id sid tid token lemma pos cord-102966-7vdz661d 1 1 key key JJ cord-102966-7vdz661d 1 2 : : : cord-102966-7vdz661d 1 3 cord-102966 cord-102966 NNP cord-102966-7vdz661d 1 4 - - HYPH cord-102966-7vdz661d 1 5 7vdz661d 7vdz661d NNP cord-102966-7vdz661d 1 6 authors author NNS cord-102966-7vdz661d 1 7 : : : cord-102966-7vdz661d 1 8 Nikolaou Nikolaou NNP cord-102966-7vdz661d 1 9 , , , cord-102966-7vdz661d 1 10 M. M. NNP cord-102966-7vdz661d 1 11 title title NN cord-102966-7vdz661d 1 12 : : : cord-102966-7vdz661d 2 1 A a DT cord-102966-7vdz661d 2 2 Fundamental fundamental JJ cord-102966-7vdz661d 2 3 Inconsistency inconsistency NN cord-102966-7vdz661d 2 4 in in IN cord-102966-7vdz661d 2 5 the the DT cord-102966-7vdz661d 2 6 SIR SIR NNP cord-102966-7vdz661d 2 7 Model Model NNP cord-102966-7vdz661d 2 8 Structure Structure NNP cord-102966-7vdz661d 2 9 and and CC cord-102966-7vdz661d 2 10 Proposed Proposed NNP cord-102966-7vdz661d 2 11 Remedies Remedies NNP cord-102966-7vdz661d 2 12 date date NN cord-102966-7vdz661d 2 13 : : : cord-102966-7vdz661d 2 14 2020 2020 CD cord-102966-7vdz661d 2 15 - - HYPH cord-102966-7vdz661d 2 16 05 05 CD cord-102966-7vdz661d 2 17 - - HYPH cord-102966-7vdz661d 2 18 01 01 CD cord-102966-7vdz661d 2 19 journal journal NN cord-102966-7vdz661d 2 20 : : : cord-102966-7vdz661d 3 1 nan nan NNP cord-102966-7vdz661d 3 2 DOI DOI NNP cord-102966-7vdz661d 3 3 : : : cord-102966-7vdz661d 4 1 10.1101/2020.04.26.20080960 10.1101/2020.04.26.20080960 CD cord-102966-7vdz661d 4 2 sha sha NNP cord-102966-7vdz661d 4 3 : : : cord-102966-7vdz661d 4 4 44babd71ee06738c5d2052f576cbbe9142bb7b51 44babd71ee06738c5d2052f576cbbe9142bb7b51 CD cord-102966-7vdz661d 4 5 doc_id doc_id CD cord-102966-7vdz661d 4 6 : : : cord-102966-7vdz661d 4 7 102966 102966 CD cord-102966-7vdz661d 4 8 cord_uid cord_uid FW cord-102966-7vdz661d 4 9 : : : cord-102966-7vdz661d 5 1 7vdz661d 7vdz661d NNP cord-102966-7vdz661d 6 1 The the DT cord-102966-7vdz661d 6 2 susceptible susceptible JJ cord-102966-7vdz661d 6 3 - - HYPH cord-102966-7vdz661d 6 4 infectious infectious RB cord-102966-7vdz661d 6 5 - - HYPH cord-102966-7vdz661d 6 6 removed remove VBN cord-102966-7vdz661d 6 7 ( ( -LRB- cord-102966-7vdz661d 6 8 SIR SIR NNP cord-102966-7vdz661d 6 9 ) ) -RRB- cord-102966-7vdz661d 6 10 compartmental compartmental JJ cord-102966-7vdz661d 6 11 model model NN cord-102966-7vdz661d 6 12 structure structure NN cord-102966-7vdz661d 6 13 and and CC cord-102966-7vdz661d 6 14 its -PRON- PRP$ cord-102966-7vdz661d 6 15 variants variant NNS cord-102966-7vdz661d 6 16 are be VBP cord-102966-7vdz661d 6 17 a a DT cord-102966-7vdz661d 6 18 fundamental fundamental JJ cord-102966-7vdz661d 6 19 modeling modeling NN cord-102966-7vdz661d 6 20 tool tool NN cord-102966-7vdz661d 6 21 in in IN cord-102966-7vdz661d 6 22 epidemiology epidemiology NN cord-102966-7vdz661d 6 23 . . . cord-102966-7vdz661d 7 1 As as RB cord-102966-7vdz661d 7 2 typically typically RB cord-102966-7vdz661d 7 3 used use VBN cord-102966-7vdz661d 7 4 , , , cord-102966-7vdz661d 7 5 however however RB cord-102966-7vdz661d 7 6 , , , cord-102966-7vdz661d 7 7 this this DT cord-102966-7vdz661d 7 8 tool tool NN cord-102966-7vdz661d 7 9 may may MD cord-102966-7vdz661d 7 10 introduce introduce VB cord-102966-7vdz661d 7 11 an an DT cord-102966-7vdz661d 7 12 inconsistency inconsistency NN cord-102966-7vdz661d 7 13 by by IN cord-102966-7vdz661d 7 14 assuming assume VBG cord-102966-7vdz661d 7 15 that that IN cord-102966-7vdz661d 7 16 the the DT cord-102966-7vdz661d 7 17 rate rate NN cord-102966-7vdz661d 7 18 of of IN cord-102966-7vdz661d 7 19 depletion depletion NN cord-102966-7vdz661d 7 20 of of IN cord-102966-7vdz661d 7 21 a a DT cord-102966-7vdz661d 7 22 compartment compartment NN cord-102966-7vdz661d 7 23 is be VBZ cord-102966-7vdz661d 7 24 proportional proportional JJ cord-102966-7vdz661d 7 25 to to IN cord-102966-7vdz661d 7 26 the the DT cord-102966-7vdz661d 7 27 content content NN cord-102966-7vdz661d 7 28 of of IN cord-102966-7vdz661d 7 29 that that DT cord-102966-7vdz661d 7 30 compartment compartment NN cord-102966-7vdz661d 7 31 . . . cord-102966-7vdz661d 8 1 As as IN cord-102966-7vdz661d 8 2 mentioned mention VBN cord-102966-7vdz661d 8 3 in in IN cord-102966-7vdz661d 8 4 the the DT cord-102966-7vdz661d 8 5 seminal seminal JJ cord-102966-7vdz661d 8 6 SIR SIR NNP cord-102966-7vdz661d 8 7 work work NN cord-102966-7vdz661d 8 8 of of IN cord-102966-7vdz661d 8 9 Kermack Kermack NNP cord-102966-7vdz661d 8 10 and and CC cord-102966-7vdz661d 8 11 McKendrick McKendrick NNP cord-102966-7vdz661d 8 12 , , , cord-102966-7vdz661d 8 13 this this DT cord-102966-7vdz661d 8 14 is be VBZ cord-102966-7vdz661d 8 15 an an DT cord-102966-7vdz661d 8 16 assumption assumption NN cord-102966-7vdz661d 8 17 of of IN cord-102966-7vdz661d 8 18 mathematical mathematical JJ cord-102966-7vdz661d 8 19 convenience convenience NN cord-102966-7vdz661d 8 20 rather rather RB cord-102966-7vdz661d 8 21 than than IN cord-102966-7vdz661d 8 22 realism realism NN cord-102966-7vdz661d 8 23 . . . cord-102966-7vdz661d 9 1 As as IN cord-102966-7vdz661d 9 2 such such JJ cord-102966-7vdz661d 9 3 , , , cord-102966-7vdz661d 9 4 it -PRON- PRP cord-102966-7vdz661d 9 5 leads lead VBZ cord-102966-7vdz661d 9 6 to to IN cord-102966-7vdz661d 9 7 underprediction underprediction NN cord-102966-7vdz661d 9 8 of of IN cord-102966-7vdz661d 9 9 the the DT cord-102966-7vdz661d 9 10 infectious infectious JJ cord-102966-7vdz661d 9 11 compartment compartment NN cord-102966-7vdz661d 9 12 peaks peak NNS cord-102966-7vdz661d 9 13 by by IN cord-102966-7vdz661d 9 14 a a DT cord-102966-7vdz661d 9 15 factor factor NN cord-102966-7vdz661d 9 16 of of IN cord-102966-7vdz661d 9 17 about about RB cord-102966-7vdz661d 9 18 two two CD cord-102966-7vdz661d 9 19 , , , cord-102966-7vdz661d 9 20 a a DT cord-102966-7vdz661d 9 21 problem problem NN cord-102966-7vdz661d 9 22 of of IN cord-102966-7vdz661d 9 23 particular particular JJ cord-102966-7vdz661d 9 24 importance importance NN cord-102966-7vdz661d 9 25 when when WRB cord-102966-7vdz661d 9 26 dealing deal VBG cord-102966-7vdz661d 9 27 with with IN cord-102966-7vdz661d 9 28 availability availability NN cord-102966-7vdz661d 9 29 of of IN cord-102966-7vdz661d 9 30 resources resource NNS cord-102966-7vdz661d 9 31 during during IN cord-102966-7vdz661d 9 32 an an DT cord-102966-7vdz661d 9 33 epidemic epidemic NN cord-102966-7vdz661d 9 34 . . . cord-102966-7vdz661d 10 1 To to TO cord-102966-7vdz661d 10 2 remedy remedy VB cord-102966-7vdz661d 10 3 this this DT cord-102966-7vdz661d 10 4 problem problem NN cord-102966-7vdz661d 10 5 , , , cord-102966-7vdz661d 10 6 we -PRON- PRP cord-102966-7vdz661d 10 7 develop develop VBP cord-102966-7vdz661d 10 8 the the DT cord-102966-7vdz661d 10 9 dSIR dsir JJ cord-102966-7vdz661d 10 10 model model NN cord-102966-7vdz661d 10 11 structure structure NN cord-102966-7vdz661d 10 12 , , , cord-102966-7vdz661d 10 13 comprising comprise VBG cord-102966-7vdz661d 10 14 a a DT cord-102966-7vdz661d 10 15 single single JJ cord-102966-7vdz661d 10 16 delay delay NN cord-102966-7vdz661d 10 17 differential differential NN cord-102966-7vdz661d 10 18 equation equation NN cord-102966-7vdz661d 10 19 and and CC cord-102966-7vdz661d 10 20 associated associated JJ cord-102966-7vdz661d 10 21 delay delay NN cord-102966-7vdz661d 10 22 algebraic algebraic JJ cord-102966-7vdz661d 10 23 equations equation NNS cord-102966-7vdz661d 10 24 . . . cord-102966-7vdz661d 11 1 We -PRON- PRP cord-102966-7vdz661d 11 2 show show VBP cord-102966-7vdz661d 11 3 that that IN cord-102966-7vdz661d 11 4 SIR SIR NNP cord-102966-7vdz661d 11 5 and and CC cord-102966-7vdz661d 11 6 dSIR dSIR VBD cord-102966-7vdz661d 11 7 fully fully RB cord-102966-7vdz661d 11 8 agree agree VB cord-102966-7vdz661d 11 9 in in IN cord-102966-7vdz661d 11 10 assessing assess VBG cord-102966-7vdz661d 11 11 stability stability NN cord-102966-7vdz661d 11 12 and and CC cord-102966-7vdz661d 11 13 long long JJ cord-102966-7vdz661d 11 14 - - HYPH cord-102966-7vdz661d 11 15 term term NN cord-102966-7vdz661d 11 16 values value NNS cord-102966-7vdz661d 11 17 of of IN cord-102966-7vdz661d 11 18 a a DT cord-102966-7vdz661d 11 19 population population NN cord-102966-7vdz661d 11 20 through through IN cord-102966-7vdz661d 11 21 an an DT cord-102966-7vdz661d 11 22 epidemic epidemic NN cord-102966-7vdz661d 11 23 , , , cord-102966-7vdz661d 11 24 but but CC cord-102966-7vdz661d 11 25 differ differ VBP cord-102966-7vdz661d 11 26 considerably considerably RB cord-102966-7vdz661d 11 27 in in IN cord-102966-7vdz661d 11 28 the the DT cord-102966-7vdz661d 11 29 exponential exponential JJ cord-102966-7vdz661d 11 30 rates rate NNS cord-102966-7vdz661d 11 31 of of IN cord-102966-7vdz661d 11 32 ascent ascent NN cord-102966-7vdz661d 11 33 and and CC cord-102966-7vdz661d 11 34 descent descent NN cord-102966-7vdz661d 11 35 as as RB cord-102966-7vdz661d 11 36 well well RB cord-102966-7vdz661d 11 37 as as IN cord-102966-7vdz661d 11 38 peak peak NN cord-102966-7vdz661d 11 39 values value NNS cord-102966-7vdz661d 11 40 during during IN cord-102966-7vdz661d 11 41 the the DT cord-102966-7vdz661d 11 42 epidemic epidemic NN cord-102966-7vdz661d 11 43 . . . cord-102966-7vdz661d 12 1 The the DT cord-102966-7vdz661d 12 2 novel novel JJ cord-102966-7vdz661d 12 3 Pade Pade NNP cord-102966-7vdz661d 12 4 - - HYPH cord-102966-7vdz661d 12 5 SIR SIR NNP cord-102966-7vdz661d 12 6 structure structure NN cord-102966-7vdz661d 12 7 is be VBZ cord-102966-7vdz661d 12 8 also also RB cord-102966-7vdz661d 12 9 introduced introduce VBN cord-102966-7vdz661d 12 10 as as IN cord-102966-7vdz661d 12 11 a a DT cord-102966-7vdz661d 12 12 approximation approximation NN cord-102966-7vdz661d 12 13 of of IN cord-102966-7vdz661d 12 14 dSIR dsir RB cord-102966-7vdz661d 12 15 by by IN cord-102966-7vdz661d 12 16 ordinary ordinary JJ cord-102966-7vdz661d 12 17 differential differential JJ cord-102966-7vdz661d 12 18 equations equation NNS cord-102966-7vdz661d 12 19 . . . cord-102966-7vdz661d 13 1 We -PRON- PRP cord-102966-7vdz661d 13 2 rigorously rigorously RB cord-102966-7vdz661d 13 3 analyze analyze VBP cord-102966-7vdz661d 13 4 the the DT cord-102966-7vdz661d 13 5 properties property NNS cord-102966-7vdz661d 13 6 of of IN cord-102966-7vdz661d 13 7 these these DT cord-102966-7vdz661d 13 8 models model NNS cord-102966-7vdz661d 13 9 and and CC cord-102966-7vdz661d 13 10 present present VBP cord-102966-7vdz661d 13 11 a a DT cord-102966-7vdz661d 13 12 number number NN cord-102966-7vdz661d 13 13 of of IN cord-102966-7vdz661d 13 14 illustrative illustrative JJ cord-102966-7vdz661d 13 15 simulations simulation NNS cord-102966-7vdz661d 13 16 , , , cord-102966-7vdz661d 13 17 particularly particularly RB cord-102966-7vdz661d 13 18 in in IN cord-102966-7vdz661d 13 19 view view NN cord-102966-7vdz661d 13 20 of of IN cord-102966-7vdz661d 13 21 the the DT cord-102966-7vdz661d 13 22 recent recent JJ cord-102966-7vdz661d 13 23 coronavirus coronavirus NN cord-102966-7vdz661d 13 24 epidemic epidemic NN cord-102966-7vdz661d 13 25 . . . cord-102966-7vdz661d 14 1 Suggestions suggestion NNS cord-102966-7vdz661d 14 2 for for IN cord-102966-7vdz661d 14 3 further further JJ cord-102966-7vdz661d 14 4 study study NN cord-102966-7vdz661d 14 5 are be VBP cord-102966-7vdz661d 14 6 made make VBN cord-102966-7vdz661d 14 7 . . . cord-102966-7vdz661d 15 1 In in IN cord-102966-7vdz661d 15 2 their -PRON- PRP$ cord-102966-7vdz661d 15 3 landmark landmark NN cord-102966-7vdz661d 15 4 1927 1927 CD cord-102966-7vdz661d 15 5 publication publication NN cord-102966-7vdz661d 15 6 Contribution Contribution NNP cord-102966-7vdz661d 15 7 to to IN cord-102966-7vdz661d 15 8 the the DT cord-102966-7vdz661d 15 9 Mathematical Mathematical NNP cord-102966-7vdz661d 15 10 Theory Theory NNP cord-102966-7vdz661d 15 11 of of IN cord-102966-7vdz661d 15 12 Epidemics Epidemics NNP cord-102966-7vdz661d 15 13 , , , cord-102966-7vdz661d 15 14 1 1 CD cord-102966-7vdz661d 15 15 , , , cord-102966-7vdz661d 15 16 2 2 CD cord-102966-7vdz661d 15 17 Kermack Kermack NNP cord-102966-7vdz661d 15 18 and and CC cord-102966-7vdz661d 15 19 McKendrick McKendrick NNP cord-102966-7vdz661d 15 20 developed develop VBD cord-102966-7vdz661d 15 21 a a DT cord-102966-7vdz661d 15 22 general general JJ cord-102966-7vdz661d 15 23 , , , cord-102966-7vdz661d 15 24 if if IN cord-102966-7vdz661d 15 25 elaborate elaborate JJ cord-102966-7vdz661d 15 26 model model NN cord-102966-7vdz661d 15 27 structure structure NN cord-102966-7vdz661d 15 28 to to TO cord-102966-7vdz661d 15 29 capture capture VB cord-102966-7vdz661d 15 30 the the DT cord-102966-7vdz661d 15 31 dynamics dynamic NNS cord-102966-7vdz661d 15 32 of of IN cord-102966-7vdz661d 15 33 a a DT cord-102966-7vdz661d 15 34 fixed fix VBN cord-102966-7vdz661d 15 35 - - HYPH cord-102966-7vdz661d 15 36 size size NN cord-102966-7vdz661d 15 37 population population NN cord-102966-7vdz661d 15 38 comprising comprise VBG cord-102966-7vdz661d 15 39 compartments compartment NNS cord-102966-7vdz661d 15 40 of of IN cord-102966-7vdz661d 15 41 individuals individual NNS cord-102966-7vdz661d 15 42 susceptible susceptible JJ cord-102966-7vdz661d 15 43 ( ( -LRB- cord-102966-7vdz661d 15 44 S s NN cord-102966-7vdz661d 15 45 ) ) -RRB- cord-102966-7vdz661d 15 46 to to IN cord-102966-7vdz661d 15 47 a a DT cord-102966-7vdz661d 15 48 spreading spread VBG cord-102966-7vdz661d 15 49 infection infection NN cord-102966-7vdz661d 15 50 , , , cord-102966-7vdz661d 15 51 infectious infectious JJ cord-102966-7vdz661d 15 52 ( ( -LRB- cord-102966-7vdz661d 15 53 I i NN cord-102966-7vdz661d 15 54 ) ) -RRB- cord-102966-7vdz661d 15 55 , , , cord-102966-7vdz661d 15 56 and and CC cord-102966-7vdz661d 15 57 removed remove VBN cord-102966-7vdz661d 15 58 ( ( -LRB- cord-102966-7vdz661d 15 59 R r NN cord-102966-7vdz661d 15 60 ) ) -RRB- cord-102966-7vdz661d 15 61 from from IN cord-102966-7vdz661d 15 62 the the DT cord-102966-7vdz661d 15 63 preceding precede VBG cord-102966-7vdz661d 15 64 two two CD cord-102966-7vdz661d 15 65 compartments compartment NNS cord-102966-7vdz661d 15 66 by by IN cord-102966-7vdz661d 15 67 recovery recovery NN cord-102966-7vdz661d 15 68 or or CC cord-102966-7vdz661d 15 69 death death NN cord-102966-7vdz661d 15 70 . . . cord-102966-7vdz661d 16 1 Propagation propagation NN cord-102966-7vdz661d 16 2 of of IN cord-102966-7vdz661d 16 3 an an DT cord-102966-7vdz661d 16 4 individual individual NN cord-102966-7vdz661d 16 5 from from IN cord-102966-7vdz661d 16 6 S S NNP cord-102966-7vdz661d 16 7 to to IN cord-102966-7vdz661d 16 8 I i NN cord-102966-7vdz661d 16 9 to to IN cord-102966-7vdz661d 16 10 R r NN cord-102966-7vdz661d 16 11 underlies underlie VBZ cord-102966-7vdz661d 16 12 the the DT cord-102966-7vdz661d 16 13 basic basic JJ cord-102966-7vdz661d 16 14 context context NN cord-102966-7vdz661d 16 15 of of IN cord-102966-7vdz661d 16 16 the the DT cord-102966-7vdz661d 16 17 exercise exercise NN cord-102966-7vdz661d 16 18 . . . cord-102966-7vdz661d 17 1 In in IN cord-102966-7vdz661d 17 2 a a DT cord-102966-7vdz661d 17 3 modeling modeling NN cord-102966-7vdz661d 17 4 tour tour NN cord-102966-7vdz661d 17 5 - - HYPH cord-102966-7vdz661d 17 6 de de NN cord-102966-7vdz661d 17 7 - - HYPH cord-102966-7vdz661d 17 8 force force NN cord-102966-7vdz661d 17 9 , , , cord-102966-7vdz661d 17 10 the the DT cord-102966-7vdz661d 17 11 authors author NNS cord-102966-7vdz661d 17 12 eventually eventually RB cord-102966-7vdz661d 17 13 present present VBP cord-102966-7vdz661d 17 14 , , , cord-102966-7vdz661d 17 15 in in IN cord-102966-7vdz661d 17 16 equations equation NNS cord-102966-7vdz661d 17 17 ( ( -LRB- cord-102966-7vdz661d 17 18 11 11 CD cord-102966-7vdz661d 17 19 ) ) -RRB- cord-102966-7vdz661d 17 20 through through IN cord-102966-7vdz661d 17 21 ( ( -LRB- cord-102966-7vdz661d 17 22 15 15 CD cord-102966-7vdz661d 17 23 ) ) -RRB- cord-102966-7vdz661d 17 24 of of IN cord-102966-7vdz661d 17 25 their -PRON- PRP$ cord-102966-7vdz661d 17 26 paper paper NN cord-102966-7vdz661d 17 27 ( ( -LRB- cord-102966-7vdz661d 17 28 ibid ibid NN cord-102966-7vdz661d 17 29 . . . cord-102966-7vdz661d 17 30 ) ) -RRB- cord-102966-7vdz661d 17 31 , , , cord-102966-7vdz661d 17 32 the the DT cord-102966-7vdz661d 17 33 general general JJ cord-102966-7vdz661d 17 34 structure structure NN cord-102966-7vdz661d 17 35 of of IN cord-102966-7vdz661d 17 36 the the DT cord-102966-7vdz661d 17 37 elaborate elaborate JJ cord-102966-7vdz661d 17 38 mathematical mathematical JJ cord-102966-7vdz661d 17 39 model model NN cord-102966-7vdz661d 17 40 they -PRON- PRP cord-102966-7vdz661d 17 41 derive derive VBP cord-102966-7vdz661d 17 42 . . . cord-102966-7vdz661d 18 1 They -PRON- PRP cord-102966-7vdz661d 18 2 proceed proceed VBP cord-102966-7vdz661d 18 3 to to TO cord-102966-7vdz661d 18 4 examine examine VB cord-102966-7vdz661d 18 5 the the DT cord-102966-7vdz661d 18 6 implications implication NNS cord-102966-7vdz661d 18 7 of of IN cord-102966-7vdz661d 18 8 their -PRON- PRP$ cord-102966-7vdz661d 18 9 model model NN cord-102966-7vdz661d 18 10 for for IN cord-102966-7vdz661d 18 11 special special JJ cord-102966-7vdz661d 18 12 cases case NNS cord-102966-7vdz661d 18 13 , , , cord-102966-7vdz661d 18 14 and and CC cord-102966-7vdz661d 18 15 finally finally RB cord-102966-7vdz661d 18 16 present present VB cord-102966-7vdz661d 18 17 a a DT cord-102966-7vdz661d 18 18 very very RB cord-102966-7vdz661d 18 19 special special JJ cord-102966-7vdz661d 18 20 case case NN cord-102966-7vdz661d 18 21 resulting result VBG cord-102966-7vdz661d 18 22 in in IN cord-102966-7vdz661d 18 23 a a DT cord-102966-7vdz661d 18 24 set set NN cord-102966-7vdz661d 18 25 of of IN cord-102966-7vdz661d 18 26 three three CD cord-102966-7vdz661d 18 27 relatively relatively RB cord-102966-7vdz661d 18 28 simple simple JJ cord-102966-7vdz661d 18 29 ordinary ordinary JJ cord-102966-7vdz661d 18 30 differential differential JJ cord-102966-7vdz661d 18 31 equations equation NNS cord-102966-7vdz661d 18 32 ( ( -LRB- cord-102966-7vdz661d 18 33 ODEs ode NNS cord-102966-7vdz661d 18 34 , , , cord-102966-7vdz661d 18 35 equations equation NNS cord-102966-7vdz661d 18 36 ( ( -LRB- cord-102966-7vdz661d 18 37 29 29 CD cord-102966-7vdz661d 18 38 ) ) -RRB- cord-102966-7vdz661d 18 39 ibid ibid NN cord-102966-7vdz661d 18 40 . . . cord-102966-7vdz661d 18 41 ) ) -RRB- cord-102966-7vdz661d 18 42 , , , cord-102966-7vdz661d 18 43 which which WDT cord-102966-7vdz661d 18 44 were be VBD cord-102966-7vdz661d 18 45 destined destine VBN cord-102966-7vdz661d 18 46 to to TO cord-102966-7vdz661d 18 47 form form VB cord-102966-7vdz661d 18 48 the the DT cord-102966-7vdz661d 18 49 basis basis NN cord-102966-7vdz661d 18 50 for for IN cord-102966-7vdz661d 18 51 a a DT cord-102966-7vdz661d 18 52 genre genre NN cord-102966-7vdz661d 18 53 of of IN cord-102966-7vdz661d 18 54 mathematical mathematical JJ cord-102966-7vdz661d 18 55 models model NNS cord-102966-7vdz661d 18 56 in in IN cord-102966-7vdz661d 18 57 epidemiology epidemiology NN cord-102966-7vdz661d 18 58 , , , cord-102966-7vdz661d 18 59 the the DT cord-102966-7vdz661d 18 60 celebrated celebrated JJ cord-102966-7vdz661d 18 61 SIR SIR NNP cord-102966-7vdz661d 18 62 model model NN cord-102966-7vdz661d 18 63 and and CC cord-102966-7vdz661d 18 64 its -PRON- PRP$ cord-102966-7vdz661d 18 65 many many JJ cord-102966-7vdz661d 18 66 variants variant NNS cord-102966-7vdz661d 18 67 . . . cord-102966-7vdz661d 19 1 3 3 LS cord-102966-7vdz661d 20 1 The the DT cord-102966-7vdz661d 20 2 three three CD cord-102966-7vdz661d 20 3 ODEs ode NNS cord-102966-7vdz661d 20 4 are be VBP cord-102966-7vdz661d 20 5 where where WRB cord-102966-7vdz661d 20 6 prime prime JJ cord-102966-7vdz661d 20 7 denotes denote VBZ cord-102966-7vdz661d 20 8 time time NN cord-102966-7vdz661d 20 9 derivative derivative JJ cord-102966-7vdz661d 20 10 . . . cord-102966-7vdz661d 21 1 2 2 LS cord-102966-7vdz661d 21 2 , , , cord-102966-7vdz661d 21 3 4 4 CD cord-102966-7vdz661d 21 4 , , , cord-102966-7vdz661d 21 5 5 5 CD cord-102966-7vdz661d 21 6 Consistent consistent JJ cord-102966-7vdz661d 21 7 with with IN cord-102966-7vdz661d 21 8 the the DT cord-102966-7vdz661d 21 9 importance importance NN cord-102966-7vdz661d 21 10 of of IN cord-102966-7vdz661d 21 11 the the DT cord-102966-7vdz661d 21 12 SIR SIR NNP cord-102966-7vdz661d 21 13 ODEs ode NNS cord-102966-7vdz661d 21 14 , , , cord-102966-7vdz661d 21 15 the the DT cord-102966-7vdz661d 21 16 basic basic JJ cord-102966-7vdz661d 21 17 reproductive reproductive JJ cord-102966-7vdz661d 21 18 ratio ratio NN cord-102966-7vdz661d 21 19 , , , cord-102966-7vdz661d 21 20 0 0 NFP cord-102966-7vdz661d 21 21 ≝ ≝ NNP cord-102966-7vdz661d 21 22 / / SYM cord-102966-7vdz661d 21 23 , , , cord-102966-7vdz661d 21 24 is be VBZ cord-102966-7vdz661d 21 25 widely widely RB cord-102966-7vdz661d 21 26 considered consider VBN cord-102966-7vdz661d 21 27 " " `` cord-102966-7vdz661d 21 28 one one CD cord-102966-7vdz661d 21 29 of of IN cord-102966-7vdz661d 21 30 the the DT cord-102966-7vdz661d 21 31 most most RBS cord-102966-7vdz661d 21 32 critical critical JJ cord-102966-7vdz661d 21 33 epidemiological epidemiological JJ cord-102966-7vdz661d 21 34 parameters parameter NNS cord-102966-7vdz661d 21 35 " " '' cord-102966-7vdz661d 21 36 2 2 CD cord-102966-7vdz661d 21 37 and and CC cord-102966-7vdz661d 21 38 has have VBZ cord-102966-7vdz661d 21 39 even even RB cord-102966-7vdz661d 21 40 become become VBN cord-102966-7vdz661d 21 41 a a DT cord-102966-7vdz661d 21 42 household household NN cord-102966-7vdz661d 21 43 name name NN cord-102966-7vdz661d 21 44 in in IN cord-102966-7vdz661d 21 45 the the DT cord-102966-7vdz661d 21 46 recent recent JJ cord-102966-7vdz661d 21 47 coronavirus coronavirus NN cord-102966-7vdz661d 21 48 epidemic epidemic NN cord-102966-7vdz661d 21 49 . . . cord-102966-7vdz661d 22 1 6 6 CD cord-102966-7vdz661d 23 1 In in IN cord-102966-7vdz661d 23 2 the the DT cord-102966-7vdz661d 23 3 sentence sentence NN cord-102966-7vdz661d 24 1 right right RB cord-102966-7vdz661d 24 2 before before IN cord-102966-7vdz661d 24 3 they -PRON- PRP cord-102966-7vdz661d 24 4 present present VBP cord-102966-7vdz661d 24 5 their -PRON- PRP$ cord-102966-7vdz661d 24 6 SIR SIR NNP cord-102966-7vdz661d 24 7 model model NN cord-102966-7vdz661d 24 8 in in IN cord-102966-7vdz661d 24 9 equation equation NN cord-102966-7vdz661d 24 10 ( ( -LRB- cord-102966-7vdz661d 24 11 29 29 CD cord-102966-7vdz661d 24 12 ) ) -RRB- cord-102966-7vdz661d 24 13 , , , cord-102966-7vdz661d 24 14 ( ( -LRB- cord-102966-7vdz661d 24 15 ibid ibid NN cord-102966-7vdz661d 24 16 . . . cord-102966-7vdz661d 25 1 , , , cord-102966-7vdz661d 25 2 cf cf NNP cord-102966-7vdz661d 25 3 . . . cord-102966-7vdz661d 26 1 the the DT cord-102966-7vdz661d 26 2 above above IN cord-102966-7vdz661d 26 3 eqns eqns NNP cord-102966-7vdz661d 26 4 . . . cord-102966-7vdz661d 27 1 The the DT cord-102966-7vdz661d 27 2 assumption assumption NN cord-102966-7vdz661d 27 3 about about IN cord-102966-7vdz661d 27 4 constant constant JJ cord-102966-7vdz661d 27 5 is be VBZ cord-102966-7vdz661d 27 6 plausible plausible JJ cord-102966-7vdz661d 27 7 , , , cord-102966-7vdz661d 27 8 as as IN cord-102966-7vdz661d 27 9 it -PRON- PRP cord-102966-7vdz661d 27 10 refers refer VBZ cord-102966-7vdz661d 27 11 to to IN cord-102966-7vdz661d 27 12 the the DT cord-102966-7vdz661d 27 13 rate rate NN cord-102966-7vdz661d 27 14 of of IN cord-102966-7vdz661d 27 15 spread spread NN cord-102966-7vdz661d 27 16 of of IN cord-102966-7vdz661d 27 17 the the DT cord-102966-7vdz661d 27 18 epidemic epidemic NN cord-102966-7vdz661d 27 19 ( ( -LRB- cord-102966-7vdz661d 27 20 cf cf NN cord-102966-7vdz661d 27 21 . . . cord-102966-7vdz661d 27 22 eqn eqn NNP cord-102966-7vdz661d 27 23 . . . cord-102966-7vdz661d 28 1 ( ( -LRB- cord-102966-7vdz661d 28 2 1 1 LS cord-102966-7vdz661d 28 3 ) ) -RRB- cord-102966-7vdz661d 28 4 ) ) -RRB- cord-102966-7vdz661d 28 5 . . . cord-102966-7vdz661d 29 1 While while IN cord-102966-7vdz661d 29 2 that that DT cord-102966-7vdz661d 29 3 parameter parameter NN cord-102966-7vdz661d 29 4 might may MD cord-102966-7vdz661d 29 5 change change VB cord-102966-7vdz661d 29 6 over over IN cord-102966-7vdz661d 29 7 time time NN cord-102966-7vdz661d 29 8 as as IN cord-102966-7vdz661d 29 9 a a DT cord-102966-7vdz661d 29 10 result result NN cord-102966-7vdz661d 29 11 of of IN cord-102966-7vdz661d 29 12 measures measure NNS cord-102966-7vdz661d 29 13 However however RB cord-102966-7vdz661d 29 14 , , , cord-102966-7vdz661d 29 15 the the DT cord-102966-7vdz661d 29 16 rate rate NN cord-102966-7vdz661d 29 17 of of IN cord-102966-7vdz661d 29 18 removal removal NN cord-102966-7vdz661d 29 19 depends depend VBZ cord-102966-7vdz661d 29 20 more more JJR cord-102966-7vdz661d 29 21 on on IN cord-102966-7vdz661d 29 22 the the DT cord-102966-7vdz661d 29 23 duration duration NN cord-102966-7vdz661d 29 24 over over IN cord-102966-7vdz661d 29 25 which which WDT cord-102966-7vdz661d 29 26 individuals individual NNS cord-102966-7vdz661d 29 27 have have VBP cord-102966-7vdz661d 29 28 remained remain VBN cord-102966-7vdz661d 29 29 infected infected JJ cord-102966-7vdz661d 29 30 and and CC cord-102966-7vdz661d 29 31 less less JJR cord-102966-7vdz661d 29 32 on on IN cord-102966-7vdz661d 29 33 the the DT cord-102966-7vdz661d 29 34 size size NN cord-102966-7vdz661d 29 35 of of IN cord-102966-7vdz661d 29 36 that that DT cord-102966-7vdz661d 29 37 group group NN cord-102966-7vdz661d 29 38 . . . cord-102966-7vdz661d 30 1 In in IN cord-102966-7vdz661d 30 2 the the DT cord-102966-7vdz661d 30 3 conceptually conceptually RB cord-102966-7vdz661d 30 4 simple simple JJ cord-102966-7vdz661d 30 5 case case NN cord-102966-7vdz661d 30 6 where where WRB cord-102966-7vdz661d 30 7 all all DT cord-102966-7vdz661d 30 8 individuals individual NNS cord-102966-7vdz661d 30 9 recover recover VBP cord-102966-7vdz661d 30 10 or or CC cord-102966-7vdz661d 30 11 die die VBP cord-102966-7vdz661d 30 12 at at IN cord-102966-7vdz661d 30 13 a a DT cord-102966-7vdz661d 30 14 single single JJ cord-102966-7vdz661d 30 15 number number NN cord-102966-7vdz661d 30 16 of of IN cord-102966-7vdz661d 30 17 days day NNS cord-102966-7vdz661d 30 18 , , , cord-102966-7vdz661d 30 19 , , , cord-102966-7vdz661d 30 20 after after IN cord-102966-7vdz661d 30 21 their -PRON- PRP$ cord-102966-7vdz661d 30 22 infection infection NN cord-102966-7vdz661d 30 23 , , , cord-102966-7vdz661d 30 24 the the DT cord-102966-7vdz661d 30 25 rate rate NN cord-102966-7vdz661d 30 26 of of IN cord-102966-7vdz661d 30 27 removal removal NN cord-102966-7vdz661d 30 28 is be VBZ cord-102966-7vdz661d 30 29 1 1 CD cord-102966-7vdz661d 30 30 or or CC cord-102966-7vdz661d 30 31 0 0 CD cord-102966-7vdz661d 30 32 , , , cord-102966-7vdz661d 30 33 depending depend VBG cord-102966-7vdz661d 30 34 on on IN cord-102966-7vdz661d 30 35 whether whether IN cord-102966-7vdz661d 30 36 is be VBZ cord-102966-7vdz661d 30 37 greater great JJR cord-102966-7vdz661d 30 38 than than IN cord-102966-7vdz661d 30 39 or or CC cord-102966-7vdz661d 30 40 not not RB cord-102966-7vdz661d 30 41 ( ( -LRB- cord-102966-7vdz661d 30 42 Figure figure NN cord-102966-7vdz661d 30 43 1 1 CD cord-102966-7vdz661d 30 44 ) ) -RRB- cord-102966-7vdz661d 30 45 . . . cord-102966-7vdz661d 31 1 Of of RB cord-102966-7vdz661d 31 2 course course RB cord-102966-7vdz661d 31 3 , , , cord-102966-7vdz661d 31 4 in in IN cord-102966-7vdz661d 31 5 reality reality NN cord-102966-7vdz661d 31 6 will will MD cord-102966-7vdz661d 31 7 likely likely RB cord-102966-7vdz661d 31 8 follow follow VB cord-102966-7vdz661d 31 9 a a DT cord-102966-7vdz661d 31 10 distribution distribution NN cord-102966-7vdz661d 31 11 ( ( -LRB- cord-102966-7vdz661d 31 12 Figure figure NN cord-102966-7vdz661d 31 13 _SP cord-102966-7vdz661d 31 14 2 2 CD cord-102966-7vdz661d 31 15 ) ) -RRB- cord-102966-7vdz661d 31 16 rather rather RB cord-102966-7vdz661d 31 17 than than IN cord-102966-7vdz661d 31 18 being be VBG cord-102966-7vdz661d 31 19 a a DT cord-102966-7vdz661d 31 20 single single JJ cord-102966-7vdz661d 31 21 number number NN cord-102966-7vdz661d 31 22 . . . cord-102966-7vdz661d 32 1 However however RB cord-102966-7vdz661d 32 2 , , , cord-102966-7vdz661d 32 3 in in IN cord-102966-7vdz661d 32 4 that that DT cord-102966-7vdz661d 32 5 case case NN cord-102966-7vdz661d 32 6 as as RB cord-102966-7vdz661d 32 7 well well RB cord-102966-7vdz661d 32 8 , , , cord-102966-7vdz661d 32 9 the the DT cord-102966-7vdz661d 32 10 removal removal NN cord-102966-7vdz661d 32 11 rate rate NN cord-102966-7vdz661d 32 12 will will MD cord-102966-7vdz661d 32 13 depend depend VB cord-102966-7vdz661d 32 14 on on IN cord-102966-7vdz661d 32 15 comparison comparison NN cord-102966-7vdz661d 32 16 between between IN cord-102966-7vdz661d 32 17 and and CC cord-102966-7vdz661d 32 18 the the DT cord-102966-7vdz661d 32 19 distribution distribution NN cord-102966-7vdz661d 32 20 of of IN cord-102966-7vdz661d 32 21 , , , cord-102966-7vdz661d 32 22 rather rather RB cord-102966-7vdz661d 32 23 than than IN cord-102966-7vdz661d 32 24 on on IN cord-102966-7vdz661d 32 25 the the DT cord-102966-7vdz661d 32 26 size size NN cord-102966-7vdz661d 32 27 of of IN cord-102966-7vdz661d 32 28 the the DT cord-102966-7vdz661d 32 29 group group NN cord-102966-7vdz661d 32 30 remaining remain VBG cord-102966-7vdz661d 32 31 infectious infectious JJ cord-102966-7vdz661d 32 32 for for IN cord-102966-7vdz661d 32 33 time time NN cord-102966-7vdz661d 32 34 . . . cord-102966-7vdz661d 33 1 Starting start VBG cord-102966-7vdz661d 33 2 with with IN cord-102966-7vdz661d 33 3 the the DT cord-102966-7vdz661d 33 4 assumption assumption NN cord-102966-7vdz661d 33 5 that that IN cord-102966-7vdz661d 33 6 individuals individual NNS cord-102966-7vdz661d 33 7 leave leave VBP cord-102966-7vdz661d 33 8 the the DT cord-102966-7vdz661d 33 9 infectious infectious JJ cord-102966-7vdz661d 33 10 group group NN cord-102966-7vdz661d 33 11 at at IN cord-102966-7vdz661d 33 12 time time NN cord-102966-7vdz661d 33 13 after after IN cord-102966-7vdz661d 33 14 infection infection NN cord-102966-7vdz661d 33 15 , , , cord-102966-7vdz661d 33 16 we -PRON- PRP cord-102966-7vdz661d 33 17 develop develop VBP cord-102966-7vdz661d 33 18 in in IN cord-102966-7vdz661d 33 19 this this DT cord-102966-7vdz661d 33 20 paper paper NN cord-102966-7vdz661d 33 21 a a DT cord-102966-7vdz661d 33 22 corresponding correspond VBG cord-102966-7vdz661d 33 23 mathematical mathematical JJ cord-102966-7vdz661d 33 24 model model NN cord-102966-7vdz661d 33 25 structure structure NN cord-102966-7vdz661d 33 26 , , , cord-102966-7vdz661d 33 27 named name VBN cord-102966-7vdz661d 33 28 delay delay NN cord-102966-7vdz661d 33 29 SIR SIR NNP cord-102966-7vdz661d 33 30 ( ( -LRB- cord-102966-7vdz661d 33 31 dSIR dsir RB cord-102966-7vdz661d 33 32 ) ) -RRB- cord-102966-7vdz661d 33 33 , , , cord-102966-7vdz661d 33 34 in in IN cord-102966-7vdz661d 33 35 the the DT cord-102966-7vdz661d 33 36 form form NN cord-102966-7vdz661d 33 37 of of IN cord-102966-7vdz661d 33 38 a a DT cord-102966-7vdz661d 33 39 single single JJ cord-102966-7vdz661d 33 40 delay delay NN cord-102966-7vdz661d 33 41 differential differential NN cord-102966-7vdz661d 33 42 equation equation NN cord-102966-7vdz661d 33 43 ( ( -LRB- cord-102966-7vdz661d 33 44 DDE DDE NNP cord-102966-7vdz661d 33 45 ) ) -RRB- cord-102966-7vdz661d 33 46 for for CC cord-102966-7vdz661d 33 47 , , , cord-102966-7vdz661d 33 48 and and CC cord-102966-7vdz661d 33 49 two two CD cord-102966-7vdz661d 33 50 associated associate VBN cord-102966-7vdz661d 33 51 delay delay NN cord-102966-7vdz661d 33 52 algebraic algebraic JJ cord-102966-7vdz661d 33 53 equations equation NNS cord-102966-7vdz661d 33 54 , , , cord-102966-7vdz661d 33 55 for for IN cord-102966-7vdz661d 33 56 and and CC cord-102966-7vdz661d 33 57 in in IN cord-102966-7vdz661d 33 58 terms term NNS cord-102966-7vdz661d 33 59 of of IN cord-102966-7vdz661d 33 60 . . . cord-102966-7vdz661d 34 1 In in IN cord-102966-7vdz661d 34 2 the the DT cord-102966-7vdz661d 34 3 rest rest NN cord-102966-7vdz661d 34 4 of of IN cord-102966-7vdz661d 34 5 the the DT cord-102966-7vdz661d 34 6 paper paper NN cord-102966-7vdz661d 34 7 we -PRON- PRP cord-102966-7vdz661d 34 8 first first RB cord-102966-7vdz661d 34 9 introduce introduce VBP cord-102966-7vdz661d 34 10 the the DT cord-102966-7vdz661d 34 11 dSIR dsir JJ cord-102966-7vdz661d 34 12 model model NN cord-102966-7vdz661d 34 13 structure structure NN cord-102966-7vdz661d 34 14 in in IN cord-102966-7vdz661d 34 15 section section NN cord-102966-7vdz661d 34 16 2 2 CD cord-102966-7vdz661d 34 17 , , , cord-102966-7vdz661d 34 18 and and CC cord-102966-7vdz661d 34 19 provide provide VB cord-102966-7vdz661d 34 20 an an DT cord-102966-7vdz661d 34 21 intuitive intuitive JJ cord-102966-7vdz661d 34 22 exposition exposition NN cord-102966-7vdz661d 34 23 of of IN cord-102966-7vdz661d 34 24 its -PRON- PRP$ cord-102966-7vdz661d 34 25 basic basic JJ cord-102966-7vdz661d 34 26 properties property NNS cord-102966-7vdz661d 34 27 in in IN cord-102966-7vdz661d 34 28 section section NN cord-102966-7vdz661d 34 29 3 3 CD cord-102966-7vdz661d 34 30 , , , cord-102966-7vdz661d 34 31 where where WRB cord-102966-7vdz661d 34 32 we -PRON- PRP cord-102966-7vdz661d 34 33 also also RB cord-102966-7vdz661d 34 34 introduce introduce VBP cord-102966-7vdz661d 34 35 the the DT cord-102966-7vdz661d 34 36 Padé Padé NNP cord-102966-7vdz661d 34 37 SIR SIR NNP cord-102966-7vdz661d 34 38 model model NN cord-102966-7vdz661d 34 39 structure structure NN cord-102966-7vdz661d 34 40 as as IN cord-102966-7vdz661d 34 41 an an DT cord-102966-7vdz661d 34 42 ODE ODE NNP cord-102966-7vdz661d 34 43 approximation approximation NN cord-102966-7vdz661d 34 44 of of IN cord-102966-7vdz661d 34 45 dSIR dsir NN cord-102966-7vdz661d 34 46 . . . cord-102966-7vdz661d 35 1 Rigorous rigorous JJ cord-102966-7vdz661d 35 2 analysis analysis NN cord-102966-7vdz661d 35 3 follows follow VBZ cord-102966-7vdz661d 35 4 in in IN cord-102966-7vdz661d 35 5 section section NN cord-102966-7vdz661d 35 6 4 4 CD cord-102966-7vdz661d 35 7 . . . cord-102966-7vdz661d 36 1 In in IN cord-102966-7vdz661d 36 2 that that DT cord-102966-7vdz661d 36 3 section section NN cord-102966-7vdz661d 36 4 we -PRON- PRP cord-102966-7vdz661d 36 5 explain explain VBP cord-102966-7vdz661d 36 6 that that IN cord-102966-7vdz661d 36 7 certain certain JJ cord-102966-7vdz661d 36 8 SIR SIR NNP cord-102966-7vdz661d 36 9 and and CC cord-102966-7vdz661d 36 10 dSIR dsir JJ cord-102966-7vdz661d 36 11 properties property NNS cord-102966-7vdz661d 36 12 are be VBP cord-102966-7vdz661d 36 13 exactly exactly RB cord-102966-7vdz661d 36 14 similar similar JJ cord-102966-7vdz661d 36 15 ( ( -LRB- cord-102966-7vdz661d 36 16 e.g. e.g. IN cord-102966-7vdz661d 36 17 herd herd NN cord-102966-7vdz661d 36 18 immunity immunity NN cord-102966-7vdz661d 36 19 , , , cord-102966-7vdz661d 36 20 total total JJ cord-102966-7vdz661d 36 21 number number NN cord-102966-7vdz661d 36 22 of of IN cord-102966-7vdz661d 36 23 infected infect VBN cord-102966-7vdz661d 36 24 ) ) -RRB- cord-102966-7vdz661d 36 25 , , , cord-102966-7vdz661d 36 26 while while IN cord-102966-7vdz661d 36 27 others other NNS cord-102966-7vdz661d 36 28 are be VBP cord-102966-7vdz661d 36 29 quite quite RB cord-102966-7vdz661d 36 30 different different JJ cord-102966-7vdz661d 36 31 ( ( -LRB- cord-102966-7vdz661d 36 32 e.g. e.g. IN cord-102966-7vdz661d 36 33 exponential exponential JJ cord-102966-7vdz661d 36 34 rates rate NNS cord-102966-7vdz661d 36 35 , , , cord-102966-7vdz661d 36 36 peak peak NN cord-102966-7vdz661d 36 37 of of IN cord-102966-7vdz661d 36 38 the the DT cord-102966-7vdz661d 36 39 infectious infectious JJ cord-102966-7vdz661d 36 40 group group NN cord-102966-7vdz661d 36 41 ) ) -RRB- cord-102966-7vdz661d 36 42 . . . cord-102966-7vdz661d 37 1 Extension extension NN cord-102966-7vdz661d 37 2 to to IN cord-102966-7vdz661d 37 3 models model NNS cord-102966-7vdz661d 37 4 with with IN cord-102966-7vdz661d 37 5 additional additional JJ cord-102966-7vdz661d 37 6 compartments compartment NNS cord-102966-7vdz661d 37 7 beyond beyond IN cord-102966-7vdz661d 37 8 S S NNP cord-102966-7vdz661d 37 9 , , , cord-102966-7vdz661d 37 10 I -PRON- PRP cord-102966-7vdz661d 37 11 , , , cord-102966-7vdz661d 37 12 and and CC cord-102966-7vdz661d 37 13 R r NN cord-102966-7vdz661d 37 14 is be VBZ cord-102966-7vdz661d 37 15 discussed discuss VBN cord-102966-7vdz661d 37 16 in in IN cord-102966-7vdz661d 37 17 section section NN cord-102966-7vdz661d 37 18 5 5 CD cord-102966-7vdz661d 37 19 , , , cord-102966-7vdz661d 37 20 with with IN cord-102966-7vdz661d 37 21 presentation presentation NN cord-102966-7vdz661d 37 22 of of IN cord-102966-7vdz661d 37 23 the the DT cord-102966-7vdz661d 37 24 dSPIR dSPIR NNP cord-102966-7vdz661d 37 25 model model NN cord-102966-7vdz661d 37 26 . . . cord-102966-7vdz661d 38 1 Finally finally RB cord-102966-7vdz661d 38 2 , , , cord-102966-7vdz661d 38 3 the the DT cord-102966-7vdz661d 38 4 significance significance NN cord-102966-7vdz661d 38 5 of of IN cord-102966-7vdz661d 38 6 this this DT cord-102966-7vdz661d 38 7 work work NN cord-102966-7vdz661d 38 8 and and CC cord-102966-7vdz661d 38 9 future future JJ cord-102966-7vdz661d 38 10 extensions extension NNS cord-102966-7vdz661d 38 11 are be VBP cord-102966-7vdz661d 38 12 discussed discuss VBN cord-102966-7vdz661d 38 13 . . . cord-102966-7vdz661d 38 14 _SP cord-102966-7vdz661d 39 1 To to TO cord-102966-7vdz661d 39 2 explain explain VB cord-102966-7vdz661d 39 3 the the DT cord-102966-7vdz661d 39 4 derivation derivation NN cord-102966-7vdz661d 39 5 of of IN cord-102966-7vdz661d 39 6 the the DT cord-102966-7vdz661d 39 7 dSIR dsir JJ cord-102966-7vdz661d 39 8 model model NN cord-102966-7vdz661d 39 9 structure structure NN cord-102966-7vdz661d 39 10 , , , cord-102966-7vdz661d 39 11 we -PRON- PRP cord-102966-7vdz661d 39 12 will will MD cord-102966-7vdz661d 39 13 rely rely VB cord-102966-7vdz661d 39 14 on on IN cord-102966-7vdz661d 39 15 the the DT cord-102966-7vdz661d 39 16 detailed detailed JJ cord-102966-7vdz661d 39 17 version version NN cord-102966-7vdz661d 39 18 of of IN cord-102966-7vdz661d 39 19 Figure figure NN cord-102966-7vdz661d 39 20 2 2 CD cord-102966-7vdz661d 39 21 shown show VBN cord-102966-7vdz661d 39 22 in in IN cord-102966-7vdz661d 39 23 Figure figure NN cord-102966-7vdz661d 39 24 3 3 CD cord-102966-7vdz661d 39 25 . . . cord-102966-7vdz661d 40 1 The the DT cord-102966-7vdz661d 40 2 schematic schematic NN cord-102966-7vdz661d 40 3 shows show VBZ cord-102966-7vdz661d 40 4 the the DT cord-102966-7vdz661d 40 5 evolution evolution NN cord-102966-7vdz661d 40 6 of of IN cord-102966-7vdz661d 40 7 , , , cord-102966-7vdz661d 40 8 , , , cord-102966-7vdz661d 40 9 over over IN cord-102966-7vdz661d 40 10 discrete discrete JJ cord-102966-7vdz661d 40 11 time time NN cord-102966-7vdz661d 40 12 steps step NNS cord-102966-7vdz661d 40 13 = = SYM cord-102966-7vdz661d 40 14 0 0 CD cord-102966-7vdz661d 40 15 , , , cord-102966-7vdz661d 40 16 1 1 CD cord-102966-7vdz661d 40 17 , , , cord-102966-7vdz661d 40 18 2 2 CD cord-102966-7vdz661d 40 19 , , , cord-102966-7vdz661d 40 20 … … NFP cord-102966-7vdz661d 40 21 of of IN cord-102966-7vdz661d 40 22 length length NN cord-102966-7vdz661d 40 23 each each DT cord-102966-7vdz661d 40 24 . . . cord-102966-7vdz661d 41 1 The the DT cord-102966-7vdz661d 41 2 thick thick JJ cord-102966-7vdz661d 41 3 - - HYPH cord-102966-7vdz661d 41 4 green green JJ cord-102966-7vdz661d 41 5 bordered border VBN cord-102966-7vdz661d 41 6 rectangle rectangle NN cord-102966-7vdz661d 41 7 in in IN cord-102966-7vdz661d 41 8 Figure figure NN cord-102966-7vdz661d 41 9 3 3 CD cord-102966-7vdz661d 41 10 suggests suggest VBZ cord-102966-7vdz661d 41 11 by by IN cord-102966-7vdz661d 41 12 visual visual JJ cord-102966-7vdz661d 41 13 inspection inspection NN cord-102966-7vdz661d 41 14 that that WDT cord-102966-7vdz661d 41 15 where where WRB cord-102966-7vdz661d 41 16 ( ( -LRB- cord-102966-7vdz661d 41 17 , , , cord-102966-7vdz661d 41 18 ) ) -RRB- cord-102966-7vdz661d 41 19 is be VBZ cord-102966-7vdz661d 41 20 the the DT cord-102966-7vdz661d 41 21 rate rate NN cord-102966-7vdz661d 41 22 at at IN cord-102966-7vdz661d 41 23 which which WDT cord-102966-7vdz661d 41 24 the the DT cord-102966-7vdz661d 41 25 infection infection NN cord-102966-7vdz661d 41 26 spreads spread VBZ cord-102966-7vdz661d 41 27 , , , cord-102966-7vdz661d 41 28 for for IN cord-102966-7vdz661d 41 29 example example NN cord-102966-7vdz661d 41 30 in in IN cord-102966-7vdz661d 41 31 proportion proportion NN cord-102966-7vdz661d 41 32 to to IN cord-102966-7vdz661d 41 33 the the DT cord-102966-7vdz661d 41 34 product product NN cord-102966-7vdz661d 41 35 , , , cord-102966-7vdz661d 41 36 as as IN cord-102966-7vdz661d 41 37 shown show VBN cord-102966-7vdz661d 41 38 above above RB cord-102966-7vdz661d 41 39 . . . cord-102966-7vdz661d 42 1 Assuming assume VBG cord-102966-7vdz661d 42 2 that that IN cord-102966-7vdz661d 42 3 each each DT cord-102966-7vdz661d 42 4 new new JJ cord-102966-7vdz661d 42 5 part part NN cord-102966-7vdz661d 42 6 of of IN cord-102966-7vdz661d 42 7 the the DT cord-102966-7vdz661d 42 8 infectious infectious JJ cord-102966-7vdz661d 42 9 fraction fraction NN cord-102966-7vdz661d 42 10 , , , cord-102966-7vdz661d 42 11 , , , cord-102966-7vdz661d 42 12 gained gain VBD cord-102966-7vdz661d 42 13 at at IN cord-102966-7vdz661d 42 14 a a DT cord-102966-7vdz661d 42 15 given give VBN cord-102966-7vdz661d 42 16 time time NN cord-102966-7vdz661d 42 17 step step NN cord-102966-7vdz661d 42 18 , , , cord-102966-7vdz661d 42 19 , , , cord-102966-7vdz661d 42 20 moves move VBZ cord-102966-7vdz661d 42 21 to to IN cord-102966-7vdz661d 42 22 the the DT cord-102966-7vdz661d 42 23 removed remove VBN cord-102966-7vdz661d 42 24 fraction fraction NN cord-102966-7vdz661d 42 25 , , , cord-102966-7vdz661d 42 26 , , , cord-102966-7vdz661d 42 27 in in IN cord-102966-7vdz661d 42 28 time time NN cord-102966-7vdz661d 42 29 steps step NNS cord-102966-7vdz661d 42 30 , , , cord-102966-7vdz661d 42 31 the the DT cord-102966-7vdz661d 42 32 thick thick JJ cord-102966-7vdz661d 42 33 - - HYPH cord-102966-7vdz661d 42 34 red red JJ cord-102966-7vdz661d 42 35 bordered bordered JJ cord-102966-7vdz661d 42 36 rectangle rectangle NN cord-102966-7vdz661d 42 37 in in IN cord-102966-7vdz661d 42 38 Figure figure NN cord-102966-7vdz661d 42 39 3 3 CD cord-102966-7vdz661d 42 40 suggests suggest VBZ cord-102966-7vdz661d 42 41 that that IN cord-102966-7vdz661d 42 42 Eqns Eqns NNP cord-102966-7vdz661d 42 43 . . . cord-102966-7vdz661d 43 1 ( ( -LRB- cord-102966-7vdz661d 43 2 4 4 LS cord-102966-7vdz661d 43 3 ) ) -RRB- cord-102966-7vdz661d 43 4 and and CC cord-102966-7vdz661d 43 5 ( ( -LRB- cord-102966-7vdz661d 43 6 5 5 LS cord-102966-7vdz661d 43 7 ) ) -RRB- cord-102966-7vdz661d 43 8 yield yield VB cord-102966-7vdz661d 43 9 where where WRB cord-102966-7vdz661d 43 10 ′ ′ CD cord-102966-7vdz661d 43 11 ≝ ≝ NNP cord-102966-7vdz661d 43 12 / / , cord-102966-7vdz661d 43 13 and and CC cord-102966-7vdz661d 43 14 − − NNP cord-102966-7vdz661d 43 15 ≝ ≝ NNP cord-102966-7vdz661d 43 16 ( ( -LRB- cord-102966-7vdz661d 43 17 − − NNP cord-102966-7vdz661d 43 18 ) ) -RRB- cord-102966-7vdz661d 43 19 . . . cord-102966-7vdz661d 44 1 Eqn Eqn NNP cord-102966-7vdz661d 44 2 . . . cord-102966-7vdz661d 45 1 ( ( -LRB- cord-102966-7vdz661d 45 2 7 7 LS cord-102966-7vdz661d 45 3 ) ) -RRB- cord-102966-7vdz661d 45 4 is be VBZ cord-102966-7vdz661d 45 5 a a DT cord-102966-7vdz661d 45 6 single single JJ cord-102966-7vdz661d 45 7 nonlinear nonlinear JJ cord-102966-7vdz661d 45 8 DDE DDE NNP cord-102966-7vdz661d 45 9 that that WDT cord-102966-7vdz661d 45 10 involves involve VBZ cord-102966-7vdz661d 45 11 only only RB cord-102966-7vdz661d 45 12 and and CC cord-102966-7vdz661d 45 13 is be VBZ cord-102966-7vdz661d 45 14 decoupled decouple VBN cord-102966-7vdz661d 45 15 from from IN cord-102966-7vdz661d 45 16 equations equation NNS cord-102966-7vdz661d 45 17 for for IN cord-102966-7vdz661d 45 18 and and CC cord-102966-7vdz661d 45 19 . . . cord-102966-7vdz661d 46 1 As as IN cord-102966-7vdz661d 46 2 such such JJ cord-102966-7vdz661d 46 3 , , , cord-102966-7vdz661d 46 4 it -PRON- PRP cord-102966-7vdz661d 46 5 captures capture VBZ cord-102966-7vdz661d 46 6 the the DT cord-102966-7vdz661d 46 7 entire entire JJ cord-102966-7vdz661d 46 8 dynamics dynamic NNS cord-102966-7vdz661d 46 9 of of IN cord-102966-7vdz661d 46 10 the the DT cord-102966-7vdz661d 46 11 dSIR dsir JJ cord-102966-7vdz661d 46 12 system system NN cord-102966-7vdz661d 46 13 . . . cord-102966-7vdz661d 47 1 medRχiv.org medRχiv.org NNP cord-102966-7vdz661d 48 1 Michael Michael NNP cord-102966-7vdz661d 48 2 Nikolaou Nikolaou NNP cord-102966-7vdz661d 48 3 3 3 CD cord-102966-7vdz661d 49 1 The the DT cord-102966-7vdz661d 49 2 remaining remain VBG cord-102966-7vdz661d 49 3 two two CD cord-102966-7vdz661d 49 4 fractions fraction NNS cord-102966-7vdz661d 49 5 of of IN cord-102966-7vdz661d 49 6 the the DT cord-102966-7vdz661d 49 7 population population NN cord-102966-7vdz661d 49 8 , , , cord-102966-7vdz661d 49 9 and and CC cord-102966-7vdz661d 49 10 , , , cord-102966-7vdz661d 49 11 can can MD cord-102966-7vdz661d 49 12 simply simply RB cord-102966-7vdz661d 49 13 be be VB cord-102966-7vdz661d 49 14 inferred infer VBN cord-102966-7vdz661d 49 15 by by IN cord-102966-7vdz661d 49 16 algebraic algebraic JJ cord-102966-7vdz661d 49 17 equations equation NNS cord-102966-7vdz661d 49 18 , , , cord-102966-7vdz661d 49 19 as as IN cord-102966-7vdz661d 49 20 eqn eqn NN cord-102966-7vdz661d 49 21 . . . cord-102966-7vdz661d 50 1 ( ( -LRB- cord-102966-7vdz661d 50 2 5 5 LS cord-102966-7vdz661d 50 3 ) ) -RRB- cord-102966-7vdz661d 50 4 implies imply VBZ cord-102966-7vdz661d 50 5 and and CC cord-102966-7vdz661d 51 1 + + CC cord-102966-7vdz661d 51 2 + + CC cord-102966-7vdz661d 51 3 = = SYM cord-102966-7vdz661d 51 4 1 1 CD cord-102966-7vdz661d 51 5 implies imply VBZ cord-102966-7vdz661d 51 6 To to TO cord-102966-7vdz661d 51 7 put put VB cord-102966-7vdz661d 51 8 the the DT cord-102966-7vdz661d 51 9 schematic schematic NN cord-102966-7vdz661d 51 10 in in IN cord-102966-7vdz661d 51 11 Figure Figure NNP cord-102966-7vdz661d 51 12 3 3 CD cord-102966-7vdz661d 51 13 in in IN cord-102966-7vdz661d 51 14 context context NN cord-102966-7vdz661d 51 15 , , , cord-102966-7vdz661d 51 16 observe observe VBP cord-102966-7vdz661d 51 17 that that IN cord-102966-7vdz661d 51 18 summation summation NN cord-102966-7vdz661d 51 19 of of IN cord-102966-7vdz661d 51 20 eqns eqn NNS cord-102966-7vdz661d 51 21 . . . cord-102966-7vdz661d 52 1 ( ( -LRB- cord-102966-7vdz661d 52 2 1)-(3 1)-(3 LS cord-102966-7vdz661d 52 3 ) ) -RRB- cord-102966-7vdz661d 52 4 and and CC cord-102966-7vdz661d 52 5 discretization discretization NN cord-102966-7vdz661d 52 6 yields yield NNS cord-102966-7vdz661d 53 1 This this DT cord-102966-7vdz661d 53 2 suggests suggest VBZ cord-102966-7vdz661d 53 3 that that IN cord-102966-7vdz661d 53 4 , , , cord-102966-7vdz661d 53 5 according accord VBG cord-102966-7vdz661d 53 6 to to IN cord-102966-7vdz661d 53 7 the the DT cord-102966-7vdz661d 53 8 SIR SIR NNP cord-102966-7vdz661d 53 9 model model NN cord-102966-7vdz661d 53 10 , , , cord-102966-7vdz661d 53 11 each each DT cord-102966-7vdz661d 53 12 thickblack thickblack RB cord-102966-7vdz661d 53 13 bordered border VBN cord-102966-7vdz661d 53 14 green green JJ cord-102966-7vdz661d 53 15 rectangle rectangle NN cord-102966-7vdz661d 53 16 in in IN cord-102966-7vdz661d 53 17 Figure figure NN cord-102966-7vdz661d 53 18 3 3 CD cord-102966-7vdz661d 53 19 would would MD cord-102966-7vdz661d 53 20 have have VB cord-102966-7vdz661d 53 21 to to TO cord-102966-7vdz661d 53 22 be be VB cord-102966-7vdz661d 53 23 a a DT cord-102966-7vdz661d 53 24 constant constant JJ cord-102966-7vdz661d 53 25 fraction fraction NN cord-102966-7vdz661d 53 26 of of IN cord-102966-7vdz661d 53 27 the the DT cord-102966-7vdz661d 53 28 immediately immediately RB cord-102966-7vdz661d 53 29 previous previous JJ cord-102966-7vdz661d 53 30 orange orange JJ cord-102966-7vdz661d 53 31 column column NN cord-102966-7vdz661d 53 32 . . . cord-102966-7vdz661d 54 1 However however RB cord-102966-7vdz661d 54 2 , , , cord-102966-7vdz661d 54 3 with with IN cord-102966-7vdz661d 54 4 each each DT cord-102966-7vdz661d 54 5 new new JJ cord-102966-7vdz661d 54 6 part part NN cord-102966-7vdz661d 54 7 of of IN cord-102966-7vdz661d 54 8 the the DT cord-102966-7vdz661d 54 9 infectious infectious JJ cord-102966-7vdz661d 54 10 fraction fraction NN cord-102966-7vdz661d 54 11 moving move VBG cord-102966-7vdz661d 54 12 to to IN cord-102966-7vdz661d 54 13 the the DT cord-102966-7vdz661d 54 14 removed remove VBN cord-102966-7vdz661d 54 15 fraction fraction NN cord-102966-7vdz661d 54 16 after after IN cord-102966-7vdz661d 54 17 steps step NNS cord-102966-7vdz661d 54 18 ( ( -LRB- cord-102966-7vdz661d 54 19 thickblack thickblack RB cord-102966-7vdz661d 54 20 bordered border VBN cord-102966-7vdz661d 54 21 orange orange NNP cord-102966-7vdz661d 54 22 rectangles rectangle NNS cord-102966-7vdz661d 54 23 moving move VBG cord-102966-7vdz661d 54 24 to to IN cord-102966-7vdz661d 54 25 thick thick JJ cord-102966-7vdz661d 54 26 - - HYPH cord-102966-7vdz661d 54 27 black black JJ cord-102966-7vdz661d 54 28 bordered border VBN cord-102966-7vdz661d 54 29 blue blue JJ cord-102966-7vdz661d 54 30 rectangles rectangle NNS cord-102966-7vdz661d 54 31 ) ) -RRB- cord-102966-7vdz661d 54 32 this this DT cord-102966-7vdz661d 54 33 can can MD cord-102966-7vdz661d 54 34 not not RB cord-102966-7vdz661d 54 35 be be VB cord-102966-7vdz661d 54 36 true true JJ cord-102966-7vdz661d 54 37 as as IN cord-102966-7vdz661d 54 38 an an DT cord-102966-7vdz661d 54 39 emerging emerge VBG cord-102966-7vdz661d 54 40 fact fact NN cord-102966-7vdz661d 54 41 , , , cord-102966-7vdz661d 54 42 by by IN cord-102966-7vdz661d 54 43 the the DT cord-102966-7vdz661d 54 44 simple simple JJ cord-102966-7vdz661d 54 45 observation observation NN cord-102966-7vdz661d 54 46 of of IN cord-102966-7vdz661d 54 47 the the DT cord-102966-7vdz661d 54 48 shapes shape NNS cord-102966-7vdz661d 54 49 of of IN cord-102966-7vdz661d 54 50 and and CC cord-102966-7vdz661d 54 51 + + CC cord-102966-7vdz661d 54 52 , , , cord-102966-7vdz661d 54 53 which which WDT cord-102966-7vdz661d 54 54 follow follow VBP cord-102966-7vdz661d 54 55 a a DT cord-102966-7vdz661d 54 56 convex convex JJ cord-102966-7vdz661d 54 57 to to IN cord-102966-7vdz661d 54 58 concave concave JJ cord-102966-7vdz661d 54 59 pattern pattern NN cord-102966-7vdz661d 54 60 after after IN cord-102966-7vdz661d 54 61 an an DT cord-102966-7vdz661d 54 62 inflection inflection NN cord-102966-7vdz661d 54 63 point point NN cord-102966-7vdz661d 54 64 . . . cord-102966-7vdz661d 55 1 Therefore therefore RB cord-102966-7vdz661d 55 2 , , , cord-102966-7vdz661d 55 3 the the DT cord-102966-7vdz661d 55 4 assumption assumption NN cord-102966-7vdz661d 55 5 of of IN cord-102966-7vdz661d 55 6 constant constant JJ cord-102966-7vdz661d 55 7 , , , cord-102966-7vdz661d 55 8 equivalent equivalent JJ cord-102966-7vdz661d 55 9 to to IN cord-102966-7vdz661d 55 10 constant constant JJ cord-102966-7vdz661d 55 11 in in IN cord-102966-7vdz661d 55 12 eqn eqn NN cord-102966-7vdz661d 55 13 . . . cord-102966-7vdz661d 56 1 ( ( -LRB- cord-102966-7vdz661d 56 2 10 10 CD cord-102966-7vdz661d 56 3 ) ) -RRB- cord-102966-7vdz661d 56 4 , , , cord-102966-7vdz661d 56 5 is be VBZ cord-102966-7vdz661d 56 6 not not RB cord-102966-7vdz661d 56 7 compatible compatible JJ cord-102966-7vdz661d 56 8 with with IN cord-102966-7vdz661d 56 9 the the DT cord-102966-7vdz661d 56 10 assumption assumption NN cord-102966-7vdz661d 56 11 of of IN cord-102966-7vdz661d 56 12 time time NN cord-102966-7vdz661d 56 13 to to TO cord-102966-7vdz661d 56 14 transition transition VB cord-102966-7vdz661d 56 15 from from IN cord-102966-7vdz661d 56 16 infectious infectious JJ cord-102966-7vdz661d 56 17 to to IN cord-102966-7vdz661d 56 18 removed remove VBN cord-102966-7vdz661d 56 19 being be VBG cord-102966-7vdz661d 56 20 independent independent JJ cord-102966-7vdz661d 56 21 of of IN cord-102966-7vdz661d 56 22 the the DT cord-102966-7vdz661d 56 23 infectious infectious JJ cord-102966-7vdz661d 56 24 fraction fraction NN cord-102966-7vdz661d 56 25 size size NN cord-102966-7vdz661d 56 26 . . . cord-102966-7vdz661d 57 1 This this DT cord-102966-7vdz661d 57 2 will will MD cord-102966-7vdz661d 57 3 be be VB cord-102966-7vdz661d 57 4 further further RB cord-102966-7vdz661d 57 5 illustrated illustrate VBN cord-102966-7vdz661d 57 6 with with IN cord-102966-7vdz661d 57 7 simulations simulation NNS cord-102966-7vdz661d 57 8 in in IN cord-102966-7vdz661d 57 9 the the DT cord-102966-7vdz661d 57 10 next next JJ cord-102966-7vdz661d 57 11 section section NN cord-102966-7vdz661d 57 12 . . . cord-102966-7vdz661d 58 1 Incidentally incidentally RB cord-102966-7vdz661d 58 2 , , , cord-102966-7vdz661d 58 3 eqns eqns NNP cord-102966-7vdz661d 58 4 . . . cord-102966-7vdz661d 59 1 ( ( -LRB- cord-102966-7vdz661d 59 2 1)-(3 1)-(3 CD cord-102966-7vdz661d 59 3 ) ) -RRB- cord-102966-7vdz661d 59 4 of of IN cord-102966-7vdz661d 59 5 the the DT cord-102966-7vdz661d 59 6 SIR SIR NNP cord-102966-7vdz661d 59 7 model model NN cord-102966-7vdz661d 59 8 can can MD cord-102966-7vdz661d 59 9 also also RB cord-102966-7vdz661d 59 10 be be VB cord-102966-7vdz661d 59 11 decoupled decouple VBN cord-102966-7vdz661d 59 12 to to IN cord-102966-7vdz661d 59 13 a a DT cord-102966-7vdz661d 59 14 single single JJ cord-102966-7vdz661d 59 15 if if IN cord-102966-7vdz661d 59 16 non non JJ cord-102966-7vdz661d 59 17 - - JJ cord-102966-7vdz661d 59 18 intuitive intuitive JJ cord-102966-7vdz661d 59 19 nonlinear nonlinear JJ cord-102966-7vdz661d 59 20 ODE ode NN cord-102966-7vdz661d 59 21 in in IN cord-102966-7vdz661d 59 22 terms term NNS cord-102966-7vdz661d 59 23 of of IN cord-102966-7vdz661d 59 24 , , , cord-102966-7vdz661d 59 25 solved solve VBN cord-102966-7vdz661d 59 26 in in IN cord-102966-7vdz661d 59 27 a a DT cord-102966-7vdz661d 59 28 form form NN cord-102966-7vdz661d 59 29 implicit implicit NN cord-102966-7vdz661d 59 30 in in IN cord-102966-7vdz661d 59 31 time time NN cord-102966-7vdz661d 59 32 , , , cord-102966-7vdz661d 59 33 . . . cord-102966-7vdz661d 60 1 7 7 CD cord-102966-7vdz661d 61 1 Before before IN cord-102966-7vdz661d 61 2 any any DT cord-102966-7vdz661d 61 3 theoretical theoretical JJ cord-102966-7vdz661d 61 4 properties property NNS cord-102966-7vdz661d 61 5 of of IN cord-102966-7vdz661d 61 6 the the DT cord-102966-7vdz661d 61 7 dSIR dsir JJ cord-102966-7vdz661d 61 8 model model NN cord-102966-7vdz661d 61 9 structure structure NN cord-102966-7vdz661d 61 10 are be VBP cord-102966-7vdz661d 61 11 analyzed analyze VBN cord-102966-7vdz661d 61 12 , , , cord-102966-7vdz661d 61 13 a a DT cord-102966-7vdz661d 61 14 simple simple JJ cord-102966-7vdz661d 61 15 visual visual JJ cord-102966-7vdz661d 61 16 comparison comparison NN cord-102966-7vdz661d 61 17 between between IN cord-102966-7vdz661d 61 18 SIR SIR NNP cord-102966-7vdz661d 61 19 and and CC cord-102966-7vdz661d 61 20 dSIR dSIR NNP cord-102966-7vdz661d 61 21 is be VBZ cord-102966-7vdz661d 61 22 presented present VBN cord-102966-7vdz661d 61 23 . . . cord-102966-7vdz661d 62 1 Unless unless IN cord-102966-7vdz661d 62 2 specifically specifically RB cord-102966-7vdz661d 62 3 stated state VBN cord-102966-7vdz661d 62 4 otherwise otherwise RB cord-102966-7vdz661d 62 5 , , , cord-102966-7vdz661d 62 6 all all DT cord-102966-7vdz661d 62 7 numerical numerical JJ cord-102966-7vdz661d 62 8 simulations simulation NNS cord-102966-7vdz661d 62 9 have have VBP cord-102966-7vdz661d 62 10 been be VBN cord-102966-7vdz661d 62 11 conducted conduct VBN cord-102966-7vdz661d 62 12 with with IN cord-102966-7vdz661d 62 13 8,9 8,9 CD cord-102966-7vdz661d 62 14 Figure figure NN cord-102966-7vdz661d 62 15 4 4 CD cord-102966-7vdz661d 62 16 is be VBZ cord-102966-7vdz661d 62 17 the the DT cord-102966-7vdz661d 62 18 standard standard NN cord-102966-7vdz661d 62 19 { { -LRB- cord-102966-7vdz661d 62 20 , , , cord-102966-7vdz661d 62 21 , , , cord-102966-7vdz661d 62 22 } } -RRB- cord-102966-7vdz661d 62 23 plot plot NN cord-102966-7vdz661d 62 24 , , , cord-102966-7vdz661d 62 25 for for IN cord-102966-7vdz661d 62 26 SIR SIR NNP cord-102966-7vdz661d 62 27 and and CC cord-102966-7vdz661d 62 28 dSIR dsir NN cord-102966-7vdz661d 62 29 . . . cord-102966-7vdz661d 63 1 Note note VB cord-102966-7vdz661d 63 2 the the DT cord-102966-7vdz661d 63 3 faster fast JJR cord-102966-7vdz661d 63 4 dynamics dynamic NNS cord-102966-7vdz661d 63 5 of of IN cord-102966-7vdz661d 63 6 dSIR dsir RB cord-102966-7vdz661d 63 7 compared compare VBN cord-102966-7vdz661d 63 8 to to IN cord-102966-7vdz661d 63 9 SIR SIR NNP cord-102966-7vdz661d 63 10 , , , cord-102966-7vdz661d 63 11 the the DT cord-102966-7vdz661d 63 12 approximately approximately RB cord-102966-7vdz661d 63 13 twice twice PDT cord-102966-7vdz661d 63 14 as as IN cord-102966-7vdz661d 63 15 high high JJ cord-102966-7vdz661d 63 16 peak peak NN cord-102966-7vdz661d 63 17 of of IN cord-102966-7vdz661d 63 18 i i PRP cord-102966-7vdz661d 63 19 for for IN cord-102966-7vdz661d 63 20 dSIR dsir RB cord-102966-7vdz661d 63 21 compared compare VBN cord-102966-7vdz661d 63 22 to to IN cord-102966-7vdz661d 63 23 SIR SIR NNP cord-102966-7vdz661d 63 24 , , , cord-102966-7vdz661d 63 25 as as RB cord-102966-7vdz661d 63 26 well well RB cord-102966-7vdz661d 63 27 as as IN cord-102966-7vdz661d 63 28 the the DT cord-102966-7vdz661d 63 29 asymmetric asymmetric JJ cord-102966-7vdz661d 63 30 profile profile NN cord-102966-7vdz661d 63 31 of of IN cord-102966-7vdz661d 63 32 for for IN cord-102966-7vdz661d 63 33 SIR SIR NNP cord-102966-7vdz661d 63 34 , , , cord-102966-7vdz661d 63 35 compared compare VBN cord-102966-7vdz661d 63 36 to to IN cord-102966-7vdz661d 63 37 the the DT cord-102966-7vdz661d 63 38 symmetric symmetric JJ cord-102966-7vdz661d 63 39 dSIR dsir JJ cord-102966-7vdz661d 63 40 profile profile NN cord-102966-7vdz661d 63 41 of of IN cord-102966-7vdz661d 63 42 . . . cord-102966-7vdz661d 64 1 ( ( -LRB- cord-102966-7vdz661d 64 2 Details detail NNS cord-102966-7vdz661d 64 3 in in IN cord-102966-7vdz661d 64 4 section section NN cord-102966-7vdz661d 64 5 4 4 CD cord-102966-7vdz661d 64 6 . . . cord-102966-7vdz661d 64 7 ) ) -RRB- cord-102966-7vdz661d 65 1 To to TO cord-102966-7vdz661d 65 2 further further RB cord-102966-7vdz661d 65 3 illustrate illustrate VB cord-102966-7vdz661d 65 4 the the DT cord-102966-7vdz661d 65 5 dSIR dsir JJ cord-102966-7vdz661d 65 6 / / SYM cord-102966-7vdz661d 65 7 SIR SIR NNP cord-102966-7vdz661d 65 8 relationship relationship NN cord-102966-7vdz661d 65 9 , , , cord-102966-7vdz661d 65 10 Figure figure NN cord-102966-7vdz661d 65 11 5 5 CD cord-102966-7vdz661d 65 12 and and CC cord-102966-7vdz661d 65 13 Figure figure NN cord-102966-7vdz661d 65 14 6 6 CD cord-102966-7vdz661d 65 15 show show VBP cord-102966-7vdz661d 65 16 the the DT cord-102966-7vdz661d 65 17 continuous continuous JJ cord-102966-7vdz661d 65 18 - - HYPH cord-102966-7vdz661d 65 19 time time NN cord-102966-7vdz661d 65 20 counterparts counterpart NNS cord-102966-7vdz661d 65 21 of of IN cord-102966-7vdz661d 65 22 Figure figure NN cord-102966-7vdz661d 65 23 3 3 CD cord-102966-7vdz661d 65 24 for for IN cord-102966-7vdz661d 65 25 the the DT cord-102966-7vdz661d 65 26 SIR SIR NNP cord-102966-7vdz661d 65 27 and and CC cord-102966-7vdz661d 65 28 dSIR dsir JJ cord-102966-7vdz661d 65 29 models model NNS cord-102966-7vdz661d 65 30 , , , cord-102966-7vdz661d 65 31 respectively respectively RB cord-102966-7vdz661d 65 32 . . . cord-102966-7vdz661d 66 1 In in IN cord-102966-7vdz661d 66 2 this this DT cord-102966-7vdz661d 66 3 stacked stack VBN cord-102966-7vdz661d 66 4 representation representation NN cord-102966-7vdz661d 66 5 of of IN cord-102966-7vdz661d 66 6 { { -LRB- cord-102966-7vdz661d 66 7 , , , cord-102966-7vdz661d 66 8 , , , cord-102966-7vdz661d 66 9 } } -RRB- cord-102966-7vdz661d 66 10 over over IN cord-102966-7vdz661d 66 11 time time NN cord-102966-7vdz661d 66 12 , , , cord-102966-7vdz661d 66 13 it -PRON- PRP cord-102966-7vdz661d 66 14 is be VBZ cord-102966-7vdz661d 66 15 clear clear JJ cord-102966-7vdz661d 66 16 that that IN cord-102966-7vdz661d 66 17 the the DT cord-102966-7vdz661d 66 18 SIR SIR NNP cord-102966-7vdz661d 66 19 model model NN cord-102966-7vdz661d 66 20 corresponds correspond VBZ cord-102966-7vdz661d 66 21 to to IN cord-102966-7vdz661d 66 22 a a DT cord-102966-7vdz661d 66 23 time time NN cord-102966-7vdz661d 66 24 - - HYPH cord-102966-7vdz661d 66 25 varying vary VBG cord-102966-7vdz661d 66 26 infectious infectious JJ cord-102966-7vdz661d 66 27 period period NN cord-102966-7vdz661d 66 28 for for IN cord-102966-7vdz661d 66 29 each each DT cord-102966-7vdz661d 66 30 individual individual NN cord-102966-7vdz661d 66 31 . . . cord-102966-7vdz661d 67 1 In in IN cord-102966-7vdz661d 67 2 fact fact NN cord-102966-7vdz661d 67 3 , , , cord-102966-7vdz661d 67 4 the the DT cord-102966-7vdz661d 67 5 value value NN cord-102966-7vdz661d 67 6 of of IN cord-102966-7vdz661d 67 7 calculated calculate VBN cord-102966-7vdz661d 67 8 according accord VBG cord-102966-7vdz661d 67 9 to to IN cord-102966-7vdz661d 67 10 eqn eqn NNP cord-102966-7vdz661d 67 11 . . . cord-102966-7vdz661d 67 12 ( ( -LRB- cord-102966-7vdz661d 67 13 3 3 LS cord-102966-7vdz661d 67 14 ) ) -RRB- cord-102966-7vdz661d 67 15 as as IN cord-102966-7vdz661d 67 16 with with IN cord-102966-7vdz661d 67 17 ′ ′ CD cord-102966-7vdz661d 67 18 and and CC cord-102966-7vdz661d 67 19 produced produce VBN cord-102966-7vdz661d 67 20 by by IN cord-102966-7vdz661d 67 21 the the DT cord-102966-7vdz661d 67 22 dSIR dsir JJ cord-102966-7vdz661d 67 23 model model NN cord-102966-7vdz661d 67 24 , , , cord-102966-7vdz661d 67 25 is be VBZ cord-102966-7vdz661d 67 26 time time NN cord-102966-7vdz661d 67 27 varying vary VBG cord-102966-7vdz661d 67 28 , , , cord-102966-7vdz661d 67 29 as as IN cord-102966-7vdz661d 67 30 shown show VBN cord-102966-7vdz661d 67 31 in in IN cord-102966-7vdz661d 67 32 Figure Figure NNP cord-102966-7vdz661d 67 33 7 7 CD cord-102966-7vdz661d 67 34 . . . cord-102966-7vdz661d 68 1 This this DT cord-102966-7vdz661d 68 2 discrepancy discrepancy NN cord-102966-7vdz661d 68 3 suggests suggest VBZ cord-102966-7vdz661d 68 4 that that IN cord-102966-7vdz661d 68 5 the the DT cord-102966-7vdz661d 68 6 standard standard JJ cord-102966-7vdz661d 68 7 interpretation interpretation NN cord-102966-7vdz661d 68 8 of of IN cord-102966-7vdz661d 68 9 1/ 1/ CD cord-102966-7vdz661d 68 10 as as IN cord-102966-7vdz661d 68 11 the the DT cord-102966-7vdz661d 68 12 average average JJ cord-102966-7vdz661d 68 13 infectious infectious JJ cord-102966-7vdz661d 68 14 period period NN cord-102966-7vdz661d 68 15 … … NFP cord-102966-7vdz661d 68 16 estimated estimate VBN cord-102966-7vdz661d 68 17 relatively relatively RB cord-102966-7vdz661d 68 18 precisely precisely RB cord-102966-7vdz661d 68 19 from from IN cord-102966-7vdz661d 68 20 epidemiological epidemiological JJ cord-102966-7vdz661d 68 21 data datum NNS cord-102966-7vdz661d 68 22 2 2 CD cord-102966-7vdz661d 68 23 is be VBZ cord-102966-7vdz661d 68 24 increasingly increasingly RB cord-102966-7vdz661d 68 25 inaccurate inaccurate JJ cord-102966-7vdz661d 68 26 as as IN cord-102966-7vdz661d 68 27 0 0 CD cord-102966-7vdz661d 68 28 increases increase NNS cord-102966-7vdz661d 68 29 above above IN cord-102966-7vdz661d 68 30 1 1 CD cord-102966-7vdz661d 68 31 . . . cord-102966-7vdz661d 69 1 What what WP cord-102966-7vdz661d 69 2 is be VBZ cord-102966-7vdz661d 69 3 estimated estimate VBN cord-102966-7vdz661d 69 4 from from IN cord-102966-7vdz661d 69 5 epidemiological epidemiological JJ cord-102966-7vdz661d 69 6 data data NN cord-102966-7vdz661d 69 7 is be VBZ cord-102966-7vdz661d 69 8 the the DT cord-102966-7vdz661d 69 9 delay delay NN cord-102966-7vdz661d 69 10 , , , cord-102966-7vdz661d 69 11 rather rather RB cord-102966-7vdz661d 69 12 than than IN cord-102966-7vdz661d 69 13 , , , cord-102966-7vdz661d 69 14 and and CC cord-102966-7vdz661d 69 15 if if IN cord-102966-7vdz661d 69 16 1/ 1/ CD cord-102966-7vdz661d 69 17 is be VBZ cord-102966-7vdz661d 69 18 used use VBN cord-102966-7vdz661d 69 19 as as IN cord-102966-7vdz661d 69 20 an an DT cord-102966-7vdz661d 69 21 estimate estimate NN cord-102966-7vdz661d 69 22 of of IN cord-102966-7vdz661d 69 23 , , , cord-102966-7vdz661d 69 24 as as IN cord-102966-7vdz661d 69 25 is be VBZ cord-102966-7vdz661d 69 26 typically typically RB cord-102966-7vdz661d 69 27 done do VBN cord-102966-7vdz661d 69 28 , , , cord-102966-7vdz661d 69 29 the the DT cord-102966-7vdz661d 69 30 SIR SIR NNP cord-102966-7vdz661d 69 31 model model NN cord-102966-7vdz661d 69 32 response response NN cord-102966-7vdz661d 69 33 will will MD cord-102966-7vdz661d 69 34 be be VB cord-102966-7vdz661d 69 35 too too RB cord-102966-7vdz661d 69 36 slow slow JJ cord-102966-7vdz661d 69 37 , , , cord-102966-7vdz661d 69 38 with with IN cord-102966-7vdz661d 69 39 a a DT cord-102966-7vdz661d 69 40 peak peak NN cord-102966-7vdz661d 69 41 value value NN cord-102966-7vdz661d 69 42 for for IN cord-102966-7vdz661d 69 43 lower low JJR cord-102966-7vdz661d 69 44 than than IN cord-102966-7vdz661d 69 45 its -PRON- PRP$ cord-102966-7vdz661d 69 46 dSIR dsir JJ cord-102966-7vdz661d 69 47 counterpart counterpart NN cord-102966-7vdz661d 69 48 by by IN cord-102966-7vdz661d 69 49 about about RB cord-102966-7vdz661d 69 50 half half NN cord-102966-7vdz661d 69 51 . . . cord-102966-7vdz661d 70 1 Depending depend VBG cord-102966-7vdz661d 70 2 on on IN cord-102966-7vdz661d 70 3 . . . cord-102966-7vdz661d 71 1 CC CC NNP cord-102966-7vdz661d 71 2 - - HYPH cord-102966-7vdz661d 71 3 BY BY NNP cord-102966-7vdz661d 71 4 - - HYPH cord-102966-7vdz661d 71 5 NC NC NNP cord-102966-7vdz661d 71 6 - - HYPH cord-102966-7vdz661d 71 7 ND ND NNP cord-102966-7vdz661d 71 8 4.0 4.0 CD cord-102966-7vdz661d 71 9 International international JJ cord-102966-7vdz661d 71 10 license license NN cord-102966-7vdz661d 72 1 It -PRON- PRP cord-102966-7vdz661d 72 2 is be VBZ cord-102966-7vdz661d 72 3 made make VBN cord-102966-7vdz661d 72 4 available available JJ cord-102966-7vdz661d 72 5 under under IN cord-102966-7vdz661d 72 6 a a DT cord-102966-7vdz661d 73 1 is be VBZ cord-102966-7vdz661d 73 2 the the DT cord-102966-7vdz661d 73 3 author author NN cord-102966-7vdz661d 73 4 / / SYM cord-102966-7vdz661d 73 5 funder funder NN cord-102966-7vdz661d 73 6 , , , cord-102966-7vdz661d 73 7 who who WP cord-102966-7vdz661d 73 8 has have VBZ cord-102966-7vdz661d 73 9 granted grant VBN cord-102966-7vdz661d 73 10 medRxiv medRxiv NNS cord-102966-7vdz661d 73 11 a a DT cord-102966-7vdz661d 73 12 license license NN cord-102966-7vdz661d 73 13 to to TO cord-102966-7vdz661d 73 14 display display VB cord-102966-7vdz661d 73 15 the the DT cord-102966-7vdz661d 73 16 preprint preprint NN cord-102966-7vdz661d 73 17 in in IN cord-102966-7vdz661d 73 18 perpetuity perpetuity NN cord-102966-7vdz661d 73 19 . . . cord-102966-7vdz661d 74 1 ( ( -LRB- cord-102966-7vdz661d 74 2 which which WDT cord-102966-7vdz661d 74 3 was be VBD cord-102966-7vdz661d 74 4 not not RB cord-102966-7vdz661d 74 5 certified certify VBN cord-102966-7vdz661d 74 6 by by IN cord-102966-7vdz661d 74 7 peer peer NN cord-102966-7vdz661d 74 8 review review NN cord-102966-7vdz661d 74 9 ) ) -RRB- cord-102966-7vdz661d 75 1 The the DT cord-102966-7vdz661d 75 2 copyright copyright NN cord-102966-7vdz661d 75 3 holder holder NN cord-102966-7vdz661d 75 4 for for IN cord-102966-7vdz661d 75 5 this this DT cord-102966-7vdz661d 75 6 preprint preprint NN cord-102966-7vdz661d 75 7 this this DT cord-102966-7vdz661d 75 8 version version NN cord-102966-7vdz661d 75 9 posted post VBN cord-102966-7vdz661d 75 10 May May NNP cord-102966-7vdz661d 75 11 1 1 CD cord-102966-7vdz661d 75 12 , , , cord-102966-7vdz661d 75 13 2020 2020 CD cord-102966-7vdz661d 75 14 . . . cord-102966-7vdz661d 76 1 ( ( -LRB- cord-102966-7vdz661d 76 2 9 9 CD cord-102966-7vdz661d 76 3 ) ) -RRB- cord-102966-7vdz661d 76 4 . . . cord-102966-7vdz661d 77 1 Note note VB cord-102966-7vdz661d 77 2 that that WDT cord-102966-7vdz661d 77 3 remains remain VBZ cord-102966-7vdz661d 77 4 constant constant JJ cord-102966-7vdz661d 77 5 . . . cord-102966-7vdz661d 78 1 Figure figure NN cord-102966-7vdz661d 78 2 5 5 CD cord-102966-7vdz661d 78 3 is be VBZ cord-102966-7vdz661d 78 4 also also RB cord-102966-7vdz661d 78 5 superimposed superimpose VBN cord-102966-7vdz661d 78 6 , , , cord-102966-7vdz661d 78 7 for for IN cord-102966-7vdz661d 78 8 comparison comparison NN cord-102966-7vdz661d 78 9 . . . cord-102966-7vdz661d 79 1 The the DT cord-102966-7vdz661d 79 2 correspondence correspondence NN cord-102966-7vdz661d 79 3 = = SYM cord-102966-7vdz661d 79 4 1/ 1/ CD cord-102966-7vdz661d 79 5 was be VBD cord-102966-7vdz661d 79 6 used use VBN cord-102966-7vdz661d 79 7 . . . cord-102966-7vdz661d 80 1 ( ( -LRB- cord-102966-7vdz661d 80 2 9 9 CD cord-102966-7vdz661d 80 3 ) ) -RRB- cord-102966-7vdz661d 80 4 . . . cord-102966-7vdz661d 81 1 Note note VB cord-102966-7vdz661d 81 2 that that IN cord-102966-7vdz661d 81 3 all all DT cord-102966-7vdz661d 81 4 lines line NNS cord-102966-7vdz661d 81 5 start start VBP cord-102966-7vdz661d 81 6 at at IN cord-102966-7vdz661d 81 7 = = SYM cord-102966-7vdz661d 81 8 , , , cord-102966-7vdz661d 81 9 as as IN cord-102966-7vdz661d 81 10 ′ ′ CD cord-102966-7vdz661d 81 11 ( ( -LRB- cord-102966-7vdz661d 81 12 < < XX cord-102966-7vdz661d 81 13 ) ) -RRB- cord-102966-7vdz661d 81 14 = = SYM cord-102966-7vdz661d 81 15 0 0 CD cord-102966-7vdz661d 81 16 . . . cord-102966-7vdz661d 82 1 Note note VB cord-102966-7vdz661d 82 2 also also RB cord-102966-7vdz661d 82 3 small small JJ cord-102966-7vdz661d 82 4 spurious spurious JJ cord-102966-7vdz661d 82 5 deviations deviation NNS cord-102966-7vdz661d 82 6 from from IN cord-102966-7vdz661d 82 7 constant constant JJ cord-102966-7vdz661d 82 8 shortly shortly RB cord-102966-7vdz661d 82 9 after after IN cord-102966-7vdz661d 82 10 = = SYM cord-102966-7vdz661d 82 11 , , , cord-102966-7vdz661d 82 12 due due IN cord-102966-7vdz661d 82 13 to to IN cord-102966-7vdz661d 82 14 numerical numerical JJ cord-102966-7vdz661d 82 15 approximation approximation NN cord-102966-7vdz661d 82 16 of of IN cord-102966-7vdz661d 82 17 ( ( -LRB- cord-102966-7vdz661d 82 18 ≤ ≤ NN cord-102966-7vdz661d 82 19 0 0 CD cord-102966-7vdz661d 82 20 ) ) -RRB- cord-102966-7vdz661d 82 21 , , , cord-102966-7vdz661d 82 22 by by IN cord-102966-7vdz661d 82 23 the the DT cord-102966-7vdz661d 82 24 continuous continuous JJ cord-102966-7vdz661d 82 25 function function NN cord-102966-7vdz661d 83 1 As as IN cord-102966-7vdz661d 83 2 pointed point VBN cord-102966-7vdz661d 83 3 out out RP cord-102966-7vdz661d 83 4 in in IN cord-102966-7vdz661d 83 5 the the DT cord-102966-7vdz661d 83 6 preceding precede VBG cord-102966-7vdz661d 83 7 sections section NNS cord-102966-7vdz661d 83 8 , , , cord-102966-7vdz661d 83 9 interpreting interpret VBG cord-102966-7vdz661d 83 10 the the DT cord-102966-7vdz661d 83 11 value value NN cord-102966-7vdz661d 83 12 of of IN cord-102966-7vdz661d 83 13 in in IN cord-102966-7vdz661d 83 14 the the DT cord-102966-7vdz661d 83 15 SIR SIR NNP cord-102966-7vdz661d 83 16 model model NN cord-102966-7vdz661d 83 17 as as IN cord-102966-7vdz661d 83 18 the the DT cord-102966-7vdz661d 83 19 average average JJ cord-102966-7vdz661d 83 20 infectious infectious JJ cord-102966-7vdz661d 83 21 period period NN cord-102966-7vdz661d 83 22 is be VBZ cord-102966-7vdz661d 83 23 not not RB cord-102966-7vdz661d 83 24 accurate accurate JJ cord-102966-7vdz661d 83 25 and and CC cord-102966-7vdz661d 83 26 produces produce VBZ cord-102966-7vdz661d 83 27 misleading misleading JJ cord-102966-7vdz661d 83 28 results result NNS cord-102966-7vdz661d 83 29 . . . cord-102966-7vdz661d 84 1 It -PRON- PRP cord-102966-7vdz661d 84 2 turns turn VBZ cord-102966-7vdz661d 84 3 out out RP cord-102966-7vdz661d 84 4 ( ( -LRB- cord-102966-7vdz661d 84 5 Appendix Appendix NNP cord-102966-7vdz661d 84 6 A A NNP cord-102966-7vdz661d 84 7 ) ) -RRB- cord-102966-7vdz661d 84 8 that that IN cord-102966-7vdz661d 84 9 the the DT cord-102966-7vdz661d 84 10 following follow VBG cord-102966-7vdz661d 84 11 simple simple JJ cord-102966-7vdz661d 84 12 remedy remedy NN cord-102966-7vdz661d 84 13 can can MD cord-102966-7vdz661d 84 14 be be VB cord-102966-7vdz661d 84 15 used use VBN cord-102966-7vdz661d 84 16 to to TO cord-102966-7vdz661d 84 17 retain retain VB cord-102966-7vdz661d 84 18 the the DT cord-102966-7vdz661d 84 19 ODE ODE NNP cord-102966-7vdz661d 84 20 structure structure NN cord-102966-7vdz661d 84 21 of of IN cord-102966-7vdz661d 84 22 the the DT cord-102966-7vdz661d 84 23 standard standard JJ cord-102966-7vdz661d 84 24 SIR SIR NNP cord-102966-7vdz661d 84 25 model model NN cord-102966-7vdz661d 84 26 , , , cord-102966-7vdz661d 84 27 while while IN cord-102966-7vdz661d 84 28 better well JJR cord-102966-7vdz661d 84 29 approximating approximate VBG cord-102966-7vdz661d 84 30 the the DT cord-102966-7vdz661d 84 31 DDE DDE NNP cord-102966-7vdz661d 84 32 dynamics dynamic NNS cord-102966-7vdz661d 84 33 of of IN cord-102966-7vdz661d 84 34 the the DT cord-102966-7vdz661d 84 35 more more RBR cord-102966-7vdz661d 84 36 realistic realistic JJ cord-102966-7vdz661d 84 37 dSIR dsir JJ cord-102966-7vdz661d 84 38 model model NN cord-102966-7vdz661d 84 39 structure structure NN cord-102966-7vdz661d 85 1 : : : cord-102966-7vdz661d 85 2 The the DT cord-102966-7vdz661d 85 3 SIR SIR NNP cord-102966-7vdz661d 85 4 equations equation NNS cord-102966-7vdz661d 85 5 for for IN cord-102966-7vdz661d 85 6 { { -LRB- cord-102966-7vdz661d 85 7 ′ ′ CD cord-102966-7vdz661d 85 8 , , , cord-102966-7vdz661d 85 9 ′ ′ CD cord-102966-7vdz661d 85 10 } } -RRB- cord-102966-7vdz661d 85 11 , , , cord-102966-7vdz661d 85 12 eqns eqns NNP cord-102966-7vdz661d 85 13 . . . cord-102966-7vdz661d 86 1 ( ( -LRB- cord-102966-7vdz661d 86 2 2 2 LS cord-102966-7vdz661d 86 3 ) ) -RRB- cord-102966-7vdz661d 86 4 and and CC cord-102966-7vdz661d 86 5 ( ( -LRB- cord-102966-7vdz661d 86 6 3 3 LS cord-102966-7vdz661d 86 7 ) ) -RRB- cord-102966-7vdz661d 86 8 , , , cord-102966-7vdz661d 86 9 can can MD cord-102966-7vdz661d 86 10 be be VB cord-102966-7vdz661d 86 11 replaced replace VBN cord-102966-7vdz661d 86 12 by by IN cord-102966-7vdz661d 86 13 the the DT cord-102966-7vdz661d 86 14 equally equally RB cord-102966-7vdz661d 86 15 simple simple JJ cord-102966-7vdz661d 86 16 ODEs ode NNS cord-102966-7vdz661d 86 17 or or CC cord-102966-7vdz661d 86 18 by by IN cord-102966-7vdz661d 86 19 the the DT cord-102966-7vdz661d 86 20 more more RBR cord-102966-7vdz661d 86 21 accurate accurate JJ cord-102966-7vdz661d 86 22 set set NN cord-102966-7vdz661d 86 23 of of IN cord-102966-7vdz661d 86 24 ODEs ode NNS cord-102966-7vdz661d 86 25 with with IN cord-102966-7vdz661d 86 26 2 2 CD cord-102966-7vdz661d 86 27 ( ( -LRB- cord-102966-7vdz661d 86 28 0 0 NFP cord-102966-7vdz661d 86 29 ) ) -RRB- cord-102966-7vdz661d 87 1 = = SYM cord-102966-7vdz661d 87 2 0 0 NFP cord-102966-7vdz661d 87 3 . . . cord-102966-7vdz661d 88 1 Figure figure NN cord-102966-7vdz661d 88 2 8 8 CD cord-102966-7vdz661d 88 3 confirms confirm VBZ cord-102966-7vdz661d 88 4 that that IN cord-102966-7vdz661d 88 5 the the DT cord-102966-7vdz661d 88 6 trajectories trajectory NNS cord-102966-7vdz661d 88 7 for for IN cord-102966-7vdz661d 88 8 the the DT cord-102966-7vdz661d 88 9 dSIR dsir JJ cord-102966-7vdz661d 88 10 and and CC cord-102966-7vdz661d 88 11 the the DT cord-102966-7vdz661d 88 12 modified modify VBN cord-102966-7vdz661d 88 13 SIR SIR NNP cord-102966-7vdz661d 88 14 model model NN cord-102966-7vdz661d 88 15 structures structure NNS cord-102966-7vdz661d 88 16 -eqns -eqns ADD cord-102966-7vdz661d 88 17 . . . cord-102966-7vdz661d 89 1 ( ( -LRB- cord-102966-7vdz661d 89 2 7)-(9 7)-(9 CD cord-102966-7vdz661d 89 3 ) ) -RRB- cord-102966-7vdz661d 89 4 and and CC cord-102966-7vdz661d 89 5 ( ( -LRB- cord-102966-7vdz661d 89 6 1)-(3 1)-(3 LS cord-102966-7vdz661d 89 7 ) ) -RRB- cord-102966-7vdz661d 89 8 with with IN cord-102966-7vdz661d 89 9 eqn eqn NN cord-102966-7vdz661d 89 10 . . . cord-102966-7vdz661d 90 1 ( ( -LRB- cord-102966-7vdz661d 90 2 2 2 LS cord-102966-7vdz661d 90 3 ) ) -RRB- cord-102966-7vdz661d 90 4 replaced replace VBN cord-102966-7vdz661d 90 5 by by IN cord-102966-7vdz661d 90 6 ( ( -LRB- cord-102966-7vdz661d 90 7 13 13 CD cord-102966-7vdz661d 90 8 ) ) -RRB- cord-102966-7vdz661d 90 9 or or CC cord-102966-7vdz661d 90 10 ( ( -LRB- cord-102966-7vdz661d 90 11 14 14 CD cord-102966-7vdz661d 90 12 ) ) -RRB- cord-102966-7vdz661d 90 13 , , , cord-102966-7vdz661d 90 14 respectively respectively RB cord-102966-7vdz661d 90 15 -are -are : cord-102966-7vdz661d 90 16 close close RB cord-102966-7vdz661d 90 17 to to IN cord-102966-7vdz661d 90 18 one one CD cord-102966-7vdz661d 90 19 another another DT cord-102966-7vdz661d 90 20 , , , cord-102966-7vdz661d 90 21 both both CC cord-102966-7vdz661d 90 22 in in IN cord-102966-7vdz661d 90 23 terms term NNS cord-102966-7vdz661d 90 24 of of IN cord-102966-7vdz661d 90 25 the the DT cord-102966-7vdz661d 90 26 time time NN cord-102966-7vdz661d 90 27 to to TO cord-102966-7vdz661d 90 28 peak peak VB cord-102966-7vdz661d 90 29 and and CC cord-102966-7vdz661d 90 30 the the DT cord-102966-7vdz661d 90 31 value value NN cord-102966-7vdz661d 90 32 of of IN cord-102966-7vdz661d 90 33 the the DT cord-102966-7vdz661d 90 34 peak peak NN cord-102966-7vdz661d 90 35 . . . cord-102966-7vdz661d 91 1 As as IN cord-102966-7vdz661d 91 2 already already RB cord-102966-7vdz661d 91 3 mentioned mention VBN cord-102966-7vdz661d 91 4 , , , cord-102966-7vdz661d 91 5 these these DT cord-102966-7vdz661d 91 6 properties property NNS cord-102966-7vdz661d 91 7 are be VBP cord-102966-7vdz661d 91 8 important important JJ cord-102966-7vdz661d 91 9 when when WRB cord-102966-7vdz661d 91 10 such such JJ cord-102966-7vdz661d 91 11 models model NNS cord-102966-7vdz661d 91 12 are be VBP cord-102966-7vdz661d 91 13 used use VBN cord-102966-7vdz661d 91 14 to to TO cord-102966-7vdz661d 91 15 anticipate anticipate VB cord-102966-7vdz661d 91 16 hospitalization hospitalization NN cord-102966-7vdz661d 91 17 needs need NNS cord-102966-7vdz661d 91 18 for for IN cord-102966-7vdz661d 91 19 the the DT cord-102966-7vdz661d 91 20 infected infect VBN cord-102966-7vdz661d 91 21 during during IN cord-102966-7vdz661d 91 22 an an DT cord-102966-7vdz661d 91 23 epidemic epidemic NN cord-102966-7vdz661d 91 24 . . . cord-102966-7vdz661d 92 1 Figure figure NN cord-102966-7vdz661d 92 2 8 8 CD cord-102966-7vdz661d 92 3 . . . cord-102966-7vdz661d 93 1 Comparison comparison NN cord-102966-7vdz661d 93 2 of of IN cord-102966-7vdz661d 93 3 the the DT cord-102966-7vdz661d 93 4 profiles profile NNS cord-102966-7vdz661d 93 5 for for IN cord-102966-7vdz661d 93 6 the the DT cord-102966-7vdz661d 93 7 first first JJ cord-102966-7vdz661d 93 8 - - HYPH cord-102966-7vdz661d 93 9 order order NN cord-102966-7vdz661d 93 10 Padé Padé NNP cord-102966-7vdz661d 93 11 SIR SIR NNP cord-102966-7vdz661d 93 12 , , , cord-102966-7vdz661d 93 13 second second JJ cord-102966-7vdz661d 93 14 - - HYPH cord-102966-7vdz661d 93 15 order order NN cord-102966-7vdz661d 93 16 Padé Padé NNP cord-102966-7vdz661d 93 17 SIR SIR NNP cord-102966-7vdz661d 93 18 , , , cord-102966-7vdz661d 93 19 dSIR dsir RB cord-102966-7vdz661d 93 20 , , , cord-102966-7vdz661d 93 21 and and CC cord-102966-7vdz661d 93 22 SIR SIR NNP cord-102966-7vdz661d 93 23 models model NNS cord-102966-7vdz661d 93 24 . . . cord-102966-7vdz661d 94 1 Note note VB cord-102966-7vdz661d 94 2 the the DT cord-102966-7vdz661d 94 3 improve improve NN cord-102966-7vdz661d 94 4 approximation approximation NN cord-102966-7vdz661d 94 5 of of IN cord-102966-7vdz661d 94 6 dSIR dsir RB cord-102966-7vdz661d 94 7 by by IN cord-102966-7vdz661d 94 8 the the DT cord-102966-7vdz661d 94 9 second second JJ cord-102966-7vdz661d 94 10 - - HYPH cord-102966-7vdz661d 94 11 order order NN cord-102966-7vdz661d 94 12 Padé Padé NNP cord-102966-7vdz661d 94 13 SIR SIR NNP cord-102966-7vdz661d 94 14 , , , cord-102966-7vdz661d 94 15 compared compare VBN cord-102966-7vdz661d 94 16 to to IN cord-102966-7vdz661d 94 17 first first JJ cord-102966-7vdz661d 94 18 - - HYPH cord-102966-7vdz661d 94 19 order order NN cord-102966-7vdz661d 94 20 Padé Padé NNP cord-102966-7vdz661d 94 21 SIR SIR NNP cord-102966-7vdz661d 94 22 , , , cord-102966-7vdz661d 94 23 as as IN cord-102966-7vdz661d 94 24 anticipated anticipate VBN cord-102966-7vdz661d 94 25 by by IN cord-102966-7vdz661d 94 26 eqns eqns NNP cord-102966-7vdz661d 94 27 . . . cord-102966-7vdz661d 95 1 ( ( -LRB- cord-102966-7vdz661d 95 2 13 13 CD cord-102966-7vdz661d 95 3 ) ) -RRB- cord-102966-7vdz661d 95 4 or or CC cord-102966-7vdz661d 95 5 ( ( -LRB- cord-102966-7vdz661d 95 6 14 14 CD cord-102966-7vdz661d 95 7 ) ) -RRB- cord-102966-7vdz661d 95 8 , , , cord-102966-7vdz661d 95 9 respectively respectively RB cord-102966-7vdz661d 95 10 . . . cord-102966-7vdz661d 96 1 Note note VB cord-102966-7vdz661d 96 2 ( ( -LRB- cord-102966-7vdz661d 96 3 Appendix Appendix NNP cord-102966-7vdz661d 96 4 A A NNP cord-102966-7vdz661d 96 5 ) ) -RRB- cord-102966-7vdz661d 97 1 that that IN cord-102966-7vdz661d 97 2 the the DT cord-102966-7vdz661d 97 3 essence essence NN cord-102966-7vdz661d 97 4 of of IN cord-102966-7vdz661d 97 5 eqns eqn NNS cord-102966-7vdz661d 97 6 . . . cord-102966-7vdz661d 98 1 ( ( -LRB- cord-102966-7vdz661d 98 2 13 13 CD cord-102966-7vdz661d 98 3 ) ) -RRB- cord-102966-7vdz661d 98 4 and and CC cord-102966-7vdz661d 98 5 ( ( -LRB- cord-102966-7vdz661d 98 6 14 14 CD cord-102966-7vdz661d 98 7 ) ) -RRB- cord-102966-7vdz661d 98 8 is be VBZ cord-102966-7vdz661d 98 9 in in IN cord-102966-7vdz661d 98 10 approximating approximate VBG cord-102966-7vdz661d 98 11 the the DT cord-102966-7vdz661d 98 12 pulse pulse NN cord-102966-7vdz661d 98 13 profile profile NN cord-102966-7vdz661d 98 14 ( ( -LRB- cord-102966-7vdz661d 98 15 ) ) -RRB- cord-102966-7vdz661d 98 16 − − NN cord-102966-7vdz661d 98 17 ( ( -LRB- cord-102966-7vdz661d 98 18 − − NNP cord-102966-7vdz661d 98 19 ) ) -RRB- cord-102966-7vdz661d 98 20 in in IN cord-102966-7vdz661d 98 21 Figure figure NN cord-102966-7vdz661d 98 22 2 2 CD cord-102966-7vdz661d 98 23 by by IN cord-102966-7vdz661d 98 24 a a DT cord-102966-7vdz661d 98 25 transfer transfer NN cord-102966-7vdz661d 98 26 function function NN cord-102966-7vdz661d 98 27 approximation approximation NN cord-102966-7vdz661d 98 28 based base VBN cord-102966-7vdz661d 98 29 on on IN cord-102966-7vdz661d 98 30 firstor firstor NN cord-102966-7vdz661d 98 31 second second JJ cord-102966-7vdz661d 98 32 - - HYPH cord-102966-7vdz661d 98 33 order order NN cord-102966-7vdz661d 98 34 Padé Padé NNP cord-102966-7vdz661d 98 35 - - HYPH cord-102966-7vdz661d 98 36 approximants approximant NNS cord-102966-7vdz661d 98 37 ( ( -LRB- cord-102966-7vdz661d 98 38 in in IN cord-102966-7vdz661d 98 39 the the DT cord-102966-7vdz661d 98 40 Laplace Laplace NNP cord-102966-7vdz661d 98 41 domain domain NN cord-102966-7vdz661d 98 42 ) ) -RRB- cord-102966-7vdz661d 98 43 ( ( -LRB- cord-102966-7vdz661d 98 44 rather rather RB cord-102966-7vdz661d 98 45 than than IN cord-102966-7vdz661d 98 46 by by IN cord-102966-7vdz661d 98 47 the the DT cord-102966-7vdz661d 98 48 decaying decay VBG cord-102966-7vdz661d 98 49 exponential exponential NN cord-102966-7vdz661d 98 50 of of IN cord-102966-7vdz661d 98 51 Figure figure NN cord-102966-7vdz661d 98 52 2 2 CD cord-102966-7vdz661d 98 53 ) ) -RRB- cord-102966-7vdz661d 98 54 as as IN cord-102966-7vdz661d 98 55 shown show VBN cord-102966-7vdz661d 98 56 in in IN cord-102966-7vdz661d 98 57 Figure Figure NNP cord-102966-7vdz661d 98 58 9 9 CD cord-102966-7vdz661d 98 59 . . . cord-102966-7vdz661d 99 1 Padé padé JJ cord-102966-7vdz661d 99 2 - - HYPH cord-102966-7vdz661d 99 3 approximation approximation NN cord-102966-7vdz661d 99 4 has have VBZ cord-102966-7vdz661d 99 5 long long RB cord-102966-7vdz661d 99 6 been be VBN cord-102966-7vdz661d 99 7 a a DT cord-102966-7vdz661d 99 8 popular popular JJ cord-102966-7vdz661d 99 9 . . . cord-102966-7vdz661d 100 1 CC CC NNP cord-102966-7vdz661d 100 2 - - HYPH cord-102966-7vdz661d 100 3 BY BY NNP cord-102966-7vdz661d 100 4 - - HYPH cord-102966-7vdz661d 100 5 NC NC NNP cord-102966-7vdz661d 100 6 - - HYPH cord-102966-7vdz661d 100 7 ND ND NNP cord-102966-7vdz661d 100 8 4.0 4.0 CD cord-102966-7vdz661d 100 9 International international JJ cord-102966-7vdz661d 100 10 license license NN cord-102966-7vdz661d 101 1 It -PRON- PRP cord-102966-7vdz661d 101 2 is be VBZ cord-102966-7vdz661d 101 3 made make VBN cord-102966-7vdz661d 101 4 available available JJ cord-102966-7vdz661d 101 5 under under IN cord-102966-7vdz661d 101 6 a a DT cord-102966-7vdz661d 102 1 is be VBZ cord-102966-7vdz661d 102 2 the the DT cord-102966-7vdz661d 102 3 author author NN cord-102966-7vdz661d 102 4 / / SYM cord-102966-7vdz661d 102 5 funder funder NN cord-102966-7vdz661d 102 6 , , , cord-102966-7vdz661d 102 7 who who WP cord-102966-7vdz661d 102 8 has have VBZ cord-102966-7vdz661d 102 9 granted grant VBN cord-102966-7vdz661d 102 10 medRxiv medRxiv NNS cord-102966-7vdz661d 102 11 a a DT cord-102966-7vdz661d 102 12 license license NN cord-102966-7vdz661d 102 13 to to TO cord-102966-7vdz661d 102 14 display display VB cord-102966-7vdz661d 102 15 the the DT cord-102966-7vdz661d 102 16 preprint preprint NN cord-102966-7vdz661d 102 17 in in IN cord-102966-7vdz661d 102 18 perpetuity perpetuity NN cord-102966-7vdz661d 102 19 . . . cord-102966-7vdz661d 103 1 The the DT cord-102966-7vdz661d 103 2 copyright copyright NN cord-102966-7vdz661d 103 3 holder holder NN cord-102966-7vdz661d 103 4 for for IN cord-102966-7vdz661d 103 5 this this DT cord-102966-7vdz661d 103 6 preprint preprint NN cord-102966-7vdz661d 103 7 this this DT cord-102966-7vdz661d 103 8 version version NN cord-102966-7vdz661d 103 9 posted post VBN cord-102966-7vdz661d 103 10 May May NNP cord-102966-7vdz661d 103 11 1 1 CD cord-102966-7vdz661d 103 12 , , , cord-102966-7vdz661d 103 13 2020 2020 CD cord-102966-7vdz661d 103 14 . . . cord-102966-7vdz661d 103 15 . . . cord-102966-7vdz661d 104 1 https://doi.org/10.1101/2020.04.26.20080960 https://doi.org/10.1101/2020.04.26.20080960 NNP cord-102966-7vdz661d 104 2 doi doi NNP cord-102966-7vdz661d 104 3 : : : cord-102966-7vdz661d 105 1 medRxiv medRxiv NNP cord-102966-7vdz661d 105 2 preprint preprint NNP cord-102966-7vdz661d 106 1 medRχiv.org medRχiv.org NNP cord-102966-7vdz661d 106 2 Michael Michael NNP cord-102966-7vdz661d 106 3 Nikolaou Nikolaou NNP cord-102966-7vdz661d 106 4 approach approach NN cord-102966-7vdz661d 106 5 for for IN cord-102966-7vdz661d 106 6 approximating approximate VBG cord-102966-7vdz661d 106 7 transcendental transcendental JJ cord-102966-7vdz661d 106 8 transfer transfer NN cord-102966-7vdz661d 106 9 functions function NNS cord-102966-7vdz661d 106 10 by by IN cord-102966-7vdz661d 106 11 polynomial polynomial JJ cord-102966-7vdz661d 106 12 rational rational JJ cord-102966-7vdz661d 106 13 fractions fraction NNS cord-102966-7vdz661d 106 14 in in IN cord-102966-7vdz661d 106 15 process process NN cord-102966-7vdz661d 106 16 control control NN cord-102966-7vdz661d 106 17 . . . cord-102966-7vdz661d 107 1 11 11 CD cord-102966-7vdz661d 107 2 Figure figure NN cord-102966-7vdz661d 107 3 9 9 CD cord-102966-7vdz661d 107 4 . . . cord-102966-7vdz661d 108 1 Reduction reduction NN cord-102966-7vdz661d 108 2 of of IN cord-102966-7vdz661d 108 3 the the DT cord-102966-7vdz661d 108 4 infectious infectious JJ cord-102966-7vdz661d 108 5 fraction fraction NN cord-102966-7vdz661d 108 6 from from IN cord-102966-7vdz661d 108 7 ( ( -LRB- cord-102966-7vdz661d 108 8 0 0 NFP cord-102966-7vdz661d 108 9 ) ) -RRB- cord-102966-7vdz661d 108 10 to to IN cord-102966-7vdz661d 108 11 0 0 NFP cord-102966-7vdz661d 108 12 ( ( -LRB- cord-102966-7vdz661d 108 13 a a LS cord-102966-7vdz661d 108 14 ) ) -RRB- cord-102966-7vdz661d 108 15 in in IN cord-102966-7vdz661d 108 16 a a DT cord-102966-7vdz661d 108 17 single single JJ cord-102966-7vdz661d 108 18 front front NN cord-102966-7vdz661d 108 19 in in IN cord-102966-7vdz661d 108 20 terms term NNS cord-102966-7vdz661d 108 21 of of IN cord-102966-7vdz661d 108 22 the the DT cord-102966-7vdz661d 108 23 Heaviside Heaviside NNP cord-102966-7vdz661d 108 24 step step NN cord-102966-7vdz661d 108 25 function function NN cord-102966-7vdz661d 108 26 with with IN cord-102966-7vdz661d 108 27 = = SYM cord-102966-7vdz661d 108 28 1/ 1/ CD cord-102966-7vdz661d 108 29 , , , cord-102966-7vdz661d 108 30 ( ( -LRB- cord-102966-7vdz661d 108 31 b b LS cord-102966-7vdz661d 108 32 ) ) -RRB- cord-102966-7vdz661d 108 33 following follow VBG cord-102966-7vdz661d 108 34 a a DT cord-102966-7vdz661d 108 35 first first JJ cord-102966-7vdz661d 108 36 - - HYPH cord-102966-7vdz661d 108 37 order order NN cord-102966-7vdz661d 108 38 Padé padé JJ cord-102966-7vdz661d 108 39 approximation approximation NN cord-102966-7vdz661d 108 40 , , , cord-102966-7vdz661d 108 41 and and CC cord-102966-7vdz661d 108 42 ( ( -LRB- cord-102966-7vdz661d 108 43 c c NN cord-102966-7vdz661d 108 44 ) ) -RRB- cord-102966-7vdz661d 108 45 following follow VBG cord-102966-7vdz661d 108 46 a a DT cord-102966-7vdz661d 108 47 second second JJ cord-102966-7vdz661d 108 48 - - HYPH cord-102966-7vdz661d 108 49 order order NN cord-102966-7vdz661d 108 50 Padé padé JJ cord-102966-7vdz661d 108 51 approximation approximation NN cord-102966-7vdz661d 108 52 . . . cord-102966-7vdz661d 109 1 ( ( -LRB- cord-102966-7vdz661d 109 2 cf cf NNP cord-102966-7vdz661d 109 3 . . . cord-102966-7vdz661d 110 1 Figure figure NN cord-102966-7vdz661d 110 2 2 2 CD cord-102966-7vdz661d 110 3 ) ) -RRB- cord-102966-7vdz661d 110 4 . . . cord-102966-7vdz661d 111 1 Because because IN cord-102966-7vdz661d 111 2 of of IN cord-102966-7vdz661d 111 3 the the DT cord-102966-7vdz661d 111 4 critical critical JJ cord-102966-7vdz661d 111 5 role role NN cord-102966-7vdz661d 111 6 of of IN cord-102966-7vdz661d 111 7 Padé padé JJ cord-102966-7vdz661d 111 8 approximation approximation NN cord-102966-7vdz661d 111 9 in in IN cord-102966-7vdz661d 111 10 deriving derive VBG cord-102966-7vdz661d 111 11 eqn eqn NN cord-102966-7vdz661d 111 12 . . . cord-102966-7vdz661d 112 1 ( ( -LRB- cord-102966-7vdz661d 112 2 14 14 CD cord-102966-7vdz661d 112 3 ) ) -RRB- cord-102966-7vdz661d 112 4 for for IN cord-102966-7vdz661d 112 5 the the DT cord-102966-7vdz661d 112 6 ODEs ode NNS cord-102966-7vdz661d 112 7 of of IN cord-102966-7vdz661d 112 8 the the DT cord-102966-7vdz661d 112 9 modified modify VBN cord-102966-7vdz661d 112 10 SIR SIR NNP cord-102966-7vdz661d 112 11 model model NN cord-102966-7vdz661d 112 12 to to TO cord-102966-7vdz661d 112 13 approximate approximate VB cord-102966-7vdz661d 112 14 the the DT cord-102966-7vdz661d 112 15 dSIR dsir JJ cord-102966-7vdz661d 112 16 model model NN cord-102966-7vdz661d 112 17 , , , cord-102966-7vdz661d 112 18 we -PRON- PRP cord-102966-7vdz661d 112 19 will will MD cord-102966-7vdz661d 112 20 use use VB cord-102966-7vdz661d 112 21 the the DT cord-102966-7vdz661d 112 22 term term NN cord-102966-7vdz661d 112 23 Padé Padé NNP cord-102966-7vdz661d 112 24 SIR SIR NNP cord-102966-7vdz661d 112 25 to to TO cord-102966-7vdz661d 112 26 denote denote VB cord-102966-7vdz661d 112 27 the the DT cord-102966-7vdz661d 112 28 modified modify VBN cord-102966-7vdz661d 112 29 SIR SIR NNP cord-102966-7vdz661d 112 30 model model NN cord-102966-7vdz661d 112 31 structure structure NN cord-102966-7vdz661d 112 32 . . . cord-102966-7vdz661d 113 1 Finally finally RB cord-102966-7vdz661d 113 2 , , , cord-102966-7vdz661d 113 3 it -PRON- PRP cord-102966-7vdz661d 113 4 should should MD cord-102966-7vdz661d 113 5 be be VB cord-102966-7vdz661d 113 6 noted note VBN cord-102966-7vdz661d 113 7 that that IN cord-102966-7vdz661d 113 8 eqn eqn NN cord-102966-7vdz661d 113 9 . . . cord-102966-7vdz661d 114 1 ( ( -LRB- cord-102966-7vdz661d 114 2 13 13 CD cord-102966-7vdz661d 114 3 ) ) -RRB- cord-102966-7vdz661d 114 4 may may MD cord-102966-7vdz661d 114 5 seem seem VB cord-102966-7vdz661d 114 6 counter counter JJ cord-102966-7vdz661d 114 7 - - JJ cord-102966-7vdz661d 114 8 intuitive intuitive JJ cord-102966-7vdz661d 114 9 , , , cord-102966-7vdz661d 114 10 as as IN cord-102966-7vdz661d 114 11 it -PRON- PRP cord-102966-7vdz661d 114 12 appears appear VBZ cord-102966-7vdz661d 114 13 to to TO cord-102966-7vdz661d 114 14 suggest suggest VB cord-102966-7vdz661d 114 15 that that IN cord-102966-7vdz661d 114 16 the the DT cord-102966-7vdz661d 114 17 generation generation NN cord-102966-7vdz661d 114 18 and and CC cord-102966-7vdz661d 114 19 depletion depletion NN cord-102966-7vdz661d 114 20 rates rate NNS cord-102966-7vdz661d 114 21 of of IN cord-102966-7vdz661d 114 22 are be VBP cord-102966-7vdz661d 114 23 2 2 CD cord-102966-7vdz661d 114 24 and and CC cord-102966-7vdz661d 114 25 −2 −2 NNP cord-102966-7vdz661d 114 26 / / SYM cord-102966-7vdz661d 114 27 , , , cord-102966-7vdz661d 114 28 respectively respectively RB cord-102966-7vdz661d 114 29 . . . cord-102966-7vdz661d 115 1 However however RB cord-102966-7vdz661d 115 2 , , , cord-102966-7vdz661d 115 3 eqn eqn NN cord-102966-7vdz661d 115 4 . . . cord-102966-7vdz661d 115 5 ( ( -LRB- cord-102966-7vdz661d 115 6 13 13 CD cord-102966-7vdz661d 115 7 ) ) -RRB- cord-102966-7vdz661d 115 8 rather rather RB cord-102966-7vdz661d 115 9 suggests suggest VBZ cord-102966-7vdz661d 115 10 that that IN cord-102966-7vdz661d 115 11 while while IN cord-102966-7vdz661d 115 12 the the DT cord-102966-7vdz661d 115 13 susceptible susceptible JJ cord-102966-7vdz661d 115 14 depletion depletion NN cord-102966-7vdz661d 115 15 rate rate NN cord-102966-7vdz661d 115 16 remains remain VBZ cord-102966-7vdz661d 115 17 − − NNP cord-102966-7vdz661d 115 18 , , , cord-102966-7vdz661d 115 19 the the DT cord-102966-7vdz661d 115 20 infectious infectious JJ cord-102966-7vdz661d 115 21 depletion depletion NN cord-102966-7vdz661d 115 22 rate rate NN cord-102966-7vdz661d 115 23 appears appear VBZ cord-102966-7vdz661d 115 24 as as IN cord-102966-7vdz661d 115 25 ( ( -LRB- cord-102966-7vdz661d 115 26 − − NNP cord-102966-7vdz661d 115 27 2/ 2/ CD cord-102966-7vdz661d 115 28 ) ) -RRB- cord-102966-7vdz661d 115 29 ( ( -LRB- cord-102966-7vdz661d 115 30 which which WDT cord-102966-7vdz661d 115 31 is be VBZ cord-102966-7vdz661d 115 32 -dependent -dependent VBN cord-102966-7vdz661d 115 33 ) ) -RRB- cord-102966-7vdz661d 115 34 rather rather RB cord-102966-7vdz661d 115 35 than than IN cord-102966-7vdz661d 115 36 − − NNP cord-102966-7vdz661d 115 37 / / , cord-102966-7vdz661d 115 38 ( ( -LRB- cord-102966-7vdz661d 115 39 which which WDT cord-102966-7vdz661d 115 40 is be VBZ cord-102966-7vdz661d 115 41 not not RB cord-102966-7vdz661d 115 42 ) ) -RRB- cord-102966-7vdz661d 115 43 due due JJ cord-102966-7vdz661d 115 44 simply simply RB cord-102966-7vdz661d 115 45 to to IN cord-102966-7vdz661d 115 46 replacement replacement NN cord-102966-7vdz661d 115 47 of of IN cord-102966-7vdz661d 115 48 the the DT cord-102966-7vdz661d 115 49 delay delay NN cord-102966-7vdz661d 115 50 term term NN cord-102966-7vdz661d 115 51 − − NNP cord-102966-7vdz661d 115 52 in in IN cord-102966-7vdz661d 115 53 the the DT cord-102966-7vdz661d 115 54 Laplace Laplace NNP cord-102966-7vdz661d 115 55 domain domain NN cord-102966-7vdz661d 115 56 by by IN cord-102966-7vdz661d 115 57 its -PRON- PRP$ cord-102966-7vdz661d 115 58 Padé Padé NNP cord-102966-7vdz661d 115 59 approximant approximant NN cord-102966-7vdz661d 115 60 . . . cord-102966-7vdz661d 116 1 Similarly similarly RB cord-102966-7vdz661d 116 2 , , , cord-102966-7vdz661d 116 3 the the DT cord-102966-7vdz661d 116 4 rate rate NN cord-102966-7vdz661d 116 5 of of IN cord-102966-7vdz661d 116 6 increase increase NN cord-102966-7vdz661d 116 7 for for IN cord-102966-7vdz661d 116 8 in in IN cord-102966-7vdz661d 116 9 eqn eqn NN cord-102966-7vdz661d 116 10 . . . cord-102966-7vdz661d 117 1 ( ( -LRB- cord-102966-7vdz661d 117 2 13 13 CD cord-102966-7vdz661d 117 3 ) ) -RRB- cord-102966-7vdz661d 117 4 is be VBZ cord-102966-7vdz661d 117 5 -dependent -dependent JJ cord-102966-7vdz661d 117 6 , , , cord-102966-7vdz661d 117 7 rather rather RB cord-102966-7vdz661d 117 8 than than IN cord-102966-7vdz661d 117 9 not not RB cord-102966-7vdz661d 117 10 . . . cord-102966-7vdz661d 118 1 Standard standard JJ cord-102966-7vdz661d 118 2 theory theory NN cord-102966-7vdz661d 118 3 of of IN cord-102966-7vdz661d 118 4 DDEs dde NNS cord-102966-7vdz661d 118 5 ( ( -LRB- cord-102966-7vdz661d 118 6 e.g. e.g. RB cord-102966-7vdz661d 118 7 equation equation NN cord-102966-7vdz661d 118 8 ( ( -LRB- cord-102966-7vdz661d 118 9 9.42 9.42 CD cord-102966-7vdz661d 118 10 ) ) -RRB- cord-102966-7vdz661d 118 11 in in IN cord-102966-7vdz661d 118 12 Ch Ch NNP cord-102966-7vdz661d 118 13 . . . cord-102966-7vdz661d 119 1 4 4 CD cord-102966-7vdz661d 119 2 and and CC cord-102966-7vdz661d 119 3 equation equation NN cord-102966-7vdz661d 119 4 ( ( -LRB- cord-102966-7vdz661d 119 5 1.2 1.2 CD cord-102966-7vdz661d 119 6 ) ) -RRB- cord-102966-7vdz661d 119 7 in in IN cord-102966-7vdz661d 119 8 Ch Ch NNP cord-102966-7vdz661d 119 9 . . . cord-102966-7vdz661d 120 1 5 5 CD cord-102966-7vdz661d 120 2 of of IN cord-102966-7vdz661d 120 3 Kuang Kuang NNP cord-102966-7vdz661d 120 4 , , , cord-102966-7vdz661d 120 5 12 12 CD cord-102966-7vdz661d 120 6 or or CC cord-102966-7vdz661d 120 7 Gopalsamy Gopalsamy NNP cord-102966-7vdz661d 120 8 13 13 CD cord-102966-7vdz661d 120 9 ) ) -RRB- cord-102966-7vdz661d 120 10 can can MD cord-102966-7vdz661d 120 11 be be VB cord-102966-7vdz661d 120 12 applied apply VBN cord-102966-7vdz661d 120 13 to to TO cord-102966-7vdz661d 120 14 establish establish VB cord-102966-7vdz661d 120 15 rigorous rigorous JJ cord-102966-7vdz661d 120 16 properties property NNS cord-102966-7vdz661d 120 17 for for IN cord-102966-7vdz661d 120 18 the the DT cord-102966-7vdz661d 120 19 dSIR dsir JJ cord-102966-7vdz661d 120 20 model model NN cord-102966-7vdz661d 120 21 , , , cord-102966-7vdz661d 120 22 such such JJ cord-102966-7vdz661d 120 23 as as IN cord-102966-7vdz661d 120 24 global global JJ cord-102966-7vdz661d 120 25 stability stability NN cord-102966-7vdz661d 120 26 , , , cord-102966-7vdz661d 120 27 convergence convergence NN cord-102966-7vdz661d 120 28 to to IN cord-102966-7vdz661d 120 29 a a DT cord-102966-7vdz661d 120 30 final final JJ cord-102966-7vdz661d 120 31 steady steady JJ cord-102966-7vdz661d 120 32 state state NN cord-102966-7vdz661d 120 33 , , , cord-102966-7vdz661d 120 34 and and CC cord-102966-7vdz661d 120 35 others other NNS cord-102966-7vdz661d 120 36 . . . cord-102966-7vdz661d 121 1 A a DT cord-102966-7vdz661d 121 2 complete complete JJ cord-102966-7vdz661d 121 3 analysis analysis NN cord-102966-7vdz661d 121 4 is be VBZ cord-102966-7vdz661d 121 5 beyond beyond IN cord-102966-7vdz661d 121 6 the the DT cord-102966-7vdz661d 121 7 scope scope NN cord-102966-7vdz661d 121 8 of of IN cord-102966-7vdz661d 121 9 this this DT cord-102966-7vdz661d 121 10 paper paper NN cord-102966-7vdz661d 121 11 . . . cord-102966-7vdz661d 122 1 However however RB cord-102966-7vdz661d 122 2 , , , cord-102966-7vdz661d 122 3 some some DT cord-102966-7vdz661d 122 4 important important JJ cord-102966-7vdz661d 122 5 theoretical theoretical JJ cord-102966-7vdz661d 122 6 properties property NNS cord-102966-7vdz661d 122 7 of of IN cord-102966-7vdz661d 122 8 the the DT cord-102966-7vdz661d 122 9 dSIR dsir JJ cord-102966-7vdz661d 122 10 model model NN cord-102966-7vdz661d 122 11 structure structure NN cord-102966-7vdz661d 122 12 of of IN cord-102966-7vdz661d 122 13 practical practical JJ cord-102966-7vdz661d 122 14 interest interest NN cord-102966-7vdz661d 122 15 are be VBP cord-102966-7vdz661d 122 16 discussed discuss VBN cord-102966-7vdz661d 122 17 next next RB cord-102966-7vdz661d 122 18 , , , cord-102966-7vdz661d 122 19 particularly particularly RB cord-102966-7vdz661d 122 20 in in IN cord-102966-7vdz661d 122 21 comparison comparison NN cord-102966-7vdz661d 122 22 to to IN cord-102966-7vdz661d 122 23 their -PRON- PRP$ cord-102966-7vdz661d 122 24 SIR SIR NNP cord-102966-7vdz661d 122 25 counterparts counterpart NNS cord-102966-7vdz661d 122 26 . . . cord-102966-7vdz661d 123 1 The the DT cord-102966-7vdz661d 123 2 analysis analysis NN cord-102966-7vdz661d 123 3 of of IN cord-102966-7vdz661d 123 4 the the DT cord-102966-7vdz661d 123 5 Padé Padé NNP cord-102966-7vdz661d 123 6 SIR SIR NNP cord-102966-7vdz661d 123 7 model model NN cord-102966-7vdz661d 123 8 follows follow VBZ cord-102966-7vdz661d 123 9 standard standard JJ cord-102966-7vdz661d 123 10 ODE ODE NNP cord-102966-7vdz661d 123 11 analysis analysis NN cord-102966-7vdz661d 123 12 and and CC cord-102966-7vdz661d 123 13 is be VBZ cord-102966-7vdz661d 123 14 presented present VBN cord-102966-7vdz661d 123 15 more more RBR cord-102966-7vdz661d 123 16 briefly briefly NN cord-102966-7vdz661d 123 17 , , , cord-102966-7vdz661d 123 18 except except IN cord-102966-7vdz661d 123 19 when when WRB cord-102966-7vdz661d 123 20 it -PRON- PRP cord-102966-7vdz661d 123 21 has have VBZ cord-102966-7vdz661d 123 22 important important JJ cord-102966-7vdz661d 123 23 implications implication NNS cord-102966-7vdz661d 123 24 for for IN cord-102966-7vdz661d 123 25 either either CC cord-102966-7vdz661d 123 26 theoretical theoretical JJ cord-102966-7vdz661d 123 27 or or CC cord-102966-7vdz661d 123 28 practical practical JJ cord-102966-7vdz661d 123 29 issues issue NNS cord-102966-7vdz661d 123 30 . . . cord-102966-7vdz661d 124 1 Eqn Eqn NNP cord-102966-7vdz661d 124 2 . . . cord-102966-7vdz661d 125 1 ( ( -LRB- cord-102966-7vdz661d 125 2 7 7 LS cord-102966-7vdz661d 125 3 ) ) -RRB- cord-102966-7vdz661d 125 4 can can MD cord-102966-7vdz661d 125 5 be be VB cord-102966-7vdz661d 125 6 used use VBN cord-102966-7vdz661d 125 7 to to TO cord-102966-7vdz661d 125 8 show show VB cord-102966-7vdz661d 125 9 ( ( -LRB- cord-102966-7vdz661d 125 10 Appendix Appendix NNP cord-102966-7vdz661d 125 11 B B NNP cord-102966-7vdz661d 125 12 ) ) -RRB- cord-102966-7vdz661d 125 13 that that IN cord-102966-7vdz661d 125 14 an an DT cord-102966-7vdz661d 125 15 equilibrium equilibrium NN cord-102966-7vdz661d 125 16 point point NN cord-102966-7vdz661d 125 17 ̅ ̅ NFP cord-102966-7vdz661d 125 18 is be VBZ cord-102966-7vdz661d 125 19 stable stable JJ cord-102966-7vdz661d 125 20 and and CC cord-102966-7vdz661d 125 21 an an DT cord-102966-7vdz661d 125 22 epidemic epidemic NN cord-102966-7vdz661d 125 23 outbreak outbreak NN cord-102966-7vdz661d 125 24 does do VBZ cord-102966-7vdz661d 125 25 not not RB cord-102966-7vdz661d 125 26 occur occur VB cord-102966-7vdz661d 125 27 iff iff NN cord-102966-7vdz661d 125 28 Note note VB cord-102966-7vdz661d 125 29 that that IN cord-102966-7vdz661d 125 30 the the DT cord-102966-7vdz661d 125 31 stability stability NN cord-102966-7vdz661d 125 32 upper upper RB cord-102966-7vdz661d 125 33 bound bind VBN cord-102966-7vdz661d 125 34 1/ 1/ CD cord-102966-7vdz661d 125 35 ( ( -LRB- cord-102966-7vdz661d 125 36 ) ) -RRB- cord-102966-7vdz661d 125 37 for for IN cord-102966-7vdz661d 125 38 the the DT cord-102966-7vdz661d 125 39 dSIR dsir JJ cord-102966-7vdz661d 125 40 model model NN cord-102966-7vdz661d 125 41 in in IN cord-102966-7vdz661d 125 42 the the DT cord-102966-7vdz661d 125 43 above above JJ cord-102966-7vdz661d 125 44 eqn eqn NN cord-102966-7vdz661d 125 45 . . . cord-102966-7vdz661d 126 1 ( ( -LRB- cord-102966-7vdz661d 126 2 17 17 CD cord-102966-7vdz661d 126 3 ) ) -RRB- cord-102966-7vdz661d 126 4 coincides coincide VBZ cord-102966-7vdz661d 126 5 with with IN cord-102966-7vdz661d 126 6 the the DT cord-102966-7vdz661d 126 7 well well RB cord-102966-7vdz661d 126 8 known know VBN cord-102966-7vdz661d 126 9 bound bind VBN cord-102966-7vdz661d 126 10 / / SYM cord-102966-7vdz661d 126 11 = = SYM cord-102966-7vdz661d 126 12 1/ 1/ CD cord-102966-7vdz661d 126 13 0 0 NFP cord-102966-7vdz661d 126 14 dictated dictate VBN cord-102966-7vdz661d 126 15 by by IN cord-102966-7vdz661d 126 16 the the DT cord-102966-7vdz661d 126 17 SIR SIR NNP cord-102966-7vdz661d 126 18 model model NN cord-102966-7vdz661d 126 19 under under IN cord-102966-7vdz661d 126 20 the the DT cord-102966-7vdz661d 126 21 widely widely RB cord-102966-7vdz661d 126 22 used use VBN cord-102966-7vdz661d 126 23 correspondence correspondence NN cord-102966-7vdz661d 126 24 The the DT cord-102966-7vdz661d 126 25 same same JJ cord-102966-7vdz661d 126 26 stability stability NN cord-102966-7vdz661d 126 27 bound bind VBN cord-102966-7vdz661d 126 28 can can MD cord-102966-7vdz661d 126 29 be be VB cord-102966-7vdz661d 126 30 derived derive VBN cord-102966-7vdz661d 126 31 for for IN cord-102966-7vdz661d 126 32 the the DT cord-102966-7vdz661d 126 33 Padé Padé NNP cord-102966-7vdz661d 126 34 SIR SIR NNP cord-102966-7vdz661d 126 35 model model NN cord-102966-7vdz661d 126 36 structure structure NN cord-102966-7vdz661d 126 37 using use VBG cord-102966-7vdz661d 126 38 standard standard JJ cord-102966-7vdz661d 126 39 ODE ODE NNP cord-102966-7vdz661d 126 40 analysis analysis NN cord-102966-7vdz661d 126 41 based base VBN cord-102966-7vdz661d 126 42 on on IN cord-102966-7vdz661d 126 43 linearization linearization NN cord-102966-7vdz661d 126 44 around around IN cord-102966-7vdz661d 126 45 an an DT cord-102966-7vdz661d 126 46 equilibrium equilibrium NN cord-102966-7vdz661d 126 47 point point NN cord-102966-7vdz661d 126 48 . . . cord-102966-7vdz661d 127 1 Accepting accept VBG cord-102966-7vdz661d 127 2 for for IN cord-102966-7vdz661d 127 3 now now RB cord-102966-7vdz661d 127 4 without without IN cord-102966-7vdz661d 127 5 proof proof NN cord-102966-7vdz661d 127 6 the the DT cord-102966-7vdz661d 127 7 global global JJ cord-102966-7vdz661d 127 8 stability stability NN cord-102966-7vdz661d 127 9 of of IN cord-102966-7vdz661d 127 10 eqn eqn NN cord-102966-7vdz661d 127 11 . . . cord-102966-7vdz661d 128 1 where where WRB cord-102966-7vdz661d 128 2 0 0 NFP cord-102966-7vdz661d 128 3 ≝ ≝ NN cord-102966-7vdz661d 128 4 and and CC cord-102966-7vdz661d 128 5 is be VBZ cord-102966-7vdz661d 128 6 the the DT cord-102966-7vdz661d 128 7 Lambert Lambert NNP cord-102966-7vdz661d 128 8 function function NN cord-102966-7vdz661d 128 9 14,15 14,15 CD cord-102966-7vdz661d 128 10 of of IN cord-102966-7vdz661d 128 11 order order NN cord-102966-7vdz661d 128 12 0 0 CD cord-102966-7vdz661d 128 13 . . . cord-102966-7vdz661d 129 1 The the DT cord-102966-7vdz661d 129 2 standard standard JJ cord-102966-7vdz661d 129 3 plot plot NN cord-102966-7vdz661d 129 4 for for IN cord-102966-7vdz661d 129 5 ∞ ∞ NNP cord-102966-7vdz661d 129 6 , , , cord-102966-7vdz661d 129 7 equal equal JJ cord-102966-7vdz661d 129 8 to to IN cord-102966-7vdz661d 129 9 the the DT cord-102966-7vdz661d 129 10 total total JJ cord-102966-7vdz661d 129 11 fraction fraction NN cord-102966-7vdz661d 129 12 of of IN cord-102966-7vdz661d 129 13 infected infect VBN cord-102966-7vdz661d 129 14 by by IN cord-102966-7vdz661d 129 15 the the DT cord-102966-7vdz661d 129 16 end end NN cord-102966-7vdz661d 129 17 of of IN cord-102966-7vdz661d 129 18 an an DT cord-102966-7vdz661d 129 19 epidemic epidemic NN cord-102966-7vdz661d 129 20 , , , cord-102966-7vdz661d 129 21 2 2 CD cord-102966-7vdz661d 129 22 is be VBZ cord-102966-7vdz661d 129 23 shown show VBN cord-102966-7vdz661d 129 24 in in IN cord-102966-7vdz661d 129 25 Figure figure NN cord-102966-7vdz661d 129 26 10 10 CD cord-102966-7vdz661d 129 27 for for IN cord-102966-7vdz661d 129 28 completeness completeness NN cord-102966-7vdz661d 129 29 . . . cord-102966-7vdz661d 130 1 Note note VB cord-102966-7vdz661d 130 2 that that IN cord-102966-7vdz661d 130 3 the the DT cord-102966-7vdz661d 130 4 plot plot NN cord-102966-7vdz661d 130 5 is be VBZ cord-102966-7vdz661d 130 6 valid valid JJ cord-102966-7vdz661d 130 7 for for IN cord-102966-7vdz661d 130 8 both both DT cord-102966-7vdz661d 130 9 SIR SIR NNP cord-102966-7vdz661d 130 10 and and CC cord-102966-7vdz661d 130 11 dSIR dsir JJ cord-102966-7vdz661d 130 12 models model NNS cord-102966-7vdz661d 130 13 , , , cord-102966-7vdz661d 130 14 with with IN cord-102966-7vdz661d 130 15 0 0 CD cord-102966-7vdz661d 130 16 = = SYM cord-102966-7vdz661d 130 17 / / SYM cord-102966-7vdz661d 130 18 and and CC cord-102966-7vdz661d 130 19 0 0 CD cord-102966-7vdz661d 130 20 = = SYM cord-102966-7vdz661d 130 21 1/ 1/ CD cord-102966-7vdz661d 130 22 , , , cord-102966-7vdz661d 130 23 respectively respectively RB cord-102966-7vdz661d 130 24 . . . cord-102966-7vdz661d 131 1 Interestingly interestingly RB cord-102966-7vdz661d 131 2 , , , cord-102966-7vdz661d 131 3 while while IN cord-102966-7vdz661d 131 4 use use NN cord-102966-7vdz661d 131 5 of of IN cord-102966-7vdz661d 131 6 the the DT cord-102966-7vdz661d 131 7 Lambert Lambert NNP cord-102966-7vdz661d 131 8 function function NN cord-102966-7vdz661d 131 9 to to TO cord-102966-7vdz661d 131 10 solve solve VB cord-102966-7vdz661d 131 11 problems problem NNS cord-102966-7vdz661d 131 12 such such JJ cord-102966-7vdz661d 131 13 as as IN cord-102966-7vdz661d 131 14 the the DT cord-102966-7vdz661d 131 15 above above JJ cord-102966-7vdz661d 131 16 was be VBD cord-102966-7vdz661d 131 17 pointed point VBN cord-102966-7vdz661d 131 18 out out RP cord-102966-7vdz661d 131 19 as as RB cord-102966-7vdz661d 131 20 early early RB cord-102966-7vdz661d 131 21 as as IN cord-102966-7vdz661d 131 22 1996 1996 CD cord-102966-7vdz661d 131 23 , , , cord-102966-7vdz661d 131 24 14 14 CD cord-102966-7vdz661d 131 25 it -PRON- PRP cord-102966-7vdz661d 131 26 may may MD cord-102966-7vdz661d 131 27 have have VB cord-102966-7vdz661d 131 28 escaped escape VBN cord-102966-7vdz661d 131 29 the the DT cord-102966-7vdz661d 131 30 attention attention NN cord-102966-7vdz661d 131 31 of of IN cord-102966-7vdz661d 131 32 most most JJS cord-102966-7vdz661d 131 33 literature literature NN cord-102966-7vdz661d 131 34 in in IN cord-102966-7vdz661d 131 35 this this DT cord-102966-7vdz661d 131 36 field field NN cord-102966-7vdz661d 131 37 . . . cord-102966-7vdz661d 132 1 2 2 LS cord-102966-7vdz661d 133 1 The the DT cord-102966-7vdz661d 133 2 Lambert Lambert NNP cord-102966-7vdz661d 133 3 function function NN cord-102966-7vdz661d 133 4 in in IN cord-102966-7vdz661d 133 5 its -PRON- PRP$ cord-102966-7vdz661d 133 6 various various JJ cord-102966-7vdz661d 133 7 forms form NNS cord-102966-7vdz661d 133 8 will will MD cord-102966-7vdz661d 133 9 turn turn VB cord-102966-7vdz661d 133 10 up up RP cord-102966-7vdz661d 133 11 in in IN cord-102966-7vdz661d 133 12 a a DT cord-102966-7vdz661d 133 13 number number NN cord-102966-7vdz661d 133 14 of of IN cord-102966-7vdz661d 133 15 results result NNS cord-102966-7vdz661d 133 16 below below RB cord-102966-7vdz661d 133 17 . . . cord-102966-7vdz661d 134 1 It -PRON- PRP cord-102966-7vdz661d 134 2 should should MD cord-102966-7vdz661d 134 3 also also RB cord-102966-7vdz661d 134 4 be be VB cord-102966-7vdz661d 134 5 noted note VBN cord-102966-7vdz661d 134 6 that that IN cord-102966-7vdz661d 134 7 eqns eqns NNP cord-102966-7vdz661d 134 8 . . . cord-102966-7vdz661d 135 1 ( ( -LRB- cord-102966-7vdz661d 135 2 19 19 CD cord-102966-7vdz661d 135 3 ) ) -RRB- cord-102966-7vdz661d 135 4 and and CC cord-102966-7vdz661d 135 5 ( ( -LRB- cord-102966-7vdz661d 135 6 20 20 CD cord-102966-7vdz661d 135 7 ) ) -RRB- cord-102966-7vdz661d 135 8 are be VBP cord-102966-7vdz661d 135 9 the the DT cord-102966-7vdz661d 135 10 same same JJ cord-102966-7vdz661d 135 11 for for IN cord-102966-7vdz661d 135 12 the the DT cord-102966-7vdz661d 135 13 SIR SIR NNP cord-102966-7vdz661d 135 14 and and CC cord-102966-7vdz661d 135 15 Padé Padé NNP cord-102966-7vdz661d 135 16 SIR SIR NNP cord-102966-7vdz661d 135 17 model model NN cord-102966-7vdz661d 135 18 ( ( -LRB- cord-102966-7vdz661d 135 19 Appendix Appendix NNP cord-102966-7vdz661d 135 20 C C NNP cord-102966-7vdz661d 135 21 ) ) -RRB- cord-102966-7vdz661d 135 22 under under IN cord-102966-7vdz661d 135 23 the the DT cord-102966-7vdz661d 135 24 correspondence correspondence NN cord-102966-7vdz661d 135 25 between between IN cord-102966-7vdz661d 135 26 and and CC cord-102966-7vdz661d 135 27 in in IN cord-102966-7vdz661d 135 28 eqn eqn NN cord-102966-7vdz661d 135 29 . . . cord-102966-7vdz661d 136 1 ( ( -LRB- cord-102966-7vdz661d 136 2 18 18 CD cord-102966-7vdz661d 136 3 ) ) -RRB- cord-102966-7vdz661d 136 4 . . . cord-102966-7vdz661d 137 1 For for IN cord-102966-7vdz661d 137 2 the the DT cord-102966-7vdz661d 137 3 initial initial JJ cord-102966-7vdz661d 137 4 part part NN cord-102966-7vdz661d 137 5 of of IN cord-102966-7vdz661d 137 6 a a DT cord-102966-7vdz661d 137 7 spreading spread VBG cord-102966-7vdz661d 137 8 epidemic epidemic NN cord-102966-7vdz661d 137 9 , , , cord-102966-7vdz661d 137 10 starting start VBG cord-102966-7vdz661d 137 11 from from IN cord-102966-7vdz661d 137 12 a a DT cord-102966-7vdz661d 137 13 perturbation perturbation NN cord-102966-7vdz661d 137 14 of of IN cord-102966-7vdz661d 137 15 the the DT cord-102966-7vdz661d 137 16 steady steady JJ cord-102966-7vdz661d 137 17 state state NN cord-102966-7vdz661d 137 18 ( ( -LRB- cord-102966-7vdz661d 137 19 , , , cord-102966-7vdz661d 137 20 , , , cord-102966-7vdz661d 137 21 ) ) -RRB- cord-102966-7vdz661d 137 22 = = NFP cord-102966-7vdz661d 137 23 ( ( -LRB- cord-102966-7vdz661d 137 24 ̅ ̅ UH cord-102966-7vdz661d 137 25 , , , cord-102966-7vdz661d 137 26 0,1 0,1 LS cord-102966-7vdz661d 137 27 − − NNP cord-102966-7vdz661d 137 28 ̅ ̅ UH cord-102966-7vdz661d 137 29 ) ) -RRB- cord-102966-7vdz661d 137 30 as as IN cord-102966-7vdz661d 137 31 ( ( -LRB- cord-102966-7vdz661d 137 32 < < XX cord-102966-7vdz661d 137 33 0 0 NFP cord-102966-7vdz661d 137 34 ) ) -RRB- cord-102966-7vdz661d 137 35 = = SYM cord-102966-7vdz661d 137 36 0 0 CD cord-102966-7vdz661d 137 37 , , , cord-102966-7vdz661d 137 38 ( ( -LRB- cord-102966-7vdz661d 137 39 0 0 NFP cord-102966-7vdz661d 137 40 ) ) -RRB- cord-102966-7vdz661d 137 41 = = NFP cord-102966-7vdz661d 138 1 , , , cord-102966-7vdz661d 138 2 ̅ ̅ UH cord-102966-7vdz661d 138 3 ≝ ≝ XX cord-102966-7vdz661d 138 4 ̅ ̅ JJS cord-102966-7vdz661d 138 5 0 0 NFP cord-102966-7vdz661d 138 6 > > XX cord-102966-7vdz661d 139 1 1 1 LS cord-102966-7vdz661d 140 1 it -PRON- PRP cord-102966-7vdz661d 140 2 can can MD cord-102966-7vdz661d 140 3 be be VB cord-102966-7vdz661d 140 4 shown show VBN cord-102966-7vdz661d 140 5 ( ( -LRB- cord-102966-7vdz661d 140 6 Appendix Appendix NNP cord-102966-7vdz661d 140 7 D D NNP cord-102966-7vdz661d 140 8 ) ) -RRB- cord-102966-7vdz661d 140 9 that that IN cord-102966-7vdz661d 140 10 the the DT cord-102966-7vdz661d 140 11 infectious infectious JJ cord-102966-7vdz661d 140 12 fraction fraction NN cord-102966-7vdz661d 140 13 initially initially RB cord-102966-7vdz661d 140 14 grows grow VBZ cord-102966-7vdz661d 140 15 approximately approximately RB cord-102966-7vdz661d 140 16 at at IN cord-102966-7vdz661d 140 17 an an DT cord-102966-7vdz661d 140 18 exponential exponential JJ cord-102966-7vdz661d 140 19 rate rate NN cord-102966-7vdz661d 140 20 as as IN cord-102966-7vdz661d 140 21 . . . cord-102966-7vdz661d 141 1 CC CC NNP cord-102966-7vdz661d 141 2 - - HYPH cord-102966-7vdz661d 141 3 BY BY NNP cord-102966-7vdz661d 141 4 - - HYPH cord-102966-7vdz661d 141 5 NC NC NNP cord-102966-7vdz661d 141 6 - - HYPH cord-102966-7vdz661d 141 7 ND ND NNP cord-102966-7vdz661d 141 8 4.0 4.0 CD cord-102966-7vdz661d 141 9 International international JJ cord-102966-7vdz661d 141 10 license license NN cord-102966-7vdz661d 142 1 It -PRON- PRP cord-102966-7vdz661d 142 2 is be VBZ cord-102966-7vdz661d 142 3 made make VBN cord-102966-7vdz661d 142 4 available available JJ cord-102966-7vdz661d 142 5 under under IN cord-102966-7vdz661d 142 6 a a DT cord-102966-7vdz661d 143 1 is be VBZ cord-102966-7vdz661d 143 2 the the DT cord-102966-7vdz661d 143 3 author author NN cord-102966-7vdz661d 143 4 / / SYM cord-102966-7vdz661d 143 5 funder funder NN cord-102966-7vdz661d 143 6 , , , cord-102966-7vdz661d 143 7 who who WP cord-102966-7vdz661d 143 8 has have VBZ cord-102966-7vdz661d 143 9 granted grant VBN cord-102966-7vdz661d 143 10 medRxiv medRxiv NNS cord-102966-7vdz661d 143 11 a a DT cord-102966-7vdz661d 143 12 license license NN cord-102966-7vdz661d 143 13 to to TO cord-102966-7vdz661d 143 14 display display VB cord-102966-7vdz661d 143 15 the the DT cord-102966-7vdz661d 143 16 preprint preprint NN cord-102966-7vdz661d 143 17 in in IN cord-102966-7vdz661d 143 18 perpetuity perpetuity NN cord-102966-7vdz661d 143 19 . . . cord-102966-7vdz661d 144 1 The the DT cord-102966-7vdz661d 144 2 copyright copyright NN cord-102966-7vdz661d 144 3 holder holder NN cord-102966-7vdz661d 144 4 for for IN cord-102966-7vdz661d 144 5 this this DT cord-102966-7vdz661d 144 6 preprint preprint NN cord-102966-7vdz661d 144 7 this this DT cord-102966-7vdz661d 144 8 version version NN cord-102966-7vdz661d 144 9 posted post VBN cord-102966-7vdz661d 144 10 May May NNP cord-102966-7vdz661d 144 11 1 1 CD cord-102966-7vdz661d 144 12 , , , cord-102966-7vdz661d 144 13 2020 2020 CD cord-102966-7vdz661d 144 14 . . . cord-102966-7vdz661d 144 15 _SP cord-102966-7vdz661d 145 1 where where WRB cord-102966-7vdz661d 145 2 Δ Δ NNP cord-102966-7vdz661d 145 3 ≝ ≝ NNP cord-102966-7vdz661d 145 4 − − NNP cord-102966-7vdz661d 145 5 ̅ ̅ UH cord-102966-7vdz661d 145 6 and and CC cord-102966-7vdz661d 145 7 the the DT cord-102966-7vdz661d 145 8 constants constant NNS cord-102966-7vdz661d 145 9 , , , cord-102966-7vdz661d 145 10 are be VBP cord-102966-7vdz661d 145 11 in in IN cord-102966-7vdz661d 145 12 terms term NNS cord-102966-7vdz661d 145 13 of of IN cord-102966-7vdz661d 145 14 0 0 CD cord-102966-7vdz661d 145 15 ≝ ≝ . cord-102966-7vdz661d 146 1 ( ( -LRB- cord-102966-7vdz661d 146 2 Appendix Appendix NNP cord-102966-7vdz661d 146 3 D D NNP cord-102966-7vdz661d 146 4 ) ) -RRB- cord-102966-7vdz661d 146 5 with with IN cord-102966-7vdz661d 146 6 as as IN cord-102966-7vdz661d 146 7 shown show VBN cord-102966-7vdz661d 146 8 in in IN cord-102966-7vdz661d 146 9 Figure figure NN cord-102966-7vdz661d 146 10 11 11 CD cord-102966-7vdz661d 146 11 . . . cord-102966-7vdz661d 147 1 Similarly similarly RB cord-102966-7vdz661d 147 2 , , , cord-102966-7vdz661d 147 3 the the DT cord-102966-7vdz661d 147 4 initial initial JJ cord-102966-7vdz661d 147 5 exponential exponential JJ cord-102966-7vdz661d 147 6 rate rate NN cord-102966-7vdz661d 147 7 of of IN cord-102966-7vdz661d 147 8 the the DT cord-102966-7vdz661d 147 9 Padé Padé NNP cord-102966-7vdz661d 147 10 SIR SIR NNP cord-102966-7vdz661d 147 11 model model NN cord-102966-7vdz661d 147 12 is be VBZ cord-102966-7vdz661d 147 13 given give VBN cord-102966-7vdz661d 147 14 by by IN cord-102966-7vdz661d 147 15 where where WRB cord-102966-7vdz661d 147 16 0 0 CD cord-102966-7vdz661d 147 17 = = SYM cord-102966-7vdz661d 147 18 / / SYM cord-102966-7vdz661d 147 19 , , , cord-102966-7vdz661d 147 20 and and CC cord-102966-7vdz661d 147 21 for for IN cord-102966-7vdz661d 147 22 the the DT cord-102966-7vdz661d 147 23 standard standard JJ cord-102966-7vdz661d 147 24 SIR SIR NNP cord-102966-7vdz661d 147 25 model model NN cord-102966-7vdz661d 147 26 , , , cord-102966-7vdz661d 147 27 the the DT cord-102966-7vdz661d 147 28 exponential exponential JJ cord-102966-7vdz661d 147 29 rate rate NN cord-102966-7vdz661d 147 30 is be VBZ cord-102966-7vdz661d 147 31 where where WRB cord-102966-7vdz661d 147 32 0 0 CD cord-102966-7vdz661d 147 33 = = SYM cord-102966-7vdz661d 147 34 / / SYM cord-102966-7vdz661d 147 35 , , , cord-102966-7vdz661d 147 36 shown show VBN cord-102966-7vdz661d 147 37 in in IN cord-102966-7vdz661d 147 38 Figure figure NN cord-102966-7vdz661d 147 39 11 11 CD cord-102966-7vdz661d 147 40 as as RB cord-102966-7vdz661d 147 41 well well RB cord-102966-7vdz661d 147 42 . . . cord-102966-7vdz661d 148 1 This this DT cord-102966-7vdz661d 148 2 has have VBZ cord-102966-7vdz661d 148 3 immediate immediate JJ cord-102966-7vdz661d 148 4 implications implication NNS cord-102966-7vdz661d 148 5 for for IN cord-102966-7vdz661d 148 6 the the DT cord-102966-7vdz661d 148 7 early early JJ cord-102966-7vdz661d 148 8 rate rate NN cord-102966-7vdz661d 148 9 of of IN cord-102966-7vdz661d 148 10 rise rise NN cord-102966-7vdz661d 148 11 of of IN cord-102966-7vdz661d 148 12 the the DT cord-102966-7vdz661d 148 13 infectious infectious JJ cord-102966-7vdz661d 148 14 fraction fraction NN cord-102966-7vdz661d 148 15 to to IN cord-102966-7vdz661d 148 16 its -PRON- PRP$ cord-102966-7vdz661d 148 17 peak peak NN cord-102966-7vdz661d 148 18 , , , cord-102966-7vdz661d 148 19 * * NFP cord-102966-7vdz661d 148 20 , , , cord-102966-7vdz661d 148 21 as as IN cord-102966-7vdz661d 148 22 illustrated illustrate VBN cord-102966-7vdz661d 148 23 in in IN cord-102966-7vdz661d 148 24 Figure Figure NNP cord-102966-7vdz661d 148 25 _SP cord-102966-7vdz661d 148 26 12 12 CD cord-102966-7vdz661d 148 27 . . . cord-102966-7vdz661d 149 1 Note note VB cord-102966-7vdz661d 149 2 that that IN cord-102966-7vdz661d 149 3 while while IN cord-102966-7vdz661d 149 4 the the DT cord-102966-7vdz661d 149 5 initial initial JJ cord-102966-7vdz661d 149 6 SIR SIR NNP cord-102966-7vdz661d 149 7 rate rate NN cord-102966-7vdz661d 149 8 is be VBZ cord-102966-7vdz661d 149 9 half half NN cord-102966-7vdz661d 149 10 of of IN cord-102966-7vdz661d 149 11 the the DT cord-102966-7vdz661d 149 12 Padé Padé NNP cord-102966-7vdz661d 149 13 SIR SIR NNP cord-102966-7vdz661d 149 14 rate rate NN cord-102966-7vdz661d 149 15 and and CC cord-102966-7vdz661d 149 16 about about IN cord-102966-7vdz661d 149 17 half half NN cord-102966-7vdz661d 149 18 of of IN cord-102966-7vdz661d 149 19 the the DT cord-102966-7vdz661d 149 20 dSIR dsir JJ cord-102966-7vdz661d 149 21 rate rate NN cord-102966-7vdz661d 149 22 , , , cord-102966-7vdz661d 149 23 all all DT cord-102966-7vdz661d 149 24 three three CD cord-102966-7vdz661d 149 25 models model NNS cord-102966-7vdz661d 149 26 eventually eventually RB cord-102966-7vdz661d 149 27 reach reach VBP cord-102966-7vdz661d 149 28 the the DT cord-102966-7vdz661d 149 29 exact exact JJ cord-102966-7vdz661d 149 30 same same JJ cord-102966-7vdz661d 149 31 steady steady JJ cord-102966-7vdz661d 149 32 - - HYPH cord-102966-7vdz661d 149 33 state state NN cord-102966-7vdz661d 149 34 values value NNS cord-102966-7vdz661d 149 35 , , , cord-102966-7vdz661d 149 36 as as IN cord-102966-7vdz661d 149 37 captured capture VBN cord-102966-7vdz661d 149 38 by by IN cord-102966-7vdz661d 149 39 eqns eqns NNP cord-102966-7vdz661d 149 40 . . . cord-102966-7vdz661d 150 1 ( ( -LRB- cord-102966-7vdz661d 150 2 19 19 CD cord-102966-7vdz661d 150 3 ) ) -RRB- cord-102966-7vdz661d 150 4 and and CC cord-102966-7vdz661d 150 5 ( ( -LRB- cord-102966-7vdz661d 150 6 20 20 CD cord-102966-7vdz661d 150 7 ) ) -RRB- cord-102966-7vdz661d 150 8 . . . cord-102966-7vdz661d 151 1 While while IN cord-102966-7vdz661d 151 2 it -PRON- PRP cord-102966-7vdz661d 151 3 is be VBZ cord-102966-7vdz661d 151 4 not not RB cord-102966-7vdz661d 151 5 obvious obvious JJ cord-102966-7vdz661d 151 6 to to IN cord-102966-7vdz661d 151 7 the the DT cord-102966-7vdz661d 151 8 author author NN cord-102966-7vdz661d 151 9 whether whether IN cord-102966-7vdz661d 151 10 the the DT cord-102966-7vdz661d 151 11 peak peak NN cord-102966-7vdz661d 151 12 * * NFP cord-102966-7vdz661d 151 13 can can MD cord-102966-7vdz661d 151 14 be be VB cord-102966-7vdz661d 151 15 easily easily RB cord-102966-7vdz661d 151 16 obtained obtain VBN cord-102966-7vdz661d 151 17 for for IN cord-102966-7vdz661d 151 18 the the DT cord-102966-7vdz661d 151 19 dSIR dsir JJ cord-102966-7vdz661d 151 20 model model NN cord-102966-7vdz661d 151 21 , , , cord-102966-7vdz661d 151 22 a a DT cord-102966-7vdz661d 151 23 good good JJ cord-102966-7vdz661d 151 24 approximation approximation NN cord-102966-7vdz661d 151 25 can can MD cord-102966-7vdz661d 151 26 be be VB cord-102966-7vdz661d 151 27 obtained obtain VBN cord-102966-7vdz661d 151 28 ( ( -LRB- cord-102966-7vdz661d 151 29 Appendix Appendix NNP cord-102966-7vdz661d 151 30 E E NNP cord-102966-7vdz661d 151 31 ) ) -RRB- cord-102966-7vdz661d 151 32 through through IN cord-102966-7vdz661d 151 33 the the DT cord-102966-7vdz661d 151 34 Padé Padé NNP cord-102966-7vdz661d 151 35 SIR SIR NNP cord-102966-7vdz661d 151 36 model model NN cord-102966-7vdz661d 151 37 , , , cord-102966-7vdz661d 151 38 as as IN cord-102966-7vdz661d 152 1 * * NFP cord-102966-7vdz661d 152 2 = = SYM cord-102966-7vdz661d 152 3 1 1 CD cord-102966-7vdz661d 152 4 , , , cord-102966-7vdz661d 152 5 * * NFP cord-102966-7vdz661d 152 6 = = SYM cord-102966-7vdz661d 152 7 2 2 CD cord-102966-7vdz661d 152 8 � � . cord-102966-7vdz661d 153 1 −1 −1 NNP cord-102966-7vdz661d 153 2 ln ln NNP cord-102966-7vdz661d 153 3 ( ( -LRB- cord-102966-7vdz661d 153 4 ) ) -RRB- cord-102966-7vdz661d 153 5 − − NN cord-102966-7vdz661d 153 6 1 1 CD cord-102966-7vdz661d 154 1 + + CC cord-102966-7vdz661d 155 1 1 1 LS cord-102966-7vdz661d 155 2 � � CD cord-102966-7vdz661d 156 1 ( ( -LRB- cord-102966-7vdz661d 156 2 25 25 CD cord-102966-7vdz661d 156 3 ) ) -RRB- cord-102966-7vdz661d 156 4 Note note VB cord-102966-7vdz661d 156 5 that that IN cord-102966-7vdz661d 156 6 the the DT cord-102966-7vdz661d 156 7 above above JJ cord-102966-7vdz661d 156 8 * * NFP cord-102966-7vdz661d 156 9 , , , cord-102966-7vdz661d 156 10 exact exact JJ cord-102966-7vdz661d 156 11 for for IN cord-102966-7vdz661d 156 12 the the DT cord-102966-7vdz661d 156 13 first first JJ cord-102966-7vdz661d 156 14 - - HYPH cord-102966-7vdz661d 156 15 order order NN cord-102966-7vdz661d 156 16 Padé Padé NNP cord-102966-7vdz661d 156 17 SIR SIR NNP cord-102966-7vdz661d 156 18 model model NN cord-102966-7vdz661d 156 19 and and CC cord-102966-7vdz661d 156 20 approximate approximate JJ cord-102966-7vdz661d 156 21 for for IN cord-102966-7vdz661d 156 22 the the DT cord-102966-7vdz661d 156 23 second second JJ cord-102966-7vdz661d 156 24 - - HYPH cord-102966-7vdz661d 156 25 order order NN cord-102966-7vdz661d 156 26 Padé Padé NNP cord-102966-7vdz661d 156 27 SIR SIR NNP cord-102966-7vdz661d 156 28 and and CC cord-102966-7vdz661d 156 29 dSIR dsir JJ cord-102966-7vdz661d 156 30 models model NNS cord-102966-7vdz661d 156 31 , , , cord-102966-7vdz661d 156 32 is be VBZ cord-102966-7vdz661d 156 33 double double PDT cord-102966-7vdz661d 156 34 the the DT cord-102966-7vdz661d 157 1 * * NFP cord-102966-7vdz661d 157 2 of of IN cord-102966-7vdz661d 157 3 the the DT cord-102966-7vdz661d 157 4 standard standard JJ cord-102966-7vdz661d 157 5 SIR SIR NNP cord-102966-7vdz661d 157 6 model model NN cord-102966-7vdz661d 157 7 , , , cord-102966-7vdz661d 157 8 as as IN cord-102966-7vdz661d 157 9 confirmed confirm VBN cord-102966-7vdz661d 157 10 in in IN cord-102966-7vdz661d 157 11 Figure Figure NNP cord-102966-7vdz661d 157 12 8 8 CD cord-102966-7vdz661d 157 13 . . . cord-102966-7vdz661d 158 1 Once once RB cord-102966-7vdz661d 158 2 more more JJR cord-102966-7vdz661d 158 3 , , , cord-102966-7vdz661d 158 4 there there EX cord-102966-7vdz661d 158 5 are be VBP cord-102966-7vdz661d 158 6 obvious obvious JJ cord-102966-7vdz661d 158 7 practical practical JJ cord-102966-7vdz661d 158 8 implications implication NNS cord-102966-7vdz661d 158 9 from from IN cord-102966-7vdz661d 158 10 this this DT cord-102966-7vdz661d 158 11 discrepancy discrepancy NN cord-102966-7vdz661d 158 12 . . . cord-102966-7vdz661d 159 1 Note note VB cord-102966-7vdz661d 159 2 also also RB cord-102966-7vdz661d 159 3 that that IN cord-102966-7vdz661d 159 4 in in IN cord-102966-7vdz661d 159 5 case case NN cord-102966-7vdz661d 159 6 an an DT cord-102966-7vdz661d 159 7 upper upper JJ cord-102966-7vdz661d 159 8 bound bound NN cord-102966-7vdz661d 159 9 is be VBZ cord-102966-7vdz661d 159 10 placed place VBN cord-102966-7vdz661d 159 11 on on IN cord-102966-7vdz661d 159 12 * * NFP cord-102966-7vdz661d 159 13 , , , cord-102966-7vdz661d 159 14 to to TO cord-102966-7vdz661d 159 15 avoid avoid VB cord-102966-7vdz661d 159 16 overwhelming overwhelming JJ cord-102966-7vdz661d 159 17 hospitalization hospitalization NN cord-102966-7vdz661d 159 18 facilities facility NNS cord-102966-7vdz661d 159 19 during during IN cord-102966-7vdz661d 159 20 an an DT cord-102966-7vdz661d 159 21 epidemic epidemic NN cord-102966-7vdz661d 159 22 , , , cord-102966-7vdz661d 159 23 eqn eqn NN cord-102966-7vdz661d 159 24 . . . cord-102966-7vdz661d 160 1 ( ( -LRB- cord-102966-7vdz661d 160 2 25 25 CD cord-102966-7vdz661d 160 3 ) ) -RRB- cord-102966-7vdz661d 160 4 has have VBZ cord-102966-7vdz661d 160 5 an an DT cord-102966-7vdz661d 160 6 explicit explicit JJ cord-102966-7vdz661d 160 7 solution solution NN cord-102966-7vdz661d 160 8 for for IN cord-102966-7vdz661d 160 9 the the DT cord-102966-7vdz661d 160 10 corresponding corresponding JJ cord-102966-7vdz661d 160 11 maximum maximum JJ cord-102966-7vdz661d 160 12 0 0 CD cord-102966-7vdz661d 160 13 ≝ ≝ NFP cord-102966-7vdz661d 160 14 as as IN cord-102966-7vdz661d 160 15 For for IN cord-102966-7vdz661d 160 16 comparison comparison NN cord-102966-7vdz661d 160 17 , , , cord-102966-7vdz661d 160 18 the the DT cord-102966-7vdz661d 160 19 standard standard JJ cord-102966-7vdz661d 160 20 SIR SIR NNP cord-102966-7vdz661d 160 21 model model NN cord-102966-7vdz661d 160 22 yields yield NNS cord-102966-7vdz661d 161 1 The the DT cord-102966-7vdz661d 161 2 values value NNS cord-102966-7vdz661d 161 3 of of IN cord-102966-7vdz661d 161 4 0 0 CD cord-102966-7vdz661d 161 5 indicated indicate VBN cord-102966-7vdz661d 161 6 by by IN cord-102966-7vdz661d 161 7 eqns eqn NNS cord-102966-7vdz661d 161 8 . . . cord-102966-7vdz661d 162 1 ( ( -LRB- cord-102966-7vdz661d 162 2 26 26 CD cord-102966-7vdz661d 162 3 ) ) -RRB- cord-102966-7vdz661d 162 4 and and CC cord-102966-7vdz661d 162 5 ( ( -LRB- cord-102966-7vdz661d 162 6 27 27 CD cord-102966-7vdz661d 162 7 ) ) -RRB- cord-102966-7vdz661d 162 8 , , , cord-102966-7vdz661d 162 9 with with IN cord-102966-7vdz661d 162 10 corresponding corresponding JJ cord-102966-7vdz661d 162 11 definitions definition NNS cord-102966-7vdz661d 162 12 , , , cord-102966-7vdz661d 162 13 are be VBP cord-102966-7vdz661d 162 14 shown show VBN cord-102966-7vdz661d 162 15 in in IN cord-102966-7vdz661d 162 16 Figure Figure NNP cord-102966-7vdz661d 162 17 13 13 CD cord-102966-7vdz661d 162 18 . . . cord-102966-7vdz661d 163 1 It -PRON- PRP cord-102966-7vdz661d 163 2 is be VBZ cord-102966-7vdz661d 163 3 evident evident JJ cord-102966-7vdz661d 163 4 that that IN cord-102966-7vdz661d 163 5 the the DT cord-102966-7vdz661d 163 6 Padé Padé NNP cord-102966-7vdz661d 163 7 SIR SIR NNP cord-102966-7vdz661d 163 8 model model NN cord-102966-7vdz661d 163 9 places place NNS cord-102966-7vdz661d 163 10 twice twice RB cord-102966-7vdz661d 163 11 as as RB cord-102966-7vdz661d 163 12 tight tight JJ cord-102966-7vdz661d 163 13 a a DT cord-102966-7vdz661d 163 14 restriction restriction NN cord-102966-7vdz661d 163 15 on on IN cord-102966-7vdz661d 163 16 0 0 NFP cord-102966-7vdz661d 163 17 as as IN cord-102966-7vdz661d 163 18 the the DT cord-102966-7vdz661d 163 19 standard standard JJ cord-102966-7vdz661d 163 20 SIR SIR NNP cord-102966-7vdz661d 163 21 model model NN cord-102966-7vdz661d 163 22 , , , cord-102966-7vdz661d 163 23 if if IN cord-102966-7vdz661d 163 24 is be VBZ cord-102966-7vdz661d 163 25 not not RB cord-102966-7vdz661d 163 26 to to TO cord-102966-7vdz661d 163 27 exceed exceed VB cord-102966-7vdz661d 163 28 the the DT cord-102966-7vdz661d 163 29 * * NFP cord-102966-7vdz661d 163 30 value value NN cord-102966-7vdz661d 163 31 . . . cord-102966-7vdz661d 163 32 _SP cord-102966-7vdz661d 164 1 The the DT cord-102966-7vdz661d 164 2 dSIR dsir JJ cord-102966-7vdz661d 164 3 model model NN cord-102966-7vdz661d 164 4 structure structure NN cord-102966-7vdz661d 164 5 developed develop VBN cord-102966-7vdz661d 164 6 in in IN cord-102966-7vdz661d 164 7 Figure figure NN cord-102966-7vdz661d 164 8 3 3 CD cord-102966-7vdz661d 164 9 can can MD cord-102966-7vdz661d 164 10 be be VB cord-102966-7vdz661d 164 11 easily easily RB cord-102966-7vdz661d 164 12 extended extend VBN cord-102966-7vdz661d 164 13 to to TO cord-102966-7vdz661d 164 14 include include VB cord-102966-7vdz661d 164 15 additional additional JJ cord-102966-7vdz661d 164 16 compartments compartment NNS cord-102966-7vdz661d 164 17 . . . cord-102966-7vdz661d 165 1 In in IN cord-102966-7vdz661d 165 2 fact fact NN cord-102966-7vdz661d 165 3 , , , cord-102966-7vdz661d 165 4 practically practically RB cord-102966-7vdz661d 165 5 all all DT cord-102966-7vdz661d 165 6 population population NN cord-102966-7vdz661d 165 7 models model NNS cord-102966-7vdz661d 165 8 of of IN cord-102966-7vdz661d 165 9 infections infection NNS cord-102966-7vdz661d 165 10 developed develop VBN cord-102966-7vdz661d 165 11 to to IN cord-102966-7vdz661d 165 12 date date NN cord-102966-7vdz661d 165 13 using use VBG cord-102966-7vdz661d 165 14 the the DT cord-102966-7vdz661d 165 15 concept concept NN cord-102966-7vdz661d 165 16 of of IN cord-102966-7vdz661d 165 17 exchange exchange NN cord-102966-7vdz661d 165 18 between between IN cord-102966-7vdz661d 165 19 compartments compartment NNS cord-102966-7vdz661d 165 20 3 3 CD cord-102966-7vdz661d 165 21 can can MD cord-102966-7vdz661d 165 22 be be VB cord-102966-7vdz661d 165 23 immediately immediately RB cord-102966-7vdz661d 165 24 translated translate VBN cord-102966-7vdz661d 165 25 ( ( -LRB- cord-102966-7vdz661d 165 26 a a LS cord-102966-7vdz661d 165 27 ) ) -RRB- cord-102966-7vdz661d 165 28 from from IN cord-102966-7vdz661d 165 29 ODEs ode NNS cord-102966-7vdz661d 165 30 to to IN cord-102966-7vdz661d 165 31 DDEs dde NNS cord-102966-7vdz661d 165 32 through through IN cord-102966-7vdz661d 165 33 replacement replacement NN cord-102966-7vdz661d 165 34 of of IN cord-102966-7vdz661d 165 35 compartment compartment NN cord-102966-7vdz661d 165 36 drain drain NN cord-102966-7vdz661d 165 37 rates rate NNS cord-102966-7vdz661d 165 38 proportional proportional JJ cord-102966-7vdz661d 165 39 to to IN cord-102966-7vdz661d 165 40 the the DT cord-102966-7vdz661d 165 41 drained drain VBN cord-102966-7vdz661d 165 42 quantity quantity NN cord-102966-7vdz661d 165 43 by by IN cord-102966-7vdz661d 165 44 drainage drainage NN cord-102966-7vdz661d 165 45 of of IN cord-102966-7vdz661d 165 46 amounts amount NNS cord-102966-7vdz661d 165 47 that that WDT cord-102966-7vdz661d 165 48 have have VBP cord-102966-7vdz661d 165 49 resided reside VBN cord-102966-7vdz661d 165 50 for for IN cord-102966-7vdz661d 165 51 a a DT cord-102966-7vdz661d 165 52 certain certain JJ cord-102966-7vdz661d 165 53 time time NN cord-102966-7vdz661d 165 54 , , , cord-102966-7vdz661d 165 55 , , , cord-102966-7vdz661d 165 56 in in IN cord-102966-7vdz661d 165 57 that that DT cord-102966-7vdz661d 165 58 compartment compartment NN cord-102966-7vdz661d 165 59 , , , cord-102966-7vdz661d 165 60 or or CC cord-102966-7vdz661d 165 61 ( ( -LRB- cord-102966-7vdz661d 165 62 b b NN cord-102966-7vdz661d 165 63 ) ) -RRB- cord-102966-7vdz661d 165 64 from from IN cord-102966-7vdz661d 165 65 ODEs ode NNS cord-102966-7vdz661d 165 66 to to IN cord-102966-7vdz661d 165 67 Padé padé JJ cord-102966-7vdz661d 165 68 approximations approximation NNS cord-102966-7vdz661d 165 69 that that WDT cord-102966-7vdz661d 165 70 maintain maintain VBP cord-102966-7vdz661d 165 71 the the DT cord-102966-7vdz661d 165 72 ODE ODE NNP cord-102966-7vdz661d 165 73 structure structure NN cord-102966-7vdz661d 165 74 but but CC cord-102966-7vdz661d 165 75 are be VBP cord-102966-7vdz661d 165 76 more more RBR cord-102966-7vdz661d 165 77 realistic realistic JJ cord-102966-7vdz661d 165 78 . . . cord-102966-7vdz661d 166 1 We -PRON- PRP cord-102966-7vdz661d 166 2 illustrate illustrate VBP cord-102966-7vdz661d 166 3 these these DT cord-102966-7vdz661d 166 4 ideas idea NNS cord-102966-7vdz661d 166 5 on on IN cord-102966-7vdz661d 166 6 . . . cord-102966-7vdz661d 167 1 CC CC NNP cord-102966-7vdz661d 167 2 - - HYPH cord-102966-7vdz661d 167 3 BY BY NNP cord-102966-7vdz661d 167 4 - - HYPH cord-102966-7vdz661d 167 5 NC NC NNP cord-102966-7vdz661d 167 6 - - HYPH cord-102966-7vdz661d 167 7 ND ND NNP cord-102966-7vdz661d 167 8 4.0 4.0 CD cord-102966-7vdz661d 167 9 International international JJ cord-102966-7vdz661d 167 10 license license NN cord-102966-7vdz661d 168 1 It -PRON- PRP cord-102966-7vdz661d 168 2 is be VBZ cord-102966-7vdz661d 168 3 made make VBN cord-102966-7vdz661d 168 4 available available JJ cord-102966-7vdz661d 168 5 under under IN cord-102966-7vdz661d 168 6 a a DT cord-102966-7vdz661d 169 1 is be VBZ cord-102966-7vdz661d 169 2 the the DT cord-102966-7vdz661d 169 3 author author NN cord-102966-7vdz661d 169 4 / / SYM cord-102966-7vdz661d 169 5 funder funder NN cord-102966-7vdz661d 169 6 , , , cord-102966-7vdz661d 169 7 who who WP cord-102966-7vdz661d 169 8 has have VBZ cord-102966-7vdz661d 169 9 granted grant VBN cord-102966-7vdz661d 169 10 medRxiv medRxiv NNS cord-102966-7vdz661d 169 11 a a DT cord-102966-7vdz661d 169 12 license license NN cord-102966-7vdz661d 169 13 to to TO cord-102966-7vdz661d 169 14 display display VB cord-102966-7vdz661d 169 15 the the DT cord-102966-7vdz661d 169 16 preprint preprint NN cord-102966-7vdz661d 169 17 in in IN cord-102966-7vdz661d 169 18 perpetuity perpetuity NN cord-102966-7vdz661d 169 19 . . . cord-102966-7vdz661d 170 1 The the DT cord-102966-7vdz661d 170 2 copyright copyright NN cord-102966-7vdz661d 170 3 holder holder NN cord-102966-7vdz661d 170 4 for for IN cord-102966-7vdz661d 170 5 this this DT cord-102966-7vdz661d 170 6 preprint preprint NN cord-102966-7vdz661d 170 7 this this DT cord-102966-7vdz661d 170 8 version version NN cord-102966-7vdz661d 170 9 posted post VBN cord-102966-7vdz661d 170 10 May May NNP cord-102966-7vdz661d 170 11 1 1 CD cord-102966-7vdz661d 170 12 , , , cord-102966-7vdz661d 170 13 2020 2020 CD cord-102966-7vdz661d 170 14 . . . cord-102966-7vdz661d 170 15 . . . cord-102966-7vdz661d 171 1 https://doi.org/10.1101/2020.04.26.20080960 https://doi.org/10.1101/2020.04.26.20080960 NNP cord-102966-7vdz661d 171 2 doi doi NNP cord-102966-7vdz661d 171 3 : : : cord-102966-7vdz661d 172 1 medRxiv medRxiv NNP cord-102966-7vdz661d 172 2 preprint preprint NN cord-102966-7vdz661d 172 3 medRχiv.org medRχiv.org NNP cord-102966-7vdz661d 173 1 Michael Michael NNP cord-102966-7vdz661d 173 2 Nikolaou Nikolaou NNP cord-102966-7vdz661d 173 3 the the DT cord-102966-7vdz661d 173 4 SPIR SPIR NNP cord-102966-7vdz661d 173 5 model model NN cord-102966-7vdz661d 173 6 structure structure NN cord-102966-7vdz661d 173 7 , , , cord-102966-7vdz661d 173 8 in in IN cord-102966-7vdz661d 173 9 view view NN cord-102966-7vdz661d 173 10 of of IN cord-102966-7vdz661d 173 11 its -PRON- PRP$ cord-102966-7vdz661d 173 12 importance importance NN cord-102966-7vdz661d 173 13 for for IN cord-102966-7vdz661d 173 14 the the DT cord-102966-7vdz661d 173 15 recent recent JJ cord-102966-7vdz661d 173 16 coronavirus coronavirus NN cord-102966-7vdz661d 173 17 epidemic epidemic NN cord-102966-7vdz661d 173 18 . . . cord-102966-7vdz661d 174 1 [ [ -LRB- cord-102966-7vdz661d 174 2 16 16 CD cord-102966-7vdz661d 174 3 ] ] -RRB- cord-102966-7vdz661d 174 4 [ [ -LRB- cord-102966-7vdz661d 174 5 17 17 CD cord-102966-7vdz661d 174 6 ] ] -RRB- cord-102966-7vdz661d 174 7 [ [ -LRB- cord-102966-7vdz661d 174 8 18 18 CD cord-102966-7vdz661d 174 9 ] ] -RRB- cord-102966-7vdz661d 174 10 A a DT cord-102966-7vdz661d 174 11 distinct distinct JJ cord-102966-7vdz661d 174 12 feature feature NN cord-102966-7vdz661d 174 13 of of IN cord-102966-7vdz661d 174 14 the the DT cord-102966-7vdz661d 174 15 coronavirus coronavirus NN cord-102966-7vdz661d 174 16 causing cause VBG cord-102966-7vdz661d 174 17 COVID-19 covid-19 CD cord-102966-7vdz661d 174 18 is be VBZ cord-102966-7vdz661d 174 19 that that IN cord-102966-7vdz661d 174 20 it -PRON- PRP cord-102966-7vdz661d 174 21 enables enable VBZ cord-102966-7vdz661d 174 22 infection infection NN cord-102966-7vdz661d 174 23 transmission transmission NN cord-102966-7vdz661d 174 24 at at IN cord-102966-7vdz661d 174 25 the the DT cord-102966-7vdz661d 174 26 pre pre JJ cord-102966-7vdz661d 174 27 - - JJ cord-102966-7vdz661d 174 28 symptomatic symptomatic JJ cord-102966-7vdz661d 174 29 stage stage NN cord-102966-7vdz661d 174 30 . . . cord-102966-7vdz661d 175 1 19 19 CD cord-102966-7vdz661d 176 1 Therefore therefore RB cord-102966-7vdz661d 176 2 , , , cord-102966-7vdz661d 176 3 the the DT cord-102966-7vdz661d 176 4 SPIR SPIR NNP cord-102966-7vdz661d 176 5 model model NN cord-102966-7vdz661d 176 6 structure structure NN cord-102966-7vdz661d 176 7 ( ( -LRB- cord-102966-7vdz661d 176 8 Figure Figure NNP cord-102966-7vdz661d 176 9 14 14 CD cord-102966-7vdz661d 176 10 ) ) -RRB- cord-102966-7vdz661d 176 11 comprises comprise VBZ cord-102966-7vdz661d 176 12 the the DT cord-102966-7vdz661d 176 13 usual usual JJ cord-102966-7vdz661d 176 14 population population NN cord-102966-7vdz661d 176 15 fractions fraction NNS cord-102966-7vdz661d 176 16 { { -LRB- cord-102966-7vdz661d 176 17 , , , cord-102966-7vdz661d 176 18 , , , cord-102966-7vdz661d 176 19 } } -RRB- cord-102966-7vdz661d 176 20 along along IN cord-102966-7vdz661d 176 21 with with IN cord-102966-7vdz661d 176 22 the the DT cord-102966-7vdz661d 176 23 pre pre JJ cord-102966-7vdz661d 176 24 - - JJ cord-102966-7vdz661d 176 25 symptomatic symptomatic JJ cord-102966-7vdz661d 176 26 infectious infectious JJ cord-102966-7vdz661d 176 27 fraction fraction NN cord-102966-7vdz661d 176 28 , , , cord-102966-7vdz661d 176 29 , , , cord-102966-7vdz661d 176 30 with with IN cord-102966-7vdz661d 176 31 symptomatic symptomatic JJ cord-102966-7vdz661d 176 32 infectious infectious JJ cord-102966-7vdz661d 176 33 being being NN cord-102966-7vdz661d 176 34 . . . cord-102966-7vdz661d 177 1 SPIR SPIR NNP cord-102966-7vdz661d 177 2 differs differ VBZ cord-102966-7vdz661d 177 3 from from IN cord-102966-7vdz661d 177 4 the the DT cord-102966-7vdz661d 177 5 standard standard JJ cord-102966-7vdz661d 177 6 SEIR SEIR NNP cord-102966-7vdz661d 177 7 structure structure NN cord-102966-7vdz661d 177 8 2,4,5,20 2,4,5,20 CD cord-102966-7vdz661d 177 9 by by IN cord-102966-7vdz661d 177 10 the the DT cord-102966-7vdz661d 177 11 way way NN cord-102966-7vdz661d 177 12 the the DT cord-102966-7vdz661d 177 13 four four CD cord-102966-7vdz661d 177 14 compartments compartment NNS cord-102966-7vdz661d 177 15 interact interact VBP cord-102966-7vdz661d 177 16 . . . cord-102966-7vdz661d 178 1 While while IN cord-102966-7vdz661d 178 2 it -PRON- PRP cord-102966-7vdz661d 178 3 is be VBZ cord-102966-7vdz661d 178 4 formidable formidable JJ cord-102966-7vdz661d 178 5 to to TO cord-102966-7vdz661d 178 6 practically practically RB cord-102966-7vdz661d 178 7 monitor monitor VB cord-102966-7vdz661d 178 8 infections infection NNS cord-102966-7vdz661d 178 9 on on IN cord-102966-7vdz661d 178 10 presymptomatic presymptomatic JJ cord-102966-7vdz661d 178 11 infectious infectious JJ cord-102966-7vdz661d 178 12 individuals individual NNS cord-102966-7vdz661d 178 13 , , , cord-102966-7vdz661d 178 14 monitoring monitor VBG cord-102966-7vdz661d 178 15 symptomatic symptomatic JJ cord-102966-7vdz661d 178 16 infectious infectious JJ cord-102966-7vdz661d 178 17 is be VBZ cord-102966-7vdz661d 178 18 more more RBR cord-102966-7vdz661d 178 19 reasonable reasonable JJ cord-102966-7vdz661d 178 20 , , , cord-102966-7vdz661d 178 21 as as IN cord-102966-7vdz661d 178 22 symptoms symptom NNS cord-102966-7vdz661d 178 23 are be VBP cord-102966-7vdz661d 178 24 clear clear JJ cord-102966-7vdz661d 178 25 and and CC cord-102966-7vdz661d 178 26 can can MD cord-102966-7vdz661d 178 27 be be VB cord-102966-7vdz661d 178 28 confirmed confirm VBN cord-102966-7vdz661d 178 29 by by IN cord-102966-7vdz661d 178 30 testing test VBG cord-102966-7vdz661d 178 31 . . . cord-102966-7vdz661d 179 1 Therefore therefore RB cord-102966-7vdz661d 179 2 , , , cord-102966-7vdz661d 179 3 tighter tight JJR cord-102966-7vdz661d 179 4 restrictions restriction NNS cord-102966-7vdz661d 179 5 can can MD cord-102966-7vdz661d 179 6 be be VB cord-102966-7vdz661d 179 7 placed place VBN cord-102966-7vdz661d 179 8 on on IN cord-102966-7vdz661d 179 9 the the DT cord-102966-7vdz661d 179 10 I I NNP cord-102966-7vdz661d 179 11 group group NN cord-102966-7vdz661d 179 12 , , , cord-102966-7vdz661d 179 13 in in IN cord-102966-7vdz661d 179 14 addition addition NN cord-102966-7vdz661d 179 15 to to IN cord-102966-7vdz661d 179 16 the the DT cord-102966-7vdz661d 179 17 P p NN cord-102966-7vdz661d 179 18 group group NN cord-102966-7vdz661d 179 19 typically typically RB cord-102966-7vdz661d 179 20 following follow VBG cord-102966-7vdz661d 179 21 general general JJ cord-102966-7vdz661d 179 22 restrictions restriction NNS cord-102966-7vdz661d 179 23 placed place VBN cord-102966-7vdz661d 179 24 on on IN cord-102966-7vdz661d 179 25 the the DT cord-102966-7vdz661d 179 26 general general JJ cord-102966-7vdz661d 179 27 population population NN cord-102966-7vdz661d 179 28 to to TO cord-102966-7vdz661d 179 29 curb curb VB cord-102966-7vdz661d 179 30 the the DT cord-102966-7vdz661d 179 31 spread spread NN cord-102966-7vdz661d 179 32 of of IN cord-102966-7vdz661d 179 33 the the DT cord-102966-7vdz661d 179 34 epidemic epidemic NN cord-102966-7vdz661d 179 35 , , , cord-102966-7vdz661d 179 36 as as IN cord-102966-7vdz661d 179 37 captured capture VBN cord-102966-7vdz661d 179 38 by by IN cord-102966-7vdz661d 179 39 the the DT cord-102966-7vdz661d 179 40 spread spread NN cord-102966-7vdz661d 179 41 factors factor NNS cord-102966-7vdz661d 179 42 and and CC cord-102966-7vdz661d 179 43 , , , cord-102966-7vdz661d 179 44 respectively respectively RB cord-102966-7vdz661d 179 45 , , , cord-102966-7vdz661d 179 46 in in IN cord-102966-7vdz661d 179 47 Figure Figure NNP cord-102966-7vdz661d 179 48 14 14 CD cord-102966-7vdz661d 179 49 . . . cord-102966-7vdz661d 180 1 The the DT cord-102966-7vdz661d 180 2 dynamics dynamic NNS cord-102966-7vdz661d 180 3 of of IN cord-102966-7vdz661d 180 4 the the DT cord-102966-7vdz661d 180 5 dSPIR dSPIR NNP cord-102966-7vdz661d 180 6 structure structure NN cord-102966-7vdz661d 180 7 is be VBZ cord-102966-7vdz661d 180 8 shown show VBN cord-102966-7vdz661d 180 9 in in IN cord-102966-7vdz661d 180 10 Figure Figure NNP cord-102966-7vdz661d 180 11 _SP cord-102966-7vdz661d 180 12 15 15 CD cord-102966-7vdz661d 180 13 , , , cord-102966-7vdz661d 180 14 which which WDT cord-102966-7vdz661d 180 15 follows follow VBZ cord-102966-7vdz661d 180 16 the the DT cord-102966-7vdz661d 180 17 pattern pattern NN cord-102966-7vdz661d 180 18 of of IN cord-102966-7vdz661d 180 19 Figure figure NN cord-102966-7vdz661d 180 20 3 3 CD cord-102966-7vdz661d 180 21 , , , cord-102966-7vdz661d 180 22 with with IN cord-102966-7vdz661d 180 23 the the DT cord-102966-7vdz661d 180 24 addition addition NN cord-102966-7vdz661d 180 25 of of IN cord-102966-7vdz661d 180 26 the the DT cord-102966-7vdz661d 180 27 pre pre JJ cord-102966-7vdz661d 180 28 - - JJ cord-102966-7vdz661d 180 29 symptomatic symptomatic JJ cord-102966-7vdz661d 180 30 infectious infectious JJ cord-102966-7vdz661d 180 31 fraction fraction NN cord-102966-7vdz661d 180 32 . . . cord-102966-7vdz661d 181 1 Following follow VBG cord-102966-7vdz661d 181 2 the the DT cord-102966-7vdz661d 181 3 same same JJ cord-102966-7vdz661d 181 4 technique technique NN cord-102966-7vdz661d 181 5 as as IN cord-102966-7vdz661d 181 6 in in IN cord-102966-7vdz661d 181 7 section section NN cord-102966-7vdz661d 181 8 2 2 CD cord-102966-7vdz661d 181 9 , , , cord-102966-7vdz661d 181 10 we -PRON- PRP cord-102966-7vdz661d 181 11 can can MD cord-102966-7vdz661d 181 12 immediately immediately RB cord-102966-7vdz661d 181 13 write write VB cord-102966-7vdz661d 181 14 the the DT cord-102966-7vdz661d 181 15 following follow VBG cord-102966-7vdz661d 181 16 equations equation NNS cord-102966-7vdz661d 181 17 for for IN cord-102966-7vdz661d 181 18 the the DT cord-102966-7vdz661d 181 19 dSPIR dSPIR NNP cord-102966-7vdz661d 181 20 model model NN cord-102966-7vdz661d 181 21 structure structure NN cord-102966-7vdz661d 181 22 by by IN cord-102966-7vdz661d 181 23 visual visual JJ cord-102966-7vdz661d 181 24 inspection inspection NN cord-102966-7vdz661d 181 25 of of IN cord-102966-7vdz661d 181 26 Figure figure NN cord-102966-7vdz661d 181 27 15 15 CD cord-102966-7vdz661d 181 28 : : : cord-102966-7vdz661d 182 1 Combining combine VBG cord-102966-7vdz661d 182 2 the the DT cord-102966-7vdz661d 182 3 above above JJ cord-102966-7vdz661d 182 4 equations equation NNS cord-102966-7vdz661d 182 5 and and CC cord-102966-7vdz661d 182 6 letting let VBG cord-102966-7vdz661d 182 7 → → XX cord-102966-7vdz661d 183 1 ∞ ∞ NNP cord-102966-7vdz661d 183 2 yields yield VBZ cord-102966-7vdz661d 183 3 the the DT cord-102966-7vdz661d 183 4 nonlinear nonlinear JJ cord-102966-7vdz661d 183 5 DDE DDE NNP cord-102966-7vdz661d 183 6 and and CC cord-102966-7vdz661d 183 7 associated associated JJ cord-102966-7vdz661d 183 8 delay delay NN cord-102966-7vdz661d 183 9 algebraic algebraic JJ cord-102966-7vdz661d 183 10 equations equation NNS cord-102966-7vdz661d 183 11 where where WRB cord-102966-7vdz661d 183 12 and and CC cord-102966-7vdz661d 183 13 − − NNS cord-102966-7vdz661d 183 14 are be VBP cord-102966-7vdz661d 183 15 the the DT cord-102966-7vdz661d 183 16 durations duration NNS cord-102966-7vdz661d 183 17 of of IN cord-102966-7vdz661d 183 18 an an DT cord-102966-7vdz661d 183 19 individual individual NN cord-102966-7vdz661d 183 20 's 's POS cord-102966-7vdz661d 183 21 staying stay VBG cord-102966-7vdz661d 183 22 in in IN cord-102966-7vdz661d 183 23 the the DT cord-102966-7vdz661d 183 24 P p NN cord-102966-7vdz661d 183 25 and and CC cord-102966-7vdz661d 183 26 I -PRON- PRP cord-102966-7vdz661d 183 27 compartment compartment NN cord-102966-7vdz661d 183 28 , , , cord-102966-7vdz661d 183 29 respectively respectively RB cord-102966-7vdz661d 183 30 , , , cord-102966-7vdz661d 183 31 and and CC cord-102966-7vdz661d 183 32 typically typically RB cord-102966-7vdz661d 183 33 Note note VB cord-102966-7vdz661d 183 34 that that IN cord-102966-7vdz661d 183 35 the the DT cord-102966-7vdz661d 183 36 form form NN cord-102966-7vdz661d 183 37 of of IN cord-102966-7vdz661d 183 38 the the DT cord-102966-7vdz661d 183 39 SPIR SPIR NNP cord-102966-7vdz661d 183 40 model model NN cord-102966-7vdz661d 183 41 following follow VBG cord-102966-7vdz661d 183 42 the the DT cord-102966-7vdz661d 183 43 standard standard JJ cord-102966-7vdz661d 183 44 SIR SIR NNP cord-102966-7vdz661d 183 45 pattern pattern NN cord-102966-7vdz661d 183 46 , , , cord-102966-7vdz661d 183 47 eqns eqns NNP cord-102966-7vdz661d 183 48 . . . cord-102966-7vdz661d 184 1 ( ( -LRB- cord-102966-7vdz661d 184 2 1)- 1)- CD cord-102966-7vdz661d 184 3 ( ( -LRB- cord-102966-7vdz661d 184 4 3 3 CD cord-102966-7vdz661d 184 5 ) ) -RRB- cord-102966-7vdz661d 184 6 , , , cord-102966-7vdz661d 184 7 is be VBZ cord-102966-7vdz661d 184 8 the the DT cord-102966-7vdz661d 184 9 coupled couple VBN cord-102966-7vdz661d 184 10 ODEs ode NNS cord-102966-7vdz661d 184 11 21 21 CD cord-102966-7vdz661d 185 1 In in IN cord-102966-7vdz661d 185 2 the the DT cord-102966-7vdz661d 185 3 form form NN cord-102966-7vdz661d 185 4 of of IN cord-102966-7vdz661d 185 5 these these DT cord-102966-7vdz661d 185 6 ODEs ode NNS cord-102966-7vdz661d 185 7 is be VBZ cord-102966-7vdz661d 185 8 the the DT cord-102966-7vdz661d 185 9 following follow VBG cord-102966-7vdz661d 185 10 more more RBR cord-102966-7vdz661d 185 11 realistic realistic JJ cord-102966-7vdz661d 185 12 Padé Padé NNP cord-102966-7vdz661d 185 13 SPIR SPIR NNP cord-102966-7vdz661d 185 14 model model NN cord-102966-7vdz661d 185 15 , , , cord-102966-7vdz661d 185 16 which which WDT cord-102966-7vdz661d 185 17 approximates approximate VBZ cord-102966-7vdz661d 185 18 the the DT cord-102966-7vdz661d 185 19 dSPIR dspir FW cord-102966-7vdz661d 185 20 DDEs DDEs NNPS cord-102966-7vdz661d 185 21 , , , cord-102966-7vdz661d 185 22 eqns eqns NNP cord-102966-7vdz661d 185 23 . . . cord-102966-7vdz661d 186 1 ( ( -LRB- cord-102966-7vdz661d 186 2 31)-(35 31)-(35 CD cord-102966-7vdz661d 186 3 ) ) -RRB- cord-102966-7vdz661d 186 4 , , , cord-102966-7vdz661d 186 5 significantly significantly RB cord-102966-7vdz661d 186 6 better well JJR cord-102966-7vdz661d 186 7 than than IN cord-102966-7vdz661d 186 8 the the DT cord-102966-7vdz661d 186 9 SIR SIR NNP cord-102966-7vdz661d 186 10 ODEs ode NNS cord-102966-7vdz661d 186 11 ( ( -LRB- cord-102966-7vdz661d 186 12 Appendix Appendix NNP cord-102966-7vdz661d 186 13 F F NNP cord-102966-7vdz661d 186 14 ) ) -RRB- cord-102966-7vdz661d 186 15 : : : cord-102966-7vdz661d 186 16 . . . cord-102966-7vdz661d 187 1 CC CC NNP cord-102966-7vdz661d 187 2 - - HYPH cord-102966-7vdz661d 187 3 BY BY NNP cord-102966-7vdz661d 187 4 - - HYPH cord-102966-7vdz661d 187 5 NC NC NNP cord-102966-7vdz661d 187 6 - - HYPH cord-102966-7vdz661d 187 7 ND ND NNP cord-102966-7vdz661d 187 8 4.0 4.0 CD cord-102966-7vdz661d 187 9 International international JJ cord-102966-7vdz661d 187 10 license license NN cord-102966-7vdz661d 188 1 It -PRON- PRP cord-102966-7vdz661d 188 2 is be VBZ cord-102966-7vdz661d 188 3 made make VBN cord-102966-7vdz661d 188 4 available available JJ cord-102966-7vdz661d 188 5 under under IN cord-102966-7vdz661d 188 6 a a DT cord-102966-7vdz661d 189 1 is be VBZ cord-102966-7vdz661d 189 2 the the DT cord-102966-7vdz661d 189 3 author author NN cord-102966-7vdz661d 189 4 / / SYM cord-102966-7vdz661d 189 5 funder funder NN cord-102966-7vdz661d 189 6 , , , cord-102966-7vdz661d 189 7 who who WP cord-102966-7vdz661d 189 8 has have VBZ cord-102966-7vdz661d 189 9 granted grant VBN cord-102966-7vdz661d 189 10 medRxiv medRxiv NNS cord-102966-7vdz661d 189 11 a a DT cord-102966-7vdz661d 189 12 license license NN cord-102966-7vdz661d 189 13 to to TO cord-102966-7vdz661d 189 14 display display VB cord-102966-7vdz661d 189 15 the the DT cord-102966-7vdz661d 189 16 preprint preprint NN cord-102966-7vdz661d 189 17 in in IN cord-102966-7vdz661d 189 18 perpetuity perpetuity NN cord-102966-7vdz661d 189 19 . . . cord-102966-7vdz661d 190 1 The the DT cord-102966-7vdz661d 190 2 copyright copyright NN cord-102966-7vdz661d 190 3 holder holder NN cord-102966-7vdz661d 190 4 for for IN cord-102966-7vdz661d 190 5 this this DT cord-102966-7vdz661d 190 6 preprint preprint NN cord-102966-7vdz661d 190 7 this this DT cord-102966-7vdz661d 190 8 version version NN cord-102966-7vdz661d 190 9 posted post VBN cord-102966-7vdz661d 190 10 May May NNP cord-102966-7vdz661d 190 11 1 1 CD cord-102966-7vdz661d 190 12 , , , cord-102966-7vdz661d 190 13 2020 2020 CD cord-102966-7vdz661d 190 14 . . . cord-102966-7vdz661d 190 15 _SP cord-102966-7vdz661d 191 1 The the DT cord-102966-7vdz661d 191 2 illustration illustration NN cord-102966-7vdz661d 191 3 and and CC cord-102966-7vdz661d 191 4 analysis analysis NN cord-102966-7vdz661d 191 5 presented present VBN cord-102966-7vdz661d 191 6 in in IN cord-102966-7vdz661d 191 7 sections section NNS cord-102966-7vdz661d 191 8 3 3 CD cord-102966-7vdz661d 191 9 and and CC cord-102966-7vdz661d 191 10 4 4 CD cord-102966-7vdz661d 191 11 can can MD cord-102966-7vdz661d 191 12 be be VB cord-102966-7vdz661d 191 13 easily easily RB cord-102966-7vdz661d 191 14 repeated repeat VBN cord-102966-7vdz661d 191 15 for for IN cord-102966-7vdz661d 191 16 the the DT cord-102966-7vdz661d 191 17 dSPIR dSPIR NNS cord-102966-7vdz661d 191 18 and and CC cord-102966-7vdz661d 191 19 Padé Padé NNP cord-102966-7vdz661d 191 20 SPIR SPIR NNP cord-102966-7vdz661d 191 21 structures structure NNS cord-102966-7vdz661d 191 22 . . . cord-102966-7vdz661d 192 1 To to TO cord-102966-7vdz661d 192 2 maintain maintain VB cord-102966-7vdz661d 192 3 the the DT cord-102966-7vdz661d 192 4 scope scope NN cord-102966-7vdz661d 192 5 of of IN cord-102966-7vdz661d 192 6 this this DT cord-102966-7vdz661d 192 7 publication publication NN cord-102966-7vdz661d 192 8 , , , cord-102966-7vdz661d 192 9 only only RB cord-102966-7vdz661d 192 10 a a DT cord-102966-7vdz661d 192 11 few few JJ cord-102966-7vdz661d 192 12 properties property NNS cord-102966-7vdz661d 192 13 will will MD cord-102966-7vdz661d 192 14 be be VB cord-102966-7vdz661d 192 15 explored explore VBN cord-102966-7vdz661d 192 16 below below RB cord-102966-7vdz661d 192 17 . . . cord-102966-7vdz661d 193 1 The the DT cord-102966-7vdz661d 193 2 rest rest NN cord-102966-7vdz661d 193 3 will will MD cord-102966-7vdz661d 193 4 be be VB cord-102966-7vdz661d 193 5 explored explore VBN cord-102966-7vdz661d 193 6 in in IN cord-102966-7vdz661d 193 7 more more JJR cord-102966-7vdz661d 193 8 detail detail NN cord-102966-7vdz661d 193 9 in in IN cord-102966-7vdz661d 193 10 forthcoming forthcoming JJ cord-102966-7vdz661d 193 11 publications publication NNS cord-102966-7vdz661d 193 12 . . . cord-102966-7vdz661d 194 1 We -PRON- PRP cord-102966-7vdz661d 194 2 present present VBP cord-102966-7vdz661d 194 3 here here RB cord-102966-7vdz661d 194 4 only only RB cord-102966-7vdz661d 194 5 a a DT cord-102966-7vdz661d 194 6 few few JJ cord-102966-7vdz661d 194 7 simulations simulation NNS cord-102966-7vdz661d 194 8 comparing compare VBG cord-102966-7vdz661d 194 9 the the DT cord-102966-7vdz661d 194 10 { { -LRB- cord-102966-7vdz661d 194 11 , , , cord-102966-7vdz661d 194 12 , , , cord-102966-7vdz661d 194 13 , , , cord-102966-7vdz661d 194 14 } } -RRB- cord-102966-7vdz661d 194 15 profiles profile NNS cord-102966-7vdz661d 194 16 resulting result VBG cord-102966-7vdz661d 194 17 from from IN cord-102966-7vdz661d 194 18 numerical numerical JJ cord-102966-7vdz661d 194 19 solution solution NN cord-102966-7vdz661d 194 20 of of IN cord-102966-7vdz661d 194 21 the the DT cord-102966-7vdz661d 194 22 SPIR SPIR NNP cord-102966-7vdz661d 194 23 , , , cord-102966-7vdz661d 194 24 dSPIR dSPIR NNP cord-102966-7vdz661d 194 25 , , , cord-102966-7vdz661d 194 26 and and CC cord-102966-7vdz661d 194 27 Padé Padé NNP cord-102966-7vdz661d 194 28 SPIR SPIR NNP cord-102966-7vdz661d 194 29 models model NNS cord-102966-7vdz661d 194 30 . . . cord-102966-7vdz661d 195 1 The the DT cord-102966-7vdz661d 195 2 values value NNS cord-102966-7vdz661d 195 3 are be VBP cord-102966-7vdz661d 195 4 used use VBN cord-102966-7vdz661d 195 5 in in IN cord-102966-7vdz661d 195 6 all all DT cord-102966-7vdz661d 195 7 simulations simulation NNS cord-102966-7vdz661d 195 8 . . . cord-102966-7vdz661d 196 1 8,9 8,9 CD cord-102966-7vdz661d 196 2 Figure figure NN cord-102966-7vdz661d 196 3 16 16 CD cord-102966-7vdz661d 196 4 illustrates illustrate VBZ cord-102966-7vdz661d 196 5 the the DT cord-102966-7vdz661d 196 6 differences difference NNS cord-102966-7vdz661d 196 7 in in IN cord-102966-7vdz661d 196 8 the the DT cord-102966-7vdz661d 196 9 infectious infectious JJ cord-102966-7vdz661d 196 10 peaks peak NNS cord-102966-7vdz661d 196 11 , , , cord-102966-7vdz661d 196 12 * * NFP cord-102966-7vdz661d 196 13 and and CC cord-102966-7vdz661d 196 14 * * NFP cord-102966-7vdz661d 196 15 , , , cord-102966-7vdz661d 196 16 similar similar JJ cord-102966-7vdz661d 196 17 to to IN cord-102966-7vdz661d 196 18 these these DT cord-102966-7vdz661d 196 19 in in IN cord-102966-7vdz661d 196 20 Figure Figure NNP cord-102966-7vdz661d 196 21 8 8 CD cord-102966-7vdz661d 196 22 . . . cord-102966-7vdz661d 196 23 _SP cord-102966-7vdz661d 197 1 Following follow VBG cord-102966-7vdz661d 197 2 the the DT cord-102966-7vdz661d 197 3 same same JJ cord-102966-7vdz661d 197 4 approach approach NN cord-102966-7vdz661d 197 5 as as IN cord-102966-7vdz661d 197 6 in in IN cord-102966-7vdz661d 197 7 section section NN cord-102966-7vdz661d 197 8 4.1 4.1 CD cord-102966-7vdz661d 197 9 , , , cord-102966-7vdz661d 197 10 eqn eqn NN cord-102966-7vdz661d 197 11 . . . cord-102966-7vdz661d 198 1 ( ( -LRB- cord-102966-7vdz661d 198 2 31 31 CD cord-102966-7vdz661d 198 3 ) ) -RRB- cord-102966-7vdz661d 198 4 can can MD cord-102966-7vdz661d 198 5 be be VB cord-102966-7vdz661d 198 6 used use VBN cord-102966-7vdz661d 198 7 to to TO cord-102966-7vdz661d 198 8 show show VB cord-102966-7vdz661d 198 9 ( ( -LRB- cord-102966-7vdz661d 198 10 Appendix Appendix NNP cord-102966-7vdz661d 198 11 G G NNP cord-102966-7vdz661d 198 12 ) ) -RRB- cord-102966-7vdz661d 198 13 that that IN cord-102966-7vdz661d 198 14 an an DT cord-102966-7vdz661d 198 15 epidemic epidemic NN cord-102966-7vdz661d 198 16 outbreak outbreak NN cord-102966-7vdz661d 198 17 does do VBZ cord-102966-7vdz661d 198 18 not not RB cord-102966-7vdz661d 198 19 occur occur VB cord-102966-7vdz661d 198 20 around around IN cord-102966-7vdz661d 198 21 an an DT cord-102966-7vdz661d 198 22 equilibrium equilibrium NN cord-102966-7vdz661d 198 23 point point NN cord-102966-7vdz661d 198 24 ̅ ̅ UH cord-102966-7vdz661d 198 25 iff iff NN cord-102966-7vdz661d 199 1 The the DT cord-102966-7vdz661d 199 2 proof proof NN cord-102966-7vdz661d 199 3 in in IN cord-102966-7vdz661d 199 4 Appendix Appendix NNP cord-102966-7vdz661d 199 5 G G NNP cord-102966-7vdz661d 199 6 is be VBZ cord-102966-7vdz661d 199 7 by by IN cord-102966-7vdz661d 199 8 approximation approximation NN cord-102966-7vdz661d 199 9 . . . cord-102966-7vdz661d 200 1 It -PRON- PRP cord-102966-7vdz661d 200 2 is be VBZ cord-102966-7vdz661d 200 3 conjectured conjecture VBN cord-102966-7vdz661d 200 4 that that IN cord-102966-7vdz661d 200 5 the the DT cord-102966-7vdz661d 200 6 bound bind VBN cord-102966-7vdz661d 200 7 in in IN cord-102966-7vdz661d 200 8 the the DT cord-102966-7vdz661d 200 9 above above JJ cord-102966-7vdz661d 200 10 equation equation NN cord-102966-7vdz661d 200 11 is be VBZ cord-102966-7vdz661d 200 12 exact exact JJ cord-102966-7vdz661d 200 13 . . . cord-102966-7vdz661d 201 1 This this DT cord-102966-7vdz661d 201 2 conjecture conjecture NN cord-102966-7vdz661d 201 3 will will MD cord-102966-7vdz661d 201 4 be be VB cord-102966-7vdz661d 201 5 examined examine VBN cord-102966-7vdz661d 201 6 in in IN cord-102966-7vdz661d 201 7 subsequent subsequent JJ cord-102966-7vdz661d 201 8 studies study NNS cord-102966-7vdz661d 201 9 . . . cord-102966-7vdz661d 202 1 It -PRON- PRP cord-102966-7vdz661d 202 2 can can MD cord-102966-7vdz661d 202 3 be be VB cord-102966-7vdz661d 202 4 shown show VBN cord-102966-7vdz661d 202 5 ( ( -LRB- cord-102966-7vdz661d 202 6 Appendix Appendix NNP cord-102966-7vdz661d 202 7 H H NNP cord-102966-7vdz661d 202 8 ) ) -RRB- cord-102966-7vdz661d 203 1 that that IN cord-102966-7vdz661d 203 2 the the DT cord-102966-7vdz661d 203 3 dSPIR dSPIR NNP cord-102966-7vdz661d 203 4 counterpart counterpart NN cord-102966-7vdz661d 203 5 of of IN cord-102966-7vdz661d 203 6 eqn eqn NNP cord-102966-7vdz661d 203 7 . . . cord-102966-7vdz661d 204 1 ( ( -LRB- cord-102966-7vdz661d 204 2 19 19 CD cord-102966-7vdz661d 204 3 ) ) -RRB- cord-102966-7vdz661d 204 4 is be VBZ cord-102966-7vdz661d 204 5 where where WRB cord-102966-7vdz661d 204 6 > > XX cord-102966-7vdz661d 204 7 and and CC cord-102966-7vdz661d 204 8 The the DT cord-102966-7vdz661d 204 9 counterpart counterpart NN cord-102966-7vdz661d 204 10 of of IN cord-102966-7vdz661d 204 11 the the DT cord-102966-7vdz661d 204 12 SIR SIR NNP cord-102966-7vdz661d 204 13 and and CC cord-102966-7vdz661d 204 14 dSIR dsir JJ cord-102966-7vdz661d 204 15 plot plot NN cord-102966-7vdz661d 204 16 ( ( -LRB- cord-102966-7vdz661d 204 17 Figure figure NN cord-102966-7vdz661d 204 18 10 10 CD cord-102966-7vdz661d 204 19 . . . cord-102966-7vdz661d 205 1 CC CC NNP cord-102966-7vdz661d 205 2 - - HYPH cord-102966-7vdz661d 205 3 BY BY NNP cord-102966-7vdz661d 205 4 - - HYPH cord-102966-7vdz661d 205 5 NC NC NNP cord-102966-7vdz661d 205 6 - - HYPH cord-102966-7vdz661d 205 7 ND ND NNP cord-102966-7vdz661d 205 8 4.0 4.0 CD cord-102966-7vdz661d 205 9 International international JJ cord-102966-7vdz661d 205 10 license license NN cord-102966-7vdz661d 206 1 It -PRON- PRP cord-102966-7vdz661d 206 2 is be VBZ cord-102966-7vdz661d 206 3 made make VBN cord-102966-7vdz661d 206 4 available available JJ cord-102966-7vdz661d 206 5 under under IN cord-102966-7vdz661d 206 6 a a DT cord-102966-7vdz661d 207 1 is be VBZ cord-102966-7vdz661d 207 2 the the DT cord-102966-7vdz661d 207 3 author author NN cord-102966-7vdz661d 207 4 / / SYM cord-102966-7vdz661d 207 5 funder funder NN cord-102966-7vdz661d 207 6 , , , cord-102966-7vdz661d 207 7 who who WP cord-102966-7vdz661d 207 8 has have VBZ cord-102966-7vdz661d 207 9 granted grant VBN cord-102966-7vdz661d 207 10 medRxiv medRxiv NNS cord-102966-7vdz661d 207 11 a a DT cord-102966-7vdz661d 207 12 license license NN cord-102966-7vdz661d 207 13 to to TO cord-102966-7vdz661d 207 14 display display VB cord-102966-7vdz661d 207 15 the the DT cord-102966-7vdz661d 207 16 preprint preprint NN cord-102966-7vdz661d 207 17 in in IN cord-102966-7vdz661d 207 18 perpetuity perpetuity NN cord-102966-7vdz661d 207 19 . . . cord-102966-7vdz661d 208 1 The the DT cord-102966-7vdz661d 208 2 copyright copyright NN cord-102966-7vdz661d 208 3 holder holder NN cord-102966-7vdz661d 208 4 for for IN cord-102966-7vdz661d 208 5 this this DT cord-102966-7vdz661d 208 6 preprint preprint NN cord-102966-7vdz661d 208 7 this this DT cord-102966-7vdz661d 208 8 version version NN cord-102966-7vdz661d 208 9 posted post VBN cord-102966-7vdz661d 208 10 May May NNP cord-102966-7vdz661d 208 11 1 1 CD cord-102966-7vdz661d 208 12 , , , cord-102966-7vdz661d 208 13 2020 2020 CD cord-102966-7vdz661d 208 14 . . . cord-102966-7vdz661d 208 15 _SP cord-102966-7vdz661d 209 1 A a DT cord-102966-7vdz661d 209 2 subtle subtle JJ cord-102966-7vdz661d 209 3 inconsistency inconsistency NN cord-102966-7vdz661d 209 4 in in IN cord-102966-7vdz661d 209 5 the the DT cord-102966-7vdz661d 209 6 standard standard JJ cord-102966-7vdz661d 209 7 SIR SIR NNP cord-102966-7vdz661d 209 8 model model NN cord-102966-7vdz661d 209 9 structure structure NN cord-102966-7vdz661d 209 10 was be VBD cord-102966-7vdz661d 209 11 pointed point VBN cord-102966-7vdz661d 209 12 out out RP cord-102966-7vdz661d 209 13 . . . cord-102966-7vdz661d 210 1 This this DT cord-102966-7vdz661d 210 2 inconsistency inconsistency NN cord-102966-7vdz661d 210 3 arises arise VBZ cord-102966-7vdz661d 210 4 from from IN cord-102966-7vdz661d 210 5 misinterpretation misinterpretation NN cord-102966-7vdz661d 210 6 of of IN cord-102966-7vdz661d 210 7 an an DT cord-102966-7vdz661d 210 8 assumption assumption NN cord-102966-7vdz661d 210 9 explicitly explicitly RB cord-102966-7vdz661d 210 10 articulated articulate VBN cord-102966-7vdz661d 210 11 in in IN cord-102966-7vdz661d 210 12 the the DT cord-102966-7vdz661d 210 13 original original JJ cord-102966-7vdz661d 210 14 publication publication NN cord-102966-7vdz661d 210 15 of of IN cord-102966-7vdz661d 210 16 Kermack Kermack NNP cord-102966-7vdz661d 210 17 and and CC cord-102966-7vdz661d 210 18 McKendrick McKendrick NNP cord-102966-7vdz661d 210 19 : : : cord-102966-7vdz661d 210 20 1 1 CD cord-102966-7vdz661d 210 21 that that IN cord-102966-7vdz661d 210 22 the the DT cord-102966-7vdz661d 210 23 depletion depletion NN cord-102966-7vdz661d 210 24 of of IN cord-102966-7vdz661d 210 25 the the DT cord-102966-7vdz661d 210 26 infectious infectious JJ cord-102966-7vdz661d 210 27 compartment compartment NN cord-102966-7vdz661d 210 28 is be VBZ cord-102966-7vdz661d 210 29 proportional proportional JJ cord-102966-7vdz661d 210 30 to to IN cord-102966-7vdz661d 210 31 the the DT cord-102966-7vdz661d 210 32 content content NN cord-102966-7vdz661d 210 33 of of IN cord-102966-7vdz661d 210 34 that that DT cord-102966-7vdz661d 210 35 compartment compartment NN cord-102966-7vdz661d 210 36 . . . cord-102966-7vdz661d 211 1 The the DT cord-102966-7vdz661d 211 2 depletion depletion NN cord-102966-7vdz661d 211 3 rate rate NN cord-102966-7vdz661d 211 4 constant constant NN cord-102966-7vdz661d 211 5 , , , cord-102966-7vdz661d 211 6 , , , cord-102966-7vdz661d 211 7 is be VBZ cord-102966-7vdz661d 211 8 usually usually RB cord-102966-7vdz661d 211 9 interpreted interpret VBN cord-102966-7vdz661d 211 10 as as RB cord-102966-7vdz661d 211 11 equal equal JJ cord-102966-7vdz661d 211 12 to to IN cord-102966-7vdz661d 211 13 the the DT cord-102966-7vdz661d 211 14 inverse inverse NN cord-102966-7vdz661d 211 15 of of IN cord-102966-7vdz661d 211 16 the the DT cord-102966-7vdz661d 211 17 residence residence NN cord-102966-7vdz661d 211 18 time time NN cord-102966-7vdz661d 211 19 in in IN cord-102966-7vdz661d 211 20 the the DT cord-102966-7vdz661d 211 21 infectious infectious JJ cord-102966-7vdz661d 211 22 compartment compartment NN cord-102966-7vdz661d 211 23 , , , cord-102966-7vdz661d 211 24 namely namely RB cord-102966-7vdz661d 211 25 the the DT cord-102966-7vdz661d 211 26 duration duration NN cord-102966-7vdz661d 211 27 of of IN cord-102966-7vdz661d 211 28 the the DT cord-102966-7vdz661d 211 29 infection infection NN cord-102966-7vdz661d 211 30 , , , cord-102966-7vdz661d 211 31 , , , cord-102966-7vdz661d 211 32 for for IN cord-102966-7vdz661d 211 33 each each DT cord-102966-7vdz661d 211 34 individual individual NN cord-102966-7vdz661d 211 35 ( ( -LRB- cord-102966-7vdz661d 211 36 eqn eqn NN cord-102966-7vdz661d 211 37 . . . cord-102966-7vdz661d 212 1 ( ( -LRB- cord-102966-7vdz661d 212 2 18 18 CD cord-102966-7vdz661d 212 3 ) ) -RRB- cord-102966-7vdz661d 212 4 ) ) -RRB- cord-102966-7vdz661d 212 5 . . . cord-102966-7vdz661d 213 1 To to IN cord-102966-7vdz661d 213 2 the the DT cord-102966-7vdz661d 213 3 extent extent NN cord-102966-7vdz661d 213 4 that that IN cord-102966-7vdz661d 213 5 this this DT cord-102966-7vdz661d 213 6 duration duration NN cord-102966-7vdz661d 213 7 is be VBZ cord-102966-7vdz661d 213 8 about about IN cord-102966-7vdz661d 213 9 constant constant JJ cord-102966-7vdz661d 213 10 , , , cord-102966-7vdz661d 213 11 the the DT cord-102966-7vdz661d 213 12 analysis analysis NN cord-102966-7vdz661d 213 13 presented present VBN cord-102966-7vdz661d 213 14 here here RB cord-102966-7vdz661d 213 15 suggests suggest VBZ cord-102966-7vdz661d 213 16 that that IN cord-102966-7vdz661d 213 17 the the DT cord-102966-7vdz661d 213 18 preceding precede VBG cord-102966-7vdz661d 213 19 interpretation interpretation NN cord-102966-7vdz661d 213 20 is be VBZ cord-102966-7vdz661d 213 21 incorrect incorrect JJ cord-102966-7vdz661d 213 22 , , , cord-102966-7vdz661d 213 23 leading lead VBG cord-102966-7vdz661d 213 24 to to IN cord-102966-7vdz661d 213 25 certain certain JJ cord-102966-7vdz661d 213 26 erroneous erroneous JJ cord-102966-7vdz661d 213 27 conclusions conclusion NNS cord-102966-7vdz661d 213 28 . . . cord-102966-7vdz661d 214 1 A a DT cord-102966-7vdz661d 214 2 corresponding corresponding JJ cord-102966-7vdz661d 214 3 model model NN cord-102966-7vdz661d 214 4 structure structure NN cord-102966-7vdz661d 214 5 , , , cord-102966-7vdz661d 214 6 termed term VBN cord-102966-7vdz661d 214 7 dSIR dsir RB cord-102966-7vdz661d 214 8 , , , cord-102966-7vdz661d 214 9 was be VBD cord-102966-7vdz661d 214 10 developed develop VBN cord-102966-7vdz661d 214 11 , , , cord-102966-7vdz661d 214 12 to to TO cord-102966-7vdz661d 214 13 account account VB cord-102966-7vdz661d 214 14 for for IN cord-102966-7vdz661d 214 15 each each DT cord-102966-7vdz661d 214 16 individual individual NN cord-102966-7vdz661d 214 17 leaving leave VBG cord-102966-7vdz661d 214 18 the the DT cord-102966-7vdz661d 214 19 infectious infectious JJ cord-102966-7vdz661d 214 20 compartment compartment NN cord-102966-7vdz661d 214 21 after after IN cord-102966-7vdz661d 214 22 a a DT cord-102966-7vdz661d 214 23 certain certain JJ cord-102966-7vdz661d 214 24 duration duration NN cord-102966-7vdz661d 214 25 . . . cord-102966-7vdz661d 215 1 The the DT cord-102966-7vdz661d 215 2 dSIR dsir JJ cord-102966-7vdz661d 215 3 model model NN cord-102966-7vdz661d 215 4 structure structure NN cord-102966-7vdz661d 215 5 comprises comprise VBZ cord-102966-7vdz661d 215 6 a a DT cord-102966-7vdz661d 215 7 single single JJ cord-102966-7vdz661d 215 8 DDE dde NN cord-102966-7vdz661d 215 9 for for IN cord-102966-7vdz661d 215 10 the the DT cord-102966-7vdz661d 215 11 susceptible susceptible JJ cord-102966-7vdz661d 215 12 fraction fraction NN cord-102966-7vdz661d 215 13 , , , cord-102966-7vdz661d 215 14 s s NNP cord-102966-7vdz661d 215 15 , , , cord-102966-7vdz661d 215 16 and and CC cord-102966-7vdz661d 215 17 associated associate VBD cord-102966-7vdz661d 215 18 algebraic algebraic JJ cord-102966-7vdz661d 215 19 equations equation NNS cord-102966-7vdz661d 215 20 capturing capture VBG cord-102966-7vdz661d 215 21 the the DT cord-102966-7vdz661d 215 22 dependence dependence NN cord-102966-7vdz661d 215 23 of of IN cord-102966-7vdz661d 215 24 the the DT cord-102966-7vdz661d 215 25 remaining remain VBG cord-102966-7vdz661d 215 26 population population NN cord-102966-7vdz661d 215 27 fractions fraction NNS cord-102966-7vdz661d 215 28 on on IN cord-102966-7vdz661d 215 29 . . . cord-102966-7vdz661d 216 1 While while IN cord-102966-7vdz661d 216 2 both both CC cord-102966-7vdz661d 216 3 SIR SIR NNP cord-102966-7vdz661d 216 4 and and CC cord-102966-7vdz661d 216 5 dSIR dsir RB cord-102966-7vdz661d 216 6 produce produce VB cord-102966-7vdz661d 216 7 the the DT cord-102966-7vdz661d 216 8 same same JJ cord-102966-7vdz661d 216 9 results result NNS cord-102966-7vdz661d 216 10 for for IN cord-102966-7vdz661d 216 11 assessment assessment NN cord-102966-7vdz661d 216 12 of of IN cord-102966-7vdz661d 216 13 stability stability NN cord-102966-7vdz661d 216 14 and and CC cord-102966-7vdz661d 216 15 final final JJ cord-102966-7vdz661d 216 16 values value NNS cord-102966-7vdz661d 216 17 , , , cord-102966-7vdz661d 216 18 the the DT cord-102966-7vdz661d 216 19 SIR SIR NNP cord-102966-7vdz661d 216 20 model model NN cord-102966-7vdz661d 216 21 produces produce VBZ cord-102966-7vdz661d 216 22 a a DT cord-102966-7vdz661d 216 23 maximum maximum NN cord-102966-7vdz661d 216 24 of of IN cord-102966-7vdz661d 216 25 the the DT cord-102966-7vdz661d 216 26 infectious infectious JJ cord-102966-7vdz661d 216 27 fraction fraction NN cord-102966-7vdz661d 216 28 , , , cord-102966-7vdz661d 216 29 * * NFP cord-102966-7vdz661d 216 30 , , , cord-102966-7vdz661d 216 31 about about IN cord-102966-7vdz661d 216 32 half half NN cord-102966-7vdz661d 216 33 of of IN cord-102966-7vdz661d 216 34 its -PRON- PRP$ cord-102966-7vdz661d 216 35 dSIR dsir JJ cord-102966-7vdz661d 216 36 counterpart counterpart NN cord-102966-7vdz661d 216 37 . . . cord-102966-7vdz661d 217 1 This this DT cord-102966-7vdz661d 217 2 has have VBZ cord-102966-7vdz661d 217 3 profound profound JJ cord-102966-7vdz661d 217 4 consequences consequence NNS cord-102966-7vdz661d 217 5 if if IN cord-102966-7vdz661d 217 6 the the DT cord-102966-7vdz661d 217 7 SIR SIR NNP cord-102966-7vdz661d 217 8 model model NN cord-102966-7vdz661d 217 9 is be VBZ cord-102966-7vdz661d 217 10 used use VBN cord-102966-7vdz661d 217 11 to to TO cord-102966-7vdz661d 217 12 predict predict VB cord-102966-7vdz661d 217 13 * * NFP cord-102966-7vdz661d 217 14 during during IN cord-102966-7vdz661d 217 15 an an DT cord-102966-7vdz661d 217 16 epidemic epidemic NN cord-102966-7vdz661d 217 17 . . . cord-102966-7vdz661d 218 1 It -PRON- PRP cord-102966-7vdz661d 218 2 is be VBZ cord-102966-7vdz661d 218 3 also also RB cord-102966-7vdz661d 218 4 noted note VBN cord-102966-7vdz661d 218 5 that that IN cord-102966-7vdz661d 218 6 even even RB cord-102966-7vdz661d 218 7 if if IN cord-102966-7vdz661d 218 8 the the DT cord-102966-7vdz661d 218 9 SIR SIR NNP cord-102966-7vdz661d 218 10 model model NN cord-102966-7vdz661d 218 11 parameters parameter NNS cord-102966-7vdz661d 218 12 and and CC cord-102966-7vdz661d 218 13 are be VBP cord-102966-7vdz661d 218 14 estimated estimate VBN cord-102966-7vdz661d 218 15 based base VBN cord-102966-7vdz661d 218 16 on on IN cord-102966-7vdz661d 218 17 experimental experimental JJ cord-102966-7vdz661d 218 18 data datum NNS cord-102966-7vdz661d 218 19 fit fit NN cord-102966-7vdz661d 218 20 -albeit -albeit . cord-102966-7vdz661d 219 1 under under IN cord-102966-7vdz661d 219 2 the the DT cord-102966-7vdz661d 219 3 wrong wrong JJ cord-102966-7vdz661d 219 4 interpretationmodel interpretationmodel NN cord-102966-7vdz661d 219 5 predictions prediction NNS cord-102966-7vdz661d 219 6 are be VBP cord-102966-7vdz661d 219 7 still still RB cord-102966-7vdz661d 219 8 going go VBG cord-102966-7vdz661d 219 9 to to TO cord-102966-7vdz661d 219 10 be be VB cord-102966-7vdz661d 219 11 inaccurate inaccurate JJ cord-102966-7vdz661d 219 12 . . . cord-102966-7vdz661d 220 1 This this DT cord-102966-7vdz661d 220 2 is be VBZ cord-102966-7vdz661d 220 3 because because IN cord-102966-7vdz661d 220 4 the the DT cord-102966-7vdz661d 220 5 standard standard JJ cord-102966-7vdz661d 220 6 SIR SIR NNP cord-102966-7vdz661d 220 7 model model NN cord-102966-7vdz661d 220 8 , , , cord-102966-7vdz661d 220 9 comprising comprise VBG cord-102966-7vdz661d 220 10 the the DT cord-102966-7vdz661d 220 11 three three CD cord-102966-7vdz661d 220 12 ODEs ode NNS cord-102966-7vdz661d 220 13 in in IN cord-102966-7vdz661d 220 14 eqns eqns NNP cord-102966-7vdz661d 220 15 . . . cord-102966-7vdz661d 221 1 ( ( -LRB- cord-102966-7vdz661d 221 2 1)-(3 1)-(3 CD cord-102966-7vdz661d 221 3 ) ) -RRB- cord-102966-7vdz661d 221 4 , , , cord-102966-7vdz661d 221 5 is be VBZ cord-102966-7vdz661d 221 6 structurally structurally RB cord-102966-7vdz661d 221 7 different different JJ cord-102966-7vdz661d 221 8 from from IN cord-102966-7vdz661d 221 9 the the DT cord-102966-7vdz661d 221 10 DDE DDE NNP cord-102966-7vdz661d 221 11 form form NN cord-102966-7vdz661d 221 12 of of IN cord-102966-7vdz661d 221 13 the the DT cord-102966-7vdz661d 221 14 dSIR dsir JJ cord-102966-7vdz661d 221 15 model model NN cord-102966-7vdz661d 221 16 , , , cord-102966-7vdz661d 221 17 eqns eqns NNP cord-102966-7vdz661d 221 18 . . . cord-102966-7vdz661d 222 1 ( ( -LRB- cord-102966-7vdz661d 222 2 7)-(9 7)-(9 CD cord-102966-7vdz661d 222 3 ) ) -RRB- cord-102966-7vdz661d 222 4 , , , cord-102966-7vdz661d 222 5 or or CC cord-102966-7vdz661d 222 6 even even RB cord-102966-7vdz661d 222 7 from from IN cord-102966-7vdz661d 222 8 the the DT cord-102966-7vdz661d 222 9 ODE ODE NNP cord-102966-7vdz661d 222 10 form form NN cord-102966-7vdz661d 222 11 of of IN cord-102966-7vdz661d 222 12 the the DT cord-102966-7vdz661d 222 13 Padé Padé NNP cord-102966-7vdz661d 222 14 - - HYPH cord-102966-7vdz661d 222 15 based base VBN cord-102966-7vdz661d 222 16 approximation approximation NN cord-102966-7vdz661d 222 17 of of IN cord-102966-7vdz661d 222 18 the the DT cord-102966-7vdz661d 222 19 dSIR dsir JJ cord-102966-7vdz661d 222 20 model model NN cord-102966-7vdz661d 222 21 DDEs dde NNS cord-102966-7vdz661d 222 22 , , , cord-102966-7vdz661d 222 23 eqns eqns NNP cord-102966-7vdz661d 222 24 . . . cord-102966-7vdz661d 223 1 ( ( -LRB- cord-102966-7vdz661d 223 2 1 1 CD cord-102966-7vdz661d 223 3 ) ) -RRB- cord-102966-7vdz661d 223 4 and and CC cord-102966-7vdz661d 223 5 ( ( -LRB- cord-102966-7vdz661d 223 6 13 13 CD cord-102966-7vdz661d 223 7 ) ) -RRB- cord-102966-7vdz661d 223 8 or or CC cord-102966-7vdz661d 223 9 ( ( -LRB- cord-102966-7vdz661d 223 10 1 1 CD cord-102966-7vdz661d 223 11 ) ) -RRB- cord-102966-7vdz661d 223 12 and and CC cord-102966-7vdz661d 223 13 ( ( -LRB- cord-102966-7vdz661d 223 14 14 14 CD cord-102966-7vdz661d 223 15 ) ) -RRB- cord-102966-7vdz661d 223 16 . . . cord-102966-7vdz661d 224 1 The the DT cord-102966-7vdz661d 224 2 dSIR dsir JJ cord-102966-7vdz661d 224 3 structure structure NN cord-102966-7vdz661d 224 4 can can MD cord-102966-7vdz661d 224 5 be be VB cord-102966-7vdz661d 224 6 easily easily RB cord-102966-7vdz661d 224 7 extented extented JJ cord-102966-7vdz661d 224 8 to to IN cord-102966-7vdz661d 224 9 other other JJ cord-102966-7vdz661d 224 10 compartment compartment NN cord-102966-7vdz661d 224 11 - - HYPH cord-102966-7vdz661d 224 12 based base VBN cord-102966-7vdz661d 224 13 population population NN cord-102966-7vdz661d 224 14 models model NNS cord-102966-7vdz661d 224 15 . . . cord-102966-7vdz661d 225 1 3 3 LS cord-102966-7vdz661d 225 2 Such such JJ cord-102966-7vdz661d 225 3 an an DT cord-102966-7vdz661d 225 4 extension extension NN cord-102966-7vdz661d 225 5 to to IN cord-102966-7vdz661d 225 6 the the DT cord-102966-7vdz661d 225 7 dSPIR dSPIR NNP cord-102966-7vdz661d 225 8 model model NN cord-102966-7vdz661d 225 9 structure structure NN cord-102966-7vdz661d 225 10 was be VBD cord-102966-7vdz661d 225 11 presented present VBN cord-102966-7vdz661d 225 12 and and CC cord-102966-7vdz661d 225 13 briefly briefly RB cord-102966-7vdz661d 225 14 illustrated illustrate VBN cord-102966-7vdz661d 225 15 and and CC cord-102966-7vdz661d 225 16 analyzed analyze VBD cord-102966-7vdz661d 225 17 . . . cord-102966-7vdz661d 226 1 This this DT cord-102966-7vdz661d 226 2 model model NN cord-102966-7vdz661d 226 3 is be VBZ cord-102966-7vdz661d 226 4 important important JJ cord-102966-7vdz661d 226 5 for for IN cord-102966-7vdz661d 226 6 infections infection NNS cord-102966-7vdz661d 226 7 transmitted transmit VBN cord-102966-7vdz661d 226 8 by by IN cord-102966-7vdz661d 226 9 both both DT cord-102966-7vdz661d 226 10 pre pre JJ cord-102966-7vdz661d 226 11 - - JJ cord-102966-7vdz661d 226 12 symptomatic symptomatic JJ cord-102966-7vdz661d 226 13 and and CC cord-102966-7vdz661d 226 14 symptomatic symptomatic JJ cord-102966-7vdz661d 226 15 infected infected JJ cord-102966-7vdz661d 226 16 individuals individual NNS cord-102966-7vdz661d 226 17 . . . cord-102966-7vdz661d 227 1 Similarities similarity NNS cord-102966-7vdz661d 227 2 and and CC cord-102966-7vdz661d 227 3 differences difference NNS cord-102966-7vdz661d 227 4 between between IN cord-102966-7vdz661d 227 5 SPIR SPIR NNP cord-102966-7vdz661d 227 6 and and CC cord-102966-7vdz661d 227 7 dSPIR dSPIR NNP cord-102966-7vdz661d 227 8 models model NNS cord-102966-7vdz661d 227 9 are be VBP cord-102966-7vdz661d 227 10 of of IN cord-102966-7vdz661d 227 11 the the DT cord-102966-7vdz661d 227 12 same same JJ cord-102966-7vdz661d 227 13 nature nature NN cord-102966-7vdz661d 227 14 as as IN cord-102966-7vdz661d 227 15 between between IN cord-102966-7vdz661d 227 16 SIR SIR NNP cord-102966-7vdz661d 227 17 and and CC cord-102966-7vdz661d 227 18 dSIR dsir JJ cord-102966-7vdz661d 227 19 models model NNS cord-102966-7vdz661d 227 20 . . . cord-102966-7vdz661d 228 1 Numerous numerous JJ cord-102966-7vdz661d 228 2 additional additional JJ cord-102966-7vdz661d 228 3 issues issue NNS cord-102966-7vdz661d 228 4 related relate VBN cord-102966-7vdz661d 228 5 to to IN cord-102966-7vdz661d 228 6 this this DT cord-102966-7vdz661d 228 7 work work NN cord-102966-7vdz661d 228 8 can can MD cord-102966-7vdz661d 228 9 be be VB cord-102966-7vdz661d 228 10 considered consider VBN cord-102966-7vdz661d 228 11 , , , cord-102966-7vdz661d 228 12 including include VBG cord-102966-7vdz661d 228 13 the the DT cord-102966-7vdz661d 228 14 following follow VBG cord-102966-7vdz661d 228 15 : : : cord-102966-7vdz661d 228 16 Rigorous rigorous JJ cord-102966-7vdz661d 228 17 analysis analysis NN cord-102966-7vdz661d 228 18 of of IN cord-102966-7vdz661d 228 19 DDE DDE NNP cord-102966-7vdz661d 228 20 models model NNS cord-102966-7vdz661d 228 21 ; ; : cord-102966-7vdz661d 228 22 DDE DDE NNP cord-102966-7vdz661d 228 23 modeling modeling NN cord-102966-7vdz661d 228 24 and and CC cord-102966-7vdz661d 228 25 analysis analysis NN cord-102966-7vdz661d 228 26 for for IN cord-102966-7vdz661d 228 27 a a DT cord-102966-7vdz661d 228 28 distribution distribution NN cord-102966-7vdz661d 228 29 rather rather RB cord-102966-7vdz661d 228 30 than than IN cord-102966-7vdz661d 228 31 uniform uniform JJ cord-102966-7vdz661d 228 32 delay delay NNP cord-102966-7vdz661d 228 33 ( ( -LRB- cord-102966-7vdz661d 228 34 cf cf NN cord-102966-7vdz661d 228 35 . . . cord-102966-7vdz661d 229 1 Figure figure NN cord-102966-7vdz661d 229 2 2 2 CD cord-102966-7vdz661d 229 3 ) ) -RRB- cord-102966-7vdz661d 229 4 ; ; : cord-102966-7vdz661d 229 5 resolution resolution NN cord-102966-7vdz661d 229 6 of of IN cord-102966-7vdz661d 229 7 conjectures conjecture NNS cord-102966-7vdz661d 229 8 presented present VBN cord-102966-7vdz661d 229 9 in in IN cord-102966-7vdz661d 229 10 the the DT cord-102966-7vdz661d 229 11 text text NN cord-102966-7vdz661d 229 12 ; ; : cord-102966-7vdz661d 229 13 and and CC cord-102966-7vdz661d 229 14 implications implication NNS cord-102966-7vdz661d 229 15 for for IN cord-102966-7vdz661d 229 16 different different JJ cord-102966-7vdz661d 229 17 forms form NNS cord-102966-7vdz661d 229 18 of of IN cord-102966-7vdz661d 229 19 infection infection NN cord-102966-7vdz661d 229 20 kinetics kinetics NN cord-102966-7vdz661d 229 21 . . . cord-102966-7vdz661d 230 1 Such such JJ cord-102966-7vdz661d 230 2 issues issue NNS cord-102966-7vdz661d 230 3 will will MD cord-102966-7vdz661d 230 4 be be VB cord-102966-7vdz661d 230 5 addressed address VBN cord-102966-7vdz661d 230 6 in in IN cord-102966-7vdz661d 230 7 forthcoming forthcoming JJ cord-102966-7vdz661d 230 8 publications publication NNS cord-102966-7vdz661d 230 9 . . . cord-102966-7vdz661d 231 1 All all DT cord-102966-7vdz661d 231 2 computations computation NNS cord-102966-7vdz661d 231 3 were be VBD cord-102966-7vdz661d 231 4 done do VBN cord-102966-7vdz661d 231 5 in in IN cord-102966-7vdz661d 231 6 Mathematica Mathematica NNP cord-102966-7vdz661d 231 7 , , , cord-102966-7vdz661d 231 8 available available JJ cord-102966-7vdz661d 231 9 at at IN cord-102966-7vdz661d 231 10 the the DT cord-102966-7vdz661d 231 11 University University NNP cord-102966-7vdz661d 231 12 of of IN cord-102966-7vdz661d 231 13 Houston Houston NNP cord-102966-7vdz661d 231 14 . . . cord-102966-7vdz661d 232 1 Sharing share VBG cord-102966-7vdz661d 232 2 of of IN cord-102966-7vdz661d 232 3 teaching teaching NN cord-102966-7vdz661d 232 4 material material NN cord-102966-7vdz661d 232 5 about about IN cord-102966-7vdz661d 232 6 the the DT cord-102966-7vdz661d 232 7 SIR SIR NNP cord-102966-7vdz661d 232 8 model model NN cord-102966-7vdz661d 232 9 on on IN cord-102966-7vdz661d 232 10 Github Github NNP cord-102966-7vdz661d 232 11 by by IN cord-102966-7vdz661d 232 12 Prof. Prof. NNP cord-102966-7vdz661d 232 13 Jeff Jeff NNP cord-102966-7vdz661d 232 14 Kantor Kantor NNP cord-102966-7vdz661d 232 15 of of IN cord-102966-7vdz661d 232 16 Notre Notre NNP cord-102966-7vdz661d 232 17 Dame Dame NNP cord-102966-7vdz661d 232 18 is be VBZ cord-102966-7vdz661d 232 19 also also RB cord-102966-7vdz661d 232 20 gratefully gratefully RB cord-102966-7vdz661d 232 21 acknowledged acknowledge VBN cord-102966-7vdz661d 232 22 . . . cord-102966-7vdz661d 233 1 Research research NN cord-102966-7vdz661d 233 2 reported report VBN cord-102966-7vdz661d 233 3 in in IN cord-102966-7vdz661d 233 4 this this DT cord-102966-7vdz661d 233 5 publication publication NN cord-102966-7vdz661d 233 6 was be VBD cord-102966-7vdz661d 233 7 partially partially RB cord-102966-7vdz661d 233 8 supported support VBN cord-102966-7vdz661d 233 9 by by IN cord-102966-7vdz661d 233 10 the the DT cord-102966-7vdz661d 233 11 Institute Institute NNP cord-102966-7vdz661d 233 12 of of IN cord-102966-7vdz661d 233 13 Allergy Allergy NNP cord-102966-7vdz661d 233 14 and and CC cord-102966-7vdz661d 233 15 Infectious Infectious NNP cord-102966-7vdz661d 233 16 Diseases Diseases NNPS cord-102966-7vdz661d 233 17 of of IN cord-102966-7vdz661d 233 18 the the DT cord-102966-7vdz661d 233 19 National National NNP cord-102966-7vdz661d 233 20 Institutes Institutes NNPS cord-102966-7vdz661d 233 21 of of IN cord-102966-7vdz661d 233 22 Health Health NNP cord-102966-7vdz661d 233 23 under under IN cord-102966-7vdz661d 233 24 award award NN cord-102966-7vdz661d 233 25 number number NN cord-102966-7vdz661d 233 26 R01AI140287 r01ai140287 RB cord-102966-7vdz661d 233 27 , , , cord-102966-7vdz661d 233 28 financed finance VBN cord-102966-7vdz661d 233 29 with with IN cord-102966-7vdz661d 233 30 Federal Federal NNP cord-102966-7vdz661d 233 31 money money NN cord-102966-7vdz661d 233 32 . . . cord-102966-7vdz661d 234 1 The the DT cord-102966-7vdz661d 234 2 content content NN cord-102966-7vdz661d 234 3 is be VBZ cord-102966-7vdz661d 234 4 solely solely RB cord-102966-7vdz661d 234 5 the the DT cord-102966-7vdz661d 234 6 responsibility responsibility NN cord-102966-7vdz661d 234 7 of of IN cord-102966-7vdz661d 234 8 the the DT cord-102966-7vdz661d 234 9 author author NN cord-102966-7vdz661d 234 10 and and CC cord-102966-7vdz661d 234 11 does do VBZ cord-102966-7vdz661d 234 12 not not RB cord-102966-7vdz661d 234 13 necessarily necessarily RB cord-102966-7vdz661d 234 14 represent represent VB cord-102966-7vdz661d 234 15 the the DT cord-102966-7vdz661d 234 16 official official JJ cord-102966-7vdz661d 234 17 views view NNS cord-102966-7vdz661d 234 18 of of IN cord-102966-7vdz661d 234 19 the the DT cord-102966-7vdz661d 234 20 National National NNP cord-102966-7vdz661d 234 21 Institutes Institutes NNPS cord-102966-7vdz661d 234 22 of of IN cord-102966-7vdz661d 234 23 Health Health NNP cord-102966-7vdz661d 234 24 . . . cord-102966-7vdz661d 235 1 The the DT cord-102966-7vdz661d 235 2 roots root NNS cord-102966-7vdz661d 235 3 of of IN cord-102966-7vdz661d 235 4 the the DT cord-102966-7vdz661d 235 5 transcendental transcendental JJ cord-102966-7vdz661d 235 6 characteristic characteristic JJ cord-102966-7vdz661d 235 7 equation equation NN cord-102966-7vdz661d 235 8 is be VBZ cord-102966-7vdz661d 235 9 the the DT cord-102966-7vdz661d 235 10 author author NN cord-102966-7vdz661d 235 11 / / SYM cord-102966-7vdz661d 235 12 funder funder NN cord-102966-7vdz661d 235 13 , , , cord-102966-7vdz661d 235 14 who who WP cord-102966-7vdz661d 235 15 has have VBZ cord-102966-7vdz661d 235 16 granted grant VBN cord-102966-7vdz661d 235 17 medRxiv medRxiv NNS cord-102966-7vdz661d 235 18 a a DT cord-102966-7vdz661d 235 19 license license NN cord-102966-7vdz661d 235 20 to to TO cord-102966-7vdz661d 235 21 display display VB cord-102966-7vdz661d 235 22 the the DT cord-102966-7vdz661d 235 23 preprint preprint NN cord-102966-7vdz661d 235 24 in in IN cord-102966-7vdz661d 235 25 perpetuity perpetuity NN cord-102966-7vdz661d 235 26 . . . cord-102966-7vdz661d 236 1 The the DT cord-102966-7vdz661d 236 2 copyright copyright NN cord-102966-7vdz661d 236 3 holder holder NN cord-102966-7vdz661d 236 4 for for IN cord-102966-7vdz661d 236 5 this this DT cord-102966-7vdz661d 236 6 preprint preprint NN cord-102966-7vdz661d 236 7 this this DT cord-102966-7vdz661d 236 8 version version NN cord-102966-7vdz661d 236 9 posted post VBN cord-102966-7vdz661d 236 10 May May NNP cord-102966-7vdz661d 236 11 1 1 CD cord-102966-7vdz661d 236 12 , , , cord-102966-7vdz661d 236 13 2020 2020 CD cord-102966-7vdz661d 236 14 . . . cord-102966-7vdz661d 236 15 _SP cord-102966-7vdz661d 237 1 For for IN cord-102966-7vdz661d 237 2 stability stability NN cord-102966-7vdz661d 237 3 , , , cord-102966-7vdz661d 237 4 all all DT cord-102966-7vdz661d 237 5 must must MD cord-102966-7vdz661d 237 6 be be VB cord-102966-7vdz661d 237 7 in in IN cord-102966-7vdz661d 237 8 the the DT cord-102966-7vdz661d 237 9 left left JJ cord-102966-7vdz661d 237 10 - - HYPH cord-102966-7vdz661d 237 11 half half NN cord-102966-7vdz661d 237 12 of of IN cord-102966-7vdz661d 237 13 the the DT cord-102966-7vdz661d 237 14 complex complex JJ cord-102966-7vdz661d 237 15 plane plane NN cord-102966-7vdz661d 237 16 . . . cord-102966-7vdz661d 238 1 We -PRON- PRP cord-102966-7vdz661d 238 2 show show VBP cord-102966-7vdz661d 238 3 first first RB cord-102966-7vdz661d 238 4 that that IN cord-102966-7vdz661d 238 5 for for IN cord-102966-7vdz661d 238 6 any any DT cord-102966-7vdz661d 238 7 positive positive JJ cord-102966-7vdz661d 238 8 value value NN cord-102966-7vdz661d 238 9 of of IN cord-102966-7vdz661d 238 10 ̅ ̅ NN cord-102966-7vdz661d 238 11 , , , cord-102966-7vdz661d 238 12 no no DT cord-102966-7vdz661d 238 13 complex complex JJ cord-102966-7vdz661d 238 14 root root NN cord-102966-7vdz661d 238 15 = = SYM cord-102966-7vdz661d 238 16 + + CC cord-102966-7vdz661d 238 17 can can MD cord-102966-7vdz661d 238 18 cross cross VB cord-102966-7vdz661d 238 19 the the DT cord-102966-7vdz661d 238 20 imaginary imaginary JJ cord-102966-7vdz661d 238 21 axis axis NN cord-102966-7vdz661d 238 22 to to TO cord-102966-7vdz661d 238 23 move move VB cord-102966-7vdz661d 238 24 from from IN cord-102966-7vdz661d 238 25 stability stability NN cord-102966-7vdz661d 238 26 to to IN cord-102966-7vdz661d 238 27 instability instability NN cord-102966-7vdz661d 238 28 . . . cord-102966-7vdz661d 239 1 Because because IN cord-102966-7vdz661d 239 2 , , , cord-102966-7vdz661d 239 3 if if IN cord-102966-7vdz661d 239 4 = = LS cord-102966-7vdz661d 239 5 were be VBD cord-102966-7vdz661d 239 6 a a DT cord-102966-7vdz661d 239 7 root root NN cord-102966-7vdz661d 239 8 of of IN cord-102966-7vdz661d 239 9 eqn eqn NN cord-102966-7vdz661d 239 10 . . . cord-102966-7vdz661d 240 1 ( ( -LRB- cord-102966-7vdz661d 240 2 58 58 CD cord-102966-7vdz661d 240 3 ) ) -RRB- cord-102966-7vdz661d 240 4 for for IN cord-102966-7vdz661d 240 5 ̅ ̅ NN cord-102966-7vdz661d 240 6 > > XX cord-102966-7vdz661d 240 7 0 0 NFP cord-102966-7vdz661d 240 8 , , , cord-102966-7vdz661d 240 9 it -PRON- PRP cord-102966-7vdz661d 240 10 would would MD cord-102966-7vdz661d 240 11 be be VB cord-102966-7vdz661d 240 12 Therefore therefore RB cord-102966-7vdz661d 240 13 , , , cord-102966-7vdz661d 240 14 only only RB cord-102966-7vdz661d 240 15 real real JJ cord-102966-7vdz661d 240 16 roots root NNS cord-102966-7vdz661d 240 17 should should MD cord-102966-7vdz661d 240 18 be be VB cord-102966-7vdz661d 240 19 considered consider VBN cord-102966-7vdz661d 240 20 in in IN cord-102966-7vdz661d 240 21 eqn eqn NN cord-102966-7vdz661d 240 22 . . . cord-102966-7vdz661d 241 1 ( ( -LRB- cord-102966-7vdz661d 241 2 59 59 CD cord-102966-7vdz661d 241 3 ) ) -RRB- cord-102966-7vdz661d 241 4 for for IN cord-102966-7vdz661d 241 5 stability stability NN cord-102966-7vdz661d 241 6 analysis analysis NN cord-102966-7vdz661d 241 7 . . . cord-102966-7vdz661d 242 1 Furthermore furthermore RB cord-102966-7vdz661d 242 2 , , , cord-102966-7vdz661d 242 3 since since IN cord-102966-7vdz661d 242 4 the the DT cord-102966-7vdz661d 242 5 relevant relevant JJ cord-102966-7vdz661d 242 6 values value NNS cord-102966-7vdz661d 242 7 of of IN cord-102966-7vdz661d 242 8 are be VBP cord-102966-7vdz661d 242 9 0 0 CD cord-102966-7vdz661d 242 10 , , , cord-102966-7vdz661d 242 11 −1 −1 NNP cord-102966-7vdz661d 242 12 in in IN cord-102966-7vdz661d 242 13 eqn eqn NN cord-102966-7vdz661d 242 14 . . . cord-102966-7vdz661d 243 1 ( ( -LRB- cord-102966-7vdz661d 243 2 59 59 CD cord-102966-7vdz661d 243 3 ) ) -RRB- cord-102966-7vdz661d 243 4 for for IN cord-102966-7vdz661d 243 5 ∈ ∈ NNP cord-102966-7vdz661d 243 6 ℝ ℝ NNP cord-102966-7vdz661d 243 7 , , , cord-102966-7vdz661d 243 8 and and CC cord-102966-7vdz661d 243 9 < < XX cord-102966-7vdz661d 243 10 0 0 NFP cord-102966-7vdz661d 243 11 implies imply VBZ cord-102966-7vdz661d 243 12 which which WDT cord-102966-7vdz661d 243 13 is be VBZ cord-102966-7vdz661d 243 14 satisfied satisfied JJ cord-102966-7vdz661d 243 15 for for IN cord-102966-7vdz661d 243 16 < < XX cord-102966-7vdz661d 243 17 1 1 CD cord-102966-7vdz661d 243 18 ( ( -LRB- cord-102966-7vdz661d 243 19 see see VB cord-102966-7vdz661d 243 20 figure figure NN cord-102966-7vdz661d 243 21 below below RB cord-102966-7vdz661d 243 22 ) ) -RRB- cord-102966-7vdz661d 243 23 leading lead VBG cord-102966-7vdz661d 243 24 immediately immediately RB cord-102966-7vdz661d 243 25 to to IN cord-102966-7vdz661d 243 26 eqn eqn NN cord-102966-7vdz661d 243 27 . . . cord-102966-7vdz661d 244 1 ( ( -LRB- cord-102966-7vdz661d 244 2 17 17 CD cord-102966-7vdz661d 244 3 ) ) -RRB- cord-102966-7vdz661d 244 4 . . . cord-102966-7vdz661d 245 1 Appendix Appendix NNP cord-102966-7vdz661d 245 2 C. C. NNP cord-102966-7vdz661d 245 3 Proof Proof NNP cord-102966-7vdz661d 245 4 of of IN cord-102966-7vdz661d 245 5 eqn eqn NNP cord-102966-7vdz661d 245 6 . . . cord-102966-7vdz661d 246 1 ( ( -LRB- cord-102966-7vdz661d 246 2 19 19 CD cord-102966-7vdz661d 246 3 ) ) -RRB- cord-102966-7vdz661d 246 4 Dividing divide VBG cord-102966-7vdz661d 246 5 eqn eqn NN cord-102966-7vdz661d 246 6 . . . cord-102966-7vdz661d 247 1 ( ( -LRB- cord-102966-7vdz661d 247 2 7 7 CD cord-102966-7vdz661d 247 3 ) ) -RRB- cord-102966-7vdz661d 247 4 by by IN cord-102966-7vdz661d 247 5 yields yield NNS cord-102966-7vdz661d 247 6 Continuing continue VBG cord-102966-7vdz661d 247 7 on on IN cord-102966-7vdz661d 247 8 the the DT cord-102966-7vdz661d 247 9 last last JJ cord-102966-7vdz661d 247 10 equation equation NN cord-102966-7vdz661d 247 11 we -PRON- PRP cord-102966-7vdz661d 247 12 get get VBP cord-102966-7vdz661d 247 13 which which WDT cord-102966-7vdz661d 247 14 is be VBZ cord-102966-7vdz661d 247 15 eqn eqn NN cord-102966-7vdz661d 247 16 . . . cord-102966-7vdz661d 248 1 ( ( -LRB- cord-102966-7vdz661d 248 2 19 19 CD cord-102966-7vdz661d 248 3 ) ) -RRB- cord-102966-7vdz661d 248 4 . . . cord-102966-7vdz661d 249 1 The the DT cord-102966-7vdz661d 249 2 Padé Padé NNP cord-102966-7vdz661d 249 3 SIR SIR NNP cord-102966-7vdz661d 249 4 model model NN cord-102966-7vdz661d 249 5 also also RB cord-102966-7vdz661d 249 6 reaches reach VBZ cord-102966-7vdz661d 249 7 the the DT cord-102966-7vdz661d 249 8 same same JJ cord-102966-7vdz661d 249 9 result result NN cord-102966-7vdz661d 249 10 : : : cord-102966-7vdz661d 249 11 Dividing divide VBG cord-102966-7vdz661d 249 12 eqn eqn NN cord-102966-7vdz661d 249 13 . . . cord-102966-7vdz661d 250 1 ( ( -LRB- cord-102966-7vdz661d 250 2 1 1 CD cord-102966-7vdz661d 250 3 ) ) -RRB- cord-102966-7vdz661d 250 4 by by IN cord-102966-7vdz661d 250 5 eqn eqn NN cord-102966-7vdz661d 250 6 . . . cord-102966-7vdz661d 251 1 ( ( -LRB- cord-102966-7vdz661d 251 2 13 13 CD cord-102966-7vdz661d 251 3 ) ) -RRB- cord-102966-7vdz661d 251 4 and and CC cord-102966-7vdz661d 251 5 rearranging rearrange VBG cord-102966-7vdz661d 251 6 yields yield NNS cord-102966-7vdz661d 251 7 Taking take VBG cord-102966-7vdz661d 251 8 the the DT cord-102966-7vdz661d 251 9 limit limit NN cord-102966-7vdz661d 251 10 as as IN cord-102966-7vdz661d 251 11 → → $ cord-102966-7vdz661d 251 12 ∞ ∞ NNP cord-102966-7vdz661d 251 13 with with IN cord-102966-7vdz661d 251 14 1/ 1/ CD cord-102966-7vdz661d 251 15 = = SYM cord-102966-7vdz661d 251 16 , , , cord-102966-7vdz661d 251 17 0 0 NFP cord-102966-7vdz661d 251 18 ≈ ≈ NNP cord-102966-7vdz661d 251 19 1 1 CD cord-102966-7vdz661d 251 20 , , , cord-102966-7vdz661d 251 21 and and CC cord-102966-7vdz661d 251 22 0 0 NFP cord-102966-7vdz661d 251 23 ≈ ≈ CD cord-102966-7vdz661d 251 24 0 0 NFP cord-102966-7vdz661d 251 25 yields yield VBZ cord-102966-7vdz661d 251 26 eqn eqn NN cord-102966-7vdz661d 251 27 . . . cord-102966-7vdz661d 252 1 ( ( -LRB- cord-102966-7vdz661d 252 2 19 19 CD cord-102966-7vdz661d 252 3 ) ) -RRB- cord-102966-7vdz661d 252 4 . . . cord-102966-7vdz661d 253 1 Proof proof NN cord-102966-7vdz661d 253 2 that that IN cord-102966-7vdz661d 253 3 the the DT cord-102966-7vdz661d 253 4 standard standard JJ cord-102966-7vdz661d 253 5 SIR SIR NNP cord-102966-7vdz661d 253 6 model model NN cord-102966-7vdz661d 253 7 also also RB cord-102966-7vdz661d 253 8 reaches reach VBZ cord-102966-7vdz661d 253 9 the the DT cord-102966-7vdz661d 253 10 same same JJ cord-102966-7vdz661d 253 11 result result NN cord-102966-7vdz661d 253 12 follows follow VBZ cord-102966-7vdz661d 253 13 the the DT cord-102966-7vdz661d 253 14 same same JJ cord-102966-7vdz661d 253 15 pattern pattern NN cord-102966-7vdz661d 253 16 and and CC cord-102966-7vdz661d 253 17 is be VBZ cord-102966-7vdz661d 253 18 omitted omit VBN cord-102966-7vdz661d 253 19 for for IN cord-102966-7vdz661d 253 20 brevity brevity NN cord-102966-7vdz661d 253 21 . . . cord-102966-7vdz661d 254 1 Therefore therefore RB cord-102966-7vdz661d 254 2 , , , cord-102966-7vdz661d 254 3 the the DT cord-102966-7vdz661d 254 4 terms term NNS cord-102966-7vdz661d 254 5 rapidly rapidly RB cord-102966-7vdz661d 254 6 decay decay VBP cord-102966-7vdz661d 254 7 for for IN cord-102966-7vdz661d 254 8 ≥ ≥ CD cord-102966-7vdz661d 254 9 1 1 CD cord-102966-7vdz661d 254 10 , , , cord-102966-7vdz661d 254 11 and and CC cord-102966-7vdz661d 254 12 the the DT cord-102966-7vdz661d 254 13 summation summation NN cord-102966-7vdz661d 254 14 in in IN cord-102966-7vdz661d 254 15 eqn eqn NN cord-102966-7vdz661d 254 16 . . . cord-102966-7vdz661d 255 1 ( ( -LRB- cord-102966-7vdz661d 255 2 65 65 CD cord-102966-7vdz661d 255 3 ) ) -RRB- cord-102966-7vdz661d 255 4 quickly quickly RB cord-102966-7vdz661d 255 5 becomes become VBZ cord-102966-7vdz661d 255 6 approximately approximately RB cord-102966-7vdz661d 255 7 equal equal JJ cord-102966-7vdz661d 255 8 to to IN cord-102966-7vdz661d 255 9 . . . cord-102966-7vdz661d 256 1 CC CC NNP cord-102966-7vdz661d 256 2 - - HYPH cord-102966-7vdz661d 256 3 BY BY NNP cord-102966-7vdz661d 256 4 - - HYPH cord-102966-7vdz661d 256 5 NC NC NNP cord-102966-7vdz661d 256 6 - - HYPH cord-102966-7vdz661d 256 7 ND ND NNP cord-102966-7vdz661d 256 8 4.0 4.0 CD cord-102966-7vdz661d 256 9 International international JJ cord-102966-7vdz661d 256 10 license license NN cord-102966-7vdz661d 257 1 It -PRON- PRP cord-102966-7vdz661d 257 2 is be VBZ cord-102966-7vdz661d 257 3 made make VBN cord-102966-7vdz661d 257 4 available available JJ cord-102966-7vdz661d 257 5 under under IN cord-102966-7vdz661d 257 6 a a DT cord-102966-7vdz661d 258 1 is be VBZ cord-102966-7vdz661d 258 2 the the DT cord-102966-7vdz661d 258 3 author author NN cord-102966-7vdz661d 258 4 / / SYM cord-102966-7vdz661d 258 5 funder funder NN cord-102966-7vdz661d 258 6 , , , cord-102966-7vdz661d 258 7 who who WP cord-102966-7vdz661d 258 8 has have VBZ cord-102966-7vdz661d 258 9 granted grant VBN cord-102966-7vdz661d 258 10 medRxiv medRxiv NNS cord-102966-7vdz661d 258 11 a a DT cord-102966-7vdz661d 258 12 license license NN cord-102966-7vdz661d 258 13 to to TO cord-102966-7vdz661d 258 14 display display VB cord-102966-7vdz661d 258 15 the the DT cord-102966-7vdz661d 258 16 preprint preprint NN cord-102966-7vdz661d 258 17 in in IN cord-102966-7vdz661d 258 18 perpetuity perpetuity NN cord-102966-7vdz661d 258 19 . . . cord-102966-7vdz661d 259 1 The the DT cord-102966-7vdz661d 259 2 copyright copyright NN cord-102966-7vdz661d 259 3 holder holder NN cord-102966-7vdz661d 259 4 for for IN cord-102966-7vdz661d 259 5 this this DT cord-102966-7vdz661d 259 6 preprint preprint NN cord-102966-7vdz661d 259 7 this this DT cord-102966-7vdz661d 259 8 version version NN cord-102966-7vdz661d 259 9 posted post VBN cord-102966-7vdz661d 259 10 May May NNP cord-102966-7vdz661d 259 11 1 1 CD cord-102966-7vdz661d 259 12 , , , cord-102966-7vdz661d 259 13 2020 2020 CD cord-102966-7vdz661d 259 14 . . . cord-102966-7vdz661d 259 15 . . . cord-102966-7vdz661d 260 1 CC CC NNP cord-102966-7vdz661d 260 2 - - HYPH cord-102966-7vdz661d 260 3 BY BY NNP cord-102966-7vdz661d 260 4 - - HYPH cord-102966-7vdz661d 260 5 NC NC NNP cord-102966-7vdz661d 260 6 - - HYPH cord-102966-7vdz661d 260 7 ND ND NNP cord-102966-7vdz661d 260 8 4.0 4.0 CD cord-102966-7vdz661d 260 9 International international JJ cord-102966-7vdz661d 260 10 license license NN cord-102966-7vdz661d 261 1 It -PRON- PRP cord-102966-7vdz661d 261 2 is be VBZ cord-102966-7vdz661d 261 3 made make VBN cord-102966-7vdz661d 261 4 available available JJ cord-102966-7vdz661d 261 5 under under IN cord-102966-7vdz661d 261 6 a a DT cord-102966-7vdz661d 262 1 is be VBZ cord-102966-7vdz661d 262 2 the the DT cord-102966-7vdz661d 262 3 author author NN cord-102966-7vdz661d 262 4 / / SYM cord-102966-7vdz661d 262 5 funder funder NN cord-102966-7vdz661d 262 6 , , , cord-102966-7vdz661d 262 7 who who WP cord-102966-7vdz661d 262 8 has have VBZ cord-102966-7vdz661d 262 9 granted grant VBN cord-102966-7vdz661d 262 10 medRxiv medRxiv NNS cord-102966-7vdz661d 262 11 a a DT cord-102966-7vdz661d 262 12 license license NN cord-102966-7vdz661d 262 13 to to TO cord-102966-7vdz661d 262 14 display display VB cord-102966-7vdz661d 262 15 the the DT cord-102966-7vdz661d 262 16 preprint preprint NN cord-102966-7vdz661d 262 17 in in IN cord-102966-7vdz661d 262 18 perpetuity perpetuity NN cord-102966-7vdz661d 262 19 . . . cord-102966-7vdz661d 263 1 ( ( -LRB- cord-102966-7vdz661d 263 2 which which WDT cord-102966-7vdz661d 263 3 was be VBD cord-102966-7vdz661d 263 4 not not RB cord-102966-7vdz661d 263 5 certified certify VBN cord-102966-7vdz661d 263 6 by by IN cord-102966-7vdz661d 263 7 peer peer NN cord-102966-7vdz661d 263 8 review review NN cord-102966-7vdz661d 263 9 ) ) -RRB- cord-102966-7vdz661d 264 1 The the DT cord-102966-7vdz661d 264 2 copyright copyright NN cord-102966-7vdz661d 264 3 holder holder NN cord-102966-7vdz661d 264 4 for for IN cord-102966-7vdz661d 264 5 this this DT cord-102966-7vdz661d 264 6 preprint preprint NN cord-102966-7vdz661d 264 7 this this DT cord-102966-7vdz661d 264 8 version version NN cord-102966-7vdz661d 264 9 posted post VBN cord-102966-7vdz661d 264 10 May May NNP cord-102966-7vdz661d 264 11 1 1 CD cord-102966-7vdz661d 264 12 , , , cord-102966-7vdz661d 264 13 2020 2020 CD cord-102966-7vdz661d 264 14 . . . cord-102966-7vdz661d 264 15 . . . cord-102966-7vdz661d 265 1 https://doi.org/10.1101/2020.04.26.20080960 https://doi.org/10.1101/2020.04.26.20080960 NNP cord-102966-7vdz661d 265 2 doi doi NNP cord-102966-7vdz661d 265 3 : : : cord-102966-7vdz661d 266 1 medRxiv medRxiv NNS cord-102966-7vdz661d 267 1 preprint preprint NNP cord-102966-7vdz661d 267 2 A a DT cord-102966-7vdz661d 267 3 Contribution Contribution NNP cord-102966-7vdz661d 267 4 to to IN cord-102966-7vdz661d 267 5 the the DT cord-102966-7vdz661d 267 6 Mathematical Mathematical NNP cord-102966-7vdz661d 267 7 Theory Theory NNP cord-102966-7vdz661d 267 8 of of IN cord-102966-7vdz661d 267 9 Epidemics Epidemics NNP cord-102966-7vdz661d 267 10 Modeling model VBG cord-102966-7vdz661d 267 11 Infectious infectious JJ cord-102966-7vdz661d 267 12 Diseases Diseases NNPS cord-102966-7vdz661d 267 13 in in IN cord-102966-7vdz661d 267 14 Humans Humans NNPS cord-102966-7vdz661d 267 15 and and CC cord-102966-7vdz661d 267 16 Animals Animals NNPS cord-102966-7vdz661d 267 17 Population Population NNP cord-102966-7vdz661d 267 18 biology biology NN cord-102966-7vdz661d 267 19 of of IN cord-102966-7vdz661d 267 20 infectious infectious JJ cord-102966-7vdz661d 267 21 diseases disease NNS cord-102966-7vdz661d 267 22 : : : cord-102966-7vdz661d 268 1 Part part NN cord-102966-7vdz661d 268 2 I -PRON- PRP cord-102966-7vdz661d 268 3 Mathematical mathematical JJ cord-102966-7vdz661d 268 4 Biology biology NN cord-102966-7vdz661d 268 5 : : : cord-102966-7vdz661d 268 6 I. I. NNP cord-102966-7vdz661d 268 7 An an DT cord-102966-7vdz661d 268 8 Introduction introduction NN cord-102966-7vdz661d 268 9 Infectious infectious JJ cord-102966-7vdz661d 268 10 diseases disease NNS cord-102966-7vdz661d 268 11 of of IN cord-102966-7vdz661d 268 12 humans human NNS cord-102966-7vdz661d 268 13 : : : cord-102966-7vdz661d 268 14 dynamics dynamic NNS cord-102966-7vdz661d 268 15 and and CC cord-102966-7vdz661d 268 16 control control NN cord-102966-7vdz661d 269 1 Evolving evolve VBG cord-102966-7vdz661d 269 2 Epidemiology Epidemiology NNP cord-102966-7vdz661d 269 3 and and CC cord-102966-7vdz661d 269 4 Impact Impact NNP cord-102966-7vdz661d 269 5 of of IN cord-102966-7vdz661d 269 6 Non non JJ cord-102966-7vdz661d 269 7 - - JJ cord-102966-7vdz661d 269 8 pharmaceutical pharmaceutical JJ cord-102966-7vdz661d 269 9 Interventions Interventions NNPS cord-102966-7vdz661d 269 10 on on IN cord-102966-7vdz661d 269 11 the the DT cord-102966-7vdz661d 269 12 Outbreak outbreak NN cord-102966-7vdz661d 269 13 of of IN cord-102966-7vdz661d 269 14 Coronavirus Coronavirus NNP cord-102966-7vdz661d 269 15 Disease Disease NNP cord-102966-7vdz661d 269 16 Exact Exact NNP cord-102966-7vdz661d 269 17 analytical analytical JJ cord-102966-7vdz661d 269 18 solutions solution NNS cord-102966-7vdz661d 269 19 of of IN cord-102966-7vdz661d 269 20 the the DT cord-102966-7vdz661d 269 21 Susceptible susceptible JJ cord-102966-7vdz661d 269 22 - - HYPH cord-102966-7vdz661d 269 23 Infected Infected NNP cord-102966-7vdz661d 269 24 - - HYPH cord-102966-7vdz661d 269 25 Recovered recovered JJ cord-102966-7vdz661d 269 26 ( ( -LRB- cord-102966-7vdz661d 269 27 SIR SIR NNP cord-102966-7vdz661d 269 28 ) ) -RRB- cord-102966-7vdz661d 269 29 epidemic epidemic NN cord-102966-7vdz661d 269 30 model model NN cord-102966-7vdz661d 269 31 and and CC cord-102966-7vdz661d 269 32 of of IN cord-102966-7vdz661d 269 33 the the DT cord-102966-7vdz661d 269 34 SIR SIR NNP cord-102966-7vdz661d 269 35 model model NN cord-102966-7vdz661d 269 36 with with IN cord-102966-7vdz661d 269 37 equal equal JJ cord-102966-7vdz661d 269 38 death death NN cord-102966-7vdz661d 269 39 and and CC cord-102966-7vdz661d 269 40 birth birth NN cord-102966-7vdz661d 269 41 rates rate NNS cord-102966-7vdz661d 269 42 The the DT cord-102966-7vdz661d 269 43 Incubation Incubation NNP cord-102966-7vdz661d 269 44 Period Period NNP cord-102966-7vdz661d 269 45 of of IN cord-102966-7vdz661d 269 46 Coronavirus Coronavirus NNP cord-102966-7vdz661d 269 47 Disease Disease NNP cord-102966-7vdz661d 269 48 2019 2019 CD cord-102966-7vdz661d 270 1 ( ( -LRB- cord-102966-7vdz661d 270 2 COVID-19 covid-19 VB cord-102966-7vdz661d 270 3 ) ) -RRB- cord-102966-7vdz661d 270 4 From from IN cord-102966-7vdz661d 270 5 Publicly publicly RB cord-102966-7vdz661d 270 6 Reported report VBN cord-102966-7vdz661d 270 7 Confirmed confirm VBN cord-102966-7vdz661d 270 8 Cases case NNS cord-102966-7vdz661d 270 9 : : : cord-102966-7vdz661d 271 1 Estimation Estimation NNP cord-102966-7vdz661d 271 2 and and CC cord-102966-7vdz661d 271 3 Application Application NNP cord-102966-7vdz661d 271 4 Risk Risk NNP cord-102966-7vdz661d 271 5 Assessment Assessment NNP cord-102966-7vdz661d 271 6 of of IN cord-102966-7vdz661d 271 7 Novel Novel NNP cord-102966-7vdz661d 271 8 Coronavirus Coronavirus NNP cord-102966-7vdz661d 271 9 COVID-19 covid-19 CD cord-102966-7vdz661d 271 10 Outbreaks Outbreaks NNPS cord-102966-7vdz661d 271 11 Outside Outside NNP cord-102966-7vdz661d 271 12 China China NNP cord-102966-7vdz661d 272 1 An an DT cord-102966-7vdz661d 272 2 interactive interactive JJ cord-102966-7vdz661d 272 3 web web NN cord-102966-7vdz661d 272 4 - - HYPH cord-102966-7vdz661d 272 5 based base VBN cord-102966-7vdz661d 272 6 dashboard dashboard NN cord-102966-7vdz661d 272 7 to to TO cord-102966-7vdz661d 272 8 track track VB cord-102966-7vdz661d 272 9 COVID-19 COVID-19 NNP cord-102966-7vdz661d 272 10 in in IN cord-102966-7vdz661d 272 11 real real JJ cord-102966-7vdz661d 272 12 time time NN cord-102966-7vdz661d 272 13 Chemical Chemical NNP cord-102966-7vdz661d 272 14 Process Process NNP cord-102966-7vdz661d 272 15 Control Control NNP cord-102966-7vdz661d 272 16 : : : cord-102966-7vdz661d 272 17 An an DT cord-102966-7vdz661d 272 18 Introduction introduction NN cord-102966-7vdz661d 272 19 to to IN cord-102966-7vdz661d 272 20 Theory Theory NNP cord-102966-7vdz661d 272 21 and and CC cord-102966-7vdz661d 272 22 Practice Practice NNP cord-102966-7vdz661d 272 23 Delay delay NN cord-102966-7vdz661d 272 24 Differential Differential NNP cord-102966-7vdz661d 272 25 Equations Equations NNPS cord-102966-7vdz661d 272 26 with with IN cord-102966-7vdz661d 272 27 Applications Applications NNPS cord-102966-7vdz661d 272 28 in in IN cord-102966-7vdz661d 272 29 Population Population NNP cord-102966-7vdz661d 272 30 Dynamics Dynamics NNPS cord-102966-7vdz661d 272 31 Stability Stability NNP cord-102966-7vdz661d 272 32 and and CC cord-102966-7vdz661d 272 33 Oscillations Oscillations NNPS cord-102966-7vdz661d 272 34 in in IN cord-102966-7vdz661d 272 35 Delay Delay NNP cord-102966-7vdz661d 272 36 Differential Differential NNP cord-102966-7vdz661d 272 37 Equations Equations NNPS cord-102966-7vdz661d 272 38 of of IN cord-102966-7vdz661d 272 39 Population Population NNP cord-102966-7vdz661d 272 40 Dynamics Dynamics NNPS cord-102966-7vdz661d 273 1 On on IN cord-102966-7vdz661d 273 2 the the DT cord-102966-7vdz661d 273 3 LambertW lambertw JJ cord-102966-7vdz661d 273 4 function function NN cord-102966-7vdz661d 273 5 The the DT cord-102966-7vdz661d 273 6 Lambert Lambert NNP cord-102966-7vdz661d 273 7 function function NN cord-102966-7vdz661d 273 8 belongs belong VBZ cord-102966-7vdz661d 273 9 in in IN cord-102966-7vdz661d 273 10 the the DT cord-102966-7vdz661d 273 11 Function Function NNP cord-102966-7vdz661d 273 12 Hall Hall NNP cord-102966-7vdz661d 273 13 of of IN cord-102966-7vdz661d 273 14 Fame Fame NNP cord-102966-7vdz661d 273 15 . . . cord-102966-7vdz661d 274 1 Chemical Chemical NNP cord-102966-7vdz661d 274 2 Engineering Engineering NNP cord-102966-7vdz661d 274 3 Education Education NNP cord-102966-7vdz661d 275 1 In in IN cord-102966-7vdz661d 275 2 preparation preparation NN cord-102966-7vdz661d 275 3 Report Report NNP cord-102966-7vdz661d 275 4 9 9 CD cord-102966-7vdz661d 275 5 -Impact -impact NN cord-102966-7vdz661d 275 6 of of IN cord-102966-7vdz661d 275 7 nonpharmaceutical nonpharmaceutical JJ cord-102966-7vdz661d 275 8 interventions intervention NNS cord-102966-7vdz661d 275 9 ( ( -LRB- cord-102966-7vdz661d 275 10 NPIs NPIs NNP cord-102966-7vdz661d 275 11 ) ) -RRB- cord-102966-7vdz661d 276 1 to to TO cord-102966-7vdz661d 276 2 reduce reduce VB cord-102966-7vdz661d 276 3 COVID-19 covid-19 JJ cord-102966-7vdz661d 276 4 mortality mortality NN cord-102966-7vdz661d 276 5 and and CC cord-102966-7vdz661d 276 6 healthcare healthcare NN cord-102966-7vdz661d 276 7 demand demand NN cord-102966-7vdz661d 276 8 Institute Institute NNP cord-102966-7vdz661d 276 9 for for IN cord-102966-7vdz661d 276 10 Health Health NNP cord-102966-7vdz661d 276 11 Metrics Metrics NNPS cord-102966-7vdz661d 276 12 and and CC cord-102966-7vdz661d 276 13 Evaluation Evaluation NNP cord-102966-7vdz661d 276 14 ( ( -LRB- cord-102966-7vdz661d 276 15 IHME IHME NNP cord-102966-7vdz661d 276 16 ) ) -RRB- cord-102966-7vdz661d 277 1 < < NNP cord-102966-7vdz661d 277 2 COVID-19 covid-19 CD cord-102966-7vdz661d 277 3 projections projection NNS cord-102966-7vdz661d 277 4 assuming assume VBG cord-102966-7vdz661d 277 5 full full JJ cord-102966-7vdz661d 277 6 social social JJ cord-102966-7vdz661d 277 7 distancing distancing NN cord-102966-7vdz661d 277 8 through through IN cord-102966-7vdz661d 277 9 Early early JJ cord-102966-7vdz661d 277 10 dynamics dynamic NNS cord-102966-7vdz661d 277 11 of of IN cord-102966-7vdz661d 277 12 transmission transmission NN cord-102966-7vdz661d 277 13 and and CC cord-102966-7vdz661d 277 14 control control NN cord-102966-7vdz661d 277 15 of of IN cord-102966-7vdz661d 277 16 COVID-19 COVID-19 NNP cord-102966-7vdz661d 277 17 : : : cord-102966-7vdz661d 277 18 a a DT cord-102966-7vdz661d 277 19 mathematical mathematical JJ cord-102966-7vdz661d 277 20 modelling modelling NN cord-102966-7vdz661d 277 21 study study NN cord-102966-7vdz661d 277 22 . . . cord-102966-7vdz661d 278 1 The the DT cord-102966-7vdz661d 278 2 Lancet Lancet NNP cord-102966-7vdz661d 278 3 Infectious Infectious NNP cord-102966-7vdz661d 278 4 Diseases disease NNS cord-102966-7vdz661d 279 1 Evolving evolve VBG cord-102966-7vdz661d 279 2 epidemiology epidemiology NN cord-102966-7vdz661d 279 3 and and CC cord-102966-7vdz661d 279 4 transmission transmission NN cord-102966-7vdz661d 279 5 dynamics dynamic NNS cord-102966-7vdz661d 279 6 of of IN cord-102966-7vdz661d 279 7 coronavirus coronavirus NN cord-102966-7vdz661d 279 8 disease disease NN cord-102966-7vdz661d 279 9 2019 2019 CD cord-102966-7vdz661d 279 10 outside outside IN cord-102966-7vdz661d 279 11 Hubei Hubei NNP cord-102966-7vdz661d 279 12 province province NN cord-102966-7vdz661d 279 13 , , , cord-102966-7vdz661d 279 14 China China NNP cord-102966-7vdz661d 279 15 : : : cord-102966-7vdz661d 279 16 a a DT cord-102966-7vdz661d 279 17 descriptive descriptive JJ cord-102966-7vdz661d 279 18 and and CC cord-102966-7vdz661d 279 19 modelling modelling NN cord-102966-7vdz661d 279 20 study study NN cord-102966-7vdz661d 279 21 . . . cord-102966-7vdz661d 280 1 The the DT cord-102966-7vdz661d 280 2 Lancet Lancet NNP cord-102966-7vdz661d 280 3 Infectious Infectious NNP cord-102966-7vdz661d 280 4 Diseases disease NNS cord-102966-7vdz661d 281 1 An an DT cord-102966-7vdz661d 281 2 introduction introduction NN cord-102966-7vdz661d 281 3 to to IN cord-102966-7vdz661d 281 4 compartmental compartmental JJ cord-102966-7vdz661d 281 5 modeling modeling NN cord-102966-7vdz661d 281 6 for for IN cord-102966-7vdz661d 281 7 the the DT cord-102966-7vdz661d 281 8 budding bud VBG cord-102966-7vdz661d 281 9 infectious infectious JJ cord-102966-7vdz661d 281 10 disease disease NN cord-102966-7vdz661d 281 11 modeler modeler NN cord-102966-7vdz661d 281 12 Using use VBG cord-102966-7vdz661d 281 13 Feedback Feedback NNP cord-102966-7vdz661d 281 14 on on IN cord-102966-7vdz661d 281 15 Symptomatic symptomatic JJ cord-102966-7vdz661d 281 16 Infections infection NNS cord-102966-7vdz661d 281 17 to to TO cord-102966-7vdz661d 281 18 Contain contain VB cord-102966-7vdz661d 281 19 the the DT cord-102966-7vdz661d 281 20 Coronavirus Coronavirus NNP cord-102966-7vdz661d 281 21 Epidemic epidemic NN cord-102966-7vdz661d 281 22 : : : cord-102966-7vdz661d 281 23 Insight insight NN cord-102966-7vdz661d 281 24 from from IN cord-102966-7vdz661d 281 25 a a DT cord-102966-7vdz661d 281 26 SPIR SPIR NNP cord-102966-7vdz661d 281 27 Model Model NNP cord-102966-7vdz661d 281 28 . . . cord-102966-7vdz661d 282 1 medRxiv medRxiv NNS cord-102966-7vdz661d 282 2 Introducing introduce VBG cord-102966-7vdz661d 282 3 the the DT cord-102966-7vdz661d 282 4 new new JJ cord-102966-7vdz661d 282 5 variables variable NNS cord-102966-7vdz661d 282 6 1 1 CD cord-102966-7vdz661d 282 7 ≝ ≝ NNP cord-102966-7vdz661d 282 8 , , , cord-102966-7vdz661d 282 9 2 2 CD cord-102966-7vdz661d 282 10 ≝ ≝ NN cord-102966-7vdz661d 282 11 ′ ′ CD cord-102966-7vdz661d 282 12 immediately immediately RB cord-102966-7vdz661d 282 13 yields yield VBZ cord-102966-7vdz661d 282 14 eqn eqn NN cord-102966-7vdz661d 282 15 . . . cord-102966-7vdz661d 283 1 ( ( -LRB- cord-102966-7vdz661d 283 2 14 14 CD cord-102966-7vdz661d 283 3 ) ) -RRB- cord-102966-7vdz661d 283 4 .Eqn .Eqn NFP cord-102966-7vdz661d 283 5 . . . cord-102966-7vdz661d 284 1 ( ( -LRB- cord-102966-7vdz661d 284 2 13 13 CD cord-102966-7vdz661d 284 3 ) ) -RRB- cord-102966-7vdz661d 284 4 can can MD cord-102966-7vdz661d 284 5 be be VB cord-102966-7vdz661d 284 6 proved prove VBN cord-102966-7vdz661d 284 7 similarly similarly RB cord-102966-7vdz661d 284 8 . . . cord-102966-7vdz661d 285 1 To to TO cord-102966-7vdz661d 285 2 prove prove VB cord-102966-7vdz661d 285 3 eqn eqn NN cord-102966-7vdz661d 285 4 . . . cord-102966-7vdz661d 286 1 ( ( -LRB- cord-102966-7vdz661d 286 2 16 16 CD cord-102966-7vdz661d 286 3 ) ) -RRB- cord-102966-7vdz661d 286 4 observe observe VBP cord-102966-7vdz661d 286 5 that that IN cord-102966-7vdz661d 286 6 if if IN cord-102966-7vdz661d 286 7 ( ( -LRB- cord-102966-7vdz661d 286 8 0 0 NFP cord-102966-7vdz661d 286 9 ) ) -RRB- cord-102966-7vdz661d 286 10 changes change NNS cord-102966-7vdz661d 286 11 from from IN cord-102966-7vdz661d 286 12 its -PRON- PRP$ cord-102966-7vdz661d 286 13 previous previous JJ cord-102966-7vdz661d 286 14 value value NN cord-102966-7vdz661d 286 15 of of IN cord-102966-7vdz661d 286 16 1 1 CD cord-102966-7vdz661d 286 17 by by IN cord-102966-7vdz661d 286 18 a a DT cord-102966-7vdz661d 286 19 step step NN cord-102966-7vdz661d 286 20 , , , cord-102966-7vdz661d 286 21 − − UH cord-102966-7vdz661d 286 22 , , , cord-102966-7vdz661d 286 23 then then RB cord-102966-7vdz661d 286 24 ( ( -LRB- cord-102966-7vdz661d 286 25 ) ) -RRB- cord-102966-7vdz661d 286 26 = = NFP cord-102966-7vdz661d 286 27 − − NNP cord-102966-7vdz661d 286 28 / / , cord-102966-7vdz661d 286 29 . . . cord-102966-7vdz661d 287 1 Because because IN cord-102966-7vdz661d 287 2 ( ( -LRB- cord-102966-7vdz661d 287 3 ≤ ≤ NN cord-102966-7vdz661d 287 4 0 0 CD cord-102966-7vdz661d 287 5 ) ) -RRB- cord-102966-7vdz661d 287 6 = = SYM cord-102966-7vdz661d 287 7 0 0 NFP cord-102966-7vdz661d 288 1 and and CC cord-102966-7vdz661d 288 2 + + CD cord-102966-7vdz661d 289 1 + + CC cord-102966-7vdz661d 289 2 = = SYM cord-102966-7vdz661d 289 3 1 1 CD cord-102966-7vdz661d 289 4 , , , cord-102966-7vdz661d 289 5 it -PRON- PRP cord-102966-7vdz661d 289 6 follows follow VBZ cord-102966-7vdz661d 289 7 that that DT cord-102966-7vdz661d 289 8 jumps jump VBZ cord-102966-7vdz661d 289 9 from from IN cord-102966-7vdz661d 289 10 ( ( -LRB- cord-102966-7vdz661d 289 11 < < XX cord-102966-7vdz661d 289 12 0 0 CD cord-102966-7vdz661d 289 13 ) ) -RRB- cord-102966-7vdz661d 290 1 = = LS cord-102966-7vdz661d 290 2 0 0 NFP cord-102966-7vdz661d 291 1 to to IN cord-102966-7vdz661d 291 2 ( ( -LRB- cord-102966-7vdz661d 291 3 0 0 NFP cord-102966-7vdz661d 291 4 ) ) -RRB- cord-102966-7vdz661d 291 5 = = NFP cord-102966-7vdz661d 291 6 . . . cord-102966-7vdz661d 292 1 Therefore therefore RB cord-102966-7vdz661d 292 2 , , , cord-102966-7vdz661d 292 3 the the DT cord-102966-7vdz661d 292 4 above above JJ cord-102966-7vdz661d 292 5 eqn eqn NN cord-102966-7vdz661d 292 6 . . . cord-102966-7vdz661d 293 1 ( ( -LRB- cord-102966-7vdz661d 293 2 54 54 CD cord-102966-7vdz661d 293 3 ) ) -RRB- cord-102966-7vdz661d 293 4 yields yield VBZ cord-102966-7vdz661d 293 5 _SP