy90oebs 20 10 to to IN cord-229937-fy90oebs 20 11 similar similar JJ cord-229937-fy90oebs 20 12 results result NNS cord-229937-fy90oebs 20 13 , , , cord-229937-fy90oebs 20 14 assuming assume VBG cord-229937-fy90oebs 20 15 independence independence NN cord-229937-fy90oebs 20 16 and and CC cord-229937-fy90oebs 20 17 homogeneity homogeneity NN cord-229937-fy90oebs 20 18 of of IN cord-229937-fy90oebs 20 19 disease disease NN cord-229937-fy90oebs 20 20 risks risk NNS cord-229937-fy90oebs 20 21 [ [ -LRB- cord-229937-fy90oebs 20 22 13 13 CD cord-229937-fy90oebs 20 23 ] ] -RRB- cord-229937-fy90oebs 20 24 . . . cord-229937-fy90oebs 21 1 In in IN cord-229937-fy90oebs 21 2 this this DT cord-229937-fy90oebs 21 3 work work NN cord-229937-fy90oebs 21 4 , , , cord-229937-fy90oebs 21 5 we -PRON- PRP cord-229937-fy90oebs 21 6 propose propose VBP cord-229937-fy90oebs 21 7 a a DT cord-229937-fy90oebs 21 8 simple simple JJ cord-229937-fy90oebs 21 9 and and CC cord-229937-fy90oebs 21 10 easy easy JJ cord-229937-fy90oebs 21 11 - - HYPH cord-229937-fy90oebs 21 12 to to TO cord-229937-fy90oebs 21 13 - - HYPH cord-229937-fy90oebs 21 14 use use VB cord-229937-fy90oebs 21 15 epidemiological epidemiological JJ cord-229937-fy90oebs 21 16 model model NN cord-229937-fy90oebs 21 17 -the -the ADD cord-229937-fy90oebs 21 18 Death death NN cord-229937-fy90oebs 21 19 or or CC cord-229937-fy90oebs 21 20 D d NN cord-229937-fy90oebs 21 21 model model NN cord-229937-fy90oebs 21 22 [ [ -LRB- cord-229937-fy90oebs 21 23 14 14 CD cord-229937-fy90oebs 21 24 ] ] -RRB- cord-229937-fy90oebs 22 1 -that -that WP cord-229937-fy90oebs 22 2 can can MD cord-229937-fy90oebs 22 3 be be VB cord-229937-fy90oebs 22 4 compared compare VBN cord-229937-fy90oebs 22 5 with with IN cord-229937-fy90oebs 22 6 data datum NNS cord-229937-fy90oebs 22 7 in in IN cord-229937-fy90oebs 22 8 order order NN cord-229937-fy90oebs 22 9 to to TO cord-229937-fy90oebs 22 10 investigate investigate VB cord-229937-fy90oebs 22 11 the the DT cord-229937-fy90oebs 22 12 evolution evolution NN cord-229937-fy90oebs 22 13 of of IN cord-229937-fy90oebs 22 14 the the DT cord-229937-fy90oebs 22 15 infection infection NN cord-229937-fy90oebs 22 16 and and CC cord-229937-fy90oebs 22 17 deviations deviation NNS cord-229937-fy90oebs 22 18 from from IN cord-229937-fy90oebs 22 19 the the DT cord-229937-fy90oebs 22 20 predicted predict VBN cord-229937-fy90oebs 22 21 trends trend NNS cord-229937-fy90oebs 22 22 . . . cord-229937-fy90oebs 23 1 The the DT cord-229937-fy90oebs 23 2 D d NN cord-229937-fy90oebs 23 3 model model NN cord-229937-fy90oebs 23 4 is be VBZ cord-229937-fy90oebs 23 5 a a DT cord-229937-fy90oebs 23 6 simplified simplified JJ cord-229937-fy90oebs 23 7 version version NN cord-229937-fy90oebs 23 8 of of IN cord-229937-fy90oebs 23 9 the the DT cord-229937-fy90oebs 23 10 SIR SIR NNP cord-229937-fy90oebs 23 11 model model NN cord-229937-fy90oebs 23 12 with with IN cord-229937-fy90oebs 23 13 analytical analytical JJ cord-229937-fy90oebs 23 14 solutions solution NNS cord-229937-fy90oebs 23 15 under under IN cord-229937-fy90oebs 23 16 the the DT cord-229937-fy90oebs 23 17 assumption assumption NN cord-229937-fy90oebs 23 18 of of IN cord-229937-fy90oebs 23 19 no no DT cord-229937-fy90oebs 23 20 recovery recovery NN cord-229937-fy90oebs 23 21 -at -at : cord-229937-fy90oebs 23 22 least least JJS cord-229937-fy90oebs 23 23 during during IN cord-229937-fy90oebs 23 24 the the DT cord-229937-fy90oebs 23 25 time time NN cord-229937-fy90oebs 23 26 of of IN cord-229937-fy90oebs 23 27 the the DT cord-229937-fy90oebs 23 28 pandemic pandemic NN cord-229937-fy90oebs 23 29 . . . cord-229937-fy90oebs 24 1 We -PRON- PRP cord-229937-fy90oebs 24 2 apply apply VBP cord-229937-fy90oebs 24 3 it -PRON- PRP cord-229937-fy90oebs 24 4 globally globally RB cord-229937-fy90oebs 24 5 to to IN cord-229937-fy90oebs 24 6 countries country NNS cord-229937-fy90oebs 24 7 where where WRB cord-229937-fy90oebs 24 8 the the DT cord-229937-fy90oebs 24 9 infestation infestation NN cord-229937-fy90oebs 24 10 of of IN cord-229937-fy90oebs 24 11 the the DT cord-229937-fy90oebs 24 12 COVID-19 covid-19 JJ cord-229937-fy90oebs 24 13 coronavirus coronavirus NN cord-229937-fy90oebs 24 14 has have VBZ cord-229937-fy90oebs 24 15 widespread widespread JJ cord-229937-fy90oebs 24 16 and and CC cord-229937-fy90oebs 24 17 caused cause VBD cord-229937-fy90oebs 24 18 thousands thousand NNS cord-229937-fy90oebs 24 19 of of IN cord-229937-fy90oebs 24 20 deaths death NNS cord-229937-fy90oebs 24 21 [ [ -LRB- cord-229937-fy90oebs 24 22 15 15 CD cord-229937-fy90oebs 24 23 , , , cord-229937-fy90oebs 24 24 16 16 CD cord-229937-fy90oebs 24 25 ] ] -RRB- cord-229937-fy90oebs 24 26 . . . cord-229937-fy90oebs 25 1 Additionally additionally RB cord-229937-fy90oebs 25 2 , , , cord-229937-fy90oebs 25 3 D d NN cord-229937-fy90oebs 25 4 - - HYPH cord-229937-fy90oebs 25 5 model model NN cord-229937-fy90oebs 25 6 calculations calculation NNS cord-229937-fy90oebs 25 7 are be VBP cord-229937-fy90oebs 25 8 benchmarked benchmarke VBN cord-229937-fy90oebs 25 9 with with IN cord-229937-fy90oebs 25 10 more more RBR cord-229937-fy90oebs 25 11 sophisticated sophisticated JJ cord-229937-fy90oebs 25 12 and and CC cord-229937-fy90oebs 25 13 reliable reliable JJ cord-229937-fy90oebs 25 14 calculations calculation NNS cord-229937-fy90oebs 25 15 using use VBG cord-229937-fy90oebs 25 16 the the DT cord-229937-fy90oebs 25 17 extended extended JJ cord-229937-fy90oebs 25 18 SIR SIR NNP cord-229937-fy90oebs 25 19 ( ( -LRB- cord-229937-fy90oebs 25 20 ESIR ESIR NNP cord-229937-fy90oebs 25 21 ) ) -RRB- cord-229937-fy90oebs 25 22 and and CC cord-229937-fy90oebs 25 23 Monte Monte NNP cord-229937-fy90oebs 25 24 Carlo Carlo NNP cord-229937-fy90oebs 25 25 Planck Planck NNP cord-229937-fy90oebs 25 26 ( ( -LRB- cord-229937-fy90oebs 25 27 MCP MCP NNP cord-229937-fy90oebs 25 28 ) ) -RRB- cord-229937-fy90oebs 25 29 models model NNS cord-229937-fy90oebs 25 30 -also -also RB cord-229937-fy90oebs 25 31 developed develop VBD cord-229937-fy90oebs 25 32 in in IN cord-229937-fy90oebs 25 33 this this DT cord-229937-fy90oebs 25 34 work work NN cord-229937-fy90oebs 25 35 -which -which WDT cord-229937-fy90oebs 25 36 provide provide VBP cord-229937-fy90oebs 25 37 similar similar JJ cord-229937-fy90oebs 25 38 results result NNS cord-229937-fy90oebs 25 39 , , , cord-229937-fy90oebs 25 40 but but CC cord-229937-fy90oebs 25 41 allow allow VB cord-229937-fy90oebs 25 42 for for IN cord-229937-fy90oebs 25 43 a a DT cord-229937-fy90oebs 25 44 more more RBR cord-229937-fy90oebs 25 45 coherent coherent JJ cord-229937-fy90oebs 25 46 spatial spatial JJ cord-229937-fy90oebs 25 47 - - HYPH cord-229937-fy90oebs 25 48 time time NN cord-229937-fy90oebs 25 49 disentanglement disentanglement NN cord-229937-fy90oebs 25 50 of of IN cord-229937-fy90oebs 25 51 the the DT cord-229937-fy90oebs 25 52 various various JJ cord-229937-fy90oebs 25 53 effects effect NNS cord-229937-fy90oebs 25 54 present present JJ cord-229937-fy90oebs 25 55 during during IN cord-229937-fy90oebs 25 56 a a DT cord-229937-fy90oebs 25 57 pandemic pandemic NN cord-229937-fy90oebs 25 58 . . . cord-229937-fy90oebs 26 1 A a DT cord-229937-fy90oebs 26 2 similar similar JJ cord-229937-fy90oebs 26 3 ESIR ESIR NNP cord-229937-fy90oebs 26 4 model model NN cord-229937-fy90oebs 26 5 has have VBZ cord-229937-fy90oebs 26 6 recently recently RB cord-229937-fy90oebs 26 7 been be VBN cord-229937-fy90oebs 26 8 proposed propose VBN cord-229937-fy90oebs 26 9 by by IN cord-229937-fy90oebs 26 10 Squillante Squillante NNP cord-229937-fy90oebs 26 11 and and CC cord-229937-fy90oebs 26 12 collaborators collaborator NNS cord-229937-fy90oebs 26 13 for for IN cord-229937-fy90oebs 26 14 infected infected JJ cord-229937-fy90oebs 26 15 individuals individual NNS cord-229937-fy90oebs 26 16 as as IN cord-229937-fy90oebs 26 17 a a DT cord-229937-fy90oebs 26 18 function function NN cord-229937-fy90oebs 26 19 of of IN cord-229937-fy90oebs 26 20 time time NN cord-229937-fy90oebs 26 21 , , , cord-229937-fy90oebs 26 22 based base VBN cord-229937-fy90oebs 26 23 on on IN cord-229937-fy90oebs 26 24 the the DT cord-229937-fy90oebs 26 25 Ising Ising NNP cord-229937-fy90oebs 26 26 model model NN cord-229937-fy90oebs 27 1 -which -which NNP cord-229937-fy90oebs 27 2 describes describe VBZ cord-229937-fy90oebs 27 3 ferromagnetism ferromagnetism NN cord-229937-fy90oebs 27 4 in in IN cord-229937-fy90oebs 27 5 statistical statistical JJ cord-229937-fy90oebs 27 6 mechanics mechanic NNS cord-229937-fy90oebs 27 7 -and -and : cord-229937-fy90oebs 27 8 a a DT cord-229937-fy90oebs 27 9 Fermi Fermi NNP cord-229937-fy90oebs 27 10 - - HYPH cord-229937-fy90oebs 27 11 Dirac Dirac NNP cord-229937-fy90oebs 27 12 distribution distribution NN cord-229937-fy90oebs 27 13 [ [ -LRB- cord-229937-fy90oebs 27 14 17 17 CD cord-229937-fy90oebs 27 15 ] ] -RRB- cord-229937-fy90oebs 27 16 . . . cord-229937-fy90oebs 28 1 This this DT cord-229937-fy90oebs 28 2 model model NN cord-229937-fy90oebs 28 3 also also RB cord-229937-fy90oebs 28 4 reproduces reproduce VBZ cord-229937-fy90oebs 28 5 a a DT cord-229937-fy90oebs 28 6 posteriori posteriori NN cord-229937-fy90oebs 28 7 the the DT cord-229937-fy90oebs 28 8 COVID-19 COVID-19 NNP cord-229937-fy90oebs 28 9 data datum NNS cord-229937-fy90oebs 28 10 for for IN cord-229937-fy90oebs 28 11 infestations infestation NNS cord-229937-fy90oebs 28 12 in in IN cord-229937-fy90oebs 28 13 China China NNP cord-229937-fy90oebs 28 14 as as RB cord-229937-fy90oebs 28 15 well well RB cord-229937-fy90oebs 28 16 as as IN cord-229937-fy90oebs 28 17 other other JJ cord-229937-fy90oebs 28 18 pandemics pandemic NNS cord-229937-fy90oebs 28 19 such such JJ cord-229937-fy90oebs 28 20 as as IN cord-229937-fy90oebs 28 21 Ebola Ebola NNP cord-229937-fy90oebs 28 22 , , , cord-229937-fy90oebs 28 23 SARS SARS NNP cord-229937-fy90oebs 28 24 , , , cord-229937-fy90oebs 28 25 and and CC cord-229937-fy90oebs 28 26 influenza influenza NN cord-229937-fy90oebs 28 27 A A NNP cord-229937-fy90oebs 28 28 / / SYM cord-229937-fy90oebs 28 29 H1N1 H1N1 NNP cord-229937-fy90oebs 28 30 . . . cord-229937-fy90oebs 29 1 The the DT cord-229937-fy90oebs 29 2 SIR SIR NNP cord-229937-fy90oebs 29 3 model model NN cord-229937-fy90oebs 29 4 considers consider VBZ cord-229937-fy90oebs 29 5 the the DT cord-229937-fy90oebs 29 6 three three CD cord-229937-fy90oebs 29 7 possible possible JJ cord-229937-fy90oebs 29 8 states state NNS cord-229937-fy90oebs 29 9 of of IN cord-229937-fy90oebs 29 10 the the DT cord-229937-fy90oebs 29 11 members member NNS cord-229937-fy90oebs 29 12 of of IN cord-229937-fy90oebs 29 13 a a DT cord-229937-fy90oebs 29 14 closed closed JJ cord-229937-fy90oebs 29 15 population population NN cord-229937-fy90oebs 29 16 affected affect VBN cord-229937-fy90oebs 29 17 by by IN cord-229937-fy90oebs 29 18 a a DT cord-229937-fy90oebs 29 19 contagious contagious JJ cord-229937-fy90oebs 29 20 disease disease NN cord-229937-fy90oebs 29 21 . . . cord-229937-fy90oebs 30 1 It -PRON- PRP cord-229937-fy90oebs 30 2 is be VBZ cord-229937-fy90oebs 30 3 , , , cord-229937-fy90oebs 30 4 therefore therefore RB cord-229937-fy90oebs 30 5 , , , cord-229937-fy90oebs 30 6 characterized characterize VBN cord-229937-fy90oebs 30 7 by by IN cord-229937-fy90oebs 30 8 a a DT cord-229937-fy90oebs 30 9 system system NN cord-229937-fy90oebs 30 10 of of IN cord-229937-fy90oebs 30 11 three three CD cord-229937-fy90oebs 30 12 coupled couple VBN cord-229937-fy90oebs 30 13 non non JJ cord-229937-fy90oebs 30 14 - - JJ cord-229937-fy90oebs 30 15 linear linear JJ cord-229937-fy90oebs 30 16 ordinary ordinary JJ cord-229937-fy90oebs 30 17 differential differential JJ cord-229937-fy90oebs 30 18 equations equation NNS cord-229937-fy90oebs 30 19 [ [ -LRB- cord-229937-fy90oebs 30 20 18 18 CD cord-229937-fy90oebs 30 21 ] ] -RRB- cord-229937-fy90oebs 30 22 , , , cord-229937-fy90oebs 30 23 which which WDT cord-229937-fy90oebs 30 24 involve involve VBP cord-229937-fy90oebs 30 25 three three CD cord-229937-fy90oebs 30 26 time time NN cord-229937-fy90oebs 30 27 - - HYPH cord-229937-fy90oebs 30 28 dependent dependent JJ cord-229937-fy90oebs 30 29 functions function NNS cord-229937-fy90oebs 30 30 : : : cord-229937-fy90oebs 31 1 • • NNP cord-229937-fy90oebs 32 1 Susceptible susceptible JJ cord-229937-fy90oebs 32 2 individuals individual NNS cord-229937-fy90oebs 32 3 , , , cord-229937-fy90oebs 32 4 S(t S(t NNPS cord-229937-fy90oebs 32 5 ) ) -RRB- cord-229937-fy90oebs 32 6 , , , cord-229937-fy90oebs 32 7 at at IN cord-229937-fy90oebs 32 8 risk risk NN cord-229937-fy90oebs 32 9 of of IN cord-229937-fy90oebs 32 10 becoming become VBG cord-229937-fy90oebs 32 11 infected infect VBN cord-229937-fy90oebs 32 12 by by IN cord-229937-fy90oebs 32 13 the the DT cord-229937-fy90oebs 32 14 disease disease NN cord-229937-fy90oebs 32 15 . . . cord-229937-fy90oebs 33 1 • • NNP cord-229937-fy90oebs 34 1 Infected infected JJ cord-229937-fy90oebs 34 2 individuals individual NNS cord-229937-fy90oebs 34 3 , , , cord-229937-fy90oebs 34 4 I(t I(t NNP cord-229937-fy90oebs 34 5 ) ) -RRB- cord-229937-fy90oebs 34 6 . . . cord-229937-fy90oebs 35 1 • • NNP cord-229937-fy90oebs 36 1 Recovered recover VBN cord-229937-fy90oebs 36 2 or or CC cord-229937-fy90oebs 36 3 removed remove VBN cord-229937-fy90oebs 36 4 individuals individual NNS cord-229937-fy90oebs 36 5 , , , cord-229937-fy90oebs 36 6 R(t R(t NNP cord-229937-fy90oebs 36 7 ) ) -RRB- cord-229937-fy90oebs 36 8 , , , cord-229937-fy90oebs 36 9 who who WP cord-229937-fy90oebs 36 10 were be VBD cord-229937-fy90oebs 36 11 infected infect VBN cord-229937-fy90oebs 36 12 and and CC cord-229937-fy90oebs 36 13 may may MD cord-229937-fy90oebs 36 14 have have VB cord-229937-fy90oebs 36 15 developed develop VBN cord-229937-fy90oebs 36 16 an an DT cord-229937-fy90oebs 36 17 immunity immunity NN cord-229937-fy90oebs 36 18 system system NN cord-229937-fy90oebs 36 19 or or CC cord-229937-fy90oebs 36 20 die die VB cord-229937-fy90oebs 36 21 . . . cord-229937-fy90oebs 37 1 The the DT cord-229937-fy90oebs 37 2 SIR SIR NNP cord-229937-fy90oebs 37 3 model model NN cord-229937-fy90oebs 37 4 describes describe VBZ cord-229937-fy90oebs 37 5 well well RB cord-229937-fy90oebs 37 6 a a DT cord-229937-fy90oebs 37 7 viral viral JJ cord-229937-fy90oebs 37 8 disease disease NN cord-229937-fy90oebs 37 9 , , , cord-229937-fy90oebs 37 10 where where WRB cord-229937-fy90oebs 37 11 individuals individual NNS cord-229937-fy90oebs 37 12 typically typically RB cord-229937-fy90oebs 37 13 go go VBP cord-229937-fy90oebs 37 14 from from IN cord-229937-fy90oebs 37 15 the the DT cord-229937-fy90oebs 37 16 susceptible susceptible JJ cord-229937-fy90oebs 37 17 class class NN cord-229937-fy90oebs 37 18 S s NN cord-229937-fy90oebs 37 19 to to IN cord-229937-fy90oebs 37 20 the the DT cord-229937-fy90oebs 37 21 infected infected JJ cord-229937-fy90oebs 37 22 class class NN cord-229937-fy90oebs 37 23 I i NN cord-229937-fy90oebs 37 24 , , , cord-229937-fy90oebs 37 25 and and CC cord-229937-fy90oebs 37 26 finally finally RB cord-229937-fy90oebs 37 27 to to IN cord-229937-fy90oebs 37 28 the the DT cord-229937-fy90oebs 37 29 removed remove VBN cord-229937-fy90oebs 37 30 class class NN cord-229937-fy90oebs 37 31 R. R. NNP cord-229937-fy90oebs 37 32 Recovered recover VBN cord-229937-fy90oebs 37 33 individuals individual NNS cord-229937-fy90oebs 37 34 can can MD cord-229937-fy90oebs 37 35 not not RB cord-229937-fy90oebs 37 36 go go VB cord-229937-fy90oebs 37 37 back back RB cord-229937-fy90oebs 37 38 to to TO cord-229937-fy90oebs 37 39 be be VB cord-229937-fy90oebs 37 40 susceptible susceptible JJ cord-229937-fy90oebs 37 41 or or CC cord-229937-fy90oebs 37 42 infected infected JJ cord-229937-fy90oebs 37 43 classes class NNS cord-229937-fy90oebs 37 44 , , , cord-229937-fy90oebs 37 45 as as IN cord-229937-fy90oebs 37 46 it -PRON- PRP cord-229937-fy90oebs 37 47 is be VBZ cord-229937-fy90oebs 37 48 , , , cord-229937-fy90oebs 37 49 potentially potentially RB cord-229937-fy90oebs 37 50 , , , cord-229937-fy90oebs 37 51 the the DT cord-229937-fy90oebs 37 52 case case NN cord-229937-fy90oebs 37 53 of of IN cord-229937-fy90oebs 37 54 bacterial bacterial JJ cord-229937-fy90oebs 37 55 infection infection NN cord-229937-fy90oebs 37 56 . . . cord-229937-fy90oebs 38 1 The the DT cord-229937-fy90oebs 38 2 resulting result VBG cord-229937-fy90oebs 38 3 transmission transmission NN cord-229937-fy90oebs 38 4 - - HYPH cord-229937-fy90oebs 38 5 dynamics dynamic NNS cord-229937-fy90oebs 38 6 system system NN cord-229937-fy90oebs 38 7 for for IN cord-229937-fy90oebs 38 8 a a DT cord-229937-fy90oebs 38 9 closed closed JJ cord-229937-fy90oebs 38 10 population population NN cord-229937-fy90oebs 38 11 is be VBZ cord-229937-fy90oebs 38 12 described describe VBN cord-229937-fy90oebs 38 13 by by IN cord-229937-fy90oebs 38 14 where where WRB cord-229937-fy90oebs 38 15 λ λ NN cord-229937-fy90oebs 38 16 > > XX cord-229937-fy90oebs 39 1 0 0 NFP cord-229937-fy90oebs 39 2 is be VBZ cord-229937-fy90oebs 39 3 the the DT cord-229937-fy90oebs 39 4 transmission transmission NN cord-229937-fy90oebs 39 5 or or CC cord-229937-fy90oebs 39 6 spreading spreading NN cord-229937-fy90oebs 39 7 rate rate NN cord-229937-fy90oebs 39 8 , , , cord-229937-fy90oebs 39 9 β β NN cord-229937-fy90oebs 39 10 > > XX cord-229937-fy90oebs 39 11 0 0 NFP cord-229937-fy90oebs 39 12 is be VBZ cord-229937-fy90oebs 39 13 the the DT cord-229937-fy90oebs 39 14 removal removal NN cord-229937-fy90oebs 39 15 rate rate NN cord-229937-fy90oebs 39 16 and and CC cord-229937-fy90oebs 39 17 N n NN cord-229937-fy90oebs 39 18 is be VBZ cord-229937-fy90oebs 39 19 the the DT cord-229937-fy90oebs 39 20 fixed fix VBN cord-229937-fy90oebs 39 21 population population NN cord-229937-fy90oebs 39 22 size size NN cord-229937-fy90oebs 39 23 , , , cord-229937-fy90oebs 39 24 which which WDT cord-229937-fy90oebs 39 25 implies imply VBZ cord-229937-fy90oebs 39 26 that that IN cord-229937-fy90oebs 39 27 the the DT cord-229937-fy90oebs 39 28 model model NN cord-229937-fy90oebs 39 29 neglects neglect VBZ cord-229937-fy90oebs 39 30 the the DT cord-229937-fy90oebs 39 31 effects effect NNS cord-229937-fy90oebs 39 32 of of IN cord-229937-fy90oebs 39 33 spatial spatial JJ cord-229937-fy90oebs 39 34 migration migration NN cord-229937-fy90oebs 39 35 . . . cord-229937-fy90oebs 40 1 Currently currently RB cord-229937-fy90oebs 40 2 , , , cord-229937-fy90oebs 40 3 there there EX cord-229937-fy90oebs 40 4 is be VBZ cord-229937-fy90oebs 40 5 no no DT cord-229937-fy90oebs 40 6 vaccination vaccination NN cord-229937-fy90oebs 40 7 available available JJ cord-229937-fy90oebs 40 8 for for IN cord-229937-fy90oebs 40 9 COVID-19 COVID-19 NNP cord-229937-fy90oebs 40 10 , , , cord-229937-fy90oebs 40 11 and and CC cord-229937-fy90oebs 40 12 the the DT cord-229937-fy90oebs 40 13 only only JJ cord-229937-fy90oebs 40 14 way way NN cord-229937-fy90oebs 40 15 to to TO cord-229937-fy90oebs 40 16 reduce reduce VB cord-229937-fy90oebs 40 17 the the DT cord-229937-fy90oebs 40 18 transmission transmission NN cord-229937-fy90oebs 40 19 or or CC cord-229937-fy90oebs 40 20 infection infection NN cord-229937-fy90oebs 40 21 rate rate NN cord-229937-fy90oebs 40 22 λ λ NN cord-229937-fy90oebs 40 23 -which -which WDT cord-229937-fy90oebs 40 24 is be VBZ cord-229937-fy90oebs 40 25 often often RB cord-229937-fy90oebs 40 26 referred refer VBN cord-229937-fy90oebs 40 27 to to IN cord-229937-fy90oebs 40 28 as as IN cord-229937-fy90oebs 40 29 " " `` cord-229937-fy90oebs 40 30 flattening flatten VBG cord-229937-fy90oebs 40 31 the the DT cord-229937-fy90oebs 40 32 curve"-is curve"-is NN cord-229937-fy90oebs 40 33 by by IN cord-229937-fy90oebs 40 34 implementing implement VBG cord-229937-fy90oebs 40 35 strong strong JJ cord-229937-fy90oebs 40 36 social social JJ cord-229937-fy90oebs 40 37 distancing distancing NN cord-229937-fy90oebs 40 38 and and CC cord-229937-fy90oebs 40 39 hygiene hygiene NN cord-229937-fy90oebs 40 40 measures measure NNS cord-229937-fy90oebs 40 41 . . . cord-229937-fy90oebs 41 1 The the DT cord-229937-fy90oebs 41 2 system system NN cord-229937-fy90oebs 41 3 is be VBZ cord-229937-fy90oebs 41 4 reduced reduce VBN cord-229937-fy90oebs 41 5 to to IN cord-229937-fy90oebs 41 6 a a DT cord-229937-fy90oebs 41 7 first first JJ cord-229937-fy90oebs 41 8 - - HYPH cord-229937-fy90oebs 41 9 order order NN cord-229937-fy90oebs 41 10 differential differential JJ cord-229937-fy90oebs 41 11 equation equation NN cord-229937-fy90oebs 41 12 , , , cord-229937-fy90oebs 41 13 which which WDT cord-229937-fy90oebs 41 14 does do VBZ cord-229937-fy90oebs 41 15 not not RB cord-229937-fy90oebs 41 16 possess possess VB cord-229937-fy90oebs 41 17 an an DT cord-229937-fy90oebs 41 18 explicit explicit JJ cord-229937-fy90oebs 41 19 solution solution NN cord-229937-fy90oebs 41 20 , , , cord-229937-fy90oebs 41 21 but but CC cord-229937-fy90oebs 41 22 can can MD cord-229937-fy90oebs 41 23 be be VB cord-229937-fy90oebs 41 24 solved solve VBN cord-229937-fy90oebs 41 25 numerically numerically RB cord-229937-fy90oebs 41 26 . . . cord-229937-fy90oebs 42 1 The the DT cord-229937-fy90oebs 42 2 SIR SIR NNP cord-229937-fy90oebs 42 3 model model NN cord-229937-fy90oebs 42 4 can can MD cord-229937-fy90oebs 42 5 then then RB cord-229937-fy90oebs 42 6 be be VB cord-229937-fy90oebs 42 7 parametrized parametrize VBN cord-229937-fy90oebs 42 8 using use VBG cord-229937-fy90oebs 42 9 actual actual JJ cord-229937-fy90oebs 42 10 infection infection NN cord-229937-fy90oebs 42 11 data datum NNS cord-229937-fy90oebs 42 12 to to TO cord-229937-fy90oebs 42 13 solve solve VB cord-229937-fy90oebs 42 14 I(t I(t NNP cord-229937-fy90oebs 42 15 ) ) -RRB- cord-229937-fy90oebs 42 16 , , , cord-229937-fy90oebs 42 17 in in IN cord-229937-fy90oebs 42 18 order order NN cord-229937-fy90oebs 42 19 to to TO cord-229937-fy90oebs 42 20 investigate investigate VB cord-229937-fy90oebs 42 21 the the DT cord-229937-fy90oebs 42 22 evolution evolution NN cord-229937-fy90oebs 42 23 of of IN cord-229937-fy90oebs 42 24 the the DT cord-229937-fy90oebs 42 25 disease disease NN cord-229937-fy90oebs 42 26 . . . cord-229937-fy90oebs 43 1 In in IN cord-229937-fy90oebs 43 2 the the DT cord-229937-fy90oebs 43 3 D d NN cord-229937-fy90oebs 43 4 model model NN cord-229937-fy90oebs 43 5 , , , cord-229937-fy90oebs 43 6 we -PRON- PRP cord-229937-fy90oebs 43 7 make make VBP cord-229937-fy90oebs 43 8 the the DT cord-229937-fy90oebs 43 9 drastic drastic JJ cord-229937-fy90oebs 43 10 assumption assumption NN cord-229937-fy90oebs 43 11 of of IN cord-229937-fy90oebs 43 12 no no DT cord-229937-fy90oebs 43 13 recovery recovery NN cord-229937-fy90oebs 43 14 in in IN cord-229937-fy90oebs 43 15 order order NN cord-229937-fy90oebs 43 16 to to TO cord-229937-fy90oebs 43 17 obtain obtain VB cord-229937-fy90oebs 43 18 an an DT cord-229937-fy90oebs 43 19 analytical analytical JJ cord-229937-fy90oebs 43 20 formula formula NN cord-229937-fy90oebs 43 21 to to IN cord-229937-fy90oebs 43 22 describeinstead describeinstead NN cord-229937-fy90oebs 43 23 of of IN cord-229937-fy90oebs 43 24 infestations infestation NNS cord-229937-fy90oebs 43 25 -the -the ADD cord-229937-fy90oebs 43 26 death death NN cord-229937-fy90oebs 43 27 evolution evolution NN cord-229937-fy90oebs 43 28 by by IN cord-229937-fy90oebs 43 29 COVID-19 COVID-19 NNP cord-229937-fy90oebs 43 30 . . . cord-229937-fy90oebs 44 1 This this DT cord-229937-fy90oebs 44 2 can can MD cord-229937-fy90oebs 44 3 be be VB cord-229937-fy90oebs 44 4 useful useful JJ cord-229937-fy90oebs 44 5 as as IN cord-229937-fy90oebs 44 6 a a DT cord-229937-fy90oebs 44 7 fast fast JJ cord-229937-fy90oebs 44 8 method method NN cord-229937-fy90oebs 44 9 to to TO cord-229937-fy90oebs 44 10 foresee foresee VB cord-229937-fy90oebs 44 11 the the DT cord-229937-fy90oebs 44 12 global global JJ cord-229937-fy90oebs 44 13 behavior behavior NN cord-229937-fy90oebs 44 14 as as IN cord-229937-fy90oebs 44 15 a a DT cord-229937-fy90oebs 44 16 first first JJ cord-229937-fy90oebs 44 17 approach approach NN cord-229937-fy90oebs 44 18 , , , cord-229937-fy90oebs 44 19 before before IN cord-229937-fy90oebs 44 20 applying apply VBG cord-229937-fy90oebs 44 21 more more RBR cord-229937-fy90oebs 44 22 sophisticated sophisticated JJ cord-229937-fy90oebs 44 23 methods method NNS cord-229937-fy90oebs 44 24 . . . cord-229937-fy90oebs 45 1 We -PRON- PRP cord-229937-fy90oebs 45 2 shall shall MD cord-229937-fy90oebs 45 3 see see VB cord-229937-fy90oebs 45 4 that that IN cord-229937-fy90oebs 45 5 the the DT cord-229937-fy90oebs 45 6 resulting result VBG cord-229937-fy90oebs 45 7 D d NN cord-229937-fy90oebs 45 8 model model NN cord-229937-fy90oebs 45 9 describes describe VBZ cord-229937-fy90oebs 45 10 well well RB cord-229937-fy90oebs 45 11 enough enough RB cord-229937-fy90oebs 45 12 the the DT cord-229937-fy90oebs 45 13 data datum NNS cord-229937-fy90oebs 45 14 of of IN cord-229937-fy90oebs 45 15 the the DT cord-229937-fy90oebs 45 16 current current JJ cord-229937-fy90oebs 45 17 pandemics pandemic NNS cord-229937-fy90oebs 45 18 in in IN cord-229937-fy90oebs 45 19 different different JJ cord-229937-fy90oebs 45 20 countries country NNS cord-229937-fy90oebs 45 21 . . . cord-229937-fy90oebs 46 1 The the DT cord-229937-fy90oebs 46 2 main main JJ cord-229937-fy90oebs 46 3 assumption assumption NN cord-229937-fy90oebs 46 4 of of IN cord-229937-fy90oebs 46 5 the the DT cord-229937-fy90oebs 46 6 D D NNP cord-229937-fy90oebs 46 7 model model NN cord-229937-fy90oebs 46 8 is be VBZ cord-229937-fy90oebs 46 9 the the DT cord-229937-fy90oebs 46 10 absence absence NN cord-229937-fy90oebs 46 11 of of IN cord-229937-fy90oebs 46 12 recovery recovery NN cord-229937-fy90oebs 46 13 from from IN cord-229937-fy90oebs 46 14 coronavirus coronavirus NN cord-229937-fy90oebs 46 15 , , , cord-229937-fy90oebs 46 16 i.e. i.e. FW cord-229937-fy90oebs 46 17 R(t r(t NN cord-229937-fy90oebs 46 18 ) ) -RRB- cord-229937-fy90oebs 46 19 = = SYM cord-229937-fy90oebs 46 20 0 0 CD cord-229937-fy90oebs 46 21 , , , cord-229937-fy90oebs 46 22 at at IN cord-229937-fy90oebs 46 23 least least JJS cord-229937-fy90oebs 46 24 during during IN cord-229937-fy90oebs 46 25 the the DT cord-229937-fy90oebs 46 26 pandemic pandemic NN cord-229937-fy90oebs 46 27 time time NN cord-229937-fy90oebs 46 28 interval interval NN cord-229937-fy90oebs 46 29 . . . cord-229937-fy90oebs 47 1 This this DT cord-229937-fy90oebs 47 2 assumption assumption NN cord-229937-fy90oebs 47 3 may may MD cord-229937-fy90oebs 47 4 be be VB cord-229937-fy90oebs 47 5 reasonable reasonable JJ cord-229937-fy90oebs 47 6 if if IN cord-229937-fy90oebs 47 7 the the DT cord-229937-fy90oebs 47 8 spreading spread VBG cord-229937-fy90oebs 47 9 time time NN cord-229937-fy90oebs 47 10 of of IN cord-229937-fy90oebs 47 11 the the DT cord-229937-fy90oebs 47 12 pandemic pandemic NN cord-229937-fy90oebs 47 13 is be VBZ cord-229937-fy90oebs 47 14 much much RB cord-229937-fy90oebs 47 15 faster fast JJR cord-229937-fy90oebs 47 16 than than IN cord-229937-fy90oebs 47 17 the the DT cord-229937-fy90oebs 47 18 recovery recovery NN cord-229937-fy90oebs 47 19 time time NN cord-229937-fy90oebs 47 20 , , , cord-229937-fy90oebs 47 21 i.e. i.e. FW cord-229937-fy90oebs 47 22 λ λ NN cord-229937-fy90oebs 47 23 ≫ ≫ FW cord-229937-fy90oebs 47 24 β β NN cord-229937-fy90oebs 47 25 . . . cord-229937-fy90oebs 48 1 The the DT cord-229937-fy90oebs 48 2 SIR SIR NNP cord-229937-fy90oebs 48 3 equations equation NNS cord-229937-fy90oebs 48 4 are be VBP cord-229937-fy90oebs 48 5 then then RB cord-229937-fy90oebs 48 6 reduced reduce VBN cord-229937-fy90oebs 48 7 to to IN cord-229937-fy90oebs 48 8 the the DT cord-229937-fy90oebs 48 9 single single JJ cord-229937-fy90oebs 48 10 equation equation NN cord-229937-fy90oebs 48 11 of of IN cord-229937-fy90oebs 48 12 the the DT cord-229937-fy90oebs 48 13 well well RB cord-229937-fy90oebs 48 14 - - HYPH cord-229937-fy90oebs 48 15 known know VBN cord-229937-fy90oebs 48 16 SI si NN cord-229937-fy90oebs 48 17 model model NN cord-229937-fy90oebs 48 18 , , , cord-229937-fy90oebs 48 19 which which WDT cord-229937-fy90oebs 48 20 represents represent VBZ cord-229937-fy90oebs 48 21 the the DT cord-229937-fy90oebs 48 22 simplest simple JJS cord-229937-fy90oebs 48 23 mathematical mathematical JJ cord-229937-fy90oebs 48 24 form form NN cord-229937-fy90oebs 48 25 of of IN cord-229937-fy90oebs 48 26 all all DT cord-229937-fy90oebs 48 27 disease disease NN cord-229937-fy90oebs 48 28 models model NNS cord-229937-fy90oebs 48 29 , , , cord-229937-fy90oebs 48 30 where where WRB cord-229937-fy90oebs 48 31 the the DT cord-229937-fy90oebs 48 32 infection infection NN cord-229937-fy90oebs 48 33 rate rate NN cord-229937-fy90oebs 48 34 is be VBZ cord-229937-fy90oebs 48 35 proportional proportional JJ cord-229937-fy90oebs 48 36 to to IN cord-229937-fy90oebs 48 37 both both PDT cord-229937-fy90oebs 48 38 the the DT cord-229937-fy90oebs 48 39 infected infected JJ cord-229937-fy90oebs 48 40 , , , cord-229937-fy90oebs 48 41 I -PRON- PRP cord-229937-fy90oebs 48 42 , , , cord-229937-fy90oebs 48 43 and and CC cord-229937-fy90oebs 48 44 susceptible susceptible JJ cord-229937-fy90oebs 48 45 individuals individual NNS cord-229937-fy90oebs 49 1 N N NNP cord-229937-fy90oebs 50 1 −I. −i. CC cord-229937-fy90oebs 50 2 Equation Equation NNP cord-229937-fy90oebs 50 3 5 5 CD cord-229937-fy90oebs 50 4 is be VBZ cord-229937-fy90oebs 50 5 trivially trivially RB cord-229937-fy90oebs 50 6 solved solve VBN cord-229937-fy90oebs 50 7 by by IN cord-229937-fy90oebs 50 8 multiplying multiply VBG cord-229937-fy90oebs 50 9 by by IN cord-229937-fy90oebs 50 10 dt dt NN cord-229937-fy90oebs 50 11 and and CC cord-229937-fy90oebs 50 12 dividing divide VBG cord-229937-fy90oebs 50 13 by by IN cord-229937-fy90oebs 50 14 ( ( -LRB- cord-229937-fy90oebs 50 15 N n NN cord-229937-fy90oebs 50 16 − − NN cord-229937-fy90oebs 50 17 I)I i)i NN cord-229937-fy90oebs 50 18 , , , cord-229937-fy90oebs 50 19 Integrating integrate VBG cord-229937-fy90oebs 50 20 over over IN cord-229937-fy90oebs 50 21 an an DT cord-229937-fy90oebs 50 22 initial initial JJ cord-229937-fy90oebs 50 23 t t NN cord-229937-fy90oebs 50 24 = = SYM cord-229937-fy90oebs 50 25 0 0 CD cord-229937-fy90oebs 50 26 and and CC cord-229937-fy90oebs 50 27 final final JJ cord-229937-fy90oebs 50 28 t t NN cord-229937-fy90oebs 51 1 we -PRON- PRP cord-229937-fy90oebs 51 2 obtain obtain VBP cord-229937-fy90oebs 51 3 where where WRB cord-229937-fy90oebs 51 4 I -PRON- PRP cord-229937-fy90oebs 51 5 0 0 CD cord-229937-fy90oebs 51 6 = = SYM cord-229937-fy90oebs 51 7 I(t I(t NNP cord-229937-fy90oebs 51 8 0 0 CD cord-229937-fy90oebs 51 9 ) ) -RRB- cord-229937-fy90oebs 51 10 . . . cord-229937-fy90oebs 52 1 Taking take VBG cord-229937-fy90oebs 52 2 the the DT cord-229937-fy90oebs 52 3 exponential exponential NN cord-229937-fy90oebs 52 4 on on IN cord-229937-fy90oebs 52 5 both both DT cord-229937-fy90oebs 52 6 sides side NNS cord-229937-fy90oebs 52 7 Finally finally RB cord-229937-fy90oebs 52 8 , , , cord-229937-fy90oebs 52 9 solving solve VBG cord-229937-fy90oebs 52 10 this this DT cord-229937-fy90oebs 52 11 algebraic algebraic JJ cord-229937-fy90oebs 52 12 equation equation NN cord-229937-fy90oebs 52 13 we -PRON- PRP cord-229937-fy90oebs 52 14 obtain obtain VBP cord-229937-fy90oebs 52 15 the the DT cord-229937-fy90oebs 52 16 solution solution NN cord-229937-fy90oebs 52 17 I(t I(t NNP cord-229937-fy90oebs 52 18 ) ) -RRB- cord-229937-fy90oebs 52 19 which which WDT cord-229937-fy90oebs 52 20 can can MD cord-229937-fy90oebs 52 21 be be VB cord-229937-fy90oebs 52 22 written write VBN cord-229937-fy90oebs 52 23 in in IN cord-229937-fy90oebs 52 24 the the DT cord-229937-fy90oebs 52 25 form form NN cord-229937-fy90oebs 52 26 where where WRB cord-229937-fy90oebs 52 27 we -PRON- PRP cord-229937-fy90oebs 52 28 have have VBP cord-229937-fy90oebs 52 29 defined define VBN cord-229937-fy90oebs 52 30 the the DT cord-229937-fy90oebs 52 31 constants constant NNS cord-229937-fy90oebs 52 32 The the DT cord-229937-fy90oebs 52 33 parameter parameter NN cord-229937-fy90oebs 52 34 b b NN cord-229937-fy90oebs 52 35 is be VBZ cord-229937-fy90oebs 52 36 the the DT cord-229937-fy90oebs 52 37 characteristic characteristic JJ cord-229937-fy90oebs 52 38 evolution evolution NN cord-229937-fy90oebs 52 39 time time NN cord-229937-fy90oebs 52 40 of of IN cord-229937-fy90oebs 52 41 the the DT cord-229937-fy90oebs 52 42 initial initial JJ cord-229937-fy90oebs 52 43 exponential exponential JJ cord-229937-fy90oebs 52 44 increase increase NN cord-229937-fy90oebs 52 45 of of IN cord-229937-fy90oebs 52 46 the the DT cord-229937-fy90oebs 52 47 pandemic pandemic NN cord-229937-fy90oebs 52 48 . . . cord-229937-fy90oebs 53 1 The the DT cord-229937-fy90oebs 53 2 constant constant JJ cord-229937-fy90oebs 53 3 C c NN cord-229937-fy90oebs 53 4 is be VBZ cord-229937-fy90oebs 53 5 the the DT cord-229937-fy90oebs 53 6 initial initial JJ cord-229937-fy90oebs 53 7 infestation infestation NN cord-229937-fy90oebs 53 8 rate rate NN cord-229937-fy90oebs 53 9 with with IN cord-229937-fy90oebs 53 10 respect respect NN cord-229937-fy90oebs 53 11 to to IN cord-229937-fy90oebs 53 12 the the DT cord-229937-fy90oebs 53 13 total total JJ cord-229937-fy90oebs 53 14 population population NN cord-229937-fy90oebs 53 15 N N NNP cord-229937-fy90oebs 53 16 . . . cord-229937-fy90oebs 54 1 Assuming assume VBG cord-229937-fy90oebs 54 2 C C NNP cord-229937-fy90oebs 54 3 ≪ ≪ NNP cord-229937-fy90oebs 54 4 1 1 CD cord-229937-fy90oebs 54 5 , , , cord-229937-fy90oebs 54 6 Eq Eq NNP cord-229937-fy90oebs 54 7 . . . cord-229937-fy90oebs 55 1 11 11 CD cord-229937-fy90oebs 55 2 yields yield NNS cord-229937-fy90oebs 56 1 In in IN cord-229937-fy90oebs 56 2 order order NN cord-229937-fy90oebs 56 3 to to TO cord-229937-fy90oebs 56 4 predict predict VB cord-229937-fy90oebs 56 5 the the DT cord-229937-fy90oebs 56 6 number number NN cord-229937-fy90oebs 56 7 of of IN cord-229937-fy90oebs 56 8 deaths death NNS cord-229937-fy90oebs 56 9 in in IN cord-229937-fy90oebs 56 10 the the DT cord-229937-fy90oebs 56 11 D d NN cord-229937-fy90oebs 56 12 model model NN cord-229937-fy90oebs 56 13 we -PRON- PRP cord-229937-fy90oebs 56 14 assume assume VBP cord-229937-fy90oebs 56 15 that that IN cord-229937-fy90oebs 56 16 the the DT cord-229937-fy90oebs 56 17 number number NN cord-229937-fy90oebs 56 18 of of IN cord-229937-fy90oebs 56 19 deaths death NNS cord-229937-fy90oebs 56 20 at at IN cord-229937-fy90oebs 56 21 some some DT cord-229937-fy90oebs 56 22 time time NN cord-229937-fy90oebs 56 23 t t NN cord-229937-fy90oebs 56 24 is be VBZ cord-229937-fy90oebs 56 25 proportional proportional JJ cord-229937-fy90oebs 56 26 to to IN cord-229937-fy90oebs 56 27 the the DT cord-229937-fy90oebs 56 28 infestation infestation NN cord-229937-fy90oebs 56 29 at at IN cord-229937-fy90oebs 56 30 some some DT cord-229937-fy90oebs 56 31 former former JJ cord-229937-fy90oebs 56 32 time time NN cord-229937-fy90oebs 56 33 τ τ NN cord-229937-fy90oebs 56 34 , , , cord-229937-fy90oebs 56 35 that that RB cord-229937-fy90oebs 56 36 is is RB cord-229937-fy90oebs 56 37 , , , cord-229937-fy90oebs 56 38 where where WRB cord-229937-fy90oebs 56 39 µ µ NN cord-229937-fy90oebs 56 40 is be VBZ cord-229937-fy90oebs 56 41 the the DT cord-229937-fy90oebs 56 42 death death NN cord-229937-fy90oebs 56 43 rate rate NN cord-229937-fy90oebs 56 44 , , , cord-229937-fy90oebs 56 45 and and CC cord-229937-fy90oebs 56 46 τ τ NN cord-229937-fy90oebs 56 47 is be VBZ cord-229937-fy90oebs 56 48 the the DT cord-229937-fy90oebs 56 49 death death NN cord-229937-fy90oebs 56 50 time time NN cord-229937-fy90oebs 56 51 . . . cord-229937-fy90oebs 57 1 With with IN cord-229937-fy90oebs 57 2 this this DT cord-229937-fy90oebs 57 3 assumption assumption NN cord-229937-fy90oebs 57 4 we -PRON- PRP cord-229937-fy90oebs 57 5 can can MD cord-229937-fy90oebs 57 6 finally finally RB cord-229937-fy90oebs 57 7 write write VB cord-229937-fy90oebs 57 8 the the DT cord-229937-fy90oebs 57 9 D d NN cord-229937-fy90oebs 57 10 - - HYPH cord-229937-fy90oebs 57 11 model model NN cord-229937-fy90oebs 57 12 equation equation NN cord-229937-fy90oebs 57 13 as as IN cord-229937-fy90oebs 57 14 where where WRB cord-229937-fy90oebs 57 15 a a DT cord-229937-fy90oebs 57 16 = = SYM cord-229937-fy90oebs 57 17 µI µi NN cord-229937-fy90oebs 57 18 0 0 CD cord-229937-fy90oebs 57 19 e e NN cord-229937-fy90oebs 57 20 −τ −τ NNP cord-229937-fy90oebs 57 21 /b /b NNP cord-229937-fy90oebs 57 22 , , , cord-229937-fy90oebs 57 23 c c NN cord-229937-fy90oebs 57 24 = = SYM cord-229937-fy90oebs 57 25 C c NN cord-229937-fy90oebs 57 26 e e NN cord-229937-fy90oebs 57 27 −τ −τ NNP cord-229937-fy90oebs 57 28 /b /b NNP cord-229937-fy90oebs 57 29 , , , cord-229937-fy90oebs 57 30 and and CC cord-229937-fy90oebs 57 31 a a DT cord-229937-fy90oebs 57 32 / / SYM cord-229937-fy90oebs 57 33 c c NN cord-229937-fy90oebs 57 34 yields yield VBZ cord-229937-fy90oebs 57 35 the the DT cord-229937-fy90oebs 57 36 total total JJ cord-229937-fy90oebs 57 37 number number NN cord-229937-fy90oebs 57 38 of of IN cord-229937-fy90oebs 57 39 deaths death NNS cord-229937-fy90oebs 57 40 predicted predict VBN cord-229937-fy90oebs 57 41 by by IN cord-229937-fy90oebs 57 42 the the DT cord-229937-fy90oebs 57 43 model model NN cord-229937-fy90oebs 57 44 . . . cord-229937-fy90oebs 58 1 This this DT cord-229937-fy90oebs 58 2 is be VBZ cord-229937-fy90oebs 58 3 the the DT cord-229937-fy90oebs 58 4 final final JJ cord-229937-fy90oebs 58 5 equation equation NN cord-229937-fy90oebs 58 6 for for IN cord-229937-fy90oebs 58 7 the the DT cord-229937-fy90oebs 58 8 D d NN cord-229937-fy90oebs 58 9 - - HYPH cord-229937-fy90oebs 58 10 model model NN cord-229937-fy90oebs 58 11 , , , cord-229937-fy90oebs 58 12 which which WDT cord-229937-fy90oebs 58 13 presents present VBZ cord-229937-fy90oebs 58 14 a a DT cord-229937-fy90oebs 58 15 similar similar JJ cord-229937-fy90oebs 58 16 shape shape NN cord-229937-fy90oebs 58 17 to to IN cord-229937-fy90oebs 58 18 the the DT cord-229937-fy90oebs 58 19 well well RB cord-229937-fy90oebs 58 20 - - HYPH cord-229937-fy90oebs 58 21 known know VBN cord-229937-fy90oebs 58 22 Woods Woods NNP cord-229937-fy90oebs 58 23 - - HYPH cord-229937-fy90oebs 58 24 Saxon Saxon NNP cord-229937-fy90oebs 58 25 potential potential NN cord-229937-fy90oebs 58 26 for for IN cord-229937-fy90oebs 58 27 the the DT cord-229937-fy90oebs 58 28 nucleons nucleon NNS cord-229937-fy90oebs 58 29 inside inside IN cord-229937-fy90oebs 58 30 the the DT cord-229937-fy90oebs 58 31 atomic atomic JJ cord-229937-fy90oebs 58 32 nucleus nucleus NN cord-229937-fy90oebs 58 33 or or CC cord-229937-fy90oebs 58 34 the the DT cord-229937-fy90oebs 58 35 bacterial bacterial JJ cord-229937-fy90oebs 58 36 growth growth NN cord-229937-fy90oebs 58 37 curve curve NN cord-229937-fy90oebs 58 38 . . . cord-229937-fy90oebs 59 1 The the DT cord-229937-fy90oebs 59 2 rest rest NN cord-229937-fy90oebs 59 3 of of IN cord-229937-fy90oebs 59 4 the the DT cord-229937-fy90oebs 59 5 parameters parameter NNS cord-229937-fy90oebs 59 6 , , , cord-229937-fy90oebs 59 7 µ µ NN cord-229937-fy90oebs 59 8 , , , cord-229937-fy90oebs 59 9 τ τ NN cord-229937-fy90oebs 59 10 , , , cord-229937-fy90oebs 59 11 I -PRON- PRP cord-229937-fy90oebs 59 12 0 0 CD cord-229937-fy90oebs 59 13 and and CC cord-229937-fy90oebs 59 14 N N NNP cord-229937-fy90oebs 59 15 are be VBP cord-229937-fy90oebs 59 16 embedded embed VBN cord-229937-fy90oebs 59 17 in in IN cord-229937-fy90oebs 59 18 the the DT cord-229937-fy90oebs 59 19 parameters parameter NNS cord-229937-fy90oebs 59 20 a a DT cord-229937-fy90oebs 59 21 , , , cord-229937-fy90oebs 59 22 b b NN cord-229937-fy90oebs 59 23 , , , cord-229937-fy90oebs 59 24 c c NNP cord-229937-fy90oebs 59 25 , , , cord-229937-fy90oebs 59 26 which which WDT cord-229937-fy90oebs 59 27 represent represent VBP cord-229937-fy90oebs 59 28 space space NN cord-229937-fy90oebs 59 29 - - HYPH cord-229937-fy90oebs 59 30 time time NN cord-229937-fy90oebs 59 31 averages average NNS cord-229937-fy90oebs 59 32 and and CC cord-229937-fy90oebs 59 33 can can MD cord-229937-fy90oebs 59 34 be be VB cord-229937-fy90oebs 59 35 fitted fit VBN cord-229937-fy90oebs 59 36 to to IN cord-229937-fy90oebs 59 37 the the DT cord-229937-fy90oebs 59 38 timely timely RB cord-229937-fy90oebs 59 39 available available JJ cord-229937-fy90oebs 59 40 data datum NNS cord-229937-fy90oebs 59 41 . . . cord-229937-fy90oebs 60 1 In in IN cord-229937-fy90oebs 60 2 Fig Fig NNP cord-229937-fy90oebs 60 3 . . . cord-229937-fy90oebs 61 1 1 1 LS cord-229937-fy90oebs 61 2 , , , cord-229937-fy90oebs 61 3 we -PRON- PRP cord-229937-fy90oebs 61 4 present present VBP cord-229937-fy90oebs 61 5 the the DT cord-229937-fy90oebs 61 6 fit fit NN cord-229937-fy90oebs 61 7 of of IN cord-229937-fy90oebs 61 8 the the DT cord-229937-fy90oebs 61 9 D d NN cord-229937-fy90oebs 61 10 - - HYPH cord-229937-fy90oebs 61 11 model model NN cord-229937-fy90oebs 61 12 to to IN cord-229937-fy90oebs 61 13 the the DT cord-229937-fy90oebs 61 14 COVID-19 COVID-19 NNP cord-229937-fy90oebs 61 15 death death NN cord-229937-fy90oebs 61 16 data datum NNS cord-229937-fy90oebs 61 17 for for IN cord-229937-fy90oebs 61 18 China China NNP cord-229937-fy90oebs 61 19 , , , cord-229937-fy90oebs 61 20 where where WRB cord-229937-fy90oebs 61 21 its -PRON- PRP$ cord-229937-fy90oebs 61 22 evolution evolution NN cord-229937-fy90oebs 61 23 has have VBZ cord-229937-fy90oebs 61 24 apparently apparently RB cord-229937-fy90oebs 61 25 been be VBN cord-229937-fy90oebs 61 26 controlled control VBN cord-229937-fy90oebs 61 27 and and CC cord-229937-fy90oebs 61 28 the the DT cord-229937-fy90oebs 61 29 D d NN cord-229937-fy90oebs 61 30 function function NN cord-229937-fy90oebs 61 31 has have VBZ cord-229937-fy90oebs 61 32 reached reach VBN cord-229937-fy90oebs 61 33 the the DT cord-229937-fy90oebs 61 34 plateau plateau NN cord-229937-fy90oebs 61 35 zone zone NN cord-229937-fy90oebs 61 36 , , , cord-229937-fy90oebs 61 37 with with IN cord-229937-fy90oebs 61 38 few few JJ cord-229937-fy90oebs 61 39 increments increment NNS cord-229937-fy90oebs 61 40 over over IN cord-229937-fy90oebs 61 41 time time NN cord-229937-fy90oebs 61 42 , , , cord-229937-fy90oebs 61 43 or or CC cord-229937-fy90oebs 61 44 fluctuations fluctuation NNS cord-229937-fy90oebs 61 45 that that WDT cord-229937-fy90oebs 61 46 are be VBP cord-229937-fy90oebs 61 47 beyond beyond IN cord-229937-fy90oebs 61 48 the the DT cord-229937-fy90oebs 61 49 model model NN cord-229937-fy90oebs 61 50 assumptions assumption NNS cord-229937-fy90oebs 61 51 . . . cord-229937-fy90oebs 62 1 This this DT cord-229937-fy90oebs 62 2 plot plot NN cord-229937-fy90oebs 62 3 shows show VBZ cord-229937-fy90oebs 62 4 the the DT cord-229937-fy90oebs 62 5 duration duration NN cord-229937-fy90oebs 62 6 of of IN cord-229937-fy90oebs 62 7 the the DT cord-229937-fy90oebs 62 8 pandemic pandemic NN cord-229937-fy90oebs 62 9 -about -about RB cord-229937-fy90oebs 62 10 two two CD cord-229937-fy90oebs 62 11 months month NNS cord-229937-fy90oebs 62 12 to to TO cord-229937-fy90oebs 62 13 reach reach VB cord-229937-fy90oebs 62 14 the the DT cord-229937-fy90oebs 62 15 top top JJ cord-229937-fy90oebs 62 16 end end NN cord-229937-fy90oebs 62 17 of of IN cord-229937-fy90oebs 62 18 the the DT cord-229937-fy90oebs 62 19 curve curve NN cord-229937-fy90oebs 62 20 -and -and : cord-229937-fy90oebs 62 21 the the DT cord-229937-fy90oebs 62 22 agreement agreement NN cord-229937-fy90oebs 62 23 , , , cord-229937-fy90oebs 62 24 despite despite IN cord-229937-fy90oebs 62 25 the the DT cord-229937-fy90oebs 62 26 crude crude JJ cord-229937-fy90oebs 62 27 assumptions assumption NNS cord-229937-fy90oebs 62 28 , , , cord-229937-fy90oebs 62 29 between between IN cord-229937-fy90oebs 62 30 data datum NNS cord-229937-fy90oebs 62 31 and and CC cord-229937-fy90oebs 62 32 the the DT cord-229937-fy90oebs 62 33 evolution evolution NN cord-229937-fy90oebs 62 34 trend trend NN cord-229937-fy90oebs 62 35 described describe VBN cord-229937-fy90oebs 62 36 by by IN cord-229937-fy90oebs 62 37 the the DT cord-229937-fy90oebs 62 38 D d NN cord-229937-fy90oebs 62 39 - - HYPH cord-229937-fy90oebs 62 40 model model NN cord-229937-fy90oebs 62 41 . . . cord-229937-fy90oebs 63 1 This this DT cord-229937-fy90oebs 63 2 agreement agreement NN cord-229937-fy90oebs 63 3 encourages encourage VBZ cord-229937-fy90oebs 63 4 the the DT cord-229937-fy90oebs 63 5 application application NN cord-229937-fy90oebs 63 6 of of IN cord-229937-fy90oebs 63 7 the the DT cord-229937-fy90oebs 63 8 D D NNP cord-229937-fy90oebs 63 9 model model NN cord-229937-fy90oebs 63 10 to to IN cord-229937-fy90oebs 63 11 other other JJ cord-229937-fy90oebs 63 12 countries country NNS cord-229937-fy90oebs 63 13 in in IN cord-229937-fy90oebs 63 14 order order NN cord-229937-fy90oebs 63 15 to to TO cord-229937-fy90oebs 63 16 investigate investigate VB cord-229937-fy90oebs 63 17 the the DT cord-229937-fy90oebs 63 18 different different JJ cord-229937-fy90oebs 63 19 trends trend NNS cord-229937-fy90oebs 63 20 . . . cord-229937-fy90oebs 64 1 In in IN cord-229937-fy90oebs 64 2 order order NN cord-229937-fy90oebs 64 3 to to TO cord-229937-fy90oebs 64 4 get get VB cord-229937-fy90oebs 64 5 insight insight NN cord-229937-fy90oebs 64 6 into into IN cord-229937-fy90oebs 64 7 the the DT cord-229937-fy90oebs 64 8 stability stability NN cord-229937-fy90oebs 64 9 and and CC cord-229937-fy90oebs 64 10 uncertainty uncertainty NN cord-229937-fy90oebs 64 11 of of IN cord-229937-fy90oebs 64 12 our -PRON- PRP$ cord-229937-fy90oebs 64 13 predictions prediction NNS cord-229937-fy90oebs 64 14 , , , cord-229937-fy90oebs 64 15 Fig Fig NNP cord-229937-fy90oebs 64 16 . . . cord-229937-fy90oebs 65 1 II II NNP cord-229937-fy90oebs 65 2 shows show VBZ cord-229937-fy90oebs 65 3 the the DT cord-229937-fy90oebs 65 4 evolution evolution NN cord-229937-fy90oebs 65 5 of of IN cord-229937-fy90oebs 65 6 a a DT cord-229937-fy90oebs 65 7 , , , cord-229937-fy90oebs 65 8 b b NN cord-229937-fy90oebs 65 9 , , , cord-229937-fy90oebs 65 10 and and CC cord-229937-fy90oebs 65 11 c c NN cord-229937-fy90oebs 65 12 and and CC cord-229937-fy90oebs 65 13 other other JJ cord-229937-fy90oebs 65 14 model model NN cord-229937-fy90oebs 65 15 predictions prediction NNS cord-229937-fy90oebs 65 16 from from IN cord-229937-fy90oebs 65 17 fits fit NNS cord-229937-fy90oebs 65 18 to to IN cord-229937-fy90oebs 65 19 the the DT cord-229937-fy90oebs 65 20 daily daily JJ cord-229937-fy90oebs 65 21 data datum NNS cord-229937-fy90oebs 65 22 in in IN cord-229937-fy90oebs 65 23 Spain Spain NNP cord-229937-fy90oebs 65 24 . . . cord-229937-fy90oebs 66 1 The the DT cord-229937-fy90oebs 66 2 meaning meaning NN cord-229937-fy90oebs 66 3 of of IN cord-229937-fy90oebs 66 4 these these DT cord-229937-fy90oebs 66 5 quantities quantity NNS cord-229937-fy90oebs 66 6 is be VBZ cord-229937-fy90oebs 66 7 explained explain VBN cord-229937-fy90oebs 66 8 below below RB cord-229937-fy90oebs 66 9 : : : cord-229937-fy90oebs 67 1 • • NNP cord-229937-fy90oebs 68 1 The the DT cord-229937-fy90oebs 68 2 parameter parameter NN cord-229937-fy90oebs 68 3 a a NN cord-229937-fy90oebs 68 4 is be VBZ cord-229937-fy90oebs 68 5 the the DT cord-229937-fy90oebs 68 6 theoretical theoretical JJ cord-229937-fy90oebs 68 7 number number NN cord-229937-fy90oebs 68 8 of of IN cord-229937-fy90oebs 68 9 deaths death NNS cord-229937-fy90oebs 68 10 at at IN cord-229937-fy90oebs 68 11 the the DT cord-229937-fy90oebs 68 12 day day NN cord-229937-fy90oebs 68 13 corresponding correspond VBG cord-229937-fy90oebs 68 14 to to IN cord-229937-fy90oebs 68 15 t t NN cord-229937-fy90oebs 68 16 = = SYM cord-229937-fy90oebs 68 17 0 0 CD cord-229937-fy90oebs 68 18 . . . cord-229937-fy90oebs 69 1 In in IN cord-229937-fy90oebs 69 2 general general JJ cord-229937-fy90oebs 69 3 , , , cord-229937-fy90oebs 69 4 it -PRON- PRP cord-229937-fy90oebs 69 5 differs differ VBZ cord-229937-fy90oebs 69 6 from from IN cord-229937-fy90oebs 69 7 the the DT cord-229937-fy90oebs 69 8 experimental experimental JJ cord-229937-fy90oebs 69 9 value value NN cord-229937-fy90oebs 69 10 and and CC cord-229937-fy90oebs 69 11 can can MD cord-229937-fy90oebs 69 12 be be VB cord-229937-fy90oebs 69 13 interpreted interpret VBN cord-229937-fy90oebs 69 14 as as IN cord-229937-fy90oebs 69 15 the the DT cord-229937-fy90oebs 69 16 expected expect VBN cord-229937-fy90oebs 69 17 value value NN cord-229937-fy90oebs 69 18 of of IN cord-229937-fy90oebs 69 19 deaths death NNS cord-229937-fy90oebs 69 20 that that DT cord-229937-fy90oebs 69 21 day day NN cord-229937-fy90oebs 69 22 . . . cord-229937-fy90oebs 70 1 Note note VB cord-229937-fy90oebs 70 2 that that IN cord-229937-fy90oebs 70 3 experimental experimental JJ cord-229937-fy90oebs 70 4 data datum NNS cord-229937-fy90oebs 70 5 may may MD cord-229937-fy90oebs 70 6 be be VB cord-229937-fy90oebs 70 7 subject subject JJ cord-229937-fy90oebs 70 8 to to IN cord-229937-fy90oebs 70 9 unknown unknown JJ cord-229937-fy90oebs 70 10 systematic systematic JJ cord-229937-fy90oebs 70 11 errors error NNS cord-229937-fy90oebs 70 12 and and CC cord-229937-fy90oebs 70 13 different different JJ cord-229937-fy90oebs 70 14 counting counting NN cord-229937-fy90oebs 70 15 methods method NNS cord-229937-fy90oebs 70 16 . . . cord-229937-fy90oebs 71 1 • • NNP cord-229937-fy90oebs 72 1 The the DT cord-229937-fy90oebs 72 2 parameter parameter NN cord-229937-fy90oebs 72 3 b b NN cord-229937-fy90oebs 72 4 , , , cord-229937-fy90oebs 72 5 as as IN cord-229937-fy90oebs 72 6 mentioned mention VBN cord-229937-fy90oebs 72 7 above above RB cord-229937-fy90oebs 72 8 , , , cord-229937-fy90oebs 72 9 is be VBZ cord-229937-fy90oebs 72 10 the the DT cord-229937-fy90oebs 72 11 char- char- NN cord-229937-fy90oebs 72 12 acteristic acteristic NNP cord-229937-fy90oebs 72 13 evolution evolution NN cord-229937-fy90oebs 72 14 time time NN cord-229937-fy90oebs 72 15 . . . cord-229937-fy90oebs 73 1 During during IN cord-229937-fy90oebs 73 2 the the DT cord-229937-fy90oebs 73 3 initial initial JJ cord-229937-fy90oebs 73 4 expo expo NN cord-229937-fy90oebs 73 5 - - HYPH cord-229937-fy90oebs 73 6 nential nential JJ cord-229937-fy90oebs 73 7 behavior behavior NN cord-229937-fy90oebs 73 8 , , , cord-229937-fy90oebs 73 9 it -PRON- PRP cord-229937-fy90oebs 73 10 indicates indicate VBZ cord-229937-fy90oebs 73 11 the the DT cord-229937-fy90oebs 73 12 number number NN cord-229937-fy90oebs 73 13 of of IN cord-229937-fy90oebs 73 14 days day NNS cord-229937-fy90oebs 73 15 for for IN cord-229937-fy90oebs 73 16 the the DT cord-229937-fy90oebs 73 17 number number NN cord-229937-fy90oebs 73 18 of of IN cord-229937-fy90oebs 73 19 deaths death NNS cord-229937-fy90oebs 73 20 to to TO cord-229937-fy90oebs 73 21 double double VB cord-229937-fy90oebs 73 22 . . . cord-229937-fy90oebs 74 1 Moreover moreover RB cord-229937-fy90oebs 74 2 , , , cord-229937-fy90oebs 74 3 1 1 CD cord-229937-fy90oebs 74 4 / / SYM cord-229937-fy90oebs 74 5 b b NN cord-229937-fy90oebs 74 6 is be VBZ cord-229937-fy90oebs 74 7 proportional proportional JJ cord-229937-fy90oebs 74 8 to to IN cord-229937-fy90oebs 74 9 the the DT cord-229937-fy90oebs 74 10 slope slope NN cord-229937-fy90oebs 74 11 of of IN cord-229937-fy90oebs 74 12 the the DT cord-229937-fy90oebs 74 13 almost almost RB cord-229937-fy90oebs 74 14 linear linear JJ cord-229937-fy90oebs 74 15 behavior behavior NN cord-229937-fy90oebs 74 16 in in IN cord-229937-fy90oebs 74 17 the the DT cord-229937-fy90oebs 74 18 mid mid JJ cord-229937-fy90oebs 74 19 region region NN cord-229937-fy90oebs 74 20 of of IN cord-229937-fy90oebs 74 21 the the DT cord-229937-fy90oebs 74 22 D d NN cord-229937-fy90oebs 74 23 function function NN cord-229937-fy90oebs 74 24 . . . cord-229937-fy90oebs 75 1 That that DT cord-229937-fy90oebs 75 2 behavior behavior NN cord-229937-fy90oebs 75 3 can can MD cord-229937-fy90oebs 75 4 be be VB cord-229937-fy90oebs 75 5 obtained obtain VBN cord-229937-fy90oebs 75 6 by by IN cord-229937-fy90oebs 75 7 doing do VBG cord-229937-fy90oebs 75 8 a a DT cord-229937-fy90oebs 75 9 Taylor Taylor NNP cord-229937-fy90oebs 75 10 expansion expansion NN cord-229937-fy90oebs 75 11 around around IN cord-229937-fy90oebs 75 12 t t NN cord-229937-fy90oebs 75 13 0 0 CD cord-229937-fy90oebs 75 14 = = SYM cord-229937-fy90oebs 75 15 −b −b JJS cord-229937-fy90oebs 75 16 ℓn ℓn IN cord-229937-fy90oebs 75 17 c c NN cord-229937-fy90oebs 75 18 and and CC cord-229937-fy90oebs 75 19 is be VBZ cord-229937-fy90oebs 75 20 given give VBN cord-229937-fy90oebs 75 21 by by IN cord-229937-fy90oebs 75 22 • • NNP cord-229937-fy90oebs 76 1 The the DT cord-229937-fy90oebs 76 2 parameter parameter NN cord-229937-fy90oebs 76 3 c c NN cord-229937-fy90oebs 76 4 is be VBZ cord-229937-fy90oebs 76 5 called call VBN cord-229937-fy90oebs 76 6 the the DT cord-229937-fy90oebs 76 7 inverse inverse JJ cord-229937-fy90oebs 76 8 dead dead JJ cord-229937-fy90oebs 76 9 factor factor NN cord-229937-fy90oebs 76 10 because because IN cord-229937-fy90oebs 76 11 D(t D(t NNP cord-229937-fy90oebs 77 1 → → IN cord-229937-fy90oebs 77 2 ∞ ∞ NNP cord-229937-fy90oebs 77 3 ) ) -RRB- cord-229937-fy90oebs 77 4 = = NFP cord-229937-fy90oebs 77 5 a a NNP cord-229937-fy90oebs 77 6 / / SYM cord-229937-fy90oebs 77 7 c c NN cord-229937-fy90oebs 77 8 provides provide VBZ cord-229937-fy90oebs 77 9 the the DT cord-229937-fy90oebs 77 10 asymptotic asymptotic JJ cord-229937-fy90oebs 77 11 or or CC cord-229937-fy90oebs 77 12 expected expect VBD cord-229937-fy90oebs 77 13 total total JJ cord-229937-fy90oebs 77 14 number number NN cord-229937-fy90oebs 77 15 of of IN cord-229937-fy90oebs 77 16 deaths death NNS cord-229937-fy90oebs 77 17 . . . cord-229937-fy90oebs 78 1 Figure figure NN cord-229937-fy90oebs 78 2 II ii CD cord-229937-fy90oebs 78 3 shows show VBZ cord-229937-fy90oebs 78 4 the the DT cord-229937-fy90oebs 78 5 stable stable JJ cord-229937-fy90oebs 78 6 trend trend NN cord-229937-fy90oebs 78 7 of of IN cord-229937-fy90oebs 78 8 the the DT cord-229937-fy90oebs 78 9 parameters parameter NNS cord-229937-fy90oebs 78 10 between between IN cord-229937-fy90oebs 78 11 days day NNS cord-229937-fy90oebs 78 12 19 19 CD cord-229937-fy90oebs 78 13 to to TO cord-229937-fy90oebs 78 14 24 24 CD cord-229937-fy90oebs 78 15 ( ( -LRB- cord-229937-fy90oebs 78 16 corresponding correspond VBG cord-229937-fy90oebs 78 17 to to IN cord-229937-fy90oebs 78 18 March March NNP cord-229937-fy90oebs 78 19 27 27 CD cord-229937-fy90oebs 78 20 - - SYM cord-229937-fy90oebs 78 21 30 30 CD cord-229937-fy90oebs 78 22 ) ) -RRB- cord-229937-fy90oebs 78 23 , , , cord-229937-fy90oebs 78 24 right right RB cord-229937-fy90oebs 78 25 before before IN cord-229937-fy90oebs 78 26 reaching reach VBG cord-229937-fy90oebs 78 27 the the DT cord-229937-fy90oebs 78 28 peak peak NN cord-229937-fy90oebs 78 29 of of IN cord-229937-fy90oebs 78 30 deaths death NNS cord-229937-fy90oebs 78 31 cases case NNS cord-229937-fy90oebs 78 32 , , , cord-229937-fy90oebs 78 33 which which WDT cord-229937-fy90oebs 78 34 occurred occur VBD cord-229937-fy90oebs 78 35 in in IN cord-229937-fy90oebs 78 36 Spain Spain NNP cord-229937-fy90oebs 78 37 around around IN cord-229937-fy90oebs 78 38 April April NNP cord-229937-fy90oebs 78 39 1 1 CD cord-229937-fy90oebs 78 40 . . . cord-229937-fy90oebs 79 1 Such such JJ cord-229937-fy90oebs 79 2 stability stability NN cord-229937-fy90oebs 79 3 validates validate VBZ cord-229937-fy90oebs 79 4 the the DT cord-229937-fy90oebs 79 5 D d NN cord-229937-fy90oebs 79 6 - - HYPH cord-229937-fy90oebs 79 7 model model NN cord-229937-fy90oebs 79 8 predictions prediction NNS cord-229937-fy90oebs 79 9 during during IN cord-229937-fy90oebs 79 10 this this DT cord-229937-fy90oebs 79 11 time time NN cord-229937-fy90oebs 79 12 . . . cord-229937-fy90oebs 80 1 However however RB cord-229937-fy90oebs 80 2 , , , cord-229937-fy90oebs 80 3 a a DT cord-229937-fy90oebs 80 4 rapid rapid JJ cord-229937-fy90oebs 80 5 change change NN cord-229937-fy90oebs 80 6 of of IN cord-229937-fy90oebs 80 7 the the DT cord-229937-fy90oebs 80 8 parameters parameter NNS cord-229937-fy90oebs 80 9 is be VBZ cord-229937-fy90oebs 80 10 observed observe VBN cord-229937-fy90oebs 80 11 , , , cord-229937-fy90oebs 80 12 especially especially RB cord-229937-fy90oebs 80 13 for for IN cord-229937-fy90oebs 80 14 a a DT cord-229937-fy90oebs 80 15 , , , cord-229937-fy90oebs 80 16 once once IN cord-229937-fy90oebs 80 17 the the DT cord-229937-fy90oebs 80 18 peak peak NN cord-229937-fy90oebs 80 19 is be VBZ cord-229937-fy90oebs 80 20 reached reach VBN cord-229937-fy90oebs 80 21 , , , cord-229937-fy90oebs 80 22 drastically drastically RB cord-229937-fy90oebs 80 23 changing change VBG cord-229937-fy90oebs 80 24 the the DT cord-229937-fy90oebs 80 25 prediction prediction NN cord-229937-fy90oebs 80 26 of of IN cord-229937-fy90oebs 80 27 the the DT cord-229937-fy90oebs 80 28 number number NN cord-229937-fy90oebs 80 29 of of IN cord-229937-fy90oebs 80 30 deaths death NNS cord-229937-fy90oebs 80 31 given give VBN cord-229937-fy90oebs 80 32 by by IN cord-229937-fy90oebs 80 33 a a DT cord-229937-fy90oebs 80 34 / / SYM cord-229937-fy90oebs 80 35 c c NN cord-229937-fy90oebs 80 36 . . . cord-229937-fy90oebs 81 1 This this DT cord-229937-fy90oebs 81 2 sudden sudden JJ cord-229937-fy90oebs 81 3 change change NN cord-229937-fy90oebs 81 4 results result NNS cord-229937-fy90oebs 81 5 in in IN cord-229937-fy90oebs 81 6 the the DT cord-229937-fy90oebs 81 7 slowing slowing NN cord-229937-fy90oebs 81 8 down down RP cord-229937-fy90oebs 81 9 of of IN cord-229937-fy90oebs 81 10 deaths death NNS cord-229937-fy90oebs 81 11 per per IN cord-229937-fy90oebs 81 12 day day NN cord-229937-fy90oebs 81 13 and and CC cord-229937-fy90oebs 82 1 longer long JJR cord-229937-fy90oebs 82 2 time time NN cord-229937-fy90oebs 82 3 predictions prediction NNS cord-229937-fy90oebs 82 4 T T NNP cord-229937-fy90oebs 82 5 95 95 CD cord-229937-fy90oebs 82 6 and and CC cord-229937-fy90oebs 82 7 T T NNP cord-229937-fy90oebs 82 8 99 99 CD cord-229937-fy90oebs 82 9 . . . cord-229937-fy90oebs 83 1 The the DT cord-229937-fy90oebs 83 2 parameters parameter NNS cord-229937-fy90oebs 83 3 of of IN cord-229937-fy90oebs 83 4 the the DT cord-229937-fy90oebs 83 5 D d NN cord-229937-fy90oebs 83 6 model model NN cord-229937-fy90oebs 83 7 correspond correspond VB cord-229937-fy90oebs 83 8 to to IN cord-229937-fy90oebs 83 9 average average JJ cord-229937-fy90oebs 83 10 values value NNS cord-229937-fy90oebs 83 11 over over IN cord-229937-fy90oebs 83 12 time time NN cord-229937-fy90oebs 83 13 of of IN cord-229937-fy90oebs 83 14 the the DT cord-229937-fy90oebs 83 15 interaction interaction NN cord-229937-fy90oebs 83 16 coefficients coefficient NNS cord-229937-fy90oebs 83 17 between between IN cord-229937-fy90oebs 83 18 individuals individual NNS cord-229937-fy90oebs 83 19 , , , cord-229937-fy90oebs 83 20 i.e. i.e. FW cord-229937-fy90oebs 83 21 they -PRON- PRP cord-229937-fy90oebs 83 22 are be VBP cord-229937-fy90oebs 83 23 sensitive sensitive JJ cord-229937-fy90oebs 83 24 to to IN cord-229937-fy90oebs 83 25 an an DT cord-229937-fy90oebs 83 26 additional additional JJ cord-229937-fy90oebs 83 27 external external JJ cord-229937-fy90oebs 83 28 effect effect NN cord-229937-fy90oebs 83 29 on on IN cord-229937-fy90oebs 83 30 the the DT cord-229937-fy90oebs 83 31 pandemic pandemic NN cord-229937-fy90oebs 83 32 evolution evolution NN cord-229937-fy90oebs 83 33 . . . cord-229937-fy90oebs 84 1 These these DT cord-229937-fy90oebs 84 2 may may MD cord-229937-fy90oebs 84 3 include include VB cord-229937-fy90oebs 84 4 the the DT cord-229937-fy90oebs 84 5 lockdown lockdown NN cord-229937-fy90oebs 84 6 effect effect NN cord-229937-fy90oebs 84 7 imposed impose VBN cord-229937-fy90oebs 84 8 in in IN cord-229937-fy90oebs 84 9 Spain Spain NNP cord-229937-fy90oebs 84 10 in in IN cord-229937-fy90oebs 84 11 March March NNP cord-229937-fy90oebs 84 12 14 14 CD cord-229937-fy90oebs 84 13 and and CC cord-229937-fy90oebs 84 14 other other JJ cord-229937-fy90oebs 84 15 effects effect NNS cord-229937-fy90oebs 84 16 such such JJ cord-229937-fy90oebs 84 17 as as IN cord-229937-fy90oebs 84 18 new new JJ cord-229937-fy90oebs 84 19 sources source NNS cord-229937-fy90oebs 84 20 of of IN cord-229937-fy90oebs 84 21 infection infection NN cord-229937-fy90oebs 84 22 or or CC cord-229937-fy90oebs 84 23 a a DT cord-229937-fy90oebs 84 24 sudden sudden JJ cord-229937-fy90oebs 84 25 increase increase NN cord-229937-fy90oebs 84 26 of of IN cord-229937-fy90oebs 84 27 the the DT cord-229937-fy90oebs 84 28 total total JJ cord-229937-fy90oebs 84 29 susceptible susceptible JJ cord-229937-fy90oebs 84 30 individuals individual NNS cord-229937-fy90oebs 84 31 due due JJ cord-229937-fy90oebs 84 32 to to IN cord-229937-fy90oebs 84 33 social social JJ cord-229937-fy90oebs 84 34 migration migration NN cord-229937-fy90oebs 84 35 and and CC cord-229937-fy90oebs 84 36 large large JJ cord-229937-fy90oebs 84 37 mass mass NN cord-229937-fy90oebs 84 38 gatherings gathering NNS cord-229937-fy90oebs 84 39 [ [ -LRB- cord-229937-fy90oebs 84 40 20 20 CD cord-229937-fy90oebs 84 41 ] ] -RRB- cord-229937-fy90oebs 84 42 . . . cord-229937-fy90oebs 85 1 It -PRON- PRP cord-229937-fy90oebs 85 2 is be VBZ cord-229937-fy90oebs 85 3 not not RB cord-229937-fy90oebs 85 4 possible possible JJ cord-229937-fy90oebs 85 5 to to TO cord-229937-fy90oebs 85 6 identify identify VB cord-229937-fy90oebs 85 7 a a DT cord-229937-fy90oebs 85 8 specific specific JJ cord-229937-fy90oebs 85 9 cause cause NN cord-229937-fy90oebs 85 10 because because IN cord-229937-fy90oebs 85 11 its -PRON- PRP$ cord-229937-fy90oebs 85 12 effects effect NNS cord-229937-fy90oebs 85 13 are be VBP cord-229937-fy90oebs 85 14 blurred blur VBN cord-229937-fy90oebs 85 15 by by IN cord-229937-fy90oebs 85 16 the the DT cord-229937-fy90oebs 85 17 stochastic stochastic JJ cord-229937-fy90oebs 85 18 evolution evolution NN cord-229937-fy90oebs 85 19 of of IN cord-229937-fy90oebs 85 20 the the DT cord-229937-fy90oebs 85 21 pandemic pandemic NN cord-229937-fy90oebs 85 22 , , , cord-229937-fy90oebs 85 23 which which WDT cord-229937-fy90oebs 85 24 is be VBZ cord-229937-fy90oebs 85 25 why why WRB cord-229937-fy90oebs 85 26 any any DT cord-229937-fy90oebs 85 27 reliable reliable JJ cord-229937-fy90oebs 85 28 forecast forecast NN cord-229937-fy90oebs 85 29 presents present VBZ cord-229937-fy90oebs 85 30 large large JJ cord-229937-fy90oebs 85 31 errors error NNS cord-229937-fy90oebs 85 32 . . . cord-229937-fy90oebs 86 1 One one PRP cord-229937-fy90oebs 86 2 can can MD cord-229937-fy90oebs 86 3 also also RB cord-229937-fy90oebs 86 4 determine determine VB cord-229937-fy90oebs 86 5 deaths death NNS cord-229937-fy90oebs 86 6 / / SYM cord-229937-fy90oebs 86 7 day day NN cord-229937-fy90oebs 86 8 rates rate NNS cord-229937-fy90oebs 86 9 by by IN cord-229937-fy90oebs 86 10 applying apply VBG cord-229937-fy90oebs 86 11 the the DT cord-229937-fy90oebs 86 12 first first JJ cord-229937-fy90oebs 86 13 derivative derivative NN cord-229937-fy90oebs 86 14 to to IN cord-229937-fy90oebs 86 15 Eq Eq NNP cord-229937-fy90oebs 86 16 . . . cord-229937-fy90oebs 87 1 15 15 CD cord-229937-fy90oebs 87 2 , , , cord-229937-fy90oebs 87 3 which which WDT cord-229937-fy90oebs 87 4 allows allow VBZ cord-229937-fy90oebs 87 5 for for IN cord-229937-fy90oebs 87 6 a a DT cord-229937-fy90oebs 87 7 determination determination NN cord-229937-fy90oebs 87 8 of of IN cord-229937-fy90oebs 87 9 the the DT cord-229937-fy90oebs 87 10 pandemics pandemic NNS cord-229937-fy90oebs 87 11 peak peak NN cord-229937-fy90oebs 87 12 and and CC cord-229937-fy90oebs 87 13 evolution evolution NN cord-229937-fy90oebs 87 14 after after IN cord-229937-fy90oebs 87 15 its -PRON- PRP$ cord-229937-fy90oebs 87 16 turning turning NN cord-229937-fy90oebs 87 17 point point NN cord-229937-fy90oebs 87 18 . . . cord-229937-fy90oebs 88 1 The the DT cord-229937-fy90oebs 88 2 D d NN cord-229937-fy90oebs 88 3 model model NN cord-229937-fy90oebs 88 4 describes describe VBZ cord-229937-fy90oebs 88 5 well well RB cord-229937-fy90oebs 88 6 the the DT cord-229937-fy90oebs 88 7 cumulative cumulative JJ cord-229937-fy90oebs 88 8 deaths death NNS cord-229937-fy90oebs 88 9 because because IN cord-229937-fy90oebs 88 10 the the DT cord-229937-fy90oebs 88 11 sum sum NN cord-229937-fy90oebs 88 12 of of IN cord-229937-fy90oebs 88 13 discrete discrete JJ cord-229937-fy90oebs 88 14 data datum NNS cord-229937-fy90oebs 88 15 reduce reduce VBP cord-229937-fy90oebs 88 16 the the DT cord-229937-fy90oebs 88 17 fluctuations fluctuation NNS cord-229937-fy90oebs 88 18 , , , cord-229937-fy90oebs 88 19 in in IN cord-229937-fy90oebs 88 20 the the DT cord-229937-fy90oebs 88 21 same same JJ cord-229937-fy90oebs 88 22 way way NN cord-229937-fy90oebs 88 23 as as IN cord-229937-fy90oebs 88 24 the the DT cord-229937-fy90oebs 88 25 integral integral NN cord-229937-fy90oebs 88 26 of of IN cord-229937-fy90oebs 88 27 a a DT cord-229937-fy90oebs 88 28 discontinuous discontinuous JJ cord-229937-fy90oebs 88 29 function function NN cord-229937-fy90oebs 88 30 is be VBZ cord-229937-fy90oebs 88 31 a a DT cord-229937-fy90oebs 88 32 continuous continuous JJ cord-229937-fy90oebs 88 33 function function NN cord-229937-fy90oebs 88 34 . . . cord-229937-fy90oebs 89 1 However however RB cord-229937-fy90oebs 89 2 , , , cord-229937-fy90oebs 89 3 the the DT cord-229937-fy90oebs 89 4 daily daily JJ cord-229937-fy90oebs 89 5 data datum NNS cord-229937-fy90oebs 89 6 required require VBN cord-229937-fy90oebs 89 7 for for IN cord-229937-fy90oebs 89 8 D D NNP cord-229937-fy90oebs 89 9 ′ ′ CD cord-229937-fy90oebs 89 10 have have VBP cord-229937-fy90oebs 89 11 large large JJ cord-229937-fy90oebs 89 12 fluctuations fluctuation NNS cord-229937-fy90oebs 89 13 -both -both . cord-229937-fy90oebs 90 1 statistical statistical JJ cord-229937-fy90oebs 90 2 and and CC cord-229937-fy90oebs 90 3 systematic systematic JJ cord-229937-fy90oebs 90 4 -which -which : cord-229937-fy90oebs 90 5 normally normally RB cord-229937-fy90oebs 90 6 gives give VBZ cord-229937-fy90oebs 90 7 a a DT cord-229937-fy90oebs 90 8 slightly slightly RB cord-229937-fy90oebs 90 9 different different JJ cord-229937-fy90oebs 90 10 set set NN cord-229937-fy90oebs 90 11 of of IN cord-229937-fy90oebs 90 12 parameters parameter NNS cord-229937-fy90oebs 90 13 when when WRB cord-229937-fy90oebs 90 14 compared compare VBN cord-229937-fy90oebs 90 15 with with IN cord-229937-fy90oebs 90 16 the the DT cord-229937-fy90oebs 90 17 D d NN cord-229937-fy90oebs 90 18 model model NN cord-229937-fy90oebs 90 19 . . . cord-229937-fy90oebs 91 1 Using use VBG cord-229937-fy90oebs 91 2 the the DT cord-229937-fy90oebs 91 3 D d NN cord-229937-fy90oebs 91 4 model model NN cord-229937-fy90oebs 91 5 fitted fit VBN cord-229937-fy90oebs 91 6 to to IN cord-229937-fy90oebs 91 7 cumulative cumulative JJ cord-229937-fy90oebs 91 8 deaths death NNS cord-229937-fy90oebs 91 9 allows allow VBZ cord-229937-fy90oebs 91 10 to to TO cord-229937-fy90oebs 91 11 compute compute VB cord-229937-fy90oebs 91 12 deaths death NNS cord-229937-fy90oebs 91 13 / / SYM cord-229937-fy90oebs 91 14 day day NN cord-229937-fy90oebs 91 15 as as IN cord-229937-fy90oebs 91 16 where where WRB cord-229937-fy90oebs 91 17 ∆t ∆t NN cord-229937-fy90oebs 91 18 = = SYM cord-229937-fy90oebs 91 19 1 1 CD cord-229937-fy90oebs 91 20 day day NN cord-229937-fy90oebs 91 21 . . . cord-229937-fy90oebs 92 1 Figure figure NN cord-229937-fy90oebs 92 2 3 3 CD cord-229937-fy90oebs 92 3 shows show VBZ cord-229937-fy90oebs 92 4 that that IN cord-229937-fy90oebs 92 5 Eqs Eqs NNP cord-229937-fy90oebs 92 6 . . . cord-229937-fy90oebs 93 1 18 18 CD cord-229937-fy90oebs 93 2 and and CC cord-229937-fy90oebs 93 3 19 19 CD cord-229937-fy90oebs 93 4 yield yield VBP cord-229937-fy90oebs 93 5 similar similar JJ cord-229937-fy90oebs 93 6 parameters parameter NNS cord-229937-fy90oebs 93 7 , , , cord-229937-fy90oebs 93 8 as as IN cord-229937-fy90oebs 93 9 the the DT cord-229937-fy90oebs 93 10 time time NN cord-229937-fy90oebs 93 11 increment increment NN cord-229937-fy90oebs 93 12 is be VBZ cord-229937-fy90oebs 93 13 small small JJ cord-229937-fy90oebs 93 14 enough enough RB cord-229937-fy90oebs 93 15 compared compare VBN cord-229937-fy90oebs 93 16 with with IN cord-229937-fy90oebs 93 17 the the DT cord-229937-fy90oebs 93 18 time time NN cord-229937-fy90oebs 93 19 evolution evolution NN cord-229937-fy90oebs 93 20 of of IN cord-229937-fy90oebs 93 21 the the DT cord-229937-fy90oebs 93 22 D(t D(t NNP cord-229937-fy90oebs 93 23 ) ) -RRB- cord-229937-fy90oebs 93 24 function function NN cord-229937-fy90oebs 93 25 . . . cord-229937-fy90oebs 94 1 Hence hence RB cord-229937-fy90oebs 94 2 , , , cord-229937-fy90oebs 94 3 the the DT cord-229937-fy90oebs 94 4 first first JJ cord-229937-fy90oebs 94 5 derivative derivative JJ cord-229937-fy90oebs 94 6 D d NN cord-229937-fy90oebs 94 7 ′ ′ CD cord-229937-fy90oebs 94 8 ( ( -LRB- cord-229937-fy90oebs 94 9 t t NN cord-229937-fy90oebs 94 10 ) ) -RRB- cord-229937-fy90oebs 94 11 can can MD cord-229937-fy90oebs 94 12 be be VB cord-229937-fy90oebs 94 13 used use VBN cord-229937-fy90oebs 94 14 to to TO cord-229937-fy90oebs 94 15 describe describe VB cord-229937-fy90oebs 94 16 deaths death NNS cord-229937-fy90oebs 94 17 per per IN cord-229937-fy90oebs 94 18 day day NN cord-229937-fy90oebs 94 19 . . . cord-229937-fy90oebs 95 1 In in IN cord-229937-fy90oebs 95 2 addition addition NN cord-229937-fy90oebs 95 3 , , , cord-229937-fy90oebs 95 4 Fig Fig NNP cord-229937-fy90oebs 95 5 . . NNP cord-229937-fy90oebs 95 6 4 4 CD cord-229937-fy90oebs 95 7 shows show VBZ cord-229937-fy90oebs 95 8 that that IN cord-229937-fy90oebs 95 9 the the DT cord-229937-fy90oebs 95 10 parameters parameter NNS cord-229937-fy90oebs 95 11 may may MD cord-229937-fy90oebs 95 12 be be VB cord-229937-fy90oebs 95 13 different different JJ cord-229937-fy90oebs 95 14 for for IN cord-229937-fy90oebs 95 15 both both CC cord-229937-fy90oebs 95 16 D d NN cord-229937-fy90oebs 95 17 and and CC cord-229937-fy90oebs 95 18 D D NNP cord-229937-fy90oebs 95 19 ′ ′ CD cord-229937-fy90oebs 95 20 functions function NNS cord-229937-fy90oebs 95 21 using use VBG cord-229937-fy90oebs 95 22 cumulative cumulative JJ cord-229937-fy90oebs 95 23 and and CC cord-229937-fy90oebs 95 24 daily daily JJ cord-229937-fy90oebs 95 25 deaths death NNS cord-229937-fy90oebs 95 26 , , , cord-229937-fy90oebs 95 27 respectively respectively RB cord-229937-fy90oebs 95 28 , , , cord-229937-fy90oebs 95 29 as as IN cord-229937-fy90oebs 95 30 shown show VBN cord-229937-fy90oebs 95 31 for for IN cord-229937-fy90oebs 95 32 Spain Spain NNP cord-229937-fy90oebs 95 33 on on IN cord-229937-fy90oebs 95 34 April April NNP cord-229937-fy90oebs 95 35 5 5 CD cord-229937-fy90oebs 95 36 . . . cord-229937-fy90oebs 96 1 It -PRON- PRP cord-229937-fy90oebs 96 2 is be VBZ cord-229937-fy90oebs 96 3 also also RB cord-229937-fy90oebs 96 4 important important JJ cord-229937-fy90oebs 96 5 to to TO cord-229937-fy90oebs 96 6 note note VB cord-229937-fy90oebs 96 7 that that DT cord-229937-fy90oebs 96 8 b b NN cord-229937-fy90oebs 96 9 is be VBZ cord-229937-fy90oebs 96 10 directly directly RB cord-229937-fy90oebs 96 11 proportional proportional JJ cord-229937-fy90oebs 96 12 to to IN cord-229937-fy90oebs 96 13 the the DT cord-229937-fy90oebs 96 14 full full JJ cord-229937-fy90oebs 96 15 width width NN cord-229937-fy90oebs 96 16 at at IN cord-229937-fy90oebs 96 17 half half JJ cord-229937-fy90oebs 96 18 maximum maximum NN cord-229937-fy90oebs 96 19 ( ( -LRB- cord-229937-fy90oebs 96 20 F F NNP cord-229937-fy90oebs 96 21 W W NNP cord-229937-fy90oebs 96 22 HM HM NNP cord-229937-fy90oebs 96 23 ) ) -RRB- cord-229937-fy90oebs 96 24 of of IN cord-229937-fy90oebs 96 25 the the DT cord-229937-fy90oebs 96 26 D d NN cord-229937-fy90oebs 96 27 ′ ′ CD cord-229937-fy90oebs 96 28 ( ( -LRB- cord-229937-fy90oebs 96 29 t t NN cord-229937-fy90oebs 96 30 ) ) -RRB- cord-229937-fy90oebs 96 31 distribution distribution NN cord-229937-fy90oebs 96 32 , , , cord-229937-fy90oebs 97 1 As as IN cord-229937-fy90oebs 97 2 shown show VBN cord-229937-fy90oebs 97 3 below below RB cord-229937-fy90oebs 97 4 , , , cord-229937-fy90oebs 97 5 the the DT cord-229937-fy90oebs 97 6 b b NN cord-229937-fy90oebs 97 7 parameter parameter NN cord-229937-fy90oebs 97 8 presents present VBZ cord-229937-fy90oebs 97 9 typical typical JJ cord-229937-fy90oebs 97 10 values value NNS cord-229937-fy90oebs 97 11 between between IN cord-229937-fy90oebs 97 12 4 4 CD cord-229937-fy90oebs 97 13 and and CC cord-229937-fy90oebs 97 14 10 10 CD cord-229937-fy90oebs 97 15 for for IN cord-229937-fy90oebs 97 16 most most JJS cord-229937-fy90oebs 97 17 countries country NNS cord-229937-fy90oebs 97 18 undergoing undergo VBG cord-229937-fy90oebs 97 19 the the DT cord-229937-fy90oebs 97 20 initial initial JJ cord-229937-fy90oebs 97 21 exponential exponential JJ cord-229937-fy90oebs 97 22 phase phase NN cord-229937-fy90oebs 97 23 , , , cord-229937-fy90oebs 97 24 which which WDT cord-229937-fy90oebs 97 25 yields yield VBZ cord-229937-fy90oebs 97 26 a a DT cord-229937-fy90oebs 97 27 minimum minimum NN cord-229937-fy90oebs 97 28 and and CC cord-229937-fy90oebs 97 29 maximum maximum JJ cord-229937-fy90oebs 97 30 time time NN cord-229937-fy90oebs 97 31 of of IN cord-229937-fy90oebs 97 32 14 14 CD cord-229937-fy90oebs 97 33 and and CC cord-229937-fy90oebs 97 34 35 35 CD cord-229937-fy90oebs 97 35 days day NNS cord-229937-fy90oebs 97 36 , , , cord-229937-fy90oebs 97 37 respectively respectively RB cord-229937-fy90oebs 97 38 , , , cord-229937-fy90oebs 97 39 between between IN cord-229937-fy90oebs 97 40 the the DT cord-229937-fy90oebs 97 41 two two CD cord-229937-fy90oebs 97 42 extreme extreme JJ cord-229937-fy90oebs 97 43 values value NNS cord-229937-fy90oebs 97 44 of of IN cord-229937-fy90oebs 97 45 the the DT cord-229937-fy90oebs 97 46 F F NNP cord-229937-fy90oebs 97 47 W W NNP cord-229937-fy90oebs 97 48 HM HM NNP cord-229937-fy90oebs 97 49 . . . cord-229937-fy90oebs 98 1 C. C. NNP cord-229937-fy90oebs 98 2 Dn Dn NNP cord-229937-fy90oebs 98 3 model model NN cord-229937-fy90oebs 98 4 with with IN cord-229937-fy90oebs 98 5 two two CD cord-229937-fy90oebs 98 6 or or CC cord-229937-fy90oebs 98 7 more more JJR cord-229937-fy90oebs 98 8 channels channel NNS cord-229937-fy90oebs 98 9 of of IN cord-229937-fy90oebs 98 10 infection infection NN cord-229937-fy90oebs 99 1 Some some DT cord-229937-fy90oebs 99 2 models model NNS cord-229937-fy90oebs 99 3 [ [ -LRB- cord-229937-fy90oebs 99 4 21 21 CD cord-229937-fy90oebs 99 5 ] ] -RRB- cord-229937-fy90oebs 99 6 include include VBP cord-229937-fy90oebs 99 7 changes change NNS cord-229937-fy90oebs 99 8 in in IN cord-229937-fy90oebs 99 9 the the DT cord-229937-fy90oebs 99 10 transmission transmission NN cord-229937-fy90oebs 99 11 rate rate NN cord-229937-fy90oebs 99 12 due due IN cord-229937-fy90oebs 99 13 to to IN cord-229937-fy90oebs 99 14 various various JJ cord-229937-fy90oebs 99 15 interventions intervention NNS cord-229937-fy90oebs 99 16 implemented implement VBN cord-229937-fy90oebs 99 17 to to TO cord-229937-fy90oebs 99 18 contain contain VB cord-229937-fy90oebs 99 19 the the DT cord-229937-fy90oebs 99 20 outbreak outbreak NN cord-229937-fy90oebs 99 21 . . . cord-229937-fy90oebs 100 1 The the DT cord-229937-fy90oebs 100 2 simple simple JJ cord-229937-fy90oebs 100 3 D d NN cord-229937-fy90oebs 100 4 model model NN cord-229937-fy90oebs 100 5 does do VBZ cord-229937-fy90oebs 100 6 not not RB cord-229937-fy90oebs 100 7 allow allow VB cord-229937-fy90oebs 100 8 to to TO cord-229937-fy90oebs 100 9 do do VB cord-229937-fy90oebs 100 10 this this DT cord-229937-fy90oebs 100 11 explicitly explicitly RB cord-229937-fy90oebs 100 12 , , , cord-229937-fy90oebs 100 13 but but CC cord-229937-fy90oebs 100 14 changes change NNS cord-229937-fy90oebs 100 15 in in IN cord-229937-fy90oebs 100 16 the the DT cord-229937-fy90oebs 100 17 spread spread NN cord-229937-fy90oebs 100 18 can can MD cord-229937-fy90oebs 100 19 be be VB cord-229937-fy90oebs 100 20 taken take VBN cord-229937-fy90oebs 100 21 into into IN cord-229937-fy90oebs 100 22 account account NN cord-229937-fy90oebs 100 23 by by IN cord-229937-fy90oebs 100 24 considering consider VBG cord-229937-fy90oebs 100 25 the the DT cord-229937-fy90oebs 100 26 total total JJ cord-229937-fy90oebs 100 27 D d NN cord-229937-fy90oebs 100 28 or or CC cord-229937-fy90oebs 100 29 D d NN cord-229937-fy90oebs 100 30 n n NN cord-229937-fy90oebs 100 31 function function NN cord-229937-fy90oebs 100 32 as as IN cord-229937-fy90oebs 100 33 the the DT cord-229937-fy90oebs 100 34 sum sum NN cord-229937-fy90oebs 100 35 of of IN cord-229937-fy90oebs 100 36 two two CD cord-229937-fy90oebs 100 37 or or CC cord-229937-fy90oebs 100 38 more more JJR cord-229937-fy90oebs 100 39 independent independent JJ cord-229937-fy90oebs 100 40 D d NN cord-229937-fy90oebs 100 41 - - HYPH cord-229937-fy90oebs 100 42 functions function NNS cord-229937-fy90oebs 100 43 with with IN cord-229937-fy90oebs 100 44 different different JJ cord-229937-fy90oebs 100 45 parameters parameter NNS cord-229937-fy90oebs 100 46 , , , cord-229937-fy90oebs 100 47 which which WDT cord-229937-fy90oebs 100 48 may may MD cord-229937-fy90oebs 100 49 reveal reveal VB cord-229937-fy90oebs 100 50 the the DT cord-229937-fy90oebs 100 51 existence existence NN cord-229937-fy90oebs 100 52 of of IN cord-229937-fy90oebs 100 53 several several JJ cord-229937-fy90oebs 100 54 independent independent JJ cord-229937-fy90oebs 100 55 sources source NNS cord-229937-fy90oebs 100 56 , , , cord-229937-fy90oebs 100 57 or or CC cord-229937-fy90oebs 100 58 virus virus NN cord-229937-fy90oebs 100 59 channels channel NNS cord-229937-fy90oebs 100 60 . . . cord-229937-fy90oebs 101 1 An an DT cord-229937-fy90oebs 101 2 example example NN cord-229937-fy90oebs 101 3 is be VBZ cord-229937-fy90oebs 101 4 shown show VBN cord-229937-fy90oebs 101 5 in in IN cord-229937-fy90oebs 101 6 Fig Fig NNP cord-229937-fy90oebs 101 7 . . . cord-229937-fy90oebs 102 1 5 5 LS cord-229937-fy90oebs 102 2 , , , cord-229937-fy90oebs 102 3 where where WRB cord-229937-fy90oebs 102 4 the the DT cord-229937-fy90oebs 102 5 two two CD cord-229937-fy90oebs 102 6 - - HYPH cord-229937-fy90oebs 102 7 channel channel NN cord-229937-fy90oebs 102 8 function function NN cord-229937-fy90oebs 102 9 has have VBZ cord-229937-fy90oebs 102 10 been be VBN cord-229937-fy90oebs 102 11 fitted fit VBN cord-229937-fy90oebs 102 12 with with IN cord-229937-fy90oebs 102 13 six six CD cord-229937-fy90oebs 102 14 parameters parameter NNS cord-229937-fy90oebs 102 15 to to IN cord-229937-fy90oebs 102 16 the the DT cord-229937-fy90oebs 102 17 Spanish spanish JJ cord-229937-fy90oebs 102 18 data datum NNS cord-229937-fy90oebs 102 19 up up IN cord-229937-fy90oebs 102 20 to to IN cord-229937-fy90oebs 102 21 April April NNP cord-229937-fy90oebs 102 22 13 13 CD cord-229937-fy90oebs 102 23 . . . cord-229937-fy90oebs 103 1 The the DT cord-229937-fy90oebs 103 2 fit fit NN cord-229937-fy90oebs 103 3 reveals reveal VBZ cord-229937-fy90oebs 103 4 a a DT cord-229937-fy90oebs 103 5 second second JJ cord-229937-fy90oebs 103 6 , , , cord-229937-fy90oebs 103 7 smaller small JJR cord-229937-fy90oebs 103 8 death death NN cord-229937-fy90oebs 103 9 peak peak NN cord-229937-fy90oebs 103 10 , , , cord-229937-fy90oebs 103 11 which which WDT cord-229937-fy90oebs 103 12 substantially substantially RB cord-229937-fy90oebs 103 13 increase increase VBP cord-229937-fy90oebs 103 14 the the DT cord-229937-fy90oebs 103 15 number number NN cord-229937-fy90oebs 103 16 of of IN cord-229937-fy90oebs 103 17 deaths death NNS cord-229937-fy90oebs 103 18 per per IN cord-229937-fy90oebs 103 19 day day NN cord-229937-fy90oebs 103 20 and and CC cord-229937-fy90oebs 103 21 the the DT cord-229937-fy90oebs 103 22 duration duration NN cord-229937-fy90oebs 103 23 of of IN cord-229937-fy90oebs 103 24 the the DT cord-229937-fy90oebs 103 25 pandemic pandemic NN cord-229937-fy90oebs 103 26 . . . cord-229937-fy90oebs 104 1 This this DT cord-229937-fy90oebs 104 2 is be VBZ cord-229937-fy90oebs 104 3 equivalent equivalent JJ cord-229937-fy90oebs 104 4 to to TO cord-229937-fy90oebs 104 5 add add VB cord-229937-fy90oebs 104 6 a a DT cord-229937-fy90oebs 104 7 second second JJ cord-229937-fy90oebs 104 8 , , , cord-229937-fy90oebs 104 9 independent independent JJ cord-229937-fy90oebs 104 10 , , , cord-229937-fy90oebs 104 11 source source NN cord-229937-fy90oebs 104 12 of of IN cord-229937-fy90oebs 104 13 infection infection NN cord-229937-fy90oebs 104 14 several several JJ cord-229937-fy90oebs 104 15 weeks week NNS cord-229937-fy90oebs 104 16 after after IN cord-229937-fy90oebs 104 17 the the DT cord-229937-fy90oebs 104 18 initial initial JJ cord-229937-fy90oebs 104 19 pandemic pandemic NN cord-229937-fy90oebs 104 20 . . . cord-229937-fy90oebs 105 1 The the DT cord-229937-fy90oebs 105 2 second second JJ cord-229937-fy90oebs 105 3 peak peak NN cord-229937-fy90oebs 105 4 may may MD cord-229937-fy90oebs 105 5 as as RB cord-229937-fy90oebs 105 6 well well RB cord-229937-fy90oebs 105 7 represent represent VB cord-229937-fy90oebs 105 8 a a DT cord-229937-fy90oebs 105 9 second second JJ cord-229937-fy90oebs 105 10 pandemic pandemic NN cord-229937-fy90oebs 105 11 phase phase NN cord-229937-fy90oebs 105 12 driving drive VBG cord-229937-fy90oebs 105 13 the the DT cord-229937-fy90oebs 105 14 effects effect NNS cord-229937-fy90oebs 105 15 of of IN cord-229937-fy90oebs 105 16 quarantine quarantine NN cord-229937-fy90oebs 105 17 during during IN cord-229937-fy90oebs 105 18 the the DT cord-229937-fy90oebs 105 19 descendant descendant JJ cord-229937-fy90oebs 105 20 part part NN cord-229937-fy90oebs 105 21 of of IN cord-229937-fy90oebs 105 22 the the DT cord-229937-fy90oebs 105 23 curve curve NN cord-229937-fy90oebs 105 24 . . . cord-229937-fy90oebs 106 1 Additionally additionally RB cord-229937-fy90oebs 106 2 , , , cord-229937-fy90oebs 106 3 the the DT cord-229937-fy90oebs 106 4 cumulative cumulative JJ cord-229937-fy90oebs 106 5 D d NN cord-229937-fy90oebs 106 6 - - HYPH cord-229937-fy90oebs 106 7 function function NN cord-229937-fy90oebs 106 8 can can MD cord-229937-fy90oebs 106 9 also also RB cord-229937-fy90oebs 106 10 be be VB cord-229937-fy90oebs 106 11 computed compute VBN cord-229937-fy90oebs 106 12 with with IN cord-229937-fy90oebs 106 13 a a DT cord-229937-fy90oebs 106 14 two two CD cord-229937-fy90oebs 106 15 - - HYPH cord-229937-fy90oebs 106 16 channel channel NN cord-229937-fy90oebs 106 17 function function NN cord-229937-fy90oebs 106 18 , , , cord-229937-fy90oebs 106 19 which which WDT cord-229937-fy90oebs 106 20 provides provide VBZ cord-229937-fy90oebs 106 21 , , , cord-229937-fy90oebs 106 22 as as IN cord-229937-fy90oebs 106 23 shown show VBN cord-229937-fy90oebs 106 24 in in IN cord-229937-fy90oebs 106 25 Fig Fig NNP cord-229937-fy90oebs 106 26 . . . cord-229937-fy90oebs 107 1 6 6 LS cord-229937-fy90oebs 107 2 , , , cord-229937-fy90oebs 107 3 a a DT cord-229937-fy90oebs 107 4 more more RBR cord-229937-fy90oebs 107 5 accurate accurate JJ cord-229937-fy90oebs 107 6 prediction prediction NN cord-229937-fy90oebs 107 7 for for IN cord-229937-fy90oebs 107 8 the the DT cord-229937-fy90oebs 107 9 total total JJ cord-229937-fy90oebs 107 10 number number NN cord-229937-fy90oebs 107 11 of of IN cord-229937-fy90oebs 107 12 deaths death NNS cord-229937-fy90oebs 107 13 and and CC cord-229937-fy90oebs 107 14 clearly clearly RB cord-229937-fy90oebs 107 15 illustrates illustrate VBZ cord-229937-fy90oebs 107 16 the the DT cord-229937-fy90oebs 107 17 separate separate JJ cord-229937-fy90oebs 107 18 effect effect NN cord-229937-fy90oebs 107 19 of of IN cord-229937-fy90oebs 107 20 both both DT cord-229937-fy90oebs 107 21 source source NN cord-229937-fy90oebs 107 22 peaks peak NNS cord-229937-fy90oebs 107 23 . . . cord-229937-fy90oebs 108 1 It -PRON- PRP cord-229937-fy90oebs 108 2 is be VBZ cord-229937-fy90oebs 108 3 interesting interesting JJ cord-229937-fy90oebs 108 4 to to TO cord-229937-fy90oebs 108 5 note note VB cord-229937-fy90oebs 108 6 that that IN cord-229937-fy90oebs 108 7 for for IN cord-229937-fy90oebs 108 8 large large JJ cord-229937-fy90oebs 108 9 t t NN cord-229937-fy90oebs 108 10 , , , cord-229937-fy90oebs 108 11 a a DT cord-229937-fy90oebs 108 12 ≈ ≈ NNP cord-229937-fy90oebs 108 13 a a DT cord-229937-fy90oebs 108 14 2 2 CD cord-229937-fy90oebs 109 1 , , , cord-229937-fy90oebs 109 2 c c NNP cord-229937-fy90oebs 109 3 ≈ ≈ NNP cord-229937-fy90oebs 109 4 c c NN cord-229937-fy90oebs 109 5 2 2 CD cord-229937-fy90oebs 109 6 and and CC cord-229937-fy90oebs 109 7 b b NN cord-229937-fy90oebs 109 8 2 2 CD cord-229937-fy90oebs 109 9 ≈ ≈ NNP cord-229937-fy90oebs 109 10 2b 2b CD cord-229937-fy90oebs 109 11 . . . cord-229937-fy90oebs 110 1 In in IN cord-229937-fy90oebs 110 2 such such PDT cord-229937-fy90oebs 110 3 a a DT cord-229937-fy90oebs 110 4 case case NN cord-229937-fy90oebs 110 5 , , , cord-229937-fy90oebs 110 6 the the DT cord-229937-fy90oebs 110 7 total total JJ cord-229937-fy90oebs 110 8 number number NN cord-229937-fy90oebs 110 9 of of IN cord-229937-fy90oebs 110 10 deaths death NNS cord-229937-fy90oebs 110 11 expected expect VBN cord-229937-fy90oebs 110 12 during during IN cord-229937-fy90oebs 110 13 the the DT cord-229937-fy90oebs 110 14 pandemic pandemic NN cord-229937-fy90oebs 110 15 is be VBZ cord-229937-fy90oebs 110 16 given give VBN cord-229937-fy90oebs 110 17 by by IN cord-229937-fy90oebs 110 18 D D NNP cord-229937-fy90oebs 110 19 2 2 CD cord-229937-fy90oebs 110 20 ( ( -LRB- cord-229937-fy90oebs 110 21 ∞ ∞ NNP cord-229937-fy90oebs 110 22 ) ) -RRB- cord-229937-fy90oebs 110 23 = = NFP cord-229937-fy90oebs 111 1 2a 2a NNP cord-229937-fy90oebs 111 2 / / SYM cord-229937-fy90oebs 111 3 c c NN cord-229937-fy90oebs 111 4 . . . cord-229937-fy90oebs 111 5 _SP cord-229937-fy90oebs 112 1 The the DT cord-229937-fy90oebs 112 2 D d NN cord-229937-fy90oebs 112 3 - - HYPH cord-229937-fy90oebs 112 4 model model NN cord-229937-fy90oebs 112 5 can can MD cord-229937-fy90oebs 112 6 also also RB cord-229937-fy90oebs 112 7 be be VB cord-229937-fy90oebs 112 8 used use VBN cord-229937-fy90oebs 112 9 to to TO cord-229937-fy90oebs 112 10 estimate estimate VB cord-229937-fy90oebs 112 11 I(t I(t NNP cord-229937-fy90oebs 112 12 ) ) -RRB- cord-229937-fy90oebs 112 13 using use VBG cord-229937-fy90oebs 112 14 the the DT cord-229937-fy90oebs 112 15 initial initial JJ cord-229937-fy90oebs 112 16 values value NNS cord-229937-fy90oebs 112 17 of of IN cord-229937-fy90oebs 112 18 I i NN cord-229937-fy90oebs 112 19 0 0 CD cord-229937-fy90oebs 112 20 = = NFP cord-229937-fy90oebs 113 1 I(0 I(0 NNP cord-229937-fy90oebs 113 2 ) ) -RRB- cord-229937-fy90oebs 114 1 and and CC cord-229937-fy90oebs 114 2 the the DT cord-229937-fy90oebs 114 3 total total JJ cord-229937-fy90oebs 114 4 number number NN cord-229937-fy90oebs 114 5 of of IN cord-229937-fy90oebs 114 6 susceptible susceptible JJ cord-229937-fy90oebs 114 7 people people NNS cord-229937-fy90oebs 114 8 N n NN cord-229937-fy90oebs 114 9 = = NN cord-229937-fy90oebs 114 10 S(0 S(0 NNP cord-229937-fy90oebs 114 11 ) ) -RRB- cord-229937-fy90oebs 114 12 . . . cord-229937-fy90oebs 115 1 The the DT cord-229937-fy90oebs 115 2 initial initial JJ cord-229937-fy90oebs 115 3 value value NN cord-229937-fy90oebs 115 4 of of IN cord-229937-fy90oebs 115 5 N n NN cord-229937-fy90oebs 115 6 is be VBZ cord-229937-fy90oebs 115 7 unknown unknown JJ cord-229937-fy90oebs 115 8 , , , cord-229937-fy90oebs 115 9 and and CC cord-229937-fy90oebs 115 10 not not RB cord-229937-fy90oebs 115 11 necessarily necessarily RB cord-229937-fy90oebs 115 12 equal equal JJ cord-229937-fy90oebs 115 13 to to IN cord-229937-fy90oebs 115 14 the the DT cord-229937-fy90oebs 115 15 population population NN cord-229937-fy90oebs 115 16 of of IN cord-229937-fy90oebs 115 17 the the DT cord-229937-fy90oebs 115 18 whole whole JJ cord-229937-fy90oebs 115 19 country country NN cord-229937-fy90oebs 115 20 since since IN cord-229937-fy90oebs 115 21 the the DT cord-229937-fy90oebs 115 22 pandemic pandemic NN cord-229937-fy90oebs 115 23 started start VBD cord-229937-fy90oebs 115 24 in in IN cord-229937-fy90oebs 115 25 localized localize VBN cord-229937-fy90oebs 115 26 areas area NNS cord-229937-fy90oebs 115 27 . . . cord-229937-fy90oebs 116 1 Here here RB cord-229937-fy90oebs 116 2 , , , cord-229937-fy90oebs 116 3 we -PRON- PRP cord-229937-fy90oebs 116 4 shall shall MD cord-229937-fy90oebs 116 5 assume assume VB cord-229937-fy90oebs 116 6 N N NNP cord-229937-fy90oebs 116 7 = = SYM cord-229937-fy90oebs 116 8 10 10 CD cord-229937-fy90oebs 116 9 6 6 CD cord-229937-fy90oebs 116 10 , , , cord-229937-fy90oebs 116 11 although although IN cord-229937-fy90oebs 116 12 plausible plausible JJ cord-229937-fy90oebs 116 13 values value NNS cord-229937-fy90oebs 116 14 of of IN cord-229937-fy90oebs 116 15 N N NNP cord-229937-fy90oebs 116 16 can can MD cord-229937-fy90oebs 116 17 be be VB cord-229937-fy90oebs 116 18 tens ten NNS cord-229937-fy90oebs 116 19 of of IN cord-229937-fy90oebs 116 20 millions million NNS cord-229937-fy90oebs 116 21 . . . cord-229937-fy90oebs 117 1 Note note VB cord-229937-fy90oebs 117 2 that that IN cord-229937-fy90oebs 117 3 the the DT cord-229937-fy90oebs 117 4 no no DT cord-229937-fy90oebs 117 5 - - HYPH cord-229937-fy90oebs 117 6 recovery recovery NN cord-229937-fy90oebs 117 7 assumption assumption NN cord-229937-fy90oebs 117 8 of of IN cord-229937-fy90oebs 117 9 the the DT cord-229937-fy90oebs 117 10 D D NNP cord-229937-fy90oebs 117 11 model model NN cord-229937-fy90oebs 117 12 is be VBZ cord-229937-fy90oebs 117 13 unrealistic unrealistic JJ cord-229937-fy90oebs 117 14 , , , cord-229937-fy90oebs 117 15 and and CC cord-229937-fy90oebs 117 16 this this DT cord-229937-fy90oebs 117 17 calculation calculation NN cord-229937-fy90oebs 117 18 only only RB cord-229937-fy90oebs 117 19 provides provide VBZ cord-229937-fy90oebs 117 20 an an DT cord-229937-fy90oebs 117 21 estimation estimation NN cord-229937-fy90oebs 117 22 of of IN cord-229937-fy90oebs 117 23 the the DT cord-229937-fy90oebs 117 24 number number NN cord-229937-fy90oebs 117 25 of of IN cord-229937-fy90oebs 117 26 individuals individual NNS cord-229937-fy90oebs 117 27 that that WDT cord-229937-fy90oebs 117 28 were be VBD cord-229937-fy90oebs 117 29 infected infect VBN cord-229937-fy90oebs 117 30 at at IN cord-229937-fy90oebs 117 31 some some DT cord-229937-fy90oebs 117 32 time time NN cord-229937-fy90oebs 117 33 , , , cord-229937-fy90oebs 117 34 independently independently RB cord-229937-fy90oebs 117 35 of of IN cord-229937-fy90oebs 117 36 whether whether IN cord-229937-fy90oebs 117 37 they -PRON- PRP cord-229937-fy90oebs 117 38 recovered recover VBD cord-229937-fy90oebs 117 39 or or CC cord-229937-fy90oebs 117 40 not not RB cord-229937-fy90oebs 117 41 . . . cord-229937-fy90oebs 118 1 From from IN cord-229937-fy90oebs 118 2 the the DT cord-229937-fy90oebs 118 3 definition definition NN cord-229937-fy90oebs 118 4 of of IN cord-229937-fy90oebs 118 5 D(t D(t NNP cord-229937-fy90oebs 118 6 ) ) -RRB- cord-229937-fy90oebs 118 7 in in IN cord-229937-fy90oebs 118 8 Eq Eq NNP cord-229937-fy90oebs 118 9 . . . cord-229937-fy90oebs 119 1 14 14 CD cord-229937-fy90oebs 119 2 , , , cord-229937-fy90oebs 119 3 the the DT cord-229937-fy90oebs 119 4 following follow VBG cord-229937-fy90oebs 119 5 relations relation NNS cord-229937-fy90oebs 119 6 between between IN cord-229937-fy90oebs 119 7 the the DT cord-229937-fy90oebs 119 8 several several JJ cord-229937-fy90oebs 119 9 parameters parameter NNS cord-229937-fy90oebs 119 10 of of IN cord-229937-fy90oebs 119 11 the the DT cord-229937-fy90oebs 119 12 model model NN cord-229937-fy90oebs 119 13 were be VBD cord-229937-fy90oebs 119 14 extracted extract VBN cord-229937-fy90oebs 119 15 Solving solve VBG cord-229937-fy90oebs 119 16 the the DT cord-229937-fy90oebs 119 17 first first JJ cord-229937-fy90oebs 119 18 two two CD cord-229937-fy90oebs 119 19 equations equation NNS cord-229937-fy90oebs 119 20 for for IN cord-229937-fy90oebs 119 21 µ µ NN cord-229937-fy90oebs 119 22 and and CC cord-229937-fy90oebs 119 23 I i NN cord-229937-fy90oebs 119 24 0 0 CD cord-229937-fy90oebs 119 25 we -PRON- PRP cord-229937-fy90oebs 119 26 obtain obtain VBP cord-229937-fy90oebs 119 27 Hence hence RB cord-229937-fy90oebs 119 28 , , , cord-229937-fy90oebs 119 29 µ µ NN cord-229937-fy90oebs 119 30 can can MD cord-229937-fy90oebs 119 31 be be VB cord-229937-fy90oebs 119 32 computed compute VBN cord-229937-fy90oebs 119 33 by by IN cord-229937-fy90oebs 119 34 knowing know VBG cord-229937-fy90oebs 119 35 N n CD cord-229937-fy90oebs 119 36 . . . cord-229937-fy90oebs 120 1 However however RB cord-229937-fy90oebs 120 2 , , , cord-229937-fy90oebs 120 3 to to TO cord-229937-fy90oebs 120 4 obtain obtain VB cord-229937-fy90oebs 120 5 I -PRON- PRP cord-229937-fy90oebs 120 6 0 0 CD cord-229937-fy90oebs 120 7 one one NN cord-229937-fy90oebs 120 8 needs need VBZ cord-229937-fy90oebs 120 9 to to TO cord-229937-fy90oebs 120 10 know know VB cord-229937-fy90oebs 120 11 the the DT cord-229937-fy90oebs 120 12 death death NN cord-229937-fy90oebs 120 13 time time NN cord-229937-fy90oebs 120 14 τ τ NN cord-229937-fy90oebs 120 15 . . . cord-229937-fy90oebs 121 1 This this DT cord-229937-fy90oebs 121 2 has have VBZ cord-229937-fy90oebs 121 3 been be VBN cord-229937-fy90oebs 121 4 estimated estimate VBN cord-229937-fy90oebs 121 5 to to TO cord-229937-fy90oebs 121 6 be be VB cord-229937-fy90oebs 121 7 about about RB cord-229937-fy90oebs 121 8 15 15 CD cord-229937-fy90oebs 121 9 to to TO cord-229937-fy90oebs 121 10 20 20 CD cord-229937-fy90oebs 121 11 days day NNS cord-229937-fy90oebs 121 12 for for IN cord-229937-fy90oebs 121 13 COVID-19 covid-19 JJ cord-229937-fy90oebs 121 14 cases case NNS cord-229937-fy90oebs 121 15 , , , cord-229937-fy90oebs 121 16 which which WDT cord-229937-fy90oebs 121 17 can can MD cord-229937-fy90oebs 121 18 be be VB cord-229937-fy90oebs 121 19 used use VBN cord-229937-fy90oebs 121 20 to to TO cord-229937-fy90oebs 121 21 compute compute VB cord-229937-fy90oebs 121 22 two two CD cord-229937-fy90oebs 121 23 estimates estimate NNS cord-229937-fy90oebs 121 24 of of IN cord-229937-fy90oebs 121 25 I(t I(t NNP cord-229937-fy90oebs 121 26 ) ) -RRB- cord-229937-fy90oebs 121 27 . . . cord-229937-fy90oebs 122 1 These these DT cord-229937-fy90oebs 122 2 are be VBP cord-229937-fy90oebs 122 3 given give VBN cord-229937-fy90oebs 122 4 in in IN cord-229937-fy90oebs 122 5 Fig Fig NNP cord-229937-fy90oebs 122 6 . . . cord-229937-fy90oebs 123 1 7 7 CD cord-229937-fy90oebs 123 2 for for IN cord-229937-fy90oebs 123 3 the the DT cord-229937-fy90oebs 123 4 case case NN cord-229937-fy90oebs 123 5 of of IN cord-229937-fy90oebs 123 6 Spain Spain NNP cord-229937-fy90oebs 123 7 . . . cord-229937-fy90oebs 124 1 Since since IN cord-229937-fy90oebs 124 2 there there EX cord-229937-fy90oebs 124 3 is be VBZ cord-229937-fy90oebs 124 4 no no DT cord-229937-fy90oebs 124 5 recovery recovery NN cord-229937-fy90oebs 124 6 in in IN cord-229937-fy90oebs 124 7 the the DT cord-229937-fy90oebs 124 8 D d NN cord-229937-fy90oebs 124 9 model model NN cord-229937-fy90oebs 124 10 , , , cord-229937-fy90oebs 124 11 the the DT cord-229937-fy90oebs 124 12 total total JJ cord-229937-fy90oebs 124 13 number number NN cord-229937-fy90oebs 124 14 of of IN cord-229937-fy90oebs 124 15 infected infected JJ cord-229937-fy90oebs 124 16 people people NNS cord-229937-fy90oebs 124 17 is be VBZ cord-229937-fy90oebs 124 18 I -PRON- PRP cord-229937-fy90oebs 124 19 ∼ ∼ NNP cord-229937-fy90oebs 124 20 N n CD cord-229937-fy90oebs 124 21 for for IN cord-229937-fy90oebs 124 22 large large JJ cord-229937-fy90oebs 124 23 t t NN cord-229937-fy90oebs 124 24 , , , cord-229937-fy90oebs 124 25 i.e. i.e. FW cord-229937-fy90oebs 124 26 N n NN cord-229937-fy90oebs 124 27 = = SYM cord-229937-fy90oebs 124 28 10 10 CD cord-229937-fy90oebs 124 29 6 6 CD cord-229937-fy90oebs 124 30 in in IN cord-229937-fy90oebs 124 31 our -PRON- PRP$ cord-229937-fy90oebs 124 32 case case NN cord-229937-fy90oebs 124 33 . . . cord-229937-fy90oebs 125 1 In in IN cord-229937-fy90oebs 125 2 Fig Fig NNP cord-229937-fy90oebs 125 3 . . . cord-229937-fy90oebs 125 4 7 7 CD cord-229937-fy90oebs 125 5 _SP cord-229937-fy90oebs 125 6 which which WDT cord-229937-fy90oebs 125 7 also also RB cord-229937-fy90oebs 125 8 depends depend VBZ cord-229937-fy90oebs 125 9 on on IN cord-229937-fy90oebs 125 10 N n NN cord-229937-fy90oebs 125 11 and and CC cord-229937-fy90oebs 125 12 τ τ NN cord-229937-fy90oebs 125 13 . . . cord-229937-fy90oebs 126 1 For for IN cord-229937-fy90oebs 126 2 N n NN cord-229937-fy90oebs 126 3 = = SYM cord-229937-fy90oebs 126 4 10 10 CD cord-229937-fy90oebs 126 5 6 6 CD cord-229937-fy90oebs 126 6 , , , cord-229937-fy90oebs 126 7 the the DT cord-229937-fy90oebs 126 8 ratio ratio NN cord-229937-fy90oebs 126 9 D d NN cord-229937-fy90oebs 126 10 / / , cord-229937-fy90oebs 126 11 I -PRON- PRP cord-229937-fy90oebs 126 12 increases increase VBZ cord-229937-fy90oebs 126 13 similarly similarly RB cord-229937-fy90oebs 126 14 to to IN cord-229937-fy90oebs 126 15 the the DT cord-229937-fy90oebs 126 16 separate separate JJ cord-229937-fy90oebs 126 17 functions function NNS cord-229937-fy90oebs 126 18 D d NN cord-229937-fy90oebs 126 19 and and CC cord-229937-fy90oebs 126 20 I -PRON- PRP cord-229937-fy90oebs 126 21 between between IN cord-229937-fy90oebs 126 22 the the DT cord-229937-fy90oebs 126 23 initial initial JJ cord-229937-fy90oebs 126 24 and and CC cord-229937-fy90oebs 126 25 final final JJ cord-229937-fy90oebs 126 26 values value NNS cord-229937-fy90oebs 126 27 , , , cord-229937-fy90oebs 126 28 These these DT cord-229937-fy90oebs 126 29 results result NNS cord-229937-fy90oebs 126 30 depend depend VBP cord-229937-fy90oebs 126 31 on on IN cord-229937-fy90oebs 126 32 the the DT cord-229937-fy90oebs 126 33 total total JJ cord-229937-fy90oebs 126 34 susceptible susceptible JJ cord-229937-fy90oebs 126 35 population population NN cord-229937-fy90oebs 126 36 N n NN cord-229937-fy90oebs 126 37 . . . cord-229937-fy90oebs 127 1 However however RB cord-229937-fy90oebs 127 2 , , , cord-229937-fy90oebs 127 3 the the DT cord-229937-fy90oebs 127 4 ratio ratio NN cord-229937-fy90oebs 127 5 of of IN cord-229937-fy90oebs 127 6 infected infect VBN cord-229937-fy90oebs 127 7 with with IN cord-229937-fy90oebs 127 8 respect respect NN cord-229937-fy90oebs 127 9 to to IN cord-229937-fy90oebs 127 10 susceptibles susceptible NNS cord-229937-fy90oebs 127 11 , , , cord-229937-fy90oebs 127 12 I I NNP cord-229937-fy90oebs 127 13 / / SYM cord-229937-fy90oebs 127 14 N N NNP cord-229937-fy90oebs 127 15 , , , cord-229937-fy90oebs 127 16 is be VBZ cord-229937-fy90oebs 127 17 independent independent JJ cord-229937-fy90oebs 127 18 on on IN cord-229937-fy90oebs 127 19 N N NNP cord-229937-fy90oebs 127 20 . . . cord-229937-fy90oebs 128 1 This this DT cord-229937-fy90oebs 128 2 function function NN cord-229937-fy90oebs 128 3 depends depend VBZ cord-229937-fy90oebs 128 4 only only RB cord-229937-fy90oebs 128 5 on on IN cord-229937-fy90oebs 128 6 τ τ NN cord-229937-fy90oebs 128 7 and and CC cord-229937-fy90oebs 128 8 is be VBZ cord-229937-fy90oebs 128 9 shown show VBN cord-229937-fy90oebs 128 10 in in IN cord-229937-fy90oebs 128 11 the the DT cord-229937-fy90oebs 128 12 bottom bottom JJ cord-229937-fy90oebs 128 13 panel panel NN cord-229937-fy90oebs 128 14 of of IN cord-229937-fy90oebs 128 15 Fig Fig NNP cord-229937-fy90oebs 128 16 . . . cord-229937-fy90oebs 129 1 8 8 CD cord-229937-fy90oebs 130 1 for for IN cord-229937-fy90oebs 130 2 τ τ NN cord-229937-fy90oebs 130 3 = = SYM cord-229937-fy90oebs 130 4 15 15 CD cord-229937-fy90oebs 130 5 and and CC cord-229937-fy90oebs 130 6 20 20 CD cord-229937-fy90oebs 130 7 days day NNS cord-229937-fy90oebs 130 8 , , , cord-229937-fy90oebs 130 9 which which WDT cord-229937-fy90oebs 130 10 reveals reveal VBZ cord-229937-fy90oebs 130 11 the the DT cord-229937-fy90oebs 130 12 rapid rapid JJ cord-229937-fy90oebs 130 13 spread spread NN cord-229937-fy90oebs 130 14 of of IN cord-229937-fy90oebs 130 15 the the DT cord-229937-fy90oebs 130 16 pandemic pandemic NN cord-229937-fy90oebs 130 17 . . . cord-229937-fy90oebs 131 1 Accordingly accordingly RB cord-229937-fy90oebs 131 2 , , , cord-229937-fy90oebs 131 3 between between IN cord-229937-fy90oebs 131 4 10 10 CD cord-229937-fy90oebs 131 5 % % NN cord-229937-fy90oebs 131 6 and and CC cord-229937-fy90oebs 131 7 30 30 CD cord-229937-fy90oebs 131 8 % % NN cord-229937-fy90oebs 131 9 of of IN cord-229937-fy90oebs 131 10 the the DT cord-229937-fy90oebs 131 11 susceptibles susceptible NNS cord-229937-fy90oebs 131 12 were be VBD cord-229937-fy90oebs 131 13 infected infect VBN cord-229937-fy90oebs 131 14 in in IN cord-229937-fy90oebs 131 15 March March NNP cord-229937-fy90oebs 131 16 7 7 CD cord-229937-fy90oebs 131 17 , , , cord-229937-fy90oebs 131 18 and and CC cord-229937-fy90oebs 131 19 one one CD cord-229937-fy90oebs 131 20 month month NN cord-229937-fy90oebs 131 21 later later RB cord-229937-fy90oebs 131 22 ( ( -LRB- cord-229937-fy90oebs 131 23 April April NNP cord-229937-fy90oebs 131 24 6 6 CD cord-229937-fy90oebs 131 25 ) ) -RRB- cord-229937-fy90oebs 131 26 , , , cord-229937-fy90oebs 131 27 when when WRB cord-229937-fy90oebs 131 28 the the DT cord-229937-fy90oebs 131 29 fit fit NN cord-229937-fy90oebs 131 30 was be VBD cord-229937-fy90oebs 131 31 made make VBN cord-229937-fy90oebs 131 32 , , , cord-229937-fy90oebs 131 33 all all DT cord-229937-fy90oebs 131 34 susceptibles susceptible NNS cord-229937-fy90oebs 131 35 had have VBD cord-229937-fy90oebs 131 36 been be VBN cord-229937-fy90oebs 131 37 infected infect VBN cord-229937-fy90oebs 131 38 . . . cord-229937-fy90oebs 132 1 This this DT cord-229937-fy90oebs 132 2 does do VBZ cord-229937-fy90oebs 132 3 not not RB cord-229937-fy90oebs 132 4 means mean VBZ cord-229937-fy90oebs 132 5 that that IN cord-229937-fy90oebs 132 6 the the DT cord-229937-fy90oebs 132 7 full full JJ cord-229937-fy90oebs 132 8 population population NN cord-229937-fy90oebs 132 9 of of IN cord-229937-fy90oebs 132 10 the the DT cord-229937-fy90oebs 132 11 country country NN cord-229937-fy90oebs 132 12 got get VBD cord-229937-fy90oebs 132 13 infected infect VBN cord-229937-fy90oebs 132 14 , , , cord-229937-fy90oebs 132 15 since since IN cord-229937-fy90oebs 132 16 the the DT cord-229937-fy90oebs 132 17 number number NN cord-229937-fy90oebs 132 18 N N NNP cord-229937-fy90oebs 132 19 is be VBZ cord-229937-fy90oebs 132 20 unknown unknown JJ cord-229937-fy90oebs 132 21 and and CC cord-229937-fy90oebs 132 22 , , , cord-229937-fy90oebs 132 23 for for IN cord-229937-fy90oebs 132 24 instance instance NN cord-229937-fy90oebs 132 25 , , , cord-229937-fy90oebs 132 26 excludes exclude VBZ cord-229937-fy90oebs 132 27 individuals individual NNS cord-229937-fy90oebs 132 28 in in IN cord-229937-fy90oebs 132 29 isolated isolate VBN cord-229937-fy90oebs 132 30 regions region NNS cord-229937-fy90oebs 132 31 , , , cord-229937-fy90oebs 132 32 and and CC cord-229937-fy90oebs 132 33 it -PRON- PRP cord-229937-fy90oebs 132 34 may may MD cord-229937-fy90oebs 132 35 additionally additionally RB cord-229937-fy90oebs 132 36 change change VB cord-229937-fy90oebs 132 37 because because IN cord-229937-fy90oebs 132 38 of of IN cord-229937-fy90oebs 132 39 spatial spatial JJ cord-229937-fy90oebs 132 40 migration migration NN cord-229937-fy90oebs 132 41 , , , cord-229937-fy90oebs 132 42 not not RB cord-229937-fy90oebs 132 43 considered consider VBN cord-229937-fy90oebs 132 44 in in IN cord-229937-fy90oebs 132 45 the the DT cord-229937-fy90oebs 132 46 model model NN cord-229937-fy90oebs 132 47 . . . cord-229937-fy90oebs 133 1 D d JJ cord-229937-fy90oebs 133 2 - - HYPH cord-229937-fy90oebs 133 3 model model NN cord-229937-fy90oebs 133 4 predictions prediction NNS cord-229937-fy90oebs 133 5 can can MD cord-229937-fy90oebs 133 6 be be VB cord-229937-fy90oebs 133 7 compared compare VBN cord-229937-fy90oebs 133 8 with with IN cord-229937-fy90oebs 133 9 more more RBR cord-229937-fy90oebs 133 10 realistic realistic JJ cord-229937-fy90oebs 133 11 results result NNS cord-229937-fy90oebs 133 12 given give VBN cord-229937-fy90oebs 133 13 by by IN cord-229937-fy90oebs 133 14 the the DT cord-229937-fy90oebs 133 15 complete complete JJ cord-229937-fy90oebs 133 16 SIR SIR NNP cord-229937-fy90oebs 133 17 model model NN cord-229937-fy90oebs 133 18 [ [ -LRB- cord-229937-fy90oebs 133 19 9 9 CD cord-229937-fy90oebs 133 20 , , , cord-229937-fy90oebs 133 21 11 11 CD cord-229937-fy90oebs 133 22 ] ] -RRB- cord-229937-fy90oebs 133 23 , , , cord-229937-fy90oebs 133 24 which which WDT cord-229937-fy90oebs 133 25 is be VBZ cord-229937-fy90oebs 133 26 characterized characterize VBN cord-229937-fy90oebs 133 27 by by IN cord-229937-fy90oebs 133 28 Eqs Eqs NNP cord-229937-fy90oebs 133 29 . . . cord-229937-fy90oebs 134 1 1 1 CD cord-229937-fy90oebs 134 2 , , , cord-229937-fy90oebs 134 3 2 2 CD cord-229937-fy90oebs 134 4 , , , cord-229937-fy90oebs 134 5 3 3 CD cord-229937-fy90oebs 134 6 and and CC cord-229937-fy90oebs 134 7 4 4 CD cord-229937-fy90oebs 134 8 with with IN cord-229937-fy90oebs 134 9 initial initial JJ cord-229937-fy90oebs 134 10 conditions condition NNS cord-229937-fy90oebs 134 11 R(0 R(0 NNP cord-229937-fy90oebs 134 12 ) ) -RRB- cord-229937-fy90oebs 135 1 = = SYM cord-229937-fy90oebs 135 2 0 0 CD cord-229937-fy90oebs 135 3 , , , cord-229937-fy90oebs 136 1 I(0 I(0 NNP cord-229937-fy90oebs 136 2 ) ) -RRB- cord-229937-fy90oebs 136 3 = = NFP cord-229937-fy90oebs 137 1 I -PRON- PRP cord-229937-fy90oebs 137 2 0 0 CD cord-229937-fy90oebs 137 3 , , , cord-229937-fy90oebs 137 4 S(0 S(0 NNP cord-229937-fy90oebs 137 5 ) ) -RRB- cord-229937-fy90oebs 138 1 = = NFP cord-229937-fy90oebs 139 1 N N NNP cord-229937-fy90oebs 139 2 − − NNP cord-229937-fy90oebs 140 1 I -PRON- PRP cord-229937-fy90oebs 140 2 0 0 CD cord-229937-fy90oebs 140 3 . . . cord-229937-fy90oebs 141 1 The the DT cord-229937-fy90oebs 141 2 SIR SIR NNP cord-229937-fy90oebs 141 3 system system NN cord-229937-fy90oebs 141 4 of of IN cord-229937-fy90oebs 141 5 dynamical dynamical JJ cord-229937-fy90oebs 141 6 equations equation NNS cord-229937-fy90oebs 141 7 can can MD cord-229937-fy90oebs 141 8 be be VB cord-229937-fy90oebs 141 9 reduced reduce VBN cord-229937-fy90oebs 141 10 to to IN cord-229937-fy90oebs 141 11 a a DT cord-229937-fy90oebs 141 12 non non JJ cord-229937-fy90oebs 141 13 - - JJ cord-229937-fy90oebs 141 14 linear linear JJ cord-229937-fy90oebs 141 15 differential differential JJ cord-229937-fy90oebs 141 16 equation equation NN cord-229937-fy90oebs 141 17 . . . cord-229937-fy90oebs 142 1 First first RB cord-229937-fy90oebs 142 2 , , , cord-229937-fy90oebs 142 3 dividing divide VBG cord-229937-fy90oebs 142 4 Eq Eq NNP cord-229937-fy90oebs 142 5 . . NNP cord-229937-fy90oebs 142 6 1 1 CD cord-229937-fy90oebs 142 7 by by IN cord-229937-fy90oebs 142 8 Eq Eq NNP cord-229937-fy90oebs 142 9 . . . cord-229937-fy90oebs 143 1 3 3 LS cord-229937-fy90oebs 143 2 one one NN cord-229937-fy90oebs 143 3 obtains obtain VBZ cord-229937-fy90oebs 143 4 , , , cord-229937-fy90oebs 143 5 which which WDT cord-229937-fy90oebs 143 6 yields yield VBZ cord-229937-fy90oebs 143 7 the the DT cord-229937-fy90oebs 143 8 following follow VBG cord-229937-fy90oebs 143 9 exponential exponential JJ cord-229937-fy90oebs 143 10 relation relation NN cord-229937-fy90oebs 143 11 between between IN cord-229937-fy90oebs 143 12 the the DT cord-229937-fy90oebs 143 13 susceptible susceptible JJ cord-229937-fy90oebs 143 14 and and CC cord-229937-fy90oebs 143 15 the the DT cord-229937-fy90oebs 143 16 removed remove VBN cord-229937-fy90oebs 143 17 functions function NNS cord-229937-fy90oebs 143 18 , , , cord-229937-fy90oebs 143 19 Moreover moreover RB cord-229937-fy90oebs 143 20 , , , cord-229937-fy90oebs 143 21 Eq Eq NNP cord-229937-fy90oebs 143 22 . . . cord-229937-fy90oebs 144 1 4 4 LS cord-229937-fy90oebs 144 2 provides provide VBZ cord-229937-fy90oebs 144 3 a a DT cord-229937-fy90oebs 144 4 relation relation NN cord-229937-fy90oebs 144 5 between between IN cord-229937-fy90oebs 144 6 the the DT cord-229937-fy90oebs 144 7 infected infected JJ cord-229937-fy90oebs 144 8 and and CC cord-229937-fy90oebs 144 9 the the DT cord-229937-fy90oebs 144 10 removed remove VBN cord-229937-fy90oebs 144 11 functions function NNS cord-229937-fy90oebs 144 12 , , , cord-229937-fy90oebs 144 13 which which WDT cord-229937-fy90oebs 144 14 yields yield NNS cord-229937-fy90oebs 144 15 , , , cord-229937-fy90oebs 144 16 by by IN cord-229937-fy90oebs 144 17 inserting insert VBG cord-229937-fy90oebs 144 18 into into IN cord-229937-fy90oebs 144 19 Eq Eq NNP cord-229937-fy90oebs 144 20 . . . cord-229937-fy90oebs 145 1 3 3 LS cord-229937-fy90oebs 145 2 , , , cord-229937-fy90oebs 145 3 the the DT cord-229937-fy90oebs 145 4 final final JJ cord-229937-fy90oebs 145 5 SIR SIR NNP cord-229937-fy90oebs 145 6 differential differential JJ cord-229937-fy90oebs 145 7 equation equation NN cord-229937-fy90oebs 146 1 In in IN cord-229937-fy90oebs 146 2 order order NN cord-229937-fy90oebs 146 3 to to TO cord-229937-fy90oebs 146 4 obtain obtain VB cord-229937-fy90oebs 146 5 R(t R(t . cord-229937-fy90oebs 146 6 ) ) -RRB- cord-229937-fy90oebs 147 1 we -PRON- PRP cord-229937-fy90oebs 147 2 only only RB cord-229937-fy90oebs 147 3 need need VBP cord-229937-fy90oebs 147 4 to to TO cord-229937-fy90oebs 147 5 solve solve VB cord-229937-fy90oebs 147 6 this this DT cord-229937-fy90oebs 147 7 first first JJ cord-229937-fy90oebs 147 8 - - HYPH cord-229937-fy90oebs 147 9 order order NN cord-229937-fy90oebs 147 10 differential differential JJ cord-229937-fy90oebs 147 11 equation equation NN cord-229937-fy90oebs 147 12 with with IN cord-229937-fy90oebs 147 13 the the DT cord-229937-fy90oebs 147 14 initial initial JJ cord-229937-fy90oebs 147 15 condition condition NN cord-229937-fy90oebs 147 16 _SP cord-229937-fy90oebs 148 1 so so IN cord-229937-fy90oebs 148 2 that that DT cord-229937-fy90oebs 148 3 s s VBZ cord-229937-fy90oebs 149 1 + + CC cord-229937-fy90oebs 150 1 i i PRP cord-229937-fy90oebs 151 1 + + CC cord-229937-fy90oebs 152 1 r r LS cord-229937-fy90oebs 152 2 = = SYM cord-229937-fy90oebs 152 3 1 1 CD cord-229937-fy90oebs 152 4 , , , cord-229937-fy90oebs 152 5 then then RB cord-229937-fy90oebs 152 6 r(t r(t NNP cord-229937-fy90oebs 152 7 ) ) -RRB- cord-229937-fy90oebs 152 8 verifies verify VBZ cord-229937-fy90oebs 152 9 which which WDT cord-229937-fy90oebs 152 10 can can MD cord-229937-fy90oebs 152 11 be be VB cord-229937-fy90oebs 152 12 solved solve VBN cord-229937-fy90oebs 152 13 numerically numerically RB cord-229937-fy90oebs 152 14 , , , cord-229937-fy90oebs 152 15 or or CC cord-229937-fy90oebs 152 16 by by IN cord-229937-fy90oebs 152 17 approximate approximate JJ cord-229937-fy90oebs 152 18 methods method NNS cord-229937-fy90oebs 152 19 in in IN cord-229937-fy90oebs 152 20 some some DT cord-229937-fy90oebs 152 21 cases case NNS cord-229937-fy90oebs 152 22 . . . cord-229937-fy90oebs 153 1 In in IN cord-229937-fy90oebs 153 2 Ref Ref NNP cord-229937-fy90oebs 153 3 . . . cord-229937-fy90oebs 154 1 [ [ -LRB- cord-229937-fy90oebs 154 2 9 9 CD cord-229937-fy90oebs 154 3 ] ] -RRB- cord-229937-fy90oebs 154 4 , , , cord-229937-fy90oebs 154 5 a a DT cord-229937-fy90oebs 154 6 solution solution NN cord-229937-fy90oebs 154 7 was be VBD cord-229937-fy90oebs 154 8 found find VBN cord-229937-fy90oebs 154 9 for for IN cord-229937-fy90oebs 154 10 small small JJ cord-229937-fy90oebs 154 11 values value NNS cord-229937-fy90oebs 154 12 of of IN cord-229937-fy90oebs 154 13 the the DT cord-229937-fy90oebs 154 14 exponent exponent NN cord-229937-fy90oebs 154 15 λN λn NN cord-229937-fy90oebs 154 16 r r NN cord-229937-fy90oebs 154 17 / / SYM cord-229937-fy90oebs 154 18 β β NN cord-229937-fy90oebs 154 19 . . . cord-229937-fy90oebs 155 1 For for IN cord-229937-fy90oebs 155 2 the the DT cord-229937-fy90oebs 155 3 coronavirus coronavirus NN cord-229937-fy90oebs 155 4 pandemic pandemic NN cord-229937-fy90oebs 155 5 , , , cord-229937-fy90oebs 155 6 however however RB cord-229937-fy90oebs 155 7 , , , cord-229937-fy90oebs 155 8 this this DT cord-229937-fy90oebs 155 9 number number NN cord-229937-fy90oebs 155 10 is be VBZ cord-229937-fy90oebs 155 11 expected expect VBN cord-229937-fy90oebs 155 12 to to TO cord-229937-fy90oebs 155 13 increase increase VB cord-229937-fy90oebs 155 14 and and CC cord-229937-fy90oebs 155 15 be be VB cord-229937-fy90oebs 155 16 close close JJ cord-229937-fy90oebs 155 17 to to IN cord-229937-fy90oebs 155 18 one one CD cord-229937-fy90oebs 155 19 at at IN cord-229937-fy90oebs 155 20 the the DT cord-229937-fy90oebs 155 21 pandemic pandemic NN cord-229937-fy90oebs 155 22 end end NN cord-229937-fy90oebs 155 23 . . . cord-229937-fy90oebs 156 1 At at IN cord-229937-fy90oebs 156 2 this this DT cord-229937-fy90oebs 156 3 point point NN cord-229937-fy90oebs 156 4 , , , cord-229937-fy90oebs 156 5 we -PRON- PRP cord-229937-fy90oebs 156 6 propose propose VBP cord-229937-fy90oebs 156 7 a a DT cord-229937-fy90oebs 156 8 modification modification NN cord-229937-fy90oebs 156 9 of of IN cord-229937-fy90oebs 156 10 the the DT cord-229937-fy90oebs 156 11 standard standard JJ cord-229937-fy90oebs 156 12 SIR SIR NNP cord-229937-fy90oebs 156 13 model model NN cord-229937-fy90oebs 156 14 . . . cord-229937-fy90oebs 157 1 Instead instead RB cord-229937-fy90oebs 157 2 of of IN cord-229937-fy90oebs 157 3 solving solve VBG cord-229937-fy90oebs 157 4 Eq Eq NNP cord-229937-fy90oebs 157 5 . . . cord-229937-fy90oebs 158 1 38 38 CD cord-229937-fy90oebs 158 2 numerically numerically RB cord-229937-fy90oebs 158 3 and and CC cord-229937-fy90oebs 158 4 fitting fit VBG cord-229937-fy90oebs 158 5 the the DT cord-229937-fy90oebs 158 6 parameters parameter NNS cord-229937-fy90oebs 158 7 to to IN cord-229937-fy90oebs 158 8 data datum NNS cord-229937-fy90oebs 159 1 , , , cord-229937-fy90oebs 159 2 the the DT cord-229937-fy90oebs 159 3 solution solution NN cord-229937-fy90oebs 159 4 can can MD cord-229937-fy90oebs 159 5 be be VB cord-229937-fy90oebs 159 6 parametrized parametrize VBN cord-229937-fy90oebs 159 7 as as IN cord-229937-fy90oebs 159 8 which which WDT cord-229937-fy90oebs 159 9 presents present VBZ cord-229937-fy90oebs 159 10 the the DT cord-229937-fy90oebs 159 11 same same JJ cord-229937-fy90oebs 159 12 functional functional JJ cord-229937-fy90oebs 159 13 form form NN cord-229937-fy90oebs 159 14 as as IN cord-229937-fy90oebs 159 15 the the DT cord-229937-fy90oebs 159 16 D d NN cord-229937-fy90oebs 159 17 - - HYPH cord-229937-fy90oebs 159 18 model model NN cord-229937-fy90oebs 159 19 and and CC cord-229937-fy90oebs 159 20 , , , cord-229937-fy90oebs 159 21 conveniently conveniently RB cord-229937-fy90oebs 159 22 , , , cord-229937-fy90oebs 159 23 provides provide VBZ cord-229937-fy90oebs 159 24 a a DT cord-229937-fy90oebs 159 25 faster fast JJR cord-229937-fy90oebs 159 26 way way NN cord-229937-fy90oebs 159 27 to to TO cord-229937-fy90oebs 159 28 fit fit VB cord-229937-fy90oebs 159 29 the the DT cord-229937-fy90oebs 159 30 model model NN cord-229937-fy90oebs 159 31 parameters parameter NNS cord-229937-fy90oebs 159 32 by by IN cord-229937-fy90oebs 159 33 avoiding avoid VBG cord-229937-fy90oebs 159 34 the the DT cord-229937-fy90oebs 159 35 numerical numerical JJ cord-229937-fy90oebs 159 36 problem problem NN cord-229937-fy90oebs 159 37 of of IN cord-229937-fy90oebs 159 38 solving solve VBG cord-229937-fy90oebs 159 39 Eq Eq NNP cord-229937-fy90oebs 159 40 . . . cord-229937-fy90oebs 160 1 38 38 CD cord-229937-fy90oebs 160 2 . . . cord-229937-fy90oebs 161 1 In in IN cord-229937-fy90oebs 161 2 fact fact NN cord-229937-fy90oebs 161 3 , , , cord-229937-fy90oebs 161 4 numerical numerical JJ cord-229937-fy90oebs 161 5 solutions solution NNS cord-229937-fy90oebs 161 6 of of IN cord-229937-fy90oebs 161 7 the the DT cord-229937-fy90oebs 161 8 SIR SIR NNP cord-229937-fy90oebs 161 9 model model NN cord-229937-fy90oebs 161 10 present present VBP cord-229937-fy90oebs 161 11 a a DT cord-229937-fy90oebs 161 12 similar similar JJ cord-229937-fy90oebs 161 13 step step NN cord-229937-fy90oebs 161 14 function function NN cord-229937-fy90oebs 161 15 for for IN cord-229937-fy90oebs 161 16 R(t R(t NNP cord-229937-fy90oebs 161 17 ) ) -RRB- cord-229937-fy90oebs 161 18 . . . cord-229937-fy90oebs 162 1 Additionally additionally RB cord-229937-fy90oebs 162 2 , , , cord-229937-fy90oebs 162 3 one one PRP cord-229937-fy90oebs 162 4 can can MD cord-229937-fy90oebs 162 5 assume assume VB cord-229937-fy90oebs 162 6 that that IN cord-229937-fy90oebs 162 7 D(t D(t NNP cord-229937-fy90oebs 162 8 ) ) -RRB- cord-229937-fy90oebs 162 9 is be VBZ cord-229937-fy90oebs 162 10 proportional proportional JJ cord-229937-fy90oebs 162 11 to to IN cord-229937-fy90oebs 162 12 R(t R(t NNP cord-229937-fy90oebs 162 13 ) ) -RRB- cord-229937-fy90oebs 162 14 , , , cord-229937-fy90oebs 162 15 and and CC cord-229937-fy90oebs 162 16 can can MD cord-229937-fy90oebs 162 17 also also RB cord-229937-fy90oebs 162 18 be be VB cord-229937-fy90oebs 162 19 written write VBN cord-229937-fy90oebs 162 20 as as IN cord-229937-fy90oebs 162 21 where where WRB cord-229937-fy90oebs 162 22 a a DT cord-229937-fy90oebs 162 23 2 2 CD cord-229937-fy90oebs 162 24 , , , cord-229937-fy90oebs 162 25 c c NN cord-229937-fy90oebs 162 26 2 2 CD cord-229937-fy90oebs 162 27 = = SYM cord-229937-fy90oebs 162 28 s s NN cord-229937-fy90oebs 162 29 0 0 CD cord-229937-fy90oebs 162 30 and and CC cord-229937-fy90oebs 162 31 b b NN cord-229937-fy90oebs 162 32 2 2 CD cord-229937-fy90oebs 163 1 = = LS cord-229937-fy90oebs 163 2 β/(λN β/(λN NNP cord-229937-fy90oebs 163 3 ) ) -RRB- cord-229937-fy90oebs 163 4 are be VBP cord-229937-fy90oebs 163 5 unknown unknown JJ cord-229937-fy90oebs 163 6 parameters parameter NNS cord-229937-fy90oebs 163 7 to to TO cord-229937-fy90oebs 163 8 be be VB cord-229937-fy90oebs 163 9 fitted fit VBN cord-229937-fy90oebs 163 10 to to IN cord-229937-fy90oebs 163 11 deaths death NNS cord-229937-fy90oebs 163 12 - - HYPH cord-229937-fy90oebs 163 13 per per IN cord-229937-fy90oebs 163 14 - - HYPH cord-229937-fy90oebs 163 15 day day NN cord-229937-fy90oebs 163 16 data datum NNS cord-229937-fy90oebs 163 17 , , , cord-229937-fy90oebs 163 18 together together RB cord-229937-fy90oebs 163 19 with with IN cord-229937-fy90oebs 163 20 the the DT cord-229937-fy90oebs 163 21 three three CD cord-229937-fy90oebs 163 22 parameters parameter NNS cord-229937-fy90oebs 163 23 of of IN cord-229937-fy90oebs 163 24 the the DT cord-229937-fy90oebs 163 25 r(t)-function r(t)-function NN cord-229937-fy90oebs 163 26 : : : cord-229937-fy90oebs 163 27 a a LS cord-229937-fy90oebs 163 28 , , , cord-229937-fy90oebs 163 29 b b NN cord-229937-fy90oebs 163 30 , , , cord-229937-fy90oebs 163 31 c. c. NNP cord-229937-fy90oebs 163 32 Figure Figure NNP cord-229937-fy90oebs 163 33 9 9 CD cord-229937-fy90oebs 163 34 shows show VBZ cord-229937-fy90oebs 163 35 fits fit NNS cord-229937-fy90oebs 163 36 of of IN cord-229937-fy90oebs 163 37 the the DT cord-229937-fy90oebs 163 38 ESIR ESIR NNP cord-229937-fy90oebs 163 39 model model NN cord-229937-fy90oebs 163 40 to to IN cord-229937-fy90oebs 163 41 daily daily JJ cord-229937-fy90oebs 163 42 deaths death NNS cord-229937-fy90oebs 163 43 in in IN cord-229937-fy90oebs 163 44 Spain Spain NNP cord-229937-fy90oebs 163 45 during during IN cord-229937-fy90oebs 163 46 the the DT cord-229937-fy90oebs 163 47 coronavirus coronavirus NN cord-229937-fy90oebs 163 48 spread spread VBD cord-229937-fy90oebs 163 49 . . . cord-229937-fy90oebs 164 1 The the DT cord-229937-fy90oebs 164 2 use use NN cord-229937-fy90oebs 164 3 of of IN cord-229937-fy90oebs 164 4 no no DT cord-229937-fy90oebs 164 5 boundary boundary JJ cord-229937-fy90oebs 164 6 condition condition NN cord-229937-fy90oebs 164 7 for for IN cord-229937-fy90oebs 164 8 the the DT cord-229937-fy90oebs 164 9 number number NN cord-229937-fy90oebs 164 10 of of IN cord-229937-fy90oebs 164 11 deaths death NNS cord-229937-fy90oebs 164 12 ( ( -LRB- cord-229937-fy90oebs 164 13 left left JJ cord-229937-fy90oebs 164 14 panel panel NN cord-229937-fy90oebs 164 15 ) ) -RRB- cord-229937-fy90oebs 164 16 is be VBZ cord-229937-fy90oebs 164 17 not not RB cord-229937-fy90oebs 164 18 an an DT cord-229937-fy90oebs 164 19 exact exact JJ cord-229937-fy90oebs 164 20 solution solution NN cord-229937-fy90oebs 164 21 of of IN cord-229937-fy90oebs 164 22 the the DT cord-229937-fy90oebs 164 23 SIR SIR NNP cord-229937-fy90oebs 164 24 differential differential JJ cord-229937-fy90oebs 164 25 equation equation NN cord-229937-fy90oebs 164 26 . . . cord-229937-fy90oebs 165 1 A a DT cord-229937-fy90oebs 165 2 way way NN cord-229937-fy90oebs 165 3 to to TO cord-229937-fy90oebs 165 4 solve solve VB cord-229937-fy90oebs 165 5 this this DT cord-229937-fy90oebs 165 6 problem problem NN cord-229937-fy90oebs 165 7 is be VBZ cord-229937-fy90oebs 165 8 to to TO cord-229937-fy90oebs 165 9 impose impose VB cord-229937-fy90oebs 165 10 the the DT cord-229937-fy90oebs 165 11 condition condition NN cord-229937-fy90oebs 165 12 D d NN cord-229937-fy90oebs 165 13 ′ ′ CD cord-229937-fy90oebs 165 14 ( ( -LRB- cord-229937-fy90oebs 165 15 ∞ ∞ NNP cord-229937-fy90oebs 165 16 ) ) -RRB- cord-229937-fy90oebs 165 17 = = SYM cord-229937-fy90oebs 165 18 0 0 CD cord-229937-fy90oebs 165 19 , , , cord-229937-fy90oebs 165 20 as as IN cord-229937-fy90oebs 165 21 the the DT cord-229937-fy90oebs 165 22 number number NN cord-229937-fy90oebs 165 23 of of IN cord-229937-fy90oebs 165 24 deaths death NNS cord-229937-fy90oebs 165 25 must must MD cord-229937-fy90oebs 165 26 stop stop VB cord-229937-fy90oebs 165 27 at at IN cord-229937-fy90oebs 165 28 some some DT cord-229937-fy90oebs 165 29 time time NN cord-229937-fy90oebs 165 30 . . . cord-229937-fy90oebs 166 1 Numerically numerically RB cord-229937-fy90oebs 166 2 , , , cord-229937-fy90oebs 166 3 it -PRON- PRP cord-229937-fy90oebs 166 4 is be VBZ cord-229937-fy90oebs 166 5 enough enough JJ cord-229937-fy90oebs 166 6 to to TO cord-229937-fy90oebs 166 7 choose choose VB cord-229937-fy90oebs 166 8 a a DT cord-229937-fy90oebs 166 9 small small JJ cord-229937-fy90oebs 166 10 value value NN cord-229937-fy90oebs 166 11 of of IN cord-229937-fy90oebs 166 12 D d NN cord-229937-fy90oebs 166 13 ′ ′ CD cord-229937-fy90oebs 166 14 ( ( -LRB- cord-229937-fy90oebs 166 15 t t NN cord-229937-fy90oebs 166 16 ) ) -RRB- cord-229937-fy90oebs 166 17 for for IN cord-229937-fy90oebs 166 18 an an DT cord-229937-fy90oebs 166 19 arbitrary arbitrary JJ cord-229937-fy90oebs 166 20 large large JJ cord-229937-fy90oebs 166 21 t. t. NN cord-229937-fy90oebs 167 1 The the DT cord-229937-fy90oebs 167 2 middle middle JJ cord-229937-fy90oebs 167 3 and and CC cord-229937-fy90oebs 167 4 right right JJ cord-229937-fy90oebs 167 5 panels panel NNS cord-229937-fy90oebs 167 6 of of IN cord-229937-fy90oebs 167 7 Fig Fig NNP cord-229937-fy90oebs 167 8 . . . cord-229937-fy90oebs 168 1 9 9 CD cord-229937-fy90oebs 168 2 show show VBP cord-229937-fy90oebs 168 3 different different JJ cord-229937-fy90oebs 168 4 boundary boundary JJ cord-229937-fy90oebs 168 5 conditions condition NNS cord-229937-fy90oebs 168 6 of of IN cord-229937-fy90oebs 168 7 D d NN cord-229937-fy90oebs 168 8 ′ ′ CD cord-229937-fy90oebs 168 9 ( ( -LRB- cord-229937-fy90oebs 168 10 100 100 CD cord-229937-fy90oebs 168 11 ) ) -RRB- cord-229937-fy90oebs 168 12 = = SYM cord-229937-fy90oebs 168 13 10 10 CD cord-229937-fy90oebs 168 14 and and CC cord-229937-fy90oebs 168 15 D D NNP cord-229937-fy90oebs 168 16 ′ ′ CD cord-229937-fy90oebs 168 17 ( ( -LRB- cord-229937-fy90oebs 168 18 100 100 CD cord-229937-fy90oebs 168 19 ) ) -RRB- cord-229937-fy90oebs 168 20 = = SYM cord-229937-fy90oebs 168 21 5 5 CD cord-229937-fy90oebs 168 22 , , , cord-229937-fy90oebs 168 23 respectively respectively RB cord-229937-fy90oebs 168 24 , , , cord-229937-fy90oebs 168 25 which which WDT cord-229937-fy90oebs 168 26 yield yield VBP cord-229937-fy90oebs 168 27 the the DT cord-229937-fy90oebs 168 28 same same JJ cord-229937-fy90oebs 168 29 results result NNS cord-229937-fy90oebs 168 30 and and CC cord-229937-fy90oebs 168 31 the the DT cord-229937-fy90oebs 168 32 expected expect VBN cord-229937-fy90oebs 168 33 behavior behavior NN cord-229937-fy90oebs 168 34 for for IN cord-229937-fy90oebs 168 35 a a DT cord-229937-fy90oebs 168 36 viral viral JJ cord-229937-fy90oebs 168 37 disease disease NN cord-229937-fy90oebs 168 38 spreading spread VBG cord-229937-fy90oebs 168 39 and and CC cord-229937-fy90oebs 168 40 declining decline VBG cord-229937-fy90oebs 168 41 . . . cord-229937-fy90oebs 169 1 It -PRON- PRP cord-229937-fy90oebs 169 2 is be VBZ cord-229937-fy90oebs 169 3 also also RB cord-229937-fy90oebs 169 4 consistently consistently RB cord-229937-fy90oebs 169 5 observed observe VBN cord-229937-fy90oebs 169 6 ( ( -LRB- cord-229937-fy90oebs 169 7 e.g. e.g. RB cord-229937-fy90oebs 169 8 see see VBP cord-229937-fy90oebs 169 9 middle middle JJ cord-229937-fy90oebs 169 10 and and CC cord-229937-fy90oebs 169 11 right right JJ cord-229937-fy90oebs 169 12 panels panel NNS cord-229937-fy90oebs 169 13 of of IN cord-229937-fy90oebs 169 14 Fig Fig NNP cord-229937-fy90oebs 169 15 . . . cord-229937-fy90oebs 170 1 9 9 LS cord-229937-fy90oebs 170 2 ) ) -RRB- cord-229937-fy90oebs 170 3 , , , cord-229937-fy90oebs 170 4 that that IN cord-229937-fy90oebs 170 5 at at IN cord-229937-fy90oebs 170 6 large large JJ cord-229937-fy90oebs 170 7 t t NN cord-229937-fy90oebs 170 8 , , , cord-229937-fy90oebs 170 9 r(t r(t NNP cord-229937-fy90oebs 170 10 ) ) -RRB- cord-229937-fy90oebs 170 11 → → WDT cord-229937-fy90oebs 170 12 a a DT cord-229937-fy90oebs 170 13 c c NN cord-229937-fy90oebs 170 14 ≈ ≈ NNP cord-229937-fy90oebs 170 15 1 1 CD cord-229937-fy90oebs 170 16 , , , cord-229937-fy90oebs 170 17 which which WDT cord-229937-fy90oebs 170 18 essentially essentially RB cord-229937-fy90oebs 170 19 means mean VBZ cord-229937-fy90oebs 170 20 that that IN cord-229937-fy90oebs 170 21 most most JJS cord-229937-fy90oebs 170 22 of of IN cord-229937-fy90oebs 170 23 the the DT cord-229937-fy90oebs 170 24 susceptible susceptible JJ cord-229937-fy90oebs 170 25 population population NN cord-229937-fy90oebs 170 26 N N NNP cord-229937-fy90oebs 170 27 recovers recover VBZ cord-229937-fy90oebs 170 28 , , , cord-229937-fy90oebs 170 29 as as IN cord-229937-fy90oebs 170 30 we -PRON- PRP cord-229937-fy90oebs 170 31 previously previously RB cord-229937-fy90oebs 170 32 inferred infer VBD cord-229937-fy90oebs 170 33 from from IN cord-229937-fy90oebs 170 34 the the DT cord-229937-fy90oebs 170 35 D D NNP cord-229937-fy90oebs 170 36 model model NN cord-229937-fy90oebs 170 37 . . . cord-229937-fy90oebs 171 1 This this DT cord-229937-fy90oebs 171 2 , , , cord-229937-fy90oebs 171 3 together together RB cord-229937-fy90oebs 171 4 with with IN cord-229937-fy90oebs 171 5 the the DT cord-229937-fy90oebs 171 6 fact fact NN cord-229937-fy90oebs 171 7 that that IN cord-229937-fy90oebs 171 8 c c NN cord-229937-fy90oebs 171 9 2 2 CD cord-229937-fy90oebs 171 10 can can MD cord-229937-fy90oebs 171 11 always always RB cord-229937-fy90oebs 171 12 be be VB cord-229937-fy90oebs 171 13 adjusted adjust VBN cord-229937-fy90oebs 171 14 to to IN cord-229937-fy90oebs 171 15 1 1 CD cord-229937-fy90oebs 171 16 , , , cord-229937-fy90oebs 171 17 leaves leave VBZ cord-229937-fy90oebs 171 18 the the DT cord-229937-fy90oebs 171 19 ESIR ESIR NNP cord-229937-fy90oebs 171 20 model model NN cord-229937-fy90oebs 171 21 with with IN cord-229937-fy90oebs 171 22 essentially essentially RB cord-229937-fy90oebs 171 23 4 4 CD cord-229937-fy90oebs 171 24 free free JJ cord-229937-fy90oebs 171 25 parameters parameter NNS cord-229937-fy90oebs 171 26 to to TO cord-229937-fy90oebs 171 27 fit fit VB cord-229937-fy90oebs 171 28 to to IN cord-229937-fy90oebs 171 29 the the DT cord-229937-fy90oebs 171 30 daily daily JJ cord-229937-fy90oebs 171 31 death death NN cord-229937-fy90oebs 171 32 data datum NNS cord-229937-fy90oebs 171 33 ; ; : cord-229937-fy90oebs 171 34 i.e. i.e. FW cord-229937-fy90oebs 171 35 the the DT cord-229937-fy90oebs 171 36 same same JJ cord-229937-fy90oebs 171 37 number number NN cord-229937-fy90oebs 171 38 of of IN cord-229937-fy90oebs 171 39 parameters parameter NNS cord-229937-fy90oebs 171 40 than than IN cord-229937-fy90oebs 171 41 the the DT cord-229937-fy90oebs 171 42 original original JJ cord-229937-fy90oebs 171 43 SIR SIR NNP cord-229937-fy90oebs 171 44 model model NN cord-229937-fy90oebs 171 45 . . . cord-229937-fy90oebs 172 1 As as IN cord-229937-fy90oebs 172 2 shown show VBN cord-229937-fy90oebs 172 3 in in IN cord-229937-fy90oebs 172 4 Fig Fig NNP cord-229937-fy90oebs 172 5 . . . cord-229937-fy90oebs 173 1 10 10 CD cord-229937-fy90oebs 173 2 , , , cord-229937-fy90oebs 173 3 ESIR ESIR NNP cord-229937-fy90oebs 173 4 fits fit VBZ cord-229937-fy90oebs 173 5 reproduce reproduce VBP cord-229937-fy90oebs 173 6 well well RB cord-229937-fy90oebs 173 7 the the DT cord-229937-fy90oebs 173 8 long long JJ cord-229937-fy90oebs 173 9 flattening flatten VBG cord-229937-fy90oebs 173 10 behavior behavior NN cord-229937-fy90oebs 173 11 observed observe VBN cord-229937-fy90oebs 173 12 in in IN cord-229937-fy90oebs 173 13 UK UK NNP cord-229937-fy90oebs 173 14 , , , cord-229937-fy90oebs 173 15 USA USA NNP cord-229937-fy90oebs 173 16 , , , cord-229937-fy90oebs 173 17 Germany Germany NNP cord-229937-fy90oebs 173 18 or or CC cord-229937-fy90oebs 173 19 Iran Iran NNP cord-229937-fy90oebs 173 20 , , , cord-229937-fy90oebs 173 21 whereas whereas IN cord-229937-fy90oebs 173 22 it -PRON- PRP cord-229937-fy90oebs 173 23 fails fail VBZ cord-229937-fy90oebs 173 24 to to TO cord-229937-fy90oebs 173 25 reproduce reproduce VB cord-229937-fy90oebs 173 26 the the DT cord-229937-fy90oebs 173 27 more more RBR cord-229937-fy90oebs 173 28 - - HYPH cord-229937-fy90oebs 173 29 pronounced pronounce VBN cord-229937-fy90oebs 173 30 double double JJ cord-229937-fy90oebs 173 31 - - HYPH cord-229937-fy90oebs 173 32 peak peak NN cord-229937-fy90oebs 173 33 structure structure NN cord-229937-fy90oebs 173 34 typically typically RB cord-229937-fy90oebs 173 35 observed observe VBD cord-229937-fy90oebs 173 36 in in IN cord-229937-fy90oebs 173 37 countries country NNS cord-229937-fy90oebs 173 38 like like IN cord-229937-fy90oebs 173 39 France France NNP cord-229937-fy90oebs 173 40 , , , cord-229937-fy90oebs 173 41 Italy Italy NNP cord-229937-fy90oebs 173 42 , , , cord-229937-fy90oebs 173 43 Spain Spain NNP cord-229937-fy90oebs 173 44 or or CC cord-229937-fy90oebs 173 45 Belgium Belgium NNP cord-229937-fy90oebs 173 46 . . . cord-229937-fy90oebs 174 1 As as IN cord-229937-fy90oebs 174 2 previously previously RB cord-229937-fy90oebs 174 3 done do VBN cord-229937-fy90oebs 174 4 with with IN cord-229937-fy90oebs 174 5 the the DT cord-229937-fy90oebs 174 6 D D NNP cord-229937-fy90oebs 174 7 model model NN cord-229937-fy90oebs 174 8 , , , cord-229937-fy90oebs 174 9 one one PRP cord-229937-fy90oebs 174 10 can can MD cord-229937-fy90oebs 174 11 also also RB cord-229937-fy90oebs 174 12 expand expand VB cord-229937-fy90oebs 174 13 the the DT cord-229937-fy90oebs 174 14 ESIR ESIR NNP cord-229937-fy90oebs 174 15 model model NN cord-229937-fy90oebs 174 16 to to TO cord-229937-fy90oebs 174 17 accommodate accommodate VB cord-229937-fy90oebs 174 18 this this DT cord-229937-fy90oebs 174 19 apparent apparent JJ cord-229937-fy90oebs 174 20 failure failure NN cord-229937-fy90oebs 174 21 to to TO cord-229937-fy90oebs 174 22 take take VB cord-229937-fy90oebs 174 23 lockdown lockdown NN cord-229937-fy90oebs 174 24 effects effect NNS cord-229937-fy90oebs 174 25 into into IN cord-229937-fy90oebs 174 26 account account NN cord-229937-fy90oebs 174 27 . . . cord-229937-fy90oebs 175 1 Similarly similarly RB cord-229937-fy90oebs 175 2 , , , cord-229937-fy90oebs 175 3 the the DT cord-229937-fy90oebs 175 4 ESIR2 esir2 NN cord-229937-fy90oebs 175 5 model model NN cord-229937-fy90oebs 175 6 is be VBZ cord-229937-fy90oebs 175 7 proposed propose VBN cord-229937-fy90oebs 175 8 as as IN cord-229937-fy90oebs 175 9 , , , cord-229937-fy90oebs 175 10 with with IN cord-229937-fy90oebs 175 11 where where WRB cord-229937-fy90oebs 175 12 we -PRON- PRP cord-229937-fy90oebs 175 13 have have VBP cord-229937-fy90oebs 175 14 assumed assume VBN cord-229937-fy90oebs 175 15 that that IN cord-229937-fy90oebs 175 16 a a DT cord-229937-fy90oebs 175 17 = = SYM cord-229937-fy90oebs 175 18 a a NN cord-229937-fy90oebs 175 19 ′ ′ CD cord-229937-fy90oebs 175 20 and and CC cord-229937-fy90oebs 175 21 c c NN cord-229937-fy90oebs 175 22 = = SYM cord-229937-fy90oebs 175 23 2a 2a NN cord-229937-fy90oebs 175 24 to to TO cord-229937-fy90oebs 175 25 accommodate accommodate VB cord-229937-fy90oebs 175 26 that that DT cord-229937-fy90oebs 175 27 r(∞ r(∞ NN cord-229937-fy90oebs 175 28 ) ) -RRB- cord-229937-fy90oebs 176 1 → → IN cord-229937-fy90oebs 176 2 1 1 CD cord-229937-fy90oebs 176 3 and and CC cord-229937-fy90oebs 176 4 c c NN cord-229937-fy90oebs 176 5 2 2 CD cord-229937-fy90oebs 176 6 = = SYM cord-229937-fy90oebs 176 7 1 1 CD cord-229937-fy90oebs 176 8 . . . cord-229937-fy90oebs 177 1 Hence hence RB cord-229937-fy90oebs 177 2 , , , cord-229937-fy90oebs 177 3 we -PRON- PRP cord-229937-fy90oebs 177 4 are be VBP cord-229937-fy90oebs 177 5 left leave VBN cord-229937-fy90oebs 177 6 with with IN cord-229937-fy90oebs 177 7 five five CD cord-229937-fy90oebs 177 8 free free JJ cord-229937-fy90oebs 177 9 parameters parameter NNS cord-229937-fy90oebs 177 10 . . . cord-229937-fy90oebs 178 1 Finally finally RB cord-229937-fy90oebs 178 2 , , , cord-229937-fy90oebs 178 3 Fig Fig NNP cord-229937-fy90oebs 178 4 . . NNP cord-229937-fy90oebs 178 5 11 11 CD cord-229937-fy90oebs 178 6 shows show VBZ cord-229937-fy90oebs 178 7 the the DT cord-229937-fy90oebs 178 8 comparison comparison NN cord-229937-fy90oebs 178 9 between between IN cord-229937-fy90oebs 178 10 the the DT cord-229937-fy90oebs 178 11 ESIR2 esir2 NN cord-229937-fy90oebs 178 12 and and CC cord-229937-fy90oebs 178 13 D D NNP cord-229937-fy90oebs 178 14 ′ ′ CD cord-229937-fy90oebs 178 15 2 2 CD cord-229937-fy90oebs 178 16 fits fit VBZ cord-229937-fy90oebs 178 17 to to IN cord-229937-fy90oebs 178 18 real real JJ cord-229937-fy90oebs 178 19 data datum NNS cord-229937-fy90oebs 178 20 for for IN cord-229937-fy90oebs 178 21 countries country NNS cord-229937-fy90oebs 178 22 where where WRB cord-229937-fy90oebs 178 23 COVID-19 COVID-19 NNP cord-229937-fy90oebs 178 24 has have VBZ cord-229937-fy90oebs 178 25 widely widely RB cord-229937-fy90oebs 178 26 spread spread VBN cord-229937-fy90oebs 178 27 : : : cord-229937-fy90oebs 178 28 Belgium Belgium NNP cord-229937-fy90oebs 178 29 , , , cord-229937-fy90oebs 178 30 USA USA NNP cord-229937-fy90oebs 178 31 , , , cord-229937-fy90oebs 178 32 France France NNP cord-229937-fy90oebs 178 33 , , , cord-229937-fy90oebs 178 34 Germany Germany NNP cord-229937-fy90oebs 178 35 , , , cord-229937-fy90oebs 178 36 Iran Iran NNP cord-229937-fy90oebs 178 37 , , , cord-229937-fy90oebs 178 38 Italy Italy NNP cord-229937-fy90oebs 178 39 , , , cord-229937-fy90oebs 178 40 Spain Spain NNP cord-229937-fy90oebs 178 41 and and CC cord-229937-fy90oebs 178 42 UK UK NNP cord-229937-fy90oebs 178 43 , , , cord-229937-fy90oebs 178 44 USA USA NNP cord-229937-fy90oebs 178 45 . . . cord-229937-fy90oebs 179 1 Death death NN cord-229937-fy90oebs 179 2 data datum NNS cord-229937-fy90oebs 179 3 are be VBP cord-229937-fy90oebs 179 4 taken take VBN cord-229937-fy90oebs 179 5 from from IN cord-229937-fy90oebs 179 6 Refs ref NNS cord-229937-fy90oebs 179 7 . . . cord-229937-fy90oebs 180 1 [ [ -LRB- cord-229937-fy90oebs 180 2 19 19 CD cord-229937-fy90oebs 180 3 , , , cord-229937-fy90oebs 180 4 22 22 CD cord-229937-fy90oebs 180 5 , , , cord-229937-fy90oebs 180 6 23 23 CD cord-229937-fy90oebs 180 7 ] ] -RRB- cord-229937-fy90oebs 180 8 and and CC cord-229937-fy90oebs 180 9 consider consider VB cord-229937-fy90oebs 180 10 7-day 7-day JJ cord-229937-fy90oebs 180 11 average average JJ cord-229937-fy90oebs 180 12 smoothing smoothing NN cord-229937-fy90oebs 180 13 to to TO cord-229937-fy90oebs 180 14 correct correct VB cord-229937-fy90oebs 180 15 for for IN cord-229937-fy90oebs 180 16 anomalies anomaly NNS cord-229937-fy90oebs 180 17 in in IN cord-229937-fy90oebs 180 18 data datum NNS cord-229937-fy90oebs 180 19 collection collection NN cord-229937-fy90oebs 180 20 such such JJ cord-229937-fy90oebs 180 21 as as IN cord-229937-fy90oebs 180 22 the the DT cord-229937-fy90oebs 180 23 typical typical JJ cord-229937-fy90oebs 180 24 weekend weekend NN cord-229937-fy90oebs 180 25 staggering stagger VBG cord-229937-fy90oebs 180 26 observed observe VBN cord-229937-fy90oebs 180 27 in in IN cord-229937-fy90oebs 180 28 various various JJ cord-229937-fy90oebs 180 29 countries country NNS cord-229937-fy90oebs 180 30 , , , cord-229937-fy90oebs 180 31 where where WRB cord-229937-fy90oebs 180 32 weekend weekend NN cord-229937-fy90oebs 180 33 data datum NNS cord-229937-fy90oebs 180 34 are be VBP cord-229937-fy90oebs 180 35 counted count VBN cord-229937-fy90oebs 180 36 at at IN cord-229937-fy90oebs 180 37 the the DT cord-229937-fy90oebs 180 38 beginning beginning NN cord-229937-fy90oebs 180 39 of of IN cord-229937-fy90oebs 180 40 the the DT cord-229937-fy90oebs 180 41 next next JJ cord-229937-fy90oebs 180 42 week week NN cord-229937-fy90oebs 180 43 . . . cord-229937-fy90oebs 181 1 Real real JJ cord-229937-fy90oebs 181 2 error error NN cord-229937-fy90oebs 181 3 intervals interval NNS cord-229937-fy90oebs 181 4 are be VBP cord-229937-fy90oebs 181 5 extracted extract VBN cord-229937-fy90oebs 181 6 from from IN cord-229937-fy90oebs 181 7 the the DT cord-229937-fy90oebs 181 8 correlation correlation NN cord-229937-fy90oebs 181 9 matrix matrix NN cord-229937-fy90oebs 181 10 . . . cord-229937-fy90oebs 182 1 As as IN cord-229937-fy90oebs 182 2 discussed discuss VBN cord-229937-fy90oebs 182 3 in in IN cord-229937-fy90oebs 182 4 Section section NN cord-229937-fy90oebs 182 5 2.3 2.3 CD cord-229937-fy90oebs 182 6 , , , cord-229937-fy90oebs 182 7 the the DT cord-229937-fy90oebs 182 8 reduced reduce VBN cord-229937-fy90oebs 182 9 D d NN cord-229937-fy90oebs 182 10 ′ ′ CD cord-229937-fy90oebs 182 11 2 2 CD cord-229937-fy90oebs 182 12 model model NN cord-229937-fy90oebs 182 13 has have VBZ cord-229937-fy90oebs 182 14 been be VBN cord-229937-fy90oebs 182 15 used use VBN cord-229937-fy90oebs 182 16 with with IN cord-229937-fy90oebs 182 17 a a DT cord-229937-fy90oebs 182 18 = = SYM cord-229937-fy90oebs 182 19 a a DT cord-229937-fy90oebs 182 20 2 2 CD cord-229937-fy90oebs 182 21 and and CC cord-229937-fy90oebs 182 22 c c NN cord-229937-fy90oebs 182 23 = = SYM cord-229937-fy90oebs 182 24 c c NN cord-229937-fy90oebs 182 25 2 2 CD cord-229937-fy90oebs 182 26 . . . cord-229937-fy90oebs 183 1 Although although IN cord-229937-fy90oebs 183 2 arising arise VBG cord-229937-fy90oebs 183 3 from from IN cord-229937-fy90oebs 183 4 different different JJ cord-229937-fy90oebs 183 5 assumptions assumption NNS cord-229937-fy90oebs 183 6 , , , cord-229937-fy90oebs 183 7 both both DT cord-229937-fy90oebs 183 8 models model NNS cord-229937-fy90oebs 183 9 provide provide VBP cord-229937-fy90oebs 183 10 similar similar JJ cord-229937-fy90oebs 183 11 data datum NNS cord-229937-fy90oebs 183 12 descriptions description NNS cord-229937-fy90oebs 183 13 and and CC cord-229937-fy90oebs 183 14 predictions prediction NNS cord-229937-fy90oebs 183 15 , , , cord-229937-fy90oebs 183 16 with with IN cord-229937-fy90oebs 183 17 slightly slightly RB cord-229937-fy90oebs 183 18 better well JJR cord-229937-fy90oebs 183 19 values value NNS cord-229937-fy90oebs 183 20 of of IN cord-229937-fy90oebs 183 21 χ χ CD cord-229937-fy90oebs 183 22 2 2 CD cord-229937-fy90oebs 183 23 per per IN cord-229937-fy90oebs 183 24 degree degree NN cord-229937-fy90oebs 183 25 of of IN cord-229937-fy90oebs 183 26 freedom freedom NN cord-229937-fy90oebs 183 27 for for IN cord-229937-fy90oebs 183 28 the the DT cord-229937-fy90oebs 183 29 ESIR2 esir2 NN cord-229937-fy90oebs 183 30 model model NN cord-229937-fy90oebs 183 31 . . . cord-229937-fy90oebs 184 1 It -PRON- PRP cord-229937-fy90oebs 184 2 is be VBZ cord-229937-fy90oebs 184 3 also also RB cord-229937-fy90oebs 184 4 interesting interesting JJ cord-229937-fy90oebs 184 5 to to TO cord-229937-fy90oebs 184 6 note note VB cord-229937-fy90oebs 184 7 that that IN cord-229937-fy90oebs 184 8 the the DT cord-229937-fy90oebs 184 9 reduced reduce VBN cord-229937-fy90oebs 184 10 ESIR2 esir2 NN cord-229937-fy90oebs 184 11 model model NN cord-229937-fy90oebs 184 12 with with IN cord-229937-fy90oebs 184 13 five five CD cord-229937-fy90oebs 184 14 parameters parameter NNS cord-229937-fy90oebs 184 15 yields yield NNS cord-229937-fy90oebs 184 16 similar similar JJ cord-229937-fy90oebs 184 17 results result NNS cord-229937-fy90oebs 184 18 to to IN cord-229937-fy90oebs 184 19 the the DT cord-229937-fy90oebs 184 20 full full JJ cord-229937-fy90oebs 184 21 ESIR2 esir2 NN cord-229937-fy90oebs 184 22 model model NN cord-229937-fy90oebs 184 23 , , , cord-229937-fy90oebs 184 24 with with IN cord-229937-fy90oebs 184 25 eight eight CD cord-229937-fy90oebs 184 26 parameters parameter NNS cord-229937-fy90oebs 184 27 . . . cord-229937-fy90oebs 185 1 As as IN cord-229937-fy90oebs 185 2 data datum NNS cord-229937-fy90oebs 185 3 become become VBP cord-229937-fy90oebs 185 4 available available JJ cord-229937-fy90oebs 185 5 , , , cord-229937-fy90oebs 185 6 daily daily JJ cord-229937-fy90oebs 185 7 predictions prediction NNS cord-229937-fy90oebs 185 8 vary vary VBP cord-229937-fy90oebs 185 9 for for IN cord-229937-fy90oebs 185 10 both both DT cord-229937-fy90oebs 185 11 ESIR2 ESIR2 NNS cord-229937-fy90oebs 185 12 and and CC cord-229937-fy90oebs 185 13 the the DT cord-229937-fy90oebs 185 14 D d NN cord-229937-fy90oebs 185 15 ′ ′ CD cord-229937-fy90oebs 185 16 2 2 CD cord-229937-fy90oebs 185 17 models model NNS cord-229937-fy90oebs 185 18 . . . cord-229937-fy90oebs 186 1 This this DT cord-229937-fy90oebs 186 2 is be VBZ cord-229937-fy90oebs 186 3 because because IN cord-229937-fy90oebs 186 4 the the DT cord-229937-fy90oebs 186 5 model model NN cord-229937-fy90oebs 186 6 parameters parameter NNS cord-229937-fy90oebs 186 7 are be VBP cord-229937-fy90oebs 186 8 actually actually RB cord-229937-fy90oebs 186 9 statistical statistical JJ cord-229937-fy90oebs 186 10 averages average NNS cord-229937-fy90oebs 186 11 over over IN cord-229937-fy90oebs 186 12 space space NN cord-229937-fy90oebs 186 13 - - HYPH cord-229937-fy90oebs 186 14 time time NN cord-229937-fy90oebs 186 15 of of IN cord-229937-fy90oebs 186 16 the the DT cord-229937-fy90oebs 186 17 properties property NNS cord-229937-fy90oebs 186 18 of of IN cord-229937-fy90oebs 186 19 the the DT cord-229937-fy90oebs 186 20 complex complex JJ cord-229937-fy90oebs 186 21 system system NN cord-229937-fy90oebs 186 22 . . . cord-229937-fy90oebs 187 1 No no DT cord-229937-fy90oebs 187 2 model model NN cord-229937-fy90oebs 187 3 is be VBZ cord-229937-fy90oebs 187 4 able able JJ cord-229937-fy90oebs 187 5 to to TO cord-229937-fy90oebs 187 6 predict predict VB cord-229937-fy90oebs 187 7 changes change NNS cord-229937-fy90oebs 187 8 over over IN cord-229937-fy90oebs 187 9 time time NN cord-229937-fy90oebs 187 10 of of IN cord-229937-fy90oebs 187 11 these these DT cord-229937-fy90oebs 187 12 properties property NNS cord-229937-fy90oebs 187 13 if if IN cord-229937-fy90oebs 187 14 the the DT cord-229937-fy90oebs 187 15 physical physical JJ cord-229937-fy90oebs 187 16 causes cause NNS cord-229937-fy90oebs 187 17 of of IN cord-229937-fy90oebs 187 18 these these DT cord-229937-fy90oebs 187 19 changes change NNS cord-229937-fy90oebs 187 20 are be VBP cord-229937-fy90oebs 187 21 not not RB cord-229937-fy90oebs 187 22 included include VBN cord-229937-fy90oebs 187 23 . . . cord-229937-fy90oebs 188 1 The the DT cord-229937-fy90oebs 188 2 values value NNS cord-229937-fy90oebs 188 3 of of IN cord-229937-fy90oebs 188 4 the the DT cord-229937-fy90oebs 188 5 model model NN cord-229937-fy90oebs 188 6 parameters parameter NNS cord-229937-fy90oebs 188 7 are be VBP cord-229937-fy90oebs 188 8 only only RB cord-229937-fy90oebs 188 9 well well RB cord-229937-fy90oebs 188 10 defined define VBN cord-229937-fy90oebs 188 11 when when WRB cord-229937-fy90oebs 188 12 the the DT cord-229937-fy90oebs 188 13 disease disease NN cord-229937-fy90oebs 188 14 spread spread VBD cord-229937-fy90oebs 188 15 is be VBZ cord-229937-fy90oebs 188 16 coming come VBG cord-229937-fy90oebs 188 17 to to IN cord-229937-fy90oebs 188 18 an an DT cord-229937-fy90oebs 188 19 end end NN cord-229937-fy90oebs 188 20 and and CC cord-229937-fy90oebs 188 21 time time NN cord-229937-fy90oebs 188 22 changes change NNS cord-229937-fy90oebs 188 23 in in IN cord-229937-fy90oebs 188 24 the the DT cord-229937-fy90oebs 188 25 parameters parameter NNS cord-229937-fy90oebs 188 26 have have VBP cord-229937-fy90oebs 188 27 little little JJ cord-229937-fy90oebs 188 28 influence influence NN cord-229937-fy90oebs 188 29 . . . cord-229937-fy90oebs 189 1 More more RBR cord-229937-fy90oebs 189 2 sophisticated sophisticated JJ cord-229937-fy90oebs 189 3 calculations calculation NNS cord-229937-fy90oebs 189 4 can can MD cord-229937-fy90oebs 189 5 be be VB cord-229937-fy90oebs 189 6 compared compare VBN cord-229937-fy90oebs 189 7 with with IN cord-229937-fy90oebs 189 8 ESIR2 esir2 NN cord-229937-fy90oebs 189 9 and and CC cord-229937-fy90oebs 189 10 D D NNP cord-229937-fy90oebs 189 11 ′ ′ CD cord-229937-fy90oebs 189 12 2 2 CD cord-229937-fy90oebs 189 13 predictions prediction NNS cord-229937-fy90oebs 189 14 . . . cord-229937-fy90oebs 190 1 In in IN cord-229937-fy90oebs 190 2 particular particular JJ cord-229937-fy90oebs 190 3 , , , cord-229937-fy90oebs 190 4 Monte Monte NNP cord-229937-fy90oebs 190 5 Carlo Carlo NNP cord-229937-fy90oebs 190 6 ( ( -LRB- cord-229937-fy90oebs 190 7 MC MC NNP cord-229937-fy90oebs 190 8 ) ) -RRB- cord-229937-fy90oebs 190 9 simulations simulation NNS cord-229937-fy90oebs 190 10 have have VBP cord-229937-fy90oebs 190 11 also also RB cord-229937-fy90oebs 190 12 been be VBN cord-229937-fy90oebs 190 13 performed perform VBN cord-229937-fy90oebs 190 14 in in IN cord-229937-fy90oebs 190 15 this this DT cord-229937-fy90oebs 190 16 work work NN cord-229937-fy90oebs 190 17 for for IN cord-229937-fy90oebs 190 18 the the DT cord-229937-fy90oebs 190 19 Spanish spanish JJ cord-229937-fy90oebs 190 20 case case NN cord-229937-fy90oebs 190 21 [ [ -LRB- cord-229937-fy90oebs 190 22 24 24 CD cord-229937-fy90oebs 190 23 ] ] -RRB- cord-229937-fy90oebs 190 24 , , , cord-229937-fy90oebs 190 25 which which WDT cord-229937-fy90oebs 190 26 consist consist VBP cord-229937-fy90oebs 190 27 of of IN cord-229937-fy90oebs 190 28 a a DT cord-229937-fy90oebs 190 29 lattice lattice NN cord-229937-fy90oebs 190 30 of of IN cord-229937-fy90oebs 190 31 cells cell NNS cord-229937-fy90oebs 190 32 that that WDT cord-229937-fy90oebs 190 33 can can MD cord-229937-fy90oebs 190 34 be be VB cord-229937-fy90oebs 190 35 in in IN cord-229937-fy90oebs 190 36 four four CD cord-229937-fy90oebs 190 37 different different JJ cord-229937-fy90oebs 190 38 states state NNS cord-229937-fy90oebs 190 39 : : : cord-229937-fy90oebs 190 40 susceptible susceptible JJ cord-229937-fy90oebs 190 41 , , , cord-229937-fy90oebs 190 42 infected infected JJ cord-229937-fy90oebs 190 43 , , , cord-229937-fy90oebs 190 44 recovered recover VBN cord-229937-fy90oebs 190 45 or or CC cord-229937-fy90oebs 190 46 death death NN cord-229937-fy90oebs 190 47 . . . cord-229937-fy90oebs 191 1 An an DT cord-229937-fy90oebs 191 2 infected infected JJ cord-229937-fy90oebs 191 3 cell cell NN cord-229937-fy90oebs 191 4 can can MD cord-229937-fy90oebs 191 5 transmit transmit VB cord-229937-fy90oebs 191 6 the the DT cord-229937-fy90oebs 191 7 disease disease NN cord-229937-fy90oebs 191 8 to to IN cord-229937-fy90oebs 191 9 any any DT cord-229937-fy90oebs 191 10 other other JJ cord-229937-fy90oebs 191 11 susceptible susceptible JJ cord-229937-fy90oebs 191 12 cell cell NN cord-229937-fy90oebs 191 13 within within IN cord-229937-fy90oebs 191 14 some some DT cord-229937-fy90oebs 191 15 random random JJ cord-229937-fy90oebs 191 16 range range NN cord-229937-fy90oebs 192 1 R. R. NNP cord-229937-fy90oebs 193 1 The the DT cord-229937-fy90oebs 193 2 transmission transmission NN cord-229937-fy90oebs 193 3 mechanism mechanism NN cord-229937-fy90oebs 193 4 follows follow VBZ cord-229937-fy90oebs 193 5 principles principle NNS cord-229937-fy90oebs 193 6 of of IN cord-229937-fy90oebs 193 7 nuclear nuclear JJ cord-229937-fy90oebs 193 8 physics physics NN cord-229937-fy90oebs 193 9 for for IN cord-229937-fy90oebs 193 10 the the DT cord-229937-fy90oebs 193 11 interaction interaction NN cord-229937-fy90oebs 193 12 of of IN cord-229937-fy90oebs 193 13 a a DT cord-229937-fy90oebs 193 14 particle particle NN cord-229937-fy90oebs 193 15 with with IN cord-229937-fy90oebs 193 16 a a DT cord-229937-fy90oebs 193 17 target target NN cord-229937-fy90oebs 193 18 . . . cord-229937-fy90oebs 194 1 Each each DT cord-229937-fy90oebs 194 2 infected infected JJ cord-229937-fy90oebs 194 3 particle particle NN cord-229937-fy90oebs 194 4 interacts interact VBZ cord-229937-fy90oebs 194 5 a a DT cord-229937-fy90oebs 194 6 number number NN cord-229937-fy90oebs 194 7 n n NN cord-229937-fy90oebs 194 8 of of IN cord-229937-fy90oebs 194 9 times time NNS cord-229937-fy90oebs 194 10 over over IN cord-229937-fy90oebs 194 11 the the DT cord-229937-fy90oebs 194 12 interaction interaction NN cord-229937-fy90oebs 194 13 region region NN cord-229937-fy90oebs 194 14 , , , cord-229937-fy90oebs 194 15 according accord VBG cord-229937-fy90oebs 194 16 to to IN cord-229937-fy90oebs 194 17 its -PRON- PRP$ cord-229937-fy90oebs 194 18 energy energy NN cord-229937-fy90oebs 194 19 . . . cord-229937-fy90oebs 195 1 The the DT cord-229937-fy90oebs 195 2 number number NN cord-229937-fy90oebs 195 3 of of IN cord-229937-fy90oebs 195 4 interactions interaction NNS cord-229937-fy90oebs 195 5 is be VBZ cord-229937-fy90oebs 195 6 proportional proportional JJ cord-229937-fy90oebs 195 7 to to IN cord-229937-fy90oebs 195 8 the the DT cord-229937-fy90oebs 195 9 interaction interaction NN cord-229937-fy90oebs 195 10 cross cross NNP cord-229937-fy90oebs 195 11 section section NN cord-229937-fy90oebs 195 12 σ σ NNP cord-229937-fy90oebs 195 13 and and CC cord-229937-fy90oebs 195 14 to to IN cord-229937-fy90oebs 195 15 the the DT cord-229937-fy90oebs 195 16 target target NN cord-229937-fy90oebs 195 17 surface surface NN cord-229937-fy90oebs 195 18 density density NN cord-229937-fy90oebs 195 19 ρ ρ NNP cord-229937-fy90oebs 195 20 . . . cord-229937-fy90oebs 196 1 The the DT cord-229937-fy90oebs 196 2 discrete discrete JJ cord-229937-fy90oebs 196 3 energy energy NN cord-229937-fy90oebs 196 4 follows follow VBZ cord-229937-fy90oebs 196 5 a a DT cord-229937-fy90oebs 196 6 Planck Planck NNP cord-229937-fy90oebs 196 7 distribution distribution NN cord-229937-fy90oebs 196 8 law law NN cord-229937-fy90oebs 196 9 depending depend VBG cord-229937-fy90oebs 196 10 on on IN cord-229937-fy90oebs 196 11 the the DT cord-229937-fy90oebs 196 12 ' ' `` cord-229937-fy90oebs 196 13 temperature temperature NN cord-229937-fy90oebs 196 14 ' ' '' cord-229937-fy90oebs 196 15 of of IN cord-229937-fy90oebs 196 16 the the DT cord-229937-fy90oebs 196 17 system system NN cord-229937-fy90oebs 196 18 . . . cord-229937-fy90oebs 197 1 For for IN cord-229937-fy90oebs 197 2 any any DT cord-229937-fy90oebs 197 3 interaction interaction NN cord-229937-fy90oebs 197 4 , , , cord-229937-fy90oebs 197 5 an an DT cord-229937-fy90oebs 197 6 infection infection NN cord-229937-fy90oebs 197 7 probability probability NN cord-229937-fy90oebs 197 8 is be VBZ cord-229937-fy90oebs 197 9 applied apply VBN cord-229937-fy90oebs 197 10 . . . cord-229937-fy90oebs 198 1 Finally finally RB cord-229937-fy90oebs 198 2 , , , cord-229937-fy90oebs 198 3 time time NN cord-229937-fy90oebs 198 4 - - HYPH cord-229937-fy90oebs 198 5 dependent dependent JJ cord-229937-fy90oebs 198 6 recovery recovery NN cord-229937-fy90oebs 198 7 and and CC cord-229937-fy90oebs 198 8 death death NN cord-229937-fy90oebs 198 9 probabilities probability NNS cord-229937-fy90oebs 198 10 are be VBP cord-229937-fy90oebs 198 11 also also RB cord-229937-fy90oebs 198 12 applied apply VBN cord-229937-fy90oebs 198 13 . . . cord-229937-fy90oebs 199 1 The the DT cord-229937-fy90oebs 199 2 resulting result VBG cord-229937-fy90oebs 199 3 virus virus NN cord-229937-fy90oebs 199 4 spread spread VBD cord-229937-fy90oebs 199 5 for for IN cord-229937-fy90oebs 199 6 different different JJ cord-229937-fy90oebs 199 7 sets set NNS cord-229937-fy90oebs 199 8 of of IN cord-229937-fy90oebs 199 9 parameters parameter NNS cord-229937-fy90oebs 199 10 can can MD cord-229937-fy90oebs 199 11 be be VB cord-229937-fy90oebs 199 12 adjusted adjust VBN cord-229937-fy90oebs 199 13 from from IN cord-229937-fy90oebs 199 14 COVID-19 COVID-19 NNP cord-229937-fy90oebs 199 15 pandemic pandemic NNP cord-229937-fy90oebs 199 16 data datum NNS cord-229937-fy90oebs 199 17 . . . cord-229937-fy90oebs 200 1 In in IN cord-229937-fy90oebs 200 2 addition addition NN cord-229937-fy90oebs 200 3 , , , cord-229937-fy90oebs 200 4 parameters parameter NNS cord-229937-fy90oebs 200 5 can can MD cord-229937-fy90oebs 200 6 be be VB cord-229937-fy90oebs 200 7 made make VBN cord-229937-fy90oebs 200 8 time time NN cord-229937-fy90oebs 200 9 dependent dependent JJ cord-229937-fy90oebs 200 10 in in IN cord-229937-fy90oebs 200 11 order order NN cord-229937-fy90oebs 200 12 to to TO cord-229937-fy90oebs 200 13 investigate investigate VB cord-229937-fy90oebs 200 14 , , , cord-229937-fy90oebs 200 15 for for IN cord-229937-fy90oebs 200 16 instance instance NN cord-229937-fy90oebs 200 17 , , , cord-229937-fy90oebs 200 18 the the DT cord-229937-fy90oebs 200 19 effect effect NN cord-229937-fy90oebs 200 20 of of IN cord-229937-fy90oebs 200 21 an an DT cord-229937-fy90oebs 200 22 early early JJ cord-229937-fy90oebs 200 23 lockdown lockdown NN cord-229937-fy90oebs 200 24 or or CC cord-229937-fy90oebs 200 25 large large JJ cord-229937-fy90oebs 200 26 mass mass JJ cord-229937-fy90oebs 200 27 gatherings gathering NNS cord-229937-fy90oebs 200 28 at at IN cord-229937-fy90oebs 200 29 the the DT cord-229937-fy90oebs 200 30 rise rise NN cord-229937-fy90oebs 200 31 of of IN cord-229937-fy90oebs 200 32 the the DT cord-229937-fy90oebs 200 33 pandemic pandemic NN cord-229937-fy90oebs 200 34 . . . cord-229937-fy90oebs 201 1 As as IN cord-229937-fy90oebs 201 2 shown show VBN cord-229937-fy90oebs 201 3 in in IN cord-229937-fy90oebs 201 4 Fig Fig NNP cord-229937-fy90oebs 201 5 . . . cord-229937-fy90oebs 202 1 12 12 CD cord-229937-fy90oebs 202 2 , , , cord-229937-fy90oebs 202 3 our -PRON- PRP$ cord-229937-fy90oebs 202 4 MC MC NNP cord-229937-fy90oebs 202 5 simulations simulation NNS cord-229937-fy90oebs 202 6 present present VBP cord-229937-fy90oebs 202 7 similar similar JJ cord-229937-fy90oebs 202 8 results result NNS cord-229937-fy90oebs 202 9 to to IN cord-229937-fy90oebs 202 10 the the DT cord-229937-fy90oebs 202 11 D d NN cord-229937-fy90oebs 202 12 ′ ′ CD cord-229937-fy90oebs 202 13 2 2 CD cord-229937-fy90oebs 202 14 model model NN cord-229937-fy90oebs 202 15 , , , cord-229937-fy90oebs 202 16 which which WDT cord-229937-fy90oebs 202 17 validates validate VBZ cord-229937-fy90oebs 202 18 the the DT cord-229937-fy90oebs 202 19 use use NN cord-229937-fy90oebs 202 20 of of IN cord-229937-fy90oebs 202 21 the the DT cord-229937-fy90oebs 202 22 simple simple JJ cord-229937-fy90oebs 202 23 D d NN cord-229937-fy90oebs 202 24 - - HYPH cord-229937-fy90oebs 202 25 model model NN cord-229937-fy90oebs 202 26 as as IN cord-229937-fy90oebs 202 27 a a DT cord-229937-fy90oebs 202 28 first first JJ cord-229937-fy90oebs 202 29 - - HYPH cord-229937-fy90oebs 202 30 order order NN cord-229937-fy90oebs 202 31 approximation approximation NN cord-229937-fy90oebs 202 32 . . . cord-229937-fy90oebs 203 1 More More JJR cord-229937-fy90oebs 203 2 details detail NNS cord-229937-fy90oebs 203 3 on on IN cord-229937-fy90oebs 203 4 the the DT cord-229937-fy90oebs 203 5 MC MC NNP cord-229937-fy90oebs 203 6 simulation simulation NN cord-229937-fy90oebs 203 7 will will MD cord-229937-fy90oebs 203 8 be be VB cord-229937-fy90oebs 203 9 presented present VBN cord-229937-fy90oebs 203 10 in in IN cord-229937-fy90oebs 203 11 a a DT cord-229937-fy90oebs 203 12 separate separate JJ cord-229937-fy90oebs 203 13 manuscript manuscript NN cord-229937-fy90oebs 203 14 [ [ -LRB- cord-229937-fy90oebs 203 15 24 24 CD cord-229937-fy90oebs 203 16 ] ] -RRB- cord-229937-fy90oebs 203 17 . . . cord-229937-fy90oebs 204 1 Interestingly interestingly RB cord-229937-fy90oebs 204 2 , , , cord-229937-fy90oebs 204 3 MC MC NNP cord-229937-fy90oebs 204 4 simulations simulation NNS cord-229937-fy90oebs 204 5 follow follow VBP cord-229937-fy90oebs 204 6 the the DT cord-229937-fy90oebs 204 7 data data NN cord-229937-fy90oebs 204 8 trend trend NN cord-229937-fy90oebs 204 9 up up IN cord-229937-fy90oebs 204 10 to to IN cord-229937-fy90oebs 204 11 May May NNP cord-229937-fy90oebs 204 12 11 11 CD cord-229937-fy90oebs 204 13 without without IN cord-229937-fy90oebs 204 14 any any DT cord-229937-fy90oebs 204 15 changes change NNS cord-229937-fy90oebs 204 16 in in IN cord-229937-fy90oebs 204 17 the the DT cord-229937-fy90oebs 204 18 parameters parameter NNS cord-229937-fy90oebs 204 19 for for IN cord-229937-fy90oebs 204 20 nearly nearly RB cord-229937-fy90oebs 204 21 two two CD cord-229937-fy90oebs 204 22 weeks week NNS cord-229937-fy90oebs 204 23 . . . cord-229937-fy90oebs 205 1 An an DT cord-229937-fy90oebs 205 2 app app NN cord-229937-fy90oebs 205 3 for for IN cord-229937-fy90oebs 205 4 Android Android NNP cord-229937-fy90oebs 205 5 devices device NNS cord-229937-fy90oebs 205 6 , , , cord-229937-fy90oebs 205 7 where where WRB cord-229937-fy90oebs 205 8 the the DT cord-229937-fy90oebs 205 9 Monte Monte NNP cord-229937-fy90oebs 205 10 Carlo Carlo NNP cord-229937-fy90oebs 205 11 Planck Planck NNP cord-229937-fy90oebs 205 12 model model NN cord-229937-fy90oebs 205 13 has have VBZ cord-229937-fy90oebs 205 14 been be VBN cord-229937-fy90oebs 205 15 implemented implement VBN cord-229937-fy90oebs 205 16 to to TO cord-229937-fy90oebs 205 17 visualize visualize VB cord-229937-fy90oebs 205 18 the the DT cord-229937-fy90oebs 205 19 simulation simulation NN cord-229937-fy90oebs 205 20 is be VBZ cord-229937-fy90oebs 205 21 available available JJ cord-229937-fy90oebs 205 22 from from IN cord-229937-fy90oebs 205 23 Ref Ref NNP cord-229937-fy90oebs 205 24 . . . cord-229937-fy90oebs 206 1 [ [ -LRB- cord-229937-fy90oebs 206 2 25 25 CD cord-229937-fy90oebs 206 3 ] ] -RRB- cord-229937-fy90oebs 206 4 . . . cord-229937-fy90oebs 207 1 In in IN cord-229937-fy90oebs 207 2 order order NN cord-229937-fy90oebs 207 3 to to TO cord-229937-fy90oebs 207 4 investigate investigate VB cord-229937-fy90oebs 207 5 the the DT cord-229937-fy90oebs 207 6 universality universality NN cord-229937-fy90oebs 207 7 of of IN cord-229937-fy90oebs 207 8 the the DT cord-229937-fy90oebs 207 9 pandemic pandemic NN cord-229937-fy90oebs 207 10 , , , cord-229937-fy90oebs 207 11 it -PRON- PRP cord-229937-fy90oebs 207 12 is be VBZ cord-229937-fy90oebs 207 13 interesting interesting JJ cord-229937-fy90oebs 207 14 to to TO cord-229937-fy90oebs 207 15 compare compare VB cord-229937-fy90oebs 207 16 all all DT cord-229937-fy90oebs 207 17 countries country NNS cord-229937-fy90oebs 207 18 by by IN cord-229937-fy90oebs 207 19 plotting plot VBG cord-229937-fy90oebs 207 20 the the DT cord-229937-fy90oebs 207 21 D d NN cord-229937-fy90oebs 207 22 model model NN cord-229937-fy90oebs 207 23 in in IN cord-229937-fy90oebs 207 24 terms term NNS cord-229937-fy90oebs 207 25 of of IN cord-229937-fy90oebs 207 26 the the DT cord-229937-fy90oebs 207 27 variable variable NN cord-229937-fy90oebs 207 28 ( ( -LRB- cord-229937-fy90oebs 207 29 t t NN cord-229937-fy90oebs 207 30 − − NN cord-229937-fy90oebs 207 31 t t NN cord-229937-fy90oebs 207 32 0 0 CD cord-229937-fy90oebs 207 33 ) ) -RRB- cord-229937-fy90oebs 207 34 /b /b NNP cord-229937-fy90oebs 207 35 , , , cord-229937-fy90oebs 207 36 where where WRB cord-229937-fy90oebs 207 37 t t NN cord-229937-fy90oebs 207 38 0 0 CD cord-229937-fy90oebs 207 39 is be VBZ cord-229937-fy90oebs 207 40 the the DT cord-229937-fy90oebs 207 41 maximum maximum NN cord-229937-fy90oebs 207 42 of of IN cord-229937-fy90oebs 207 43 the the DT cord-229937-fy90oebs 207 44 daily daily JJ cord-229937-fy90oebs 207 45 curve curve NN cord-229937-fy90oebs 207 46 given give VBN cord-229937-fy90oebs 207 47 by by IN cord-229937-fy90oebs 207 48 t t NNP cord-229937-fy90oebs 207 49 max max NN cord-229937-fy90oebs 207 50 = = SYM cord-229937-fy90oebs 207 51 −b −b NNP cord-229937-fy90oebs 207 52 ℓn(c ℓn(c ADD cord-229937-fy90oebs 207 53 ) ) -RRB- cord-229937-fy90oebs 207 54 . . . cord-229937-fy90oebs 208 1 By by IN cord-229937-fy90oebs 208 2 shifting shift VBG cord-229937-fy90oebs 208 3 Eq Eq NNP cord-229937-fy90oebs 208 4 . . . cord-229937-fy90oebs 209 1 15 15 CD cord-229937-fy90oebs 209 2 by by IN cord-229937-fy90oebs 209 3 t t NNP cord-229937-fy90oebs 209 4 max max NNP cord-229937-fy90oebs 209 5 = = SYM cord-229937-fy90oebs 209 6 −b −b NNP cord-229937-fy90oebs 209 7 ℓn(c ℓn(c NFP cord-229937-fy90oebs 209 8 ) ) -RRB- cord-229937-fy90oebs 209 9 and and CC cord-229937-fy90oebs 209 10 dividing divide VBG cord-229937-fy90oebs 209 11 by by IN cord-229937-fy90oebs 209 12 t t NNP cord-229937-fy90oebs 209 13 max max NN cord-229937-fy90oebs 209 14 = = NNP cord-229937-fy90oebs 210 1 a a LS cord-229937-fy90oebs 210 2 / / SYM cord-229937-fy90oebs 210 3 c c NN cord-229937-fy90oebs 210 4 , , , cord-229937-fy90oebs 210 5 the the DT cord-229937-fy90oebs 210 6 normalized normalized JJ cord-229937-fy90oebs 210 7 D d NN cord-229937-fy90oebs 210 8 function function NN cord-229937-fy90oebs 210 9 is be VBZ cord-229937-fy90oebs 210 10 given give VBN cord-229937-fy90oebs 210 11 by by IN cord-229937-fy90oebs 210 12 , , . cord-229937-fy90oebs 211 1 The the DT cord-229937-fy90oebs 211 2 left left NN cord-229937-fy90oebs 211 3 of of IN cord-229937-fy90oebs 211 4 Fig Fig NNP cord-229937-fy90oebs 211 5 . . . cord-229937-fy90oebs 212 1 13 13 CD cord-229937-fy90oebs 212 2 shows show VBZ cord-229937-fy90oebs 212 3 similar similar JJ cord-229937-fy90oebs 212 4 trends trend NNS cord-229937-fy90oebs 212 5 for for IN cord-229937-fy90oebs 212 6 the the DT cord-229937-fy90oebs 212 7 normalized normalized JJ cord-229937-fy90oebs 212 8 D d NN cord-229937-fy90oebs 212 9 curves curve NNS cord-229937-fy90oebs 212 10 of of IN cord-229937-fy90oebs 212 11 different different JJ cord-229937-fy90oebs 212 12 countries country NNS cord-229937-fy90oebs 212 13 , , , cord-229937-fy90oebs 212 14 which which WDT cord-229937-fy90oebs 212 15 suggests suggest VBZ cord-229937-fy90oebs 212 16 a a DT cord-229937-fy90oebs 212 17 universal universal JJ cord-229937-fy90oebs 212 18 behavior behavior NN cord-229937-fy90oebs 212 19 of of IN cord-229937-fy90oebs 212 20 the the DT cord-229937-fy90oebs 212 21 COVID-19 COVID-19 NNP cord-229937-fy90oebs 212 22 pandemic pandemic NN cord-229937-fy90oebs 212 23 . . . cord-229937-fy90oebs 213 1 Only only RB cord-229937-fy90oebs 213 2 Iran Iran NNP cord-229937-fy90oebs 213 3 seems seem VBZ cord-229937-fy90oebs 213 4 to to TO cord-229937-fy90oebs 213 5 slightly slightly RB cord-229937-fy90oebs 213 6 deviate deviate VB cord-229937-fy90oebs 213 7 from from IN cord-229937-fy90oebs 213 8 the the DT cord-229937-fy90oebs 213 9 global global JJ cord-229937-fy90oebs 213 10 trend trend NN cord-229937-fy90oebs 213 11 , , , cord-229937-fy90oebs 213 12 which which WDT cord-229937-fy90oebs 213 13 may may MD cord-229937-fy90oebs 213 14 indicate indicate VB cord-229937-fy90oebs 213 15 an an DT cord-229937-fy90oebs 213 16 early early JJ cord-229937-fy90oebs 213 17 and and CC cord-229937-fy90oebs 213 18 more more RBR cord-229937-fy90oebs 213 19 effective effective JJ cord-229937-fy90oebs 213 20 initial initial JJ cord-229937-fy90oebs 213 21 lockdown lockdown NN cord-229937-fy90oebs 213 22 . . . cord-229937-fy90oebs 214 1 A a DT cord-229937-fy90oebs 214 2 similar similar JJ cord-229937-fy90oebs 214 3 approach approach NN cord-229937-fy90oebs 214 4 can can MD cord-229937-fy90oebs 214 5 be be VB cord-229937-fy90oebs 214 6 done do VBN cord-229937-fy90oebs 214 7 for for IN cord-229937-fy90oebs 214 8 the the DT cord-229937-fy90oebs 214 9 daily daily JJ cord-229937-fy90oebs 214 10 data datum NNS cord-229937-fy90oebs 214 11 using use VBG cord-229937-fy90oebs 214 12 peaks peak NNS cord-229937-fy90oebs 214 13 . . . cord-229937-fy90oebs 215 1 The the DT cord-229937-fy90oebs 215 2 global global JJ cord-229937-fy90oebs 215 3 models model NNS cord-229937-fy90oebs 215 4 considered consider VBN cord-229937-fy90oebs 215 5 in in IN cord-229937-fy90oebs 215 6 this this DT cord-229937-fy90oebs 215 7 work work NN cord-229937-fy90oebs 215 8 present present VBP cord-229937-fy90oebs 215 9 some some DT cord-229937-fy90oebs 215 10 differences difference NNS cord-229937-fy90oebs 215 11 with with IN cord-229937-fy90oebs 215 12 respect respect NN cord-229937-fy90oebs 215 13 to to IN cord-229937-fy90oebs 215 14 other other JJ cord-229937-fy90oebs 215 15 existing exist VBG cord-229937-fy90oebs 215 16 models model NNS cord-229937-fy90oebs 215 17 . . . cord-229937-fy90oebs 216 1 First first RB cord-229937-fy90oebs 216 2 , , , cord-229937-fy90oebs 216 3 in in IN cord-229937-fy90oebs 216 4 this this DT cord-229937-fy90oebs 216 5 work work NN cord-229937-fy90oebs 216 6 we -PRON- PRP cord-229937-fy90oebs 216 7 have have VBP cord-229937-fy90oebs 216 8 tried try VBN cord-229937-fy90oebs 216 9 to to TO cord-229937-fy90oebs 216 10 keep keep VB cord-229937-fy90oebs 216 11 the the DT cord-229937-fy90oebs 216 12 models model NNS cord-229937-fy90oebs 216 13 as as RB cord-229937-fy90oebs 216 14 simple simple JJ cord-229937-fy90oebs 216 15 as as IN cord-229937-fy90oebs 216 16 possible possible JJ cord-229937-fy90oebs 216 17 . . . cord-229937-fy90oebs 217 1 This this DT cord-229937-fy90oebs 217 2 allows allow VBZ cord-229937-fy90oebs 217 3 to to TO cord-229937-fy90oebs 217 4 use use VB cord-229937-fy90oebs 217 5 theoretical theoretical JJ cord-229937-fy90oebs 217 6 - - HYPH cord-229937-fy90oebs 217 7 inspired inspire VBN cord-229937-fy90oebs 217 8 analytical analytical JJ cord-229937-fy90oebs 217 9 expressions expression NNS cord-229937-fy90oebs 217 10 or or CC cord-229937-fy90oebs 217 11 semi semi JJ cord-229937-fy90oebs 217 12 - - JJ cord-229937-fy90oebs 217 13 empirical empirical JJ cord-229937-fy90oebs 217 14 formulae formula NNS cord-229937-fy90oebs 217 15 to to TO cord-229937-fy90oebs 217 16 perform perform VB cord-229937-fy90oebs 217 17 the the DT cord-229937-fy90oebs 217 18 data data NN cord-229937-fy90oebs 217 19 analysis analysis NN cord-229937-fy90oebs 217 20 . . . cord-229937-fy90oebs 218 1 The the DT cord-229937-fy90oebs 218 2 use use NN cord-229937-fy90oebs 218 3 of of IN cord-229937-fy90oebs 218 4 semi semi JJ cord-229937-fy90oebs 218 5 - - JJ cord-229937-fy90oebs 218 6 empirical empirical JJ cord-229937-fy90oebs 218 7 expressions expression NNS cord-229937-fy90oebs 218 8 for for IN cord-229937-fy90oebs 218 9 describing describe VBG cord-229937-fy90oebs 218 10 physical physical JJ cord-229937-fy90oebs 218 11 phenomena phenomenon NNS cord-229937-fy90oebs 218 12 is be VBZ cord-229937-fy90oebs 218 13 recurrent recurrent JJ cord-229937-fy90oebs 218 14 in in IN cord-229937-fy90oebs 218 15 physics physics NN cord-229937-fy90oebs 218 16 . . . cord-229937-fy90oebs 219 1 One one CD cord-229937-fy90oebs 219 2 of of IN cord-229937-fy90oebs 219 3 the the DT cord-229937-fy90oebs 219 4 most most RBS cord-229937-fy90oebs 219 5 famous famous JJ cord-229937-fy90oebs 219 6 is be VBZ cord-229937-fy90oebs 219 7 the the DT cord-229937-fy90oebs 219 8 semi semi JJ cord-229937-fy90oebs 219 9 - - JJ cord-229937-fy90oebs 219 10 empirical empirical JJ cord-229937-fy90oebs 219 11 mass mass NN cord-229937-fy90oebs 219 12 formula formula NN cord-229937-fy90oebs 219 13 from from IN cord-229937-fy90oebs 219 14 nuclear nuclear JJ cord-229937-fy90oebs 219 15 physics physics NN cord-229937-fy90oebs 219 16 . . . cord-229937-fy90oebs 220 1 Of of RB cord-229937-fy90oebs 220 2 course course RB cord-229937-fy90oebs 220 3 the the DT cord-229937-fy90oebs 220 4 free free JJ cord-229937-fy90oebs 220 5 parameters parameter NNS cord-229937-fy90oebs 220 6 need need VBP cord-229937-fy90oebs 220 7 to to TO cord-229937-fy90oebs 220 8 be be VB cord-229937-fy90oebs 220 9 fitted fit VBN cord-229937-fy90oebs 220 10 from from IN cord-229937-fy90oebs 220 11 known know VBN cord-229937-fy90oebs 220 12 data datum NNS cord-229937-fy90oebs 220 13 , , , cord-229937-fy90oebs 220 14 but but CC cord-229937-fy90oebs 220 15 this this DT cord-229937-fy90oebs 220 16 allowed allow VBD cord-229937-fy90oebs 220 17 to to TO cord-229937-fy90oebs 220 18 obtain obtain VB cord-229937-fy90oebs 220 19 predictions prediction NNS cord-229937-fy90oebs 220 20 for for IN cord-229937-fy90oebs 220 21 unknown unknown JJ cord-229937-fy90oebs 220 22 elements element NNS cord-229937-fy90oebs 220 23 . . . cord-229937-fy90oebs 221 1 In in IN cord-229937-fy90oebs 221 2 our -PRON- PRP$ cord-229937-fy90oebs 221 3 case case NN cord-229937-fy90oebs 221 4 we -PRON- PRP cord-229937-fy90oebs 221 5 were be VBD cord-229937-fy90oebs 221 6 inspired inspire VBN cord-229937-fy90oebs 221 7 by by IN cord-229937-fy90oebs 221 8 the the DT cord-229937-fy90oebs 221 9 well well RB cord-229937-fy90oebs 221 10 known know VBN cord-229937-fy90oebs 221 11 statistical statistical JJ cord-229937-fy90oebs 221 12 SIR sir NN cord-229937-fy90oebs 221 13 - - HYPH cord-229937-fy90oebs 221 14 kind kind NN cord-229937-fy90oebs 221 15 models model NNS cord-229937-fy90oebs 221 16 slightly slightly RB cord-229937-fy90oebs 221 17 modified modify VBN cord-229937-fy90oebs 221 18 to to TO cord-229937-fy90oebs 221 19 obtain obtain VB cord-229937-fy90oebs 221 20 analytical analytical JJ cord-229937-fy90oebs 221 21 expressions expression NNS cord-229937-fy90oebs 221 22 that that WDT cord-229937-fy90oebs 221 23 carry carry VBP cord-229937-fy90oebs 221 24 the the DT cord-229937-fy90oebs 221 25 leading leading JJ cord-229937-fy90oebs 221 26 time time NN cord-229937-fy90oebs 221 27 dependence dependence NN cord-229937-fy90oebs 221 28 . . . cord-229937-fy90oebs 222 1 We -PRON- PRP cord-229937-fy90oebs 222 2 have have VBP cord-229937-fy90oebs 222 3 found find VBN cord-229937-fy90oebs 222 4 that that IN cord-229937-fy90oebs 222 5 the the DT cord-229937-fy90oebs 222 6 D d NN cord-229937-fy90oebs 222 7 and and CC cord-229937-fy90oebs 222 8 D D NNP cord-229937-fy90oebs 222 9 2 2 CD cord-229937-fy90oebs 222 10 models model NNS cord-229937-fy90oebs 222 11 allow allow VBP cord-229937-fy90oebs 222 12 a a DT cord-229937-fy90oebs 222 13 fast fast JJ cord-229937-fy90oebs 222 14 and and CC cord-229937-fy90oebs 222 15 efficient efficient JJ cord-229937-fy90oebs 222 16 analysis analysis NN cord-229937-fy90oebs 222 17 of of IN cord-229937-fy90oebs 222 18 the the DT cord-229937-fy90oebs 222 19 pandemics pandemic NNS cord-229937-fy90oebs 222 20 in in IN cord-229937-fy90oebs 222 21 the the DT cord-229937-fy90oebs 222 22 initial initial JJ cord-229937-fy90oebs 222 23 and and CC cord-229937-fy90oebs 222 24 advanced advanced JJ cord-229937-fy90oebs 222 25 stages stage NNS cord-229937-fy90oebs 222 26 . . . cord-229937-fy90oebs 223 1 Our -PRON- PRP$ cord-229937-fy90oebs 223 2 results result NNS cord-229937-fy90oebs 223 3 show show VBP cord-229937-fy90oebs 223 4 that that IN cord-229937-fy90oebs 223 5 the the DT cord-229937-fy90oebs 223 6 time time NN cord-229937-fy90oebs 223 7 dependence dependence NN cord-229937-fy90oebs 223 8 of of IN cord-229937-fy90oebs 223 9 the the DT cord-229937-fy90oebs 223 10 pandemic pandemic NN cord-229937-fy90oebs 223 11 parameters parameter NNS cord-229937-fy90oebs 223 12 due due JJ cord-229937-fy90oebs 223 13 to to IN cord-229937-fy90oebs 223 14 the the DT cord-229937-fy90oebs 223 15 lockdown lockdown NN cord-229937-fy90oebs 223 16 can can MD cord-229937-fy90oebs 223 17 be be VB cord-229937-fy90oebs 223 18 effectively effectively RB cord-229937-fy90oebs 223 19 simulated simulate VBN cord-229937-fy90oebs 223 20 by by IN cord-229937-fy90oebs 223 21 the the DT cord-229937-fy90oebs 223 22 sum sum NN cord-229937-fy90oebs 223 23 of of IN cord-229937-fy90oebs 223 24 two two CD cord-229937-fy90oebs 223 25 Dfunctions dfunction NNS cord-229937-fy90oebs 223 26 with with IN cord-229937-fy90oebs 223 27 different different JJ cord-229937-fy90oebs 223 28 widths width NNS cord-229937-fy90oebs 223 29 and and CC cord-229937-fy90oebs 223 30 heights height NNS cord-229937-fy90oebs 223 31 and and CC cord-229937-fy90oebs 223 32 centered center VBN cord-229937-fy90oebs 223 33 at at IN cord-229937-fy90oebs 223 34 different different JJ cord-229937-fy90oebs 223 35 times time NNS cord-229937-fy90oebs 223 36 . . . cord-229937-fy90oebs 224 1 The the DT cord-229937-fy90oebs 224 2 distance distance NN cord-229937-fy90oebs 224 3 between between IN cord-229937-fy90oebs 224 4 the the DT cord-229937-fy90oebs 224 5 maxima maxima NN cord-229937-fy90oebs 224 6 of of IN cord-229937-fy90oebs 224 7 the the DT cord-229937-fy90oebs 224 8 two two CD cord-229937-fy90oebs 224 9 D d NN cord-229937-fy90oebs 224 10 - - HYPH cord-229937-fy90oebs 224 11 functions function NNS cord-229937-fy90oebs 224 12 should should MD cord-229937-fy90oebs 224 13 be be VB cord-229937-fy90oebs 224 14 a a DT cord-229937-fy90oebs 224 15 measure measure NN cord-229937-fy90oebs 224 16 of of IN cord-229937-fy90oebs 224 17 the the DT cord-229937-fy90oebs 224 18 time time NN cord-229937-fy90oebs 224 19 between between IN cord-229937-fy90oebs 224 20 the the DT cord-229937-fy90oebs 224 21 effective effective JJ cord-229937-fy90oebs 224 22 pandemic pandemic NN cord-229937-fy90oebs 224 23 beginning beginning NN cord-229937-fy90oebs 224 24 and and CC cord-229937-fy90oebs 224 25 lockdown lockdown NN cord-229937-fy90oebs 224 26 . . . cord-229937-fy90oebs 225 1 In in IN cord-229937-fy90oebs 225 2 the the DT cord-229937-fy90oebs 225 3 Spanish spanish JJ cord-229937-fy90oebs 225 4 case case NN cord-229937-fy90oebs 225 5 this this DT cord-229937-fy90oebs 225 6 is be VBZ cord-229937-fy90oebs 225 7 about about RB cord-229937-fy90oebs 225 8 20 20 CD cord-229937-fy90oebs 225 9 days day NNS cord-229937-fy90oebs 225 10 . . . cord-229937-fy90oebs 226 1 Taking take VBG cord-229937-fy90oebs 226 2 into into IN cord-229937-fy90oebs 226 3 account account NN cord-229937-fy90oebs 226 4 that that DT cord-229937-fy90oebs 226 5 lockdown lockdown NN cord-229937-fy90oebs 226 6 started start VBD cord-229937-fy90oebs 226 7 in in IN cord-229937-fy90oebs 226 8 March March NNP cord-229937-fy90oebs 226 9 14 14 CD cord-229937-fy90oebs 226 10 , , , cord-229937-fy90oebs 226 11 this this DT cord-229937-fy90oebs 226 12 marks mark VBZ cord-229937-fy90oebs 226 13 the the DT cord-229937-fy90oebs 226 14 pandemic pandemic NN cord-229937-fy90oebs 226 15 starting start VBG cord-229937-fy90oebs 226 16 time time NN cord-229937-fy90oebs 226 17 as as IN cord-229937-fy90oebs 226 18 about about IN cord-229937-fy90oebs 226 19 February February NNP cord-229937-fy90oebs 226 20 22 22 CD cord-229937-fy90oebs 226 21 . . . cord-229937-fy90oebs 227 1 Had have VBD cord-229937-fy90oebs 227 2 the the DT cord-229937-fy90oebs 227 3 lockdown lockdown NN cord-229937-fy90oebs 227 4 started start VBD cord-229937-fy90oebs 227 5 on on IN cord-229937-fy90oebs 227 6 that that DT cord-229937-fy90oebs 227 7 date date NN cord-229937-fy90oebs 227 8 , , , cord-229937-fy90oebs 227 9 the the DT cord-229937-fy90oebs 227 10 deaths death NNS cord-229937-fy90oebs 227 11 would would MD cord-229937-fy90oebs 227 12 had have VBD cord-229937-fy90oebs 227 13 been be VBN cord-229937-fy90oebs 227 14 highly highly RB cord-229937-fy90oebs 227 15 reduced reduce VBN cord-229937-fy90oebs 227 16 . . . cord-229937-fy90oebs 228 1 The the DT cord-229937-fy90oebs 228 2 smooth smooth JJ cord-229937-fy90oebs 228 3 blending blending NN cord-229937-fy90oebs 228 4 between between IN cord-229937-fy90oebs 228 5 the the DT cord-229937-fy90oebs 228 6 two two CD cord-229937-fy90oebs 228 7 peaks peak NNS cord-229937-fy90oebs 228 8 provides provide VBZ cord-229937-fy90oebs 228 9 a a DT cord-229937-fy90oebs 228 10 transition transition NN cord-229937-fy90oebs 228 11 between between IN cord-229937-fy90oebs 228 12 the the DT cord-229937-fy90oebs 228 13 two two CD cord-229937-fy90oebs 228 14 statistical statistical JJ cord-229937-fy90oebs 228 15 regimes regime NNS cord-229937-fy90oebs 228 16 ( ( -LRB- cord-229937-fy90oebs 228 17 or or CC cord-229937-fy90oebs 228 18 physical physical JJ cord-229937-fy90oebs 228 19 phases phase NNS cord-229937-fy90oebs 228 20 ) ) -RRB- cord-229937-fy90oebs 228 21 with with IN cord-229937-fy90oebs 228 22 and and CC cord-229937-fy90oebs 228 23 without without IN cord-229937-fy90oebs 228 24 lockdown lockdown NN cord-229937-fy90oebs 228 25 . . . cord-229937-fy90oebs 229 1 The the DT cord-229937-fy90oebs 229 2 Monte Monte NNP cord-229937-fy90oebs 229 3 Carlo Carlo NNP cord-229937-fy90oebs 229 4 simulation simulation NN cord-229937-fy90oebs 229 5 results result NNS cord-229937-fy90oebs 229 6 are be VBP cord-229937-fy90oebs 229 7 in in IN cord-229937-fy90oebs 229 8 agreement agreement NN cord-229937-fy90oebs 229 9 with with IN cord-229937-fy90oebs 229 10 our -PRON- PRP$ cord-229937-fy90oebs 229 11 previous previous JJ cord-229937-fy90oebs 229 12 analysis analysis NN cord-229937-fy90oebs 229 13 with with IN cord-229937-fy90oebs 229 14 the the DT cord-229937-fy90oebs 229 15 D d NN cord-229937-fy90oebs 229 16 and and CC cord-229937-fy90oebs 229 17 D D NNP cord-229937-fy90oebs 229 18 2 2 CD cord-229937-fy90oebs 229 19 models model NNS cord-229937-fy90oebs 229 20 . . . cord-229937-fy90oebs 230 1 The the DT cord-229937-fy90oebs 230 2 Monte Monte NNP cord-229937-fy90oebs 230 3 Carlo Carlo NNP cord-229937-fy90oebs 230 4 generates generate VBZ cord-229937-fy90oebs 230 5 events event NNS cord-229937-fy90oebs 230 6 in in IN cord-229937-fy90oebs 230 7 a a DT cord-229937-fy90oebs 230 8 population population NN cord-229937-fy90oebs 230 9 of of IN cord-229937-fy90oebs 230 10 in in NN cord-229937-fy90oebs 230 11 - - HYPH cord-229937-fy90oebs 230 12 dividuals dividual NNS cord-229937-fy90oebs 230 13 in in IN cord-229937-fy90oebs 230 14 a a DT cord-229937-fy90oebs 230 15 lattice lattice NN cord-229937-fy90oebs 230 16 or or CC cord-229937-fy90oebs 230 17 grid grid NN cord-229937-fy90oebs 230 18 of of IN cord-229937-fy90oebs 230 19 cells cell NNS cord-229937-fy90oebs 230 20 . . . cord-229937-fy90oebs 231 1 We -PRON- PRP cord-229937-fy90oebs 231 2 simulate simulate VBP cord-229937-fy90oebs 231 3 the the DT cord-229937-fy90oebs 231 4 movement movement NN cord-229937-fy90oebs 231 5 of of IN cord-229937-fy90oebs 231 6 individuals individual NNS cord-229937-fy90oebs 231 7 outside outside RB cord-229937-fy90oebs 231 8 of of IN cord-229937-fy90oebs 231 9 the the DT cord-229937-fy90oebs 231 10 cells cell NNS cord-229937-fy90oebs 231 11 and and CC cord-229937-fy90oebs 231 12 interactions interaction NNS cord-229937-fy90oebs 231 13 with with IN cord-229937-fy90oebs 231 14 the the DT cord-229937-fy90oebs 231 15 susceptible susceptible JJ cord-229937-fy90oebs 231 16 individuals individual NNS cord-229937-fy90oebs 231 17 within within IN cord-229937-fy90oebs 231 18 a a DT cord-229937-fy90oebs 231 19 finite finite JJ cord-229937-fy90oebs 231 20 range range NN cord-229937-fy90oebs 231 21 . . . cord-229937-fy90oebs 232 1 The the DT cord-229937-fy90oebs 232 2 randon randon JJ cord-229937-fy90oebs 232 3 events event NNS cord-229937-fy90oebs 232 4 follow follow VBP cord-229937-fy90oebs 232 5 statistical statistical JJ cord-229937-fy90oebs 232 6 distributions distribution NNS cord-229937-fy90oebs 232 7 based base VBN cord-229937-fy90oebs 232 8 on on IN cord-229937-fy90oebs 232 9 the the DT cord-229937-fy90oebs 232 10 exponential exponential JJ cord-229937-fy90oebs 232 11 laws law NNS cord-229937-fy90oebs 232 12 of of IN cord-229937-fy90oebs 232 13 statistical statistical JJ cord-229937-fy90oebs 232 14 mechanics mechanic NNS cord-229937-fy90oebs 232 15 for for IN cord-229937-fy90oebs 232 16 a a DT cord-229937-fy90oebs 232 17 system system NN cord-229937-fy90oebs 232 18 of of IN cord-229937-fy90oebs 232 19 interacting interact VBG cord-229937-fy90oebs 232 20 particles particle NNS cord-229937-fy90oebs 232 21 , , , cord-229937-fy90oebs 232 22 driven drive VBN cord-229937-fy90oebs 232 23 by by IN cord-229937-fy90oebs 232 24 macroscopic macroscopic JJ cord-229937-fy90oebs 232 25 magnitudes magnitude NNS cord-229937-fy90oebs 232 26 as as IN cord-229937-fy90oebs 232 27 the the DT cord-229937-fy90oebs 232 28 temperature temperature NN cord-229937-fy90oebs 232 29 , , , cord-229937-fy90oebs 232 30 and and CC cord-229937-fy90oebs 232 31 interaction interaction NN cord-229937-fy90oebs 232 32 probabilities probability NNS cord-229937-fy90oebs 232 33 between between IN cord-229937-fy90oebs 232 34 individuals individual NNS cord-229937-fy90oebs 232 35 , , , cord-229937-fy90oebs 232 36 that that WDT cord-229937-fy90oebs 232 37 can can MD cord-229937-fy90oebs 232 38 be be VB cord-229937-fy90oebs 232 39 related relate VBN cord-229937-fy90oebs 232 40 to to IN cord-229937-fy90oebs 232 41 interaction interaction NN cord-229937-fy90oebs 232 42 cross cross NN cord-229937-fy90oebs 232 43 sections section NNS cord-229937-fy90oebs 232 44 . . . cord-229937-fy90oebs 233 1 The the DT cord-229937-fy90oebs 233 2 Monte Monte NNP cord-229937-fy90oebs 233 3 Carlo Carlo NNP cord-229937-fy90oebs 233 4 simulation simulation NN cord-229937-fy90oebs 233 5 spread spread VBD cord-229937-fy90oebs 233 6 the the DT cord-229937-fy90oebs 233 7 virus virus NN cord-229937-fy90oebs 233 8 in in IN cord-229937-fy90oebs 233 9 spacetime spacetime NN cord-229937-fy90oebs 233 10 , , , cord-229937-fy90oebs 233 11 and and CC cord-229937-fy90oebs 233 12 allows allow VBZ cord-229937-fy90oebs 233 13 also also RB cord-229937-fy90oebs 233 14 space space NN cord-229937-fy90oebs 233 15 - - HYPH cord-229937-fy90oebs 233 16 time time NN cord-229937-fy90oebs 233 17 dependence dependence NN cord-229937-fy90oebs 233 18 on on IN cord-229937-fy90oebs 233 19 the the DT cord-229937-fy90oebs 233 20 parameters parameter NNS cord-229937-fy90oebs 233 21 . . . cord-229937-fy90oebs 234 1 In in IN cord-229937-fy90oebs 234 2 this this DT cord-229937-fy90oebs 234 3 work work NN cord-229937-fy90oebs 234 4 we -PRON- PRP cord-229937-fy90oebs 234 5 have have VBP cord-229937-fy90oebs 234 6 made make VBN cord-229937-fy90oebs 234 7 the the DT cord-229937-fy90oebs 234 8 simplest simple JJS cord-229937-fy90oebs 234 9 assumptions assumption NNS cord-229937-fy90oebs 234 10 , , , cord-229937-fy90oebs 234 11 only only RB cord-229937-fy90oebs 234 12 allowing allow VBG cord-229937-fy90oebs 234 13 for for IN cord-229937-fy90oebs 234 14 a a DT cord-229937-fy90oebs 234 15 lockdown lockdown NN cord-229937-fy90oebs 234 16 effect effect NN cord-229937-fy90oebs 234 17 by by IN cord-229937-fy90oebs 234 18 reducing reduce VBG cord-229937-fy90oebs 234 19 the the DT cord-229937-fy90oebs 234 20 range range NN cord-229937-fy90oebs 234 21 of of IN cord-229937-fy90oebs 234 22 the the DT cord-229937-fy90oebs 234 23 interaction interaction NN cord-229937-fy90oebs 234 24 starting start VBG cord-229937-fy90oebs 234 25 on on IN cord-229937-fy90oebs 234 26 a a DT cord-229937-fy90oebs 234 27 fixed fixed JJ cord-229937-fy90oebs 234 28 day day NN cord-229937-fy90oebs 234 29 . . . cord-229937-fy90oebs 235 1 This this DT cord-229937-fy90oebs 235 2 simple simple JJ cord-229937-fy90oebs 235 3 modification modification NN cord-229937-fy90oebs 235 4 allowed allow VBN cord-229937-fy90oebs 235 5 to to TO cord-229937-fy90oebs 235 6 reproduce reproduce VB cord-229937-fy90oebs 235 7 nicely nicely RB cord-229937-fy90oebs 235 8 the the DT cord-229937-fy90oebs 235 9 Spanish spanish JJ cord-229937-fy90oebs 235 10 death death NN cord-229937-fy90oebs 235 11 - - HYPH cord-229937-fy90oebs 235 12 per per IN cord-229937-fy90oebs 235 13 - - HYPH cord-229937-fy90oebs 235 14 day day NN cord-229937-fy90oebs 235 15 curve curve NN cord-229937-fy90oebs 235 16 . . . cord-229937-fy90oebs 236 1 The the DT cord-229937-fy90oebs 236 2 lockdown lockdown NN cord-229937-fy90oebs 236 3 produces produce VBZ cord-229937-fy90oebs 236 4 a a DT cord-229937-fy90oebs 236 5 relatively relatively RB cord-229937-fy90oebs 236 6 long long JJ cord-229937-fy90oebs 236 7 broadening broadening NN cord-229937-fy90oebs 236 8 of of IN cord-229937-fy90oebs 236 9 the the DT cord-229937-fy90oebs 236 10 curve curve NN cord-229937-fy90oebs 236 11 and and CC cord-229937-fy90oebs 236 12 a a DT cord-229937-fy90oebs 236 13 slow slow JJ cord-229937-fy90oebs 236 14 decay decay NN cord-229937-fy90oebs 236 15 . . . cord-229937-fy90oebs 237 1 Similar similar JJ cord-229937-fy90oebs 237 2 MC MC NNP cord-229937-fy90oebs 237 3 calculations calculation NNS cord-229937-fy90oebs 237 4 can can MD cord-229937-fy90oebs 237 5 be be VB cord-229937-fy90oebs 237 6 performed perform VBN cord-229937-fy90oebs 237 7 in in IN cord-229937-fy90oebs 237 8 several several JJ cord-229937-fy90oebs 237 9 countries country NNS cord-229937-fy90oebs 237 10 to to TO cord-229937-fy90oebs 237 11 infer infer VB cord-229937-fy90oebs 237 12 the the DT cord-229937-fy90oebs 237 13 devastating devastating JJ cord-229937-fy90oebs 237 14 effect effect NN cord-229937-fy90oebs 237 15 of of IN cord-229937-fy90oebs 237 16 a a DT cord-229937-fy90oebs 237 17 late late JJ cord-229937-fy90oebs 237 18 lockdown lockdown NN cord-229937-fy90oebs 237 19 as as IN cord-229937-fy90oebs 237 20 compared compare VBN cord-229937-fy90oebs 237 21 with with IN cord-229937-fy90oebs 237 22 early early JJ cord-229937-fy90oebs 237 23 lockdown lockdown NN cord-229937-fy90oebs 237 24 measures measure NNS cord-229937-fy90oebs 237 25 . . . cord-229937-fy90oebs 238 1 The the DT cord-229937-fy90oebs 238 2 later later RB cord-229937-fy90oebs 238 3 is be VBZ cord-229937-fy90oebs 238 4 the the DT cord-229937-fy90oebs 238 5 case case NN cord-229937-fy90oebs 238 6 of of IN cord-229937-fy90oebs 238 7 South South NNP cord-229937-fy90oebs 238 8 Africa Africa NNP cord-229937-fy90oebs 238 9 and and CC cord-229937-fy90oebs 238 10 other other JJ cord-229937-fy90oebs 238 11 countries country NNS cord-229937-fy90oebs 238 12 , , , cord-229937-fy90oebs 238 13 which which WDT cord-229937-fy90oebs 238 14 have have VBP cord-229937-fy90oebs 238 15 not not RB cord-229937-fy90oebs 238 16 reached reach VBN cord-229937-fy90oebs 238 17 the the DT cord-229937-fy90oebs 238 18 exponential exponential JJ cord-229937-fy90oebs 238 19 growth growth NN cord-229937-fy90oebs 238 20 . . . cord-229937-fy90oebs 239 1 The the DT cord-229937-fy90oebs 239 2 Death death NN cord-229937-fy90oebs 239 3 and and CC cord-229937-fy90oebs 239 4 extended extend VBD cord-229937-fy90oebs 239 5 SIR SIR NNP cord-229937-fy90oebs 239 6 models model NNS cord-229937-fy90oebs 239 7 are be VBP cord-229937-fy90oebs 239 8 simple simple JJ cord-229937-fy90oebs 239 9 enough enough RB cord-229937-fy90oebs 239 10 to to TO cord-229937-fy90oebs 239 11 provide provide VB cord-229937-fy90oebs 239 12 fast fast JJ cord-229937-fy90oebs 239 13 estimations estimation NNS cord-229937-fy90oebs 239 14 of of IN cord-229937-fy90oebs 239 15 pandemic pandemic JJ cord-229937-fy90oebs 239 16 evolution evolution NN cord-229937-fy90oebs 239 17 by by IN cord-229937-fy90oebs 239 18 fitting fit VBG cord-229937-fy90oebs 239 19 spatial spatial JJ cord-229937-fy90oebs 239 20 - - HYPH cord-229937-fy90oebs 239 21 time time NN cord-229937-fy90oebs 239 22 average average JJ cord-229937-fy90oebs 239 23 parameters parameter NNS cord-229937-fy90oebs 239 24 , , , cord-229937-fy90oebs 239 25 and and CC cord-229937-fy90oebs 239 26 present present VB cord-229937-fy90oebs 239 27 a a DT cord-229937-fy90oebs 239 28 good good JJ cord-229937-fy90oebs 239 29 first first JJ cord-229937-fy90oebs 239 30 - - HYPH cord-229937-fy90oebs 239 31 order order NN cord-229937-fy90oebs 239 32 approximation approximation NN cord-229937-fy90oebs 239 33 to to TO cord-229937-fy90oebs 239 34 understand understand VB cord-229937-fy90oebs 239 35 secondary secondary JJ cord-229937-fy90oebs 239 36 effects effect NNS cord-229937-fy90oebs 239 37 during during IN cord-229937-fy90oebs 239 38 the the DT cord-229937-fy90oebs 239 39 pandemic pandemic NN cord-229937-fy90oebs 239 40 , , , cord-229937-fy90oebs 239 41 such such JJ cord-229937-fy90oebs 239 42 as as IN cord-229937-fy90oebs 239 43 lockdown lockdown NN cord-229937-fy90oebs 239 44 and and CC cord-229937-fy90oebs 239 45 population population NN cord-229937-fy90oebs 239 46 migrations migration NNS cord-229937-fy90oebs 239 47 , , , cord-229937-fy90oebs 239 48 which which WDT cord-229937-fy90oebs 239 49 may may MD cord-229937-fy90oebs 239 50 help help VB cord-229937-fy90oebs 239 51 to to TO cord-229937-fy90oebs 239 52 control control VB cord-229937-fy90oebs 239 53 the the DT cord-229937-fy90oebs 239 54 disease disease NN cord-229937-fy90oebs 239 55 . . . cord-229937-fy90oebs 240 1 Similar similar JJ cord-229937-fy90oebs 240 2 models model NNS cord-229937-fy90oebs 240 3 are be VBP cord-229937-fy90oebs 240 4 available available JJ cord-229937-fy90oebs 240 5 [ [ -LRB- cord-229937-fy90oebs 240 6 17 17 CD cord-229937-fy90oebs 240 7 , , , cord-229937-fy90oebs 240 8 26 26 CD cord-229937-fy90oebs 240 9 ] ] -RRB- cord-229937-fy90oebs 240 10 , , , cord-229937-fy90oebs 240 11 but but CC cord-229937-fy90oebs 240 12 challenges challenge NNS cord-229937-fy90oebs 240 13 in in IN cord-229937-fy90oebs 240 14 epidemiological epidemiological JJ cord-229937-fy90oebs 240 15 modeling modeling NN cord-229937-fy90oebs 240 16 remain remain VBP cord-229937-fy90oebs 240 17 [ [ -LRB- cord-229937-fy90oebs 240 18 27 27 CD cord-229937-fy90oebs 240 19 ] ] -RRB- cord-229937-fy90oebs 241 1 [ [ -LRB- cord-229937-fy90oebs 241 2 28 28 CD cord-229937-fy90oebs 241 3 ] ] -RRB- cord-229937-fy90oebs 242 1 [ [ -LRB- cord-229937-fy90oebs 242 2 29 29 CD cord-229937-fy90oebs 242 3 ] ] -RRB- cord-229937-fy90oebs 242 4 [ [ -LRB- cord-229937-fy90oebs 242 5 30 30 CD cord-229937-fy90oebs 242 6 ] ] -RRB- cord-229937-fy90oebs 242 7 . . . cord-229937-fy90oebs 243 1 This this DT cord-229937-fy90oebs 243 2 is be VBZ cord-229937-fy90oebs 243 3 a a DT cord-229937-fy90oebs 243 4 very very RB cord-229937-fy90oebs 243 5 complex complex JJ cord-229937-fy90oebs 243 6 system system NN cord-229937-fy90oebs 243 7 , , , cord-229937-fy90oebs 243 8 which which WDT cord-229937-fy90oebs 243 9 involves involve VBZ cord-229937-fy90oebs 243 10 many many JJ cord-229937-fy90oebs 243 11 degrees degree NNS cord-229937-fy90oebs 243 12 of of IN cord-229937-fy90oebs 243 13 freedom freedom NN cord-229937-fy90oebs 243 14 and and CC cord-229937-fy90oebs 243 15 millions million NNS cord-229937-fy90oebs 243 16 of of IN cord-229937-fy90oebs 243 17 people people NNS cord-229937-fy90oebs 243 18 , , , cord-229937-fy90oebs 243 19 and and CC cord-229937-fy90oebs 243 20 even even RB cord-229937-fy90oebs 243 21 assuming assume VBG cord-229937-fy90oebs 243 22 consistent consistent JJ cord-229937-fy90oebs 243 23 disease disease NN cord-229937-fy90oebs 243 24 reporting report VBG cord-229937-fy90oebs 243 25 -which -which : cord-229937-fy90oebs 243 26 is be VBZ cord-229937-fy90oebs 243 27 rarely rarely RB cord-229937-fy90oebs 243 28 the the DT cord-229937-fy90oebs 243 29 case case NN cord-229937-fy90oebs 243 30 -there -there NN cord-229937-fy90oebs 243 31 remains remain VBZ cord-229937-fy90oebs 243 32 an an DT cord-229937-fy90oebs 243 33 important important JJ cord-229937-fy90oebs 243 34 open open JJ cord-229937-fy90oebs 243 35 question question NN cord-229937-fy90oebs 243 36 : : : cord-229937-fy90oebs 243 37 Can Can MD cord-229937-fy90oebs 243 38 any any DT cord-229937-fy90oebs 243 39 model model NN cord-229937-fy90oebs 243 40 predict predict VB cord-229937-fy90oebs 243 41 the the DT cord-229937-fy90oebs 243 42 evolution evolution NN cord-229937-fy90oebs 243 43 of of IN cord-229937-fy90oebs 243 44 an an DT cord-229937-fy90oebs 243 45 epidemic epidemic NN cord-229937-fy90oebs 243 46 from from IN cord-229937-fy90oebs 243 47 partial partial JJ cord-229937-fy90oebs 243 48 data datum NNS cord-229937-fy90oebs 243 49 ? ? . cord-229937-fy90oebs 244 1 Or or CC cord-229937-fy90oebs 244 2 similarly similarly RB cord-229937-fy90oebs 244 3 , , , cord-229937-fy90oebs 244 4 Is be VBZ cord-229937-fy90oebs 244 5 it -PRON- PRP cord-229937-fy90oebs 244 6 possible possible JJ cord-229937-fy90oebs 244 7 , , , cord-229937-fy90oebs 244 8 at at IN cord-229937-fy90oebs 244 9 any any DT cord-229937-fy90oebs 244 10 given give VBN cord-229937-fy90oebs 244 11 time time NN cord-229937-fy90oebs 244 12 and and CC cord-229937-fy90oebs 244 13 data datum NNS cord-229937-fy90oebs 244 14 , , , cord-229937-fy90oebs 244 15 to to TO cord-229937-fy90oebs 244 16 measure measure VB cord-229937-fy90oebs 244 17 the the DT cord-229937-fy90oebs 244 18 validity validity NN cord-229937-fy90oebs 244 19 of of IN cord-229937-fy90oebs 244 20 an an DT cord-229937-fy90oebs 244 21 epidemic epidemic NN cord-229937-fy90oebs 244 22 growth growth NN cord-229937-fy90oebs 244 23 curve curve NN cord-229937-fy90oebs 244 24 ? ? . cord-229937-fy90oebs 245 1 We -PRON- PRP cord-229937-fy90oebs 245 2 finally finally RB cord-229937-fy90oebs 245 3 hope hope VBP cord-229937-fy90oebs 245 4 that that IN cord-229937-fy90oebs 245 5 we -PRON- PRP cord-229937-fy90oebs 245 6 have have VBP cord-229937-fy90oebs 245 7 added add VBN cord-229937-fy90oebs 245 8 new new JJ cord-229937-fy90oebs 245 9 insightful insightful JJ cord-229937-fy90oebs 245 10 ideas idea NNS cord-229937-fy90oebs 245 11 with with IN cord-229937-fy90oebs 245 12 the the DT cord-229937-fy90oebs 245 13 Death death NN cord-229937-fy90oebs 245 14 , , , cord-229937-fy90oebs 245 15 the the DT cord-229937-fy90oebs 245 16 extended extended JJ cord-229937-fy90oebs 245 17 SIR SIR NNP cord-229937-fy90oebs 245 18 and and CC cord-229937-fy90oebs 245 19 Monte Monte NNP cord-229937-fy90oebs 245 20 Carlo Carlo NNP cord-229937-fy90oebs 245 21 models model NNS cord-229937-fy90oebs 245 22 , , , cord-229937-fy90oebs 245 23 which which WDT cord-229937-fy90oebs 245 24 can can MD cord-229937-fy90oebs 245 25 now now RB cord-229937-fy90oebs 245 26 be be VB cord-229937-fy90oebs 245 27 applied apply VBN cord-229937-fy90oebs 245 28 to to IN cord-229937-fy90oebs 245 29 any any DT cord-229937-fy90oebs 245 30 country country NN cord-229937-fy90oebs 245 31 which which WDT cord-229937-fy90oebs 245 32 has have VBZ cord-229937-fy90oebs 245 33 followed follow VBN cord-229937-fy90oebs 245 34 the the DT cord-229937-fy90oebs 245 35 initial initial JJ cord-229937-fy90oebs 245 36 exponential exponential JJ cord-229937-fy90oebs 245 37 pandemic pandemic NN cord-229937-fy90oebs 245 38 growth growth NN cord-229937-fy90oebs 245 39 . . . cord-229937-fy90oebs 246 1 Discussion discussion NN cord-229937-fy90oebs 246 2 : : : cord-229937-fy90oebs 246 3 the the DT cord-229937-fy90oebs 246 4 Kermack Kermack NNP cord-229937-fy90oebs 246 5 - - HYPH cord-229937-fy90oebs 246 6 McKendrick McKendrick NNP cord-229937-fy90oebs 246 7 epidemic epidemic NN cord-229937-fy90oebs 246 8 threshold threshold NN cord-229937-fy90oebs 246 9 theorem theorem NN cord-229937-fy90oebs 246 10 Stability stability NN cord-229937-fy90oebs 246 11 analysis analysis NN cord-229937-fy90oebs 246 12 of of IN cord-229937-fy90oebs 246 13 SIR SIR NNP cord-229937-fy90oebs 246 14 model model NN cord-229937-fy90oebs 246 15 with with IN cord-229937-fy90oebs 246 16 vaccination vaccination NN cord-229937-fy90oebs 246 17 Seasonality seasonality NN cord-229937-fy90oebs 246 18 and and CC cord-229937-fy90oebs 246 19 the the DT cord-229937-fy90oebs 246 20 effectiveness effectiveness NN cord-229937-fy90oebs 246 21 of of IN cord-229937-fy90oebs 246 22 mass mass JJ cord-229937-fy90oebs 246 23 vaccination vaccination NN cord-229937-fy90oebs 246 24 Application Application NNP cord-229937-fy90oebs 246 25 of of IN cord-229937-fy90oebs 246 26 SIR SIR NNP cord-229937-fy90oebs 246 27 epidemiological epidemiological JJ cord-229937-fy90oebs 246 28 model model NN cord-229937-fy90oebs 246 29 : : : cord-229937-fy90oebs 246 30 new new JJ cord-229937-fy90oebs 246 31 trends trend NNS cord-229937-fy90oebs 246 32 Epidemic epidemic NN cord-229937-fy90oebs 246 33 disease disease NN cord-229937-fy90oebs 246 34 in in IN cord-229937-fy90oebs 246 35 England England NNP cord-229937-fy90oebs 247 1 -the -the DT cord-229937-fy90oebs 247 2 evidence evidence NN cord-229937-fy90oebs 247 3 of of IN cord-229937-fy90oebs 247 4 variability variability NN cord-229937-fy90oebs 247 5 and and CC cord-229937-fy90oebs 247 6 of of IN cord-229937-fy90oebs 247 7 persistency persistency NN cord-229937-fy90oebs 247 8 of of IN cord-229937-fy90oebs 247 9 type type NN cord-229937-fy90oebs 247 10 Report Report NNP cord-229937-fy90oebs 247 11 on on IN cord-229937-fy90oebs 247 12 the the DT cord-229937-fy90oebs 247 13 Prevention Prevention NNP cord-229937-fy90oebs 247 14 of of IN cord-229937-fy90oebs 247 15 Malaria Malaria NNP cord-229937-fy90oebs 247 16 in in IN cord-229937-fy90oebs 247 17 Mauritius Mauritius NNP cord-229937-fy90oebs 248 1 An an DT cord-229937-fy90oebs 248 2 application application NN cord-229937-fy90oebs 248 3 of of IN cord-229937-fy90oebs 248 4 the the DT cord-229937-fy90oebs 248 5 theory theory NN cord-229937-fy90oebs 248 6 of of IN cord-229937-fy90oebs 248 7 probabilities probability NNS cord-229937-fy90oebs 248 8 to to IN cord-229937-fy90oebs 248 9 the the DT cord-229937-fy90oebs 248 10 study study NN cord-229937-fy90oebs 248 11 of of IN cord-229937-fy90oebs 248 12 a a DT cord-229937-fy90oebs 248 13 priori priori FW cord-229937-fy90oebs 248 14 pathometry pathometry NN cord-229937-fy90oebs 248 15 . . . cord-229937-fy90oebs 249 1 -Part -Part : cord-229937-fy90oebs 250 1 I -PRON- PRP cord-229937-fy90oebs 251 1 An an DT cord-229937-fy90oebs 251 2 application application NN cord-229937-fy90oebs 251 3 of of IN cord-229937-fy90oebs 251 4 the the DT cord-229937-fy90oebs 251 5 theory theory NN cord-229937-fy90oebs 251 6 of of IN cord-229937-fy90oebs 251 7 probabilities probability NNS cord-229937-fy90oebs 251 8 to to IN cord-229937-fy90oebs 251 9 the the DT cord-229937-fy90oebs 251 10 study study NN cord-229937-fy90oebs 251 11 of of IN cord-229937-fy90oebs 251 12 a a DT cord-229937-fy90oebs 251 13 priori priori FW cord-229937-fy90oebs 251 14 pathometry.-Part pathometry.-Part NNP cord-229937-fy90oebs 251 15 III III NNP cord-229937-fy90oebs 251 16 A a DT cord-229937-fy90oebs 251 17 contribution contribution NN cord-229937-fy90oebs 251 18 to to IN cord-229937-fy90oebs 251 19 the the DT cord-229937-fy90oebs 251 20 mathematical mathematical JJ cord-229937-fy90oebs 251 21 theory theory NN cord-229937-fy90oebs 251 22 of of IN cord-229937-fy90oebs 251 23 epidemics epidemic NNS cord-229937-fy90oebs 251 24 Discussion Discussion NNP cord-229937-fy90oebs 251 25 of of IN cord-229937-fy90oebs 251 26 Measles Measles NNP cord-229937-fy90oebs 251 27 periodicity periodicity NN cord-229937-fy90oebs 251 28 and and CC cord-229937-fy90oebs 251 29 community community NN cord-229937-fy90oebs 251 30 size size NN cord-229937-fy90oebs 251 31 by by IN cord-229937-fy90oebs 251 32 Measles Measles NNP cord-229937-fy90oebs 251 33 Periodicity Periodicity NNP cord-229937-fy90oebs 251 34 and and CC cord-229937-fy90oebs 251 35 Community Community NNP cord-229937-fy90oebs 251 36 Size Size NNP cord-229937-fy90oebs 251 37 Deterministic deterministic JJ cord-229937-fy90oebs 251 38 and and CC cord-229937-fy90oebs 251 39 Stochastic Stochastic NNP cord-229937-fy90oebs 251 40 Models Models NNPS cord-229937-fy90oebs 251 41 for for IN cord-229937-fy90oebs 251 42 Recurrent Recurrent NNP cord-229937-fy90oebs 251 43 Epidemics epidemic NNS cord-229937-fy90oebs 252 1 Basic basic JJ cord-229937-fy90oebs 252 2 Models Models NNPS cord-229937-fy90oebs 252 3 for for IN cord-229937-fy90oebs 252 4 Disease Disease NNP cord-229937-fy90oebs 252 5 Occurrence Occurrence NNP cord-229937-fy90oebs 252 6 in in IN cord-229937-fy90oebs 252 7 Epidemiology epidemiology NN cord-229937-fy90oebs 253 1 The the DT cord-229937-fy90oebs 253 2 D d NN cord-229937-fy90oebs 253 3 model model NN cord-229937-fy90oebs 253 4 for for IN cord-229937-fy90oebs 253 5 deaths death NNS cord-229937-fy90oebs 253 6 by by IN cord-229937-fy90oebs 253 7 COVID-19 COVID-19 NNP cord-229937-fy90oebs 253 8 The the DT cord-229937-fy90oebs 253 9 continuing continue VBG cord-229937-fy90oebs 253 10 2019-nCoV 2019-ncov CD cord-229937-fy90oebs 253 11 epidemic epidemic NN cord-229937-fy90oebs 253 12 threat threat NN cord-229937-fy90oebs 253 13 of of IN cord-229937-fy90oebs 253 14 novel novel JJ cord-229937-fy90oebs 253 15 coronaviruses coronaviruse NNS cord-229937-fy90oebs 253 16 to to IN cord-229937-fy90oebs 253 17 global global JJ cord-229937-fy90oebs 253 18 health health NN cord-229937-fy90oebs 254 1 The the DT cord-229937-fy90oebs 254 2 latest late JJS cord-229937-fy90oebs 254 3 2019 2019 CD cord-229937-fy90oebs 254 4 novel novel JJ cord-229937-fy90oebs 254 5 coronavirus coronavirus NN cord-229937-fy90oebs 254 6 outbreak outbreak NN cord-229937-fy90oebs 254 7 in in IN cord-229937-fy90oebs 254 8 Wuhan Wuhan NNP cord-229937-fy90oebs 254 9 , , , cord-229937-fy90oebs 254 10 China China NNP cord-229937-fy90oebs 254 11 WHO who WP cord-229937-fy90oebs 254 12 . . . cord-229937-fy90oebs 255 1 Coronavirus Coronavirus NNP cord-229937-fy90oebs 255 2 disease disease NN cord-229937-fy90oebs 255 3 2019 2019 CD cord-229937-fy90oebs 256 1 Attacking attack VBG cord-229937-fy90oebs 256 2 the the DT cord-229937-fy90oebs 256 3 Covid-19 covid-19 NN cord-229937-fy90oebs 256 4 with with IN cord-229937-fy90oebs 256 5 the the DT cord-229937-fy90oebs 256 6 Isingmodel Isingmodel NNP cord-229937-fy90oebs 256 7 and and CC cord-229937-fy90oebs 256 8 the the DT cord-229937-fy90oebs 256 9 Fermi Fermi NNP cord-229937-fy90oebs 256 10 - - HYPH cord-229937-fy90oebs 256 11 Dirac Dirac NNP cord-229937-fy90oebs 256 12 Distribution Distribution NNP cord-229937-fy90oebs 256 13 Function Function NNP cord-229937-fy90oebs 257 1 The the DT cord-229937-fy90oebs 257 2 SIR SIR NNP cord-229937-fy90oebs 257 3 model model NN cord-229937-fy90oebs 257 4 and and CC cord-229937-fy90oebs 257 5 the the DT cord-229937-fy90oebs 257 6 Foundations Foundations NNPS cord-229937-fy90oebs 257 7 of of IN cord-229937-fy90oebs 257 8 Public Public NNP cord-229937-fy90oebs 257 9 Health Health NNP cord-229937-fy90oebs 257 10 Impact Impact NNP cord-229937-fy90oebs 257 11 of of IN cord-229937-fy90oebs 257 12 non non JJ cord-229937-fy90oebs 257 13 - - JJ cord-229937-fy90oebs 257 14 pharmaceutical pharmaceutical JJ cord-229937-fy90oebs 257 15 interventions intervention NNS cord-229937-fy90oebs 257 16 against against IN cord-229937-fy90oebs 257 17 COVID-19 COVID-19 NNP cord-229937-fy90oebs 257 18 in in IN cord-229937-fy90oebs 257 19 Europe Europe NNP cord-229937-fy90oebs 257 20 : : : cord-229937-fy90oebs 257 21 a a DT cord-229937-fy90oebs 257 22 quasi quasi JJ cord-229937-fy90oebs 257 23 - - JJ cord-229937-fy90oebs 257 24 experimental experimental JJ cord-229937-fy90oebs 257 25 study study NN cord-229937-fy90oebs 257 26 Inferring Inferring NNP cord-229937-fy90oebs 257 27 COVID-19 covid-19 DT cord-229937-fy90oebs 257 28 spreading spread VBG cord-229937-fy90oebs 257 29 rates rate NNS cord-229937-fy90oebs 257 30 and and CC cord-229937-fy90oebs 257 31 potential potential JJ cord-229937-fy90oebs 257 32 change change NN cord-229937-fy90oebs 257 33 points point NNS cord-229937-fy90oebs 257 34 for for IN cord-229937-fy90oebs 257 35 case case NN cord-229937-fy90oebs 257 36 number number NN cord-229937-fy90oebs 257 37 forecasts forecast NNS cord-229937-fy90oebs 257 38 Special special JJ cord-229937-fy90oebs 257 39 Issue Issue NNP cord-229937-fy90oebs 257 40 on on IN cord-229937-fy90oebs 257 41 Challenges challenge NNS cord-229937-fy90oebs 257 42 in in IN cord-229937-fy90oebs 257 43 Modelling model VBG cord-229937-fy90oebs 257 44 Infectious infectious JJ cord-229937-fy90oebs 257 45 Disease Disease NNP cord-229937-fy90oebs 258 1 Dynamics dynamic NNS cord-229937-fy90oebs 258 2 Modeling model VBG cord-229937-fy90oebs 258 3 infectious infectious JJ cord-229937-fy90oebs 258 4 disease disease NN cord-229937-fy90oebs 258 5 dynamics dynamic NNS cord-229937-fy90oebs 258 6 in in IN cord-229937-fy90oebs 258 7 the the DT cord-229937-fy90oebs 258 8 complex complex JJ cord-229937-fy90oebs 258 9 landscape landscape NN cord-229937-fy90oebs 258 10 of of IN cord-229937-fy90oebs 258 11 global global JJ cord-229937-fy90oebs 258 12 health health NN cord-229937-fy90oebs 258 13 Mathematical Mathematical NNP cord-229937-fy90oebs 258 14 epidemiology epidemiology NN cord-229937-fy90oebs 258 15 : : : cord-229937-fy90oebs 258 16 past past JJ cord-229937-fy90oebs 258 17 , , , cord-229937-fy90oebs 258 18 present present JJ cord-229937-fy90oebs 258 19 , , , cord-229937-fy90oebs 258 20 and and CC cord-229937-fy90oebs 258 21 future future JJ cord-229937-fy90oebs 258 22 True true JJ cord-229937-fy90oebs 258 23 epidemic epidemic NN cord-229937-fy90oebs 258 24 growth growth NN cord-229937-fy90oebs 258 25 construction construction NN cord-229937-fy90oebs 258 26 through through IN cord-229937-fy90oebs 258 27 harmonic harmonic JJ cord-229937-fy90oebs 258 28 analysis analysis NN cord-229937-fy90oebs 259 1 The the DT cord-229937-fy90oebs 259 2 authors author NNS cord-229937-fy90oebs 259 3 thank thank VBP cord-229937-fy90oebs 259 4 useful useful JJ cord-229937-fy90oebs 259 5 comments comment NNS cord-229937-fy90oebs 259 6 from from IN cord-229937-fy90oebs 259 7 Emmanuel Emmanuel NNP cord-229937-fy90oebs 259 8 Clément Clément NNP cord-229937-fy90oebs 259 9 , , , cord-229937-fy90oebs 259 10 Araceli Araceli NNP cord-229937-fy90oebs 259 11 Lopez Lopez NNP cord-229937-fy90oebs 259 12 - - HYPH cord-229937-fy90oebs 259 13 Martens Martens NNPS cord-229937-fy90oebs 259 14 , , , cord-229937-fy90oebs 259 15 David David NNP cord-229937-fy90oebs 259 16 Jenkins Jenkins NNP cord-229937-fy90oebs 259 17 , , , cord-229937-fy90oebs 259 18 Ra Ra NNP cord-229937-fy90oebs 259 19 - - HYPH cord-229937-fy90oebs 259 20 mon mon NNP cord-229937-fy90oebs 259 21 Wyss Wyss NNP cord-229937-fy90oebs 259 22 , , , cord-229937-fy90oebs 259 23 Liam Liam NNP cord-229937-fy90oebs 259 24 Gaffney Gaffney NNP cord-229937-fy90oebs 259 25 and and CC cord-229937-fy90oebs 259 26 Hans Hans NNP cord-229937-fy90oebs 259 27 Fynbo Fynbo NNP cord-229937-fy90oebs 259 28 . . . cord-229937-fy90oebs 260 1 This this DT cord-229937-fy90oebs 260 2 work work NN cord-229937-fy90oebs 260 3 was be VBD cord-229937-fy90oebs 260 4 supported support VBN cord-229937-fy90oebs 260 5 by by IN cord-229937-fy90oebs 260 6 the the DT cord-229937-fy90oebs 260 7 Spanish spanish JJ cord-229937-fy90oebs 260 8 Ministerio Ministerio NNP cord-229937-fy90oebs 260 9 de de NNP cord-229937-fy90oebs 260 10 Economía Economía NNP cord-229937-fy90oebs 260 11 y y NNP cord-229937-fy90oebs 260 12 Competitividad Competitividad NNP cord-229937-fy90oebs 260 13 and and CC cord-229937-fy90oebs 260 14 European European NNP cord-229937-fy90oebs 260 15 FEDER FEDER NNP cord-229937-fy90oebs 260 16 funds fund NNS cord-229937-fy90oebs 260 17 ( ( -LRB- cord-229937-fy90oebs 260 18 grant grant VBP cord-229937-fy90oebs 260 19 FIS2017 FIS2017 NNP cord-229937-fy90oebs 260 20 - - HYPH cord-229937-fy90oebs 260 21 85053-C2 85053-c2 NN cord-229937-fy90oebs 260 22 - - HYPH cord-229937-fy90oebs 260 23 1-P 1-p CD cord-229937-fy90oebs 260 24 ) ) -RRB- cord-229937-fy90oebs 260 25 , , , cord-229937-fy90oebs 260 26 Junta Junta NNP cord-229937-fy90oebs 260 27 de de NNP cord-229937-fy90oebs 260 28 Andalucía Andalucía NNP cord-229937-fy90oebs 260 29 ( ( -LRB- cord-229937-fy90oebs 260 30 grant grant NNP cord-229937-fy90oebs 260 31 FQM-225 FQM-225 NNP cord-229937-fy90oebs 260 32 ) ) -RRB- cord-229937-fy90oebs 260 33 and and CC cord-229937-fy90oebs 260 34 the the DT cord-229937-fy90oebs 260 35 South South NNP cord-229937-fy90oebs 260 36 African African NNP cord-229937-fy90oebs 260 37 National National NNP cord-229937-fy90oebs 260 38 Research Research NNP cord-229937-fy90oebs 260 39 Foundation Foundation NNP cord-229937-fy90oebs 260 40 ( ( -LRB- cord-229937-fy90oebs 260 41 NRF NRF NNP cord-229937-fy90oebs 260 42 ) ) -RRB- cord-229937-fy90oebs 260 43 under under IN cord-229937-fy90oebs 260 44 Grant Grant NNP cord-229937-fy90oebs 260 45 93500 93500 CD cord-229937-fy90oebs 260 46 . . .