id sid tid token lemma pos cord-340851-lnv8yi9l 1 1 key key JJ cord-340851-lnv8yi9l 1 2 : : : cord-340851-lnv8yi9l 1 3 cord-340851-lnv8yi9l cord-340851-lnv8yi9l NN cord-340851-lnv8yi9l 1 4 authors author NNS cord-340851-lnv8yi9l 1 5 : : : cord-340851-lnv8yi9l 1 6 Perkins Perkins NNP cord-340851-lnv8yi9l 1 7 , , , cord-340851-lnv8yi9l 1 8 Alex Alex NNP cord-340851-lnv8yi9l 1 9 ; ; : cord-340851-lnv8yi9l 1 10 Espana Espana NNP cord-340851-lnv8yi9l 1 11 , , , cord-340851-lnv8yi9l 1 12 Guido Guido NNP cord-340851-lnv8yi9l 1 13 title title NN cord-340851-lnv8yi9l 1 14 : : : cord-340851-lnv8yi9l 1 15 Optimal optimal JJ cord-340851-lnv8yi9l 1 16 control control NN cord-340851-lnv8yi9l 1 17 of of IN cord-340851-lnv8yi9l 1 18 the the DT cord-340851-lnv8yi9l 1 19 COVID-19 covid-19 JJ cord-340851-lnv8yi9l 1 20 pandemic pandemic NN cord-340851-lnv8yi9l 1 21 with with IN cord-340851-lnv8yi9l 1 22 non non JJ cord-340851-lnv8yi9l 1 23 - - JJ cord-340851-lnv8yi9l 1 24 pharmaceutical pharmaceutical JJ cord-340851-lnv8yi9l 1 25 interventions intervention NNS cord-340851-lnv8yi9l 1 26 date date NN cord-340851-lnv8yi9l 1 27 : : : cord-340851-lnv8yi9l 1 28 2020 2020 CD cord-340851-lnv8yi9l 1 29 - - HYPH cord-340851-lnv8yi9l 1 30 04 04 CD cord-340851-lnv8yi9l 1 31 - - HYPH cord-340851-lnv8yi9l 1 32 23 23 CD cord-340851-lnv8yi9l 1 33 journal journal NN cord-340851-lnv8yi9l 1 34 : : : cord-340851-lnv8yi9l 1 35 nan nan NNP cord-340851-lnv8yi9l 1 36 DOI DOI NNP cord-340851-lnv8yi9l 1 37 : : : cord-340851-lnv8yi9l 2 1 10.1101/2020.04.22.20076018 10.1101/2020.04.22.20076018 CD cord-340851-lnv8yi9l 2 2 sha sha NNP cord-340851-lnv8yi9l 2 3 : : : cord-340851-lnv8yi9l 3 1 abb6e8d359bfe7356e7b0c6f7e9c6ed596a8d8e3 abb6e8d359bfe7356e7b0c6f7e9c6ed596a8d8e3 CC cord-340851-lnv8yi9l 3 2 doc_id doc_id CD cord-340851-lnv8yi9l 3 3 : : : cord-340851-lnv8yi9l 3 4 340851 340851 CD cord-340851-lnv8yi9l 3 5 cord_uid cord_uid NNS cord-340851-lnv8yi9l 3 6 : : : cord-340851-lnv8yi9l 3 7 lnv8yi9l lnv8yi9l NNP cord-340851-lnv8yi9l 3 8 The the DT cord-340851-lnv8yi9l 3 9 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 3 10 pandemic pandemic NN cord-340851-lnv8yi9l 3 11 has have VBZ cord-340851-lnv8yi9l 3 12 forced force VBN cord-340851-lnv8yi9l 3 13 societies society NNS cord-340851-lnv8yi9l 3 14 across across IN cord-340851-lnv8yi9l 3 15 the the DT cord-340851-lnv8yi9l 3 16 world world NN cord-340851-lnv8yi9l 3 17 to to TO cord-340851-lnv8yi9l 3 18 resort resort VB cord-340851-lnv8yi9l 3 19 to to IN cord-340851-lnv8yi9l 3 20 social social JJ cord-340851-lnv8yi9l 3 21 distancing distancing NN cord-340851-lnv8yi9l 3 22 to to TO cord-340851-lnv8yi9l 3 23 slow slow VB cord-340851-lnv8yi9l 3 24 the the DT cord-340851-lnv8yi9l 3 25 spread spread NN cord-340851-lnv8yi9l 3 26 of of IN cord-340851-lnv8yi9l 3 27 the the DT cord-340851-lnv8yi9l 3 28 SARS SARS NNP cord-340851-lnv8yi9l 3 29 - - HYPH cord-340851-lnv8yi9l 3 30 CoV-2 CoV-2 NNP cord-340851-lnv8yi9l 3 31 virus virus NN cord-340851-lnv8yi9l 3 32 . . . cord-340851-lnv8yi9l 4 1 Due due IN cord-340851-lnv8yi9l 4 2 to to IN cord-340851-lnv8yi9l 4 3 the the DT cord-340851-lnv8yi9l 4 4 economic economic JJ cord-340851-lnv8yi9l 4 5 impacts impact NNS cord-340851-lnv8yi9l 4 6 of of IN cord-340851-lnv8yi9l 4 7 social social JJ cord-340851-lnv8yi9l 4 8 distancing distancing NN cord-340851-lnv8yi9l 4 9 , , , cord-340851-lnv8yi9l 4 10 there there EX cord-340851-lnv8yi9l 4 11 is be VBZ cord-340851-lnv8yi9l 4 12 growing grow VBG cord-340851-lnv8yi9l 4 13 desire desire NN cord-340851-lnv8yi9l 4 14 to to TO cord-340851-lnv8yi9l 4 15 relax relax VB cord-340851-lnv8yi9l 4 16 these these DT cord-340851-lnv8yi9l 4 17 measures measure NNS cord-340851-lnv8yi9l 4 18 . . . cord-340851-lnv8yi9l 5 1 To to TO cord-340851-lnv8yi9l 5 2 characterize characterize VB cord-340851-lnv8yi9l 5 3 a a DT cord-340851-lnv8yi9l 5 4 range range NN cord-340851-lnv8yi9l 5 5 of of IN cord-340851-lnv8yi9l 5 6 possible possible JJ cord-340851-lnv8yi9l 5 7 strategies strategy NNS cord-340851-lnv8yi9l 5 8 for for IN cord-340851-lnv8yi9l 5 9 control control NN cord-340851-lnv8yi9l 5 10 and and CC cord-340851-lnv8yi9l 5 11 to to TO cord-340851-lnv8yi9l 5 12 understand understand VB cord-340851-lnv8yi9l 5 13 their -PRON- PRP$ cord-340851-lnv8yi9l 5 14 consequences consequence NNS cord-340851-lnv8yi9l 5 15 , , , cord-340851-lnv8yi9l 5 16 we -PRON- PRP cord-340851-lnv8yi9l 5 17 performed perform VBD cord-340851-lnv8yi9l 5 18 an an DT cord-340851-lnv8yi9l 5 19 optimal optimal JJ cord-340851-lnv8yi9l 5 20 control control NN cord-340851-lnv8yi9l 5 21 analysis analysis NN cord-340851-lnv8yi9l 5 22 of of IN cord-340851-lnv8yi9l 5 23 a a DT cord-340851-lnv8yi9l 5 24 mathematical mathematical JJ cord-340851-lnv8yi9l 5 25 model model NN cord-340851-lnv8yi9l 5 26 of of IN cord-340851-lnv8yi9l 5 27 SARS SARS NNP cord-340851-lnv8yi9l 5 28 - - HYPH cord-340851-lnv8yi9l 5 29 CoV-2 CoV-2 NNP cord-340851-lnv8yi9l 5 30 transmission transmission NN cord-340851-lnv8yi9l 5 31 . . . cord-340851-lnv8yi9l 6 1 Given give VBN cord-340851-lnv8yi9l 6 2 that that IN cord-340851-lnv8yi9l 6 3 the the DT cord-340851-lnv8yi9l 6 4 pandemic pandemic NN cord-340851-lnv8yi9l 6 5 is be VBZ cord-340851-lnv8yi9l 6 6 already already RB cord-340851-lnv8yi9l 6 7 underway underway JJ cord-340851-lnv8yi9l 6 8 and and CC cord-340851-lnv8yi9l 6 9 controls control NNS cord-340851-lnv8yi9l 6 10 have have VBP cord-340851-lnv8yi9l 6 11 already already RB cord-340851-lnv8yi9l 6 12 been be VBN cord-340851-lnv8yi9l 6 13 initiated initiate VBN cord-340851-lnv8yi9l 6 14 , , , cord-340851-lnv8yi9l 6 15 we -PRON- PRP cord-340851-lnv8yi9l 6 16 calibrated calibrate VBD cord-340851-lnv8yi9l 6 17 our -PRON- PRP$ cord-340851-lnv8yi9l 6 18 model model NN cord-340851-lnv8yi9l 6 19 to to IN cord-340851-lnv8yi9l 6 20 data datum NNS cord-340851-lnv8yi9l 6 21 from from IN cord-340851-lnv8yi9l 6 22 the the DT cord-340851-lnv8yi9l 6 23 US US NNP cord-340851-lnv8yi9l 6 24 and and CC cord-340851-lnv8yi9l 6 25 focused focus VBD cord-340851-lnv8yi9l 6 26 our -PRON- PRP$ cord-340851-lnv8yi9l 6 27 analysis analysis NN cord-340851-lnv8yi9l 6 28 on on IN cord-340851-lnv8yi9l 6 29 optimal optimal JJ cord-340851-lnv8yi9l 6 30 controls control NNS cord-340851-lnv8yi9l 6 31 from from IN cord-340851-lnv8yi9l 6 32 May May NNP cord-340851-lnv8yi9l 6 33 2020 2020 CD cord-340851-lnv8yi9l 6 34 through through IN cord-340851-lnv8yi9l 6 35 December December NNP cord-340851-lnv8yi9l 6 36 2021 2021 CD cord-340851-lnv8yi9l 6 37 . . . cord-340851-lnv8yi9l 7 1 We -PRON- PRP cord-340851-lnv8yi9l 7 2 found find VBD cord-340851-lnv8yi9l 7 3 that that IN cord-340851-lnv8yi9l 7 4 a a DT cord-340851-lnv8yi9l 7 5 major major JJ cord-340851-lnv8yi9l 7 6 factor factor NN cord-340851-lnv8yi9l 7 7 that that WDT cord-340851-lnv8yi9l 7 8 differentiates differentiate VBZ cord-340851-lnv8yi9l 7 9 strategies strategy NNS cord-340851-lnv8yi9l 7 10 that that WDT cord-340851-lnv8yi9l 7 11 prioritize prioritize VBP cord-340851-lnv8yi9l 7 12 lives life NNS cord-340851-lnv8yi9l 7 13 saved save VBN cord-340851-lnv8yi9l 7 14 versus versus IN cord-340851-lnv8yi9l 7 15 reduced reduce VBN cord-340851-lnv8yi9l 7 16 time time NN cord-340851-lnv8yi9l 7 17 under under IN cord-340851-lnv8yi9l 7 18 control control NN cord-340851-lnv8yi9l 7 19 is be VBZ cord-340851-lnv8yi9l 7 20 how how WRB cord-340851-lnv8yi9l 7 21 quickly quickly RB cord-340851-lnv8yi9l 7 22 control control NN cord-340851-lnv8yi9l 7 23 is be VBZ cord-340851-lnv8yi9l 7 24 relaxed relaxed JJ cord-340851-lnv8yi9l 7 25 once once IN cord-340851-lnv8yi9l 7 26 social social JJ cord-340851-lnv8yi9l 7 27 distancing distancing NN cord-340851-lnv8yi9l 7 28 restrictions restriction NNS cord-340851-lnv8yi9l 7 29 expire expire VBP cord-340851-lnv8yi9l 7 30 in in IN cord-340851-lnv8yi9l 7 31 May May NNP cord-340851-lnv8yi9l 7 32 2020 2020 CD cord-340851-lnv8yi9l 7 33 . . . cord-340851-lnv8yi9l 8 1 Strategies strategy NNS cord-340851-lnv8yi9l 8 2 that that WDT cord-340851-lnv8yi9l 8 3 maintain maintain VBP cord-340851-lnv8yi9l 8 4 control control NN cord-340851-lnv8yi9l 8 5 at at IN cord-340851-lnv8yi9l 8 6 a a DT cord-340851-lnv8yi9l 8 7 high high JJ cord-340851-lnv8yi9l 8 8 level level NN cord-340851-lnv8yi9l 8 9 until until IN cord-340851-lnv8yi9l 8 10 summer summer NN cord-340851-lnv8yi9l 8 11 2020 2020 CD cord-340851-lnv8yi9l 8 12 allow allow VB cord-340851-lnv8yi9l 8 13 for for IN cord-340851-lnv8yi9l 8 14 tapering taper VBG cord-340851-lnv8yi9l 8 15 of of IN cord-340851-lnv8yi9l 8 16 control control NN cord-340851-lnv8yi9l 8 17 thereafter thereafter RB cord-340851-lnv8yi9l 8 18 and and CC cord-340851-lnv8yi9l 8 19 minimal minimal JJ cord-340851-lnv8yi9l 8 20 deaths death NNS cord-340851-lnv8yi9l 8 21 , , , cord-340851-lnv8yi9l 8 22 whereas whereas IN cord-340851-lnv8yi9l 8 23 strategies strategy NNS cord-340851-lnv8yi9l 8 24 that that WDT cord-340851-lnv8yi9l 8 25 relax relax VBP cord-340851-lnv8yi9l 8 26 control control NN cord-340851-lnv8yi9l 8 27 in in IN cord-340851-lnv8yi9l 8 28 the the DT cord-340851-lnv8yi9l 8 29 short short JJ cord-340851-lnv8yi9l 8 30 term term NN cord-340851-lnv8yi9l 8 31 lead lead VB cord-340851-lnv8yi9l 8 32 to to IN cord-340851-lnv8yi9l 8 33 fewer few JJR cord-340851-lnv8yi9l 8 34 options option NNS cord-340851-lnv8yi9l 8 35 for for IN cord-340851-lnv8yi9l 8 36 control control NN cord-340851-lnv8yi9l 8 37 later later RB cord-340851-lnv8yi9l 8 38 and and CC cord-340851-lnv8yi9l 8 39 a a DT cord-340851-lnv8yi9l 8 40 higher high JJR cord-340851-lnv8yi9l 8 41 likelihood likelihood NN cord-340851-lnv8yi9l 8 42 of of IN cord-340851-lnv8yi9l 8 43 exceeding exceed VBG cord-340851-lnv8yi9l 8 44 hospital hospital NN cord-340851-lnv8yi9l 8 45 capacity capacity NN cord-340851-lnv8yi9l 8 46 . . . cord-340851-lnv8yi9l 9 1 Our -PRON- PRP$ cord-340851-lnv8yi9l 9 2 results result NNS cord-340851-lnv8yi9l 9 3 also also RB cord-340851-lnv8yi9l 9 4 highlight highlight VBP cord-340851-lnv8yi9l 9 5 that that IN cord-340851-lnv8yi9l 9 6 the the DT cord-340851-lnv8yi9l 9 7 potential potential JJ cord-340851-lnv8yi9l 9 8 scope scope NN cord-340851-lnv8yi9l 9 9 for for IN cord-340851-lnv8yi9l 9 10 controlling control VBG cord-340851-lnv8yi9l 9 11 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 9 12 until until IN cord-340851-lnv8yi9l 9 13 a a DT cord-340851-lnv8yi9l 9 14 vaccine vaccine NN cord-340851-lnv8yi9l 9 15 is be VBZ cord-340851-lnv8yi9l 9 16 available available JJ cord-340851-lnv8yi9l 9 17 depends depend VBZ cord-340851-lnv8yi9l 9 18 on on IN cord-340851-lnv8yi9l 9 19 epidemiological epidemiological JJ cord-340851-lnv8yi9l 9 20 parameters parameter NNS cord-340851-lnv8yi9l 9 21 about about IN cord-340851-lnv8yi9l 9 22 which which WDT cord-340851-lnv8yi9l 9 23 there there EX cord-340851-lnv8yi9l 9 24 is be VBZ cord-340851-lnv8yi9l 9 25 still still RB cord-340851-lnv8yi9l 9 26 considerable considerable JJ cord-340851-lnv8yi9l 9 27 uncertainty uncertainty NN cord-340851-lnv8yi9l 9 28 , , , cord-340851-lnv8yi9l 9 29 including include VBG cord-340851-lnv8yi9l 9 30 the the DT cord-340851-lnv8yi9l 9 31 basic basic JJ cord-340851-lnv8yi9l 9 32 reproduction reproduction NN cord-340851-lnv8yi9l 9 33 number number NN cord-340851-lnv8yi9l 9 34 and and CC cord-340851-lnv8yi9l 9 35 the the DT cord-340851-lnv8yi9l 9 36 effectiveness effectiveness NN cord-340851-lnv8yi9l 9 37 of of IN cord-340851-lnv8yi9l 9 38 social social JJ cord-340851-lnv8yi9l 9 39 distancing distancing NN cord-340851-lnv8yi9l 9 40 . . . cord-340851-lnv8yi9l 10 1 In in IN cord-340851-lnv8yi9l 10 2 light light NN cord-340851-lnv8yi9l 10 3 of of IN cord-340851-lnv8yi9l 10 4 those those DT cord-340851-lnv8yi9l 10 5 uncertainties uncertainty NNS cord-340851-lnv8yi9l 10 6 , , , cord-340851-lnv8yi9l 10 7 our -PRON- PRP$ cord-340851-lnv8yi9l 10 8 results result NNS cord-340851-lnv8yi9l 10 9 do do VBP cord-340851-lnv8yi9l 10 10 not not RB cord-340851-lnv8yi9l 10 11 constitute constitute VB cord-340851-lnv8yi9l 10 12 a a DT cord-340851-lnv8yi9l 10 13 quantitative quantitative JJ cord-340851-lnv8yi9l 10 14 forecast forecast NN cord-340851-lnv8yi9l 10 15 and and CC cord-340851-lnv8yi9l 10 16 instead instead RB cord-340851-lnv8yi9l 10 17 provide provide VB cord-340851-lnv8yi9l 10 18 a a DT cord-340851-lnv8yi9l 10 19 qualitative qualitative JJ cord-340851-lnv8yi9l 10 20 portrayal portrayal NN cord-340851-lnv8yi9l 10 21 of of IN cord-340851-lnv8yi9l 10 22 possible possible JJ cord-340851-lnv8yi9l 10 23 outcomes outcome NNS cord-340851-lnv8yi9l 10 24 from from IN cord-340851-lnv8yi9l 10 25 alternative alternative JJ cord-340851-lnv8yi9l 10 26 approaches approach NNS cord-340851-lnv8yi9l 10 27 to to TO cord-340851-lnv8yi9l 10 28 control control VB cord-340851-lnv8yi9l 10 29 . . . cord-340851-lnv8yi9l 11 1 The the DT cord-340851-lnv8yi9l 11 2 first first JJ cord-340851-lnv8yi9l 11 3 known know VBN cord-340851-lnv8yi9l 11 4 case case NN cord-340851-lnv8yi9l 11 5 of of IN cord-340851-lnv8yi9l 11 6 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 11 7 in in IN cord-340851-lnv8yi9l 11 8 the the DT cord-340851-lnv8yi9l 11 9 United United NNP cord-340851-lnv8yi9l 11 10 States States NNP cord-340851-lnv8yi9l 11 11 arrived arrive VBD cord-340851-lnv8yi9l 11 12 from from IN cord-340851-lnv8yi9l 11 13 China China NNP cord-340851-lnv8yi9l 11 14 on on IN cord-340851-lnv8yi9l 11 15 January January NNP cord-340851-lnv8yi9l 11 16 15 15 CD cord-340851-lnv8yi9l 11 17 , , , cord-340851-lnv8yi9l 11 18 2020 2020 CD cord-340851-lnv8yi9l 11 19 [ [ -LRB- cord-340851-lnv8yi9l 11 20 22 22 CD cord-340851-lnv8yi9l 11 21 ] ] -RRB- cord-340851-lnv8yi9l 11 22 . . . cord-340851-lnv8yi9l 12 1 In in IN cord-340851-lnv8yi9l 12 2 the the DT cord-340851-lnv8yi9l 12 3 weeks week NNS cord-340851-lnv8yi9l 12 4 that that WDT cord-340851-lnv8yi9l 12 5 followed follow VBD cord-340851-lnv8yi9l 12 6 , , , cord-340851-lnv8yi9l 12 7 deficiencies deficiency NNS cord-340851-lnv8yi9l 12 8 in in IN cord-340851-lnv8yi9l 12 9 testing testing NN cord-340851-lnv8yi9l 12 10 allowed allow VBD cord-340851-lnv8yi9l 12 11 the the DT cord-340851-lnv8yi9l 12 12 virus virus NN cord-340851-lnv8yi9l 12 13 that that WDT cord-340851-lnv8yi9l 12 14 causes cause VBZ cord-340851-lnv8yi9l 12 15 this this DT cord-340851-lnv8yi9l 12 16 disease disease NN cord-340851-lnv8yi9l 12 17 to to TO cord-340851-lnv8yi9l 12 18 spread spread VB cord-340851-lnv8yi9l 12 19 largely largely RB cord-340851-lnv8yi9l 12 20 undetected undetected JJ cord-340851-lnv8yi9l 12 21 [ [ -LRB- cord-340851-lnv8yi9l 12 22 41 41 CD cord-340851-lnv8yi9l 12 23 ] ] -RRB- cord-340851-lnv8yi9l 12 24 , , , cord-340851-lnv8yi9l 12 25 with with IN cord-340851-lnv8yi9l 12 26 the the DT cord-340851-lnv8yi9l 12 27 number number NN cord-340851-lnv8yi9l 12 28 of of IN cord-340851-lnv8yi9l 12 29 reported report VBN cord-340851-lnv8yi9l 12 30 cases case NNS cord-340851-lnv8yi9l 12 31 growing grow VBG cord-340851-lnv8yi9l 12 32 to to IN cord-340851-lnv8yi9l 12 33 429,319 429,319 CD cord-340851-lnv8yi9l 12 34 by by IN cord-340851-lnv8yi9l 12 35 April April NNP cord-340851-lnv8yi9l 12 36 8 8 CD cord-340851-lnv8yi9l 12 37 , , , cord-340851-lnv8yi9l 12 38 2020 2020 CD cord-340851-lnv8yi9l 12 39 [ [ -LRB- cord-340851-lnv8yi9l 12 40 36 36 CD cord-340851-lnv8yi9l 12 41 ] ] -RRB- cord-340851-lnv8yi9l 12 42 . . . cord-340851-lnv8yi9l 13 1 Social social JJ cord-340851-lnv8yi9l 13 2 distancing distancing NN cord-340851-lnv8yi9l 13 3 - - , cord-340851-lnv8yi9l 13 4 such such JJ cord-340851-lnv8yi9l 13 5 as as IN cord-340851-lnv8yi9l 13 6 closing closing NN cord-340851-lnv8yi9l 13 7 schools school NNS cord-340851-lnv8yi9l 13 8 , , , cord-340851-lnv8yi9l 13 9 working work VBG cord-340851-lnv8yi9l 13 10 from from IN cord-340851-lnv8yi9l 13 11 home home NN cord-340851-lnv8yi9l 13 12 , , , cord-340851-lnv8yi9l 13 13 and and CC cord-340851-lnv8yi9l 13 14 sheltering shelter VBG cord-340851-lnv8yi9l 13 15 in in IN cord-340851-lnv8yi9l 13 16 place place NN cord-340851-lnv8yi9l 13 17 - - : cord-340851-lnv8yi9l 13 18 has have VBZ cord-340851-lnv8yi9l 13 19 been be VBN cord-340851-lnv8yi9l 13 20 adopted adopt VBN cord-340851-lnv8yi9l 13 21 widely widely RB cord-340851-lnv8yi9l 13 22 and and CC cord-340851-lnv8yi9l 13 23 appears appear VBZ cord-340851-lnv8yi9l 13 24 capable capable JJ cord-340851-lnv8yi9l 13 25 of of IN cord-340851-lnv8yi9l 13 26 impacting impact VBG cord-340851-lnv8yi9l 13 27 transmission transmission NN cord-340851-lnv8yi9l 13 28 [ [ -LRB- cord-340851-lnv8yi9l 13 29 26 26 CD cord-340851-lnv8yi9l 13 30 , , , cord-340851-lnv8yi9l 13 31 12 12 CD cord-340851-lnv8yi9l 13 32 ] ] -RRB- cord-340851-lnv8yi9l 13 33 . . . cord-340851-lnv8yi9l 14 1 These these DT cord-340851-lnv8yi9l 14 2 practices practice NNS cord-340851-lnv8yi9l 14 3 have have VBP cord-340851-lnv8yi9l 14 4 tremendous tremendous JJ cord-340851-lnv8yi9l 14 5 economic economic JJ cord-340851-lnv8yi9l 14 6 and and CC cord-340851-lnv8yi9l 14 7 social social JJ cord-340851-lnv8yi9l 14 8 consequences consequence NNS cord-340851-lnv8yi9l 14 9 , , , cord-340851-lnv8yi9l 14 10 however however RB cord-340851-lnv8yi9l 14 11 , , , cord-340851-lnv8yi9l 14 12 which which WDT cord-340851-lnv8yi9l 14 13 has have VBZ cord-340851-lnv8yi9l 14 14 precipitated precipitate VBN cord-340851-lnv8yi9l 14 15 growing grow VBG cord-340851-lnv8yi9l 14 16 desire desire NN cord-340851-lnv8yi9l 14 17 to to TO cord-340851-lnv8yi9l 14 18 relax relax VB cord-340851-lnv8yi9l 14 19 them -PRON- PRP cord-340851-lnv8yi9l 14 20 [ [ -LRB- cord-340851-lnv8yi9l 14 21 16 16 CD cord-340851-lnv8yi9l 14 22 ] ] -RRB- cord-340851-lnv8yi9l 14 23 . . . cord-340851-lnv8yi9l 15 1 A a DT cord-340851-lnv8yi9l 15 2 danger danger NN cord-340851-lnv8yi9l 15 3 in in IN cord-340851-lnv8yi9l 15 4 relaxing relax VBG cord-340851-lnv8yi9l 15 5 the the DT cord-340851-lnv8yi9l 15 6 use use NN cord-340851-lnv8yi9l 15 7 of of IN cord-340851-lnv8yi9l 15 8 social social JJ cord-340851-lnv8yi9l 15 9 distancing distancing NN cord-340851-lnv8yi9l 15 10 is be VBZ cord-340851-lnv8yi9l 15 11 that that IN cord-340851-lnv8yi9l 15 12 the the DT cord-340851-lnv8yi9l 15 13 virus virus NN cord-340851-lnv8yi9l 15 14 could could MD cord-340851-lnv8yi9l 15 15 resurge resurge VB cord-340851-lnv8yi9l 15 16 in in IN cord-340851-lnv8yi9l 15 17 its -PRON- PRP$ cord-340851-lnv8yi9l 15 18 absence absence NN cord-340851-lnv8yi9l 15 19 [ [ -LRB- cord-340851-lnv8yi9l 15 20 44 44 CD cord-340851-lnv8yi9l 15 21 ] ] -RRB- cord-340851-lnv8yi9l 15 22 . . . cord-340851-lnv8yi9l 16 1 A a DT cord-340851-lnv8yi9l 16 2 safe safe JJ cord-340851-lnv8yi9l 16 3 , , , cord-340851-lnv8yi9l 16 4 effective effective JJ cord-340851-lnv8yi9l 16 5 , , , cord-340851-lnv8yi9l 16 6 and and CC cord-340851-lnv8yi9l 16 7 widely widely RB cord-340851-lnv8yi9l 16 8 used use VBN cord-340851-lnv8yi9l 16 9 vaccine vaccine NN cord-340851-lnv8yi9l 16 10 would would MD cord-340851-lnv8yi9l 16 11 obviate obviate VB cord-340851-lnv8yi9l 16 12 the the DT cord-340851-lnv8yi9l 16 13 need need NN cord-340851-lnv8yi9l 16 14 for for IN cord-340851-lnv8yi9l 16 15 social social JJ cord-340851-lnv8yi9l 16 16 distancing distancing NN cord-340851-lnv8yi9l 16 17 , , , cord-340851-lnv8yi9l 16 18 but but CC cord-340851-lnv8yi9l 16 19 there there EX cord-340851-lnv8yi9l 16 20 are be VBP cord-340851-lnv8yi9l 16 21 many many JJ cord-340851-lnv8yi9l 16 22 challenges challenge NNS cord-340851-lnv8yi9l 16 23 associated associate VBN cord-340851-lnv8yi9l 16 24 with with IN cord-340851-lnv8yi9l 16 25 developing develop VBG cord-340851-lnv8yi9l 16 26 a a DT cord-340851-lnv8yi9l 16 27 vaccine vaccine NN cord-340851-lnv8yi9l 16 28 against against IN cord-340851-lnv8yi9l 16 29 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 16 30 [ [ -LRB- cord-340851-lnv8yi9l 16 31 30 30 CD cord-340851-lnv8yi9l 16 32 ] ] -RRB- cord-340851-lnv8yi9l 16 33 and and CC cord-340851-lnv8yi9l 16 34 one one NN cord-340851-lnv8yi9l 16 35 is be VBZ cord-340851-lnv8yi9l 16 36 not not RB cord-340851-lnv8yi9l 16 37 likely likely JJ cord-340851-lnv8yi9l 16 38 to to TO cord-340851-lnv8yi9l 16 39 be be VB cord-340851-lnv8yi9l 16 40 available available JJ cord-340851-lnv8yi9l 16 41 until until IN cord-340851-lnv8yi9l 16 42 at at IN cord-340851-lnv8yi9l 16 43 least least JJS cord-340851-lnv8yi9l 16 44 spring spring NN cord-340851-lnv8yi9l 16 45 2021 2021 CD cord-340851-lnv8yi9l 16 46 [ [ -LRB- cord-340851-lnv8yi9l 16 47 4 4 CD cord-340851-lnv8yi9l 16 48 ] ] -RRB- cord-340851-lnv8yi9l 16 49 . . . cord-340851-lnv8yi9l 17 1 Strategies strategy NNS cord-340851-lnv8yi9l 17 2 for for IN cord-340851-lnv8yi9l 17 3 successfully successfully RB cord-340851-lnv8yi9l 17 4 controlling control VBG cord-340851-lnv8yi9l 17 5 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 17 6 until until IN cord-340851-lnv8yi9l 17 7 then then RB cord-340851-lnv8yi9l 17 8 will will MD cord-340851-lnv8yi9l 17 9 depend depend VB cord-340851-lnv8yi9l 17 10 on on IN cord-340851-lnv8yi9l 17 11 a a DT cord-340851-lnv8yi9l 17 12 suite suite NN cord-340851-lnv8yi9l 17 13 of of IN cord-340851-lnv8yi9l 17 14 non non JJ cord-340851-lnv8yi9l 17 15 - - JJ cord-340851-lnv8yi9l 17 16 pharmaceutical pharmaceutical JJ cord-340851-lnv8yi9l 17 17 interventions intervention NNS cord-340851-lnv8yi9l 17 18 ( ( -LRB- cord-340851-lnv8yi9l 17 19 NPIs NPIs NNP cord-340851-lnv8yi9l 17 20 ) ) -RRB- cord-340851-lnv8yi9l 17 21 [ [ -LRB- cord-340851-lnv8yi9l 17 22 3 3 CD cord-340851-lnv8yi9l 17 23 ] ] -RRB- cord-340851-lnv8yi9l 17 24 , , , cord-340851-lnv8yi9l 17 25 including include VBG cord-340851-lnv8yi9l 17 26 some some DT cord-340851-lnv8yi9l 17 27 degree degree NN cord-340851-lnv8yi9l 17 28 of of IN cord-340851-lnv8yi9l 17 29 social social JJ cord-340851-lnv8yi9l 17 30 distancing distancing NN cord-340851-lnv8yi9l 17 31 but but CC cord-340851-lnv8yi9l 17 32 also also RB cord-340851-lnv8yi9l 17 33 diagnostic diagnostic JJ cord-340851-lnv8yi9l 17 34 testing testing NN cord-340851-lnv8yi9l 17 35 , , , cord-340851-lnv8yi9l 17 36 contact contact NN cord-340851-lnv8yi9l 17 37 tracing tracing NN cord-340851-lnv8yi9l 17 38 , , , cord-340851-lnv8yi9l 17 39 and and CC cord-340851-lnv8yi9l 17 40 case case NN cord-340851-lnv8yi9l 17 41 isolation isolation NN cord-340851-lnv8yi9l 17 42 [ [ -LRB- cord-340851-lnv8yi9l 17 43 5 5 CD cord-340851-lnv8yi9l 17 44 ] ] -RRB- cord-340851-lnv8yi9l 17 45 . . . cord-340851-lnv8yi9l 18 1 In in IN cord-340851-lnv8yi9l 18 2 models model NNS cord-340851-lnv8yi9l 18 3 of of IN cord-340851-lnv8yi9l 18 4 pathogen pathogen NN cord-340851-lnv8yi9l 18 5 transmission transmission NN cord-340851-lnv8yi9l 18 6 based base VBN cord-340851-lnv8yi9l 18 7 on on IN cord-340851-lnv8yi9l 18 8 mass mass JJ cord-340851-lnv8yi9l 18 9 - - HYPH cord-340851-lnv8yi9l 18 10 action action NN cord-340851-lnv8yi9l 18 11 assumptions assumption NNS cord-340851-lnv8yi9l 18 12 , , , cord-340851-lnv8yi9l 18 13 NPIs NPIs NNP cord-340851-lnv8yi9l 18 14 all all DT cord-340851-lnv8yi9l 18 15 act act VBP cord-340851-lnv8yi9l 18 16 in in IN cord-340851-lnv8yi9l 18 17 a a DT cord-340851-lnv8yi9l 18 18 similar similar JJ cord-340851-lnv8yi9l 18 19 way way NN cord-340851-lnv8yi9l 18 20 by by IN cord-340851-lnv8yi9l 18 21 reducing reduce VBG cord-340851-lnv8yi9l 18 22 the the DT cord-340851-lnv8yi9l 18 23 transmission transmission NN cord-340851-lnv8yi9l 18 24 coefficient coefficient NN cord-340851-lnv8yi9l 18 25 . . . cord-340851-lnv8yi9l 19 1 This this DT cord-340851-lnv8yi9l 19 2 parameter parameter NN cord-340851-lnv8yi9l 19 3 , , , cord-340851-lnv8yi9l 19 4 often often RB cord-340851-lnv8yi9l 19 5 denoted denote VBD cord-340851-lnv8yi9l 19 6 β β NN cord-340851-lnv8yi9l 19 7 , , , cord-340851-lnv8yi9l 19 8 reflects reflect VBZ cord-340851-lnv8yi9l 19 9 the the DT cord-340851-lnv8yi9l 19 10 product product NN cord-340851-lnv8yi9l 19 11 of of IN cord-340851-lnv8yi9l 19 12 the the DT cord-340851-lnv8yi9l 19 13 rate rate NN cord-340851-lnv8yi9l 19 14 of of IN cord-340851-lnv8yi9l 19 15 contact contact NN cord-340851-lnv8yi9l 19 16 between between IN cord-340851-lnv8yi9l 19 17 susceptible susceptible JJ cord-340851-lnv8yi9l 19 18 and and CC cord-340851-lnv8yi9l 19 19 infectious infectious JJ cord-340851-lnv8yi9l 19 20 people people NNS cord-340851-lnv8yi9l 19 21 and and CC cord-340851-lnv8yi9l 19 22 the the DT cord-340851-lnv8yi9l 19 23 probability probability NN cord-340851-lnv8yi9l 19 24 of of IN cord-340851-lnv8yi9l 19 25 transmission transmission NN cord-340851-lnv8yi9l 19 26 upon upon IN cord-340851-lnv8yi9l 19 27 contact contact NN cord-340851-lnv8yi9l 19 28 [ [ -LRB- cord-340851-lnv8yi9l 19 29 24 24 CD cord-340851-lnv8yi9l 19 30 ] ] -RRB- cord-340851-lnv8yi9l 19 31 . . . cord-340851-lnv8yi9l 20 1 Due due IN cord-340851-lnv8yi9l 20 2 to to IN cord-340851-lnv8yi9l 20 3 the the DT cord-340851-lnv8yi9l 20 4 extent extent NN cord-340851-lnv8yi9l 20 5 to to TO cord-340851-lnv8yi9l 20 6 which which WDT cord-340851-lnv8yi9l 20 7 they -PRON- PRP cord-340851-lnv8yi9l 20 8 reduce reduce VBP cord-340851-lnv8yi9l 20 9 contact contact NN cord-340851-lnv8yi9l 20 10 , , , cord-340851-lnv8yi9l 20 11 full full JJ cord-340851-lnv8yi9l 20 12 - - HYPH cord-340851-lnv8yi9l 20 13 scale scale NN cord-340851-lnv8yi9l 20 14 lockdowns lockdown NNS cord-340851-lnv8yi9l 20 15 appear appear VBP cord-340851-lnv8yi9l 20 16 to to TO cord-340851-lnv8yi9l 20 17 be be VB cord-340851-lnv8yi9l 20 18 the the DT cord-340851-lnv8yi9l 20 19 most most RBS cord-340851-lnv8yi9l 20 20 effective effective JJ cord-340851-lnv8yi9l 20 21 strategy strategy NN cord-340851-lnv8yi9l 20 22 for for IN cord-340851-lnv8yi9l 20 23 reducing reduce VBG cord-340851-lnv8yi9l 20 24 transmission transmission NN cord-340851-lnv8yi9l 20 25 available available JJ cord-340851-lnv8yi9l 20 26 at at IN cord-340851-lnv8yi9l 20 27 present present JJ cord-340851-lnv8yi9l 20 28 [ [ -LRB- cord-340851-lnv8yi9l 20 29 18 18 CD cord-340851-lnv8yi9l 20 30 ] ] -RRB- cord-340851-lnv8yi9l 20 31 . . . cord-340851-lnv8yi9l 21 1 Until until IN cord-340851-lnv8yi9l 21 2 alternative alternative JJ cord-340851-lnv8yi9l 21 3 NPI npi NN cord-340851-lnv8yi9l 21 4 - - HYPH cord-340851-lnv8yi9l 21 5 based base VBN cord-340851-lnv8yi9l 21 6 strategies strategy NNS cord-340851-lnv8yi9l 21 7 can can MD cord-340851-lnv8yi9l 21 8 be be VB cord-340851-lnv8yi9l 21 9 implemented implement VBN cord-340851-lnv8yi9l 21 10 that that WDT cord-340851-lnv8yi9l 21 11 are be VBP cord-340851-lnv8yi9l 21 12 similarly similarly RB cord-340851-lnv8yi9l 21 13 effective effective JJ cord-340851-lnv8yi9l 21 14 but but CC cord-340851-lnv8yi9l 21 15 less less RBR cord-340851-lnv8yi9l 21 16 disruptive disruptive JJ cord-340851-lnv8yi9l 21 17 economically economically RB cord-340851-lnv8yi9l 21 18 , , , cord-340851-lnv8yi9l 21 19 it -PRON- PRP cord-340851-lnv8yi9l 21 20 is be VBZ cord-340851-lnv8yi9l 21 21 urgently urgently RB cord-340851-lnv8yi9l 21 22 important important JJ cord-340851-lnv8yi9l 21 23 to to TO cord-340851-lnv8yi9l 21 24 determine determine VB cord-340851-lnv8yi9l 21 25 the the DT cord-340851-lnv8yi9l 21 26 minimal minimal JJ cord-340851-lnv8yi9l 21 27 extent extent NN cord-340851-lnv8yi9l 21 28 to to TO cord-340851-lnv8yi9l 21 29 which which WDT cord-340851-lnv8yi9l 21 30 contact contact NN cord-340851-lnv8yi9l 21 31 must must MD cord-340851-lnv8yi9l 21 32 be be VB cord-340851-lnv8yi9l 21 33 reduced reduce VBN cord-340851-lnv8yi9l 21 34 to to TO cord-340851-lnv8yi9l 21 35 achieve achieve VB cord-340851-lnv8yi9l 21 36 public public JJ cord-340851-lnv8yi9l 21 37 health health NN cord-340851-lnv8yi9l 21 38 objectives objective NNS cord-340851-lnv8yi9l 21 39 . . . cord-340851-lnv8yi9l 22 1 Optimal optimal JJ cord-340851-lnv8yi9l 22 2 control control NN cord-340851-lnv8yi9l 22 3 theory theory NN cord-340851-lnv8yi9l 22 4 offers offer VBZ cord-340851-lnv8yi9l 22 5 a a DT cord-340851-lnv8yi9l 22 6 way way NN cord-340851-lnv8yi9l 22 7 to to TO cord-340851-lnv8yi9l 22 8 understand understand VB cord-340851-lnv8yi9l 22 9 how how WRB cord-340851-lnv8yi9l 22 10 to to TO cord-340851-lnv8yi9l 22 11 apply apply VB cord-340851-lnv8yi9l 22 12 one one CD cord-340851-lnv8yi9l 22 13 or or CC cord-340851-lnv8yi9l 22 14 more more JJR cord-340851-lnv8yi9l 22 15 time time NN cord-340851-lnv8yi9l 22 16 - - HYPH cord-340851-lnv8yi9l 22 17 varying vary VBG cord-340851-lnv8yi9l 22 18 control control NN cord-340851-lnv8yi9l 22 19 measures measure NNS cord-340851-lnv8yi9l 22 20 to to IN cord-340851-lnv8yi9l 22 21 a a DT cord-340851-lnv8yi9l 22 22 nonlinear nonlinear JJ cord-340851-lnv8yi9l 22 23 , , , cord-340851-lnv8yi9l 22 24 dynamical dynamical JJ cord-340851-lnv8yi9l 22 25 system system NN cord-340851-lnv8yi9l 22 26 in in IN cord-340851-lnv8yi9l 22 27 such such PDT cord-340851-lnv8yi9l 22 28 a a DT cord-340851-lnv8yi9l 22 29 way way NN cord-340851-lnv8yi9l 22 30 that that WDT cord-340851-lnv8yi9l 22 31 a a DT cord-340851-lnv8yi9l 22 32 given give VBN cord-340851-lnv8yi9l 22 33 objective objective NN cord-340851-lnv8yi9l 22 34 is be VBZ cord-340851-lnv8yi9l 22 35 optimized optimize VBN cord-340851-lnv8yi9l 22 36 [ [ -LRB- cord-340851-lnv8yi9l 22 37 28 28 CD cord-340851-lnv8yi9l 22 38 ] ] -RRB- cord-340851-lnv8yi9l 22 39 . . . cord-340851-lnv8yi9l 23 1 These these DT cord-340851-lnv8yi9l 23 2 techniques technique NNS cord-340851-lnv8yi9l 23 3 have have VBP cord-340851-lnv8yi9l 23 4 been be VBN cord-340851-lnv8yi9l 23 5 widely widely RB cord-340851-lnv8yi9l 23 6 applied apply VBN cord-340851-lnv8yi9l 23 7 to to IN cord-340851-lnv8yi9l 23 8 a a DT cord-340851-lnv8yi9l 23 9 variety variety NN cord-340851-lnv8yi9l 23 10 of of IN cord-340851-lnv8yi9l 23 11 pathogen pathogen NN cord-340851-lnv8yi9l 23 12 transmission transmission NN cord-340851-lnv8yi9l 23 13 systems system NNS cord-340851-lnv8yi9l 23 14 before before IN cord-340851-lnv8yi9l 23 15 ( ( -LRB- cord-340851-lnv8yi9l 23 16 e.g. e.g. RB cord-340851-lnv8yi9l 23 17 , , , cord-340851-lnv8yi9l 23 18 [ [ -LRB- cord-340851-lnv8yi9l 23 19 6 6 CD cord-340851-lnv8yi9l 23 20 , , , cord-340851-lnv8yi9l 23 21 33 33 CD cord-340851-lnv8yi9l 23 22 , , , cord-340851-lnv8yi9l 23 23 11 11 CD cord-340851-lnv8yi9l 23 24 , , , cord-340851-lnv8yi9l 23 25 2 2 CD cord-340851-lnv8yi9l 23 26 ] ] -RRB- cord-340851-lnv8yi9l 23 27 ) ) -RRB- cord-340851-lnv8yi9l 23 28 , , , cord-340851-lnv8yi9l 23 29 including include VBG cord-340851-lnv8yi9l 23 30 in in IN cord-340851-lnv8yi9l 23 31 the the DT cord-340851-lnv8yi9l 23 32 context context NN cord-340851-lnv8yi9l 23 33 of of IN cord-340851-lnv8yi9l 23 34 a a DT cord-340851-lnv8yi9l 23 35 pandemic pandemic NN cord-340851-lnv8yi9l 23 36 of of IN cord-340851-lnv8yi9l 23 37 a a DT cord-340851-lnv8yi9l 23 38 respiratory respiratory JJ cord-340851-lnv8yi9l 23 39 pathogen pathogen NN cord-340851-lnv8yi9l 23 40 ( ( -LRB- cord-340851-lnv8yi9l 23 41 e.g. e.g. RB cord-340851-lnv8yi9l 23 42 , , , cord-340851-lnv8yi9l 23 43 [ [ -LRB- cord-340851-lnv8yi9l 23 44 29 29 CD cord-340851-lnv8yi9l 23 45 , , , cord-340851-lnv8yi9l 23 46 48 48 CD cord-340851-lnv8yi9l 23 47 , , , cord-340851-lnv8yi9l 23 48 46 46 CD cord-340851-lnv8yi9l 23 49 ] ] -RRB- cord-340851-lnv8yi9l 23 50 ) ) -RRB- cord-340851-lnv8yi9l 23 51 . . . cord-340851-lnv8yi9l 24 1 The the DT cord-340851-lnv8yi9l 24 2 latter latter JJ cord-340851-lnv8yi9l 24 3 studies study NNS cord-340851-lnv8yi9l 24 4 indicate indicate VBP cord-340851-lnv8yi9l 24 5 that that IN cord-340851-lnv8yi9l 24 6 the the DT cord-340851-lnv8yi9l 24 7 level level NN cord-340851-lnv8yi9l 24 8 of of IN cord-340851-lnv8yi9l 24 9 NPI npi NN cord-340851-lnv8yi9l 24 10 - - HYPH cord-340851-lnv8yi9l 24 11 based base VBN cord-340851-lnv8yi9l 24 12 control control NN cord-340851-lnv8yi9l 24 13 required require VBD cord-340851-lnv8yi9l 24 14 is be VBZ cord-340851-lnv8yi9l 24 15 dependent dependent JJ cord-340851-lnv8yi9l 24 16 on on IN cord-340851-lnv8yi9l 24 17 model model NN cord-340851-lnv8yi9l 24 18 parameters parameter NNS cord-340851-lnv8yi9l 24 19 , , , cord-340851-lnv8yi9l 24 20 and and CC cord-340851-lnv8yi9l 24 21 that that DT cord-340851-lnv8yi9l 24 22 application application NN cord-340851-lnv8yi9l 24 23 of of IN cord-340851-lnv8yi9l 24 24 NPIs npi NNS cord-340851-lnv8yi9l 24 25 can can MD cord-340851-lnv8yi9l 24 26 be be VB cord-340851-lnv8yi9l 24 27 required require VBN cord-340851-lnv8yi9l 24 28 at at IN cord-340851-lnv8yi9l 24 29 a a DT cord-340851-lnv8yi9l 24 30 high high JJ cord-340851-lnv8yi9l 24 31 level level NN cord-340851-lnv8yi9l 24 32 and and CC cord-340851-lnv8yi9l 24 33 for for IN cord-340851-lnv8yi9l 24 34 a a DT cord-340851-lnv8yi9l 24 35 long long JJ cord-340851-lnv8yi9l 24 36 duration duration NN cord-340851-lnv8yi9l 24 37 in in IN cord-340851-lnv8yi9l 24 38 the the DT cord-340851-lnv8yi9l 24 39 absence absence NN cord-340851-lnv8yi9l 24 40 of of IN cord-340851-lnv8yi9l 24 41 a a DT cord-340851-lnv8yi9l 24 42 vaccine vaccine NN cord-340851-lnv8yi9l 24 43 . . . cord-340851-lnv8yi9l 25 1 Here here RB cord-340851-lnv8yi9l 25 2 , , , cord-340851-lnv8yi9l 25 3 we -PRON- PRP cord-340851-lnv8yi9l 25 4 apply apply VBP cord-340851-lnv8yi9l 25 5 optimal optimal JJ cord-340851-lnv8yi9l 25 6 control control NN cord-340851-lnv8yi9l 25 7 theory theory NN cord-340851-lnv8yi9l 25 8 to to TO cord-340851-lnv8yi9l 25 9 determine determine VB cord-340851-lnv8yi9l 25 10 optimal optimal JJ cord-340851-lnv8yi9l 25 11 strategies strategy NNS cord-340851-lnv8yi9l 25 12 for for IN cord-340851-lnv8yi9l 25 13 the the DT cord-340851-lnv8yi9l 25 14 implementation implementation NN cord-340851-lnv8yi9l 25 15 of of IN cord-340851-lnv8yi9l 25 16 NPIs npi NNS cord-340851-lnv8yi9l 25 17 to to TO cord-340851-lnv8yi9l 25 18 control control VB cord-340851-lnv8yi9l 25 19 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 25 20 , , , cord-340851-lnv8yi9l 25 21 with with IN cord-340851-lnv8yi9l 25 22 a a DT cord-340851-lnv8yi9l 25 23 focus focus NN cord-340851-lnv8yi9l 25 24 on on IN cord-340851-lnv8yi9l 25 25 the the DT cord-340851-lnv8yi9l 25 26 US US NNP cord-340851-lnv8yi9l 25 27 . . . cord-340851-lnv8yi9l 26 1 An an DT cord-340851-lnv8yi9l 26 2 optimal optimal JJ cord-340851-lnv8yi9l 26 3 strategy strategy NN cord-340851-lnv8yi9l 26 4 in in IN cord-340851-lnv8yi9l 26 5 this this DT cord-340851-lnv8yi9l 26 6 sense sense NN cord-340851-lnv8yi9l 26 7 involves involve VBZ cord-340851-lnv8yi9l 26 8 weighing weigh VBG cord-340851-lnv8yi9l 26 9 the the DT cord-340851-lnv8yi9l 26 10 relative relative JJ cord-340851-lnv8yi9l 26 11 costs cost NNS cord-340851-lnv8yi9l 26 12 of of IN cord-340851-lnv8yi9l 26 13 control control NN cord-340851-lnv8yi9l 26 14 and and CC cord-340851-lnv8yi9l 26 15 COVID COVID NNP cord-340851-lnv8yi9l 26 16 - - HYPH cord-340851-lnv8yi9l 26 17 related relate VBN cord-340851-lnv8yi9l 26 18 mortality mortality NN cord-340851-lnv8yi9l 26 19 , , , cord-340851-lnv8yi9l 26 20 and and CC cord-340851-lnv8yi9l 26 21 finding find VBG cord-340851-lnv8yi9l 26 22 an an DT cord-340851-lnv8yi9l 26 23 approach approach NN cord-340851-lnv8yi9l 26 24 to to TO cord-340851-lnv8yi9l 26 25 control control VB cord-340851-lnv8yi9l 26 26 that that DT cord-340851-lnv8yi9l 26 27 minimizes minimize VBZ cord-340851-lnv8yi9l 26 28 that that IN cord-340851-lnv8yi9l 26 29 combined combine VBN cord-340851-lnv8yi9l 26 30 cost cost NN cord-340851-lnv8yi9l 26 31 . . . cord-340851-lnv8yi9l 27 1 Other other JJ cord-340851-lnv8yi9l 27 2 optimal optimal JJ cord-340851-lnv8yi9l 27 3 control control NN cord-340851-lnv8yi9l 27 4 analyses analysis NNS cord-340851-lnv8yi9l 27 5 of of IN cord-340851-lnv8yi9l 27 6 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 27 7 are be VBP cord-340851-lnv8yi9l 27 8 beginning begin VBG cord-340851-lnv8yi9l 27 9 to to TO cord-340851-lnv8yi9l 27 10 emerge emerge VB cord-340851-lnv8yi9l 27 11 [ [ -LRB- cord-340851-lnv8yi9l 27 12 14 14 CD cord-340851-lnv8yi9l 27 13 , , , cord-340851-lnv8yi9l 27 14 31 31 CD cord-340851-lnv8yi9l 27 15 , , , cord-340851-lnv8yi9l 27 16 40 40 CD cord-340851-lnv8yi9l 27 17 , , , cord-340851-lnv8yi9l 27 18 43 43 CD cord-340851-lnv8yi9l 27 19 , , , cord-340851-lnv8yi9l 27 20 45 45 CD cord-340851-lnv8yi9l 27 21 ] ] -RRB- cord-340851-lnv8yi9l 27 22 , , , cord-340851-lnv8yi9l 27 23 although although IN cord-340851-lnv8yi9l 27 24 these these DT cord-340851-lnv8yi9l 27 25 have have VBP cord-340851-lnv8yi9l 27 26 been be VBN cord-340851-lnv8yi9l 27 27 less less RBR cord-340851-lnv8yi9l 27 28 focused focus VBN cord-340851-lnv8yi9l 27 29 on on IN cord-340851-lnv8yi9l 27 30 any any DT cord-340851-lnv8yi9l 27 31 particular particular JJ cord-340851-lnv8yi9l 27 32 geographic geographic JJ cord-340851-lnv8yi9l 27 33 setting setting NN cord-340851-lnv8yi9l 27 34 . . . cord-340851-lnv8yi9l 28 1 One one CD cord-340851-lnv8yi9l 28 2 contextual contextual JJ cord-340851-lnv8yi9l 28 3 feature feature NN cord-340851-lnv8yi9l 28 4 of of IN cord-340851-lnv8yi9l 28 5 the the DT cord-340851-lnv8yi9l 28 6 US US NNP cord-340851-lnv8yi9l 28 7 that that WDT cord-340851-lnv8yi9l 28 8 our -PRON- PRP$ cord-340851-lnv8yi9l 28 9 analysis analysis NN cord-340851-lnv8yi9l 28 10 considers consider VBZ cord-340851-lnv8yi9l 28 11 is be VBZ cord-340851-lnv8yi9l 28 12 the the DT cord-340851-lnv8yi9l 28 13 level level NN cord-340851-lnv8yi9l 28 14 of of IN cord-340851-lnv8yi9l 28 15 control control NN cord-340851-lnv8yi9l 28 16 that that WDT cord-340851-lnv8yi9l 28 17 was be VBD cord-340851-lnv8yi9l 28 18 implemented implement VBN cord-340851-lnv8yi9l 28 19 early early RB cord-340851-lnv8yi9l 28 20 in in IN cord-340851-lnv8yi9l 28 21 the the DT cord-340851-lnv8yi9l 28 22 pandemic pandemic NN cord-340851-lnv8yi9l 28 23 . . . cord-340851-lnv8yi9l 29 1 We -PRON- PRP cord-340851-lnv8yi9l 29 2 account account VBP cord-340851-lnv8yi9l 29 3 for for IN cord-340851-lnv8yi9l 29 4 this this DT cord-340851-lnv8yi9l 29 5 , , , cord-340851-lnv8yi9l 29 6 because because IN cord-340851-lnv8yi9l 29 7 our -PRON- PRP$ cord-340851-lnv8yi9l 29 8 objective objective NN cord-340851-lnv8yi9l 29 9 is be VBZ cord-340851-lnv8yi9l 29 10 less less JJR cord-340851-lnv8yi9l 29 11 about about IN cord-340851-lnv8yi9l 29 12 understanding understand VBG cord-340851-lnv8yi9l 29 13 what what WDT cord-340851-lnv8yi9l 29 14 level level NN cord-340851-lnv8yi9l 29 15 of of IN cord-340851-lnv8yi9l 29 16 control control NN cord-340851-lnv8yi9l 29 17 would would MD cord-340851-lnv8yi9l 29 18 have have VB cord-340851-lnv8yi9l 29 19 been be VBN cord-340851-lnv8yi9l 29 20 optimal optimal JJ cord-340851-lnv8yi9l 29 21 earlier early RBR cord-340851-lnv8yi9l 29 22 on on RB cord-340851-lnv8yi9l 29 23 and and CC cord-340851-lnv8yi9l 29 24 more more JJR cord-340851-lnv8yi9l 29 25 about about IN cord-340851-lnv8yi9l 29 26 understanding understand VBG cord-340851-lnv8yi9l 29 27 what what WDT cord-340851-lnv8yi9l 29 28 level level NN cord-340851-lnv8yi9l 29 29 of of IN cord-340851-lnv8yi9l 29 30 control control NN cord-340851-lnv8yi9l 29 31 would would MD cord-340851-lnv8yi9l 29 32 be be VB cord-340851-lnv8yi9l 29 33 optimal optimal JJ cord-340851-lnv8yi9l 29 34 going go VBG cord-340851-lnv8yi9l 29 35 forward forward RB cord-340851-lnv8yi9l 29 36 , , , cord-340851-lnv8yi9l 29 37 conditional conditional JJ cord-340851-lnv8yi9l 29 38 on on IN cord-340851-lnv8yi9l 29 39 what what WP cord-340851-lnv8yi9l 29 40 has have VBZ cord-340851-lnv8yi9l 29 41 happened happen VBN cord-340851-lnv8yi9l 29 42 already already RB cord-340851-lnv8yi9l 29 43 . . . cord-340851-lnv8yi9l 30 1 In in IN cord-340851-lnv8yi9l 30 2 addition addition NN cord-340851-lnv8yi9l 30 3 , , , cord-340851-lnv8yi9l 30 4 we -PRON- PRP cord-340851-lnv8yi9l 30 5 emphasize emphasize VBP cord-340851-lnv8yi9l 30 6 the the DT cord-340851-lnv8yi9l 30 7 sensitivity sensitivity NN cord-340851-lnv8yi9l 30 8 of of IN cord-340851-lnv8yi9l 30 9 our -PRON- PRP$ cord-340851-lnv8yi9l 30 10 results result NNS cord-340851-lnv8yi9l 30 11 to to IN cord-340851-lnv8yi9l 30 12 epidemiological epidemiological JJ cord-340851-lnv8yi9l 30 13 parameters parameter NNS cord-340851-lnv8yi9l 30 14 that that WDT cord-340851-lnv8yi9l 30 15 are be VBP cord-340851-lnv8yi9l 30 16 not not RB cord-340851-lnv8yi9l 30 17 yet yet RB cord-340851-lnv8yi9l 30 18 well well RB cord-340851-lnv8yi9l 30 19 characterized characterized JJ cord-340851-lnv8yi9l 30 20 but but CC cord-340851-lnv8yi9l 30 21 appear appear VBP cord-340851-lnv8yi9l 30 22 influential influential JJ cord-340851-lnv8yi9l 30 23 in in IN cord-340851-lnv8yi9l 30 24 determining determine VBG cord-340851-lnv8yi9l 30 25 what what WDT cord-340851-lnv8yi9l 30 26 range range NN cord-340851-lnv8yi9l 30 27 of of IN cord-340851-lnv8yi9l 30 28 impacts impact NNS cord-340851-lnv8yi9l 30 29 of of IN cord-340851-lnv8yi9l 30 30 NPIs npi NNS cord-340851-lnv8yi9l 30 31 on on IN cord-340851-lnv8yi9l 30 32 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 30 33 are be VBP cord-340851-lnv8yi9l 30 34 possible possible JJ cord-340851-lnv8yi9l 30 35 . . . cord-340851-lnv8yi9l 31 1 All all DT cord-340851-lnv8yi9l 31 2 code code NN cord-340851-lnv8yi9l 31 3 and and CC cord-340851-lnv8yi9l 31 4 data datum NNS cord-340851-lnv8yi9l 31 5 used use VBN cord-340851-lnv8yi9l 31 6 in in IN cord-340851-lnv8yi9l 31 7 our -PRON- PRP$ cord-340851-lnv8yi9l 31 8 analysis analysis NN cord-340851-lnv8yi9l 31 9 is be VBZ cord-340851-lnv8yi9l 31 10 available available JJ cord-340851-lnv8yi9l 31 11 at at IN cord-340851-lnv8yi9l 31 12 http://github.com/TAlexPerkins/covid19optimalcontrol http://github.com/TAlexPerkins/covid19optimalcontrol NNP cord-340851-lnv8yi9l 31 13 . . . cord-340851-lnv8yi9l 32 1 We -PRON- PRP cord-340851-lnv8yi9l 32 2 modeled model VBD cord-340851-lnv8yi9l 32 3 SARS SARS NNP cord-340851-lnv8yi9l 32 4 - - HYPH cord-340851-lnv8yi9l 32 5 CoV-2 CoV-2 NNP cord-340851-lnv8yi9l 32 6 transmission transmission NN cord-340851-lnv8yi9l 32 7 according accord VBG cord-340851-lnv8yi9l 32 8 to to IN cord-340851-lnv8yi9l 32 9 a a DT cord-340851-lnv8yi9l 32 10 system system NN cord-340851-lnv8yi9l 32 11 of of IN cord-340851-lnv8yi9l 32 12 ordinary ordinary JJ cord-340851-lnv8yi9l 32 13 differential differential JJ cord-340851-lnv8yi9l 32 14 equations equation NNS cord-340851-lnv8yi9l 32 15 , , , cord-340851-lnv8yi9l 32 16 with with IN cord-340851-lnv8yi9l 32 17 variables variable NNS cord-340851-lnv8yi9l 32 18 and and CC cord-340851-lnv8yi9l 32 19 parameters parameter NNS cord-340851-lnv8yi9l 32 20 defined define VBN cord-340851-lnv8yi9l 32 21 in in IN cord-340851-lnv8yi9l 32 22 Tables table NNS cord-340851-lnv8yi9l 32 23 1 1 CD cord-340851-lnv8yi9l 32 24 and and CC cord-340851-lnv8yi9l 32 25 2 2 CD cord-340851-lnv8yi9l 32 26 . . . cord-340851-lnv8yi9l 33 1 In in IN cord-340851-lnv8yi9l 33 2 the the DT cord-340851-lnv8yi9l 33 3 model model NN cord-340851-lnv8yi9l 33 4 , , , cord-340851-lnv8yi9l 33 5 all all DT cord-340851-lnv8yi9l 33 6 individuals individual NNS cord-340851-lnv8yi9l 33 7 are be VBP cord-340851-lnv8yi9l 33 8 initially initially RB cord-340851-lnv8yi9l 33 9 susceptible susceptible JJ cord-340851-lnv8yi9l 33 10 , , , cord-340851-lnv8yi9l 33 11 S S NNP cord-340851-lnv8yi9l 33 12 , , , cord-340851-lnv8yi9l 33 13 with with IN cord-340851-lnv8yi9l 33 14 infections infection NNS cord-340851-lnv8yi9l 33 15 introduced introduce VBN cord-340851-lnv8yi9l 33 16 at at IN cord-340851-lnv8yi9l 33 17 a a DT cord-340851-lnv8yi9l 33 18 constant constant JJ cord-340851-lnv8yi9l 33 19 rate rate NN cord-340851-lnv8yi9l 33 20 , , , cord-340851-lnv8yi9l 33 21 ι ι NNS cord-340851-lnv8yi9l 33 22 , , , cord-340851-lnv8yi9l 33 23 from from IN cord-340851-lnv8yi9l 33 24 outside outside IN cord-340851-lnv8yi9l 33 25 the the DT cord-340851-lnv8yi9l 33 26 population population NN cord-340851-lnv8yi9l 33 27 . . . cord-340851-lnv8yi9l 34 1 Individuals individual NNS cord-340851-lnv8yi9l 34 2 then then RB cord-340851-lnv8yi9l 34 3 transition transition VBP cord-340851-lnv8yi9l 34 4 to to IN cord-340851-lnv8yi9l 34 5 the the DT cord-340851-lnv8yi9l 34 6 exposed expose VBN cord-340851-lnv8yi9l 34 7 class class NN cord-340851-lnv8yi9l 34 8 , , , cord-340851-lnv8yi9l 34 9 E E NNP cord-340851-lnv8yi9l 34 10 , , , cord-340851-lnv8yi9l 34 11 where where WRB cord-340851-lnv8yi9l 34 12 they -PRON- PRP cord-340851-lnv8yi9l 34 13 reside reside VBP cord-340851-lnv8yi9l 34 14 for for IN cord-340851-lnv8yi9l 34 15 an an DT cord-340851-lnv8yi9l 34 16 average average NN cord-340851-lnv8yi9l 34 17 of of IN cord-340851-lnv8yi9l 34 18 ρ ρ NNP cord-340851-lnv8yi9l 34 19 −1 −1 NNP cord-340851-lnv8yi9l 34 20 days day NNS cord-340851-lnv8yi9l 34 21 . . . cord-340851-lnv8yi9l 35 1 A a DT cord-340851-lnv8yi9l 35 2 proportion proportion NN cord-340851-lnv8yi9l 35 3 σ σ NN cord-340851-lnv8yi9l 35 4 experience experience VB cord-340851-lnv8yi9l 35 5 a a DT cord-340851-lnv8yi9l 35 6 symptomatic symptomatic JJ cord-340851-lnv8yi9l 35 7 infection infection NN cord-340851-lnv8yi9l 35 8 , , , cord-340851-lnv8yi9l 36 1 I. i. LS cord-340851-lnv8yi9l 36 2 The the DT cord-340851-lnv8yi9l 36 3 remainder remainder NN cord-340851-lnv8yi9l 36 4 experience experience NN cord-340851-lnv8yi9l 36 5 an an DT cord-340851-lnv8yi9l 36 6 asymptomatic asymptomatic JJ cord-340851-lnv8yi9l 36 7 infection infection NN cord-340851-lnv8yi9l 36 8 , , , cord-340851-lnv8yi9l 36 9 A A NNP cord-340851-lnv8yi9l 36 10 , , , cord-340851-lnv8yi9l 36 11 and and CC cord-340851-lnv8yi9l 36 12 have have VBP cord-340851-lnv8yi9l 36 13 a a DT cord-340851-lnv8yi9l 36 14 fraction fraction NN cord-340851-lnv8yi9l 36 15 , , , cord-340851-lnv8yi9l 36 16 α α NN cord-340851-lnv8yi9l 36 17 , , , cord-340851-lnv8yi9l 36 18 of of IN cord-340851-lnv8yi9l 36 19 the the DT cord-340851-lnv8yi9l 36 20 infectiousness infectiousness NN cord-340851-lnv8yi9l 36 21 of of IN cord-340851-lnv8yi9l 36 22 symptomatic symptomatic JJ cord-340851-lnv8yi9l 36 23 infections infection NNS cord-340851-lnv8yi9l 36 24 . . . cord-340851-lnv8yi9l 37 1 Individuals individual NNS cord-340851-lnv8yi9l 37 2 reside reside VBP cord-340851-lnv8yi9l 37 3 in in IN cord-340851-lnv8yi9l 37 4 the the DT cord-340851-lnv8yi9l 37 5 I I NNP cord-340851-lnv8yi9l 37 6 and and CC cord-340851-lnv8yi9l 37 7 A a DT cord-340851-lnv8yi9l 37 8 classes class NNS cord-340851-lnv8yi9l 37 9 for for IN cord-340851-lnv8yi9l 37 10 an an DT cord-340851-lnv8yi9l 37 11 average average NN cord-340851-lnv8yi9l 37 12 of of IN cord-340851-lnv8yi9l 37 13 γ γ NN cord-340851-lnv8yi9l 37 14 −1 −1 NNP cord-340851-lnv8yi9l 37 15 days day NNS cord-340851-lnv8yi9l 37 16 . . . cord-340851-lnv8yi9l 38 1 All all DT cord-340851-lnv8yi9l 38 2 asymptomatic asymptomatic JJ cord-340851-lnv8yi9l 38 3 infections infection NNS cord-340851-lnv8yi9l 38 4 and and CC cord-340851-lnv8yi9l 38 5 a a DT cord-340851-lnv8yi9l 38 6 proportion proportion NN cord-340851-lnv8yi9l 38 7 _SP cord-340851-lnv8yi9l 38 8 Relationship relationship NN cord-340851-lnv8yi9l 38 9 between between IN cord-340851-lnv8yi9l 38 10 the the DT cord-340851-lnv8yi9l 38 11 number number NN cord-340851-lnv8yi9l 38 12 of of IN cord-340851-lnv8yi9l 38 13 hospitalizations hospitalization NNS cord-340851-lnv8yi9l 38 14 and and CC cord-340851-lnv8yi9l 38 15 the the DT cord-340851-lnv8yi9l 38 16 probability probability NN cord-340851-lnv8yi9l 38 17 of of IN cord-340851-lnv8yi9l 38 18 death death NN cord-340851-lnv8yi9l 38 19 from from IN cord-340851-lnv8yi9l 38 20 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 38 21 among among IN cord-340851-lnv8yi9l 38 22 hospitalized hospitalize VBN cord-340851-lnv8yi9l 38 23 patients patient NNS cord-340851-lnv8yi9l 38 24 . . . cord-340851-lnv8yi9l 39 1 The the DT cord-340851-lnv8yi9l 39 2 parameters parameter NNS cord-340851-lnv8yi9l 39 3 ∆ ∆ NNP cord-340851-lnv8yi9l 39 4 − − NNP cord-340851-lnv8yi9l 39 5 and and CC cord-340851-lnv8yi9l 39 6 ∆ ∆ NNP cord-340851-lnv8yi9l 39 7 + + CC cord-340851-lnv8yi9l 39 8 represent represent VBP cord-340851-lnv8yi9l 39 9 lower low JJR cord-340851-lnv8yi9l 39 10 and and CC cord-340851-lnv8yi9l 39 11 upper upper JJ cord-340851-lnv8yi9l 39 12 bounds bound NNS cord-340851-lnv8yi9l 39 13 on on IN cord-340851-lnv8yi9l 39 14 the the DT cord-340851-lnv8yi9l 39 15 probability probability NN cord-340851-lnv8yi9l 39 16 of of IN cord-340851-lnv8yi9l 39 17 death death NN cord-340851-lnv8yi9l 39 18 , , , cord-340851-lnv8yi9l 39 19 and and CC cord-340851-lnv8yi9l 39 20 Hmax Hmax NNP cord-340851-lnv8yi9l 39 21 represents represent VBZ cord-340851-lnv8yi9l 39 22 the the DT cord-340851-lnv8yi9l 39 23 hospital hospital NN cord-340851-lnv8yi9l 39 24 capacity capacity NN cord-340851-lnv8yi9l 39 25 above above IN cord-340851-lnv8yi9l 39 26 which which WDT cord-340851-lnv8yi9l 39 27 the the DT cord-340851-lnv8yi9l 39 28 probability probability NN cord-340851-lnv8yi9l 39 29 of of IN cord-340851-lnv8yi9l 39 30 death death NN cord-340851-lnv8yi9l 39 31 exceeds exceed VBZ cord-340851-lnv8yi9l 39 32 ∆ ∆ NNP cord-340851-lnv8yi9l 39 33 − − NNP cord-340851-lnv8yi9l 39 34 . . . cord-340851-lnv8yi9l 40 1 Hospitalizations hospitalization NNS cord-340851-lnv8yi9l 40 2 are be VBP cord-340851-lnv8yi9l 40 3 quantified quantify VBN cord-340851-lnv8yi9l 40 4 as as IN cord-340851-lnv8yi9l 40 5 a a DT cord-340851-lnv8yi9l 40 6 proportion proportion NN cord-340851-lnv8yi9l 40 7 of of IN cord-340851-lnv8yi9l 40 8 the the DT cord-340851-lnv8yi9l 40 9 overall overall JJ cord-340851-lnv8yi9l 40 10 population population NN cord-340851-lnv8yi9l 40 11 . . . cord-340851-lnv8yi9l 41 1 1 1 CD cord-340851-lnv8yi9l 41 2 − − NN cord-340851-lnv8yi9l 41 3 κ κ NN cord-340851-lnv8yi9l 41 4 of of IN cord-340851-lnv8yi9l 41 5 symptomatic symptomatic JJ cord-340851-lnv8yi9l 41 6 infections infection NNS cord-340851-lnv8yi9l 41 7 then then RB cord-340851-lnv8yi9l 41 8 recover recover VBP cord-340851-lnv8yi9l 41 9 and and CC cord-340851-lnv8yi9l 41 10 become become VBP cord-340851-lnv8yi9l 41 11 fully fully RB cord-340851-lnv8yi9l 41 12 immune immune JJ cord-340851-lnv8yi9l 41 13 to to IN cord-340851-lnv8yi9l 41 14 subsequent subsequent JJ cord-340851-lnv8yi9l 41 15 infection infection NN cord-340851-lnv8yi9l 41 16 . . . cord-340851-lnv8yi9l 42 1 The the DT cord-340851-lnv8yi9l 42 2 remaining remain VBG cord-340851-lnv8yi9l 42 3 proportion proportion NN cord-340851-lnv8yi9l 42 4 κ κ NN cord-340851-lnv8yi9l 42 5 of of IN cord-340851-lnv8yi9l 42 6 symptomatic symptomatic JJ cord-340851-lnv8yi9l 42 7 infections infection NNS cord-340851-lnv8yi9l 42 8 transition transition NN cord-340851-lnv8yi9l 42 9 to to IN cord-340851-lnv8yi9l 42 10 the the DT cord-340851-lnv8yi9l 42 11 hospitalized hospitalize VBN cord-340851-lnv8yi9l 42 12 class class NN cord-340851-lnv8yi9l 42 13 , , , cord-340851-lnv8yi9l 42 14 H H NNP cord-340851-lnv8yi9l 42 15 , , , cord-340851-lnv8yi9l 42 16 from from IN cord-340851-lnv8yi9l 42 17 which which WDT cord-340851-lnv8yi9l 42 18 they -PRON- PRP cord-340851-lnv8yi9l 42 19 exit exit VBP cord-340851-lnv8yi9l 42 20 through through IN cord-340851-lnv8yi9l 42 21 either either DT cord-340851-lnv8yi9l 42 22 recovery recovery NN cord-340851-lnv8yi9l 42 23 or or CC cord-340851-lnv8yi9l 42 24 death death NN cord-340851-lnv8yi9l 42 25 after after IN cord-340851-lnv8yi9l 42 26 an an DT cord-340851-lnv8yi9l 42 27 average average NN cord-340851-lnv8yi9l 42 28 of of IN cord-340851-lnv8yi9l 42 29 η η NN cord-340851-lnv8yi9l 42 30 −1 −1 NNP cord-340851-lnv8yi9l 42 31 days day NNS cord-340851-lnv8yi9l 42 32 . . . cord-340851-lnv8yi9l 43 1 Rather rather RB cord-340851-lnv8yi9l 43 2 than than IN cord-340851-lnv8yi9l 43 3 track track NN cord-340851-lnv8yi9l 43 4 deaths death NNS cord-340851-lnv8yi9l 43 5 due due JJ cord-340851-lnv8yi9l 43 6 to to IN cord-340851-lnv8yi9l 43 7 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 43 8 , , , cord-340851-lnv8yi9l 43 9 D(t D(t NNP cord-340851-lnv8yi9l 43 10 ) ) -RRB- cord-340851-lnv8yi9l 43 11 , , , cord-340851-lnv8yi9l 43 12 as as IN cord-340851-lnv8yi9l 43 13 a a DT cord-340851-lnv8yi9l 43 14 state state NN cord-340851-lnv8yi9l 43 15 variable variable NN cord-340851-lnv8yi9l 43 16 in in IN cord-340851-lnv8yi9l 43 17 eqn eqn NN cord-340851-lnv8yi9l 43 18 . . . cord-340851-lnv8yi9l 44 1 ( ( -LRB- cord-340851-lnv8yi9l 44 2 1 1 LS cord-340851-lnv8yi9l 44 3 ) ) -RRB- cord-340851-lnv8yi9l 44 4 , , , cord-340851-lnv8yi9l 44 5 we -PRON- PRP cord-340851-lnv8yi9l 44 6 assume assume VBP cord-340851-lnv8yi9l 44 7 that that IN cord-340851-lnv8yi9l 44 8 they -PRON- PRP cord-340851-lnv8yi9l 44 9 follow follow VBP cord-340851-lnv8yi9l 44 10 directly directly RB cord-340851-lnv8yi9l 44 11 from from IN cord-340851-lnv8yi9l 44 12 hospitalizations hospitalization NNS cord-340851-lnv8yi9l 44 13 , , , cord-340851-lnv8yi9l 44 14 H(t H(t NNP cord-340851-lnv8yi9l 44 15 ) ) -RRB- cord-340851-lnv8yi9l 44 16 , , , cord-340851-lnv8yi9l 44 17 according accord VBG cord-340851-lnv8yi9l 44 18 to to IN cord-340851-lnv8yi9l 44 19 This this DT cord-340851-lnv8yi9l 44 20 results result NNS cord-340851-lnv8yi9l 44 21 in in IN cord-340851-lnv8yi9l 44 22 the the DT cord-340851-lnv8yi9l 44 23 probability probability NN cord-340851-lnv8yi9l 44 24 of of IN cord-340851-lnv8yi9l 44 25 death death NN cord-340851-lnv8yi9l 44 26 moving move VBG cord-340851-lnv8yi9l 44 27 beyond beyond IN cord-340851-lnv8yi9l 44 28 a a DT cord-340851-lnv8yi9l 44 29 minimum minimum NN cord-340851-lnv8yi9l 44 30 of of IN cord-340851-lnv8yi9l 44 31 ∆ ∆ NNP cord-340851-lnv8yi9l 44 32 − − NNP cord-340851-lnv8yi9l 44 33 towards towards IN cord-340851-lnv8yi9l 44 34 a a DT cord-340851-lnv8yi9l 44 35 maximum maximum NN cord-340851-lnv8yi9l 44 36 of of IN cord-340851-lnv8yi9l 44 37 ∆ ∆ NN cord-340851-lnv8yi9l 44 38 + + CC cord-340851-lnv8yi9l 44 39 as as IN cord-340851-lnv8yi9l 44 40 H(t H(t NNP cord-340851-lnv8yi9l 44 41 ) ) -RRB- cord-340851-lnv8yi9l 44 42 exceeds exceed VBZ cord-340851-lnv8yi9l 44 43 H h NN cord-340851-lnv8yi9l 44 44 max max NN cord-340851-lnv8yi9l 44 45 , , , cord-340851-lnv8yi9l 44 46 as as IN cord-340851-lnv8yi9l 44 47 illustrated illustrate VBN cord-340851-lnv8yi9l 44 48 in in IN cord-340851-lnv8yi9l 44 49 Figure Figure NNP cord-340851-lnv8yi9l 44 50 1 1 CD cord-340851-lnv8yi9l 44 51 . . . cord-340851-lnv8yi9l 45 1 The the DT cord-340851-lnv8yi9l 45 2 motivation motivation NN cord-340851-lnv8yi9l 45 3 for for IN cord-340851-lnv8yi9l 45 4 this this DT cord-340851-lnv8yi9l 45 5 choice choice NN cord-340851-lnv8yi9l 45 6 is be VBZ cord-340851-lnv8yi9l 45 7 to to TO cord-340851-lnv8yi9l 45 8 account account VB cord-340851-lnv8yi9l 45 9 for for IN cord-340851-lnv8yi9l 45 10 the the DT cord-340851-lnv8yi9l 45 11 possibility possibility NN cord-340851-lnv8yi9l 45 12 that that IN cord-340851-lnv8yi9l 45 13 patients patient NNS cord-340851-lnv8yi9l 45 14 could could MD cord-340851-lnv8yi9l 45 15 experience experience VB cord-340851-lnv8yi9l 45 16 increased increase VBN cord-340851-lnv8yi9l 45 17 mortality mortality NN cord-340851-lnv8yi9l 45 18 when when WRB cord-340851-lnv8yi9l 45 19 the the DT cord-340851-lnv8yi9l 45 20 demand demand NN cord-340851-lnv8yi9l 45 21 for for IN cord-340851-lnv8yi9l 45 22 certain certain JJ cord-340851-lnv8yi9l 45 23 resources resource NNS cord-340851-lnv8yi9l 45 24 , , , cord-340851-lnv8yi9l 45 25 such such JJ cord-340851-lnv8yi9l 45 26 as as IN cord-340851-lnv8yi9l 45 27 intensive intensive JJ cord-340851-lnv8yi9l 45 28 care care NN cord-340851-lnv8yi9l 45 29 unit unit NN cord-340851-lnv8yi9l 45 30 beds bed NNS cord-340851-lnv8yi9l 45 31 or or CC cord-340851-lnv8yi9l 45 32 ventilators ventilator NNS cord-340851-lnv8yi9l 45 33 , , , cord-340851-lnv8yi9l 45 34 exceeds exceed VBZ cord-340851-lnv8yi9l 45 35 their -PRON- PRP$ cord-340851-lnv8yi9l 45 36 availability availability NN cord-340851-lnv8yi9l 45 37 . . . cord-340851-lnv8yi9l 46 1 One one CD cord-340851-lnv8yi9l 46 2 other other JJ cord-340851-lnv8yi9l 46 3 optimal optimal JJ cord-340851-lnv8yi9l 46 4 control control NN cord-340851-lnv8yi9l 46 5 analysis analysis NN cord-340851-lnv8yi9l 46 6 of of IN cord-340851-lnv8yi9l 46 7 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 46 8 has have VBZ cord-340851-lnv8yi9l 46 9 incorporated incorporate VBN cord-340851-lnv8yi9l 46 10 a a DT cord-340851-lnv8yi9l 46 11 similar similar JJ cord-340851-lnv8yi9l 46 12 phenomenon phenomenon NN cord-340851-lnv8yi9l 46 13 [ [ -LRB- cord-340851-lnv8yi9l 46 14 43 43 CD cord-340851-lnv8yi9l 46 15 ] ] -RRB- cord-340851-lnv8yi9l 46 16 , , , cord-340851-lnv8yi9l 46 17 albeit albeit IN cord-340851-lnv8yi9l 46 18 with with IN cord-340851-lnv8yi9l 46 19 a a DT cord-340851-lnv8yi9l 46 20 different different JJ cord-340851-lnv8yi9l 46 21 functional functional JJ cord-340851-lnv8yi9l 46 22 form form NN cord-340851-lnv8yi9l 46 23 . . . cord-340851-lnv8yi9l 47 1 Individuals individual NNS cord-340851-lnv8yi9l 47 2 who who WP cord-340851-lnv8yi9l 47 3 are be VBP cord-340851-lnv8yi9l 47 4 recovered recover VBN cord-340851-lnv8yi9l 47 5 and and CC cord-340851-lnv8yi9l 47 6 immune immune JJ cord-340851-lnv8yi9l 47 7 are be VBP cord-340851-lnv8yi9l 47 8 not not RB cord-340851-lnv8yi9l 47 9 followed follow VBN cord-340851-lnv8yi9l 47 10 explicitly explicitly RB cord-340851-lnv8yi9l 47 11 , , , cord-340851-lnv8yi9l 47 12 as as IN cord-340851-lnv8yi9l 47 13 the the DT cord-340851-lnv8yi9l 47 14 model model NN cord-340851-lnv8yi9l 47 15 's 's POS cord-340851-lnv8yi9l 47 16 assumption assumption NN cord-340851-lnv8yi9l 47 17 of of IN cord-340851-lnv8yi9l 47 18 density density NN cord-340851-lnv8yi9l 47 19 - - HYPH cord-340851-lnv8yi9l 47 20 dependent dependent JJ cord-340851-lnv8yi9l 47 21 transmission transmission NN cord-340851-lnv8yi9l 47 22 only only RB cord-340851-lnv8yi9l 47 23 requires require VBZ cord-340851-lnv8yi9l 47 24 spec- spec- NN cord-340851-lnv8yi9l 47 25 . . . cord-340851-lnv8yi9l 48 1 CC CC NNP cord-340851-lnv8yi9l 48 2 - - : cord-340851-lnv8yi9l 48 3 BY by IN cord-340851-lnv8yi9l 48 4 4.0 4.0 CD cord-340851-lnv8yi9l 48 5 International international JJ cord-340851-lnv8yi9l 48 6 license license NN cord-340851-lnv8yi9l 49 1 It -PRON- PRP cord-340851-lnv8yi9l 49 2 is be VBZ cord-340851-lnv8yi9l 49 3 made make VBN cord-340851-lnv8yi9l 49 4 available available JJ cord-340851-lnv8yi9l 49 5 under under IN cord-340851-lnv8yi9l 49 6 a a DT cord-340851-lnv8yi9l 50 1 is be VBZ cord-340851-lnv8yi9l 50 2 the the DT cord-340851-lnv8yi9l 50 3 author author NN cord-340851-lnv8yi9l 50 4 / / SYM cord-340851-lnv8yi9l 50 5 funder funder NN cord-340851-lnv8yi9l 50 6 , , , cord-340851-lnv8yi9l 50 7 who who WP cord-340851-lnv8yi9l 50 8 has have VBZ cord-340851-lnv8yi9l 50 9 granted grant VBN cord-340851-lnv8yi9l 50 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 50 11 a a DT cord-340851-lnv8yi9l 50 12 license license NN cord-340851-lnv8yi9l 50 13 to to TO cord-340851-lnv8yi9l 50 14 display display VB cord-340851-lnv8yi9l 50 15 the the DT cord-340851-lnv8yi9l 50 16 preprint preprint NN cord-340851-lnv8yi9l 50 17 in in IN cord-340851-lnv8yi9l 50 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 50 19 . . . cord-340851-lnv8yi9l 51 1 ( ( -LRB- cord-340851-lnv8yi9l 51 2 which which WDT cord-340851-lnv8yi9l 51 3 was be VBD cord-340851-lnv8yi9l 51 4 not not RB cord-340851-lnv8yi9l 51 5 certified certify VBN cord-340851-lnv8yi9l 51 6 by by IN cord-340851-lnv8yi9l 51 7 peer peer NN cord-340851-lnv8yi9l 51 8 review review NN cord-340851-lnv8yi9l 51 9 ) ) -RRB- cord-340851-lnv8yi9l 52 1 The the DT cord-340851-lnv8yi9l 52 2 copyright copyright NN cord-340851-lnv8yi9l 52 3 holder holder NN cord-340851-lnv8yi9l 52 4 for for IN cord-340851-lnv8yi9l 52 5 this this DT cord-340851-lnv8yi9l 52 6 preprint preprint NN cord-340851-lnv8yi9l 52 7 this this DT cord-340851-lnv8yi9l 52 8 version version NN cord-340851-lnv8yi9l 52 9 posted post VBN cord-340851-lnv8yi9l 52 10 April April NNP cord-340851-lnv8yi9l 52 11 23 23 CD cord-340851-lnv8yi9l 52 12 , , , cord-340851-lnv8yi9l 52 13 2020 2020 CD cord-340851-lnv8yi9l 52 14 . . . cord-340851-lnv8yi9l 52 15 . . . cord-340851-lnv8yi9l 53 1 https://doi.org/10.1101/2020.04 https://doi.org/10.1101/2020.04 UH cord-340851-lnv8yi9l 53 2 . . . cord-340851-lnv8yi9l 54 1 22.20076018 22.20076018 CD cord-340851-lnv8yi9l 54 2 doi doi NN cord-340851-lnv8yi9l 54 3 : : : cord-340851-lnv8yi9l 55 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 55 2 preprint preprint NN cord-340851-lnv8yi9l 55 3 ification ification NN cord-340851-lnv8yi9l 55 4 of of IN cord-340851-lnv8yi9l 55 5 susceptible susceptible JJ cord-340851-lnv8yi9l 55 6 and and CC cord-340851-lnv8yi9l 55 7 infectious infectious JJ cord-340851-lnv8yi9l 55 8 classes class NNS cord-340851-lnv8yi9l 55 9 in in IN cord-340851-lnv8yi9l 55 10 the the DT cord-340851-lnv8yi9l 55 11 transmission transmission NN cord-340851-lnv8yi9l 55 12 term term NN cord-340851-lnv8yi9l 55 13 . . . cord-340851-lnv8yi9l 56 1 Due due IN cord-340851-lnv8yi9l 56 2 to to IN cord-340851-lnv8yi9l 56 3 our -PRON- PRP$ cord-340851-lnv8yi9l 56 4 assumption assumption NN cord-340851-lnv8yi9l 56 5 that that IN cord-340851-lnv8yi9l 56 6 rates rate NNS cord-340851-lnv8yi9l 56 7 of of IN cord-340851-lnv8yi9l 56 8 birth birth NN cord-340851-lnv8yi9l 56 9 , , , cord-340851-lnv8yi9l 56 10 µ µ NN cord-340851-lnv8yi9l 56 11 , , , cord-340851-lnv8yi9l 56 12 and and CC cord-340851-lnv8yi9l 56 13 death death NN cord-340851-lnv8yi9l 56 14 due due IN cord-340851-lnv8yi9l 56 15 to to IN cord-340851-lnv8yi9l 56 16 reasons reason NNS cord-340851-lnv8yi9l 56 17 other other JJ cord-340851-lnv8yi9l 56 18 than than IN cord-340851-lnv8yi9l 56 19 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 56 20 , , , cord-340851-lnv8yi9l 56 21 δ δ NN cord-340851-lnv8yi9l 56 22 , , , cord-340851-lnv8yi9l 56 23 are be VBP cord-340851-lnv8yi9l 56 24 equal equal JJ cord-340851-lnv8yi9l 56 25 , , , cord-340851-lnv8yi9l 56 26 changes change NNS cord-340851-lnv8yi9l 56 27 in in IN cord-340851-lnv8yi9l 56 28 population population NN cord-340851-lnv8yi9l 56 29 size size NN cord-340851-lnv8yi9l 56 30 over over IN cord-340851-lnv8yi9l 56 31 the the DT cord-340851-lnv8yi9l 56 32 course course NN cord-340851-lnv8yi9l 56 33 of of IN cord-340851-lnv8yi9l 56 34 the the DT cord-340851-lnv8yi9l 56 35 epidemic epidemic NN cord-340851-lnv8yi9l 56 36 are be VBP cord-340851-lnv8yi9l 56 37 modest modest JJ cord-340851-lnv8yi9l 56 38 , , , cord-340851-lnv8yi9l 56 39 making make VBG cord-340851-lnv8yi9l 56 40 the the DT cord-340851-lnv8yi9l 56 41 distinction distinction NN cord-340851-lnv8yi9l 56 42 between between IN cord-340851-lnv8yi9l 56 43 density density NN cord-340851-lnv8yi9l 56 44 - - HYPH cord-340851-lnv8yi9l 56 45 and and CC cord-340851-lnv8yi9l 56 46 frequencydependent frequencydependent NN cord-340851-lnv8yi9l 56 47 transmission transmission NN cord-340851-lnv8yi9l 56 48 negligible negligible JJ cord-340851-lnv8yi9l 56 49 . . . cord-340851-lnv8yi9l 57 1 The the DT cord-340851-lnv8yi9l 57 2 primary primary JJ cord-340851-lnv8yi9l 57 3 form form NN cord-340851-lnv8yi9l 57 4 of of IN cord-340851-lnv8yi9l 57 5 control control NN cord-340851-lnv8yi9l 57 6 in in IN cord-340851-lnv8yi9l 57 7 the the DT cord-340851-lnv8yi9l 57 8 model model NN cord-340851-lnv8yi9l 57 9 is be VBZ cord-340851-lnv8yi9l 57 10 achieved achieve VBN cord-340851-lnv8yi9l 57 11 through through IN cord-340851-lnv8yi9l 57 12 the the DT cord-340851-lnv8yi9l 57 13 variable variable NN cord-340851-lnv8yi9l 57 14 u u NN cord-340851-lnv8yi9l 57 15 , , , cord-340851-lnv8yi9l 57 16 which which WDT cord-340851-lnv8yi9l 57 17 represents represent VBZ cord-340851-lnv8yi9l 57 18 a a DT cord-340851-lnv8yi9l 57 19 proportional proportional JJ cord-340851-lnv8yi9l 57 20 reduction reduction NN cord-340851-lnv8yi9l 57 21 in in IN cord-340851-lnv8yi9l 57 22 the the DT cord-340851-lnv8yi9l 57 23 transmission transmission NN cord-340851-lnv8yi9l 57 24 coefficient coefficient NN cord-340851-lnv8yi9l 57 25 , , , cord-340851-lnv8yi9l 57 26 β β NN cord-340851-lnv8yi9l 57 27 . . . cord-340851-lnv8yi9l 58 1 As as IN cord-340851-lnv8yi9l 58 2 is be VBZ cord-340851-lnv8yi9l 58 3 standard standard JJ cord-340851-lnv8yi9l 58 4 for for IN cord-340851-lnv8yi9l 58 5 mass mass JJ cord-340851-lnv8yi9l 58 6 - - HYPH cord-340851-lnv8yi9l 58 7 action action NN cord-340851-lnv8yi9l 58 8 models model NNS cord-340851-lnv8yi9l 58 9 of of IN cord-340851-lnv8yi9l 58 10 directly directly RB cord-340851-lnv8yi9l 58 11 - - HYPH cord-340851-lnv8yi9l 58 12 transmitted transmit VBN cord-340851-lnv8yi9l 58 13 pathogens pathogen NNS cord-340851-lnv8yi9l 58 14 , , , cord-340851-lnv8yi9l 58 15 β β NN cord-340851-lnv8yi9l 58 16 reflects reflect VBZ cord-340851-lnv8yi9l 58 17 the the DT cord-340851-lnv8yi9l 58 18 product product NN cord-340851-lnv8yi9l 58 19 of of IN cord-340851-lnv8yi9l 58 20 the the DT cord-340851-lnv8yi9l 58 21 rate rate NN cord-340851-lnv8yi9l 58 22 at at IN cord-340851-lnv8yi9l 58 23 which which WDT cord-340851-lnv8yi9l 58 24 susceptible susceptible JJ cord-340851-lnv8yi9l 58 25 and and CC cord-340851-lnv8yi9l 58 26 infectious infectious JJ cord-340851-lnv8yi9l 58 27 individuals individual NNS cord-340851-lnv8yi9l 58 28 come come VBP cord-340851-lnv8yi9l 58 29 into into IN cord-340851-lnv8yi9l 58 30 contact contact NN cord-340851-lnv8yi9l 58 31 and and CC cord-340851-lnv8yi9l 58 32 the the DT cord-340851-lnv8yi9l 58 33 probability probability NN cord-340851-lnv8yi9l 58 34 of of IN cord-340851-lnv8yi9l 58 35 transmission transmission NN cord-340851-lnv8yi9l 58 36 given give VBN cord-340851-lnv8yi9l 58 37 that that IN cord-340851-lnv8yi9l 58 38 a a DT cord-340851-lnv8yi9l 58 39 contact contact NN cord-340851-lnv8yi9l 58 40 has have VBZ cord-340851-lnv8yi9l 58 41 occurred occur VBN cord-340851-lnv8yi9l 58 42 [ [ -LRB- cord-340851-lnv8yi9l 58 43 24 24 CD cord-340851-lnv8yi9l 58 44 ] ] -RRB- cord-340851-lnv8yi9l 58 45 . . . cord-340851-lnv8yi9l 59 1 Thus thus RB cord-340851-lnv8yi9l 59 2 , , , cord-340851-lnv8yi9l 59 3 a a DT cord-340851-lnv8yi9l 59 4 wide wide JJ cord-340851-lnv8yi9l 59 5 range range NN cord-340851-lnv8yi9l 59 6 of of IN cord-340851-lnv8yi9l 59 7 NPIs npi NNS cord-340851-lnv8yi9l 59 8 could could MD cord-340851-lnv8yi9l 59 9 result result VB cord-340851-lnv8yi9l 59 10 in in IN cord-340851-lnv8yi9l 59 11 changes change NNS cord-340851-lnv8yi9l 59 12 in in IN cord-340851-lnv8yi9l 59 13 u u NNP cord-340851-lnv8yi9l 59 14 , , , cord-340851-lnv8yi9l 59 15 including include VBG cord-340851-lnv8yi9l 59 16 school school NN cord-340851-lnv8yi9l 59 17 closures closure NNS cord-340851-lnv8yi9l 59 18 , , , cord-340851-lnv8yi9l 59 19 work work VBP cord-340851-lnv8yi9l 59 20 from from IN cord-340851-lnv8yi9l 59 21 home home NN cord-340851-lnv8yi9l 59 22 policies policy NNS cord-340851-lnv8yi9l 59 23 , , , cord-340851-lnv8yi9l 59 24 and and CC cord-340851-lnv8yi9l 59 25 shelter shelter NN cord-340851-lnv8yi9l 59 26 in in IN cord-340851-lnv8yi9l 59 27 place place NN cord-340851-lnv8yi9l 59 28 mandates mandate NNS cord-340851-lnv8yi9l 59 29 , , , cord-340851-lnv8yi9l 59 30 as as RB cord-340851-lnv8yi9l 59 31 well well RB cord-340851-lnv8yi9l 59 32 as as IN cord-340851-lnv8yi9l 59 33 more more RBR cord-340851-lnv8yi9l 59 34 targeted target VBN cord-340851-lnv8yi9l 59 35 approaches approach NNS cord-340851-lnv8yi9l 59 36 , , , cord-340851-lnv8yi9l 59 37 such such JJ cord-340851-lnv8yi9l 59 38 as as IN cord-340851-lnv8yi9l 59 39 isolation isolation NN cord-340851-lnv8yi9l 59 40 based base VBN cord-340851-lnv8yi9l 59 41 on on IN cord-340851-lnv8yi9l 59 42 self self NN cord-340851-lnv8yi9l 59 43 - - HYPH cord-340851-lnv8yi9l 59 44 awareness awareness NN cord-340851-lnv8yi9l 59 45 of of IN cord-340851-lnv8yi9l 59 46 symptoms symptom NNS cord-340851-lnv8yi9l 59 47 or or CC cord-340851-lnv8yi9l 59 48 contact contact NN cord-340851-lnv8yi9l 59 49 tracing tracing NN cord-340851-lnv8yi9l 59 50 . . . cord-340851-lnv8yi9l 60 1 In in IN cord-340851-lnv8yi9l 60 2 addition addition NN cord-340851-lnv8yi9l 60 3 to to TO cord-340851-lnv8yi9l 60 4 control control VB cord-340851-lnv8yi9l 60 5 through through IN cord-340851-lnv8yi9l 60 6 u u NNP cord-340851-lnv8yi9l 60 7 , , , cord-340851-lnv8yi9l 60 8 the the DT cord-340851-lnv8yi9l 60 9 V V NNP cord-340851-lnv8yi9l 60 10 class class NN cord-340851-lnv8yi9l 60 11 represents represent VBZ cord-340851-lnv8yi9l 60 12 individuals individual NNS cord-340851-lnv8yi9l 60 13 who who WP cord-340851-lnv8yi9l 60 14 have have VBP cord-340851-lnv8yi9l 60 15 been be VBN cord-340851-lnv8yi9l 60 16 vaccinated vaccinate VBN cord-340851-lnv8yi9l 60 17 , , , cord-340851-lnv8yi9l 60 18 with with IN cord-340851-lnv8yi9l 60 19 individuals individual NNS cord-340851-lnv8yi9l 60 20 entering enter VBG cord-340851-lnv8yi9l 60 21 V v NN cord-340851-lnv8yi9l 60 22 from from IN cord-340851-lnv8yi9l 60 23 S S NNP cord-340851-lnv8yi9l 60 24 at at IN cord-340851-lnv8yi9l 60 25 rate rate NN cord-340851-lnv8yi9l 60 26 ν ν NN cord-340851-lnv8yi9l 60 27 beginning begin VBG cord-340851-lnv8yi9l 60 28 on on IN cord-340851-lnv8yi9l 60 29 day day NN cord-340851-lnv8yi9l 60 30 τ τ NN cord-340851-lnv8yi9l 60 31 ν ν NNP cord-340851-lnv8yi9l 60 32 . . . cord-340851-lnv8yi9l 61 1 We -PRON- PRP cord-340851-lnv8yi9l 61 2 assume assume VBP cord-340851-lnv8yi9l 61 3 that that IN cord-340851-lnv8yi9l 61 4 vaccination vaccination NN cord-340851-lnv8yi9l 61 5 may may MD cord-340851-lnv8yi9l 61 6 not not RB cord-340851-lnv8yi9l 61 7 provide provide VB cord-340851-lnv8yi9l 61 8 complete complete JJ cord-340851-lnv8yi9l 61 9 protection protection NN cord-340851-lnv8yi9l 61 10 , , , cord-340851-lnv8yi9l 61 11 resulting result VBG cord-340851-lnv8yi9l 61 12 in in IN cord-340851-lnv8yi9l 61 13 vaccinated vaccinate VBN cord-340851-lnv8yi9l 61 14 individuals individual NNS cord-340851-lnv8yi9l 61 15 becoming become VBG cord-340851-lnv8yi9l 61 16 infected infect VBN cord-340851-lnv8yi9l 61 17 at at IN cord-340851-lnv8yi9l 61 18 a a DT cord-340851-lnv8yi9l 61 19 fraction fraction NN cord-340851-lnv8yi9l 61 20 1 1 CD cord-340851-lnv8yi9l 61 21 − − CD cord-340851-lnv8yi9l 61 22 of of IN cord-340851-lnv8yi9l 61 23 the the DT cord-340851-lnv8yi9l 61 24 rate rate NN cord-340851-lnv8yi9l 61 25 at at IN cord-340851-lnv8yi9l 61 26 which which WDT cord-340851-lnv8yi9l 61 27 fully fully RB cord-340851-lnv8yi9l 61 28 susceptible susceptible JJ cord-340851-lnv8yi9l 61 29 individuals individual NNS cord-340851-lnv8yi9l 61 30 become become VBP cord-340851-lnv8yi9l 61 31 infected infected JJ cord-340851-lnv8yi9l 61 32 . . . cord-340851-lnv8yi9l 62 1 At at IN cord-340851-lnv8yi9l 62 2 its -PRON- PRP$ cord-340851-lnv8yi9l 62 3 core core NN cord-340851-lnv8yi9l 62 4 , , , cord-340851-lnv8yi9l 62 5 the the DT cord-340851-lnv8yi9l 62 6 behavior behavior NN cord-340851-lnv8yi9l 62 7 of of IN cord-340851-lnv8yi9l 62 8 this this DT cord-340851-lnv8yi9l 62 9 model model NN cord-340851-lnv8yi9l 62 10 is be VBZ cord-340851-lnv8yi9l 62 11 similar similar JJ cord-340851-lnv8yi9l 62 12 to to IN cord-340851-lnv8yi9l 62 13 that that DT cord-340851-lnv8yi9l 62 14 of of IN cord-340851-lnv8yi9l 62 15 an an DT cord-340851-lnv8yi9l 62 16 SEIR SEIR NNP cord-340851-lnv8yi9l 62 17 model model NN cord-340851-lnv8yi9l 62 18 with with IN cord-340851-lnv8yi9l 62 19 demography demography NN cord-340851-lnv8yi9l 62 20 . . . cord-340851-lnv8yi9l 63 1 Because because IN cord-340851-lnv8yi9l 63 2 analyses analysis NNS cord-340851-lnv8yi9l 63 3 of of IN cord-340851-lnv8yi9l 63 4 the the DT cord-340851-lnv8yi9l 63 5 transient transient JJ cord-340851-lnv8yi9l 63 6 and and CC cord-340851-lnv8yi9l 63 7 asymptotic asymptotic JJ cord-340851-lnv8yi9l 63 8 properties property NNS cord-340851-lnv8yi9l 63 9 of of IN cord-340851-lnv8yi9l 63 10 this this DT cord-340851-lnv8yi9l 63 11 class class NN cord-340851-lnv8yi9l 63 12 of of IN cord-340851-lnv8yi9l 63 13 models model NNS cord-340851-lnv8yi9l 63 14 are be VBP cord-340851-lnv8yi9l 63 15 plentiful plentiful JJ cord-340851-lnv8yi9l 63 16 in in IN cord-340851-lnv8yi9l 63 17 textbooks textbook NNS cord-340851-lnv8yi9l 63 18 and and CC cord-340851-lnv8yi9l 63 19 elsewhere elsewhere RB cord-340851-lnv8yi9l 63 20 ( ( -LRB- cord-340851-lnv8yi9l 63 21 e.g. e.g. RB cord-340851-lnv8yi9l 63 22 , , , cord-340851-lnv8yi9l 63 23 [ [ -LRB- cord-340851-lnv8yi9l 63 24 24 24 CD cord-340851-lnv8yi9l 63 25 ] ] -RRB- cord-340851-lnv8yi9l 63 26 ) ) -RRB- cord-340851-lnv8yi9l 63 27 , , , cord-340851-lnv8yi9l 63 28 we -PRON- PRP cord-340851-lnv8yi9l 63 29 omit omit VBP cord-340851-lnv8yi9l 63 30 such such PDT cord-340851-lnv8yi9l 63 31 an an DT cord-340851-lnv8yi9l 63 32 analysis analysis NN cord-340851-lnv8yi9l 63 33 here here RB cord-340851-lnv8yi9l 63 34 . . . cord-340851-lnv8yi9l 64 1 We -PRON- PRP cord-340851-lnv8yi9l 64 2 do do VBP cord-340851-lnv8yi9l 64 3 , , , cord-340851-lnv8yi9l 64 4 however however RB cord-340851-lnv8yi9l 64 5 , , , cord-340851-lnv8yi9l 64 6 derive derive VB cord-340851-lnv8yi9l 64 7 a a DT cord-340851-lnv8yi9l 64 8 formula formula NN cord-340851-lnv8yi9l 64 9 to to TO cord-340851-lnv8yi9l 64 10 express express VB cord-340851-lnv8yi9l 64 11 the the DT cord-340851-lnv8yi9l 64 12 basic basic JJ cord-340851-lnv8yi9l 64 13 reproduction reproduction NN cord-340851-lnv8yi9l 64 14 number number NN cord-340851-lnv8yi9l 64 15 , , , cord-340851-lnv8yi9l 64 16 R r NN cord-340851-lnv8yi9l 64 17 0 0 CD cord-340851-lnv8yi9l 64 18 , , , cord-340851-lnv8yi9l 64 19 as as IN cord-340851-lnv8yi9l 64 20 a a DT cord-340851-lnv8yi9l 64 21 function function NN cord-340851-lnv8yi9l 64 22 of of IN cord-340851-lnv8yi9l 64 23 model model NN cord-340851-lnv8yi9l 64 24 parameters parameter NNS cord-340851-lnv8yi9l 64 25 . . . cord-340851-lnv8yi9l 65 1 This this DT cord-340851-lnv8yi9l 65 2 relationship relationship NN cord-340851-lnv8yi9l 65 3 plays play VBZ cord-340851-lnv8yi9l 65 4 a a DT cord-340851-lnv8yi9l 65 5 role role NN cord-340851-lnv8yi9l 65 6 in in IN cord-340851-lnv8yi9l 65 7 how how WRB cord-340851-lnv8yi9l 65 8 we -PRON- PRP cord-340851-lnv8yi9l 65 9 parameterize parameterize VBP cord-340851-lnv8yi9l 65 10 the the DT cord-340851-lnv8yi9l 65 11 model model NN cord-340851-lnv8yi9l 65 12 . . . cord-340851-lnv8yi9l 66 1 We -PRON- PRP cord-340851-lnv8yi9l 66 2 use use VBP cord-340851-lnv8yi9l 66 3 the the DT cord-340851-lnv8yi9l 66 4 next next JJ cord-340851-lnv8yi9l 66 5 - - HYPH cord-340851-lnv8yi9l 66 6 generation generation NN cord-340851-lnv8yi9l 66 7 method method NN cord-340851-lnv8yi9l 66 8 [ [ -LRB- cord-340851-lnv8yi9l 66 9 15 15 CD cord-340851-lnv8yi9l 66 10 ] ] -RRB- cord-340851-lnv8yi9l 66 11 to to TO cord-340851-lnv8yi9l 66 12 obtain obtain VB cord-340851-lnv8yi9l 66 13 a a DT cord-340851-lnv8yi9l 66 14 formula formula NN cord-340851-lnv8yi9l 66 15 describing describe VBG cord-340851-lnv8yi9l 66 16 R r NN cord-340851-lnv8yi9l 66 17 0 0 CD cord-340851-lnv8yi9l 66 18 as as IN cord-340851-lnv8yi9l 66 19 a a DT cord-340851-lnv8yi9l 66 20 function function NN cord-340851-lnv8yi9l 66 21 of of IN cord-340851-lnv8yi9l 66 22 model model NN cord-340851-lnv8yi9l 66 23 parameters parameter NNS cord-340851-lnv8yi9l 66 24 . . . cord-340851-lnv8yi9l 67 1 This this DT cord-340851-lnv8yi9l 67 2 method method NN cord-340851-lnv8yi9l 67 3 depends depend VBZ cord-340851-lnv8yi9l 67 4 on on IN cord-340851-lnv8yi9l 67 5 matrices matrix NNS cord-340851-lnv8yi9l 67 6 F F NNP cord-340851-lnv8yi9l 67 7 and and CC cord-340851-lnv8yi9l 67 8 V V NNP cord-340851-lnv8yi9l 67 9 , , , cord-340851-lnv8yi9l 67 10 whose whose WP$ cord-340851-lnv8yi9l 67 11 elements element NNS cord-340851-lnv8yi9l 67 12 are be VBP cord-340851-lnv8yi9l 67 13 defined define VBN cord-340851-lnv8yi9l 67 14 as as IN cord-340851-lnv8yi9l 67 15 the the DT cord-340851-lnv8yi9l 67 16 rates rate NNS cord-340851-lnv8yi9l 67 17 at at IN cord-340851-lnv8yi9l 67 18 which which WDT cord-340851-lnv8yi9l 67 19 secondary secondary JJ cord-340851-lnv8yi9l 67 20 infections infection NNS cord-340851-lnv8yi9l 67 21 increase increase VBP cord-340851-lnv8yi9l 67 22 the the DT cord-340851-lnv8yi9l 67 23 i i NN cord-340851-lnv8yi9l 67 24 th th XX cord-340851-lnv8yi9l 67 25 compartment compartment NN cord-340851-lnv8yi9l 67 26 and and CC cord-340851-lnv8yi9l 67 27 the the DT cord-340851-lnv8yi9l 67 28 rates rate NNS cord-340851-lnv8yi9l 67 29 at at IN cord-340851-lnv8yi9l 67 30 which which WDT cord-340851-lnv8yi9l 67 31 disease disease NN cord-340851-lnv8yi9l 67 32 progression progression NN cord-340851-lnv8yi9l 67 33 , , , cord-340851-lnv8yi9l 67 34 death death NN cord-340851-lnv8yi9l 67 35 , , , cord-340851-lnv8yi9l 67 36 and and CC cord-340851-lnv8yi9l 67 37 recovery recovery NN cord-340851-lnv8yi9l 67 38 decrease decrease NN cord-340851-lnv8yi9l 67 39 the the DT cord-340851-lnv8yi9l 67 40 i i NN cord-340851-lnv8yi9l 67 41 th th XX cord-340851-lnv8yi9l 67 42 compartment compartment NN cord-340851-lnv8yi9l 67 43 , , , cord-340851-lnv8yi9l 67 44 respectively respectively RB cord-340851-lnv8yi9l 67 45 . . . cord-340851-lnv8yi9l 68 1 For for IN cord-340851-lnv8yi9l 68 2 " " `` cord-340851-lnv8yi9l 68 3 disease disease NN cord-340851-lnv8yi9l 68 4 compartments compartment NNS cord-340851-lnv8yi9l 68 5 " " '' cord-340851-lnv8yi9l 68 6 E e NN cord-340851-lnv8yi9l 68 7 , , , cord-340851-lnv8yi9l 68 8 A A NNP cord-340851-lnv8yi9l 68 9 , , , cord-340851-lnv8yi9l 68 10 I -PRON- PRP cord-340851-lnv8yi9l 68 11 , , , cord-340851-lnv8yi9l 68 12 and and CC cord-340851-lnv8yi9l 68 13 H H NNP cord-340851-lnv8yi9l 68 14 , , , cord-340851-lnv8yi9l 68 15 these these DT cord-340851-lnv8yi9l 68 16 matrices matrix NNS cord-340851-lnv8yi9l 68 17 are be VBP cord-340851-lnv8yi9l 68 18 defined define VBN cord-340851-lnv8yi9l 68 19 as as IN cord-340851-lnv8yi9l 68 20 These these DT cord-340851-lnv8yi9l 68 21 matrices matrix NNS cord-340851-lnv8yi9l 68 22 are be VBP cord-340851-lnv8yi9l 68 23 then then RB cord-340851-lnv8yi9l 68 24 used use VBN cord-340851-lnv8yi9l 68 25 to to TO cord-340851-lnv8yi9l 68 26 define define VB cord-340851-lnv8yi9l 68 27 two two CD cord-340851-lnv8yi9l 68 28 others other NNS cord-340851-lnv8yi9l 68 29 , , , cord-340851-lnv8yi9l 68 30 . . . cord-340851-lnv8yi9l 69 1 CC CC NNP cord-340851-lnv8yi9l 69 2 - - : cord-340851-lnv8yi9l 69 3 BY by IN cord-340851-lnv8yi9l 69 4 4.0 4.0 CD cord-340851-lnv8yi9l 69 5 International international JJ cord-340851-lnv8yi9l 69 6 license license NN cord-340851-lnv8yi9l 70 1 It -PRON- PRP cord-340851-lnv8yi9l 70 2 is be VBZ cord-340851-lnv8yi9l 70 3 made make VBN cord-340851-lnv8yi9l 70 4 available available JJ cord-340851-lnv8yi9l 70 5 under under IN cord-340851-lnv8yi9l 70 6 a a DT cord-340851-lnv8yi9l 71 1 is be VBZ cord-340851-lnv8yi9l 71 2 the the DT cord-340851-lnv8yi9l 71 3 author author NN cord-340851-lnv8yi9l 71 4 / / SYM cord-340851-lnv8yi9l 71 5 funder funder NN cord-340851-lnv8yi9l 71 6 , , , cord-340851-lnv8yi9l 71 7 who who WP cord-340851-lnv8yi9l 71 8 has have VBZ cord-340851-lnv8yi9l 71 9 granted grant VBN cord-340851-lnv8yi9l 71 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 71 11 a a DT cord-340851-lnv8yi9l 71 12 license license NN cord-340851-lnv8yi9l 71 13 to to TO cord-340851-lnv8yi9l 71 14 display display VB cord-340851-lnv8yi9l 71 15 the the DT cord-340851-lnv8yi9l 71 16 preprint preprint NN cord-340851-lnv8yi9l 71 17 in in IN cord-340851-lnv8yi9l 71 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 71 19 . . . cord-340851-lnv8yi9l 72 1 ( ( -LRB- cord-340851-lnv8yi9l 72 2 which which WDT cord-340851-lnv8yi9l 72 3 was be VBD cord-340851-lnv8yi9l 72 4 not not RB cord-340851-lnv8yi9l 72 5 certified certify VBN cord-340851-lnv8yi9l 72 6 by by IN cord-340851-lnv8yi9l 72 7 peer peer NN cord-340851-lnv8yi9l 72 8 review review NN cord-340851-lnv8yi9l 72 9 ) ) -RRB- cord-340851-lnv8yi9l 73 1 The the DT cord-340851-lnv8yi9l 73 2 copyright copyright NN cord-340851-lnv8yi9l 73 3 holder holder NN cord-340851-lnv8yi9l 73 4 for for IN cord-340851-lnv8yi9l 73 5 this this DT cord-340851-lnv8yi9l 73 6 preprint preprint NN cord-340851-lnv8yi9l 73 7 this this DT cord-340851-lnv8yi9l 73 8 version version NN cord-340851-lnv8yi9l 73 9 posted post VBN cord-340851-lnv8yi9l 73 10 April April NNP cord-340851-lnv8yi9l 73 11 23 23 CD cord-340851-lnv8yi9l 73 12 , , , cord-340851-lnv8yi9l 73 13 2020 2020 CD cord-340851-lnv8yi9l 73 14 . . . cord-340851-lnv8yi9l 73 15 _SP cord-340851-lnv8yi9l 74 1 where where WRB cord-340851-lnv8yi9l 74 2 x x NN cord-340851-lnv8yi9l 74 3 represents represent VBZ cord-340851-lnv8yi9l 74 4 disease disease NN cord-340851-lnv8yi9l 74 5 compartments compartment NNS cord-340851-lnv8yi9l 74 6 and and CC cord-340851-lnv8yi9l 74 7 y y NNP cord-340851-lnv8yi9l 74 8 non non JJ cord-340851-lnv8yi9l 74 9 - - JJ cord-340851-lnv8yi9l 74 10 disease disease JJ cord-340851-lnv8yi9l 74 11 compartments compartment NNS cord-340851-lnv8yi9l 74 12 . . . cord-340851-lnv8yi9l 75 1 The the DT cord-340851-lnv8yi9l 75 2 inverse inverse NN cord-340851-lnv8yi9l 75 3 of of IN cord-340851-lnv8yi9l 75 4 V v NN cord-340851-lnv8yi9l 75 5 is be VBZ cord-340851-lnv8yi9l 75 6 which which WDT cord-340851-lnv8yi9l 75 7 , , , cord-340851-lnv8yi9l 75 8 along along IN cord-340851-lnv8yi9l 75 9 with with IN cord-340851-lnv8yi9l 75 10 F F NNP cord-340851-lnv8yi9l 75 11 , , , cord-340851-lnv8yi9l 75 12 defines define VBZ cord-340851-lnv8yi9l 75 13 the the DT cord-340851-lnv8yi9l 75 14 matrix matrix NN cord-340851-lnv8yi9l 75 15 K k NN cord-340851-lnv8yi9l 75 16 = = SYM cord-340851-lnv8yi9l 75 17 F f NN cord-340851-lnv8yi9l 75 18 V V NNP cord-340851-lnv8yi9l 75 19 −1 −1 NNP cord-340851-lnv8yi9l 75 20 . . . cord-340851-lnv8yi9l 76 1 Specifying specify VBG cord-340851-lnv8yi9l 76 2 we -PRON- PRP cord-340851-lnv8yi9l 76 3 obtain obtain VBP cord-340851-lnv8yi9l 76 4 as as IN cord-340851-lnv8yi9l 76 5 the the DT cord-340851-lnv8yi9l 76 6 maximum maximum JJ cord-340851-lnv8yi9l 76 7 eigenvalue eigenvalue NN cord-340851-lnv8yi9l 76 8 of of IN cord-340851-lnv8yi9l 76 9 K. K. NNP cord-340851-lnv8yi9l 77 1 The the DT cord-340851-lnv8yi9l 77 2 optimal optimal JJ cord-340851-lnv8yi9l 77 3 control control NN cord-340851-lnv8yi9l 77 4 problem problem NN cord-340851-lnv8yi9l 77 5 is be VBZ cord-340851-lnv8yi9l 77 6 to to TO cord-340851-lnv8yi9l 77 7 minimize minimize VB cord-340851-lnv8yi9l 77 8 the the DT cord-340851-lnv8yi9l 77 9 objective objective JJ cord-340851-lnv8yi9l 77 10 functional functional JJ cord-340851-lnv8yi9l 77 11 subject subject NN cord-340851-lnv8yi9l 77 12 to to IN cord-340851-lnv8yi9l 77 13 the the DT cord-340851-lnv8yi9l 77 14 constraints constraint NNS cord-340851-lnv8yi9l 77 15 of of IN cord-340851-lnv8yi9l 77 16 the the DT cord-340851-lnv8yi9l 77 17 state state NN cord-340851-lnv8yi9l 77 18 dynamics dynamic NNS cord-340851-lnv8yi9l 77 19 described describe VBN cord-340851-lnv8yi9l 77 20 in in IN cord-340851-lnv8yi9l 77 21 eqn eqn NNP cord-340851-lnv8yi9l 77 22 . . . cord-340851-lnv8yi9l 78 1 ( ( -LRB- cord-340851-lnv8yi9l 78 2 1 1 CD cord-340851-lnv8yi9l 78 3 ) ) -RRB- cord-340851-lnv8yi9l 78 4 and and CC cord-340851-lnv8yi9l 78 5 the the DT cord-340851-lnv8yi9l 78 6 initial initial JJ cord-340851-lnv8yi9l 78 7 conditions condition NNS cord-340851-lnv8yi9l 78 8 that that WDT cord-340851-lnv8yi9l 78 9 S(t S(t NNP cord-340851-lnv8yi9l 78 10 0 0 CD cord-340851-lnv8yi9l 78 11 ) ) -RRB- cord-340851-lnv8yi9l 79 1 = = SYM cord-340851-lnv8yi9l 79 2 1 1 CD cord-340851-lnv8yi9l 79 3 and and CC cord-340851-lnv8yi9l 79 4 all all DT cord-340851-lnv8yi9l 79 5 other other JJ cord-340851-lnv8yi9l 79 6 state state NN cord-340851-lnv8yi9l 79 7 variables variable NNS cord-340851-lnv8yi9l 79 8 equal equal VBP cord-340851-lnv8yi9l 79 9 zero zero CD cord-340851-lnv8yi9l 79 10 at at IN cord-340851-lnv8yi9l 79 11 time time NN cord-340851-lnv8yi9l 79 12 t t NN cord-340851-lnv8yi9l 79 13 0 0 CD cord-340851-lnv8yi9l 79 14 . . . cord-340851-lnv8yi9l 80 1 The the DT cord-340851-lnv8yi9l 80 2 parameter parameter NN cord-340851-lnv8yi9l 80 3 c c NN cord-340851-lnv8yi9l 80 4 weights weight VBZ cord-340851-lnv8yi9l 80 5 the the DT cord-340851-lnv8yi9l 80 6 extent extent NN cord-340851-lnv8yi9l 80 7 to to TO cord-340851-lnv8yi9l 80 8 which which WDT cord-340851-lnv8yi9l 80 9 the the DT cord-340851-lnv8yi9l 80 10 control control NN cord-340851-lnv8yi9l 80 11 , , , cord-340851-lnv8yi9l 80 12 u(t u(t NNP cord-340851-lnv8yi9l 80 13 ) ) -RRB- cord-340851-lnv8yi9l 80 14 , , , cord-340851-lnv8yi9l 80 15 is be VBZ cord-340851-lnv8yi9l 80 16 prioritized prioritize VBN cord-340851-lnv8yi9l 80 17 for for IN cord-340851-lnv8yi9l 80 18 minimization minimization NN cord-340851-lnv8yi9l 80 19 relative relative JJ cord-340851-lnv8yi9l 80 20 to to IN cord-340851-lnv8yi9l 80 21 deaths death NNS cord-340851-lnv8yi9l 80 22 , , , cord-340851-lnv8yi9l 80 23 D(t D(t NNP cord-340851-lnv8yi9l 80 24 ) ) -RRB- cord-340851-lnv8yi9l 80 25 . . . cord-340851-lnv8yi9l 81 1 Squared squared JJ cord-340851-lnv8yi9l 81 2 terms term NNS cord-340851-lnv8yi9l 81 3 for for IN cord-340851-lnv8yi9l 81 4 D(t D(t NNP cord-340851-lnv8yi9l 81 5 ) ) -RRB- cord-340851-lnv8yi9l 81 6 and and CC cord-340851-lnv8yi9l 81 7 u(t u(t NNP cord-340851-lnv8yi9l 81 8 ) ) -RRB- cord-340851-lnv8yi9l 81 9 are be VBP cord-340851-lnv8yi9l 81 10 chosen choose VBN cord-340851-lnv8yi9l 81 11 both both DT cord-340851-lnv8yi9l 81 12 for for IN cord-340851-lnv8yi9l 81 13 mathematical mathematical JJ cord-340851-lnv8yi9l 81 14 convenience convenience NN cord-340851-lnv8yi9l 81 15 in in IN cord-340851-lnv8yi9l 81 16 the the DT cord-340851-lnv8yi9l 81 17 case case NN cord-340851-lnv8yi9l 81 18 of of IN cord-340851-lnv8yi9l 81 19 u(t u(t NNP cord-340851-lnv8yi9l 81 20 ) ) -RRB- cord-340851-lnv8yi9l 81 21 and and CC cord-340851-lnv8yi9l 81 22 to to TO cord-340851-lnv8yi9l 81 23 more more RBR cord-340851-lnv8yi9l 81 24 heavily heavily RB cord-340851-lnv8yi9l 81 25 penalize penalize VB cord-340851-lnv8yi9l 81 26 solutions solution NNS cord-340851-lnv8yi9l 81 27 for for IN cord-340851-lnv8yi9l 81 28 u(t u(t NN cord-340851-lnv8yi9l 81 29 ) ) -RRB- cord-340851-lnv8yi9l 81 30 that that WDT cord-340851-lnv8yi9l 81 31 permit permit VBP cord-340851-lnv8yi9l 81 32 relatively relatively RB cord-340851-lnv8yi9l 81 33 high high JJ cord-340851-lnv8yi9l 81 34 values value NNS cord-340851-lnv8yi9l 81 35 of of IN cord-340851-lnv8yi9l 81 36 D(t D(t NNP cord-340851-lnv8yi9l 81 37 ) ) -RRB- cord-340851-lnv8yi9l 81 38 or or CC cord-340851-lnv8yi9l 81 39 u(t u(t NNP cord-340851-lnv8yi9l 81 40 ) ) -RRB- cord-340851-lnv8yi9l 81 41 at at IN cord-340851-lnv8yi9l 81 42 any any DT cord-340851-lnv8yi9l 81 43 given give VBN cord-340851-lnv8yi9l 81 44 time time NN cord-340851-lnv8yi9l 81 45 . . . cord-340851-lnv8yi9l 82 1 To to TO cord-340851-lnv8yi9l 82 2 find find VB cord-340851-lnv8yi9l 82 3 the the DT cord-340851-lnv8yi9l 82 4 optimal optimal JJ cord-340851-lnv8yi9l 82 5 control control NN cord-340851-lnv8yi9l 82 6 , , , cord-340851-lnv8yi9l 82 7 u u NNP cord-340851-lnv8yi9l 82 8 * * NFP cord-340851-lnv8yi9l 82 9 ( ( -LRB- cord-340851-lnv8yi9l 82 10 t t NNP cord-340851-lnv8yi9l 82 11 ) ) -RRB- cord-340851-lnv8yi9l 82 12 , , , cord-340851-lnv8yi9l 82 13 that that WDT cord-340851-lnv8yi9l 82 14 minimizes minimize VBZ cord-340851-lnv8yi9l 82 15 J(u J(u NNP cord-340851-lnv8yi9l 82 16 ) ) -RRB- cord-340851-lnv8yi9l 82 17 , , , cord-340851-lnv8yi9l 82 18 we -PRON- PRP cord-340851-lnv8yi9l 82 19 follow follow VBP cord-340851-lnv8yi9l 82 20 standard standard JJ cord-340851-lnv8yi9l 82 21 results result NNS cord-340851-lnv8yi9l 82 22 from from IN cord-340851-lnv8yi9l 82 23 optimal optimal JJ cord-340851-lnv8yi9l 82 24 control control NN cord-340851-lnv8yi9l 82 25 theory theory NN cord-340851-lnv8yi9l 82 26 applied apply VBN cord-340851-lnv8yi9l 82 27 to to IN cord-340851-lnv8yi9l 82 28 systems system NNS cord-340851-lnv8yi9l 82 29 of of IN cord-340851-lnv8yi9l 82 30 ordinary ordinary JJ cord-340851-lnv8yi9l 82 31 differential differential NN cord-340851-lnv8yi9l 82 32 . . . cord-340851-lnv8yi9l 83 1 CC CC NNP cord-340851-lnv8yi9l 83 2 - - : cord-340851-lnv8yi9l 83 3 BY by IN cord-340851-lnv8yi9l 83 4 4.0 4.0 CD cord-340851-lnv8yi9l 83 5 International international JJ cord-340851-lnv8yi9l 83 6 license license NN cord-340851-lnv8yi9l 84 1 It -PRON- PRP cord-340851-lnv8yi9l 84 2 is be VBZ cord-340851-lnv8yi9l 84 3 made make VBN cord-340851-lnv8yi9l 84 4 available available JJ cord-340851-lnv8yi9l 84 5 under under IN cord-340851-lnv8yi9l 84 6 a a DT cord-340851-lnv8yi9l 85 1 is be VBZ cord-340851-lnv8yi9l 85 2 the the DT cord-340851-lnv8yi9l 85 3 author author NN cord-340851-lnv8yi9l 85 4 / / SYM cord-340851-lnv8yi9l 85 5 funder funder NN cord-340851-lnv8yi9l 85 6 , , , cord-340851-lnv8yi9l 85 7 who who WP cord-340851-lnv8yi9l 85 8 has have VBZ cord-340851-lnv8yi9l 85 9 granted grant VBN cord-340851-lnv8yi9l 85 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 85 11 a a DT cord-340851-lnv8yi9l 85 12 license license NN cord-340851-lnv8yi9l 85 13 to to TO cord-340851-lnv8yi9l 85 14 display display VB cord-340851-lnv8yi9l 85 15 the the DT cord-340851-lnv8yi9l 85 16 preprint preprint NN cord-340851-lnv8yi9l 85 17 in in IN cord-340851-lnv8yi9l 85 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 85 19 . . . cord-340851-lnv8yi9l 86 1 ( ( -LRB- cord-340851-lnv8yi9l 86 2 which which WDT cord-340851-lnv8yi9l 86 3 was be VBD cord-340851-lnv8yi9l 86 4 not not RB cord-340851-lnv8yi9l 86 5 certified certify VBN cord-340851-lnv8yi9l 86 6 by by IN cord-340851-lnv8yi9l 86 7 peer peer NN cord-340851-lnv8yi9l 86 8 review review NN cord-340851-lnv8yi9l 86 9 ) ) -RRB- cord-340851-lnv8yi9l 87 1 The the DT cord-340851-lnv8yi9l 87 2 copyright copyright NN cord-340851-lnv8yi9l 87 3 holder holder NN cord-340851-lnv8yi9l 87 4 for for IN cord-340851-lnv8yi9l 87 5 this this DT cord-340851-lnv8yi9l 87 6 preprint preprint NN cord-340851-lnv8yi9l 87 7 this this DT cord-340851-lnv8yi9l 87 8 version version NN cord-340851-lnv8yi9l 87 9 posted post VBN cord-340851-lnv8yi9l 87 10 April April NNP cord-340851-lnv8yi9l 87 11 23 23 CD cord-340851-lnv8yi9l 87 12 , , , cord-340851-lnv8yi9l 87 13 2020 2020 CD cord-340851-lnv8yi9l 87 14 . . . cord-340851-lnv8yi9l 87 15 . . . cord-340851-lnv8yi9l 88 1 https://doi.org/10.1101/2020.04 https://doi.org/10.1101/2020.04 UH cord-340851-lnv8yi9l 88 2 . . . cord-340851-lnv8yi9l 89 1 22.20076018 22.20076018 CD cord-340851-lnv8yi9l 89 2 doi doi NN cord-340851-lnv8yi9l 89 3 : : : cord-340851-lnv8yi9l 90 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 90 2 preprint preprint NN cord-340851-lnv8yi9l 90 3 equations equation NNS cord-340851-lnv8yi9l 90 4 [ [ -LRB- cord-340851-lnv8yi9l 90 5 28 28 CD cord-340851-lnv8yi9l 90 6 ] ] -RRB- cord-340851-lnv8yi9l 90 7 . . . cord-340851-lnv8yi9l 91 1 These these DT cord-340851-lnv8yi9l 91 2 techniques technique NNS cord-340851-lnv8yi9l 91 3 make make VBP cord-340851-lnv8yi9l 91 4 use use NN cord-340851-lnv8yi9l 91 5 of of IN cord-340851-lnv8yi9l 91 6 Pontryagin Pontryagin NNP cord-340851-lnv8yi9l 91 7 's 's POS cord-340851-lnv8yi9l 91 8 Maximum Maximum NNP cord-340851-lnv8yi9l 91 9 Principle Principle NNP cord-340851-lnv8yi9l 91 10 to to TO cord-340851-lnv8yi9l 91 11 determine determine VB cord-340851-lnv8yi9l 91 12 the the DT cord-340851-lnv8yi9l 91 13 pointwise pointwise JJ cord-340851-lnv8yi9l 91 14 minimum minimum NN cord-340851-lnv8yi9l 91 15 of of IN cord-340851-lnv8yi9l 91 16 the the DT cord-340851-lnv8yi9l 91 17 Hamiltonian Hamiltonian NNP cord-340851-lnv8yi9l 91 18 of of IN cord-340851-lnv8yi9l 91 19 the the DT cord-340851-lnv8yi9l 91 20 system system NN cord-340851-lnv8yi9l 91 21 , , , cord-340851-lnv8yi9l 91 22 H H NNP cord-340851-lnv8yi9l 91 23 , , , cord-340851-lnv8yi9l 91 24 using use VBG cord-340851-lnv8yi9l 91 25 adjoint adjoint NN cord-340851-lnv8yi9l 91 26 variables variable NNS cord-340851-lnv8yi9l 91 27 , , , cord-340851-lnv8yi9l 91 28 λ λ NN cord-340851-lnv8yi9l 91 29 , , , cord-340851-lnv8yi9l 91 30 that that WDT cord-340851-lnv8yi9l 91 31 correspond correspond VBP cord-340851-lnv8yi9l 91 32 to to IN cord-340851-lnv8yi9l 91 33 each each DT cord-340851-lnv8yi9l 91 34 of of IN cord-340851-lnv8yi9l 91 35 the the DT cord-340851-lnv8yi9l 91 36 state state NN cord-340851-lnv8yi9l 91 37 variables variable NNS cord-340851-lnv8yi9l 91 38 . . . cord-340851-lnv8yi9l 92 1 To to TO cord-340851-lnv8yi9l 92 2 solve solve VB cord-340851-lnv8yi9l 92 3 for for IN cord-340851-lnv8yi9l 92 4 the the DT cord-340851-lnv8yi9l 92 5 adjoint adjoint JJ cord-340851-lnv8yi9l 92 6 variables variable NNS cord-340851-lnv8yi9l 92 7 , , , cord-340851-lnv8yi9l 92 8 we -PRON- PRP cord-340851-lnv8yi9l 92 9 first first RB cord-340851-lnv8yi9l 92 10 define define VBP cord-340851-lnv8yi9l 92 11 the the DT cord-340851-lnv8yi9l 92 12 Hamiltonian Hamiltonian NNP cord-340851-lnv8yi9l 92 13 , , , cord-340851-lnv8yi9l 92 14 We -PRON- PRP cord-340851-lnv8yi9l 92 15 then then RB cord-340851-lnv8yi9l 92 16 define define VBP cord-340851-lnv8yi9l 92 17 differential differential JJ cord-340851-lnv8yi9l 92 18 equations equation NNS cord-340851-lnv8yi9l 92 19 describing describe VBG cord-340851-lnv8yi9l 92 20 the the DT cord-340851-lnv8yi9l 92 21 behavior behavior NN cord-340851-lnv8yi9l 92 22 of of IN cord-340851-lnv8yi9l 92 23 each each DT cord-340851-lnv8yi9l 92 24 adjoint adjoint NN cord-340851-lnv8yi9l 92 25 variable variable NN cord-340851-lnv8yi9l 92 26 as as IN cord-340851-lnv8yi9l 92 27 the the DT cord-340851-lnv8yi9l 92 28 negative negative NN cord-340851-lnv8yi9l 92 29 of of IN cord-340851-lnv8yi9l 92 30 the the DT cord-340851-lnv8yi9l 92 31 partial partial JJ cord-340851-lnv8yi9l 92 32 derivative derivative NN cord-340851-lnv8yi9l 92 33 of of IN cord-340851-lnv8yi9l 92 34 H h NN cord-340851-lnv8yi9l 92 35 with with IN cord-340851-lnv8yi9l 92 36 respect respect NN cord-340851-lnv8yi9l 92 37 to to IN cord-340851-lnv8yi9l 92 38 the the DT cord-340851-lnv8yi9l 92 39 state state NN cord-340851-lnv8yi9l 92 40 variable variable NN cord-340851-lnv8yi9l 92 41 corresponding correspond VBG cord-340851-lnv8yi9l 92 42 to to IN cord-340851-lnv8yi9l 92 43 each each DT cord-340851-lnv8yi9l 92 44 adjoint adjoint JJ cord-340851-lnv8yi9l 92 45 variable variable NN cord-340851-lnv8yi9l 92 46 . . . cord-340851-lnv8yi9l 93 1 This this DT cord-340851-lnv8yi9l 93 2 yields yield NNS cord-340851-lnv8yi9l 93 3 where where WRB cord-340851-lnv8yi9l 93 4 Eqn Eqn NNP cord-340851-lnv8yi9l 93 5 . . . cord-340851-lnv8yi9l 94 1 ( ( -LRB- cord-340851-lnv8yi9l 94 2 9 9 LS cord-340851-lnv8yi9l 94 3 ) ) -RRB- cord-340851-lnv8yi9l 94 4 can can MD cord-340851-lnv8yi9l 94 5 be be VB cord-340851-lnv8yi9l 94 6 solved solve VBN cord-340851-lnv8yi9l 94 7 backwards backwards RB cord-340851-lnv8yi9l 94 8 in in IN cord-340851-lnv8yi9l 94 9 time time NN cord-340851-lnv8yi9l 94 10 with with IN cord-340851-lnv8yi9l 94 11 transversality transversality NN cord-340851-lnv8yi9l 94 12 conditions condition NNS cord-340851-lnv8yi9l 94 13 at at IN cord-340851-lnv8yi9l 94 14 time time NN cord-340851-lnv8yi9l 94 15 t t NNP cord-340851-lnv8yi9l 94 16 1 1 CD cord-340851-lnv8yi9l 94 17 equal equal JJ cord-340851-lnv8yi9l 94 18 to to IN cord-340851-lnv8yi9l 94 19 zero zero CD cord-340851-lnv8yi9l 94 20 for for IN cord-340851-lnv8yi9l 94 21 each each DT cord-340851-lnv8yi9l 94 22 adjoint adjoint JJ cord-340851-lnv8yi9l 94 23 variable variable NN cord-340851-lnv8yi9l 94 24 . . . cord-340851-lnv8yi9l 95 1 To to TO cord-340851-lnv8yi9l 95 2 find find VB cord-340851-lnv8yi9l 95 3 the the DT cord-340851-lnv8yi9l 95 4 pointwise pointwise JJ cord-340851-lnv8yi9l 95 5 optimal optimal JJ cord-340851-lnv8yi9l 95 6 control control NN cord-340851-lnv8yi9l 95 7 , , , cord-340851-lnv8yi9l 95 8 u u NNP cord-340851-lnv8yi9l 95 9 * * NFP cord-340851-lnv8yi9l 95 10 , , , cord-340851-lnv8yi9l 95 11 we -PRON- PRP cord-340851-lnv8yi9l 95 12 find find VBP cord-340851-lnv8yi9l 95 13 the the DT cord-340851-lnv8yi9l 95 14 value value NN cord-340851-lnv8yi9l 95 15 of of IN cord-340851-lnv8yi9l 95 16 u u NN cord-340851-lnv8yi9l 95 17 that that WDT cord-340851-lnv8yi9l 95 18 minimizes minimize VBZ cord-340851-lnv8yi9l 95 19 ∂H ∂h IN cord-340851-lnv8yi9l 95 20 ∂u ∂u ADD cord-340851-lnv8yi9l 95 21 , , , cord-340851-lnv8yi9l 95 22 which which WDT cord-340851-lnv8yi9l 95 23 yields yield VBZ cord-340851-lnv8yi9l 95 24 . . . cord-340851-lnv8yi9l 96 1 CC CC NNP cord-340851-lnv8yi9l 96 2 - - : cord-340851-lnv8yi9l 96 3 BY by IN cord-340851-lnv8yi9l 96 4 4.0 4.0 CD cord-340851-lnv8yi9l 96 5 International international JJ cord-340851-lnv8yi9l 96 6 license license NN cord-340851-lnv8yi9l 97 1 It -PRON- PRP cord-340851-lnv8yi9l 97 2 is be VBZ cord-340851-lnv8yi9l 97 3 made make VBN cord-340851-lnv8yi9l 97 4 available available JJ cord-340851-lnv8yi9l 97 5 under under IN cord-340851-lnv8yi9l 97 6 a a DT cord-340851-lnv8yi9l 98 1 is be VBZ cord-340851-lnv8yi9l 98 2 the the DT cord-340851-lnv8yi9l 98 3 author author NN cord-340851-lnv8yi9l 98 4 / / SYM cord-340851-lnv8yi9l 98 5 funder funder NN cord-340851-lnv8yi9l 98 6 , , , cord-340851-lnv8yi9l 98 7 who who WP cord-340851-lnv8yi9l 98 8 has have VBZ cord-340851-lnv8yi9l 98 9 granted grant VBN cord-340851-lnv8yi9l 98 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 98 11 a a DT cord-340851-lnv8yi9l 98 12 license license NN cord-340851-lnv8yi9l 98 13 to to TO cord-340851-lnv8yi9l 98 14 display display VB cord-340851-lnv8yi9l 98 15 the the DT cord-340851-lnv8yi9l 98 16 preprint preprint NN cord-340851-lnv8yi9l 98 17 in in IN cord-340851-lnv8yi9l 98 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 98 19 . . . cord-340851-lnv8yi9l 99 1 The the DT cord-340851-lnv8yi9l 99 2 copyright copyright NN cord-340851-lnv8yi9l 99 3 holder holder NN cord-340851-lnv8yi9l 99 4 for for IN cord-340851-lnv8yi9l 99 5 this this DT cord-340851-lnv8yi9l 99 6 preprint preprint NN cord-340851-lnv8yi9l 99 7 this this DT cord-340851-lnv8yi9l 99 8 version version NN cord-340851-lnv8yi9l 99 9 posted post VBN cord-340851-lnv8yi9l 99 10 April April NNP cord-340851-lnv8yi9l 99 11 23 23 CD cord-340851-lnv8yi9l 99 12 , , , cord-340851-lnv8yi9l 99 13 2020 2020 CD cord-340851-lnv8yi9l 99 14 . . . cord-340851-lnv8yi9l 99 15 _SP cord-340851-lnv8yi9l 100 1 The the DT cord-340851-lnv8yi9l 100 2 optimal optimal JJ cord-340851-lnv8yi9l 100 3 control control NN cord-340851-lnv8yi9l 100 4 is be VBZ cord-340851-lnv8yi9l 100 5 subject subject JJ cord-340851-lnv8yi9l 100 6 to to IN cord-340851-lnv8yi9l 100 7 a a DT cord-340851-lnv8yi9l 100 8 lower lower RBR cord-340851-lnv8yi9l 100 9 bound bind VBN cord-340851-lnv8yi9l 100 10 of of IN cord-340851-lnv8yi9l 100 11 0 0 CD cord-340851-lnv8yi9l 100 12 and and CC cord-340851-lnv8yi9l 100 13 an an DT cord-340851-lnv8yi9l 100 14 upper upper JJ cord-340851-lnv8yi9l 100 15 bound bound NN cord-340851-lnv8yi9l 100 16 of of IN cord-340851-lnv8yi9l 100 17 u u NNP cord-340851-lnv8yi9l 100 18 max max NNP cord-340851-lnv8yi9l 100 19 , , , cord-340851-lnv8yi9l 100 20 with with IN cord-340851-lnv8yi9l 100 21 those those DT cord-340851-lnv8yi9l 100 22 values value NNS cord-340851-lnv8yi9l 100 23 used use VBN cord-340851-lnv8yi9l 100 24 for for IN cord-340851-lnv8yi9l 100 25 u u NNP cord-340851-lnv8yi9l 100 26 * * NFP cord-340851-lnv8yi9l 101 1 whenever whenever WRB cord-340851-lnv8yi9l 101 2 the the DT cord-340851-lnv8yi9l 101 3 right right JJ cord-340851-lnv8yi9l 101 4 hand hand NN cord-340851-lnv8yi9l 101 5 side side NN cord-340851-lnv8yi9l 101 6 of of IN cord-340851-lnv8yi9l 101 7 eq eq NNP cord-340851-lnv8yi9l 101 8 . . . cord-340851-lnv8yi9l 102 1 ( ( -LRB- cord-340851-lnv8yi9l 102 2 10 10 CD cord-340851-lnv8yi9l 102 3 ) ) -RRB- cord-340851-lnv8yi9l 102 4 yields yield VBZ cord-340851-lnv8yi9l 102 5 values value NNS cord-340851-lnv8yi9l 102 6 outside outside IN cord-340851-lnv8yi9l 102 7 those those DT cord-340851-lnv8yi9l 102 8 bounds bound NNS cord-340851-lnv8yi9l 102 9 . . . cord-340851-lnv8yi9l 103 1 To to TO cord-340851-lnv8yi9l 103 2 find find VB cord-340851-lnv8yi9l 103 3 u u NNP cord-340851-lnv8yi9l 103 4 * * NFP cord-340851-lnv8yi9l 103 5 ( ( -LRB- cord-340851-lnv8yi9l 103 6 t t NN cord-340851-lnv8yi9l 103 7 ) ) -RRB- cord-340851-lnv8yi9l 103 8 numerically numerically RB cord-340851-lnv8yi9l 103 9 , , , cord-340851-lnv8yi9l 103 10 we -PRON- PRP cord-340851-lnv8yi9l 103 11 use use VBP cord-340851-lnv8yi9l 103 12 the the DT cord-340851-lnv8yi9l 103 13 forward forward RB cord-340851-lnv8yi9l 103 14 - - HYPH cord-340851-lnv8yi9l 103 15 backward backward JJ cord-340851-lnv8yi9l 103 16 sweep sweep NN cord-340851-lnv8yi9l 103 17 method method NN cord-340851-lnv8yi9l 103 18 [ [ -LRB- cord-340851-lnv8yi9l 103 19 28 28 CD cord-340851-lnv8yi9l 103 20 ] ] -RRB- cord-340851-lnv8yi9l 103 21 , , , cord-340851-lnv8yi9l 103 22 which which WDT cord-340851-lnv8yi9l 103 23 involves involve VBZ cord-340851-lnv8yi9l 103 24 first first RB cord-340851-lnv8yi9l 103 25 solving solve VBG cord-340851-lnv8yi9l 103 26 for for IN cord-340851-lnv8yi9l 103 27 the the DT cord-340851-lnv8yi9l 103 28 state state NN cord-340851-lnv8yi9l 103 29 variables variable NNS cord-340851-lnv8yi9l 103 30 forward forward RB cord-340851-lnv8yi9l 103 31 in in IN cord-340851-lnv8yi9l 103 32 time time NN cord-340851-lnv8yi9l 103 33 , , , cord-340851-lnv8yi9l 103 34 next next JJ cord-340851-lnv8yi9l 103 35 solving solve VBG cord-340851-lnv8yi9l 103 36 for for IN cord-340851-lnv8yi9l 103 37 the the DT cord-340851-lnv8yi9l 103 38 adjoint adjoint NN cord-340851-lnv8yi9l 103 39 variables variable NNS cord-340851-lnv8yi9l 103 40 backward backward RB cord-340851-lnv8yi9l 103 41 in in IN cord-340851-lnv8yi9l 103 42 time time NN cord-340851-lnv8yi9l 103 43 , , , cord-340851-lnv8yi9l 103 44 and and CC cord-340851-lnv8yi9l 103 45 then then RB cord-340851-lnv8yi9l 103 46 plugging plug VBG cord-340851-lnv8yi9l 103 47 the the DT cord-340851-lnv8yi9l 103 48 solutions solution NNS cord-340851-lnv8yi9l 103 49 for for IN cord-340851-lnv8yi9l 103 50 the the DT cord-340851-lnv8yi9l 103 51 relevant relevant JJ cord-340851-lnv8yi9l 103 52 state state NN cord-340851-lnv8yi9l 103 53 and and CC cord-340851-lnv8yi9l 103 54 adjoint adjoint NN cord-340851-lnv8yi9l 103 55 variables variable NNS cord-340851-lnv8yi9l 103 56 into into IN cord-340851-lnv8yi9l 103 57 eqn eqn NN cord-340851-lnv8yi9l 103 58 . . . cord-340851-lnv8yi9l 104 1 ( ( -LRB- cord-340851-lnv8yi9l 104 2 10 10 CD cord-340851-lnv8yi9l 104 3 ) ) -RRB- cord-340851-lnv8yi9l 104 4 , , , cord-340851-lnv8yi9l 104 5 subject subject JJ cord-340851-lnv8yi9l 104 6 to to IN cord-340851-lnv8yi9l 104 7 bounds bound NNS cord-340851-lnv8yi9l 104 8 on on IN cord-340851-lnv8yi9l 104 9 u(t u(t NNP cord-340851-lnv8yi9l 104 10 ) ) -RRB- cord-340851-lnv8yi9l 104 11 . . . cord-340851-lnv8yi9l 105 1 As as IN cord-340851-lnv8yi9l 105 2 is be VBZ cord-340851-lnv8yi9l 105 3 often often RB cord-340851-lnv8yi9l 105 4 the the DT cord-340851-lnv8yi9l 105 5 case case NN cord-340851-lnv8yi9l 105 6 for for IN cord-340851-lnv8yi9l 105 7 optimal optimal JJ cord-340851-lnv8yi9l 105 8 control control NN cord-340851-lnv8yi9l 105 9 problems problem NNS cord-340851-lnv8yi9l 105 10 [ [ -LRB- cord-340851-lnv8yi9l 105 11 28 28 CD cord-340851-lnv8yi9l 105 12 ] ] -RRB- cord-340851-lnv8yi9l 105 13 , , , cord-340851-lnv8yi9l 105 14 we -PRON- PRP cord-340851-lnv8yi9l 105 15 found find VBD cord-340851-lnv8yi9l 105 16 that that IN cord-340851-lnv8yi9l 105 17 we -PRON- PRP cord-340851-lnv8yi9l 105 18 needed need VBD cord-340851-lnv8yi9l 105 19 to to TO cord-340851-lnv8yi9l 105 20 perform perform VB cord-340851-lnv8yi9l 105 21 these these DT cord-340851-lnv8yi9l 105 22 steps step NNS cord-340851-lnv8yi9l 105 23 iteratively iteratively RB cord-340851-lnv8yi9l 105 24 and and CC cord-340851-lnv8yi9l 105 25 with with IN cord-340851-lnv8yi9l 105 26 a a DT cord-340851-lnv8yi9l 105 27 convex convex JJ cord-340851-lnv8yi9l 105 28 combination combination NN cord-340851-lnv8yi9l 105 29 of of IN cord-340851-lnv8yi9l 105 30 controls control NNS cord-340851-lnv8yi9l 105 31 across across IN cord-340851-lnv8yi9l 105 32 iterations iteration NNS cord-340851-lnv8yi9l 105 33 to to TO cord-340851-lnv8yi9l 105 34 achieve achieve VB cord-340851-lnv8yi9l 105 35 convergence convergence NN cord-340851-lnv8yi9l 105 36 . . . cord-340851-lnv8yi9l 106 1 Specifically specifically RB cord-340851-lnv8yi9l 106 2 , , , cord-340851-lnv8yi9l 106 3 we -PRON- PRP cord-340851-lnv8yi9l 106 4 repeated repeat VBD cord-340851-lnv8yi9l 106 5 the the DT cord-340851-lnv8yi9l 106 6 forward forward RB cord-340851-lnv8yi9l 106 7 - - HYPH cord-340851-lnv8yi9l 106 8 backward backward JJ cord-340851-lnv8yi9l 106 9 sweep sweep NN cord-340851-lnv8yi9l 106 10 process process NN cord-340851-lnv8yi9l 106 11 50 50 CD cord-340851-lnv8yi9l 106 12 times time NNS cord-340851-lnv8yi9l 106 13 , , , cord-340851-lnv8yi9l 106 14 after after IN cord-340851-lnv8yi9l 106 15 which which WDT cord-340851-lnv8yi9l 106 16 we -PRON- PRP cord-340851-lnv8yi9l 106 17 took take VBD cord-340851-lnv8yi9l 106 18 newly newly RB cord-340851-lnv8yi9l 106 19 proposed propose VBN cord-340851-lnv8yi9l 106 20 solutions solution NNS cord-340851-lnv8yi9l 106 21 of of IN cord-340851-lnv8yi9l 106 22 u u NNP cord-340851-lnv8yi9l 106 23 * * NFP cord-340851-lnv8yi9l 106 24 ( ( -LRB- cord-340851-lnv8yi9l 106 25 t t NN cord-340851-lnv8yi9l 106 26 ) ) -RRB- cord-340851-lnv8yi9l 106 27 as as IN cord-340851-lnv8yi9l 106 28 the the DT cord-340851-lnv8yi9l 106 29 average average NN cord-340851-lnv8yi9l 106 30 of of IN cord-340851-lnv8yi9l 106 31 the the DT cord-340851-lnv8yi9l 106 32 20 20 CD cord-340851-lnv8yi9l 106 33 most most RBS cord-340851-lnv8yi9l 106 34 recent recent JJ cord-340851-lnv8yi9l 106 35 solutions solution NNS cord-340851-lnv8yi9l 106 36 , , , cord-340851-lnv8yi9l 106 37 until until IN cord-340851-lnv8yi9l 106 38 the the DT cord-340851-lnv8yi9l 106 39 algorithm algorithm NN cord-340851-lnv8yi9l 106 40 was be VBD cord-340851-lnv8yi9l 106 41 stopped stop VBN cord-340851-lnv8yi9l 106 42 after after IN cord-340851-lnv8yi9l 106 43 2,000 2,000 CD cord-340851-lnv8yi9l 106 44 iterations iteration NNS cord-340851-lnv8yi9l 106 45 . . . cord-340851-lnv8yi9l 107 1 We -PRON- PRP cord-340851-lnv8yi9l 107 2 assessed assess VBD cord-340851-lnv8yi9l 107 3 convergence convergence NN cord-340851-lnv8yi9l 107 4 with with IN cord-340851-lnv8yi9l 107 5 a a DT cord-340851-lnv8yi9l 107 6 statistic statistic NN cord-340851-lnv8yi9l 107 7 defined define VBN cord-340851-lnv8yi9l 107 8 as as IN cord-340851-lnv8yi9l 107 9 where where WRB cord-340851-lnv8yi9l 107 10 smaller small JJR cord-340851-lnv8yi9l 107 11 values value NNS cord-340851-lnv8yi9l 107 12 indicate indicate VBP cord-340851-lnv8yi9l 107 13 better well JJR cord-340851-lnv8yi9l 107 14 convergence convergence NN cord-340851-lnv8yi9l 107 15 . . . cord-340851-lnv8yi9l 108 1 All all DT cord-340851-lnv8yi9l 108 2 numerical numerical JJ cord-340851-lnv8yi9l 108 3 solutions solution NNS cord-340851-lnv8yi9l 108 4 were be VBD cord-340851-lnv8yi9l 108 5 obtained obtain VBN cord-340851-lnv8yi9l 108 6 with with IN cord-340851-lnv8yi9l 108 7 a a DT cord-340851-lnv8yi9l 108 8 Runge Runge NNP cord-340851-lnv8yi9l 108 9 - - HYPH cord-340851-lnv8yi9l 108 10 Kutta Kutta NNP cord-340851-lnv8yi9l 108 11 4 4 CD cord-340851-lnv8yi9l 108 12 routine routine NN cord-340851-lnv8yi9l 108 13 implemented implement VBN cord-340851-lnv8yi9l 108 14 with with IN cord-340851-lnv8yi9l 108 15 the the DT cord-340851-lnv8yi9l 108 16 ode ode NN cord-340851-lnv8yi9l 108 17 function function NN cord-340851-lnv8yi9l 108 18 from from IN cord-340851-lnv8yi9l 108 19 the the DT cord-340851-lnv8yi9l 108 20 deSolve deSolve NNP cord-340851-lnv8yi9l 108 21 package package NN cord-340851-lnv8yi9l 108 22 [ [ -LRB- cord-340851-lnv8yi9l 108 23 47 47 CD cord-340851-lnv8yi9l 108 24 ] ] -RRB- cord-340851-lnv8yi9l 108 25 in in IN cord-340851-lnv8yi9l 108 26 R. R. NNP cord-340851-lnv8yi9l 109 1 In in IN cord-340851-lnv8yi9l 109 2 Table Table NNP cord-340851-lnv8yi9l 109 3 2 2 CD cord-340851-lnv8yi9l 109 4 , , , cord-340851-lnv8yi9l 109 5 we -PRON- PRP cord-340851-lnv8yi9l 109 6 specify specify VBP cord-340851-lnv8yi9l 109 7 low low JJ cord-340851-lnv8yi9l 109 8 , , , cord-340851-lnv8yi9l 109 9 intermediate intermediate JJ cord-340851-lnv8yi9l 109 10 , , , cord-340851-lnv8yi9l 109 11 and and CC cord-340851-lnv8yi9l 109 12 high high JJ cord-340851-lnv8yi9l 109 13 values value NNS cord-340851-lnv8yi9l 109 14 of of IN cord-340851-lnv8yi9l 109 15 each each DT cord-340851-lnv8yi9l 109 16 parameter parameter NN cord-340851-lnv8yi9l 109 17 . . . cord-340851-lnv8yi9l 110 1 For for IN cord-340851-lnv8yi9l 110 2 some some DT cord-340851-lnv8yi9l 110 3 parameters parameter NNS cord-340851-lnv8yi9l 110 4 , , , cord-340851-lnv8yi9l 110 5 estimates estimate NNS cord-340851-lnv8yi9l 110 6 matching match VBG cord-340851-lnv8yi9l 110 7 our -PRON- PRP$ cord-340851-lnv8yi9l 110 8 parameter parameter NN cord-340851-lnv8yi9l 110 9 definitions definition NNS cord-340851-lnv8yi9l 110 10 were be VBD cord-340851-lnv8yi9l 110 11 taken take VBN cord-340851-lnv8yi9l 110 12 from from IN cord-340851-lnv8yi9l 110 13 other other JJ cord-340851-lnv8yi9l 110 14 studies study NNS cord-340851-lnv8yi9l 110 15 . . . cord-340851-lnv8yi9l 111 1 For for IN cord-340851-lnv8yi9l 111 2 other other JJ cord-340851-lnv8yi9l 111 3 parameters parameter NNS cord-340851-lnv8yi9l 111 4 , , , cord-340851-lnv8yi9l 111 5 additional additional JJ cord-340851-lnv8yi9l 111 6 steps step NNS cord-340851-lnv8yi9l 111 7 were be VBD cord-340851-lnv8yi9l 111 8 necessary necessary JJ cord-340851-lnv8yi9l 111 9 to to TO cord-340851-lnv8yi9l 111 10 match match VB cord-340851-lnv8yi9l 111 11 our -PRON- PRP$ cord-340851-lnv8yi9l 111 12 parameter parameter NN cord-340851-lnv8yi9l 111 13 definitions definition NNS cord-340851-lnv8yi9l 111 14 . . . cord-340851-lnv8yi9l 112 1 We -PRON- PRP cord-340851-lnv8yi9l 112 2 elaborate elaborate VBP cord-340851-lnv8yi9l 112 3 on on IN cord-340851-lnv8yi9l 112 4 the the DT cord-340851-lnv8yi9l 112 5 latter latter JJ cord-340851-lnv8yi9l 112 6 below below RB cord-340851-lnv8yi9l 112 7 . . . cord-340851-lnv8yi9l 113 1 Transmission transmission NN cord-340851-lnv8yi9l 113 2 coefficient coefficient NN cord-340851-lnv8yi9l 113 3 , , , cord-340851-lnv8yi9l 113 4 β β NN cord-340851-lnv8yi9l 113 5 . . . cord-340851-lnv8yi9l 114 1 We -PRON- PRP cord-340851-lnv8yi9l 114 2 based base VBD cord-340851-lnv8yi9l 114 3 values value NNS cord-340851-lnv8yi9l 114 4 of of IN cord-340851-lnv8yi9l 114 5 this this DT cord-340851-lnv8yi9l 114 6 parameter parameter NN cord-340851-lnv8yi9l 114 7 on on IN cord-340851-lnv8yi9l 114 8 assumptions assumption NNS cord-340851-lnv8yi9l 114 9 about about IN cord-340851-lnv8yi9l 114 10 R r NN cord-340851-lnv8yi9l 114 11 0 0 CD cord-340851-lnv8yi9l 114 12 by by IN cord-340851-lnv8yi9l 114 13 solving solve VBG cord-340851-lnv8yi9l 114 14 for for IN cord-340851-lnv8yi9l 114 15 β β NN cord-340851-lnv8yi9l 114 16 as as IN cord-340851-lnv8yi9l 114 17 a a DT cord-340851-lnv8yi9l 114 18 function function NN cord-340851-lnv8yi9l 114 19 of of IN cord-340851-lnv8yi9l 114 20 R r NN cord-340851-lnv8yi9l 114 21 0 0 CD cord-340851-lnv8yi9l 114 22 and and CC cord-340851-lnv8yi9l 114 23 other other JJ cord-340851-lnv8yi9l 114 24 parameters parameter NNS cord-340851-lnv8yi9l 114 25 in in IN cord-340851-lnv8yi9l 114 26 eqn eqn NN cord-340851-lnv8yi9l 114 27 . . . cord-340851-lnv8yi9l 115 1 ( ( -LRB- cord-340851-lnv8yi9l 115 2 6 6 CD cord-340851-lnv8yi9l 115 3 ) ) -RRB- cord-340851-lnv8yi9l 115 4 . . . cord-340851-lnv8yi9l 116 1 Because because IN cord-340851-lnv8yi9l 116 2 estimates estimate NNS cord-340851-lnv8yi9l 116 3 of of IN cord-340851-lnv8yi9l 116 4 R r NN cord-340851-lnv8yi9l 116 5 0 0 CD cord-340851-lnv8yi9l 116 6 for for IN cord-340851-lnv8yi9l 116 7 COVID-19 covid-19 CD cord-340851-lnv8yi9l 116 8 vary vary VBP cord-340851-lnv8yi9l 116 9 widely widely RB cord-340851-lnv8yi9l 116 10 [ [ -LRB- cord-340851-lnv8yi9l 116 11 39 39 CD cord-340851-lnv8yi9l 116 12 ] ] -RRB- cord-340851-lnv8yi9l 116 13 , , , cord-340851-lnv8yi9l 116 14 we -PRON- PRP cord-340851-lnv8yi9l 116 15 chose choose VBD cord-340851-lnv8yi9l 116 16 values value NNS cord-340851-lnv8yi9l 116 17 that that WDT cord-340851-lnv8yi9l 116 18 span span VBP cord-340851-lnv8yi9l 116 19 a a DT cord-340851-lnv8yi9l 116 20 range range NN cord-340851-lnv8yi9l 116 21 of of IN cord-340851-lnv8yi9l 116 22 estimates estimate NNS cord-340851-lnv8yi9l 116 23 that that WDT cord-340851-lnv8yi9l 116 24 may may MD cord-340851-lnv8yi9l 116 25 be be VB cord-340851-lnv8yi9l 116 26 applicable applicable JJ cord-340851-lnv8yi9l 116 27 to to IN cord-340851-lnv8yi9l 116 28 the the DT cord-340851-lnv8yi9l 116 29 US US NNP cord-340851-lnv8yi9l 116 30 . . . cord-340851-lnv8yi9l 117 1 Background background NN cord-340851-lnv8yi9l 117 2 birth birth NN cord-340851-lnv8yi9l 117 3 and and CC cord-340851-lnv8yi9l 117 4 death death NN cord-340851-lnv8yi9l 117 5 rates rate NNS cord-340851-lnv8yi9l 117 6 , , , cord-340851-lnv8yi9l 117 7 µ µ NN cord-340851-lnv8yi9l 117 8 and and CC cord-340851-lnv8yi9l 117 9 δ δ NN cord-340851-lnv8yi9l 117 10 . . . cord-340851-lnv8yi9l 118 1 We -PRON- PRP cord-340851-lnv8yi9l 118 2 parameterized parameterize VBD cord-340851-lnv8yi9l 118 3 µ µ NN cord-340851-lnv8yi9l 118 4 consistent consistent JJ cord-340851-lnv8yi9l 118 5 with with IN cord-340851-lnv8yi9l 118 6 a a DT cord-340851-lnv8yi9l 118 7 rate rate NN cord-340851-lnv8yi9l 118 8 of of IN cord-340851-lnv8yi9l 118 9 3,791,712 3,791,712 CD cord-340851-lnv8yi9l 118 10 births birth NNS cord-340851-lnv8yi9l 118 11 in in IN cord-340851-lnv8yi9l 118 12 a a DT cord-340851-lnv8yi9l 118 13 population population NN cord-340851-lnv8yi9l 118 14 of of IN cord-340851-lnv8yi9l 118 15 331 331 CD cord-340851-lnv8yi9l 118 16 million million CD cord-340851-lnv8yi9l 118 17 in in IN cord-340851-lnv8yi9l 118 18 the the DT cord-340851-lnv8yi9l 118 19 US US NNP cord-340851-lnv8yi9l 118 20 in in IN cord-340851-lnv8yi9l 118 21 2018 2018 CD cord-340851-lnv8yi9l 118 22 [ [ -LRB- cord-340851-lnv8yi9l 118 23 32 32 CD cord-340851-lnv8yi9l 118 24 ] ] -RRB- cord-340851-lnv8yi9l 118 25 . . . cord-340851-lnv8yi9l 119 1 To to TO cord-340851-lnv8yi9l 119 2 achieve achieve VB cord-340851-lnv8yi9l 119 3 a a DT cord-340851-lnv8yi9l 119 4 constant constant JJ cord-340851-lnv8yi9l 119 5 population population NN cord-340851-lnv8yi9l 119 6 size size NN cord-340851-lnv8yi9l 119 7 in in IN cord-340851-lnv8yi9l 119 8 the the DT cord-340851-lnv8yi9l 119 9 absence absence NN cord-340851-lnv8yi9l 119 10 of of IN cord-340851-lnv8yi9l 119 11 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 119 12 , , , cord-340851-lnv8yi9l 119 13 we -PRON- PRP cord-340851-lnv8yi9l 119 14 set set VBP cord-340851-lnv8yi9l 119 15 δ δ NN cord-340851-lnv8yi9l 119 16 equal equal JJ cord-340851-lnv8yi9l 119 17 to to IN cord-340851-lnv8yi9l 119 18 µ. µ. NN cord-340851-lnv8yi9l 119 19 . . . cord-340851-lnv8yi9l 120 1 CC CC NNP cord-340851-lnv8yi9l 120 2 - - : cord-340851-lnv8yi9l 120 3 BY by IN cord-340851-lnv8yi9l 120 4 4.0 4.0 CD cord-340851-lnv8yi9l 120 5 International international JJ cord-340851-lnv8yi9l 120 6 license license NN cord-340851-lnv8yi9l 121 1 It -PRON- PRP cord-340851-lnv8yi9l 121 2 is be VBZ cord-340851-lnv8yi9l 121 3 made make VBN cord-340851-lnv8yi9l 121 4 available available JJ cord-340851-lnv8yi9l 121 5 under under IN cord-340851-lnv8yi9l 121 6 a a DT cord-340851-lnv8yi9l 122 1 is be VBZ cord-340851-lnv8yi9l 122 2 the the DT cord-340851-lnv8yi9l 122 3 author author NN cord-340851-lnv8yi9l 122 4 / / SYM cord-340851-lnv8yi9l 122 5 funder funder NN cord-340851-lnv8yi9l 122 6 , , , cord-340851-lnv8yi9l 122 7 who who WP cord-340851-lnv8yi9l 122 8 has have VBZ cord-340851-lnv8yi9l 122 9 granted grant VBN cord-340851-lnv8yi9l 122 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 122 11 a a DT cord-340851-lnv8yi9l 122 12 license license NN cord-340851-lnv8yi9l 122 13 to to TO cord-340851-lnv8yi9l 122 14 display display VB cord-340851-lnv8yi9l 122 15 the the DT cord-340851-lnv8yi9l 122 16 preprint preprint NN cord-340851-lnv8yi9l 122 17 in in IN cord-340851-lnv8yi9l 122 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 122 19 . . . cord-340851-lnv8yi9l 123 1 The the DT cord-340851-lnv8yi9l 123 2 copyright copyright NN cord-340851-lnv8yi9l 123 3 holder holder NN cord-340851-lnv8yi9l 123 4 for for IN cord-340851-lnv8yi9l 123 5 this this DT cord-340851-lnv8yi9l 123 6 preprint preprint NN cord-340851-lnv8yi9l 123 7 this this DT cord-340851-lnv8yi9l 123 8 version version NN cord-340851-lnv8yi9l 123 9 posted post VBN cord-340851-lnv8yi9l 123 10 April April NNP cord-340851-lnv8yi9l 123 11 23 23 CD cord-340851-lnv8yi9l 123 12 , , , cord-340851-lnv8yi9l 123 13 2020 2020 CD cord-340851-lnv8yi9l 123 14 . . . cord-340851-lnv8yi9l 123 15 . . . cord-340851-lnv8yi9l 124 1 CC CC NNP cord-340851-lnv8yi9l 124 2 - - : cord-340851-lnv8yi9l 124 3 BY by IN cord-340851-lnv8yi9l 124 4 4.0 4.0 CD cord-340851-lnv8yi9l 124 5 International international JJ cord-340851-lnv8yi9l 124 6 license license NN cord-340851-lnv8yi9l 125 1 It -PRON- PRP cord-340851-lnv8yi9l 125 2 is be VBZ cord-340851-lnv8yi9l 125 3 made make VBN cord-340851-lnv8yi9l 125 4 available available JJ cord-340851-lnv8yi9l 125 5 under under IN cord-340851-lnv8yi9l 125 6 a a DT cord-340851-lnv8yi9l 126 1 is be VBZ cord-340851-lnv8yi9l 126 2 the the DT cord-340851-lnv8yi9l 126 3 author author NN cord-340851-lnv8yi9l 126 4 / / SYM cord-340851-lnv8yi9l 126 5 funder funder NN cord-340851-lnv8yi9l 126 6 , , , cord-340851-lnv8yi9l 126 7 who who WP cord-340851-lnv8yi9l 126 8 has have VBZ cord-340851-lnv8yi9l 126 9 granted grant VBN cord-340851-lnv8yi9l 126 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 126 11 a a DT cord-340851-lnv8yi9l 126 12 license license NN cord-340851-lnv8yi9l 126 13 to to TO cord-340851-lnv8yi9l 126 14 display display VB cord-340851-lnv8yi9l 126 15 the the DT cord-340851-lnv8yi9l 126 16 preprint preprint NN cord-340851-lnv8yi9l 126 17 in in IN cord-340851-lnv8yi9l 126 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 126 19 . . . cord-340851-lnv8yi9l 127 1 The the DT cord-340851-lnv8yi9l 127 2 copyright copyright NN cord-340851-lnv8yi9l 127 3 holder holder NN cord-340851-lnv8yi9l 127 4 for for IN cord-340851-lnv8yi9l 127 5 this this DT cord-340851-lnv8yi9l 127 6 preprint preprint NN cord-340851-lnv8yi9l 127 7 this this DT cord-340851-lnv8yi9l 127 8 version version NN cord-340851-lnv8yi9l 127 9 posted post VBN cord-340851-lnv8yi9l 127 10 April April NNP cord-340851-lnv8yi9l 127 11 23 23 CD cord-340851-lnv8yi9l 127 12 , , , cord-340851-lnv8yi9l 127 13 2020 2020 CD cord-340851-lnv8yi9l 127 14 . . . cord-340851-lnv8yi9l 127 15 . . . cord-340851-lnv8yi9l 128 1 https://doi.org/10.1101/2020.04 https://doi.org/10.1101/2020.04 UH cord-340851-lnv8yi9l 128 2 . . . cord-340851-lnv8yi9l 129 1 22.20076018 22.20076018 CD cord-340851-lnv8yi9l 129 2 doi doi NN cord-340851-lnv8yi9l 129 3 : : : cord-340851-lnv8yi9l 130 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 130 2 preprint preprint NN cord-340851-lnv8yi9l 130 3 Probability probability NN cord-340851-lnv8yi9l 130 4 of of IN cord-340851-lnv8yi9l 130 5 death death NN cord-340851-lnv8yi9l 130 6 among among IN cord-340851-lnv8yi9l 130 7 hospitalized hospitalize VBN cord-340851-lnv8yi9l 130 8 cases case NNS cord-340851-lnv8yi9l 130 9 , , , cord-340851-lnv8yi9l 130 10 ∆ ∆ NNP cord-340851-lnv8yi9l 130 11 and and CC cord-340851-lnv8yi9l 130 12 h. h. NNP cord-340851-lnv8yi9l 131 1 We -PRON- PRP cord-340851-lnv8yi9l 131 2 assume assume VBP cord-340851-lnv8yi9l 131 3 that that IN cord-340851-lnv8yi9l 131 4 ∆ ∆ NNP cord-340851-lnv8yi9l 131 5 − − NNP cord-340851-lnv8yi9l 131 6 is be VBZ cord-340851-lnv8yi9l 131 7 equal equal JJ cord-340851-lnv8yi9l 131 8 to to IN cord-340851-lnv8yi9l 131 9 early early JJ cord-340851-lnv8yi9l 131 10 estimates estimate NNS cord-340851-lnv8yi9l 131 11 from from IN cord-340851-lnv8yi9l 131 12 the the DT cord-340851-lnv8yi9l 131 13 US US NNP cord-340851-lnv8yi9l 131 14 ( ( -LRB- cord-340851-lnv8yi9l 131 15 2.6 2.6 CD cord-340851-lnv8yi9l 131 16 % % NN cord-340851-lnv8yi9l 131 17 ) ) -RRB- cord-340851-lnv8yi9l 131 18 [ [ -LRB- cord-340851-lnv8yi9l 131 19 9 9 CD cord-340851-lnv8yi9l 131 20 ] ] -RRB- cord-340851-lnv8yi9l 131 21 and and CC cord-340851-lnv8yi9l 131 22 that that IN cord-340851-lnv8yi9l 131 23 ∆ ∆ NN cord-340851-lnv8yi9l 131 24 + + CC cord-340851-lnv8yi9l 131 25 is be VBZ cord-340851-lnv8yi9l 131 26 equal equal JJ cord-340851-lnv8yi9l 131 27 to to IN cord-340851-lnv8yi9l 131 28 estimates estimate NNS cord-340851-lnv8yi9l 131 29 from from IN cord-340851-lnv8yi9l 131 30 Italy Italy NNP cord-340851-lnv8yi9l 131 31 ( ( -LRB- cord-340851-lnv8yi9l 131 32 7.2 7.2 CD cord-340851-lnv8yi9l 131 33 % % NN cord-340851-lnv8yi9l 131 34 ) ) -RRB- cord-340851-lnv8yi9l 131 35 [ [ -LRB- cord-340851-lnv8yi9l 131 36 38 38 CD cord-340851-lnv8yi9l 131 37 ] ] -RRB- cord-340851-lnv8yi9l 131 38 . . . cord-340851-lnv8yi9l 132 1 Estimates estimate NNS cord-340851-lnv8yi9l 132 2 of of IN cord-340851-lnv8yi9l 132 3 how how WRB cord-340851-lnv8yi9l 132 4 quickly quickly RB cord-340851-lnv8yi9l 132 5 ∆ ∆ NNP cord-340851-lnv8yi9l 132 6 + + CC cord-340851-lnv8yi9l 132 7 might may MD cord-340851-lnv8yi9l 132 8 be be VB cord-340851-lnv8yi9l 132 9 approached approach VBN cord-340851-lnv8yi9l 132 10 have have VBP cord-340851-lnv8yi9l 132 11 not not RB cord-340851-lnv8yi9l 132 12 been be VBN cord-340851-lnv8yi9l 132 13 made make VBN cord-340851-lnv8yi9l 132 14 empirically empirically RB cord-340851-lnv8yi9l 132 15 , , , cord-340851-lnv8yi9l 132 16 so so RB cord-340851-lnv8yi9l 132 17 the the DT cord-340851-lnv8yi9l 132 18 value value NN cord-340851-lnv8yi9l 132 19 of of IN cord-340851-lnv8yi9l 132 20 h h NNP cord-340851-lnv8yi9l 132 21 was be VBD cord-340851-lnv8yi9l 132 22 assumed assume VBN cord-340851-lnv8yi9l 132 23 . . . cord-340851-lnv8yi9l 133 1 The the DT cord-340851-lnv8yi9l 133 2 intermediate intermediate JJ cord-340851-lnv8yi9l 133 3 value value NN cord-340851-lnv8yi9l 133 4 of of IN cord-340851-lnv8yi9l 133 5 h h NN cord-340851-lnv8yi9l 133 6 = = NFP cord-340851-lnv8yi9l 134 1 701 701 CD cord-340851-lnv8yi9l 134 2 corresponds correspond VBZ cord-340851-lnv8yi9l 134 3 to to IN cord-340851-lnv8yi9l 134 4 an an DT cord-340851-lnv8yi9l 134 5 increase increase NN cord-340851-lnv8yi9l 134 6 of of IN cord-340851-lnv8yi9l 134 7 H h NN cord-340851-lnv8yi9l 134 8 of of IN cord-340851-lnv8yi9l 134 9 50 50 CD cord-340851-lnv8yi9l 134 10 % % NN cord-340851-lnv8yi9l 134 11 beyond beyond IN cord-340851-lnv8yi9l 134 12 H h NN cord-340851-lnv8yi9l 134 13 max max NN cord-340851-lnv8yi9l 134 14 resulting result VBG cord-340851-lnv8yi9l 134 15 in in IN cord-340851-lnv8yi9l 134 16 50 50 CD cord-340851-lnv8yi9l 134 17 % % NN cord-340851-lnv8yi9l 134 18 of of IN cord-340851-lnv8yi9l 134 19 the the DT cord-340851-lnv8yi9l 134 20 maximum maximum JJ cord-340851-lnv8yi9l 134 21 increase increase NN cord-340851-lnv8yi9l 134 22 from from IN cord-340851-lnv8yi9l 134 23 ∆ ∆ NNP cord-340851-lnv8yi9l 134 24 − − NNP cord-340851-lnv8yi9l 134 25 to to IN cord-340851-lnv8yi9l 134 26 ∆ ∆ NNP cord-340851-lnv8yi9l 135 1 + + UH cord-340851-lnv8yi9l 135 2 . . . cord-340851-lnv8yi9l 136 1 Progression progression NN cord-340851-lnv8yi9l 136 2 through through IN cord-340851-lnv8yi9l 136 3 hospitalization hospitalization NN cord-340851-lnv8yi9l 136 4 , , , cord-340851-lnv8yi9l 136 5 η η NN cord-340851-lnv8yi9l 136 6 . . . cord-340851-lnv8yi9l 137 1 We -PRON- PRP cord-340851-lnv8yi9l 137 2 used use VBD cord-340851-lnv8yi9l 137 3 line line NN cord-340851-lnv8yi9l 137 4 - - HYPH cord-340851-lnv8yi9l 137 5 list list NN cord-340851-lnv8yi9l 137 6 data datum NNS cord-340851-lnv8yi9l 137 7 [ [ -LRB- cord-340851-lnv8yi9l 137 8 1 1 CD cord-340851-lnv8yi9l 137 9 ] ] -RRB- cord-340851-lnv8yi9l 137 10 to to TO cord-340851-lnv8yi9l 137 11 estimate estimate VB cord-340851-lnv8yi9l 137 12 a a DT cord-340851-lnv8yi9l 137 13 mean mean NN cord-340851-lnv8yi9l 137 14 ( ( -LRB- cord-340851-lnv8yi9l 137 15 13.2 13.2 CD cord-340851-lnv8yi9l 137 16 days day NNS cord-340851-lnv8yi9l 137 17 ) ) -RRB- cord-340851-lnv8yi9l 137 18 and and CC cord-340851-lnv8yi9l 137 19 standard standard JJ cord-340851-lnv8yi9l 137 20 deviation deviation NN cord-340851-lnv8yi9l 137 21 ( ( -LRB- cord-340851-lnv8yi9l 137 22 7.39 7.39 CD cord-340851-lnv8yi9l 137 23 days day NNS cord-340851-lnv8yi9l 137 24 ) ) -RRB- cord-340851-lnv8yi9l 137 25 of of IN cord-340851-lnv8yi9l 137 26 the the DT cord-340851-lnv8yi9l 137 27 time time NN cord-340851-lnv8yi9l 137 28 between between IN cord-340851-lnv8yi9l 137 29 hospital hospital NN cord-340851-lnv8yi9l 137 30 admission admission NN cord-340851-lnv8yi9l 137 31 and and CC cord-340851-lnv8yi9l 137 32 either either CC cord-340851-lnv8yi9l 137 33 discharge discharge NN cord-340851-lnv8yi9l 137 34 or or CC cord-340851-lnv8yi9l 137 35 death death NN cord-340851-lnv8yi9l 137 36 . . . cord-340851-lnv8yi9l 138 1 Timing timing NN cord-340851-lnv8yi9l 138 2 of of IN cord-340851-lnv8yi9l 138 3 vaccine vaccine NN cord-340851-lnv8yi9l 138 4 introduction introduction NN cord-340851-lnv8yi9l 138 5 , , , cord-340851-lnv8yi9l 138 6 τ τ NN cord-340851-lnv8yi9l 138 7 ν ν NNP cord-340851-lnv8yi9l 138 8 . . . cord-340851-lnv8yi9l 139 1 Experts expert NNS cord-340851-lnv8yi9l 139 2 have have VBP cord-340851-lnv8yi9l 139 3 stated state VBN cord-340851-lnv8yi9l 139 4 that that IN cord-340851-lnv8yi9l 139 5 a a DT cord-340851-lnv8yi9l 139 6 vaccine vaccine NN cord-340851-lnv8yi9l 139 7 against against IN cord-340851-lnv8yi9l 139 8 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 139 9 could could MD cord-340851-lnv8yi9l 139 10 be be VB cord-340851-lnv8yi9l 139 11 available available JJ cord-340851-lnv8yi9l 139 12 to to IN cord-340851-lnv8yi9l 139 13 the the DT cord-340851-lnv8yi9l 139 14 public public NN cord-340851-lnv8yi9l 139 15 by by IN cord-340851-lnv8yi9l 139 16 spring spring NN cord-340851-lnv8yi9l 139 17 2021 2021 CD cord-340851-lnv8yi9l 139 18 [ [ -LRB- cord-340851-lnv8yi9l 139 19 4 4 CD cord-340851-lnv8yi9l 139 20 ] ] -RRB- cord-340851-lnv8yi9l 139 21 . . . cord-340851-lnv8yi9l 140 1 We -PRON- PRP cord-340851-lnv8yi9l 140 2 used use VBD cord-340851-lnv8yi9l 140 3 April April NNP cord-340851-lnv8yi9l 140 4 1 1 CD cord-340851-lnv8yi9l 140 5 , , , cord-340851-lnv8yi9l 140 6 2021 2021 CD cord-340851-lnv8yi9l 140 7 as as IN cord-340851-lnv8yi9l 140 8 our -PRON- PRP$ cord-340851-lnv8yi9l 140 9 default default NN cord-340851-lnv8yi9l 140 10 value value NN cord-340851-lnv8yi9l 140 11 for for IN cord-340851-lnv8yi9l 140 12 this this DT cord-340851-lnv8yi9l 140 13 parameter parameter NN cord-340851-lnv8yi9l 140 14 . . . cord-340851-lnv8yi9l 141 1 Vaccination vaccination NN cord-340851-lnv8yi9l 141 2 rate rate NN cord-340851-lnv8yi9l 141 3 , , , cord-340851-lnv8yi9l 141 4 ν ν NNP cord-340851-lnv8yi9l 141 5 . . . cord-340851-lnv8yi9l 142 1 In in IN cord-340851-lnv8yi9l 142 2 the the DT cord-340851-lnv8yi9l 142 3 2009 2009 CD cord-340851-lnv8yi9l 142 4 H1N1 H1N1 NNP cord-340851-lnv8yi9l 142 5 pandemic pandemic NN cord-340851-lnv8yi9l 142 6 , , , cord-340851-lnv8yi9l 142 7 100 100 CD cord-340851-lnv8yi9l 142 8 million million CD cord-340851-lnv8yi9l 142 9 doses dose NNS cord-340851-lnv8yi9l 142 10 of of IN cord-340851-lnv8yi9l 142 11 vaccine vaccine NN cord-340851-lnv8yi9l 142 12 were be VBD cord-340851-lnv8yi9l 142 13 administered administer VBN cord-340851-lnv8yi9l 142 14 between between IN cord-340851-lnv8yi9l 142 15 October October NNP cord-340851-lnv8yi9l 142 16 2009 2009 CD cord-340851-lnv8yi9l 142 17 and and CC cord-340851-lnv8yi9l 142 18 April April NNP cord-340851-lnv8yi9l 142 19 2010 2010 CD cord-340851-lnv8yi9l 142 20 [ [ -LRB- cord-340851-lnv8yi9l 142 21 7 7 CD cord-340851-lnv8yi9l 142 22 , , , cord-340851-lnv8yi9l 142 23 8 8 CD cord-340851-lnv8yi9l 142 24 ] ] -RRB- cord-340851-lnv8yi9l 142 25 . . . cord-340851-lnv8yi9l 143 1 Consistent consistent JJ cord-340851-lnv8yi9l 143 2 with with IN cord-340851-lnv8yi9l 143 3 that that DT cord-340851-lnv8yi9l 143 4 , , , cord-340851-lnv8yi9l 143 5 our -PRON- PRP$ cord-340851-lnv8yi9l 143 6 default default NN cord-340851-lnv8yi9l 143 7 value value NN cord-340851-lnv8yi9l 143 8 of of IN cord-340851-lnv8yi9l 143 9 ν ν NNP cord-340851-lnv8yi9l 143 10 resulted result VBD cord-340851-lnv8yi9l 143 11 in in IN cord-340851-lnv8yi9l 143 12 0.197 0.197 CD cord-340851-lnv8yi9l 143 13 % % NN cord-340851-lnv8yi9l 143 14 of of IN cord-340851-lnv8yi9l 143 15 the the DT cord-340851-lnv8yi9l 143 16 population population NN cord-340851-lnv8yi9l 143 17 being be VBG cord-340851-lnv8yi9l 143 18 vaccinated vaccinate VBN cord-340851-lnv8yi9l 143 19 each each DT cord-340851-lnv8yi9l 143 20 day day NN cord-340851-lnv8yi9l 143 21 . . . cord-340851-lnv8yi9l 144 1 Hospital hospital NN cord-340851-lnv8yi9l 144 2 capacity capacity NN cord-340851-lnv8yi9l 144 3 , , , cord-340851-lnv8yi9l 144 4 H h NN cord-340851-lnv8yi9l 144 5 max max NN cord-340851-lnv8yi9l 144 6 . . . cord-340851-lnv8yi9l 145 1 We -PRON- PRP cord-340851-lnv8yi9l 145 2 based base VBD cord-340851-lnv8yi9l 145 3 our -PRON- PRP$ cord-340851-lnv8yi9l 145 4 definition definition NN cord-340851-lnv8yi9l 145 5 of of IN cord-340851-lnv8yi9l 145 6 this this DT cord-340851-lnv8yi9l 145 7 parameter parameter NN cord-340851-lnv8yi9l 145 8 on on IN cord-340851-lnv8yi9l 145 9 hospital hospital NN cord-340851-lnv8yi9l 145 10 beds bed NNS cord-340851-lnv8yi9l 145 11 and and CC cord-340851-lnv8yi9l 145 12 did do VBD cord-340851-lnv8yi9l 145 13 not not RB cord-340851-lnv8yi9l 145 14 include include VB cord-340851-lnv8yi9l 145 15 other other JJ cord-340851-lnv8yi9l 145 16 aspects aspect NNS cord-340851-lnv8yi9l 145 17 of of IN cord-340851-lnv8yi9l 145 18 hospital hospital NN cord-340851-lnv8yi9l 145 19 resources resource NNS cord-340851-lnv8yi9l 145 20 , , , cord-340851-lnv8yi9l 145 21 such such JJ cord-340851-lnv8yi9l 145 22 as as IN cord-340851-lnv8yi9l 145 23 ICU ICU NNP cord-340851-lnv8yi9l 145 24 beds bed NNS cord-340851-lnv8yi9l 145 25 , , , cord-340851-lnv8yi9l 145 26 ventilators ventilator NNS cord-340851-lnv8yi9l 145 27 , , , cord-340851-lnv8yi9l 145 28 or or CC cord-340851-lnv8yi9l 145 29 hospital hospital NN cord-340851-lnv8yi9l 145 30 staffing staffing NN cord-340851-lnv8yi9l 145 31 . . . cord-340851-lnv8yi9l 146 1 Specifically specifically RB cord-340851-lnv8yi9l 146 2 , , , cord-340851-lnv8yi9l 146 3 we -PRON- PRP cord-340851-lnv8yi9l 146 4 adopted adopt VBD cord-340851-lnv8yi9l 146 5 an an DT cord-340851-lnv8yi9l 146 6 estimate estimate NN cord-340851-lnv8yi9l 146 7 of of IN cord-340851-lnv8yi9l 146 8 312,090 312,090 CD cord-340851-lnv8yi9l 146 9 beds bed NNS cord-340851-lnv8yi9l 146 10 available available JJ cord-340851-lnv8yi9l 146 11 for for IN cord-340851-lnv8yi9l 146 12 COVID-19 covid-19 JJ cord-340851-lnv8yi9l 146 13 patients patient NNS cord-340851-lnv8yi9l 146 14 in in IN cord-340851-lnv8yi9l 146 15 the the DT cord-340851-lnv8yi9l 146 16 US US NNP cord-340851-lnv8yi9l 146 17 by by IN cord-340851-lnv8yi9l 146 18 the the DT cord-340851-lnv8yi9l 146 19 Institute Institute NNP cord-340851-lnv8yi9l 146 20 for for IN cord-340851-lnv8yi9l 146 21 Health Health NNP cord-340851-lnv8yi9l 146 22 Metrics Metrics NNPS cord-340851-lnv8yi9l 146 23 and and CC cord-340851-lnv8yi9l 146 24 Evaluation Evaluation NNP cord-340851-lnv8yi9l 146 25 [ [ -LRB- cord-340851-lnv8yi9l 146 26 50 50 CD cord-340851-lnv8yi9l 146 27 ] ] -RRB- cord-340851-lnv8yi9l 146 28 . . . cord-340851-lnv8yi9l 147 1 Maximum maximum JJ cord-340851-lnv8yi9l 147 2 effect effect NN cord-340851-lnv8yi9l 147 3 of of IN cord-340851-lnv8yi9l 147 4 control control NN cord-340851-lnv8yi9l 147 5 , , , cord-340851-lnv8yi9l 147 6 u u NNP cord-340851-lnv8yi9l 147 7 max max NNP cord-340851-lnv8yi9l 147 8 . . . cord-340851-lnv8yi9l 148 1 A a DT cord-340851-lnv8yi9l 148 2 model model NN cord-340851-lnv8yi9l 148 3 incorporating incorporate VBG cord-340851-lnv8yi9l 148 4 survey survey NN cord-340851-lnv8yi9l 148 5 data datum NNS cord-340851-lnv8yi9l 148 6 and and CC cord-340851-lnv8yi9l 148 7 agebased agebase VBN cord-340851-lnv8yi9l 148 8 contact contact NN cord-340851-lnv8yi9l 148 9 patterns pattern NNS cord-340851-lnv8yi9l 148 10 estimated estimate VBN cord-340851-lnv8yi9l 148 11 that that IN cord-340851-lnv8yi9l 148 12 social social JJ cord-340851-lnv8yi9l 148 13 distancing distancing NN cord-340851-lnv8yi9l 148 14 could could MD cord-340851-lnv8yi9l 148 15 reduce reduce VB cord-340851-lnv8yi9l 148 16 transmission transmission NN cord-340851-lnv8yi9l 148 17 of of IN cord-340851-lnv8yi9l 148 18 SARS SARS NNP cord-340851-lnv8yi9l 148 19 - - HYPH cord-340851-lnv8yi9l 148 20 CoV-2 CoV-2 NNP cord-340851-lnv8yi9l 148 21 by by IN cord-340851-lnv8yi9l 148 22 73 73 CD cord-340851-lnv8yi9l 148 23 % % NN cord-340851-lnv8yi9l 148 24 [ [ -LRB- cord-340851-lnv8yi9l 148 25 23 23 CD cord-340851-lnv8yi9l 148 26 ] ] -RRB- cord-340851-lnv8yi9l 148 27 . . . cord-340851-lnv8yi9l 149 1 Based base VBN cord-340851-lnv8yi9l 149 2 on on IN cord-340851-lnv8yi9l 149 3 this this DT cord-340851-lnv8yi9l 149 4 , , , cord-340851-lnv8yi9l 149 5 we -PRON- PRP cord-340851-lnv8yi9l 149 6 used use VBD cord-340851-lnv8yi9l 149 7 0.7 0.7 CD cord-340851-lnv8yi9l 149 8 as as IN cord-340851-lnv8yi9l 149 9 an an DT cord-340851-lnv8yi9l 149 10 intermediate intermediate JJ cord-340851-lnv8yi9l 149 11 value value NN cord-340851-lnv8yi9l 149 12 of of IN cord-340851-lnv8yi9l 149 13 this this DT cord-340851-lnv8yi9l 149 14 parameter parameter NN cord-340851-lnv8yi9l 149 15 and and CC cord-340851-lnv8yi9l 149 16 0.5 0.5 CD cord-340851-lnv8yi9l 149 17 and and CC cord-340851-lnv8yi9l 149 18 0.9 0.9 CD cord-340851-lnv8yi9l 149 19 as as IN cord-340851-lnv8yi9l 149 20 lower low JJR cord-340851-lnv8yi9l 149 21 and and CC cord-340851-lnv8yi9l 149 22 upper upper JJ cord-340851-lnv8yi9l 149 23 values value NNS cord-340851-lnv8yi9l 149 24 . . . cord-340851-lnv8yi9l 150 1 To to TO cord-340851-lnv8yi9l 150 2 obtain obtain VB cord-340851-lnv8yi9l 150 3 realistic realistic JJ cord-340851-lnv8yi9l 150 4 behavior behavior NN cord-340851-lnv8yi9l 150 5 of of IN cord-340851-lnv8yi9l 150 6 the the DT cord-340851-lnv8yi9l 150 7 model model NN cord-340851-lnv8yi9l 150 8 , , , cord-340851-lnv8yi9l 150 9 we -PRON- PRP cord-340851-lnv8yi9l 150 10 calibrated calibrate VBD cord-340851-lnv8yi9l 150 11 it -PRON- PRP cord-340851-lnv8yi9l 150 12 to to TO cord-340851-lnv8yi9l 150 13 match match VB cord-340851-lnv8yi9l 150 14 the the DT cord-340851-lnv8yi9l 150 15 cumulative cumulative JJ cord-340851-lnv8yi9l 150 16 number number NN cord-340851-lnv8yi9l 150 17 of of IN cord-340851-lnv8yi9l 150 18 reported report VBN cord-340851-lnv8yi9l 150 19 deaths death NNS cord-340851-lnv8yi9l 150 20 in in IN cord-340851-lnv8yi9l 150 21 the the DT cord-340851-lnv8yi9l 150 22 US US NNP cord-340851-lnv8yi9l 150 23 within within IN cord-340851-lnv8yi9l 150 24 the the DT cord-340851-lnv8yi9l 150 25 first first JJ cord-340851-lnv8yi9l 150 26 100 100 CD cord-340851-lnv8yi9l 150 27 days day NNS cord-340851-lnv8yi9l 150 28 of of IN cord-340851-lnv8yi9l 150 29 2020 2020 CD cord-340851-lnv8yi9l 150 30 ( ( -LRB- cord-340851-lnv8yi9l 150 31 i.e. i.e. FW cord-340851-lnv8yi9l 150 32 , , , cord-340851-lnv8yi9l 150 33 by by IN cord-340851-lnv8yi9l 150 34 April April NNP cord-340851-lnv8yi9l 150 35 9 9 CD cord-340851-lnv8yi9l 150 36 ) ) -RRB- cord-340851-lnv8yi9l 150 37 , , , cord-340851-lnv8yi9l 150 38 which which WDT cord-340851-lnv8yi9l 150 39 we -PRON- PRP cord-340851-lnv8yi9l 150 40 obtained obtain VBD cord-340851-lnv8yi9l 150 41 from from IN cord-340851-lnv8yi9l 150 42 the the DT cord-340851-lnv8yi9l 150 43 New New NNP cord-340851-lnv8yi9l 150 44 York York NNP cord-340851-lnv8yi9l 150 45 Times Times NNP cord-340851-lnv8yi9l 150 46 [ [ -LRB- cord-340851-lnv8yi9l 150 47 36 36 CD cord-340851-lnv8yi9l 150 48 ] ] -RRB- cord-340851-lnv8yi9l 150 49 . . . cord-340851-lnv8yi9l 151 1 We -PRON- PRP cord-340851-lnv8yi9l 151 2 focused focus VBD cord-340851-lnv8yi9l 151 3 our -PRON- PRP$ cord-340851-lnv8yi9l 151 4 calibration calibration NN cord-340851-lnv8yi9l 151 5 on on IN cord-340851-lnv8yi9l 151 6 the the DT cord-340851-lnv8yi9l 151 7 parameter parameter NN cord-340851-lnv8yi9l 151 8 ι ι NNS cord-340851-lnv8yi9l 151 9 , , , cord-340851-lnv8yi9l 151 10 due due IN cord-340851-lnv8yi9l 151 11 to to IN cord-340851-lnv8yi9l 151 12 the the DT cord-340851-lnv8yi9l 151 13 difficulty difficulty NN cord-340851-lnv8yi9l 151 14 of of IN cord-340851-lnv8yi9l 151 15 empirically empirically RB cord-340851-lnv8yi9l 151 16 estimating estimate VBG cord-340851-lnv8yi9l 151 17 the the DT cord-340851-lnv8yi9l 151 18 rate rate NN cord-340851-lnv8yi9l 151 19 at at IN cord-340851-lnv8yi9l 151 20 which which WDT cord-340851-lnv8yi9l 151 21 imported import VBN cord-340851-lnv8yi9l 151 22 infections infection NNS cord-340851-lnv8yi9l 151 23 appear appear VBP cord-340851-lnv8yi9l 151 24 . . . cord-340851-lnv8yi9l 152 1 To to TO cord-340851-lnv8yi9l 152 2 obtain obtain VB cord-340851-lnv8yi9l 152 3 a a DT cord-340851-lnv8yi9l 152 4 value value NN cord-340851-lnv8yi9l 152 5 of of IN cord-340851-lnv8yi9l 152 6 ι ι NNS cord-340851-lnv8yi9l 152 7 that that WDT cord-340851-lnv8yi9l 152 8 resulted result VBD cord-340851-lnv8yi9l 152 9 in in IN cord-340851-lnv8yi9l 152 10 the the DT cord-340851-lnv8yi9l 152 11 model model NN cord-340851-lnv8yi9l 152 12 matching match VBG cord-340851-lnv8yi9l 152 13 the the DT cord-340851-lnv8yi9l 152 14 reported report VBN cord-340851-lnv8yi9l 152 15 number number NN cord-340851-lnv8yi9l 152 16 of of IN cord-340851-lnv8yi9l 152 17 deaths death NNS cord-340851-lnv8yi9l 152 18 , , , cord-340851-lnv8yi9l 152 19 we -PRON- PRP cord-340851-lnv8yi9l 152 20 simulated simulate VBD cord-340851-lnv8yi9l 152 21 the the DT cord-340851-lnv8yi9l 152 22 model model NN cord-340851-lnv8yi9l 152 23 across across IN cord-340851-lnv8yi9l 152 24 300 300 CD cord-340851-lnv8yi9l 152 25 values value NNS cord-340851-lnv8yi9l 152 26 of of IN cord-340851-lnv8yi9l 152 27 ι ι NNS cord-340851-lnv8yi9l 152 28 evenly evenly RB cord-340851-lnv8yi9l 152 29 spaced space VBN cord-340851-lnv8yi9l 152 30 between between IN cord-340851-lnv8yi9l 152 31 10 10 CD cord-340851-lnv8yi9l 152 32 −12 −12 NN cord-340851-lnv8yi9l 152 33 and and CC cord-340851-lnv8yi9l 152 34 10 10 CD cord-340851-lnv8yi9l 152 35 −4 −4 CD cord-340851-lnv8yi9l 152 36 on on IN cord-340851-lnv8yi9l 152 37 a a DT cord-340851-lnv8yi9l 152 38 log log NN cord-340851-lnv8yi9l 152 39 scale scale NN cord-340851-lnv8yi9l 152 40 , , , cord-340851-lnv8yi9l 152 41 performed perform VBD cord-340851-lnv8yi9l 152 42 a a DT cord-340851-lnv8yi9l 152 43 linear linear JJ cord-340851-lnv8yi9l 152 44 interpolation interpolation NN cord-340851-lnv8yi9l 152 45 of of IN cord-340851-lnv8yi9l 152 46 the the DT cord-340851-lnv8yi9l 152 47 simulated simulated JJ cord-340851-lnv8yi9l 152 48 number number NN cord-340851-lnv8yi9l 152 49 of of IN cord-340851-lnv8yi9l 152 50 deaths death NNS cord-340851-lnv8yi9l 152 51 across across IN cord-340851-lnv8yi9l 152 52 those those DT cord-340851-lnv8yi9l 152 53 values value NNS cord-340851-lnv8yi9l 152 54 of of IN cord-340851-lnv8yi9l 152 55 ι ι NNS cord-340851-lnv8yi9l 152 56 , , , cord-340851-lnv8yi9l 152 57 and and CC cord-340851-lnv8yi9l 152 58 found find VBD cord-340851-lnv8yi9l 152 59 the the DT cord-340851-lnv8yi9l 152 60 value value NN cord-340851-lnv8yi9l 152 61 of of IN cord-340851-lnv8yi9l 152 62 ι ι NNS cord-340851-lnv8yi9l 152 63 that that WDT cord-340851-lnv8yi9l 152 64 most most RBS cord-340851-lnv8yi9l 152 65 closely closely RB cord-340851-lnv8yi9l 152 66 matched match VBN cord-340851-lnv8yi9l 152 67 reported report VBN cord-340851-lnv8yi9l 152 68 deaths death NNS cord-340851-lnv8yi9l 152 69 . . . cord-340851-lnv8yi9l 153 1 We -PRON- PRP cord-340851-lnv8yi9l 153 2 calibrated calibrate VBD cord-340851-lnv8yi9l 153 3 the the DT cord-340851-lnv8yi9l 153 4 model model NN cord-340851-lnv8yi9l 153 5 under under IN cord-340851-lnv8yi9l 153 6 a a DT cord-340851-lnv8yi9l 153 7 total total NN cord-340851-lnv8yi9l 153 8 of of IN cord-340851-lnv8yi9l 153 9 18 18 CD cord-340851-lnv8yi9l 153 10 different different JJ cord-340851-lnv8yi9l 153 11 parameter parameter NN cord-340851-lnv8yi9l 153 12 scenarios scenario NNS cord-340851-lnv8yi9l 153 13 , , , cord-340851-lnv8yi9l 153 14 crossing cross VBG cord-340851-lnv8yi9l 153 15 low low JJ cord-340851-lnv8yi9l 153 16 , , , cord-340851-lnv8yi9l 153 17 intermediate intermediate JJ cord-340851-lnv8yi9l 153 18 , , , cord-340851-lnv8yi9l 153 19 and and CC cord-340851-lnv8yi9l 153 20 high high JJ cord-340851-lnv8yi9l 153 21 values value NNS cord-340851-lnv8yi9l 153 22 of of IN cord-340851-lnv8yi9l 153 23 R r NN cord-340851-lnv8yi9l 153 24 0 0 CD cord-340851-lnv8yi9l 153 25 with with IN cord-340851-lnv8yi9l 153 26 low low JJ cord-340851-lnv8yi9l 153 27 , , , cord-340851-lnv8yi9l 153 28 intermediate intermediate JJ cord-340851-lnv8yi9l 153 29 , , , cord-340851-lnv8yi9l 153 30 and and CC cord-340851-lnv8yi9l 153 31 . . . cord-340851-lnv8yi9l 154 1 CC CC NNP cord-340851-lnv8yi9l 154 2 - - : cord-340851-lnv8yi9l 154 3 BY by IN cord-340851-lnv8yi9l 154 4 4.0 4.0 CD cord-340851-lnv8yi9l 154 5 International international JJ cord-340851-lnv8yi9l 154 6 license license NN cord-340851-lnv8yi9l 155 1 It -PRON- PRP cord-340851-lnv8yi9l 155 2 is be VBZ cord-340851-lnv8yi9l 155 3 made make VBN cord-340851-lnv8yi9l 155 4 available available JJ cord-340851-lnv8yi9l 155 5 under under IN cord-340851-lnv8yi9l 155 6 a a DT cord-340851-lnv8yi9l 156 1 is be VBZ cord-340851-lnv8yi9l 156 2 the the DT cord-340851-lnv8yi9l 156 3 author author NN cord-340851-lnv8yi9l 156 4 / / SYM cord-340851-lnv8yi9l 156 5 funder funder NN cord-340851-lnv8yi9l 156 6 , , , cord-340851-lnv8yi9l 156 7 who who WP cord-340851-lnv8yi9l 156 8 has have VBZ cord-340851-lnv8yi9l 156 9 granted grant VBN cord-340851-lnv8yi9l 156 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 156 11 a a DT cord-340851-lnv8yi9l 156 12 license license NN cord-340851-lnv8yi9l 156 13 to to TO cord-340851-lnv8yi9l 156 14 display display VB cord-340851-lnv8yi9l 156 15 the the DT cord-340851-lnv8yi9l 156 16 preprint preprint NN cord-340851-lnv8yi9l 156 17 in in IN cord-340851-lnv8yi9l 156 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 156 19 . . . cord-340851-lnv8yi9l 157 1 The the DT cord-340851-lnv8yi9l 157 2 copyright copyright NN cord-340851-lnv8yi9l 157 3 holder holder NN cord-340851-lnv8yi9l 157 4 for for IN cord-340851-lnv8yi9l 157 5 this this DT cord-340851-lnv8yi9l 157 6 preprint preprint NN cord-340851-lnv8yi9l 157 7 this this DT cord-340851-lnv8yi9l 157 8 version version NN cord-340851-lnv8yi9l 157 9 posted post VBN cord-340851-lnv8yi9l 157 10 April April NNP cord-340851-lnv8yi9l 157 11 23 23 CD cord-340851-lnv8yi9l 157 12 , , , cord-340851-lnv8yi9l 157 13 2020 2020 CD cord-340851-lnv8yi9l 157 14 . . . cord-340851-lnv8yi9l 158 1 high high JJ cord-340851-lnv8yi9l 158 2 values value NNS cord-340851-lnv8yi9l 158 3 of of IN cord-340851-lnv8yi9l 158 4 u u NNP cord-340851-lnv8yi9l 158 5 max max NNP cord-340851-lnv8yi9l 158 6 and and CC cord-340851-lnv8yi9l 158 7 low low JJ cord-340851-lnv8yi9l 158 8 and and CC cord-340851-lnv8yi9l 158 9 high high JJ cord-340851-lnv8yi9l 158 10 values value NNS cord-340851-lnv8yi9l 158 11 of of IN cord-340851-lnv8yi9l 158 12 ω ω CD cord-340851-lnv8yi9l 158 13 . . . cord-340851-lnv8yi9l 159 1 The the DT cord-340851-lnv8yi9l 159 2 latter latter JJ cord-340851-lnv8yi9l 159 3 represents represent VBZ cord-340851-lnv8yi9l 159 4 the the DT cord-340851-lnv8yi9l 159 5 proportion proportion NN cord-340851-lnv8yi9l 159 6 of of IN cord-340851-lnv8yi9l 159 7 all all DT cord-340851-lnv8yi9l 159 8 deaths death NNS cord-340851-lnv8yi9l 159 9 caused cause VBN cord-340851-lnv8yi9l 159 10 by by IN cord-340851-lnv8yi9l 159 11 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 159 12 that that WDT cord-340851-lnv8yi9l 159 13 were be VBD cord-340851-lnv8yi9l 159 14 reported report VBN cord-340851-lnv8yi9l 159 15 . . . cord-340851-lnv8yi9l 160 1 Because because IN cord-340851-lnv8yi9l 160 2 NPIs npi NNS cord-340851-lnv8yi9l 160 3 began begin VBD cord-340851-lnv8yi9l 160 4 going go VBG cord-340851-lnv8yi9l 160 5 into into IN cord-340851-lnv8yi9l 160 6 effect effect NN cord-340851-lnv8yi9l 160 7 in in IN cord-340851-lnv8yi9l 160 8 the the DT cord-340851-lnv8yi9l 160 9 US US NNP cord-340851-lnv8yi9l 160 10 within within IN cord-340851-lnv8yi9l 160 11 the the DT cord-340851-lnv8yi9l 160 12 timeframe timeframe NN cord-340851-lnv8yi9l 160 13 of of IN cord-340851-lnv8yi9l 160 14 this this DT cord-340851-lnv8yi9l 160 15 calibration calibration NN cord-340851-lnv8yi9l 160 16 period period NN cord-340851-lnv8yi9l 160 17 , , , cord-340851-lnv8yi9l 160 18 we -PRON- PRP cord-340851-lnv8yi9l 160 19 calibrated calibrate VBD cord-340851-lnv8yi9l 160 20 the the DT cord-340851-lnv8yi9l 160 21 model model NN cord-340851-lnv8yi9l 160 22 subject subject JJ cord-340851-lnv8yi9l 160 23 to to IN cord-340851-lnv8yi9l 160 24 an an DT cord-340851-lnv8yi9l 160 25 assumed assumed JJ cord-340851-lnv8yi9l 160 26 pattern pattern NN cord-340851-lnv8yi9l 160 27 of of IN cord-340851-lnv8yi9l 160 28 u(t u(t NNP cord-340851-lnv8yi9l 160 29 ) ) -RRB- cord-340851-lnv8yi9l 160 30 through through IN cord-340851-lnv8yi9l 160 31 the the DT cord-340851-lnv8yi9l 160 32 first first JJ cord-340851-lnv8yi9l 160 33 100 100 CD cord-340851-lnv8yi9l 160 34 days day NNS cord-340851-lnv8yi9l 160 35 of of IN cord-340851-lnv8yi9l 160 36 2020 2020 CD cord-340851-lnv8yi9l 160 37 . . . cord-340851-lnv8yi9l 161 1 We -PRON- PRP cord-340851-lnv8yi9l 161 2 chose choose VBD cord-340851-lnv8yi9l 161 3 a a DT cord-340851-lnv8yi9l 161 4 logistic logistic JJ cord-340851-lnv8yi9l 161 5 functional functional JJ cord-340851-lnv8yi9l 161 6 form form NN cord-340851-lnv8yi9l 161 7 for for IN cord-340851-lnv8yi9l 161 8 this this DT cord-340851-lnv8yi9l 161 9 , , , cord-340851-lnv8yi9l 161 10 with with IN cord-340851-lnv8yi9l 161 11 a a DT cord-340851-lnv8yi9l 161 12 minimum minimum NN cord-340851-lnv8yi9l 161 13 of of IN cord-340851-lnv8yi9l 161 14 0 0 CD cord-340851-lnv8yi9l 161 15 and and CC cord-340851-lnv8yi9l 161 16 a a DT cord-340851-lnv8yi9l 161 17 maximum maximum NN cord-340851-lnv8yi9l 161 18 of of IN cord-340851-lnv8yi9l 161 19 u u NNP cord-340851-lnv8yi9l 161 20 max max NN cord-340851-lnv8yi9l 161 21 . . . cord-340851-lnv8yi9l 162 1 Two two CD cord-340851-lnv8yi9l 162 2 parameters parameter NNS cord-340851-lnv8yi9l 162 3 that that WDT cord-340851-lnv8yi9l 162 4 control control VBP cord-340851-lnv8yi9l 162 5 the the DT cord-340851-lnv8yi9l 162 6 midpoint midpoint NN cord-340851-lnv8yi9l 162 7 and and CC cord-340851-lnv8yi9l 162 8 slope slope NN cord-340851-lnv8yi9l 162 9 of of IN cord-340851-lnv8yi9l 162 10 the the DT cord-340851-lnv8yi9l 162 11 increase increase NN cord-340851-lnv8yi9l 162 12 from from IN cord-340851-lnv8yi9l 162 13 0 0 CD cord-340851-lnv8yi9l 162 14 to to IN cord-340851-lnv8yi9l 162 15 u u NNP cord-340851-lnv8yi9l 162 16 max max NNP cord-340851-lnv8yi9l 162 17 were be VBD cord-340851-lnv8yi9l 162 18 selected select VBN cord-340851-lnv8yi9l 162 19 by by IN cord-340851-lnv8yi9l 162 20 an an DT cord-340851-lnv8yi9l 162 21 informal informal JJ cord-340851-lnv8yi9l 162 22 process process NN cord-340851-lnv8yi9l 162 23 of of IN cord-340851-lnv8yi9l 162 24 trial trial NN cord-340851-lnv8yi9l 162 25 and and CC cord-340851-lnv8yi9l 162 26 error error NN cord-340851-lnv8yi9l 162 27 , , , cord-340851-lnv8yi9l 162 28 with with IN cord-340851-lnv8yi9l 162 29 the the DT cord-340851-lnv8yi9l 162 30 goal goal NN cord-340851-lnv8yi9l 162 31 of of IN cord-340851-lnv8yi9l 162 32 having have VBG cord-340851-lnv8yi9l 162 33 the the DT cord-340851-lnv8yi9l 162 34 model model NN cord-340851-lnv8yi9l 162 35 's 's POS cord-340851-lnv8yi9l 162 36 predictions prediction NNS cord-340851-lnv8yi9l 162 37 of of IN cord-340851-lnv8yi9l 162 38 deaths death NNS cord-340851-lnv8yi9l 162 39 over over IN cord-340851-lnv8yi9l 162 40 time time NN cord-340851-lnv8yi9l 162 41 match match VBP cord-340851-lnv8yi9l 162 42 the the DT cord-340851-lnv8yi9l 162 43 timing timing NN cord-340851-lnv8yi9l 162 44 of of IN cord-340851-lnv8yi9l 162 45 reported report VBN cord-340851-lnv8yi9l 162 46 deaths death NNS cord-340851-lnv8yi9l 162 47 under under IN cord-340851-lnv8yi9l 162 48 all all DT cord-340851-lnv8yi9l 162 49 18 18 CD cord-340851-lnv8yi9l 162 50 parameter parameter NN cord-340851-lnv8yi9l 162 51 scenarios scenario NNS cord-340851-lnv8yi9l 162 52 . . . cord-340851-lnv8yi9l 163 1 We -PRON- PRP cord-340851-lnv8yi9l 163 2 also also RB cord-340851-lnv8yi9l 163 3 used use VBD cord-340851-lnv8yi9l 163 4 this this DT cord-340851-lnv8yi9l 163 5 process process NN cord-340851-lnv8yi9l 163 6 to to TO cord-340851-lnv8yi9l 163 7 select select VB cord-340851-lnv8yi9l 163 8 the the DT cord-340851-lnv8yi9l 163 9 date date NN cord-340851-lnv8yi9l 163 10 on on IN cord-340851-lnv8yi9l 163 11 which which WDT cord-340851-lnv8yi9l 163 12 importations importation NNS cord-340851-lnv8yi9l 163 13 were be VBD cord-340851-lnv8yi9l 163 14 initiated initiate VBN cord-340851-lnv8yi9l 163 15 through through IN cord-340851-lnv8yi9l 163 16 ι ι NNS cord-340851-lnv8yi9l 163 17 . . . cord-340851-lnv8yi9l 164 1 Under under IN cord-340851-lnv8yi9l 164 2 each each DT cord-340851-lnv8yi9l 164 3 of of IN cord-340851-lnv8yi9l 164 4 the the DT cord-340851-lnv8yi9l 164 5 18 18 CD cord-340851-lnv8yi9l 164 6 different different JJ cord-340851-lnv8yi9l 164 7 scenarios scenario NNS cord-340851-lnv8yi9l 164 8 we -PRON- PRP cord-340851-lnv8yi9l 164 9 considered consider VBD cord-340851-lnv8yi9l 164 10 about about RB cord-340851-lnv8yi9l 164 11 R r NN cord-340851-lnv8yi9l 164 12 0 0 CD cord-340851-lnv8yi9l 164 13 , , , cord-340851-lnv8yi9l 164 14 u u NNP cord-340851-lnv8yi9l 164 15 max max NNP cord-340851-lnv8yi9l 164 16 , , , cord-340851-lnv8yi9l 164 17 and and CC cord-340851-lnv8yi9l 164 18 ω ω NN cord-340851-lnv8yi9l 164 19 , , , cord-340851-lnv8yi9l 164 20 our -PRON- PRP$ cord-340851-lnv8yi9l 164 21 model model NN cord-340851-lnv8yi9l 164 22 was be VBD cord-340851-lnv8yi9l 164 23 able able JJ cord-340851-lnv8yi9l 164 24 to to TO cord-340851-lnv8yi9l 164 25 reproduce reproduce VB cord-340851-lnv8yi9l 164 26 the the DT cord-340851-lnv8yi9l 164 27 numbers number NNS cord-340851-lnv8yi9l 164 28 and and CC cord-340851-lnv8yi9l 164 29 timing timing NN cord-340851-lnv8yi9l 164 30 of of IN cord-340851-lnv8yi9l 164 31 reported report VBN cord-340851-lnv8yi9l 164 32 deaths death NNS cord-340851-lnv8yi9l 164 33 in in IN cord-340851-lnv8yi9l 164 34 the the DT cord-340851-lnv8yi9l 164 35 US US NNP cord-340851-lnv8yi9l 164 36 reasonably reasonably RB cord-340851-lnv8yi9l 164 37 well well RB cord-340851-lnv8yi9l 165 1 ( ( -LRB- cord-340851-lnv8yi9l 165 2 Figure figure NN cord-340851-lnv8yi9l 165 3 2 2 CD cord-340851-lnv8yi9l 165 4 ) ) -RRB- cord-340851-lnv8yi9l 165 5 . . . cord-340851-lnv8yi9l 166 1 Different different JJ cord-340851-lnv8yi9l 166 2 values value NNS cord-340851-lnv8yi9l 166 3 of of IN cord-340851-lnv8yi9l 166 4 ι ι NNS cord-340851-lnv8yi9l 166 5 were be VBD cord-340851-lnv8yi9l 166 6 required require VBN cord-340851-lnv8yi9l 166 7 to to TO cord-340851-lnv8yi9l 166 8 do do VB cord-340851-lnv8yi9l 166 9 so so RB cord-340851-lnv8yi9l 166 10 under under IN cord-340851-lnv8yi9l 166 11 different different JJ cord-340851-lnv8yi9l 166 12 values value NNS cord-340851-lnv8yi9l 166 13 of of IN cord-340851-lnv8yi9l 166 14 those those DT cord-340851-lnv8yi9l 166 15 other other JJ cord-340851-lnv8yi9l 166 16 three three CD cord-340851-lnv8yi9l 166 17 parameters parameter NNS cord-340851-lnv8yi9l 166 18 , , , cord-340851-lnv8yi9l 166 19 but but CC cord-340851-lnv8yi9l 166 20 all all DT cord-340851-lnv8yi9l 166 21 values value NNS cord-340851-lnv8yi9l 166 22 of of IN cord-340851-lnv8yi9l 166 23 ι ι NNS cord-340851-lnv8yi9l 166 24 ranged range VBD cord-340851-lnv8yi9l 166 25 10 10 CD cord-340851-lnv8yi9l 167 1 −7 −7 NNP cord-340851-lnv8yi9l 167 2 -10 -10 IN cord-340851-lnv8yi9l 167 3 −6 −6 NNP cord-340851-lnv8yi9l 167 4 ( ( -LRB- cord-340851-lnv8yi9l 167 5 Table Table NNP cord-340851-lnv8yi9l 167 6 3 3 CD cord-340851-lnv8yi9l 167 7 ) ) -RRB- cord-340851-lnv8yi9l 167 8 . . . cord-340851-lnv8yi9l 168 1 Taking take VBG cord-340851-lnv8yi9l 168 2 into into IN cord-340851-lnv8yi9l 168 3 account account NN cord-340851-lnv8yi9l 168 4 the the DT cord-340851-lnv8yi9l 168 5 population population NN cord-340851-lnv8yi9l 168 6 of of IN cord-340851-lnv8yi9l 168 7 the the DT cord-340851-lnv8yi9l 168 8 US US NNP cord-340851-lnv8yi9l 168 9 , , , cord-340851-lnv8yi9l 168 10 this this DT cord-340851-lnv8yi9l 168 11 equates equate VBZ cord-340851-lnv8yi9l 168 12 to to IN cord-340851-lnv8yi9l 168 13 a a DT cord-340851-lnv8yi9l 168 14 range range NN cord-340851-lnv8yi9l 168 15 of of IN cord-340851-lnv8yi9l 168 16 33 33 CD cord-340851-lnv8yi9l 168 17 -331 -331 NN cord-340851-lnv8yi9l 168 18 imported import VBN cord-340851-lnv8yi9l 168 19 infections infection NNS cord-340851-lnv8yi9l 168 20 per per IN cord-340851-lnv8yi9l 168 21 day day NN cord-340851-lnv8yi9l 168 22 . . . cord-340851-lnv8yi9l 169 1 Higher high JJR cord-340851-lnv8yi9l 169 2 values value NNS cord-340851-lnv8yi9l 169 3 of of IN cord-340851-lnv8yi9l 169 4 R r NN cord-340851-lnv8yi9l 169 5 0 0 CD cord-340851-lnv8yi9l 169 6 resulted result VBD cord-340851-lnv8yi9l 169 7 in in IN cord-340851-lnv8yi9l 169 8 lower low JJR cord-340851-lnv8yi9l 169 9 values value NNS cord-340851-lnv8yi9l 169 10 of of IN cord-340851-lnv8yi9l 169 11 ι ι NNS cord-340851-lnv8yi9l 169 12 , , , cord-340851-lnv8yi9l 169 13 given give VBN cord-340851-lnv8yi9l 169 14 that that IN cord-340851-lnv8yi9l 169 15 fewer few JJR cord-340851-lnv8yi9l 169 16 importations importation NNS cord-340851-lnv8yi9l 169 17 were be VBD cord-340851-lnv8yi9l 169 18 required require VBN cord-340851-lnv8yi9l 169 19 to to TO cord-340851-lnv8yi9l 169 20 generate generate VB cord-340851-lnv8yi9l 169 21 the the DT cord-340851-lnv8yi9l 169 22 reported report VBN cord-340851-lnv8yi9l 169 23 numbers number NNS cord-340851-lnv8yi9l 169 24 of of IN cord-340851-lnv8yi9l 169 25 deaths death NNS cord-340851-lnv8yi9l 169 26 when when WRB cord-340851-lnv8yi9l 169 27 there there EX cord-340851-lnv8yi9l 169 28 was be VBD cord-340851-lnv8yi9l 169 29 more more JJR cord-340851-lnv8yi9l 169 30 local local JJ cord-340851-lnv8yi9l 169 31 transmission transmission NN cord-340851-lnv8yi9l 169 32 . . . cord-340851-lnv8yi9l 170 1 For for IN cord-340851-lnv8yi9l 170 2 similar similar JJ cord-340851-lnv8yi9l 170 3 reasons reason NNS cord-340851-lnv8yi9l 170 4 , , , cord-340851-lnv8yi9l 170 5 ι ι NNS cord-340851-lnv8yi9l 170 6 was be VBD cord-340851-lnv8yi9l 170 7 lower low JJR cord-340851-lnv8yi9l 170 8 when when WRB cord-340851-lnv8yi9l 170 9 u u NNP cord-340851-lnv8yi9l 170 10 max max NNP cord-340851-lnv8yi9l 170 11 was be VBD cord-340851-lnv8yi9l 170 12 lower low JJR cord-340851-lnv8yi9l 170 13 . . . cord-340851-lnv8yi9l 171 1 The the DT cord-340851-lnv8yi9l 171 2 value value NN cord-340851-lnv8yi9l 171 3 of of IN cord-340851-lnv8yi9l 171 4 ω ω NN cord-340851-lnv8yi9l 171 5 had have VBD cord-340851-lnv8yi9l 171 6 a a DT cord-340851-lnv8yi9l 171 7 negligible negligible JJ cord-340851-lnv8yi9l 171 8 effect effect NN cord-340851-lnv8yi9l 171 9 on on IN cord-340851-lnv8yi9l 171 10 ι ι NNS cord-340851-lnv8yi9l 171 11 . . . cord-340851-lnv8yi9l 172 1 In in IN cord-340851-lnv8yi9l 172 2 addition addition NN cord-340851-lnv8yi9l 172 3 to to IN cord-340851-lnv8yi9l 172 4 ι ι NNS cord-340851-lnv8yi9l 172 5 , , , cord-340851-lnv8yi9l 172 6 we -PRON- PRP cord-340851-lnv8yi9l 172 7 also also RB cord-340851-lnv8yi9l 172 8 calibrated calibrate VBD cord-340851-lnv8yi9l 172 9 the the DT cord-340851-lnv8yi9l 172 10 date date NN cord-340851-lnv8yi9l 172 11 on on IN cord-340851-lnv8yi9l 172 12 which which WDT cord-340851-lnv8yi9l 172 13 importations importation NNS cord-340851-lnv8yi9l 172 14 began begin VBD cord-340851-lnv8yi9l 172 15 ( ( -LRB- cord-340851-lnv8yi9l 172 16 February February NNP cord-340851-lnv8yi9l 172 17 1 1 CD cord-340851-lnv8yi9l 172 18 ) ) -RRB- cord-340851-lnv8yi9l 172 19 and and CC cord-340851-lnv8yi9l 172 20 u(t u(t NNP cord-340851-lnv8yi9l 172 21 ) ) -RRB- cord-340851-lnv8yi9l 172 22 during during IN cord-340851-lnv8yi9l 172 23 the the DT cord-340851-lnv8yi9l 172 24 first first JJ cord-340851-lnv8yi9l 172 25 100 100 CD cord-340851-lnv8yi9l 172 26 days day NNS cord-340851-lnv8yi9l 172 27 of of IN cord-340851-lnv8yi9l 172 28 2020 2020 CD cord-340851-lnv8yi9l 172 29 . . . cord-340851-lnv8yi9l 173 1 Even even RB cord-340851-lnv8yi9l 173 2 though though IN cord-340851-lnv8yi9l 173 3 the the DT cord-340851-lnv8yi9l 173 4 first first JJ cord-340851-lnv8yi9l 173 5 imported import VBN cord-340851-lnv8yi9l 173 6 cases case NNS cord-340851-lnv8yi9l 173 7 in in IN cord-340851-lnv8yi9l 173 8 the the DT cord-340851-lnv8yi9l 173 9 US US NNP cord-340851-lnv8yi9l 173 10 began begin VBD cord-340851-lnv8yi9l 173 11 appearing appear VBG cord-340851-lnv8yi9l 173 12 before before IN cord-340851-lnv8yi9l 173 13 February February NNP cord-340851-lnv8yi9l 173 14 1 1 CD cord-340851-lnv8yi9l 173 15 [ [ -LRB- cord-340851-lnv8yi9l 173 16 22 22 CD cord-340851-lnv8yi9l 173 17 ] ] -RRB- cord-340851-lnv8yi9l 173 18 , , , cord-340851-lnv8yi9l 173 19 it -PRON- PRP cord-340851-lnv8yi9l 173 20 is be VBZ cord-340851-lnv8yi9l 173 21 . . . cord-340851-lnv8yi9l 174 1 CC CC NNP cord-340851-lnv8yi9l 174 2 - - : cord-340851-lnv8yi9l 174 3 BY by IN cord-340851-lnv8yi9l 174 4 4.0 4.0 CD cord-340851-lnv8yi9l 174 5 International international JJ cord-340851-lnv8yi9l 174 6 license license NN cord-340851-lnv8yi9l 175 1 It -PRON- PRP cord-340851-lnv8yi9l 175 2 is be VBZ cord-340851-lnv8yi9l 175 3 made make VBN cord-340851-lnv8yi9l 175 4 available available JJ cord-340851-lnv8yi9l 175 5 under under IN cord-340851-lnv8yi9l 175 6 a a DT cord-340851-lnv8yi9l 176 1 is be VBZ cord-340851-lnv8yi9l 176 2 the the DT cord-340851-lnv8yi9l 176 3 author author NN cord-340851-lnv8yi9l 176 4 / / SYM cord-340851-lnv8yi9l 176 5 funder funder NN cord-340851-lnv8yi9l 176 6 , , , cord-340851-lnv8yi9l 176 7 who who WP cord-340851-lnv8yi9l 176 8 has have VBZ cord-340851-lnv8yi9l 176 9 granted grant VBN cord-340851-lnv8yi9l 176 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 176 11 a a DT cord-340851-lnv8yi9l 176 12 license license NN cord-340851-lnv8yi9l 176 13 to to TO cord-340851-lnv8yi9l 176 14 display display VB cord-340851-lnv8yi9l 176 15 the the DT cord-340851-lnv8yi9l 176 16 preprint preprint NN cord-340851-lnv8yi9l 176 17 in in IN cord-340851-lnv8yi9l 176 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 176 19 . . . cord-340851-lnv8yi9l 177 1 The the DT cord-340851-lnv8yi9l 177 2 copyright copyright NN cord-340851-lnv8yi9l 177 3 holder holder NN cord-340851-lnv8yi9l 177 4 for for IN cord-340851-lnv8yi9l 177 5 this this DT cord-340851-lnv8yi9l 177 6 preprint preprint NN cord-340851-lnv8yi9l 177 7 this this DT cord-340851-lnv8yi9l 177 8 version version NN cord-340851-lnv8yi9l 177 9 posted post VBN cord-340851-lnv8yi9l 177 10 April April NNP cord-340851-lnv8yi9l 177 11 23 23 CD cord-340851-lnv8yi9l 177 12 , , , cord-340851-lnv8yi9l 177 13 2020 2020 CD cord-340851-lnv8yi9l 177 14 . . . cord-340851-lnv8yi9l 177 15 . . . cord-340851-lnv8yi9l 178 1 https://doi.org/10.1101/2020.04 https://doi.org/10.1101/2020.04 UH cord-340851-lnv8yi9l 178 2 . . . cord-340851-lnv8yi9l 179 1 22.20076018 22.20076018 CD cord-340851-lnv8yi9l 179 2 doi doi NN cord-340851-lnv8yi9l 179 3 : : : cord-340851-lnv8yi9l 180 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 180 2 preprint preprint NN cord-340851-lnv8yi9l 180 3 not not RB cord-340851-lnv8yi9l 180 4 surprising surprising JJ cord-340851-lnv8yi9l 180 5 that that IN cord-340851-lnv8yi9l 180 6 our -PRON- PRP$ cord-340851-lnv8yi9l 180 7 model model NN cord-340851-lnv8yi9l 180 8 better well RBR cord-340851-lnv8yi9l 180 9 matched match VBD cord-340851-lnv8yi9l 180 10 the the DT cord-340851-lnv8yi9l 180 11 data datum NNS cord-340851-lnv8yi9l 180 12 with with IN cord-340851-lnv8yi9l 180 13 a a DT cord-340851-lnv8yi9l 180 14 slightly slightly RB cord-340851-lnv8yi9l 180 15 later later JJ cord-340851-lnv8yi9l 180 16 start start NN cord-340851-lnv8yi9l 180 17 date date NN cord-340851-lnv8yi9l 180 18 , , , cord-340851-lnv8yi9l 180 19 given give VBN cord-340851-lnv8yi9l 180 20 that that IN cord-340851-lnv8yi9l 180 21 the the DT cord-340851-lnv8yi9l 180 22 model model NN cord-340851-lnv8yi9l 180 23 did do VBD cord-340851-lnv8yi9l 180 24 not not RB cord-340851-lnv8yi9l 180 25 allow allow VB cord-340851-lnv8yi9l 180 26 for for IN cord-340851-lnv8yi9l 180 27 increases increase NNS cord-340851-lnv8yi9l 180 28 in in IN cord-340851-lnv8yi9l 180 29 importation importation NN cord-340851-lnv8yi9l 180 30 over over IN cord-340851-lnv8yi9l 180 31 time time NN cord-340851-lnv8yi9l 180 32 , , , cord-340851-lnv8yi9l 180 33 as as IN cord-340851-lnv8yi9l 180 34 likely likely RB cord-340851-lnv8yi9l 180 35 occurred occur VBD cord-340851-lnv8yi9l 180 36 [ [ -LRB- cord-340851-lnv8yi9l 180 37 41 41 CD cord-340851-lnv8yi9l 180 38 ] ] -RRB- cord-340851-lnv8yi9l 180 39 . . . cord-340851-lnv8yi9l 181 1 The the DT cord-340851-lnv8yi9l 181 2 calibration calibration NN cord-340851-lnv8yi9l 181 3 of of IN cord-340851-lnv8yi9l 181 4 u(t u(t NNP cord-340851-lnv8yi9l 181 5 ) ) -RRB- cord-340851-lnv8yi9l 181 6 was be VBD cord-340851-lnv8yi9l 181 7 consistent consistent JJ cord-340851-lnv8yi9l 181 8 with with IN cord-340851-lnv8yi9l 181 9 u(t u(t NNP cord-340851-lnv8yi9l 181 10 ) ) -RRB- cord-340851-lnv8yi9l 181 11 starting start VBG cord-340851-lnv8yi9l 181 12 at at IN cord-340851-lnv8yi9l 181 13 zero zero CD cord-340851-lnv8yi9l 181 14 , , , cord-340851-lnv8yi9l 181 15 reaching reach VBG cord-340851-lnv8yi9l 181 16 half half NN cord-340851-lnv8yi9l 181 17 of of IN cord-340851-lnv8yi9l 181 18 u u NNP cord-340851-lnv8yi9l 181 19 max max NNP cord-340851-lnv8yi9l 181 20 on on IN cord-340851-lnv8yi9l 181 21 April April NNP cord-340851-lnv8yi9l 181 22 4 4 CD cord-340851-lnv8yi9l 181 23 , , , cord-340851-lnv8yi9l 181 24 2020 2020 CD cord-340851-lnv8yi9l 181 25 , , , cord-340851-lnv8yi9l 181 26 and and CC cord-340851-lnv8yi9l 181 27 increasing increase VBG cord-340851-lnv8yi9l 181 28 by by IN cord-340851-lnv8yi9l 181 29 a a DT cord-340851-lnv8yi9l 181 30 maximum maximum NN cord-340851-lnv8yi9l 181 31 of of IN cord-340851-lnv8yi9l 181 32 0.075 0.075 CD cord-340851-lnv8yi9l 181 33 u u NNP cord-340851-lnv8yi9l 181 34 max max NN cord-340851-lnv8yi9l 181 35 per per IN cord-340851-lnv8yi9l 181 36 day day NN cord-340851-lnv8yi9l 181 37 around around IN cord-340851-lnv8yi9l 181 38 that that DT cord-340851-lnv8yi9l 181 39 time time NN cord-340851-lnv8yi9l 181 40 . . . cord-340851-lnv8yi9l 182 1 The the DT cord-340851-lnv8yi9l 182 2 timing timing NN cord-340851-lnv8yi9l 182 3 of of IN cord-340851-lnv8yi9l 182 4 these these DT cord-340851-lnv8yi9l 182 5 changes change NNS cord-340851-lnv8yi9l 182 6 is be VBZ cord-340851-lnv8yi9l 182 7 approximately approximately RB cord-340851-lnv8yi9l 182 8 two two CD cord-340851-lnv8yi9l 182 9 weeks week NNS cord-340851-lnv8yi9l 182 10 later later RB cord-340851-lnv8yi9l 182 11 than than IN cord-340851-lnv8yi9l 182 12 changes change NNS cord-340851-lnv8yi9l 182 13 in in IN cord-340851-lnv8yi9l 182 14 Google Google NNP cord-340851-lnv8yi9l 182 15 mobility mobility NN cord-340851-lnv8yi9l 182 16 data datum NNS cord-340851-lnv8yi9l 182 17 from from IN cord-340851-lnv8yi9l 182 18 the the DT cord-340851-lnv8yi9l 182 19 US US NNP cord-340851-lnv8yi9l 182 20 [ [ -LRB- cord-340851-lnv8yi9l 182 21 20 20 CD cord-340851-lnv8yi9l 182 22 ] ] -RRB- cord-340851-lnv8yi9l 182 23 , , , cord-340851-lnv8yi9l 182 24 which which WDT cord-340851-lnv8yi9l 182 25 may may MD cord-340851-lnv8yi9l 182 26 be be VB cord-340851-lnv8yi9l 182 27 a a DT cord-340851-lnv8yi9l 182 28 consequence consequence NN cord-340851-lnv8yi9l 182 29 of of IN cord-340851-lnv8yi9l 182 30 our -PRON- PRP$ cord-340851-lnv8yi9l 182 31 model model NN cord-340851-lnv8yi9l 182 32 moving move VBG cord-340851-lnv8yi9l 182 33 some some DT cord-340851-lnv8yi9l 182 34 individuals individual NNS cord-340851-lnv8yi9l 182 35 from from IN cord-340851-lnv8yi9l 182 36 exposure exposure NN cord-340851-lnv8yi9l 182 37 to to IN cord-340851-lnv8yi9l 182 38 death death NN cord-340851-lnv8yi9l 182 39 too too RB cord-340851-lnv8yi9l 182 40 quickly quickly RB cord-340851-lnv8yi9l 182 41 given give VBN cord-340851-lnv8yi9l 182 42 that that DT cord-340851-lnv8yi9l 182 43 residence residence NN cord-340851-lnv8yi9l 182 44 time time NN cord-340851-lnv8yi9l 182 45 in in IN cord-340851-lnv8yi9l 182 46 each each DT cord-340851-lnv8yi9l 182 47 compartment compartment NN cord-340851-lnv8yi9l 182 48 is be VBZ cord-340851-lnv8yi9l 182 49 exponentially exponentially RB cord-340851-lnv8yi9l 182 50 distributed distribute VBN cord-340851-lnv8yi9l 182 51 . . . cord-340851-lnv8yi9l 183 1 In in IN cord-340851-lnv8yi9l 183 2 general general JJ cord-340851-lnv8yi9l 183 3 , , , cord-340851-lnv8yi9l 183 4 we -PRON- PRP cord-340851-lnv8yi9l 183 5 do do VBP cord-340851-lnv8yi9l 183 6 not not RB cord-340851-lnv8yi9l 183 7 interpret interpret VB cord-340851-lnv8yi9l 183 8 any any DT cord-340851-lnv8yi9l 183 9 of of IN cord-340851-lnv8yi9l 183 10 the the DT cord-340851-lnv8yi9l 183 11 calibrated calibrate VBN cord-340851-lnv8yi9l 183 12 parameter parameter NN cord-340851-lnv8yi9l 183 13 values value NNS cord-340851-lnv8yi9l 183 14 as as IN cord-340851-lnv8yi9l 183 15 reliable reliable JJ cord-340851-lnv8yi9l 183 16 estimates estimate NNS cord-340851-lnv8yi9l 183 17 of of IN cord-340851-lnv8yi9l 183 18 empirical empirical JJ cord-340851-lnv8yi9l 183 19 quantities quantity NNS cord-340851-lnv8yi9l 183 20 . . . cord-340851-lnv8yi9l 184 1 Such such PDT cord-340851-lnv8yi9l 184 2 an an DT cord-340851-lnv8yi9l 184 3 interpretation interpretation NN cord-340851-lnv8yi9l 184 4 would would MD cord-340851-lnv8yi9l 184 5 require require VB cord-340851-lnv8yi9l 184 6 analyses analysis NNS cord-340851-lnv8yi9l 184 7 that that WDT cord-340851-lnv8yi9l 184 8 more more RBR cord-340851-lnv8yi9l 184 9 carefully carefully RB cord-340851-lnv8yi9l 184 10 account account VB cord-340851-lnv8yi9l 184 11 for for IN cord-340851-lnv8yi9l 184 12 data data NN cord-340851-lnv8yi9l 184 13 - - HYPH cord-340851-lnv8yi9l 184 14 generating generate VBG cord-340851-lnv8yi9l 184 15 processes process NNS cord-340851-lnv8yi9l 184 16 and and CC cord-340851-lnv8yi9l 184 17 sources source NNS cord-340851-lnv8yi9l 184 18 of of IN cord-340851-lnv8yi9l 184 19 uncertainty uncertainty NN cord-340851-lnv8yi9l 184 20 . . . cord-340851-lnv8yi9l 185 1 Rather rather RB cord-340851-lnv8yi9l 185 2 , , , cord-340851-lnv8yi9l 185 3 our -PRON- PRP$ cord-340851-lnv8yi9l 185 4 objective objective NN cord-340851-lnv8yi9l 185 5 in in IN cord-340851-lnv8yi9l 185 6 this this DT cord-340851-lnv8yi9l 185 7 calibration calibration NN cord-340851-lnv8yi9l 185 8 exercise exercise NN cord-340851-lnv8yi9l 185 9 was be VBD cord-340851-lnv8yi9l 185 10 to to TO cord-340851-lnv8yi9l 185 11 ensure ensure VB cord-340851-lnv8yi9l 185 12 that that IN cord-340851-lnv8yi9l 185 13 the the DT cord-340851-lnv8yi9l 185 14 model model NN cord-340851-lnv8yi9l 185 15 's 's POS cord-340851-lnv8yi9l 185 16 behavior behavior NN cord-340851-lnv8yi9l 185 17 is be VBZ cord-340851-lnv8yi9l 185 18 reasonably reasonably RB cord-340851-lnv8yi9l 185 19 consistent consistent JJ cord-340851-lnv8yi9l 185 20 with with IN cord-340851-lnv8yi9l 185 21 empirical empirical JJ cord-340851-lnv8yi9l 185 22 data datum NNS cord-340851-lnv8yi9l 185 23 , , , cord-340851-lnv8yi9l 185 24 which which WDT cord-340851-lnv8yi9l 185 25 we -PRON- PRP cord-340851-lnv8yi9l 185 26 feel feel VBP cord-340851-lnv8yi9l 185 27 was be VBD cord-340851-lnv8yi9l 185 28 accomplished accomplish VBN cord-340851-lnv8yi9l 185 29 . . . cord-340851-lnv8yi9l 185 30 _SP cord-340851-lnv8yi9l 186 1 For for IN cord-340851-lnv8yi9l 186 2 our -PRON- PRP$ cord-340851-lnv8yi9l 186 3 main main JJ cord-340851-lnv8yi9l 186 4 results result NNS cord-340851-lnv8yi9l 186 5 , , , cord-340851-lnv8yi9l 186 6 we -PRON- PRP cord-340851-lnv8yi9l 186 7 obtained obtain VBD cord-340851-lnv8yi9l 186 8 solutions solution NNS cord-340851-lnv8yi9l 186 9 to to IN cord-340851-lnv8yi9l 186 10 u u NNP cord-340851-lnv8yi9l 186 11 * * NFP cord-340851-lnv8yi9l 186 12 ( ( -LRB- cord-340851-lnv8yi9l 186 13 t t NN cord-340851-lnv8yi9l 186 14 ) ) -RRB- cord-340851-lnv8yi9l 186 15 under under IN cord-340851-lnv8yi9l 186 16 a a DT cord-340851-lnv8yi9l 186 17 total total NN cord-340851-lnv8yi9l 186 18 of of IN cord-340851-lnv8yi9l 186 19 126 126 CD cord-340851-lnv8yi9l 186 20 parameter parameter NN cord-340851-lnv8yi9l 186 21 combinations combination NNS cord-340851-lnv8yi9l 186 22 , , , cord-340851-lnv8yi9l 186 23 crossing cross VBG cord-340851-lnv8yi9l 186 24 the the DT cord-340851-lnv8yi9l 186 25 18 18 CD cord-340851-lnv8yi9l 186 26 parameter parameter NN cord-340851-lnv8yi9l 186 27 sets set NNS cord-340851-lnv8yi9l 186 28 in in IN cord-340851-lnv8yi9l 186 29 Table Table NNP cord-340851-lnv8yi9l 186 30 3 3 CD cord-340851-lnv8yi9l 186 31 with with IN cord-340851-lnv8yi9l 186 32 seven seven CD cord-340851-lnv8yi9l 186 33 values value NNS cord-340851-lnv8yi9l 186 34 of of IN cord-340851-lnv8yi9l 186 35 c c NN cord-340851-lnv8yi9l 186 36 spanning span VBG cord-340851-lnv8yi9l 186 37 10 10 CD cord-340851-lnv8yi9l 186 38 −12 −12 NN cord-340851-lnv8yi9l 186 39 to to IN cord-340851-lnv8yi9l 186 40 10 10 CD cord-340851-lnv8yi9l 186 41 −6 −6 NNS cord-340851-lnv8yi9l 186 42 by by IN cord-340851-lnv8yi9l 186 43 factors factor NNS cord-340851-lnv8yi9l 186 44 of of IN cord-340851-lnv8yi9l 186 45 ten ten CD cord-340851-lnv8yi9l 186 46 . . . cord-340851-lnv8yi9l 187 1 In in IN cord-340851-lnv8yi9l 187 2 one one CD cord-340851-lnv8yi9l 187 3 representative representative JJ cord-340851-lnv8yi9l 187 4 example example NN cord-340851-lnv8yi9l 187 5 ( ( -LRB- cord-340851-lnv8yi9l 187 6 Figure Figure NNP cord-340851-lnv8yi9l 187 7 3 3 CD cord-340851-lnv8yi9l 187 8 , , , cord-340851-lnv8yi9l 187 9 left left RB cord-340851-lnv8yi9l 187 10 ) ) -RRB- cord-340851-lnv8yi9l 187 11 , , , cord-340851-lnv8yi9l 187 12 we -PRON- PRP cord-340851-lnv8yi9l 187 13 observed observe VBD cord-340851-lnv8yi9l 187 14 that that IN cord-340851-lnv8yi9l 187 15 solutions solution NNS cord-340851-lnv8yi9l 187 16 of of IN cord-340851-lnv8yi9l 187 17 u u NNP cord-340851-lnv8yi9l 187 18 * * NFP cord-340851-lnv8yi9l 187 19 ( ( -LRB- cord-340851-lnv8yi9l 187 20 t t NN cord-340851-lnv8yi9l 187 21 ) ) -RRB- cord-340851-lnv8yi9l 187 22 converged converge VBD cord-340851-lnv8yi9l 187 23 to to IN cord-340851-lnv8yi9l 187 24 a a DT cord-340851-lnv8yi9l 187 25 set set NN cord-340851-lnv8yi9l 187 26 of of IN cord-340851-lnv8yi9l 187 27 similar similar JJ cord-340851-lnv8yi9l 187 28 solutions solution NNS cord-340851-lnv8yi9l 187 29 after after IN cord-340851-lnv8yi9l 187 30 several several JJ cord-340851-lnv8yi9l 187 31 hundred hundred CD cord-340851-lnv8yi9l 187 32 iterations iteration NNS cord-340851-lnv8yi9l 187 33 . . . cord-340851-lnv8yi9l 188 1 As as IN cord-340851-lnv8yi9l 188 2 expected expect VBN cord-340851-lnv8yi9l 188 3 , , , cord-340851-lnv8yi9l 188 4 the the DT cord-340851-lnv8yi9l 188 5 objective objective JJ cord-340851-lnv8yi9l 188 6 functional functional JJ cord-340851-lnv8yi9l 188 7 decreased decrease VBD cord-340851-lnv8yi9l 188 8 during during IN cord-340851-lnv8yi9l 188 9 those those DT cord-340851-lnv8yi9l 188 10 initial initial JJ cord-340851-lnv8yi9l 188 11 iterations iteration NNS cord-340851-lnv8yi9l 188 12 and and CC cord-340851-lnv8yi9l 188 13 remained remain VBD cord-340851-lnv8yi9l 188 14 low low JJ cord-340851-lnv8yi9l 188 15 thereafter thereafter RB cord-340851-lnv8yi9l 188 16 . . . cord-340851-lnv8yi9l 189 1 CC CC NNP cord-340851-lnv8yi9l 189 2 - - : cord-340851-lnv8yi9l 189 3 BY by IN cord-340851-lnv8yi9l 189 4 4.0 4.0 CD cord-340851-lnv8yi9l 189 5 International international JJ cord-340851-lnv8yi9l 189 6 license license NN cord-340851-lnv8yi9l 190 1 It -PRON- PRP cord-340851-lnv8yi9l 190 2 is be VBZ cord-340851-lnv8yi9l 190 3 made make VBN cord-340851-lnv8yi9l 190 4 available available JJ cord-340851-lnv8yi9l 190 5 under under IN cord-340851-lnv8yi9l 190 6 a a DT cord-340851-lnv8yi9l 191 1 is be VBZ cord-340851-lnv8yi9l 191 2 the the DT cord-340851-lnv8yi9l 191 3 author author NN cord-340851-lnv8yi9l 191 4 / / SYM cord-340851-lnv8yi9l 191 5 funder funder NN cord-340851-lnv8yi9l 191 6 , , , cord-340851-lnv8yi9l 191 7 who who WP cord-340851-lnv8yi9l 191 8 has have VBZ cord-340851-lnv8yi9l 191 9 granted grant VBN cord-340851-lnv8yi9l 191 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 191 11 a a DT cord-340851-lnv8yi9l 191 12 license license NN cord-340851-lnv8yi9l 191 13 to to TO cord-340851-lnv8yi9l 191 14 display display VB cord-340851-lnv8yi9l 191 15 the the DT cord-340851-lnv8yi9l 191 16 preprint preprint NN cord-340851-lnv8yi9l 191 17 in in IN cord-340851-lnv8yi9l 191 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 191 19 . . . cord-340851-lnv8yi9l 192 1 The the DT cord-340851-lnv8yi9l 192 2 copyright copyright NN cord-340851-lnv8yi9l 192 3 holder holder NN cord-340851-lnv8yi9l 192 4 for for IN cord-340851-lnv8yi9l 192 5 this this DT cord-340851-lnv8yi9l 192 6 preprint preprint NN cord-340851-lnv8yi9l 192 7 this this DT cord-340851-lnv8yi9l 192 8 version version NN cord-340851-lnv8yi9l 192 9 posted post VBN cord-340851-lnv8yi9l 192 10 April April NNP cord-340851-lnv8yi9l 192 11 23 23 CD cord-340851-lnv8yi9l 192 12 , , , cord-340851-lnv8yi9l 192 13 2020 2020 CD cord-340851-lnv8yi9l 192 14 . . . cord-340851-lnv8yi9l 193 1 ( ( -LRB- cord-340851-lnv8yi9l 193 2 Figure figure NN cord-340851-lnv8yi9l 193 3 3 3 CD cord-340851-lnv8yi9l 193 4 , , , cord-340851-lnv8yi9l 193 5 right right JJ cord-340851-lnv8yi9l 193 6 ) ) -RRB- cord-340851-lnv8yi9l 193 7 . . . cord-340851-lnv8yi9l 194 1 To to TO cord-340851-lnv8yi9l 194 2 assess assess VB cord-340851-lnv8yi9l 194 3 convergence convergence NN cord-340851-lnv8yi9l 194 4 by by IN cord-340851-lnv8yi9l 194 5 the the DT cord-340851-lnv8yi9l 194 6 statistic statistic NN cord-340851-lnv8yi9l 194 7 in in IN cord-340851-lnv8yi9l 194 8 eqn eqn NN cord-340851-lnv8yi9l 194 9 . . . cord-340851-lnv8yi9l 195 1 ( ( -LRB- cord-340851-lnv8yi9l 195 2 11 11 CD cord-340851-lnv8yi9l 195 3 ) ) -RRB- cord-340851-lnv8yi9l 195 4 , , , cord-340851-lnv8yi9l 195 5 we -PRON- PRP cord-340851-lnv8yi9l 195 6 selected select VBD cord-340851-lnv8yi9l 195 7 the the DT cord-340851-lnv8yi9l 195 8 iterations iteration NNS cord-340851-lnv8yi9l 195 9 with with IN cord-340851-lnv8yi9l 195 10 the the DT cord-340851-lnv8yi9l 195 11 ten ten CD cord-340851-lnv8yi9l 195 12 lowest low JJS cord-340851-lnv8yi9l 195 13 values value NNS cord-340851-lnv8yi9l 195 14 of of IN cord-340851-lnv8yi9l 195 15 J(u J(u NNP cord-340851-lnv8yi9l 195 16 ) ) -RRB- cord-340851-lnv8yi9l 195 17 in in IN cord-340851-lnv8yi9l 195 18 the the DT cord-340851-lnv8yi9l 195 19 last last JJ cord-340851-lnv8yi9l 195 20 100 100 CD cord-340851-lnv8yi9l 195 21 iterations iteration NNS cord-340851-lnv8yi9l 195 22 . . . cord-340851-lnv8yi9l 196 1 Of of IN cord-340851-lnv8yi9l 196 2 126 126 CD cord-340851-lnv8yi9l 196 3 parameter parameter NN cord-340851-lnv8yi9l 196 4 combinations combination NNS cord-340851-lnv8yi9l 196 5 , , , cord-340851-lnv8yi9l 196 6 78 78 CD cord-340851-lnv8yi9l 196 7 % % NN cord-340851-lnv8yi9l 196 8 had have VBD cord-340851-lnv8yi9l 196 9 final final JJ cord-340851-lnv8yi9l 196 10 solutions solution NNS cord-340851-lnv8yi9l 196 11 of of IN cord-340851-lnv8yi9l 196 12 u u NNP cord-340851-lnv8yi9l 196 13 * * NFP cord-340851-lnv8yi9l 196 14 ( ( -LRB- cord-340851-lnv8yi9l 196 15 t t NN cord-340851-lnv8yi9l 196 16 ) ) -RRB- cord-340851-lnv8yi9l 196 17 with with IN cord-340851-lnv8yi9l 196 18 convergence convergence NN cord-340851-lnv8yi9l 196 19 statistics statistic NNS cord-340851-lnv8yi9l 196 20 below below IN cord-340851-lnv8yi9l 196 21 10 10 CD cord-340851-lnv8yi9l 196 22 −5 −5 NNS cord-340851-lnv8yi9l 196 23 , , , cord-340851-lnv8yi9l 196 24 94 94 CD cord-340851-lnv8yi9l 196 25 % % NN cord-340851-lnv8yi9l 196 26 below below IN cord-340851-lnv8yi9l 196 27 10 10 CD cord-340851-lnv8yi9l 196 28 −2 −2 NN cord-340851-lnv8yi9l 196 29 , , , cord-340851-lnv8yi9l 196 30 and and CC cord-340851-lnv8yi9l 196 31 all all DT cord-340851-lnv8yi9l 196 32 below below IN cord-340851-lnv8yi9l 196 33 10 10 CD cord-340851-lnv8yi9l 196 34 −1 −1 NNP cord-340851-lnv8yi9l 196 35 . . . cord-340851-lnv8yi9l 197 1 Comparing compare VBG cord-340851-lnv8yi9l 197 2 values value NNS cord-340851-lnv8yi9l 197 3 of of IN cord-340851-lnv8yi9l 197 4 the the DT cord-340851-lnv8yi9l 197 5 two two CD cord-340851-lnv8yi9l 197 6 components component NNS cord-340851-lnv8yi9l 197 7 of of IN cord-340851-lnv8yi9l 197 8 the the DT cord-340851-lnv8yi9l 197 9 objective objective JJ cord-340851-lnv8yi9l 197 10 functional functional JJ cord-340851-lnv8yi9l 197 11 , , , cord-340851-lnv8yi9l 197 12 t1 t1 NN cord-340851-lnv8yi9l 197 13 t0 t0 NNP cord-340851-lnv8yi9l 197 14 D(t D(t NNP cord-340851-lnv8yi9l 197 15 ) ) -RRB- cord-340851-lnv8yi9l 197 16 2 2 CD cord-340851-lnv8yi9l 197 17 dt dt NN cord-340851-lnv8yi9l 197 18 and and CC cord-340851-lnv8yi9l 197 19 t1 t1 NN cord-340851-lnv8yi9l 197 20 t0 t0 NNP cord-340851-lnv8yi9l 197 21 u(t u(t NNP cord-340851-lnv8yi9l 197 22 ) ) -RRB- cord-340851-lnv8yi9l 198 1 2 2 CD cord-340851-lnv8yi9l 198 2 dt dt NN cord-340851-lnv8yi9l 198 3 , , , cord-340851-lnv8yi9l 198 4 across across IN cord-340851-lnv8yi9l 198 5 different different JJ cord-340851-lnv8yi9l 198 6 parameter parameter NN cord-340851-lnv8yi9l 198 7 values value NNS cord-340851-lnv8yi9l 198 8 provides provide VBZ cord-340851-lnv8yi9l 198 9 insight insight NN cord-340851-lnv8yi9l 198 10 into into IN cord-340851-lnv8yi9l 198 11 the the DT cord-340851-lnv8yi9l 198 12 range range NN cord-340851-lnv8yi9l 198 13 of of IN cord-340851-lnv8yi9l 198 14 behavior behavior NN cord-340851-lnv8yi9l 198 15 of of IN cord-340851-lnv8yi9l 198 16 the the DT cord-340851-lnv8yi9l 198 17 model model NN cord-340851-lnv8yi9l 198 18 and and CC cord-340851-lnv8yi9l 198 19 its -PRON- PRP$ cord-340851-lnv8yi9l 198 20 response response NN cord-340851-lnv8yi9l 198 21 to to TO cord-340851-lnv8yi9l 198 22 control control VB cord-340851-lnv8yi9l 198 23 . . . cord-340851-lnv8yi9l 199 1 Because because IN cord-340851-lnv8yi9l 199 2 they -PRON- PRP cord-340851-lnv8yi9l 199 3 are be VBP cord-340851-lnv8yi9l 199 4 similar similar JJ cord-340851-lnv8yi9l 199 5 to to IN cord-340851-lnv8yi9l 199 6 the the DT cord-340851-lnv8yi9l 199 7 components component NNS cord-340851-lnv8yi9l 199 8 of of IN cord-340851-lnv8yi9l 199 9 the the DT cord-340851-lnv8yi9l 199 10 objective objective JJ cord-340851-lnv8yi9l 199 11 functional functional JJ cord-340851-lnv8yi9l 199 12 but but CC cord-340851-lnv8yi9l 199 13 more more RBR cord-340851-lnv8yi9l 199 14 easily easily RB cord-340851-lnv8yi9l 199 15 interpretable interpretable JJ cord-340851-lnv8yi9l 199 16 , , , cord-340851-lnv8yi9l 199 17 we -PRON- PRP cord-340851-lnv8yi9l 199 18 describe describe VBP cord-340851-lnv8yi9l 199 19 effects effect NNS cord-340851-lnv8yi9l 199 20 of of IN cord-340851-lnv8yi9l 199 21 model model NN cord-340851-lnv8yi9l 199 22 parameters parameter NNS cord-340851-lnv8yi9l 199 23 on on IN cord-340851-lnv8yi9l 199 24 t1 t1 NN cord-340851-lnv8yi9l 199 25 t0 t0 NNP cord-340851-lnv8yi9l 199 26 D(t)dt D(t)dt NNP cord-340851-lnv8yi9l 199 27 ( ( -LRB- cord-340851-lnv8yi9l 199 28 cumulative cumulative JJ cord-340851-lnv8yi9l 199 29 deaths death NNS cord-340851-lnv8yi9l 199 30 ) ) -RRB- cord-340851-lnv8yi9l 199 31 and and CC cord-340851-lnv8yi9l 200 1 t1 t1 NNP cord-340851-lnv8yi9l 200 2 t0 t0 NNP cord-340851-lnv8yi9l 200 3 u(t)dt u(t)dt ADD cord-340851-lnv8yi9l 200 4 ( ( -LRB- cord-340851-lnv8yi9l 200 5 cumulative cumulative JJ cord-340851-lnv8yi9l 200 6 time time NN cord-340851-lnv8yi9l 200 7 under under IN cord-340851-lnv8yi9l 200 8 control control NN cord-340851-lnv8yi9l 200 9 ) ) -RRB- cord-340851-lnv8yi9l 200 10 . . . cord-340851-lnv8yi9l 201 1 The the DT cord-340851-lnv8yi9l 201 2 parameter parameter NN cord-340851-lnv8yi9l 201 3 c c NN cord-340851-lnv8yi9l 201 4 , , , cord-340851-lnv8yi9l 201 5 which which WDT cord-340851-lnv8yi9l 201 6 controls control VBZ cord-340851-lnv8yi9l 201 7 the the DT cord-340851-lnv8yi9l 201 8 weight weight NN cord-340851-lnv8yi9l 201 9 of of IN cord-340851-lnv8yi9l 201 10 the the DT cord-340851-lnv8yi9l 201 11 two two CD cord-340851-lnv8yi9l 201 12 terms term NNS cord-340851-lnv8yi9l 201 13 in in IN cord-340851-lnv8yi9l 201 14 J(u J(u NNP cord-340851-lnv8yi9l 201 15 ) ) -RRB- cord-340851-lnv8yi9l 201 16 , , , cord-340851-lnv8yi9l 201 17 led lead VBD cord-340851-lnv8yi9l 201 18 to to IN cord-340851-lnv8yi9l 201 19 a a DT cord-340851-lnv8yi9l 201 20 transition transition NN cord-340851-lnv8yi9l 201 21 from from IN cord-340851-lnv8yi9l 201 22 minimizing minimize VBG cord-340851-lnv8yi9l 201 23 cumulative cumulative JJ cord-340851-lnv8yi9l 201 24 deaths death NNS cord-340851-lnv8yi9l 201 25 to to IN cord-340851-lnv8yi9l 201 26 minimizing minimize VBG cord-340851-lnv8yi9l 201 27 cumulative cumulative JJ cord-340851-lnv8yi9l 201 28 time time NN cord-340851-lnv8yi9l 201 29 spent spend VBN cord-340851-lnv8yi9l 201 30 under under IN cord-340851-lnv8yi9l 201 31 control control NN cord-340851-lnv8yi9l 201 32 as as IN cord-340851-lnv8yi9l 201 33 it -PRON- PRP cord-340851-lnv8yi9l 201 34 varied vary VBD cord-340851-lnv8yi9l 201 35 from from IN cord-340851-lnv8yi9l 201 36 10 10 CD cord-340851-lnv8yi9l 201 37 −9 −9 NN cord-340851-lnv8yi9l 201 38 to to IN cord-340851-lnv8yi9l 201 39 10 10 CD cord-340851-lnv8yi9l 201 40 −6 −6 NNS cord-340851-lnv8yi9l 202 1 ( ( -LRB- cord-340851-lnv8yi9l 202 2 Figure figure NN cord-340851-lnv8yi9l 202 3 4 4 CD cord-340851-lnv8yi9l 202 4 ) ) -RRB- cord-340851-lnv8yi9l 202 5 . . . cord-340851-lnv8yi9l 203 1 The the DT cord-340851-lnv8yi9l 203 2 parameters parameter NNS cord-340851-lnv8yi9l 203 3 R r NN cord-340851-lnv8yi9l 203 4 0 0 CD cord-340851-lnv8yi9l 203 5 and and CC cord-340851-lnv8yi9l 203 6 u u NNP cord-340851-lnv8yi9l 203 7 max max NNP cord-340851-lnv8yi9l 203 8 both both DT cord-340851-lnv8yi9l 203 9 influenced influence VBD cord-340851-lnv8yi9l 203 10 the the DT cord-340851-lnv8yi9l 203 11 extent extent NN cord-340851-lnv8yi9l 203 12 to to TO cord-340851-lnv8yi9l 203 13 which which WDT cord-340851-lnv8yi9l 203 14 cumulative cumulative JJ cord-340851-lnv8yi9l 203 15 deaths death NNS cord-340851-lnv8yi9l 203 16 could could MD cord-340851-lnv8yi9l 203 17 be be VB cord-340851-lnv8yi9l 203 18 minimized minimize VBN cord-340851-lnv8yi9l 203 19 . . . cord-340851-lnv8yi9l 204 1 With with IN cord-340851-lnv8yi9l 204 2 a a DT cord-340851-lnv8yi9l 204 3 high high JJ cord-340851-lnv8yi9l 204 4 value value NN cord-340851-lnv8yi9l 204 5 of of IN cord-340851-lnv8yi9l 204 6 u u NNP cord-340851-lnv8yi9l 204 7 max max NN cord-340851-lnv8yi9l 204 8 , , , cord-340851-lnv8yi9l 204 9 deaths death NNS cord-340851-lnv8yi9l 204 10 could could MD cord-340851-lnv8yi9l 204 11 be be VB cord-340851-lnv8yi9l 204 12 kept keep VBN cord-340851-lnv8yi9l 204 13 relatively relatively RB cord-340851-lnv8yi9l 204 14 low low JJ cord-340851-lnv8yi9l 204 15 across across IN cord-340851-lnv8yi9l 204 16 all all DT cord-340851-lnv8yi9l 204 17 values value NNS cord-340851-lnv8yi9l 204 18 of of IN cord-340851-lnv8yi9l 204 19 R r NN cord-340851-lnv8yi9l 204 20 0 0 CD cord-340851-lnv8yi9l 204 21 explored explore VBN cord-340851-lnv8yi9l 204 22 , , , cord-340851-lnv8yi9l 204 23 provided provide VBN cord-340851-lnv8yi9l 204 24 that that IN cord-340851-lnv8yi9l 204 25 c c NN cord-340851-lnv8yi9l 204 26 ≤ ≤ NNP cord-340851-lnv8yi9l 204 27 10 10 CD cord-340851-lnv8yi9l 204 28 −10 −10 NNP cord-340851-lnv8yi9l 204 29 . . . cord-340851-lnv8yi9l 205 1 With with IN cord-340851-lnv8yi9l 205 2 a a DT cord-340851-lnv8yi9l 205 3 low low JJ cord-340851-lnv8yi9l 205 4 value value NN cord-340851-lnv8yi9l 205 5 of of IN cord-340851-lnv8yi9l 205 6 u u NNP cord-340851-lnv8yi9l 205 7 max max NNP cord-340851-lnv8yi9l 205 8 and and CC cord-340851-lnv8yi9l 205 9 a a DT cord-340851-lnv8yi9l 205 10 high high JJ cord-340851-lnv8yi9l 205 11 value value NN cord-340851-lnv8yi9l 205 12 of of IN cord-340851-lnv8yi9l 205 13 R r NN cord-340851-lnv8yi9l 205 14 0 0 CD cord-340851-lnv8yi9l 205 15 , , , cord-340851-lnv8yi9l 205 16 cumulative cumulative JJ cord-340851-lnv8yi9l 205 17 deaths death NNS cord-340851-lnv8yi9l 205 18 could could MD cord-340851-lnv8yi9l 205 19 only only RB cord-340851-lnv8yi9l 205 20 be be VB cord-340851-lnv8yi9l 205 21 reduced reduce VBN cord-340851-lnv8yi9l 205 22 by by IN cord-340851-lnv8yi9l 205 23 around around IN cord-340851-lnv8yi9l 205 24 10 10 CD cord-340851-lnv8yi9l 205 25 % % NN cord-340851-lnv8yi9l 205 26 as as IN cord-340851-lnv8yi9l 205 27 c c NNP cord-340851-lnv8yi9l 205 28 varied vary VBN cord-340851-lnv8yi9l 205 29 across across IN cord-340851-lnv8yi9l 205 30 its -PRON- PRP$ cord-340851-lnv8yi9l 205 31 entire entire JJ cord-340851-lnv8yi9l 205 32 range range NN cord-340851-lnv8yi9l 205 33 from from IN cord-340851-lnv8yi9l 205 34 10 10 CD cord-340851-lnv8yi9l 205 35 −12 −12 NN cord-340851-lnv8yi9l 205 36 to to IN cord-340851-lnv8yi9l 205 37 10 10 CD cord-340851-lnv8yi9l 205 38 −6 −6 NNS cord-340851-lnv8yi9l 205 39 . . . cord-340851-lnv8yi9l 206 1 The the DT cord-340851-lnv8yi9l 206 2 parameter parameter NN cord-340851-lnv8yi9l 206 3 ω ω NN cord-340851-lnv8yi9l 206 4 had have VBD cord-340851-lnv8yi9l 206 5 essentially essentially RB cord-340851-lnv8yi9l 206 6 no no DT cord-340851-lnv8yi9l 206 7 influence influence NN cord-340851-lnv8yi9l 206 8 on on IN cord-340851-lnv8yi9l 206 9 the the DT cord-340851-lnv8yi9l 206 10 components component NNS cord-340851-lnv8yi9l 206 11 of of IN cord-340851-lnv8yi9l 206 12 the the DT cord-340851-lnv8yi9l 206 13 objective objective JJ cord-340851-lnv8yi9l 206 14 functional functional JJ cord-340851-lnv8yi9l 206 15 ( ( -LRB- cord-340851-lnv8yi9l 206 16 Figure figure NN cord-340851-lnv8yi9l 206 17 4 4 CD cord-340851-lnv8yi9l 206 18 ) ) -RRB- cord-340851-lnv8yi9l 206 19 . . . cord-340851-lnv8yi9l 207 1 We -PRON- PRP cord-340851-lnv8yi9l 207 2 first first RB cord-340851-lnv8yi9l 207 3 consider consider VBP cord-340851-lnv8yi9l 207 4 the the DT cord-340851-lnv8yi9l 207 5 scenario scenario NN cord-340851-lnv8yi9l 207 6 where where WRB cord-340851-lnv8yi9l 207 7 R r NN cord-340851-lnv8yi9l 207 8 0 0 CD cord-340851-lnv8yi9l 207 9 = = SYM cord-340851-lnv8yi9l 207 10 3 3 CD cord-340851-lnv8yi9l 207 11 and and CC cord-340851-lnv8yi9l 207 12 u u NNP cord-340851-lnv8yi9l 207 13 max max NN cord-340851-lnv8yi9l 207 14 = = SYM cord-340851-lnv8yi9l 207 15 0.9 0.9 CD cord-340851-lnv8yi9l 207 16 , , , cord-340851-lnv8yi9l 207 17 because because IN cord-340851-lnv8yi9l 207 18 those those DT cord-340851-lnv8yi9l 207 19 are be VBP cord-340851-lnv8yi9l 207 20 the the DT cord-340851-lnv8yi9l 207 21 conditions condition NNS cord-340851-lnv8yi9l 207 22 under under IN cord-340851-lnv8yi9l 207 23 which which WDT cord-340851-lnv8yi9l 207 24 control control NN cord-340851-lnv8yi9l 207 25 has have VBZ cord-340851-lnv8yi9l 207 26 the the DT cord-340851-lnv8yi9l 207 27 greatest great JJS cord-340851-lnv8yi9l 207 28 potential potential NN cord-340851-lnv8yi9l 207 29 to to TO cord-340851-lnv8yi9l 207 30 influence influence VB cord-340851-lnv8yi9l 207 31 . . . cord-340851-lnv8yi9l 208 1 CC CC NNP cord-340851-lnv8yi9l 208 2 - - : cord-340851-lnv8yi9l 208 3 BY by IN cord-340851-lnv8yi9l 208 4 4.0 4.0 CD cord-340851-lnv8yi9l 208 5 International international JJ cord-340851-lnv8yi9l 208 6 license license NN cord-340851-lnv8yi9l 209 1 It -PRON- PRP cord-340851-lnv8yi9l 209 2 is be VBZ cord-340851-lnv8yi9l 209 3 made make VBN cord-340851-lnv8yi9l 209 4 available available JJ cord-340851-lnv8yi9l 209 5 under under IN cord-340851-lnv8yi9l 209 6 a a DT cord-340851-lnv8yi9l 210 1 is be VBZ cord-340851-lnv8yi9l 210 2 the the DT cord-340851-lnv8yi9l 210 3 author author NN cord-340851-lnv8yi9l 210 4 / / SYM cord-340851-lnv8yi9l 210 5 funder funder NN cord-340851-lnv8yi9l 210 6 , , , cord-340851-lnv8yi9l 210 7 who who WP cord-340851-lnv8yi9l 210 8 has have VBZ cord-340851-lnv8yi9l 210 9 granted grant VBN cord-340851-lnv8yi9l 210 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 210 11 a a DT cord-340851-lnv8yi9l 210 12 license license NN cord-340851-lnv8yi9l 210 13 to to TO cord-340851-lnv8yi9l 210 14 display display VB cord-340851-lnv8yi9l 210 15 the the DT cord-340851-lnv8yi9l 210 16 preprint preprint NN cord-340851-lnv8yi9l 210 17 in in IN cord-340851-lnv8yi9l 210 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 210 19 . . . cord-340851-lnv8yi9l 211 1 The the DT cord-340851-lnv8yi9l 211 2 copyright copyright NN cord-340851-lnv8yi9l 211 3 holder holder NN cord-340851-lnv8yi9l 211 4 for for IN cord-340851-lnv8yi9l 211 5 this this DT cord-340851-lnv8yi9l 211 6 preprint preprint NN cord-340851-lnv8yi9l 211 7 this this DT cord-340851-lnv8yi9l 211 8 version version NN cord-340851-lnv8yi9l 211 9 posted post VBN cord-340851-lnv8yi9l 211 10 April April NNP cord-340851-lnv8yi9l 211 11 23 23 CD cord-340851-lnv8yi9l 211 12 , , , cord-340851-lnv8yi9l 211 13 2020 2020 CD cord-340851-lnv8yi9l 211 14 . . . cord-340851-lnv8yi9l 212 1 the the DT cord-340851-lnv8yi9l 212 2 pandemic pandemic NN cord-340851-lnv8yi9l 212 3 . . . cord-340851-lnv8yi9l 213 1 Under under IN cord-340851-lnv8yi9l 213 2 c c NN cord-340851-lnv8yi9l 213 3 = = SYM cord-340851-lnv8yi9l 213 4 10 10 CD cord-340851-lnv8yi9l 213 5 −12 −12 NN cord-340851-lnv8yi9l 213 6 , , , cord-340851-lnv8yi9l 213 7 u u NNP cord-340851-lnv8yi9l 213 8 * * NFP cord-340851-lnv8yi9l 213 9 ( ( -LRB- cord-340851-lnv8yi9l 213 10 t t NN cord-340851-lnv8yi9l 213 11 ) ) -RRB- cord-340851-lnv8yi9l 213 12 remains remain VBZ cord-340851-lnv8yi9l 213 13 at at IN cord-340851-lnv8yi9l 213 14 u u NNP cord-340851-lnv8yi9l 213 15 max max NNP cord-340851-lnv8yi9l 213 16 until until IN cord-340851-lnv8yi9l 213 17 late late JJ cord-340851-lnv8yi9l 213 18 June June NNP cord-340851-lnv8yi9l 213 19 2020 2020 CD cord-340851-lnv8yi9l 213 20 , , , cord-340851-lnv8yi9l 213 21 after after IN cord-340851-lnv8yi9l 213 22 which which WDT cord-340851-lnv8yi9l 213 23 it -PRON- PRP cord-340851-lnv8yi9l 213 24 settles settle VBZ cord-340851-lnv8yi9l 213 25 down down RP cord-340851-lnv8yi9l 213 26 to to IN cord-340851-lnv8yi9l 213 27 around around IN cord-340851-lnv8yi9l 213 28 75 75 CD cord-340851-lnv8yi9l 213 29 % % NN cord-340851-lnv8yi9l 213 30 of of IN cord-340851-lnv8yi9l 213 31 u u NNP cord-340851-lnv8yi9l 213 32 max max NNP cord-340851-lnv8yi9l 213 33 until until IN cord-340851-lnv8yi9l 213 34 late late JJ cord-340851-lnv8yi9l 213 35 2021 2021 CD cord-340851-lnv8yi9l 214 1 ( ( -LRB- cord-340851-lnv8yi9l 214 2 Figure figure NN cord-340851-lnv8yi9l 214 3 5 5 CD cord-340851-lnv8yi9l 214 4 ) ) -RRB- cord-340851-lnv8yi9l 214 5 . . . cord-340851-lnv8yi9l 215 1 This this DT cord-340851-lnv8yi9l 215 2 results result VBZ cord-340851-lnv8yi9l 215 3 in in IN cord-340851-lnv8yi9l 215 4 hospitalizations hospitalization NNS cord-340851-lnv8yi9l 215 5 dropping drop VBG cord-340851-lnv8yi9l 215 6 from from IN cord-340851-lnv8yi9l 215 7 their -PRON- PRP$ cord-340851-lnv8yi9l 215 8 peak peak NN cord-340851-lnv8yi9l 215 9 in in IN cord-340851-lnv8yi9l 215 10 April April NNP cord-340851-lnv8yi9l 215 11 2020 2020 CD cord-340851-lnv8yi9l 215 12 and and CC cord-340851-lnv8yi9l 215 13 remaining remain VBG cord-340851-lnv8yi9l 215 14 very very RB cord-340851-lnv8yi9l 215 15 low low JJ cord-340851-lnv8yi9l 215 16 through through IN cord-340851-lnv8yi9l 215 17 2021 2021 CD cord-340851-lnv8yi9l 215 18 . . . cord-340851-lnv8yi9l 216 1 The the DT cord-340851-lnv8yi9l 216 2 susceptible susceptible JJ cord-340851-lnv8yi9l 216 3 population population NN cord-340851-lnv8yi9l 216 4 remains remain VBZ cord-340851-lnv8yi9l 216 5 very very RB cord-340851-lnv8yi9l 216 6 high high JJ cord-340851-lnv8yi9l 216 7 and and CC cord-340851-lnv8yi9l 216 8 only only RB cord-340851-lnv8yi9l 216 9 begins begin VBZ cord-340851-lnv8yi9l 216 10 eroding erode VBG cord-340851-lnv8yi9l 216 11 once once RB cord-340851-lnv8yi9l 216 12 a a DT cord-340851-lnv8yi9l 216 13 vaccine vaccine NN cord-340851-lnv8yi9l 216 14 is be VBZ cord-340851-lnv8yi9l 216 15 introduced introduce VBN cord-340851-lnv8yi9l 216 16 . . . cord-340851-lnv8yi9l 217 1 With with IN cord-340851-lnv8yi9l 217 2 a a DT cord-340851-lnv8yi9l 217 3 higher high JJR cord-340851-lnv8yi9l 217 4 value value NN cord-340851-lnv8yi9l 217 5 of of IN cord-340851-lnv8yi9l 217 6 c c NN cord-340851-lnv8yi9l 217 7 = = SYM cord-340851-lnv8yi9l 217 8 10 10 CD cord-340851-lnv8yi9l 217 9 −9 −9 NNP cord-340851-lnv8yi9l 217 10 , , , cord-340851-lnv8yi9l 217 11 u u NNP cord-340851-lnv8yi9l 217 12 * * NFP cord-340851-lnv8yi9l 217 13 ( ( -LRB- cord-340851-lnv8yi9l 217 14 t t NN cord-340851-lnv8yi9l 217 15 ) ) -RRB- cord-340851-lnv8yi9l 217 16 drops drop VBZ cord-340851-lnv8yi9l 217 17 to to IN cord-340851-lnv8yi9l 217 18 around around IN cord-340851-lnv8yi9l 217 19 50 50 CD cord-340851-lnv8yi9l 217 20 % % NN cord-340851-lnv8yi9l 217 21 of of IN cord-340851-lnv8yi9l 217 22 u u NNP cord-340851-lnv8yi9l 217 23 max max NN cord-340851-lnv8yi9l 217 24 in in IN cord-340851-lnv8yi9l 217 25 May May NNP cord-340851-lnv8yi9l 217 26 2020 2020 CD cord-340851-lnv8yi9l 218 1 ( ( -LRB- cord-340851-lnv8yi9l 218 2 Figure figure NN cord-340851-lnv8yi9l 218 3 5 5 CD cord-340851-lnv8yi9l 218 4 ) ) -RRB- cord-340851-lnv8yi9l 218 5 . . . cord-340851-lnv8yi9l 219 1 As as IN cord-340851-lnv8yi9l 219 2 a a DT cord-340851-lnv8yi9l 219 3 result result NN cord-340851-lnv8yi9l 219 4 , , , cord-340851-lnv8yi9l 219 5 hospitalizations hospitalization NNS cord-340851-lnv8yi9l 219 6 rebound rebound VBP cord-340851-lnv8yi9l 219 7 and and CC cord-340851-lnv8yi9l 219 8 exceed exceed VBP cord-340851-lnv8yi9l 219 9 hospital hospital NN cord-340851-lnv8yi9l 219 10 capacity capacity NN cord-340851-lnv8yi9l 219 11 by by IN cord-340851-lnv8yi9l 219 12 around around IN cord-340851-lnv8yi9l 219 13 a a DT cord-340851-lnv8yi9l 219 14 third third NN cord-340851-lnv8yi9l 219 15 in in IN cord-340851-lnv8yi9l 219 16 June June NNP cord-340851-lnv8yi9l 219 17 and and CC cord-340851-lnv8yi9l 219 18 July July NNP cord-340851-lnv8yi9l 219 19 before before IN cord-340851-lnv8yi9l 219 20 falling fall VBG cord-340851-lnv8yi9l 219 21 again again RB cord-340851-lnv8yi9l 219 22 , , , cord-340851-lnv8yi9l 219 23 after after IN cord-340851-lnv8yi9l 219 24 u u NNP cord-340851-lnv8yi9l 219 25 * * NFP cord-340851-lnv8yi9l 219 26 ( ( -LRB- cord-340851-lnv8yi9l 219 27 t t NN cord-340851-lnv8yi9l 219 28 ) ) -RRB- cord-340851-lnv8yi9l 219 29 returns return VBZ cord-340851-lnv8yi9l 219 30 to to IN cord-340851-lnv8yi9l 219 31 u u NNP cord-340851-lnv8yi9l 219 32 max max NNP cord-340851-lnv8yi9l 219 33 . . . cord-340851-lnv8yi9l 220 1 From from IN cord-340851-lnv8yi9l 220 2 August August NNP cord-340851-lnv8yi9l 220 3 2020 2020 CD cord-340851-lnv8yi9l 220 4 onward onward RB cord-340851-lnv8yi9l 220 5 , , , cord-340851-lnv8yi9l 220 6 a a DT cord-340851-lnv8yi9l 220 7 steady steady JJ cord-340851-lnv8yi9l 220 8 decline decline NN cord-340851-lnv8yi9l 220 9 in in IN cord-340851-lnv8yi9l 220 10 u u NNP cord-340851-lnv8yi9l 220 11 * * NFP cord-340851-lnv8yi9l 220 12 ( ( -LRB- cord-340851-lnv8yi9l 220 13 t t NN cord-340851-lnv8yi9l 220 14 ) ) -RRB- cord-340851-lnv8yi9l 220 15 allows allow VBZ cord-340851-lnv8yi9l 220 16 hospitalizations hospitalization NNS cord-340851-lnv8yi9l 220 17 to to TO cord-340851-lnv8yi9l 220 18 be be VB cord-340851-lnv8yi9l 220 19 maintained maintain VBN cord-340851-lnv8yi9l 220 20 at at IN cord-340851-lnv8yi9l 220 21 moderate moderate JJ cord-340851-lnv8yi9l 220 22 levels level NNS cord-340851-lnv8yi9l 220 23 before before IN cord-340851-lnv8yi9l 220 24 rebounding rebound VBG cord-340851-lnv8yi9l 220 25 and and CC cord-340851-lnv8yi9l 220 26 exceeding exceed VBG cord-340851-lnv8yi9l 220 27 hospital hospital NN cord-340851-lnv8yi9l 220 28 capacity capacity NN cord-340851-lnv8yi9l 220 29 once once RB cord-340851-lnv8yi9l 220 30 again again RB cord-340851-lnv8yi9l 220 31 for for IN cord-340851-lnv8yi9l 220 32 several several JJ cord-340851-lnv8yi9l 220 33 months month NNS cord-340851-lnv8yi9l 220 34 in in IN cord-340851-lnv8yi9l 220 35 2021 2021 CD cord-340851-lnv8yi9l 220 36 . . . cord-340851-lnv8yi9l 221 1 With with IN cord-340851-lnv8yi9l 221 2 the the DT cord-340851-lnv8yi9l 221 3 highest high JJS cord-340851-lnv8yi9l 221 4 value value NN cord-340851-lnv8yi9l 221 5 of of IN cord-340851-lnv8yi9l 221 6 c c NN cord-340851-lnv8yi9l 221 7 = = SYM cord-340851-lnv8yi9l 221 8 10 10 CD cord-340851-lnv8yi9l 221 9 −6 −6 NNS cord-340851-lnv8yi9l 221 10 , , . cord-340851-lnv8yi9l 222 1 u u NNP cord-340851-lnv8yi9l 222 2 * * NFP cord-340851-lnv8yi9l 222 3 ( ( -LRB- cord-340851-lnv8yi9l 222 4 t t NN cord-340851-lnv8yi9l 222 5 ) ) -RRB- cord-340851-lnv8yi9l 222 6 drops drop VBZ cord-340851-lnv8yi9l 222 7 almost almost RB cord-340851-lnv8yi9l 222 8 to to IN cord-340851-lnv8yi9l 222 9 zero zero CD cord-340851-lnv8yi9l 222 10 at at IN cord-340851-lnv8yi9l 222 11 the the DT cord-340851-lnv8yi9l 222 12 beginning beginning NN cord-340851-lnv8yi9l 222 13 of of IN cord-340851-lnv8yi9l 222 14 May May NNP cord-340851-lnv8yi9l 222 15 2020 2020 CD cord-340851-lnv8yi9l 223 1 ( ( -LRB- cord-340851-lnv8yi9l 223 2 Figure figure NN cord-340851-lnv8yi9l 223 3 . . . cord-340851-lnv8yi9l 223 4 7 7 CD cord-340851-lnv8yi9l 223 5 ) ) -RRB- cord-340851-lnv8yi9l 223 6 . . . cord-340851-lnv8yi9l 224 1 This this DT cord-340851-lnv8yi9l 224 2 results result VBZ cord-340851-lnv8yi9l 224 3 in in IN cord-340851-lnv8yi9l 224 4 a a DT cord-340851-lnv8yi9l 224 5 rapid rapid JJ cord-340851-lnv8yi9l 224 6 increase increase NN cord-340851-lnv8yi9l 224 7 in in IN cord-340851-lnv8yi9l 224 8 hospitalizations hospitalization NNS cord-340851-lnv8yi9l 224 9 , , , cord-340851-lnv8yi9l 224 10 which which WDT cord-340851-lnv8yi9l 224 11 is be VBZ cord-340851-lnv8yi9l 224 12 followed follow VBN cord-340851-lnv8yi9l 224 13 by by IN cord-340851-lnv8yi9l 224 14 an an DT cord-340851-lnv8yi9l 224 15 increase increase NN cord-340851-lnv8yi9l 224 16 in in IN cord-340851-lnv8yi9l 224 17 u u NNP cord-340851-lnv8yi9l 224 18 * * NFP cord-340851-lnv8yi9l 224 19 ( ( -LRB- cord-340851-lnv8yi9l 224 20 t t NN cord-340851-lnv8yi9l 224 21 ) ) -RRB- cord-340851-lnv8yi9l 224 22 . . . cord-340851-lnv8yi9l 225 1 By by IN cord-340851-lnv8yi9l 225 2 the the DT cord-340851-lnv8yi9l 225 3 end end NN cord-340851-lnv8yi9l 225 4 of of IN cord-340851-lnv8yi9l 225 5 June June NNP cord-340851-lnv8yi9l 225 6 , , , cord-340851-lnv8yi9l 225 7 the the DT cord-340851-lnv8yi9l 225 8 susceptible susceptible JJ cord-340851-lnv8yi9l 225 9 population population NN cord-340851-lnv8yi9l 225 10 has have VBZ cord-340851-lnv8yi9l 225 11 been be VBN cord-340851-lnv8yi9l 225 12 depleted deplete VBN cord-340851-lnv8yi9l 225 13 to to IN cord-340851-lnv8yi9l 225 14 the the DT cord-340851-lnv8yi9l 225 15 point point NN cord-340851-lnv8yi9l 225 16 that that WDT cord-340851-lnv8yi9l 225 17 herd herd NN cord-340851-lnv8yi9l 225 18 immunity immunity NN cord-340851-lnv8yi9l 225 19 begins begin VBZ cord-340851-lnv8yi9l 225 20 to to TO cord-340851-lnv8yi9l 225 21 obviate obviate VB cord-340851-lnv8yi9l 225 22 the the DT cord-340851-lnv8yi9l 225 23 need need NN cord-340851-lnv8yi9l 225 24 for for IN cord-340851-lnv8yi9l 225 25 control control NN cord-340851-lnv8yi9l 225 26 and and CC cord-340851-lnv8yi9l 225 27 u u NNP cord-340851-lnv8yi9l 225 28 * * NFP cord-340851-lnv8yi9l 225 29 ( ( -LRB- cord-340851-lnv8yi9l 225 30 t t NN cord-340851-lnv8yi9l 225 31 ) ) -RRB- cord-340851-lnv8yi9l 225 32 declines decline VBZ cord-340851-lnv8yi9l 225 33 to to IN cord-340851-lnv8yi9l 225 34 zero zero CD cord-340851-lnv8yi9l 225 35 by by IN cord-340851-lnv8yi9l 225 36 October October NNP cord-340851-lnv8yi9l 225 37 2020 2020 CD cord-340851-lnv8yi9l 225 38 . . . cord-340851-lnv8yi9l 226 1 During during IN cord-340851-lnv8yi9l 226 2 this this DT cord-340851-lnv8yi9l 226 3 large large JJ cord-340851-lnv8yi9l 226 4 second second JJ cord-340851-lnv8yi9l 226 5 wave wave NN cord-340851-lnv8yi9l 226 6 in in IN cord-340851-lnv8yi9l 226 7 summer summer NN cord-340851-lnv8yi9l 226 8 2020 2020 CD cord-340851-lnv8yi9l 226 9 , , , cord-340851-lnv8yi9l 226 10 hospital hospital NN cord-340851-lnv8yi9l 226 11 capacity capacity NN cord-340851-lnv8yi9l 226 12 is be VBZ cord-340851-lnv8yi9l 226 13 ex- ex- XX cord-340851-lnv8yi9l 226 14 . . . cord-340851-lnv8yi9l 227 1 CC CC NNP cord-340851-lnv8yi9l 227 2 - - : cord-340851-lnv8yi9l 227 3 BY by IN cord-340851-lnv8yi9l 227 4 4.0 4.0 CD cord-340851-lnv8yi9l 227 5 International international JJ cord-340851-lnv8yi9l 227 6 license license NN cord-340851-lnv8yi9l 228 1 It -PRON- PRP cord-340851-lnv8yi9l 228 2 is be VBZ cord-340851-lnv8yi9l 228 3 made make VBN cord-340851-lnv8yi9l 228 4 available available JJ cord-340851-lnv8yi9l 228 5 under under IN cord-340851-lnv8yi9l 228 6 a a DT cord-340851-lnv8yi9l 229 1 is be VBZ cord-340851-lnv8yi9l 229 2 the the DT cord-340851-lnv8yi9l 229 3 author author NN cord-340851-lnv8yi9l 229 4 / / SYM cord-340851-lnv8yi9l 229 5 funder funder NN cord-340851-lnv8yi9l 229 6 , , , cord-340851-lnv8yi9l 229 7 who who WP cord-340851-lnv8yi9l 229 8 has have VBZ cord-340851-lnv8yi9l 229 9 granted grant VBN cord-340851-lnv8yi9l 229 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 229 11 a a DT cord-340851-lnv8yi9l 229 12 license license NN cord-340851-lnv8yi9l 229 13 to to TO cord-340851-lnv8yi9l 229 14 display display VB cord-340851-lnv8yi9l 229 15 the the DT cord-340851-lnv8yi9l 229 16 preprint preprint NN cord-340851-lnv8yi9l 229 17 in in IN cord-340851-lnv8yi9l 229 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 229 19 . . . cord-340851-lnv8yi9l 230 1 The the DT cord-340851-lnv8yi9l 230 2 copyright copyright NN cord-340851-lnv8yi9l 230 3 holder holder NN cord-340851-lnv8yi9l 230 4 for for IN cord-340851-lnv8yi9l 230 5 this this DT cord-340851-lnv8yi9l 230 6 preprint preprint NN cord-340851-lnv8yi9l 230 7 this this DT cord-340851-lnv8yi9l 230 8 version version NN cord-340851-lnv8yi9l 230 9 posted post VBN cord-340851-lnv8yi9l 230 10 April April NNP cord-340851-lnv8yi9l 230 11 23 23 CD cord-340851-lnv8yi9l 230 12 , , , cord-340851-lnv8yi9l 230 13 2020 2020 CD cord-340851-lnv8yi9l 230 14 . . . cord-340851-lnv8yi9l 230 15 . . . cord-340851-lnv8yi9l 231 1 CC CC NNP cord-340851-lnv8yi9l 231 2 - - : cord-340851-lnv8yi9l 231 3 BY by IN cord-340851-lnv8yi9l 231 4 4.0 4.0 CD cord-340851-lnv8yi9l 231 5 International international JJ cord-340851-lnv8yi9l 231 6 license license NN cord-340851-lnv8yi9l 232 1 It -PRON- PRP cord-340851-lnv8yi9l 232 2 is be VBZ cord-340851-lnv8yi9l 232 3 made make VBN cord-340851-lnv8yi9l 232 4 available available JJ cord-340851-lnv8yi9l 232 5 under under IN cord-340851-lnv8yi9l 232 6 a a DT cord-340851-lnv8yi9l 233 1 is be VBZ cord-340851-lnv8yi9l 233 2 the the DT cord-340851-lnv8yi9l 233 3 author author NN cord-340851-lnv8yi9l 233 4 / / SYM cord-340851-lnv8yi9l 233 5 funder funder NN cord-340851-lnv8yi9l 233 6 , , , cord-340851-lnv8yi9l 233 7 who who WP cord-340851-lnv8yi9l 233 8 has have VBZ cord-340851-lnv8yi9l 233 9 granted grant VBN cord-340851-lnv8yi9l 233 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 233 11 a a DT cord-340851-lnv8yi9l 233 12 license license NN cord-340851-lnv8yi9l 233 13 to to TO cord-340851-lnv8yi9l 233 14 display display VB cord-340851-lnv8yi9l 233 15 the the DT cord-340851-lnv8yi9l 233 16 preprint preprint NN cord-340851-lnv8yi9l 233 17 in in IN cord-340851-lnv8yi9l 233 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 233 19 . . . cord-340851-lnv8yi9l 234 1 The the DT cord-340851-lnv8yi9l 234 2 copyright copyright NN cord-340851-lnv8yi9l 234 3 holder holder NN cord-340851-lnv8yi9l 234 4 for for IN cord-340851-lnv8yi9l 234 5 this this DT cord-340851-lnv8yi9l 234 6 preprint preprint NN cord-340851-lnv8yi9l 234 7 this this DT cord-340851-lnv8yi9l 234 8 version version NN cord-340851-lnv8yi9l 234 9 posted post VBN cord-340851-lnv8yi9l 234 10 April April NNP cord-340851-lnv8yi9l 234 11 23 23 CD cord-340851-lnv8yi9l 234 12 , , , cord-340851-lnv8yi9l 234 13 2020 2020 CD cord-340851-lnv8yi9l 234 14 . . . cord-340851-lnv8yi9l 234 15 . . . cord-340851-lnv8yi9l 235 1 https://doi.org/10.1101/2020.04.22.20076018 https://doi.org/10.1101/2020.04.22.20076018 NNP cord-340851-lnv8yi9l 235 2 doi doi XX cord-340851-lnv8yi9l 235 3 : : : cord-340851-lnv8yi9l 236 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 236 2 preprint preprint NNP cord-340851-lnv8yi9l 236 3 Fig Fig NNP cord-340851-lnv8yi9l 236 4 . . . cord-340851-lnv8yi9l 237 1 7 7 CD cord-340851-lnv8yi9l 237 2 Optimal Optimal NNP cord-340851-lnv8yi9l 237 3 control control NN cord-340851-lnv8yi9l 237 4 under under IN cord-340851-lnv8yi9l 237 5 parameters parameter NNS cord-340851-lnv8yi9l 237 6 with with IN cord-340851-lnv8yi9l 237 7 maximal maximal JJ cord-340851-lnv8yi9l 237 8 ability ability NN cord-340851-lnv8yi9l 237 9 to to TO cord-340851-lnv8yi9l 237 10 control control VB cord-340851-lnv8yi9l 237 11 the the DT cord-340851-lnv8yi9l 237 12 pandemic pandemic NN cord-340851-lnv8yi9l 237 13 , , , cord-340851-lnv8yi9l 237 14 with with IN cord-340851-lnv8yi9l 237 15 minimal minimal JJ cord-340851-lnv8yi9l 237 16 weighting weighting NN cord-340851-lnv8yi9l 237 17 on on IN cord-340851-lnv8yi9l 237 18 minimization minimization NN cord-340851-lnv8yi9l 237 19 of of IN cord-340851-lnv8yi9l 237 20 deaths death NNS cord-340851-lnv8yi9l 237 21 . . . cord-340851-lnv8yi9l 238 1 Panels panel NNS cord-340851-lnv8yi9l 238 2 show show VBP cord-340851-lnv8yi9l 238 3 the the DT cord-340851-lnv8yi9l 238 4 optimal optimal JJ cord-340851-lnv8yi9l 238 5 control control NN cord-340851-lnv8yi9l 238 6 ( ( -LRB- cord-340851-lnv8yi9l 238 7 bottom bottom NN cord-340851-lnv8yi9l 238 8 ) ) -RRB- cord-340851-lnv8yi9l 238 9 and and CC cord-340851-lnv8yi9l 238 10 its -PRON- PRP$ cord-340851-lnv8yi9l 238 11 impacts impact NNS cord-340851-lnv8yi9l 238 12 on on IN cord-340851-lnv8yi9l 238 13 the the DT cord-340851-lnv8yi9l 238 14 dynamics dynamic NNS cord-340851-lnv8yi9l 238 15 of of IN cord-340851-lnv8yi9l 238 16 hospitalized hospitalize VBN cord-340851-lnv8yi9l 238 17 ( ( -LRB- cord-340851-lnv8yi9l 238 18 middle middle JJ cord-340851-lnv8yi9l 238 19 ) ) -RRB- cord-340851-lnv8yi9l 238 20 and and CC cord-340851-lnv8yi9l 238 21 susceptible susceptible JJ cord-340851-lnv8yi9l 238 22 ( ( -LRB- cord-340851-lnv8yi9l 238 23 top top JJ cord-340851-lnv8yi9l 238 24 ) ) -RRB- cord-340851-lnv8yi9l 238 25 compartments compartment NNS cord-340851-lnv8yi9l 238 26 with with IN cord-340851-lnv8yi9l 238 27 R r NN cord-340851-lnv8yi9l 238 28 0 0 CD cord-340851-lnv8yi9l 238 29 = = SYM cord-340851-lnv8yi9l 238 30 3 3 CD cord-340851-lnv8yi9l 238 31 , , , cord-340851-lnv8yi9l 238 32 umax umax NNP cord-340851-lnv8yi9l 238 33 = = SYM cord-340851-lnv8yi9l 238 34 0.9 0.9 CD cord-340851-lnv8yi9l 238 35 , , , cord-340851-lnv8yi9l 238 36 ω ω NN cord-340851-lnv8yi9l 238 37 = = SYM cord-340851-lnv8yi9l 238 38 0.8 0.8 CD cord-340851-lnv8yi9l 238 39 , , , cord-340851-lnv8yi9l 238 40 and and CC cord-340851-lnv8yi9l 238 41 c c NN cord-340851-lnv8yi9l 238 42 = = SYM cord-340851-lnv8yi9l 238 43 10 10 CD cord-340851-lnv8yi9l 238 44 −9 −9 NN cord-340851-lnv8yi9l 238 45 . . . cord-340851-lnv8yi9l 239 1 Vaccination vaccination NN cord-340851-lnv8yi9l 239 2 is be VBZ cord-340851-lnv8yi9l 239 3 introduced introduce VBN cord-340851-lnv8yi9l 239 4 at at IN cord-340851-lnv8yi9l 239 5 the the DT cord-340851-lnv8yi9l 239 6 time time NN cord-340851-lnv8yi9l 239 7 indicated indicate VBN cord-340851-lnv8yi9l 239 8 by by IN cord-340851-lnv8yi9l 239 9 the the DT cord-340851-lnv8yi9l 239 10 arrow arrow NN cord-340851-lnv8yi9l 239 11 , , , cord-340851-lnv8yi9l 239 12 with with IN cord-340851-lnv8yi9l 239 13 the the DT cord-340851-lnv8yi9l 239 14 vaccinated vaccinate VBN cord-340851-lnv8yi9l 239 15 population population NN cord-340851-lnv8yi9l 239 16 ( ( -LRB- cord-340851-lnv8yi9l 239 17 orange orange NNP cord-340851-lnv8yi9l 239 18 ) ) -RRB- cord-340851-lnv8yi9l 239 19 reducing reduce VBG cord-340851-lnv8yi9l 239 20 the the DT cord-340851-lnv8yi9l 239 21 susceptible susceptible JJ cord-340851-lnv8yi9l 239 22 population population NN cord-340851-lnv8yi9l 239 23 . . . cord-340851-lnv8yi9l 240 1 Through through IN cord-340851-lnv8yi9l 240 2 April April NNP cord-340851-lnv8yi9l 240 3 2020 2020 CD cord-340851-lnv8yi9l 240 4 ( ( -LRB- cord-340851-lnv8yi9l 240 5 gray gray JJ cord-340851-lnv8yi9l 240 6 shading shading NN cord-340851-lnv8yi9l 240 7 ) ) -RRB- cord-340851-lnv8yi9l 240 8 , , , cord-340851-lnv8yi9l 240 9 the the DT cord-340851-lnv8yi9l 240 10 value value NN cord-340851-lnv8yi9l 240 11 of of IN cord-340851-lnv8yi9l 240 12 the the DT cord-340851-lnv8yi9l 240 13 control control NN cord-340851-lnv8yi9l 240 14 is be VBZ cord-340851-lnv8yi9l 240 15 fixed fix VBN cord-340851-lnv8yi9l 240 16 according accord VBG cord-340851-lnv8yi9l 240 17 to to IN cord-340851-lnv8yi9l 240 18 its -PRON- PRP$ cord-340851-lnv8yi9l 240 19 calibrated calibrate VBN cord-340851-lnv8yi9l 240 20 trajectory trajectory NN cord-340851-lnv8yi9l 240 21 . . . cord-340851-lnv8yi9l 241 1 The the DT cord-340851-lnv8yi9l 241 2 dashed dash VBN cord-340851-lnv8yi9l 241 3 horizontal horizontal JJ cord-340851-lnv8yi9l 241 4 line line NN cord-340851-lnv8yi9l 241 5 indicates indicate VBZ cord-340851-lnv8yi9l 241 6 hospital hospital NN cord-340851-lnv8yi9l 241 7 capacity capacity NN cord-340851-lnv8yi9l 241 8 . . . cord-340851-lnv8yi9l 242 1 ceeded ceede VBN cord-340851-lnv8yi9l 242 2 by by IN cord-340851-lnv8yi9l 242 3 more more JJR cord-340851-lnv8yi9l 242 4 than than IN cord-340851-lnv8yi9l 242 5 20-fold 20-fold CD cord-340851-lnv8yi9l 242 6 . . . cord-340851-lnv8yi9l 243 1 This this DT cord-340851-lnv8yi9l 243 2 results result VBZ cord-340851-lnv8yi9l 243 3 in in IN cord-340851-lnv8yi9l 243 4 cumulative cumulative JJ cord-340851-lnv8yi9l 243 5 deaths death NNS cord-340851-lnv8yi9l 243 6 equaling equal VBG cord-340851-lnv8yi9l 243 7 5 5 CD cord-340851-lnv8yi9l 243 8 % % NN cord-340851-lnv8yi9l 243 9 of of IN cord-340851-lnv8yi9l 243 10 the the DT cord-340851-lnv8yi9l 243 11 population population NN cord-340851-lnv8yi9l 243 12 , , , cord-340851-lnv8yi9l 243 13 which which WDT cord-340851-lnv8yi9l 243 14 is be VBZ cord-340851-lnv8yi9l 243 15 approximately approximately RB cord-340851-lnv8yi9l 243 16 one one CD cord-340851-lnv8yi9l 243 17 order order NN cord-340851-lnv8yi9l 243 18 of of IN cord-340851-lnv8yi9l 243 19 magnitude magnitude NN cord-340851-lnv8yi9l 243 20 greater great JJR cord-340851-lnv8yi9l 243 21 than than IN cord-340851-lnv8yi9l 243 22 when when WRB cord-340851-lnv8yi9l 243 23 c c NN cord-340851-lnv8yi9l 243 24 = = SYM cord-340851-lnv8yi9l 243 25 10 10 CD cord-340851-lnv8yi9l 243 26 −9 −9 NN cord-340851-lnv8yi9l 243 27 and and CC cord-340851-lnv8yi9l 243 28 two two CD cord-340851-lnv8yi9l 243 29 orders order NNS cord-340851-lnv8yi9l 243 30 of of IN cord-340851-lnv8yi9l 243 31 magnitude magnitude NN cord-340851-lnv8yi9l 243 32 greater great JJR cord-340851-lnv8yi9l 243 33 than than IN cord-340851-lnv8yi9l 243 34 when when WRB cord-340851-lnv8yi9l 243 35 c c NN cord-340851-lnv8yi9l 243 36 = = SYM cord-340851-lnv8yi9l 243 37 10 10 CD cord-340851-lnv8yi9l 243 38 −12 −12 NN cord-340851-lnv8yi9l 243 39 . . . cord-340851-lnv8yi9l 244 1 Under under IN cord-340851-lnv8yi9l 244 2 other other JJ cord-340851-lnv8yi9l 244 3 conditions condition NNS cord-340851-lnv8yi9l 244 4 about about IN cord-340851-lnv8yi9l 244 5 the the DT cord-340851-lnv8yi9l 244 6 transmissibility transmissibility NN cord-340851-lnv8yi9l 244 7 of of IN cord-340851-lnv8yi9l 244 8 the the DT cord-340851-lnv8yi9l 244 9 virus virus NN cord-340851-lnv8yi9l 244 10 and and CC cord-340851-lnv8yi9l 244 11 the the DT cord-340851-lnv8yi9l 244 12 potential potential NN cord-340851-lnv8yi9l 244 13 for for IN cord-340851-lnv8yi9l 244 14 NPIs npi NNS cord-340851-lnv8yi9l 244 15 to to TO cord-340851-lnv8yi9l 244 16 reduce reduce VB cord-340851-lnv8yi9l 244 17 transmission transmission NN cord-340851-lnv8yi9l 244 18 , , , cord-340851-lnv8yi9l 244 19 control control NN cord-340851-lnv8yi9l 244 20 is be VBZ cord-340851-lnv8yi9l 244 21 less less RBR cord-340851-lnv8yi9l 244 22 capable capable JJ cord-340851-lnv8yi9l 244 23 of of IN cord-340851-lnv8yi9l 244 24 curtailing curtail VBG cord-340851-lnv8yi9l 244 25 the the DT cord-340851-lnv8yi9l 244 26 epidemic epidemic NN cord-340851-lnv8yi9l 244 27 . . . cord-340851-lnv8yi9l 245 1 With with IN cord-340851-lnv8yi9l 245 2 R r NN cord-340851-lnv8yi9l 245 3 0 0 CD cord-340851-lnv8yi9l 245 4 = = SYM cord-340851-lnv8yi9l 245 5 3.5 3.5 CD cord-340851-lnv8yi9l 245 6 and and CC cord-340851-lnv8yi9l 245 7 u u NNP cord-340851-lnv8yi9l 245 8 max max NN cord-340851-lnv8yi9l 245 9 = = NNP cord-340851-lnv8yi9l 245 10 0.7 0.7 CD cord-340851-lnv8yi9l 245 11 , , , cord-340851-lnv8yi9l 245 12 hospitalizations hospitalization NNS cord-340851-lnv8yi9l 245 13 peak peak VBP cord-340851-lnv8yi9l 245 14 in in IN cord-340851-lnv8yi9l 245 15 early early JJ cord-340851-lnv8yi9l 245 16 summer summer NN cord-340851-lnv8yi9l 245 17 2020 2020 CD cord-340851-lnv8yi9l 245 18 at at IN cord-340851-lnv8yi9l 245 19 twice twice JJ cord-340851-lnv8yi9l 245 20 hospital hospital NN cord-340851-lnv8yi9l 245 21 capacity capacity NN cord-340851-lnv8yi9l 245 22 and and CC cord-340851-lnv8yi9l 245 23 take take VB cord-340851-lnv8yi9l 245 24 until until IN cord-340851-lnv8yi9l 245 25 December December NNP cord-340851-lnv8yi9l 245 26 2020 2020 CD cord-340851-lnv8yi9l 245 27 to to TO cord-340851-lnv8yi9l 245 28 fall fall VB cord-340851-lnv8yi9l 245 29 below below IN cord-340851-lnv8yi9l 245 30 hospital hospital NN cord-340851-lnv8yi9l 245 31 capacity capacity NN cord-340851-lnv8yi9l 245 32 , , , cord-340851-lnv8yi9l 245 33 even even RB cord-340851-lnv8yi9l 245 34 with with IN cord-340851-lnv8yi9l 245 35 the the DT cord-340851-lnv8yi9l 245 36 most most RBS cord-340851-lnv8yi9l 245 37 aggressive aggressive JJ cord-340851-lnv8yi9l 245 38 value value NN cord-340851-lnv8yi9l 245 39 of of IN cord-340851-lnv8yi9l 245 40 c c NN cord-340851-lnv8yi9l 245 41 that that WDT cord-340851-lnv8yi9l 245 42 we -PRON- PRP cord-340851-lnv8yi9l 245 43 considered consider VBD cord-340851-lnv8yi9l 245 44 ( ( -LRB- cord-340851-lnv8yi9l 245 45 10 10 CD cord-340851-lnv8yi9l 245 46 −12 −12 NN cord-340851-lnv8yi9l 245 47 ) ) -RRB- cord-340851-lnv8yi9l 246 1 ( ( -LRB- cord-340851-lnv8yi9l 246 2 Figure figure NN cord-340851-lnv8yi9l 246 3 8 8 CD cord-340851-lnv8yi9l 246 4 ) ) -RRB- cord-340851-lnv8yi9l 246 5 . . . cord-340851-lnv8yi9l 247 1 With with IN cord-340851-lnv8yi9l 247 2 R r NN cord-340851-lnv8yi9l 247 3 0 0 CD cord-340851-lnv8yi9l 247 4 = = SYM cord-340851-lnv8yi9l 247 5 4 4 CD cord-340851-lnv8yi9l 247 6 , , , cord-340851-lnv8yi9l 247 7 u u NNP cord-340851-lnv8yi9l 247 8 max max NN cord-340851-lnv8yi9l 247 9 = = SYM cord-340851-lnv8yi9l 247 10 0.5 0.5 CD cord-340851-lnv8yi9l 247 11 , , , cord-340851-lnv8yi9l 247 12 and and CC cord-340851-lnv8yi9l 247 13 c c NN cord-340851-lnv8yi9l 247 14 = = SYM cord-340851-lnv8yi9l 247 15 10 10 CD cord-340851-lnv8yi9l 247 16 −12 −12 NN cord-340851-lnv8yi9l 247 17 , , , cord-340851-lnv8yi9l 247 18 hospitalizations hospitalization NNS cord-340851-lnv8yi9l 247 19 peak peak VBP cord-340851-lnv8yi9l 247 20 in in IN cord-340851-lnv8yi9l 247 21 summer summer NN cord-340851-lnv8yi9l 247 22 2020 2020 CD cord-340851-lnv8yi9l 247 23 at at IN cord-340851-lnv8yi9l 247 24 thirty thirty CD cord-340851-lnv8yi9l 247 25 times time NNS cord-340851-lnv8yi9l 247 26 hospital hospital NN cord-340851-lnv8yi9l 247 27 capacity capacity NN cord-340851-lnv8yi9l 247 28 ( ( -LRB- cord-340851-lnv8yi9l 247 29 Figure figure NN cord-340851-lnv8yi9l 247 30 9 9 CD cord-340851-lnv8yi9l 247 31 ) ) -RRB- cord-340851-lnv8yi9l 247 32 . . . cord-340851-lnv8yi9l 248 1 This this DT cord-340851-lnv8yi9l 248 2 results result VBZ cord-340851-lnv8yi9l 248 3 in in IN cord-340851-lnv8yi9l 248 4 extensive extensive JJ cord-340851-lnv8yi9l 248 5 herd herd NN cord-340851-lnv8yi9l 248 6 immunity immunity NN cord-340851-lnv8yi9l 248 7 and and CC cord-340851-lnv8yi9l 248 8 the the DT cord-340851-lnv8yi9l 248 9 relaxation relaxation NN cord-340851-lnv8yi9l 248 10 of of IN cord-340851-lnv8yi9l 248 11 control control NN cord-340851-lnv8yi9l 248 12 in in IN cord-340851-lnv8yi9l 248 13 2021 2021 CD cord-340851-lnv8yi9l 248 14 , , , cord-340851-lnv8yi9l 248 15 albeit albeit IN cord-340851-lnv8yi9l 248 16 at at IN cord-340851-lnv8yi9l 248 17 the the DT cord-340851-lnv8yi9l 248 18 cost cost NN cord-340851-lnv8yi9l 248 19 of of IN cord-340851-lnv8yi9l 248 20 extensive extensive JJ cord-340851-lnv8yi9l 248 21 deaths death NNS cord-340851-lnv8yi9l 248 22 ( ( -LRB- cord-340851-lnv8yi9l 248 23 Figure figure NN cord-340851-lnv8yi9l 248 24 4 4 CD cord-340851-lnv8yi9l 248 25 ) ) -RRB- cord-340851-lnv8yi9l 248 26 . . . cord-340851-lnv8yi9l 249 1 Optimal optimal JJ cord-340851-lnv8yi9l 249 2 controls control NNS cord-340851-lnv8yi9l 249 3 under under IN cord-340851-lnv8yi9l 249 4 a a DT cord-340851-lnv8yi9l 249 5 wider wide JJR cord-340851-lnv8yi9l 249 6 variety variety NN cord-340851-lnv8yi9l 249 7 of of IN cord-340851-lnv8yi9l 249 8 parameter parameter NN cord-340851-lnv8yi9l 249 9 combinations combination NNS cord-340851-lnv8yi9l 249 10 can can MD cord-340851-lnv8yi9l 249 11 be be VB cord-340851-lnv8yi9l 249 12 explored explore VBN cord-340851-lnv8yi9l 249 13 interactively interactively RB cord-340851-lnv8yi9l 249 14 at at IN cord-340851-lnv8yi9l 249 15 http://covid19optimalcontrol.crc.nd.edu http://covid19optimalcontrol.crc.nd.edu NNP cord-340851-lnv8yi9l 249 16 . . . cord-340851-lnv8yi9l 250 1 Our -PRON- PRP$ cord-340851-lnv8yi9l 250 2 calibration calibration NN cord-340851-lnv8yi9l 250 3 procedure procedure NN cord-340851-lnv8yi9l 250 4 resulted result VBD cord-340851-lnv8yi9l 250 5 in in IN cord-340851-lnv8yi9l 250 6 a a DT cord-340851-lnv8yi9l 250 7 single single JJ cord-340851-lnv8yi9l 250 8 assumption assumption NN cord-340851-lnv8yi9l 250 9 about about IN cord-340851-lnv8yi9l 250 10 the the DT cord-340851-lnv8yi9l 250 11 trajectory trajectory NN cord-340851-lnv8yi9l 250 12 of of IN cord-340851-lnv8yi9l 250 13 u(t u(t NNP cord-340851-lnv8yi9l 250 14 ) ) -RRB- cord-340851-lnv8yi9l 250 15 prior prior RB cord-340851-lnv8yi9l 250 16 to to IN cord-340851-lnv8yi9l 250 17 April April NNP cord-340851-lnv8yi9l 250 18 30 30 CD cord-340851-lnv8yi9l 250 19 , , , cord-340851-lnv8yi9l 250 20 2020 2020 CD cord-340851-lnv8yi9l 250 21 . . . cord-340851-lnv8yi9l 251 1 Control control NN cord-340851-lnv8yi9l 251 2 during during IN cord-340851-lnv8yi9l 251 3 this this DT cord-340851-lnv8yi9l 251 4 period period NN cord-340851-lnv8yi9l 251 5 was be VBD cord-340851-lnv8yi9l 251 6 fixed fix VBN cord-340851-lnv8yi9l 251 7 in in IN cord-340851-lnv8yi9l 251 8 analyses analysis NNS cord-340851-lnv8yi9l 251 9 in in IN cord-340851-lnv8yi9l 251 10 Section section NN cord-340851-lnv8yi9l 251 11 3.4 3.4 CD cord-340851-lnv8yi9l 251 12 , , , cord-340851-lnv8yi9l 251 13 with with IN cord-340851-lnv8yi9l 251 14 the the DT cord-340851-lnv8yi9l 251 15 flexibility flexibility NN cord-340851-lnv8yi9l 251 16 to to TO cord-340851-lnv8yi9l 251 17 define define VB cord-340851-lnv8yi9l 251 18 u u NNP cord-340851-lnv8yi9l 251 19 * * NFP cord-340851-lnv8yi9l 251 20 ( ( -LRB- cord-340851-lnv8yi9l 251 21 t t NN cord-340851-lnv8yi9l 251 22 ) ) -RRB- cord-340851-lnv8yi9l 251 23 only only RB cord-340851-lnv8yi9l 251 24 allowed allow VBN cord-340851-lnv8yi9l 251 25 during during IN cord-340851-lnv8yi9l 251 26 the the DT cord-340851-lnv8yi9l 251 27 period period NN cord-340851-lnv8yi9l 251 28 from from IN cord-340851-lnv8yi9l 251 29 May May NNP cord-340851-lnv8yi9l 251 30 1 1 CD cord-340851-lnv8yi9l 251 31 , , , cord-340851-lnv8yi9l 251 32 2020 2020 CD cord-340851-lnv8yi9l 251 33 to to IN cord-340851-lnv8yi9l 251 34 December December NNP cord-340851-lnv8yi9l 251 35 31 31 CD cord-340851-lnv8yi9l 251 36 , , , cord-340851-lnv8yi9l 251 37 2021 2021 CD cord-340851-lnv8yi9l 251 38 . . . cord-340851-lnv8yi9l 252 1 Here here RB cord-340851-lnv8yi9l 252 2 , , , cord-340851-lnv8yi9l 252 3 we -PRON- PRP cord-340851-lnv8yi9l 252 4 explore explore VBP cord-340851-lnv8yi9l 252 5 how how WRB cord-340851-lnv8yi9l 252 6 NPIs npi NNS cord-340851-lnv8yi9l 252 7 . . . cord-340851-lnv8yi9l 253 1 CC CC NNP cord-340851-lnv8yi9l 253 2 - - : cord-340851-lnv8yi9l 253 3 BY by IN cord-340851-lnv8yi9l 253 4 4.0 4.0 CD cord-340851-lnv8yi9l 253 5 International international JJ cord-340851-lnv8yi9l 253 6 license license NN cord-340851-lnv8yi9l 254 1 It -PRON- PRP cord-340851-lnv8yi9l 254 2 is be VBZ cord-340851-lnv8yi9l 254 3 made make VBN cord-340851-lnv8yi9l 254 4 available available JJ cord-340851-lnv8yi9l 254 5 under under IN cord-340851-lnv8yi9l 254 6 a a DT cord-340851-lnv8yi9l 255 1 is be VBZ cord-340851-lnv8yi9l 255 2 the the DT cord-340851-lnv8yi9l 255 3 author author NN cord-340851-lnv8yi9l 255 4 / / SYM cord-340851-lnv8yi9l 255 5 funder funder NN cord-340851-lnv8yi9l 255 6 , , , cord-340851-lnv8yi9l 255 7 who who WP cord-340851-lnv8yi9l 255 8 has have VBZ cord-340851-lnv8yi9l 255 9 granted grant VBN cord-340851-lnv8yi9l 255 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 255 11 a a DT cord-340851-lnv8yi9l 255 12 license license NN cord-340851-lnv8yi9l 255 13 to to TO cord-340851-lnv8yi9l 255 14 display display VB cord-340851-lnv8yi9l 255 15 the the DT cord-340851-lnv8yi9l 255 16 preprint preprint NN cord-340851-lnv8yi9l 255 17 in in IN cord-340851-lnv8yi9l 255 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 255 19 . . . cord-340851-lnv8yi9l 256 1 The the DT cord-340851-lnv8yi9l 256 2 copyright copyright NN cord-340851-lnv8yi9l 256 3 holder holder NN cord-340851-lnv8yi9l 256 4 for for IN cord-340851-lnv8yi9l 256 5 this this DT cord-340851-lnv8yi9l 256 6 preprint preprint NN cord-340851-lnv8yi9l 256 7 this this DT cord-340851-lnv8yi9l 256 8 version version NN cord-340851-lnv8yi9l 256 9 posted post VBN cord-340851-lnv8yi9l 256 10 April April NNP cord-340851-lnv8yi9l 256 11 23 23 CD cord-340851-lnv8yi9l 256 12 , , , cord-340851-lnv8yi9l 256 13 2020 2020 CD cord-340851-lnv8yi9l 256 14 . . . cord-340851-lnv8yi9l 256 15 . . . cord-340851-lnv8yi9l 257 1 https://doi.org/10.1101/2020.04.22.20076018 https://doi.org/10.1101/2020.04.22.20076018 NNP cord-340851-lnv8yi9l 257 2 doi doi XX cord-340851-lnv8yi9l 257 3 : : : cord-340851-lnv8yi9l 258 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 258 2 preprint preprint NNP cord-340851-lnv8yi9l 258 3 Fig Fig NNP cord-340851-lnv8yi9l 258 4 . . . cord-340851-lnv8yi9l 259 1 8 8 CD cord-340851-lnv8yi9l 260 1 Optimal optimal JJ cord-340851-lnv8yi9l 260 2 control control NN cord-340851-lnv8yi9l 260 3 under under IN cord-340851-lnv8yi9l 260 4 parameters parameter NNS cord-340851-lnv8yi9l 260 5 with with IN cord-340851-lnv8yi9l 260 6 maximal maximal JJ cord-340851-lnv8yi9l 260 7 ability ability NN cord-340851-lnv8yi9l 260 8 to to TO cord-340851-lnv8yi9l 260 9 control control VB cord-340851-lnv8yi9l 260 10 the the DT cord-340851-lnv8yi9l 260 11 pandemic pandemic NN cord-340851-lnv8yi9l 260 12 , , , cord-340851-lnv8yi9l 260 13 with with IN cord-340851-lnv8yi9l 260 14 maximal maximal JJ cord-340851-lnv8yi9l 260 15 weighting weighting NN cord-340851-lnv8yi9l 260 16 on on IN cord-340851-lnv8yi9l 260 17 minimization minimization NN cord-340851-lnv8yi9l 260 18 of of IN cord-340851-lnv8yi9l 260 19 deaths death NNS cord-340851-lnv8yi9l 260 20 . . . cord-340851-lnv8yi9l 261 1 Panels panel NNS cord-340851-lnv8yi9l 261 2 show show VBP cord-340851-lnv8yi9l 261 3 the the DT cord-340851-lnv8yi9l 261 4 optimal optimal JJ cord-340851-lnv8yi9l 261 5 control control NN cord-340851-lnv8yi9l 261 6 ( ( -LRB- cord-340851-lnv8yi9l 261 7 bottom bottom NN cord-340851-lnv8yi9l 261 8 ) ) -RRB- cord-340851-lnv8yi9l 261 9 and and CC cord-340851-lnv8yi9l 261 10 its -PRON- PRP$ cord-340851-lnv8yi9l 261 11 impacts impact NNS cord-340851-lnv8yi9l 261 12 on on IN cord-340851-lnv8yi9l 261 13 the the DT cord-340851-lnv8yi9l 261 14 dynamics dynamic NNS cord-340851-lnv8yi9l 261 15 of of IN cord-340851-lnv8yi9l 261 16 hospitalized hospitalize VBN cord-340851-lnv8yi9l 261 17 ( ( -LRB- cord-340851-lnv8yi9l 261 18 middle middle JJ cord-340851-lnv8yi9l 261 19 ) ) -RRB- cord-340851-lnv8yi9l 261 20 and and CC cord-340851-lnv8yi9l 261 21 susceptible susceptible JJ cord-340851-lnv8yi9l 261 22 ( ( -LRB- cord-340851-lnv8yi9l 261 23 top top JJ cord-340851-lnv8yi9l 261 24 ) ) -RRB- cord-340851-lnv8yi9l 261 25 compartments compartment NNS cord-340851-lnv8yi9l 261 26 with with IN cord-340851-lnv8yi9l 261 27 R r NN cord-340851-lnv8yi9l 261 28 0 0 CD cord-340851-lnv8yi9l 261 29 = = NFP cord-340851-lnv8yi9l 262 1 3.5 3.5 CD cord-340851-lnv8yi9l 262 2 , , , cord-340851-lnv8yi9l 262 3 umax umax NNP cord-340851-lnv8yi9l 262 4 = = SYM cord-340851-lnv8yi9l 262 5 0.7 0.7 CD cord-340851-lnv8yi9l 262 6 , , , cord-340851-lnv8yi9l 262 7 ω ω NN cord-340851-lnv8yi9l 262 8 = = SYM cord-340851-lnv8yi9l 262 9 0.8 0.8 CD cord-340851-lnv8yi9l 262 10 , , , cord-340851-lnv8yi9l 262 11 and and CC cord-340851-lnv8yi9l 262 12 c c NN cord-340851-lnv8yi9l 262 13 = = SYM cord-340851-lnv8yi9l 262 14 10 10 CD cord-340851-lnv8yi9l 262 15 −12 −12 NN cord-340851-lnv8yi9l 262 16 . . . cord-340851-lnv8yi9l 263 1 Vaccination vaccination NN cord-340851-lnv8yi9l 263 2 is be VBZ cord-340851-lnv8yi9l 263 3 introduced introduce VBN cord-340851-lnv8yi9l 263 4 at at IN cord-340851-lnv8yi9l 263 5 the the DT cord-340851-lnv8yi9l 263 6 time time NN cord-340851-lnv8yi9l 263 7 indicated indicate VBN cord-340851-lnv8yi9l 263 8 by by IN cord-340851-lnv8yi9l 263 9 the the DT cord-340851-lnv8yi9l 263 10 arrow arrow NN cord-340851-lnv8yi9l 263 11 , , , cord-340851-lnv8yi9l 263 12 with with IN cord-340851-lnv8yi9l 263 13 the the DT cord-340851-lnv8yi9l 263 14 vaccinated vaccinate VBN cord-340851-lnv8yi9l 263 15 population population NN cord-340851-lnv8yi9l 263 16 ( ( -LRB- cord-340851-lnv8yi9l 263 17 orange orange NNP cord-340851-lnv8yi9l 263 18 ) ) -RRB- cord-340851-lnv8yi9l 263 19 reducing reduce VBG cord-340851-lnv8yi9l 263 20 the the DT cord-340851-lnv8yi9l 263 21 susceptible susceptible JJ cord-340851-lnv8yi9l 263 22 population population NN cord-340851-lnv8yi9l 263 23 . . . cord-340851-lnv8yi9l 264 1 Through through IN cord-340851-lnv8yi9l 264 2 April April NNP cord-340851-lnv8yi9l 264 3 2020 2020 CD cord-340851-lnv8yi9l 264 4 ( ( -LRB- cord-340851-lnv8yi9l 264 5 gray gray JJ cord-340851-lnv8yi9l 264 6 shading shading NN cord-340851-lnv8yi9l 264 7 ) ) -RRB- cord-340851-lnv8yi9l 264 8 , , , cord-340851-lnv8yi9l 264 9 the the DT cord-340851-lnv8yi9l 264 10 value value NN cord-340851-lnv8yi9l 264 11 of of IN cord-340851-lnv8yi9l 264 12 the the DT cord-340851-lnv8yi9l 264 13 control control NN cord-340851-lnv8yi9l 264 14 is be VBZ cord-340851-lnv8yi9l 264 15 fixed fix VBN cord-340851-lnv8yi9l 264 16 according accord VBG cord-340851-lnv8yi9l 264 17 to to IN cord-340851-lnv8yi9l 264 18 its -PRON- PRP$ cord-340851-lnv8yi9l 264 19 calibrated calibrate VBN cord-340851-lnv8yi9l 264 20 trajectory trajectory NN cord-340851-lnv8yi9l 264 21 . . . cord-340851-lnv8yi9l 265 1 The the DT cord-340851-lnv8yi9l 265 2 dashed dash VBN cord-340851-lnv8yi9l 265 3 horizontal horizontal JJ cord-340851-lnv8yi9l 265 4 line line NN cord-340851-lnv8yi9l 265 5 indicates indicate VBZ cord-340851-lnv8yi9l 265 6 hospital hospital NN cord-340851-lnv8yi9l 265 7 capacity capacity NN cord-340851-lnv8yi9l 265 8 . . . cord-340851-lnv8yi9l 266 1 Fig Fig NNP cord-340851-lnv8yi9l 266 2 . . . cord-340851-lnv8yi9l 267 1 9 9 CD cord-340851-lnv8yi9l 268 1 Optimal optimal JJ cord-340851-lnv8yi9l 268 2 control control NN cord-340851-lnv8yi9l 268 3 under under IN cord-340851-lnv8yi9l 268 4 parameters parameter NNS cord-340851-lnv8yi9l 268 5 with with IN cord-340851-lnv8yi9l 268 6 maximal maximal JJ cord-340851-lnv8yi9l 268 7 ability ability NN cord-340851-lnv8yi9l 268 8 to to TO cord-340851-lnv8yi9l 268 9 control control VB cord-340851-lnv8yi9l 268 10 the the DT cord-340851-lnv8yi9l 268 11 pandemic pandemic NN cord-340851-lnv8yi9l 268 12 , , , cord-340851-lnv8yi9l 268 13 with with IN cord-340851-lnv8yi9l 268 14 maximal maximal JJ cord-340851-lnv8yi9l 268 15 weighting weighting NN cord-340851-lnv8yi9l 268 16 on on IN cord-340851-lnv8yi9l 268 17 minimization minimization NN cord-340851-lnv8yi9l 268 18 of of IN cord-340851-lnv8yi9l 268 19 deaths death NNS cord-340851-lnv8yi9l 268 20 . . . cord-340851-lnv8yi9l 269 1 Panels panel NNS cord-340851-lnv8yi9l 269 2 show show VBP cord-340851-lnv8yi9l 269 3 the the DT cord-340851-lnv8yi9l 269 4 optimal optimal JJ cord-340851-lnv8yi9l 269 5 control control NN cord-340851-lnv8yi9l 269 6 ( ( -LRB- cord-340851-lnv8yi9l 269 7 bottom bottom NN cord-340851-lnv8yi9l 269 8 ) ) -RRB- cord-340851-lnv8yi9l 269 9 and and CC cord-340851-lnv8yi9l 269 10 its -PRON- PRP$ cord-340851-lnv8yi9l 269 11 impacts impact NNS cord-340851-lnv8yi9l 269 12 on on IN cord-340851-lnv8yi9l 269 13 the the DT cord-340851-lnv8yi9l 269 14 dynamics dynamic NNS cord-340851-lnv8yi9l 269 15 of of IN cord-340851-lnv8yi9l 269 16 hospitalized hospitalize VBN cord-340851-lnv8yi9l 269 17 ( ( -LRB- cord-340851-lnv8yi9l 269 18 middle middle JJ cord-340851-lnv8yi9l 269 19 ) ) -RRB- cord-340851-lnv8yi9l 269 20 and and CC cord-340851-lnv8yi9l 269 21 susceptible susceptible JJ cord-340851-lnv8yi9l 269 22 ( ( -LRB- cord-340851-lnv8yi9l 269 23 top top JJ cord-340851-lnv8yi9l 269 24 ) ) -RRB- cord-340851-lnv8yi9l 269 25 compartments compartment NNS cord-340851-lnv8yi9l 269 26 with with IN cord-340851-lnv8yi9l 269 27 R r NN cord-340851-lnv8yi9l 269 28 0 0 CD cord-340851-lnv8yi9l 269 29 = = SYM cord-340851-lnv8yi9l 269 30 4 4 CD cord-340851-lnv8yi9l 269 31 , , , cord-340851-lnv8yi9l 269 32 umax umax NNP cord-340851-lnv8yi9l 269 33 = = SYM cord-340851-lnv8yi9l 269 34 0.5 0.5 CD cord-340851-lnv8yi9l 269 35 , , , cord-340851-lnv8yi9l 269 36 ω ω NN cord-340851-lnv8yi9l 269 37 = = SYM cord-340851-lnv8yi9l 269 38 0.8 0.8 CD cord-340851-lnv8yi9l 269 39 , , , cord-340851-lnv8yi9l 269 40 and and CC cord-340851-lnv8yi9l 269 41 c c NN cord-340851-lnv8yi9l 269 42 = = SYM cord-340851-lnv8yi9l 269 43 10 10 CD cord-340851-lnv8yi9l 269 44 −12 −12 NN cord-340851-lnv8yi9l 269 45 . . . cord-340851-lnv8yi9l 270 1 Vaccination vaccination NN cord-340851-lnv8yi9l 270 2 is be VBZ cord-340851-lnv8yi9l 270 3 introduced introduce VBN cord-340851-lnv8yi9l 270 4 at at IN cord-340851-lnv8yi9l 270 5 the the DT cord-340851-lnv8yi9l 270 6 time time NN cord-340851-lnv8yi9l 270 7 indicated indicate VBN cord-340851-lnv8yi9l 270 8 by by IN cord-340851-lnv8yi9l 270 9 the the DT cord-340851-lnv8yi9l 270 10 arrow arrow NN cord-340851-lnv8yi9l 270 11 , , , cord-340851-lnv8yi9l 270 12 with with IN cord-340851-lnv8yi9l 270 13 the the DT cord-340851-lnv8yi9l 270 14 vaccinated vaccinate VBN cord-340851-lnv8yi9l 270 15 population population NN cord-340851-lnv8yi9l 270 16 ( ( -LRB- cord-340851-lnv8yi9l 270 17 orange orange NNP cord-340851-lnv8yi9l 270 18 ) ) -RRB- cord-340851-lnv8yi9l 270 19 reducing reduce VBG cord-340851-lnv8yi9l 270 20 the the DT cord-340851-lnv8yi9l 270 21 susceptible susceptible JJ cord-340851-lnv8yi9l 270 22 population population NN cord-340851-lnv8yi9l 270 23 . . . cord-340851-lnv8yi9l 271 1 Through through IN cord-340851-lnv8yi9l 271 2 April April NNP cord-340851-lnv8yi9l 271 3 2020 2020 CD cord-340851-lnv8yi9l 271 4 ( ( -LRB- cord-340851-lnv8yi9l 271 5 gray gray JJ cord-340851-lnv8yi9l 271 6 shading shading NN cord-340851-lnv8yi9l 271 7 ) ) -RRB- cord-340851-lnv8yi9l 271 8 , , , cord-340851-lnv8yi9l 271 9 the the DT cord-340851-lnv8yi9l 271 10 value value NN cord-340851-lnv8yi9l 271 11 of of IN cord-340851-lnv8yi9l 271 12 the the DT cord-340851-lnv8yi9l 271 13 control control NN cord-340851-lnv8yi9l 271 14 is be VBZ cord-340851-lnv8yi9l 271 15 fixed fix VBN cord-340851-lnv8yi9l 271 16 according accord VBG cord-340851-lnv8yi9l 271 17 to to IN cord-340851-lnv8yi9l 271 18 its -PRON- PRP$ cord-340851-lnv8yi9l 271 19 calibrated calibrate VBN cord-340851-lnv8yi9l 271 20 trajectory trajectory NN cord-340851-lnv8yi9l 271 21 . . . cord-340851-lnv8yi9l 272 1 The the DT cord-340851-lnv8yi9l 272 2 dashed dash VBN cord-340851-lnv8yi9l 272 3 horizontal horizontal JJ cord-340851-lnv8yi9l 272 4 line line NN cord-340851-lnv8yi9l 272 5 indicates indicate VBZ cord-340851-lnv8yi9l 272 6 hospital hospital NN cord-340851-lnv8yi9l 272 7 capacity capacity NN cord-340851-lnv8yi9l 272 8 . . . cord-340851-lnv8yi9l 272 9 . . . cord-340851-lnv8yi9l 273 1 CC CC NNP cord-340851-lnv8yi9l 273 2 - - : cord-340851-lnv8yi9l 273 3 BY by IN cord-340851-lnv8yi9l 273 4 4.0 4.0 CD cord-340851-lnv8yi9l 273 5 International international JJ cord-340851-lnv8yi9l 273 6 license license NN cord-340851-lnv8yi9l 274 1 It -PRON- PRP cord-340851-lnv8yi9l 274 2 is be VBZ cord-340851-lnv8yi9l 274 3 made make VBN cord-340851-lnv8yi9l 274 4 available available JJ cord-340851-lnv8yi9l 274 5 under under IN cord-340851-lnv8yi9l 274 6 a a DT cord-340851-lnv8yi9l 275 1 is be VBZ cord-340851-lnv8yi9l 275 2 the the DT cord-340851-lnv8yi9l 275 3 author author NN cord-340851-lnv8yi9l 275 4 / / SYM cord-340851-lnv8yi9l 275 5 funder funder NN cord-340851-lnv8yi9l 275 6 , , , cord-340851-lnv8yi9l 275 7 who who WP cord-340851-lnv8yi9l 275 8 has have VBZ cord-340851-lnv8yi9l 275 9 granted grant VBN cord-340851-lnv8yi9l 275 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 275 11 a a DT cord-340851-lnv8yi9l 275 12 license license NN cord-340851-lnv8yi9l 275 13 to to TO cord-340851-lnv8yi9l 275 14 display display VB cord-340851-lnv8yi9l 275 15 the the DT cord-340851-lnv8yi9l 275 16 preprint preprint NN cord-340851-lnv8yi9l 275 17 in in IN cord-340851-lnv8yi9l 275 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 275 19 . . . cord-340851-lnv8yi9l 276 1 The the DT cord-340851-lnv8yi9l 276 2 copyright copyright NN cord-340851-lnv8yi9l 276 3 holder holder NN cord-340851-lnv8yi9l 276 4 for for IN cord-340851-lnv8yi9l 276 5 this this DT cord-340851-lnv8yi9l 276 6 preprint preprint NN cord-340851-lnv8yi9l 276 7 this this DT cord-340851-lnv8yi9l 276 8 version version NN cord-340851-lnv8yi9l 276 9 posted post VBN cord-340851-lnv8yi9l 276 10 April April NNP cord-340851-lnv8yi9l 276 11 23 23 CD cord-340851-lnv8yi9l 276 12 , , , cord-340851-lnv8yi9l 276 13 2020 2020 CD cord-340851-lnv8yi9l 276 14 . . . cord-340851-lnv8yi9l 276 15 . . . cord-340851-lnv8yi9l 277 1 https://doi.org/10.1101/2020.04 https://doi.org/10.1101/2020.04 UH cord-340851-lnv8yi9l 277 2 . . . cord-340851-lnv8yi9l 278 1 22.20076018 22.20076018 CD cord-340851-lnv8yi9l 278 2 doi doi NN cord-340851-lnv8yi9l 278 3 : : : cord-340851-lnv8yi9l 279 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 279 2 preprint preprint NNP cord-340851-lnv8yi9l 279 3 initiated initiate VBD cord-340851-lnv8yi9l 279 4 one one CD cord-340851-lnv8yi9l 279 5 to to IN cord-340851-lnv8yi9l 279 6 three three CD cord-340851-lnv8yi9l 279 7 weeks week NNS cord-340851-lnv8yi9l 279 8 earlier early RBR cord-340851-lnv8yi9l 279 9 or or CC cord-340851-lnv8yi9l 279 10 later later RB cord-340851-lnv8yi9l 279 11 in in IN cord-340851-lnv8yi9l 279 12 spring spring NN cord-340851-lnv8yi9l 279 13 2020 2020 CD cord-340851-lnv8yi9l 279 14 would would MD cord-340851-lnv8yi9l 279 15 affect affect VB cord-340851-lnv8yi9l 279 16 optimal optimal JJ cord-340851-lnv8yi9l 279 17 controls control NNS cord-340851-lnv8yi9l 279 18 in in IN cord-340851-lnv8yi9l 279 19 the the DT cord-340851-lnv8yi9l 279 20 period period NN cord-340851-lnv8yi9l 279 21 after after RB cord-340851-lnv8yi9l 279 22 . . . cord-340851-lnv8yi9l 280 1 We -PRON- PRP cord-340851-lnv8yi9l 280 2 focus focus VBP cord-340851-lnv8yi9l 280 3 this this DT cord-340851-lnv8yi9l 280 4 analysis analysis NN cord-340851-lnv8yi9l 280 5 on on IN cord-340851-lnv8yi9l 280 6 scenarios scenario NNS cord-340851-lnv8yi9l 280 7 in in IN cord-340851-lnv8yi9l 280 8 which which WDT cord-340851-lnv8yi9l 280 9 c c NN cord-340851-lnv8yi9l 280 10 = = SYM cord-340851-lnv8yi9l 280 11 10 10 CD cord-340851-lnv8yi9l 280 12 −12 −12 NN cord-340851-lnv8yi9l 280 13 , , , cord-340851-lnv8yi9l 280 14 which which WDT cord-340851-lnv8yi9l 280 15 results result VBZ cord-340851-lnv8yi9l 280 16 in in IN cord-340851-lnv8yi9l 280 17 the the DT cord-340851-lnv8yi9l 280 18 optimal optimal JJ cord-340851-lnv8yi9l 280 19 control control NN cord-340851-lnv8yi9l 280 20 problem problem NN cord-340851-lnv8yi9l 280 21 seeking seek VBG cord-340851-lnv8yi9l 280 22 to to TO cord-340851-lnv8yi9l 280 23 minimize minimize VB cord-340851-lnv8yi9l 280 24 deaths death NNS cord-340851-lnv8yi9l 280 25 as as RB cord-340851-lnv8yi9l 280 26 aggressively aggressively RB cord-340851-lnv8yi9l 280 27 as as IN cord-340851-lnv8yi9l 280 28 any any DT cord-340851-lnv8yi9l 280 29 scenario scenario NN cord-340851-lnv8yi9l 280 30 that that WDT cord-340851-lnv8yi9l 280 31 we -PRON- PRP cord-340851-lnv8yi9l 280 32 explored explore VBD cord-340851-lnv8yi9l 280 33 . . . cord-340851-lnv8yi9l 281 1 Consequently consequently RB cord-340851-lnv8yi9l 281 2 , , , cord-340851-lnv8yi9l 281 3 we -PRON- PRP cord-340851-lnv8yi9l 281 4 interpret interpret VBP cord-340851-lnv8yi9l 281 5 changes change NNS cord-340851-lnv8yi9l 281 6 in in IN cord-340851-lnv8yi9l 281 7 the the DT cord-340851-lnv8yi9l 281 8 optimal optimal JJ cord-340851-lnv8yi9l 281 9 control control NN cord-340851-lnv8yi9l 281 10 in in IN cord-340851-lnv8yi9l 281 11 this this DT cord-340851-lnv8yi9l 281 12 section section NN cord-340851-lnv8yi9l 281 13 to to TO cord-340851-lnv8yi9l 281 14 reflect reflect VB cord-340851-lnv8yi9l 281 15 changes change NNS cord-340851-lnv8yi9l 281 16 in in IN cord-340851-lnv8yi9l 281 17 constraints constraint NNS cord-340851-lnv8yi9l 281 18 on on IN cord-340851-lnv8yi9l 281 19 what what WDT cord-340851-lnv8yi9l 281 20 solutions solution NNS cord-340851-lnv8yi9l 281 21 of of IN cord-340851-lnv8yi9l 281 22 u u NNP cord-340851-lnv8yi9l 281 23 * * NFP cord-340851-lnv8yi9l 281 24 ( ( -LRB- cord-340851-lnv8yi9l 281 25 t t NN cord-340851-lnv8yi9l 281 26 ) ) -RRB- cord-340851-lnv8yi9l 281 27 are be VBP cord-340851-lnv8yi9l 281 28 possible possible JJ cord-340851-lnv8yi9l 281 29 , , , cord-340851-lnv8yi9l 281 30 rather rather RB cord-340851-lnv8yi9l 281 31 than than IN cord-340851-lnv8yi9l 281 32 changes change NNS cord-340851-lnv8yi9l 281 33 in in IN cord-340851-lnv8yi9l 281 34 the the DT cord-340851-lnv8yi9l 281 35 balance balance NN cord-340851-lnv8yi9l 281 36 between between IN cord-340851-lnv8yi9l 281 37 D(t D(t NNP cord-340851-lnv8yi9l 281 38 ) ) -RRB- cord-340851-lnv8yi9l 281 39 2 2 CD cord-340851-lnv8yi9l 281 40 and and CC cord-340851-lnv8yi9l 281 41 u(t u(t NN cord-340851-lnv8yi9l 281 42 ) ) -RRB- cord-340851-lnv8yi9l 281 43 2 2 CD cord-340851-lnv8yi9l 281 44 in in IN cord-340851-lnv8yi9l 281 45 the the DT cord-340851-lnv8yi9l 281 46 optimization optimization NN cord-340851-lnv8yi9l 281 47 . . . cord-340851-lnv8yi9l 282 1 Across across IN cord-340851-lnv8yi9l 282 2 all all DT cord-340851-lnv8yi9l 282 3 combinations combination NNS cord-340851-lnv8yi9l 282 4 of of IN cord-340851-lnv8yi9l 282 5 R r NN cord-340851-lnv8yi9l 282 6 0 0 CD cord-340851-lnv8yi9l 282 7 , , , cord-340851-lnv8yi9l 282 8 u u NNP cord-340851-lnv8yi9l 282 9 max max NNP cord-340851-lnv8yi9l 282 10 , , , cord-340851-lnv8yi9l 282 11 and and CC cord-340851-lnv8yi9l 282 12 ω ω NN cord-340851-lnv8yi9l 282 13 that that IN cord-340851-lnv8yi9l 282 14 we -PRON- PRP cord-340851-lnv8yi9l 282 15 considered consider VBD cord-340851-lnv8yi9l 282 16 , , , cord-340851-lnv8yi9l 282 17 cumulative cumulative JJ cord-340851-lnv8yi9l 282 18 deaths death NNS cord-340851-lnv8yi9l 282 19 through through IN cord-340851-lnv8yi9l 282 20 2020 2020 CD cord-340851-lnv8yi9l 282 21 and and CC cord-340851-lnv8yi9l 282 22 2021 2021 CD cord-340851-lnv8yi9l 282 23 decrease decrease NN cord-340851-lnv8yi9l 282 24 when when WRB cord-340851-lnv8yi9l 282 25 control control NN cord-340851-lnv8yi9l 282 26 begins begin VBZ cord-340851-lnv8yi9l 282 27 earlier early RBR cord-340851-lnv8yi9l 282 28 and and CC cord-340851-lnv8yi9l 282 29 increase increase VB cord-340851-lnv8yi9l 282 30 when when WRB cord-340851-lnv8yi9l 282 31 control control NN cord-340851-lnv8yi9l 282 32 begins begin VBZ cord-340851-lnv8yi9l 282 33 later later RB cord-340851-lnv8yi9l 282 34 ( ( -LRB- cord-340851-lnv8yi9l 282 35 Figure figure NN cord-340851-lnv8yi9l 282 36 10 10 CD cord-340851-lnv8yi9l 282 37 , , , cord-340851-lnv8yi9l 282 38 red red JJ cord-340851-lnv8yi9l 282 39 ) ) -RRB- cord-340851-lnv8yi9l 282 40 . . . cord-340851-lnv8yi9l 283 1 In in IN cord-340851-lnv8yi9l 283 2 the the DT cord-340851-lnv8yi9l 283 3 scenario scenario NN cord-340851-lnv8yi9l 283 4 in in IN cord-340851-lnv8yi9l 283 5 which which WDT cord-340851-lnv8yi9l 283 6 a a DT cord-340851-lnv8yi9l 283 7 delay delay NN cord-340851-lnv8yi9l 283 8 in in IN cord-340851-lnv8yi9l 283 9 the the DT cord-340851-lnv8yi9l 283 10 initiation initiation NN cord-340851-lnv8yi9l 283 11 of of IN cord-340851-lnv8yi9l 283 12 control control NN cord-340851-lnv8yi9l 283 13 has have VBZ cord-340851-lnv8yi9l 283 14 the the DT cord-340851-lnv8yi9l 283 15 smallest small JJS cord-340851-lnv8yi9l 283 16 effect effect NN cord-340851-lnv8yi9l 283 17 ( ( -LRB- cord-340851-lnv8yi9l 283 18 R r NN cord-340851-lnv8yi9l 283 19 0 0 CD cord-340851-lnv8yi9l 283 20 = = SYM cord-340851-lnv8yi9l 283 21 3 3 CD cord-340851-lnv8yi9l 283 22 , , , cord-340851-lnv8yi9l 283 23 u u NNP cord-340851-lnv8yi9l 283 24 max max NN cord-340851-lnv8yi9l 283 25 = = SYM cord-340851-lnv8yi9l 283 26 0.5 0.5 CD cord-340851-lnv8yi9l 283 27 ) ) -RRB- cord-340851-lnv8yi9l 283 28 , , , cord-340851-lnv8yi9l 283 29 cumulative cumulative JJ cord-340851-lnv8yi9l 283 30 deaths death NNS cord-340851-lnv8yi9l 283 31 increase increase VBP cord-340851-lnv8yi9l 283 32 by by IN cord-340851-lnv8yi9l 283 33 10 10 CD cord-340851-lnv8yi9l 283 34 % % NN cord-340851-lnv8yi9l 283 35 with with IN cord-340851-lnv8yi9l 283 36 a a DT cord-340851-lnv8yi9l 283 37 three three CD cord-340851-lnv8yi9l 283 38 - - HYPH cord-340851-lnv8yi9l 283 39 week week NN cord-340851-lnv8yi9l 283 40 delay delay NN cord-340851-lnv8yi9l 283 41 . . . cord-340851-lnv8yi9l 284 1 In in IN cord-340851-lnv8yi9l 284 2 the the DT cord-340851-lnv8yi9l 284 3 scenario scenario NN cord-340851-lnv8yi9l 284 4 in in IN cord-340851-lnv8yi9l 284 5 which which WDT cord-340851-lnv8yi9l 284 6 a a DT cord-340851-lnv8yi9l 284 7 delay delay NN cord-340851-lnv8yi9l 284 8 in in IN cord-340851-lnv8yi9l 284 9 the the DT cord-340851-lnv8yi9l 284 10 initiation initiation NN cord-340851-lnv8yi9l 284 11 of of IN cord-340851-lnv8yi9l 284 12 control control NN cord-340851-lnv8yi9l 284 13 has have VBZ cord-340851-lnv8yi9l 284 14 the the DT cord-340851-lnv8yi9l 284 15 largest large JJS cord-340851-lnv8yi9l 284 16 effect effect NN cord-340851-lnv8yi9l 284 17 ( ( -LRB- cord-340851-lnv8yi9l 284 18 R r NN cord-340851-lnv8yi9l 284 19 0 0 CD cord-340851-lnv8yi9l 284 20 = = SYM cord-340851-lnv8yi9l 284 21 4 4 CD cord-340851-lnv8yi9l 284 22 , , , cord-340851-lnv8yi9l 284 23 u u NNP cord-340851-lnv8yi9l 284 24 max max NN cord-340851-lnv8yi9l 284 25 = = SYM cord-340851-lnv8yi9l 284 26 0.9 0.9 CD cord-340851-lnv8yi9l 284 27 ) ) -RRB- cord-340851-lnv8yi9l 284 28 , , , cord-340851-lnv8yi9l 284 29 cumulative cumulative JJ cord-340851-lnv8yi9l 284 30 deaths death NNS cord-340851-lnv8yi9l 284 31 increase increase VBP cord-340851-lnv8yi9l 284 32 28-fold 28-fold CD cord-340851-lnv8yi9l 284 33 with with IN cord-340851-lnv8yi9l 284 34 a a DT cord-340851-lnv8yi9l 284 35 three three CD cord-340851-lnv8yi9l 284 36 - - HYPH cord-340851-lnv8yi9l 284 37 week week NN cord-340851-lnv8yi9l 284 38 delay delay NN cord-340851-lnv8yi9l 284 39 . . . cord-340851-lnv8yi9l 285 1 The the DT cord-340851-lnv8yi9l 285 2 overall overall JJ cord-340851-lnv8yi9l 285 3 amount amount NN cord-340851-lnv8yi9l 285 4 of of IN cord-340851-lnv8yi9l 285 5 time time NN cord-340851-lnv8yi9l 285 6 spent spend VBN cord-340851-lnv8yi9l 285 7 under under IN cord-340851-lnv8yi9l 285 8 control control NN cord-340851-lnv8yi9l 285 9 throughout throughout IN cord-340851-lnv8yi9l 285 10 2020 2020 CD cord-340851-lnv8yi9l 285 11 and and CC cord-340851-lnv8yi9l 285 12 2021 2021 CD cord-340851-lnv8yi9l 285 13 increases increase NNS cord-340851-lnv8yi9l 285 14 when when WRB cord-340851-lnv8yi9l 285 15 control control NN cord-340851-lnv8yi9l 285 16 begins begin VBZ cord-340851-lnv8yi9l 285 17 earlier early RBR cord-340851-lnv8yi9l 285 18 and and CC cord-340851-lnv8yi9l 285 19 decreases decrease VBZ cord-340851-lnv8yi9l 285 20 when when WRB cord-340851-lnv8yi9l 285 21 control control NN cord-340851-lnv8yi9l 285 22 begins begin VBZ cord-340851-lnv8yi9l 285 23 later later RB cord-340851-lnv8yi9l 285 24 ( ( -LRB- cord-340851-lnv8yi9l 285 25 Figure figure NN cord-340851-lnv8yi9l 285 26 10 10 CD cord-340851-lnv8yi9l 285 27 , , , cord-340851-lnv8yi9l 285 28 blue blue JJ cord-340851-lnv8yi9l 285 29 ) ) -RRB- cord-340851-lnv8yi9l 285 30 . . . cord-340851-lnv8yi9l 286 1 This this DT cord-340851-lnv8yi9l 286 2 is be VBZ cord-340851-lnv8yi9l 286 3 the the DT cord-340851-lnv8yi9l 286 4 case case NN cord-340851-lnv8yi9l 286 5 across across IN cord-340851-lnv8yi9l 286 6 all all DT cord-340851-lnv8yi9l 286 7 combinations combination NNS cord-340851-lnv8yi9l 286 8 of of IN cord-340851-lnv8yi9l 286 9 R r NN cord-340851-lnv8yi9l 286 10 0 0 CD cord-340851-lnv8yi9l 286 11 , , , cord-340851-lnv8yi9l 286 12 u u NNP cord-340851-lnv8yi9l 286 13 max max NNP cord-340851-lnv8yi9l 286 14 , , , cord-340851-lnv8yi9l 286 15 and and CC cord-340851-lnv8yi9l 286 16 ω ω NN cord-340851-lnv8yi9l 286 17 that that IN cord-340851-lnv8yi9l 286 18 we -PRON- PRP cord-340851-lnv8yi9l 286 19 considered consider VBD cord-340851-lnv8yi9l 286 20 . . . cord-340851-lnv8yi9l 287 1 In in IN cord-340851-lnv8yi9l 287 2 part part NN cord-340851-lnv8yi9l 287 3 , , , cord-340851-lnv8yi9l 287 4 this this DT cord-340851-lnv8yi9l 287 5 owes owe VBZ cord-340851-lnv8yi9l 287 6 to to IN cord-340851-lnv8yi9l 287 7 less less JJR cord-340851-lnv8yi9l 287 8 time time NN cord-340851-lnv8yi9l 287 9 spent spend VBN cord-340851-lnv8yi9l 287 10 under under IN cord-340851-lnv8yi9l 287 11 control control NN cord-340851-lnv8yi9l 287 12 through through IN cord-340851-lnv8yi9l 287 13 April April NNP cord-340851-lnv8yi9l 287 14 30 30 CD cord-340851-lnv8yi9l 287 15 , , , cord-340851-lnv8yi9l 287 16 2020 2020 CD cord-340851-lnv8yi9l 287 17 , , , cord-340851-lnv8yi9l 287 18 when when WRB cord-340851-lnv8yi9l 287 19 u(t u(t NNP cord-340851-lnv8yi9l 287 20 ) ) -RRB- cord-340851-lnv8yi9l 287 21 is be VBZ cord-340851-lnv8yi9l 287 22 fixed fix VBN cord-340851-lnv8yi9l 287 23 and and CC cord-340851-lnv8yi9l 287 24 not not RB cord-340851-lnv8yi9l 287 25 subject subject JJ cord-340851-lnv8yi9l 287 26 to to IN cord-340851-lnv8yi9l 287 27 optimization optimization NN cord-340851-lnv8yi9l 287 28 . . . cord-340851-lnv8yi9l 288 1 In in IN cord-340851-lnv8yi9l 288 2 addition addition NN cord-340851-lnv8yi9l 288 3 though though RB cord-340851-lnv8yi9l 288 4 , , , cord-340851-lnv8yi9l 288 5 delays delay NNS cord-340851-lnv8yi9l 288 6 in in IN cord-340851-lnv8yi9l 288 7 the the DT cord-340851-lnv8yi9l 288 8 initiation initiation NN cord-340851-lnv8yi9l 288 9 of of IN cord-340851-lnv8yi9l 288 10 control control NN cord-340851-lnv8yi9l 288 11 result result NN cord-340851-lnv8yi9l 288 12 in in IN cord-340851-lnv8yi9l 288 13 a a DT cord-340851-lnv8yi9l 288 14 higher high JJR cord-340851-lnv8yi9l 288 15 prevalence prevalence NN cord-340851-lnv8yi9l 288 16 of of IN cord-340851-lnv8yi9l 288 17 infection infection NN cord-340851-lnv8yi9l 288 18 by by IN cord-340851-lnv8yi9l 288 19 the the DT cord-340851-lnv8yi9l 288 20 beginning beginning NN cord-340851-lnv8yi9l 288 21 of of IN cord-340851-lnv8yi9l 288 22 the the DT cord-340851-lnv8yi9l 288 23 optimization optimization NN cord-340851-lnv8yi9l 288 24 period period NN cord-340851-lnv8yi9l 288 25 , , , cord-340851-lnv8yi9l 288 26 which which WDT cord-340851-lnv8yi9l 288 27 results result VBZ cord-340851-lnv8yi9l 288 28 in in IN cord-340851-lnv8yi9l 288 29 higher high JJR cord-340851-lnv8yi9l 288 30 levels level NNS cord-340851-lnv8yi9l 288 31 of of IN cord-340851-lnv8yi9l 288 32 subsequent subsequent JJ cord-340851-lnv8yi9l 288 33 transmission transmission NN cord-340851-lnv8yi9l 288 34 , , , cord-340851-lnv8yi9l 288 35 greater great JJR cord-340851-lnv8yi9l 288 36 depletion depletion NN cord-340851-lnv8yi9l 288 37 of of IN cord-340851-lnv8yi9l 288 38 the the DT cord-340851-lnv8yi9l 288 39 susceptible susceptible JJ cord-340851-lnv8yi9l 288 40 population population NN cord-340851-lnv8yi9l 288 41 , , , cord-340851-lnv8yi9l 288 42 and and CC cord-340851-lnv8yi9l 288 43 less less JJR cord-340851-lnv8yi9l 288 44 need need NN cord-340851-lnv8yi9l 288 45 for for IN cord-340851-lnv8yi9l 288 46 control control NN cord-340851-lnv8yi9l 288 47 later later RB cord-340851-lnv8yi9l 288 48 in in IN cord-340851-lnv8yi9l 288 49 the the DT cord-340851-lnv8yi9l 288 50 period period NN cord-340851-lnv8yi9l 288 51 of of IN cord-340851-lnv8yi9l 288 52 optimization optimization NN cord-340851-lnv8yi9l 288 53 ( ( -LRB- cord-340851-lnv8yi9l 288 54 compare compare VB cord-340851-lnv8yi9l 288 55 Figure figure NN cord-340851-lnv8yi9l 288 56 11 11 CD cord-340851-lnv8yi9l 288 57 with with IN cord-340851-lnv8yi9l 288 58 Figure figure NN cord-340851-lnv8yi9l 288 59 5 5 CD cord-340851-lnv8yi9l 288 60 ) ) -RRB- cord-340851-lnv8yi9l 288 61 . . . cord-340851-lnv8yi9l 289 1 Under under IN cord-340851-lnv8yi9l 289 2 our -PRON- PRP$ cord-340851-lnv8yi9l 289 3 model model NN cord-340851-lnv8yi9l 289 4 , , , cord-340851-lnv8yi9l 289 5 the the DT cord-340851-lnv8yi9l 289 6 ability ability NN cord-340851-lnv8yi9l 289 7 of of IN cord-340851-lnv8yi9l 289 8 NPIs npi NNS cord-340851-lnv8yi9l 289 9 to to TO cord-340851-lnv8yi9l 289 10 minimize minimize VB cord-340851-lnv8yi9l 289 11 deaths death NNS cord-340851-lnv8yi9l 289 12 depends depend VBZ cord-340851-lnv8yi9l 289 13 to to IN cord-340851-lnv8yi9l 289 14 a a DT cord-340851-lnv8yi9l 289 15 large large JJ cord-340851-lnv8yi9l 289 16 extent extent NN cord-340851-lnv8yi9l 289 17 on on IN cord-340851-lnv8yi9l 289 18 the the DT cord-340851-lnv8yi9l 289 19 maximum maximum JJ cord-340851-lnv8yi9l 289 20 effect effect NN cord-340851-lnv8yi9l 289 21 that that IN cord-340851-lnv8yi9l 289 22 NPIs npi NNS cord-340851-lnv8yi9l 289 23 could could MD cord-340851-lnv8yi9l 289 24 have have VB cord-340851-lnv8yi9l 289 25 on on IN cord-340851-lnv8yi9l 289 26 transmission transmission NN cord-340851-lnv8yi9l 289 27 , , , cord-340851-lnv8yi9l 289 28 as as IN cord-340851-lnv8yi9l 289 29 captured capture VBN cord-340851-lnv8yi9l 289 30 by by IN cord-340851-lnv8yi9l 289 31 the the DT cord-340851-lnv8yi9l 289 32 parameter parameter NN cord-340851-lnv8yi9l 289 33 u u NNP cord-340851-lnv8yi9l 289 34 max max NNP cord-340851-lnv8yi9l 289 35 . . . cord-340851-lnv8yi9l 290 1 If if IN cord-340851-lnv8yi9l 290 2 u u NNP cord-340851-lnv8yi9l 290 3 max max NNP cord-340851-lnv8yi9l 290 4 is be VBZ cord-340851-lnv8yi9l 290 5 high high JJ cord-340851-lnv8yi9l 290 6 ( ( -LRB- cord-340851-lnv8yi9l 290 7 0.9 0.9 CD cord-340851-lnv8yi9l 290 8 ) ) -RRB- cord-340851-lnv8yi9l 290 9 , , , cord-340851-lnv8yi9l 290 10 our -PRON- PRP$ cord-340851-lnv8yi9l 290 11 model model NN cord-340851-lnv8yi9l 290 12 predicts predict VBZ cord-340851-lnv8yi9l 290 13 that that IN cord-340851-lnv8yi9l 290 14 maintaining maintain VBG cord-340851-lnv8yi9l 290 15 transmission transmission NN cord-340851-lnv8yi9l 290 16 at at IN cord-340851-lnv8yi9l 290 17 a a DT cord-340851-lnv8yi9l 290 18 low low JJ cord-340851-lnv8yi9l 290 19 enough enough JJ cord-340851-lnv8yi9l 290 20 level level NN cord-340851-lnv8yi9l 290 21 that that DT cord-340851-lnv8yi9l 290 22 hospital hospital NN cord-340851-lnv8yi9l 290 23 capacity capacity NN cord-340851-lnv8yi9l 290 24 will will MD cord-340851-lnv8yi9l 290 25 not not RB cord-340851-lnv8yi9l 290 26 be be VB cord-340851-lnv8yi9l 290 27 exceeded exceed VBN cord-340851-lnv8yi9l 290 28 could could MD cord-340851-lnv8yi9l 290 29 be be VB cord-340851-lnv8yi9l 290 30 possible possible JJ cord-340851-lnv8yi9l 290 31 . . . cord-340851-lnv8yi9l 291 1 If if IN cord-340851-lnv8yi9l 291 2 u u NNP cord-340851-lnv8yi9l 291 3 max max NNP cord-340851-lnv8yi9l 291 4 is be VBZ cord-340851-lnv8yi9l 291 5 low low JJ cord-340851-lnv8yi9l 291 6 ( ( -LRB- cord-340851-lnv8yi9l 291 7 0.5 0.5 CD cord-340851-lnv8yi9l 291 8 ) ) -RRB- cord-340851-lnv8yi9l 291 9 , , , cord-340851-lnv8yi9l 291 10 our -PRON- PRP$ cord-340851-lnv8yi9l 291 11 model model NN cord-340851-lnv8yi9l 291 12 predicts predict VBZ cord-340851-lnv8yi9l 291 13 that that IN cord-340851-lnv8yi9l 291 14 there there EX cord-340851-lnv8yi9l 291 15 may may MD cord-340851-lnv8yi9l 291 16 be be VB cord-340851-lnv8yi9l 291 17 limited limited JJ cord-340851-lnv8yi9l 291 18 scope scope NN cord-340851-lnv8yi9l 291 19 to to TO cord-340851-lnv8yi9l 291 20 curtail curtail VB cord-340851-lnv8yi9l 291 21 the the DT cord-340851-lnv8yi9l 291 22 pandemic pandemic NN cord-340851-lnv8yi9l 291 23 , , , cord-340851-lnv8yi9l 291 24 even even RB cord-340851-lnv8yi9l 291 25 if if IN cord-340851-lnv8yi9l 291 26 control control NN cord-340851-lnv8yi9l 291 27 is be VBZ cord-340851-lnv8yi9l 291 28 sustained sustain VBN cord-340851-lnv8yi9l 291 29 for for IN cord-340851-lnv8yi9l 291 30 a a DT cord-340851-lnv8yi9l 291 31 long long JJ cord-340851-lnv8yi9l 291 32 period period NN cord-340851-lnv8yi9l 291 33 of of IN cord-340851-lnv8yi9l 291 34 time time NN cord-340851-lnv8yi9l 291 35 . . . cord-340851-lnv8yi9l 292 1 If if IN cord-340851-lnv8yi9l 292 2 u u NNP cord-340851-lnv8yi9l 292 3 max max NNP cord-340851-lnv8yi9l 292 4 is be VBZ cord-340851-lnv8yi9l 292 5 intermediate intermediate JJ cord-340851-lnv8yi9l 292 6 ( ( -LRB- cord-340851-lnv8yi9l 292 7 0.7 0.7 CD cord-340851-lnv8yi9l 292 8 ) ) -RRB- cord-340851-lnv8yi9l 292 9 , , , cord-340851-lnv8yi9l 292 10 our -PRON- PRP$ cord-340851-lnv8yi9l 292 11 model model NN cord-340851-lnv8yi9l 292 12 predicts predict VBZ cord-340851-lnv8yi9l 292 13 that that IN cord-340851-lnv8yi9l 292 14 the the DT cord-340851-lnv8yi9l 292 15 potential potential JJ cord-340851-lnv8yi9l 292 16 impact impact NN cord-340851-lnv8yi9l 292 17 of of IN cord-340851-lnv8yi9l 292 18 control control NN cord-340851-lnv8yi9l 292 19 is be VBZ cord-340851-lnv8yi9l 292 20 sensitive sensitive JJ cord-340851-lnv8yi9l 292 21 to to IN cord-340851-lnv8yi9l 292 22 the the DT cord-340851-lnv8yi9l 292 23 value value NN cord-340851-lnv8yi9l 292 24 of of IN cord-340851-lnv8yi9l 292 25 R r NN cord-340851-lnv8yi9l 292 26 0 0 CD cord-340851-lnv8yi9l 292 27 . . . cord-340851-lnv8yi9l 293 1 These these DT cord-340851-lnv8yi9l 293 2 results result NNS cord-340851-lnv8yi9l 293 3 emphasize emphasize VBP cord-340851-lnv8yi9l 293 4 the the DT cord-340851-lnv8yi9l 293 5 importance importance NN cord-340851-lnv8yi9l 293 6 of of IN cord-340851-lnv8yi9l 293 7 careful careful JJ cord-340851-lnv8yi9l 293 8 estimation estimation NN cord-340851-lnv8yi9l 293 9 of of IN cord-340851-lnv8yi9l 293 10 these these DT cord-340851-lnv8yi9l 293 11 parameters parameter NNS cord-340851-lnv8yi9l 293 12 as as IN cord-340851-lnv8yi9l 293 13 the the DT cord-340851-lnv8yi9l 293 14 pandemic pandemic NN cord-340851-lnv8yi9l 293 15 progresses progress VBZ cord-340851-lnv8yi9l 293 16 [ [ -LRB- cord-340851-lnv8yi9l 293 17 18 18 CD cord-340851-lnv8yi9l 293 18 ] ] -RRB- cord-340851-lnv8yi9l 293 19 . . . cord-340851-lnv8yi9l 294 1 This this DT cord-340851-lnv8yi9l 294 2 includes include VBZ cord-340851-lnv8yi9l 294 3 accounting account VBG cord-340851-lnv8yi9l 294 4 for for IN cord-340851-lnv8yi9l 294 5 geographic geographic JJ cord-340851-lnv8yi9l 294 6 differences difference NNS cord-340851-lnv8yi9l 294 7 in in IN cord-340851-lnv8yi9l 294 8 both both CC cord-340851-lnv8yi9l 294 9 u u NNP cord-340851-lnv8yi9l 294 10 max max NNP cord-340851-lnv8yi9l 294 11 and and CC cord-340851-lnv8yi9l 294 12 R R NNP cord-340851-lnv8yi9l 294 13 0 0 CD cord-340851-lnv8yi9l 294 14 [ [ -LRB- cord-340851-lnv8yi9l 294 15 19 19 CD cord-340851-lnv8yi9l 294 16 , , , cord-340851-lnv8yi9l 294 17 21 21 CD cord-340851-lnv8yi9l 294 18 ] ] -RRB- cord-340851-lnv8yi9l 294 19 . . . cord-340851-lnv8yi9l 295 1 The the DT cord-340851-lnv8yi9l 295 2 balance balance NN cord-340851-lnv8yi9l 295 3 between between IN cord-340851-lnv8yi9l 295 4 minimizing minimize VBG cord-340851-lnv8yi9l 295 5 deaths death NNS cord-340851-lnv8yi9l 295 6 versus versus IN cord-340851-lnv8yi9l 295 7 days day NNS cord-340851-lnv8yi9l 295 8 under under IN cord-340851-lnv8yi9l 295 9 control control NN cord-340851-lnv8yi9l 295 10 is be VBZ cord-340851-lnv8yi9l 295 11 determined determine VBN cord-340851-lnv8yi9l 295 12 by by IN cord-340851-lnv8yi9l 295 13 the the DT cord-340851-lnv8yi9l 295 14 parameter parameter NN cord-340851-lnv8yi9l 295 15 c c NN cord-340851-lnv8yi9l 295 16 in in IN cord-340851-lnv8yi9l 295 17 our -PRON- PRP$ cord-340851-lnv8yi9l 295 18 model model NN cord-340851-lnv8yi9l 295 19 , , , cord-340851-lnv8yi9l 295 20 which which WDT cord-340851-lnv8yi9l 295 21 mirrors mirror VBZ cord-340851-lnv8yi9l 295 22 the the DT cord-340851-lnv8yi9l 295 23 weighting weighting NN cord-340851-lnv8yi9l 295 24 between between IN cord-340851-lnv8yi9l 295 25 these these DT cord-340851-lnv8yi9l 295 26 factors factor NNS cord-340851-lnv8yi9l 295 27 that that WDT cord-340851-lnv8yi9l 295 28 government government NN cord-340851-lnv8yi9l 295 29 leaders leader NNS cord-340851-lnv8yi9l 295 30 will will MD cord-340851-lnv8yi9l 295 31 need need VB cord-340851-lnv8yi9l 295 32 to to TO cord-340851-lnv8yi9l 295 33 consider consider VB cord-340851-lnv8yi9l 295 34 as as IN cord-340851-lnv8yi9l 295 35 they -PRON- PRP cord-340851-lnv8yi9l 295 36 make make VBP cord-340851-lnv8yi9l 295 37 decisions decision NNS cord-340851-lnv8yi9l 295 38 in in IN cord-340851-lnv8yi9l 295 39 coming come VBG cord-340851-lnv8yi9l 295 40 months month NNS cord-340851-lnv8yi9l 295 41 . . . cord-340851-lnv8yi9l 296 1 In in IN cord-340851-lnv8yi9l 296 2 the the DT cord-340851-lnv8yi9l 296 3 event event NN cord-340851-lnv8yi9l 296 4 that that IN cord-340851-lnv8yi9l 296 5 NPIs npi NNS cord-340851-lnv8yi9l 296 6 are be VBP cord-340851-lnv8yi9l 296 7 effective effective JJ cord-340851-lnv8yi9l 296 8 , , , cord-340851-lnv8yi9l 296 9 our -PRON- PRP$ cord-340851-lnv8yi9l 296 10 analysis analysis NN cord-340851-lnv8yi9l 296 11 shows show VBZ cord-340851-lnv8yi9l 296 12 that that IN cord-340851-lnv8yi9l 296 13 they -PRON- PRP cord-340851-lnv8yi9l 296 14 will will MD cord-340851-lnv8yi9l 296 15 need need VB cord-340851-lnv8yi9l 296 16 to to TO cord-340851-lnv8yi9l 296 17 be be VB cord-340851-lnv8yi9l 296 18 sustained sustain VBN cord-340851-lnv8yi9l 296 19 at at IN cord-340851-lnv8yi9l 296 20 a a DT cord-340851-lnv8yi9l 296 21 high high JJ cord-340851-lnv8yi9l 296 22 level level NN cord-340851-lnv8yi9l 296 23 until until IN cord-340851-lnv8yi9l 296 24 sometime sometime NN cord-340851-lnv8yi9l 296 25 in in IN cord-340851-lnv8yi9l 296 26 summer summer NN cord-340851-lnv8yi9l 296 27 2020 2020 CD cord-340851-lnv8yi9l 296 28 , , , cord-340851-lnv8yi9l 296 29 at at IN cord-340851-lnv8yi9l 296 30 which which WDT cord-340851-lnv8yi9l 296 31 time time NN cord-340851-lnv8yi9l 296 32 they -PRON- PRP cord-340851-lnv8yi9l 296 33 can can MD cord-340851-lnv8yi9l 296 34 be be VB cord-340851-lnv8yi9l 296 35 relaxed relaxed JJ cord-340851-lnv8yi9l 296 36 to to IN cord-340851-lnv8yi9l 296 37 a a DT cord-340851-lnv8yi9l 296 38 small small JJ cord-340851-lnv8yi9l 296 39 degree degree NN cord-340851-lnv8yi9l 296 40 but but CC cord-340851-lnv8yi9l 296 41 will will MD cord-340851-lnv8yi9l 296 42 still still RB cord-340851-lnv8yi9l 296 43 need need VB cord-340851-lnv8yi9l 296 44 to to TO cord-340851-lnv8yi9l 296 45 be be VB cord-340851-lnv8yi9l 296 46 maintained maintain VBN cord-340851-lnv8yi9l 296 47 at at IN cord-340851-lnv8yi9l 296 48 a a DT cord-340851-lnv8yi9l 296 49 relatively relatively RB cord-340851-lnv8yi9l 296 50 high high JJ cord-340851-lnv8yi9l 296 51 level level NN cord-340851-lnv8yi9l 296 52 thereafter thereafter RB cord-340851-lnv8yi9l 296 53 . . . cord-340851-lnv8yi9l 297 1 Scenarios scenario NNS cord-340851-lnv8yi9l 297 2 that that DT cord-340851-lnv8yi9l 297 3 . . . cord-340851-lnv8yi9l 298 1 CC CC NNP cord-340851-lnv8yi9l 298 2 - - : cord-340851-lnv8yi9l 298 3 BY by IN cord-340851-lnv8yi9l 298 4 4.0 4.0 CD cord-340851-lnv8yi9l 298 5 International international JJ cord-340851-lnv8yi9l 298 6 license license NN cord-340851-lnv8yi9l 299 1 It -PRON- PRP cord-340851-lnv8yi9l 299 2 is be VBZ cord-340851-lnv8yi9l 299 3 made make VBN cord-340851-lnv8yi9l 299 4 available available JJ cord-340851-lnv8yi9l 299 5 under under IN cord-340851-lnv8yi9l 299 6 a a DT cord-340851-lnv8yi9l 300 1 is be VBZ cord-340851-lnv8yi9l 300 2 the the DT cord-340851-lnv8yi9l 300 3 author author NN cord-340851-lnv8yi9l 300 4 / / SYM cord-340851-lnv8yi9l 300 5 funder funder NN cord-340851-lnv8yi9l 300 6 , , , cord-340851-lnv8yi9l 300 7 who who WP cord-340851-lnv8yi9l 300 8 has have VBZ cord-340851-lnv8yi9l 300 9 granted grant VBN cord-340851-lnv8yi9l 300 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 300 11 a a DT cord-340851-lnv8yi9l 300 12 license license NN cord-340851-lnv8yi9l 300 13 to to TO cord-340851-lnv8yi9l 300 14 display display VB cord-340851-lnv8yi9l 300 15 the the DT cord-340851-lnv8yi9l 300 16 preprint preprint NN cord-340851-lnv8yi9l 300 17 in in IN cord-340851-lnv8yi9l 300 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 300 19 . . . cord-340851-lnv8yi9l 301 1 The the DT cord-340851-lnv8yi9l 301 2 copyright copyright NN cord-340851-lnv8yi9l 301 3 holder holder NN cord-340851-lnv8yi9l 301 4 for for IN cord-340851-lnv8yi9l 301 5 this this DT cord-340851-lnv8yi9l 301 6 preprint preprint NN cord-340851-lnv8yi9l 301 7 this this DT cord-340851-lnv8yi9l 301 8 version version NN cord-340851-lnv8yi9l 301 9 posted post VBN cord-340851-lnv8yi9l 301 10 April April NNP cord-340851-lnv8yi9l 301 11 23 23 CD cord-340851-lnv8yi9l 301 12 , , , cord-340851-lnv8yi9l 301 13 2020 2020 CD cord-340851-lnv8yi9l 301 14 . . . cord-340851-lnv8yi9l 302 1 place place VB cord-340851-lnv8yi9l 302 2 greater great JJR cord-340851-lnv8yi9l 302 3 weight weight NN cord-340851-lnv8yi9l 302 4 on on IN cord-340851-lnv8yi9l 302 5 minimizing minimize VBG cord-340851-lnv8yi9l 302 6 days day NNS cord-340851-lnv8yi9l 302 7 under under IN cord-340851-lnv8yi9l 302 8 control control NN cord-340851-lnv8yi9l 302 9 provide provide VB cord-340851-lnv8yi9l 302 10 insight insight NN cord-340851-lnv8yi9l 302 11 into into IN cord-340851-lnv8yi9l 302 12 the the DT cord-340851-lnv8yi9l 302 13 possible possible JJ cord-340851-lnv8yi9l 302 14 consequences consequence NNS cord-340851-lnv8yi9l 302 15 of of IN cord-340851-lnv8yi9l 302 16 relaxing relax VBG cord-340851-lnv8yi9l 302 17 NPIs npi NNS cord-340851-lnv8yi9l 302 18 prematurely prematurely RB cord-340851-lnv8yi9l 302 19 . . . cord-340851-lnv8yi9l 303 1 In in IN cord-340851-lnv8yi9l 303 2 a a DT cord-340851-lnv8yi9l 303 3 scenario scenario NN cord-340851-lnv8yi9l 303 4 in in IN cord-340851-lnv8yi9l 303 5 which which WDT cord-340851-lnv8yi9l 303 6 the the DT cord-340851-lnv8yi9l 303 7 effect effect NN cord-340851-lnv8yi9l 303 8 of of IN cord-340851-lnv8yi9l 303 9 NPIs npi NNS cord-340851-lnv8yi9l 303 10 is be VBZ cord-340851-lnv8yi9l 303 11 reduced reduce VBN cord-340851-lnv8yi9l 303 12 moderately moderately RB cord-340851-lnv8yi9l 303 13 in in IN cord-340851-lnv8yi9l 303 14 May May NNP cord-340851-lnv8yi9l 303 15 , , , cord-340851-lnv8yi9l 303 16 resuming resume VBG cord-340851-lnv8yi9l 303 17 NPIs npi NNS cord-340851-lnv8yi9l 303 18 at at IN cord-340851-lnv8yi9l 303 19 high high JJ cord-340851-lnv8yi9l 303 20 levels level NNS cord-340851-lnv8yi9l 303 21 soon soon RB cord-340851-lnv8yi9l 303 22 after after RB cord-340851-lnv8yi9l 303 23 becomes become VBZ cord-340851-lnv8yi9l 303 24 necessary necessary JJ cord-340851-lnv8yi9l 303 25 to to TO cord-340851-lnv8yi9l 303 26 react react VB cord-340851-lnv8yi9l 303 27 to to IN cord-340851-lnv8yi9l 303 28 a a DT cord-340851-lnv8yi9l 303 29 second second JJ cord-340851-lnv8yi9l 303 30 wave wave NN cord-340851-lnv8yi9l 303 31 later later RB cord-340851-lnv8yi9l 303 32 in in IN cord-340851-lnv8yi9l 303 33 the the DT cord-340851-lnv8yi9l 303 34 summer summer NN cord-340851-lnv8yi9l 303 35 . . . cord-340851-lnv8yi9l 304 1 In in IN cord-340851-lnv8yi9l 304 2 a a DT cord-340851-lnv8yi9l 304 3 scenario scenario NN cord-340851-lnv8yi9l 304 4 in in IN cord-340851-lnv8yi9l 304 5 which which WDT cord-340851-lnv8yi9l 304 6 NPIs npi NNS cord-340851-lnv8yi9l 304 7 are be VBP cord-340851-lnv8yi9l 304 8 reduced reduce VBN cord-340851-lnv8yi9l 304 9 more more RBR cord-340851-lnv8yi9l 304 10 drastically drastically RB cord-340851-lnv8yi9l 304 11 in in IN cord-340851-lnv8yi9l 304 12 May May NNP cord-340851-lnv8yi9l 304 13 , , , cord-340851-lnv8yi9l 304 14 an an DT cord-340851-lnv8yi9l 304 15 extremely extremely RB cord-340851-lnv8yi9l 304 16 large large JJ cord-340851-lnv8yi9l 304 17 second second JJ cord-340851-lnv8yi9l 304 18 wave wave NN cord-340851-lnv8yi9l 304 19 occurs occur VBZ cord-340851-lnv8yi9l 304 20 in in IN cord-340851-lnv8yi9l 304 21 summer summer NN cord-340851-lnv8yi9l 304 22 2020 2020 CD cord-340851-lnv8yi9l 304 23 that that WDT cord-340851-lnv8yi9l 304 24 exceeds exceed VBZ cord-340851-lnv8yi9l 304 25 hospital hospital NN cord-340851-lnv8yi9l 304 26 capacity capacity NN cord-340851-lnv8yi9l 304 27 many many JJ cord-340851-lnv8yi9l 304 28 times time NNS cord-340851-lnv8yi9l 304 29 over over RB cord-340851-lnv8yi9l 304 30 . . . cord-340851-lnv8yi9l 305 1 Our -PRON- PRP$ cord-340851-lnv8yi9l 305 2 conclusion conclusion NN cord-340851-lnv8yi9l 305 3 that that IN cord-340851-lnv8yi9l 305 4 prolonged prolong VBN cord-340851-lnv8yi9l 305 5 control control NN cord-340851-lnv8yi9l 305 6 is be VBZ cord-340851-lnv8yi9l 305 7 needed need VBN cord-340851-lnv8yi9l 305 8 to to TO cord-340851-lnv8yi9l 305 9 avoid avoid VB cord-340851-lnv8yi9l 305 10 a a DT cord-340851-lnv8yi9l 305 11 resurgence resurgence NN cord-340851-lnv8yi9l 305 12 that that WDT cord-340851-lnv8yi9l 305 13 would would MD cord-340851-lnv8yi9l 305 14 greatly greatly RB cord-340851-lnv8yi9l 305 15 exceed exceed VB cord-340851-lnv8yi9l 305 16 healthcare healthcare NN cord-340851-lnv8yi9l 305 17 capacity capacity NN cord-340851-lnv8yi9l 305 18 is be VBZ cord-340851-lnv8yi9l 305 19 in in IN cord-340851-lnv8yi9l 305 20 line line NN cord-340851-lnv8yi9l 305 21 with with IN cord-340851-lnv8yi9l 305 22 results result NNS cord-340851-lnv8yi9l 305 23 from from IN cord-340851-lnv8yi9l 305 24 other other JJ cord-340851-lnv8yi9l 305 25 modeling modeling NN cord-340851-lnv8yi9l 305 26 studies study NNS cord-340851-lnv8yi9l 305 27 [ [ -LRB- cord-340851-lnv8yi9l 305 28 13 13 CD cord-340851-lnv8yi9l 305 29 , , , cord-340851-lnv8yi9l 305 30 37 37 CD cord-340851-lnv8yi9l 305 31 , , , cord-340851-lnv8yi9l 305 32 17 17 CD cord-340851-lnv8yi9l 305 33 , , , cord-340851-lnv8yi9l 305 34 25 25 CD cord-340851-lnv8yi9l 305 35 , , , cord-340851-lnv8yi9l 305 36 51 51 CD cord-340851-lnv8yi9l 305 37 ] ] -RRB- cord-340851-lnv8yi9l 305 38 . . . cord-340851-lnv8yi9l 306 1 Some some DT cord-340851-lnv8yi9l 306 2 differ differ VBP cord-340851-lnv8yi9l 306 3 though though RB cord-340851-lnv8yi9l 306 4 in in IN cord-340851-lnv8yi9l 306 5 that that IN cord-340851-lnv8yi9l 306 6 they -PRON- PRP cord-340851-lnv8yi9l 306 7 consider consider VBP cord-340851-lnv8yi9l 306 8 scenarios scenario NNS cord-340851-lnv8yi9l 306 9 in in IN cord-340851-lnv8yi9l 306 10 which which WDT cord-340851-lnv8yi9l 306 11 control control NN cord-340851-lnv8yi9l 306 12 is be VBZ cord-340851-lnv8yi9l 306 13 implemented implement VBN cord-340851-lnv8yi9l 306 14 intermittently intermittently RB cord-340851-lnv8yi9l 306 15 , , , cord-340851-lnv8yi9l 306 16 with with IN cord-340851-lnv8yi9l 306 17 periods period NNS cord-340851-lnv8yi9l 306 18 of of IN cord-340851-lnv8yi9l 306 19 relaxed relaxed JJ cord-340851-lnv8yi9l 306 20 control control NN cord-340851-lnv8yi9l 306 21 in in IN cord-340851-lnv8yi9l 306 22 between between IN cord-340851-lnv8yi9l 306 23 periods period NNS cord-340851-lnv8yi9l 306 24 of of IN cord-340851-lnv8yi9l 306 25 maximal maximal JJ cord-340851-lnv8yi9l 306 26 control control NN cord-340851-lnv8yi9l 306 27 [ [ -LRB- cord-340851-lnv8yi9l 306 28 17 17 CD cord-340851-lnv8yi9l 306 29 , , , cord-340851-lnv8yi9l 306 30 25 25 CD cord-340851-lnv8yi9l 306 31 , , , cord-340851-lnv8yi9l 306 32 51 51 CD cord-340851-lnv8yi9l 306 33 ] ] -RRB- cord-340851-lnv8yi9l 306 34 . . . cord-340851-lnv8yi9l 307 1 In in IN cord-340851-lnv8yi9l 307 2 the the DT cord-340851-lnv8yi9l 307 3 limited limited JJ cord-340851-lnv8yi9l 307 4 number number NN cord-340851-lnv8yi9l 307 5 of of IN cord-340851-lnv8yi9l 307 6 direct direct JJ cord-340851-lnv8yi9l 307 7 comparisons comparison NNS cord-340851-lnv8yi9l 307 8 of of IN cord-340851-lnv8yi9l 307 9 intermittent intermittent JJ cord-340851-lnv8yi9l 307 10 and and CC cord-340851-lnv8yi9l 307 11 continuous continuous JJ cord-340851-lnv8yi9l 307 12 strategies strategy NNS cord-340851-lnv8yi9l 307 13 that that WDT cord-340851-lnv8yi9l 307 14 have have VBP cord-340851-lnv8yi9l 307 15 been be VBN cord-340851-lnv8yi9l 307 16 performed perform VBN cord-340851-lnv8yi9l 307 17 for for IN cord-340851-lnv8yi9l 307 18 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 307 19 to to IN cord-340851-lnv8yi9l 307 20 date date NN cord-340851-lnv8yi9l 307 21 , , , cord-340851-lnv8yi9l 307 22 continuous continuous JJ cord-340851-lnv8yi9l 307 23 strategies strategy NNS cord-340851-lnv8yi9l 307 24 appear appear VBP cord-340851-lnv8yi9l 307 25 to to TO cord-340851-lnv8yi9l 307 26 be be VB cord-340851-lnv8yi9l 307 27 capable capable JJ cord-340851-lnv8yi9l 307 28 of of IN cord-340851-lnv8yi9l 307 29 more more RBR cord-340851-lnv8yi9l 307 30 effectively effectively RB cord-340851-lnv8yi9l 307 31 limiting limit VBG cord-340851-lnv8yi9l 307 32 transmission transmission NN cord-340851-lnv8yi9l 307 33 to to IN cord-340851-lnv8yi9l 307 34 low low JJ cord-340851-lnv8yi9l 307 35 levels level NNS cord-340851-lnv8yi9l 307 36 [ [ -LRB- cord-340851-lnv8yi9l 307 37 14 14 CD cord-340851-lnv8yi9l 307 38 , , , cord-340851-lnv8yi9l 307 39 52 52 CD cord-340851-lnv8yi9l 307 40 ] ] -RRB- cord-340851-lnv8yi9l 307 41 . . . cord-340851-lnv8yi9l 308 1 The the DT cord-340851-lnv8yi9l 308 2 sustainability sustainability NN cord-340851-lnv8yi9l 308 3 of of IN cord-340851-lnv8yi9l 308 4 either either DT cord-340851-lnv8yi9l 308 5 strategy strategy NN cord-340851-lnv8yi9l 308 6 would would MD cord-340851-lnv8yi9l 308 7 benefit benefit VB cord-340851-lnv8yi9l 308 8 from from IN cord-340851-lnv8yi9l 308 9 the the DT cord-340851-lnv8yi9l 308 10 ability ability NN cord-340851-lnv8yi9l 308 11 to to TO cord-340851-lnv8yi9l 308 12 transition transition VB cord-340851-lnv8yi9l 308 13 . . . cord-340851-lnv8yi9l 309 1 CC CC NNP cord-340851-lnv8yi9l 309 2 - - : cord-340851-lnv8yi9l 309 3 BY by IN cord-340851-lnv8yi9l 309 4 4.0 4.0 CD cord-340851-lnv8yi9l 309 5 International international JJ cord-340851-lnv8yi9l 309 6 license license NN cord-340851-lnv8yi9l 310 1 It -PRON- PRP cord-340851-lnv8yi9l 310 2 is be VBZ cord-340851-lnv8yi9l 310 3 made make VBN cord-340851-lnv8yi9l 310 4 available available JJ cord-340851-lnv8yi9l 310 5 under under IN cord-340851-lnv8yi9l 310 6 a a DT cord-340851-lnv8yi9l 311 1 is be VBZ cord-340851-lnv8yi9l 311 2 the the DT cord-340851-lnv8yi9l 311 3 author author NN cord-340851-lnv8yi9l 311 4 / / SYM cord-340851-lnv8yi9l 311 5 funder funder NN cord-340851-lnv8yi9l 311 6 , , , cord-340851-lnv8yi9l 311 7 who who WP cord-340851-lnv8yi9l 311 8 has have VBZ cord-340851-lnv8yi9l 311 9 granted grant VBN cord-340851-lnv8yi9l 311 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 311 11 a a DT cord-340851-lnv8yi9l 311 12 license license NN cord-340851-lnv8yi9l 311 13 to to TO cord-340851-lnv8yi9l 311 14 display display VB cord-340851-lnv8yi9l 311 15 the the DT cord-340851-lnv8yi9l 311 16 preprint preprint NN cord-340851-lnv8yi9l 311 17 in in IN cord-340851-lnv8yi9l 311 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 311 19 . . . cord-340851-lnv8yi9l 312 1 The the DT cord-340851-lnv8yi9l 312 2 copyright copyright NN cord-340851-lnv8yi9l 312 3 holder holder NN cord-340851-lnv8yi9l 312 4 for for IN cord-340851-lnv8yi9l 312 5 this this DT cord-340851-lnv8yi9l 312 6 preprint preprint NN cord-340851-lnv8yi9l 312 7 this this DT cord-340851-lnv8yi9l 312 8 version version NN cord-340851-lnv8yi9l 312 9 posted post VBN cord-340851-lnv8yi9l 312 10 April April NNP cord-340851-lnv8yi9l 312 11 23 23 CD cord-340851-lnv8yi9l 312 12 , , , cord-340851-lnv8yi9l 312 13 2020 2020 CD cord-340851-lnv8yi9l 312 14 . . . cord-340851-lnv8yi9l 313 1 away away RB cord-340851-lnv8yi9l 313 2 from from IN cord-340851-lnv8yi9l 313 3 heightened heighten VBN cord-340851-lnv8yi9l 313 4 social social JJ cord-340851-lnv8yi9l 313 5 distancing distancing NN cord-340851-lnv8yi9l 313 6 and and CC cord-340851-lnv8yi9l 313 7 more more RBR cord-340851-lnv8yi9l 313 8 toward toward IN cord-340851-lnv8yi9l 313 9 diagnostic diagnostic JJ cord-340851-lnv8yi9l 313 10 testing testing NN cord-340851-lnv8yi9l 313 11 , , , cord-340851-lnv8yi9l 313 12 contact contact NN cord-340851-lnv8yi9l 313 13 tracing tracing NN cord-340851-lnv8yi9l 313 14 , , , cord-340851-lnv8yi9l 313 15 and and CC cord-340851-lnv8yi9l 313 16 case case NN cord-340851-lnv8yi9l 313 17 isolation isolation NN cord-340851-lnv8yi9l 313 18 [ [ -LRB- cord-340851-lnv8yi9l 313 19 51 51 CD cord-340851-lnv8yi9l 313 20 , , , cord-340851-lnv8yi9l 313 21 43 43 CD cord-340851-lnv8yi9l 313 22 ] ] -RRB- cord-340851-lnv8yi9l 313 23 . . . cord-340851-lnv8yi9l 314 1 Our -PRON- PRP$ cord-340851-lnv8yi9l 314 2 results result NNS cord-340851-lnv8yi9l 314 3 tend tend VBP cord-340851-lnv8yi9l 314 4 to to TO cord-340851-lnv8yi9l 314 5 agree agree VB cord-340851-lnv8yi9l 314 6 with with IN cord-340851-lnv8yi9l 314 7 those those DT cord-340851-lnv8yi9l 314 8 from from IN cord-340851-lnv8yi9l 314 9 other other JJ cord-340851-lnv8yi9l 314 10 optimal optimal JJ cord-340851-lnv8yi9l 314 11 control control NN cord-340851-lnv8yi9l 314 12 analyses analysis NNS cord-340851-lnv8yi9l 314 13 of of IN cord-340851-lnv8yi9l 314 14 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 314 15 , , , cord-340851-lnv8yi9l 314 16 although although IN cord-340851-lnv8yi9l 314 17 our -PRON- PRP$ cord-340851-lnv8yi9l 314 18 analysis analysis NN cord-340851-lnv8yi9l 314 19 goes go VBZ cord-340851-lnv8yi9l 314 20 beyond beyond IN cord-340851-lnv8yi9l 314 21 those those DT cord-340851-lnv8yi9l 314 22 studies study NNS cord-340851-lnv8yi9l 314 23 in in IN cord-340851-lnv8yi9l 314 24 some some DT cord-340851-lnv8yi9l 314 25 ways way NNS cord-340851-lnv8yi9l 314 26 . . . cord-340851-lnv8yi9l 315 1 In in IN cord-340851-lnv8yi9l 315 2 general general JJ cord-340851-lnv8yi9l 315 3 , , , cord-340851-lnv8yi9l 315 4 ours ours JJ cord-340851-lnv8yi9l 315 5 and and CC cord-340851-lnv8yi9l 315 6 other other JJ cord-340851-lnv8yi9l 315 7 studies study NNS cord-340851-lnv8yi9l 315 8 share share VBP cord-340851-lnv8yi9l 315 9 the the DT cord-340851-lnv8yi9l 315 10 conclusion conclusion NN cord-340851-lnv8yi9l 315 11 that that WDT cord-340851-lnv8yi9l 315 12 heightened heighten VBD cord-340851-lnv8yi9l 315 13 control control NN cord-340851-lnv8yi9l 315 14 early early RB cord-340851-lnv8yi9l 315 15 in in IN cord-340851-lnv8yi9l 315 16 the the DT cord-340851-lnv8yi9l 315 17 pandemic pandemic NN cord-340851-lnv8yi9l 315 18 is be VBZ cord-340851-lnv8yi9l 315 19 important important JJ cord-340851-lnv8yi9l 315 20 for for IN cord-340851-lnv8yi9l 315 21 achieving achieve VBG cord-340851-lnv8yi9l 315 22 long long JJ cord-340851-lnv8yi9l 315 23 - - HYPH cord-340851-lnv8yi9l 315 24 term term NN cord-340851-lnv8yi9l 315 25 success success NN cord-340851-lnv8yi9l 315 26 . . . cord-340851-lnv8yi9l 316 1 Like like IN cord-340851-lnv8yi9l 316 2 our -PRON- PRP$ cord-340851-lnv8yi9l 316 3 analysis analysis NN cord-340851-lnv8yi9l 316 4 , , , cord-340851-lnv8yi9l 316 5 some some DT cord-340851-lnv8yi9l 316 6 anticipate anticipate VBP cord-340851-lnv8yi9l 316 7 that that IN cord-340851-lnv8yi9l 316 8 partial partial JJ cord-340851-lnv8yi9l 316 9 relaxation relaxation NN cord-340851-lnv8yi9l 316 10 of of IN cord-340851-lnv8yi9l 316 11 controls control NNS cord-340851-lnv8yi9l 316 12 may may MD cord-340851-lnv8yi9l 316 13 be be VB cord-340851-lnv8yi9l 316 14 possible possible JJ cord-340851-lnv8yi9l 316 15 over over IN cord-340851-lnv8yi9l 316 16 time time NN cord-340851-lnv8yi9l 316 17 [ [ -LRB- cord-340851-lnv8yi9l 316 18 14 14 CD cord-340851-lnv8yi9l 316 19 , , , cord-340851-lnv8yi9l 316 20 45 45 CD cord-340851-lnv8yi9l 316 21 ] ] -RRB- cord-340851-lnv8yi9l 316 22 , , , cord-340851-lnv8yi9l 316 23 whereas whereas IN cord-340851-lnv8yi9l 316 24 others other NNS cord-340851-lnv8yi9l 316 25 focus focus VBP cord-340851-lnv8yi9l 316 26 on on IN cord-340851-lnv8yi9l 316 27 strategies strategy NNS cord-340851-lnv8yi9l 316 28 intended intend VBN cord-340851-lnv8yi9l 316 29 to to TO cord-340851-lnv8yi9l 316 30 have have VB cord-340851-lnv8yi9l 316 31 a a DT cord-340851-lnv8yi9l 316 32 more more RBR cord-340851-lnv8yi9l 316 33 limited limited JJ cord-340851-lnv8yi9l 316 34 duration duration NN cord-340851-lnv8yi9l 316 35 to to TO cord-340851-lnv8yi9l 316 36 begin begin VB cord-340851-lnv8yi9l 316 37 with with IN cord-340851-lnv8yi9l 316 38 [ [ -LRB- cord-340851-lnv8yi9l 316 39 40 40 CD cord-340851-lnv8yi9l 316 40 , , , cord-340851-lnv8yi9l 316 41 35 35 CD cord-340851-lnv8yi9l 316 42 , , , cord-340851-lnv8yi9l 316 43 43 43 CD cord-340851-lnv8yi9l 316 44 ] ] -RRB- cord-340851-lnv8yi9l 316 45 . . . cord-340851-lnv8yi9l 317 1 Importantly importantly RB cord-340851-lnv8yi9l 317 2 though though RB cord-340851-lnv8yi9l 317 3 , , , cord-340851-lnv8yi9l 317 4 our -PRON- PRP$ cord-340851-lnv8yi9l 317 5 analysis analysis NN cord-340851-lnv8yi9l 317 6 goes go VBZ cord-340851-lnv8yi9l 317 7 further far RBR cord-340851-lnv8yi9l 317 8 than than IN cord-340851-lnv8yi9l 317 9 others other NNS cord-340851-lnv8yi9l 317 10 in in IN cord-340851-lnv8yi9l 317 11 exploring explore VBG cord-340851-lnv8yi9l 317 12 sensitivity sensitivity NN cord-340851-lnv8yi9l 317 13 of of IN cord-340851-lnv8yi9l 317 14 the the DT cord-340851-lnv8yi9l 317 15 optimal optimal JJ cord-340851-lnv8yi9l 317 16 control control NN cord-340851-lnv8yi9l 317 17 to to TO cord-340851-lnv8yi9l 317 18 model model VB cord-340851-lnv8yi9l 317 19 parameters parameter NNS cord-340851-lnv8yi9l 317 20 . . . cord-340851-lnv8yi9l 318 1 Specifically specifically RB cord-340851-lnv8yi9l 318 2 , , , cord-340851-lnv8yi9l 318 3 we -PRON- PRP cord-340851-lnv8yi9l 318 4 show show VBP cord-340851-lnv8yi9l 318 5 that that IN cord-340851-lnv8yi9l 318 6 preventing prevent VBG cord-340851-lnv8yi9l 318 7 a a DT cord-340851-lnv8yi9l 318 8 large large JJ cord-340851-lnv8yi9l 318 9 wave wave NN cord-340851-lnv8yi9l 318 10 that that WDT cord-340851-lnv8yi9l 318 11 overwhelms overwhelm VBZ cord-340851-lnv8yi9l 318 12 health health NN cord-340851-lnv8yi9l 318 13 systems system NNS cord-340851-lnv8yi9l 318 14 may may MD cord-340851-lnv8yi9l 318 15 not not RB cord-340851-lnv8yi9l 318 16 even even RB cord-340851-lnv8yi9l 318 17 be be VB cord-340851-lnv8yi9l 318 18 possible possible JJ cord-340851-lnv8yi9l 318 19 under under IN cord-340851-lnv8yi9l 318 20 some some DT cord-340851-lnv8yi9l 318 21 parameter parameter NN cord-340851-lnv8yi9l 318 22 combinations combination NNS cord-340851-lnv8yi9l 318 23 ( ( -LRB- cord-340851-lnv8yi9l 318 24 low low JJ cord-340851-lnv8yi9l 318 25 u u NNP cord-340851-lnv8yi9l 318 26 max max NN cord-340851-lnv8yi9l 318 27 , , , cord-340851-lnv8yi9l 318 28 high high JJ cord-340851-lnv8yi9l 318 29 R r NN cord-340851-lnv8yi9l 318 30 0 0 CD cord-340851-lnv8yi9l 318 31 ) ) -RRB- cord-340851-lnv8yi9l 318 32 and and CC cord-340851-lnv8yi9l 318 33 that that IN cord-340851-lnv8yi9l 318 34 prioritizing prioritize VBG cord-340851-lnv8yi9l 318 35 the the DT cord-340851-lnv8yi9l 318 36 minimization minimization NN cord-340851-lnv8yi9l 318 37 of of IN cord-340851-lnv8yi9l 318 38 deaths death NNS cord-340851-lnv8yi9l 318 39 versus versus IN cord-340851-lnv8yi9l 318 40 days day NNS cord-340851-lnv8yi9l 318 41 under under IN cord-340851-lnv8yi9l 318 42 control control NN cord-340851-lnv8yi9l 318 43 leads lead VBZ cord-340851-lnv8yi9l 318 44 to to IN cord-340851-lnv8yi9l 318 45 vastly vastly RB cord-340851-lnv8yi9l 318 46 different different JJ cord-340851-lnv8yi9l 318 47 outcomes outcome NNS cord-340851-lnv8yi9l 318 48 . . . cord-340851-lnv8yi9l 319 1 We -PRON- PRP cord-340851-lnv8yi9l 319 2 also also RB cord-340851-lnv8yi9l 319 3 constrain constrain VBP cord-340851-lnv8yi9l 319 4 levels level NNS cord-340851-lnv8yi9l 319 5 of of IN cord-340851-lnv8yi9l 319 6 control control NN cord-340851-lnv8yi9l 319 7 applied apply VBD cord-340851-lnv8yi9l 319 8 through through IN cord-340851-lnv8yi9l 319 9 April April NNP cord-340851-lnv8yi9l 319 10 2020 2020 CD cord-340851-lnv8yi9l 319 11 , , , cord-340851-lnv8yi9l 319 12 making make VBG cord-340851-lnv8yi9l 319 13 the the DT cord-340851-lnv8yi9l 319 14 optimization optimization NN cord-340851-lnv8yi9l 319 15 more more RBR cord-340851-lnv8yi9l 319 16 relevant relevant JJ cord-340851-lnv8yi9l 319 17 to to IN cord-340851-lnv8yi9l 319 18 future future JJ cord-340851-lnv8yi9l 319 19 decision decision NN cord-340851-lnv8yi9l 319 20 making making NN cord-340851-lnv8yi9l 319 21 . . . cord-340851-lnv8yi9l 320 1 Shifting shift VBG cord-340851-lnv8yi9l 320 2 the the DT cord-340851-lnv8yi9l 320 3 timing timing NN cord-340851-lnv8yi9l 320 4 of of IN cord-340851-lnv8yi9l 320 5 the the DT cord-340851-lnv8yi9l 320 6 initiation initiation NN cord-340851-lnv8yi9l 320 7 of of IN cord-340851-lnv8yi9l 320 8 control control NN cord-340851-lnv8yi9l 320 9 shows show VBZ cord-340851-lnv8yi9l 320 10 that that IN cord-340851-lnv8yi9l 320 11 constraints constraint NNS cord-340851-lnv8yi9l 320 12 about about IN cord-340851-lnv8yi9l 320 13 past past JJ cord-340851-lnv8yi9l 320 14 levels level NNS cord-340851-lnv8yi9l 320 15 of of IN cord-340851-lnv8yi9l 320 16 control control NN cord-340851-lnv8yi9l 320 17 strongly strongly RB cord-340851-lnv8yi9l 320 18 affect affect VBP cord-340851-lnv8yi9l 320 19 future future JJ cord-340851-lnv8yi9l 320 20 possibilities possibility NNS cord-340851-lnv8yi9l 320 21 for for IN cord-340851-lnv8yi9l 320 22 the the DT cord-340851-lnv8yi9l 320 23 extent extent NN cord-340851-lnv8yi9l 320 24 to to TO cord-340851-lnv8yi9l 320 25 which which WDT cord-340851-lnv8yi9l 320 26 deaths death NNS cord-340851-lnv8yi9l 320 27 can can MD cord-340851-lnv8yi9l 320 28 be be VB cord-340851-lnv8yi9l 320 29 minimized minimize VBN cord-340851-lnv8yi9l 320 30 and and CC cord-340851-lnv8yi9l 320 31 the the DT cord-340851-lnv8yi9l 320 32 level level NN cord-340851-lnv8yi9l 320 33 of of IN cord-340851-lnv8yi9l 320 34 control control NN cord-340851-lnv8yi9l 320 35 required require VBN cord-340851-lnv8yi9l 320 36 to to TO cord-340851-lnv8yi9l 320 37 achieve achieve VB cord-340851-lnv8yi9l 320 38 that that DT cord-340851-lnv8yi9l 320 39 , , , cord-340851-lnv8yi9l 320 40 consistent consistent JJ cord-340851-lnv8yi9l 320 41 with with IN cord-340851-lnv8yi9l 320 42 other other JJ cord-340851-lnv8yi9l 320 43 results result NNS cord-340851-lnv8yi9l 320 44 [ [ -LRB- cord-340851-lnv8yi9l 320 45 27 27 CD cord-340851-lnv8yi9l 320 46 ] ] -RRB- cord-340851-lnv8yi9l 320 47 . . . cord-340851-lnv8yi9l 321 1 The the DT cord-340851-lnv8yi9l 321 2 goal goal NN cord-340851-lnv8yi9l 321 3 of of IN cord-340851-lnv8yi9l 321 4 our -PRON- PRP$ cord-340851-lnv8yi9l 321 5 analysis analysis NN cord-340851-lnv8yi9l 321 6 is be VBZ cord-340851-lnv8yi9l 321 7 to to TO cord-340851-lnv8yi9l 321 8 provide provide VB cord-340851-lnv8yi9l 321 9 qualitative qualitative JJ cord-340851-lnv8yi9l 321 10 insights insight NNS cord-340851-lnv8yi9l 321 11 into into IN cord-340851-lnv8yi9l 321 12 the the DT cord-340851-lnv8yi9l 321 13 implications implication NNS cord-340851-lnv8yi9l 321 14 of of IN cord-340851-lnv8yi9l 321 15 alternative alternative JJ cord-340851-lnv8yi9l 321 16 approaches approach NNS cord-340851-lnv8yi9l 321 17 to to TO cord-340851-lnv8yi9l 321 18 control control VB cord-340851-lnv8yi9l 321 19 , , , cord-340851-lnv8yi9l 321 20 rather rather RB cord-340851-lnv8yi9l 321 21 than than IN cord-340851-lnv8yi9l 321 22 to to TO cord-340851-lnv8yi9l 321 23 make make VB cord-340851-lnv8yi9l 321 24 quantitative quantitative JJ cord-340851-lnv8yi9l 321 25 predictions prediction NNS cord-340851-lnv8yi9l 321 26 about about IN cord-340851-lnv8yi9l 321 27 future future JJ cord-340851-lnv8yi9l 321 28 events event NNS cord-340851-lnv8yi9l 321 29 . . . cord-340851-lnv8yi9l 322 1 Some some DT cord-340851-lnv8yi9l 322 2 key key JJ cord-340851-lnv8yi9l 322 3 limitations limitation NNS cord-340851-lnv8yi9l 322 4 of of IN cord-340851-lnv8yi9l 322 5 using use VBG cord-340851-lnv8yi9l 322 6 our -PRON- PRP$ cord-340851-lnv8yi9l 322 7 model model NN cord-340851-lnv8yi9l 322 8 for for IN cord-340851-lnv8yi9l 322 9 . . . cord-340851-lnv8yi9l 323 1 CC CC NNP cord-340851-lnv8yi9l 323 2 - - : cord-340851-lnv8yi9l 323 3 BY by IN cord-340851-lnv8yi9l 323 4 4.0 4.0 CD cord-340851-lnv8yi9l 323 5 International international JJ cord-340851-lnv8yi9l 323 6 license license NN cord-340851-lnv8yi9l 324 1 It -PRON- PRP cord-340851-lnv8yi9l 324 2 is be VBZ cord-340851-lnv8yi9l 324 3 made make VBN cord-340851-lnv8yi9l 324 4 available available JJ cord-340851-lnv8yi9l 324 5 under under IN cord-340851-lnv8yi9l 324 6 a a DT cord-340851-lnv8yi9l 325 1 is be VBZ cord-340851-lnv8yi9l 325 2 the the DT cord-340851-lnv8yi9l 325 3 author author NN cord-340851-lnv8yi9l 325 4 / / SYM cord-340851-lnv8yi9l 325 5 funder funder NN cord-340851-lnv8yi9l 325 6 , , , cord-340851-lnv8yi9l 325 7 who who WP cord-340851-lnv8yi9l 325 8 has have VBZ cord-340851-lnv8yi9l 325 9 granted grant VBN cord-340851-lnv8yi9l 325 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 325 11 a a DT cord-340851-lnv8yi9l 325 12 license license NN cord-340851-lnv8yi9l 325 13 to to TO cord-340851-lnv8yi9l 325 14 display display VB cord-340851-lnv8yi9l 325 15 the the DT cord-340851-lnv8yi9l 325 16 preprint preprint NN cord-340851-lnv8yi9l 325 17 in in IN cord-340851-lnv8yi9l 325 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 325 19 . . . cord-340851-lnv8yi9l 326 1 ( ( -LRB- cord-340851-lnv8yi9l 326 2 which which WDT cord-340851-lnv8yi9l 326 3 was be VBD cord-340851-lnv8yi9l 326 4 not not RB cord-340851-lnv8yi9l 326 5 certified certify VBN cord-340851-lnv8yi9l 326 6 by by IN cord-340851-lnv8yi9l 326 7 peer peer NN cord-340851-lnv8yi9l 326 8 review review NN cord-340851-lnv8yi9l 326 9 ) ) -RRB- cord-340851-lnv8yi9l 327 1 The the DT cord-340851-lnv8yi9l 327 2 copyright copyright NN cord-340851-lnv8yi9l 327 3 holder holder NN cord-340851-lnv8yi9l 327 4 for for IN cord-340851-lnv8yi9l 327 5 this this DT cord-340851-lnv8yi9l 327 6 preprint preprint NN cord-340851-lnv8yi9l 327 7 this this DT cord-340851-lnv8yi9l 327 8 version version NN cord-340851-lnv8yi9l 327 9 posted post VBN cord-340851-lnv8yi9l 327 10 April April NNP cord-340851-lnv8yi9l 327 11 23 23 CD cord-340851-lnv8yi9l 327 12 , , , cord-340851-lnv8yi9l 327 13 2020 2020 CD cord-340851-lnv8yi9l 327 14 . . . cord-340851-lnv8yi9l 327 15 . . . cord-340851-lnv8yi9l 328 1 https://doi.org/10.1101/2020.04 https://doi.org/10.1101/2020.04 UH cord-340851-lnv8yi9l 328 2 . . . cord-340851-lnv8yi9l 329 1 22.20076018 22.20076018 CD cord-340851-lnv8yi9l 329 2 doi doi NN cord-340851-lnv8yi9l 329 3 : : : cord-340851-lnv8yi9l 330 1 medRxiv medRxiv NNS cord-340851-lnv8yi9l 330 2 preprint preprint VBP cord-340851-lnv8yi9l 330 3 the the DT cord-340851-lnv8yi9l 330 4 latter latter JJ cord-340851-lnv8yi9l 330 5 purpose purpose NN cord-340851-lnv8yi9l 330 6 include include VBP cord-340851-lnv8yi9l 330 7 our -PRON- PRP$ cord-340851-lnv8yi9l 330 8 omission omission NN cord-340851-lnv8yi9l 330 9 of of IN cord-340851-lnv8yi9l 330 10 subnational subnational JJ cord-340851-lnv8yi9l 330 11 variation variation NN cord-340851-lnv8yi9l 330 12 in in IN cord-340851-lnv8yi9l 330 13 epidemic epidemic NN cord-340851-lnv8yi9l 330 14 dynamics dynamic NNS cord-340851-lnv8yi9l 330 15 [ [ -LRB- cord-340851-lnv8yi9l 330 16 42 42 CD cord-340851-lnv8yi9l 330 17 , , , cord-340851-lnv8yi9l 330 18 49 49 CD cord-340851-lnv8yi9l 330 19 ] ] -RRB- cord-340851-lnv8yi9l 330 20 , , , cord-340851-lnv8yi9l 330 21 differentiation differentiation NN cord-340851-lnv8yi9l 330 22 among among IN cord-340851-lnv8yi9l 330 23 alternative alternative JJ cord-340851-lnv8yi9l 330 24 NPIs npi NNS cord-340851-lnv8yi9l 330 25 [ [ -LRB- cord-340851-lnv8yi9l 330 26 18 18 CD cord-340851-lnv8yi9l 330 27 ] ] -RRB- cord-340851-lnv8yi9l 330 28 , , , cord-340851-lnv8yi9l 330 29 and and CC cord-340851-lnv8yi9l 330 30 age age NN cord-340851-lnv8yi9l 330 31 differences difference NNS cord-340851-lnv8yi9l 330 32 in in IN cord-340851-lnv8yi9l 330 33 contact contact NN cord-340851-lnv8yi9l 330 34 patterns pattern NNS cord-340851-lnv8yi9l 330 35 [ [ -LRB- cord-340851-lnv8yi9l 330 36 23 23 CD cord-340851-lnv8yi9l 330 37 ] ] -RRB- cord-340851-lnv8yi9l 330 38 and and CC cord-340851-lnv8yi9l 330 39 risk risk NN cord-340851-lnv8yi9l 330 40 of of IN cord-340851-lnv8yi9l 330 41 hospitalization hospitalization NN cord-340851-lnv8yi9l 330 42 [ [ -LRB- cord-340851-lnv8yi9l 330 43 9 9 CD cord-340851-lnv8yi9l 330 44 ] ] -RRB- cord-340851-lnv8yi9l 330 45 . . . cord-340851-lnv8yi9l 331 1 At at IN cord-340851-lnv8yi9l 331 2 least least JJS cord-340851-lnv8yi9l 331 3 with with IN cord-340851-lnv8yi9l 331 4 respect respect NN cord-340851-lnv8yi9l 331 5 to to IN cord-340851-lnv8yi9l 331 6 the the DT cord-340851-lnv8yi9l 331 7 possibility possibility NN cord-340851-lnv8yi9l 331 8 of of IN cord-340851-lnv8yi9l 331 9 different different JJ cord-340851-lnv8yi9l 331 10 levels level NNS cord-340851-lnv8yi9l 331 11 of of IN cord-340851-lnv8yi9l 331 12 control control NN cord-340851-lnv8yi9l 331 13 for for IN cord-340851-lnv8yi9l 331 14 different different JJ cord-340851-lnv8yi9l 331 15 age age NN cord-340851-lnv8yi9l 331 16 groups group NNS cord-340851-lnv8yi9l 331 17 , , , cord-340851-lnv8yi9l 331 18 one one CD cord-340851-lnv8yi9l 331 19 study study NN cord-340851-lnv8yi9l 331 20 found find VBD cord-340851-lnv8yi9l 331 21 that that IN cord-340851-lnv8yi9l 331 22 age age NN cord-340851-lnv8yi9l 331 23 - - HYPH cord-340851-lnv8yi9l 331 24 specific specific JJ cord-340851-lnv8yi9l 331 25 optimal optimal JJ cord-340851-lnv8yi9l 331 26 controls control NNS cord-340851-lnv8yi9l 331 27 were be VBD cord-340851-lnv8yi9l 331 28 all all DT cord-340851-lnv8yi9l 331 29 relatively relatively RB cord-340851-lnv8yi9l 331 30 similar similar JJ cord-340851-lnv8yi9l 331 31 for for IN cord-340851-lnv8yi9l 331 32 NPIs npi NNS cord-340851-lnv8yi9l 331 33 against against IN cord-340851-lnv8yi9l 331 34 pandemic pandemic NN cord-340851-lnv8yi9l 331 35 influenza influenza NN cord-340851-lnv8yi9l 331 36 [ [ -LRB- cord-340851-lnv8yi9l 331 37 46 46 CD cord-340851-lnv8yi9l 331 38 ] ] -RRB- cord-340851-lnv8yi9l 331 39 . . . cord-340851-lnv8yi9l 332 1 Additional additional JJ cord-340851-lnv8yi9l 332 2 limitations limitation NNS cord-340851-lnv8yi9l 332 3 that that WDT cord-340851-lnv8yi9l 332 4 affect affect VBP cord-340851-lnv8yi9l 332 5 our -PRON- PRP$ cord-340851-lnv8yi9l 332 6 model model NN cord-340851-lnv8yi9l 332 7 's 's POS cord-340851-lnv8yi9l 332 8 suitability suitability NN cord-340851-lnv8yi9l 332 9 for for IN cord-340851-lnv8yi9l 332 10 making make VBG cord-340851-lnv8yi9l 332 11 future future JJ cord-340851-lnv8yi9l 332 12 predictions prediction NNS cord-340851-lnv8yi9l 332 13 include include VBP cord-340851-lnv8yi9l 332 14 its -PRON- PRP$ cord-340851-lnv8yi9l 332 15 deterministic deterministic JJ cord-340851-lnv8yi9l 332 16 nature nature NN cord-340851-lnv8yi9l 332 17 and and CC cord-340851-lnv8yi9l 332 18 the the DT cord-340851-lnv8yi9l 332 19 rudimentary rudimentary JJ cord-340851-lnv8yi9l 332 20 calibration calibration NN cord-340851-lnv8yi9l 332 21 procedure procedure NN cord-340851-lnv8yi9l 332 22 that that IN cord-340851-lnv8yi9l 332 23 we -PRON- PRP cord-340851-lnv8yi9l 332 24 performed perform VBD cord-340851-lnv8yi9l 332 25 , , , cord-340851-lnv8yi9l 332 26 which which WDT cord-340851-lnv8yi9l 332 27 was be VBD cord-340851-lnv8yi9l 332 28 sufficient sufficient JJ cord-340851-lnv8yi9l 332 29 to to TO cord-340851-lnv8yi9l 332 30 provide provide VB cord-340851-lnv8yi9l 332 31 a a DT cord-340851-lnv8yi9l 332 32 basis basis NN cord-340851-lnv8yi9l 332 33 for for IN cord-340851-lnv8yi9l 332 34 qualitative qualitative JJ cord-340851-lnv8yi9l 332 35 analyses analysis NNS cord-340851-lnv8yi9l 332 36 but but CC cord-340851-lnv8yi9l 332 37 that that DT cord-340851-lnv8yi9l 332 38 would would MD cord-340851-lnv8yi9l 332 39 need need VB cord-340851-lnv8yi9l 332 40 refinement refinement NN cord-340851-lnv8yi9l 332 41 for for IN cord-340851-lnv8yi9l 332 42 application application NN cord-340851-lnv8yi9l 332 43 of of IN cord-340851-lnv8yi9l 332 44 our -PRON- PRP$ cord-340851-lnv8yi9l 332 45 model model NN cord-340851-lnv8yi9l 332 46 to to IN cord-340851-lnv8yi9l 332 47 inference inference NN cord-340851-lnv8yi9l 332 48 or or CC cord-340851-lnv8yi9l 332 49 forecasting forecasting NN cord-340851-lnv8yi9l 332 50 . . . cord-340851-lnv8yi9l 333 1 In in IN cord-340851-lnv8yi9l 333 2 conclusion conclusion NN cord-340851-lnv8yi9l 333 3 , , , cord-340851-lnv8yi9l 333 4 our -PRON- PRP$ cord-340851-lnv8yi9l 333 5 analysis analysis NN cord-340851-lnv8yi9l 333 6 suggests suggest VBZ cord-340851-lnv8yi9l 333 7 that that IN cord-340851-lnv8yi9l 333 8 we -PRON- PRP cord-340851-lnv8yi9l 333 9 are be VBP cord-340851-lnv8yi9l 333 10 at at IN cord-340851-lnv8yi9l 333 11 a a DT cord-340851-lnv8yi9l 333 12 critical critical JJ cord-340851-lnv8yi9l 333 13 juncture juncture NN cord-340851-lnv8yi9l 333 14 in in IN cord-340851-lnv8yi9l 333 15 the the DT cord-340851-lnv8yi9l 333 16 pandemic pandemic NN cord-340851-lnv8yi9l 333 17 , , , cord-340851-lnv8yi9l 333 18 when when WRB cord-340851-lnv8yi9l 333 19 decisions decision NNS cord-340851-lnv8yi9l 333 20 about about IN cord-340851-lnv8yi9l 333 21 the the DT cord-340851-lnv8yi9l 333 22 continuation continuation NN cord-340851-lnv8yi9l 333 23 or or CC cord-340851-lnv8yi9l 333 24 relaxation relaxation NN cord-340851-lnv8yi9l 333 25 of of IN cord-340851-lnv8yi9l 333 26 NPI npi NN cord-340851-lnv8yi9l 333 27 - - HYPH cord-340851-lnv8yi9l 333 28 based base VBN cord-340851-lnv8yi9l 333 29 control control NN cord-340851-lnv8yi9l 333 30 strategies strategy NNS cord-340851-lnv8yi9l 333 31 could could MD cord-340851-lnv8yi9l 333 32 have have VB cord-340851-lnv8yi9l 333 33 major major JJ cord-340851-lnv8yi9l 333 34 implications implication NNS cord-340851-lnv8yi9l 333 35 for for IN cord-340851-lnv8yi9l 333 36 the the DT cord-340851-lnv8yi9l 333 37 possibility possibility NN cord-340851-lnv8yi9l 333 38 of of IN cord-340851-lnv8yi9l 333 39 keeping keep VBG cord-340851-lnv8yi9l 333 40 transmission transmission NN cord-340851-lnv8yi9l 333 41 below below IN cord-340851-lnv8yi9l 333 42 levels level NNS cord-340851-lnv8yi9l 333 43 that that IN cord-340851-lnv8yi9l 333 44 health health NN cord-340851-lnv8yi9l 333 45 systems system NNS cord-340851-lnv8yi9l 333 46 can can MD cord-340851-lnv8yi9l 333 47 cope cope VB cord-340851-lnv8yi9l 333 48 with with IN cord-340851-lnv8yi9l 333 49 . . . cord-340851-lnv8yi9l 334 1 At at IN cord-340851-lnv8yi9l 334 2 the the DT cord-340851-lnv8yi9l 334 3 same same JJ cord-340851-lnv8yi9l 334 4 time time NN cord-340851-lnv8yi9l 334 5 , , , cord-340851-lnv8yi9l 334 6 our -PRON- PRP$ cord-340851-lnv8yi9l 334 7 analysis analysis NN cord-340851-lnv8yi9l 334 8 highlights highlight VBZ cord-340851-lnv8yi9l 334 9 the the DT cord-340851-lnv8yi9l 334 10 role role NN cord-340851-lnv8yi9l 334 11 that that WDT cord-340851-lnv8yi9l 334 12 constraints constraint NNS cord-340851-lnv8yi9l 334 13 play play VBP cord-340851-lnv8yi9l 334 14 in in IN cord-340851-lnv8yi9l 334 15 determining determine VBG cord-340851-lnv8yi9l 334 16 optimal optimal JJ cord-340851-lnv8yi9l 334 17 levels level NNS cord-340851-lnv8yi9l 334 18 of of IN cord-340851-lnv8yi9l 334 19 control control NN cord-340851-lnv8yi9l 334 20 going go VBG cord-340851-lnv8yi9l 334 21 forward forward RB cord-340851-lnv8yi9l 334 22 , , , cord-340851-lnv8yi9l 334 23 both both CC cord-340851-lnv8yi9l 334 24 in in IN cord-340851-lnv8yi9l 334 25 terms term NNS cord-340851-lnv8yi9l 334 26 of of IN cord-340851-lnv8yi9l 334 27 constraints constraint NNS cord-340851-lnv8yi9l 334 28 on on IN cord-340851-lnv8yi9l 334 29 epidemiological epidemiological JJ cord-340851-lnv8yi9l 334 30 parameters parameter NNS cord-340851-lnv8yi9l 334 31 and and CC cord-340851-lnv8yi9l 334 32 on on IN cord-340851-lnv8yi9l 334 33 levels level NNS cord-340851-lnv8yi9l 334 34 of of IN cord-340851-lnv8yi9l 334 35 control control NN cord-340851-lnv8yi9l 334 36 prior prior RB cord-340851-lnv8yi9l 334 37 to to IN cord-340851-lnv8yi9l 334 38 the the DT cord-340851-lnv8yi9l 334 39 time time NN cord-340851-lnv8yi9l 334 40 that that WDT cord-340851-lnv8yi9l 334 41 a a DT cord-340851-lnv8yi9l 334 42 decision decision NN cord-340851-lnv8yi9l 334 43 is be VBZ cord-340851-lnv8yi9l 334 44 made make VBN cord-340851-lnv8yi9l 334 45 about about IN cord-340851-lnv8yi9l 334 46 future future JJ cord-340851-lnv8yi9l 334 47 actions action NNS cord-340851-lnv8yi9l 334 48 . . . cord-340851-lnv8yi9l 335 1 Going go VBG cord-340851-lnv8yi9l 335 2 forward forward RB cord-340851-lnv8yi9l 335 3 , , , cord-340851-lnv8yi9l 335 4 reducing reduce VBG cord-340851-lnv8yi9l 335 5 transmission transmission NN cord-340851-lnv8yi9l 335 6 in in IN cord-340851-lnv8yi9l 335 7 the the DT cord-340851-lnv8yi9l 335 8 near near JJ cord-340851-lnv8yi9l 335 9 term term NN cord-340851-lnv8yi9l 335 10 would would MD cord-340851-lnv8yi9l 335 11 give give VB cord-340851-lnv8yi9l 335 12 decision decision NN cord-340851-lnv8yi9l 335 13 makers maker NNS cord-340851-lnv8yi9l 335 14 greater great JJR cord-340851-lnv8yi9l 335 15 flexibility flexibility NN cord-340851-lnv8yi9l 335 16 in in IN cord-340851-lnv8yi9l 335 17 the the DT cord-340851-lnv8yi9l 335 18 range range NN cord-340851-lnv8yi9l 335 19 of of IN cord-340851-lnv8yi9l 335 20 decisions decision NNS cord-340851-lnv8yi9l 335 21 available available JJ cord-340851-lnv8yi9l 335 22 to to IN cord-340851-lnv8yi9l 335 23 them -PRON- PRP cord-340851-lnv8yi9l 335 24 in in IN cord-340851-lnv8yi9l 335 25 the the DT cord-340851-lnv8yi9l 335 26 future future NN cord-340851-lnv8yi9l 335 27 , , , cord-340851-lnv8yi9l 335 28 and and CC cord-340851-lnv8yi9l 335 29 gathering gather VBG cord-340851-lnv8yi9l 335 30 high high JJ cord-340851-lnv8yi9l 335 31 - - HYPH cord-340851-lnv8yi9l 335 32 quality quality NN cord-340851-lnv8yi9l 335 33 data datum NNS cord-340851-lnv8yi9l 335 34 could could MD cord-340851-lnv8yi9l 335 35 help help VB cord-340851-lnv8yi9l 335 36 reduce reduce VB cord-340851-lnv8yi9l 335 37 uncertainty uncertainty NN cord-340851-lnv8yi9l 335 38 about about IN cord-340851-lnv8yi9l 335 39 the the DT cord-340851-lnv8yi9l 335 40 consequences consequence NNS cord-340851-lnv8yi9l 335 41 of of IN cord-340851-lnv8yi9l 335 42 those those DT cord-340851-lnv8yi9l 335 43 decisions decision NNS cord-340851-lnv8yi9l 335 44 . . . cord-340851-lnv8yi9l 335 45 . . . cord-340851-lnv8yi9l 336 1 CC CC NNP cord-340851-lnv8yi9l 336 2 - - : cord-340851-lnv8yi9l 336 3 BY by IN cord-340851-lnv8yi9l 336 4 4.0 4.0 CD cord-340851-lnv8yi9l 336 5 International international JJ cord-340851-lnv8yi9l 336 6 license license NN cord-340851-lnv8yi9l 337 1 It -PRON- PRP cord-340851-lnv8yi9l 337 2 is be VBZ cord-340851-lnv8yi9l 337 3 made make VBN cord-340851-lnv8yi9l 337 4 available available JJ cord-340851-lnv8yi9l 337 5 under under IN cord-340851-lnv8yi9l 337 6 a a DT cord-340851-lnv8yi9l 338 1 is be VBZ cord-340851-lnv8yi9l 338 2 the the DT cord-340851-lnv8yi9l 338 3 author author NN cord-340851-lnv8yi9l 338 4 / / SYM cord-340851-lnv8yi9l 338 5 funder funder NN cord-340851-lnv8yi9l 338 6 , , , cord-340851-lnv8yi9l 338 7 who who WP cord-340851-lnv8yi9l 338 8 has have VBZ cord-340851-lnv8yi9l 338 9 granted grant VBN cord-340851-lnv8yi9l 338 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 338 11 a a DT cord-340851-lnv8yi9l 338 12 license license NN cord-340851-lnv8yi9l 338 13 to to TO cord-340851-lnv8yi9l 338 14 display display VB cord-340851-lnv8yi9l 338 15 the the DT cord-340851-lnv8yi9l 338 16 preprint preprint NN cord-340851-lnv8yi9l 338 17 in in IN cord-340851-lnv8yi9l 338 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 338 19 . . . cord-340851-lnv8yi9l 339 1 ( ( -LRB- cord-340851-lnv8yi9l 339 2 which which WDT cord-340851-lnv8yi9l 339 3 was be VBD cord-340851-lnv8yi9l 339 4 not not RB cord-340851-lnv8yi9l 339 5 certified certify VBN cord-340851-lnv8yi9l 339 6 by by IN cord-340851-lnv8yi9l 339 7 peer peer NN cord-340851-lnv8yi9l 339 8 review review NN cord-340851-lnv8yi9l 339 9 ) ) -RRB- cord-340851-lnv8yi9l 340 1 The the DT cord-340851-lnv8yi9l 340 2 copyright copyright NN cord-340851-lnv8yi9l 340 3 holder holder NN cord-340851-lnv8yi9l 340 4 for for IN cord-340851-lnv8yi9l 340 5 this this DT cord-340851-lnv8yi9l 340 6 preprint preprint NN cord-340851-lnv8yi9l 340 7 this this DT cord-340851-lnv8yi9l 340 8 version version NN cord-340851-lnv8yi9l 340 9 posted post VBN cord-340851-lnv8yi9l 340 10 April April NNP cord-340851-lnv8yi9l 340 11 23 23 CD cord-340851-lnv8yi9l 340 12 , , , cord-340851-lnv8yi9l 340 13 2020 2020 CD cord-340851-lnv8yi9l 340 14 . . . cord-340851-lnv8yi9l 340 15 . . . cord-340851-lnv8yi9l 341 1 https://doi.org/10.1101/2020.04 https://doi.org/10.1101/2020.04 UH cord-340851-lnv8yi9l 341 2 . . . cord-340851-lnv8yi9l 342 1 22.20076018 22.20076018 CD cord-340851-lnv8yi9l 342 2 doi doi NN cord-340851-lnv8yi9l 342 3 : : : cord-340851-lnv8yi9l 343 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 343 2 preprint preprint NN cord-340851-lnv8yi9l 343 3 . . . cord-340851-lnv8yi9l 344 1 CC CC NNP cord-340851-lnv8yi9l 344 2 - - : cord-340851-lnv8yi9l 344 3 BY by IN cord-340851-lnv8yi9l 344 4 4.0 4.0 CD cord-340851-lnv8yi9l 344 5 International international JJ cord-340851-lnv8yi9l 344 6 license license NN cord-340851-lnv8yi9l 345 1 It -PRON- PRP cord-340851-lnv8yi9l 345 2 is be VBZ cord-340851-lnv8yi9l 345 3 made make VBN cord-340851-lnv8yi9l 345 4 available available JJ cord-340851-lnv8yi9l 345 5 under under IN cord-340851-lnv8yi9l 345 6 a a DT cord-340851-lnv8yi9l 346 1 is be VBZ cord-340851-lnv8yi9l 346 2 the the DT cord-340851-lnv8yi9l 346 3 author author NN cord-340851-lnv8yi9l 346 4 / / SYM cord-340851-lnv8yi9l 346 5 funder funder NN cord-340851-lnv8yi9l 346 6 , , , cord-340851-lnv8yi9l 346 7 who who WP cord-340851-lnv8yi9l 346 8 has have VBZ cord-340851-lnv8yi9l 346 9 granted grant VBN cord-340851-lnv8yi9l 346 10 medRxiv medRxiv NNS cord-340851-lnv8yi9l 346 11 a a DT cord-340851-lnv8yi9l 346 12 license license NN cord-340851-lnv8yi9l 346 13 to to TO cord-340851-lnv8yi9l 346 14 display display VB cord-340851-lnv8yi9l 346 15 the the DT cord-340851-lnv8yi9l 346 16 preprint preprint NN cord-340851-lnv8yi9l 346 17 in in IN cord-340851-lnv8yi9l 346 18 perpetuity perpetuity NN cord-340851-lnv8yi9l 346 19 . . . cord-340851-lnv8yi9l 347 1 ( ( -LRB- cord-340851-lnv8yi9l 347 2 which which WDT cord-340851-lnv8yi9l 347 3 was be VBD cord-340851-lnv8yi9l 347 4 not not RB cord-340851-lnv8yi9l 347 5 certified certify VBN cord-340851-lnv8yi9l 347 6 by by IN cord-340851-lnv8yi9l 347 7 peer peer NN cord-340851-lnv8yi9l 347 8 review review NN cord-340851-lnv8yi9l 347 9 ) ) -RRB- cord-340851-lnv8yi9l 348 1 The the DT cord-340851-lnv8yi9l 348 2 copyright copyright NN cord-340851-lnv8yi9l 348 3 holder holder NN cord-340851-lnv8yi9l 348 4 for for IN cord-340851-lnv8yi9l 348 5 this this DT cord-340851-lnv8yi9l 348 6 preprint preprint NN cord-340851-lnv8yi9l 348 7 this this DT cord-340851-lnv8yi9l 348 8 version version NN cord-340851-lnv8yi9l 348 9 posted post VBN cord-340851-lnv8yi9l 348 10 April April NNP cord-340851-lnv8yi9l 348 11 23 23 CD cord-340851-lnv8yi9l 348 12 , , , cord-340851-lnv8yi9l 348 13 2020 2020 CD cord-340851-lnv8yi9l 348 14 . . . cord-340851-lnv8yi9l 348 15 . . . cord-340851-lnv8yi9l 349 1 https://doi.org/10.1101/2020.04 https://doi.org/10.1101/2020.04 UH cord-340851-lnv8yi9l 349 2 . . . cord-340851-lnv8yi9l 350 1 22.20076018 22.20076018 CD cord-340851-lnv8yi9l 350 2 doi doi NN cord-340851-lnv8yi9l 350 3 : : : cord-340851-lnv8yi9l 351 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 351 2 preprint preprint NNP cord-340851-lnv8yi9l 351 3 _SP cord-340851-lnv8yi9l 351 4 nCoV nCoV NNP cord-340851-lnv8yi9l 351 5 2019 2019 CD cord-340851-lnv8yi9l 351 6 Data Data NNP cord-340851-lnv8yi9l 351 7 Working Working NNP cord-340851-lnv8yi9l 351 8 Group Group NNP cord-340851-lnv8yi9l 351 9 : : : cord-340851-lnv8yi9l 352 1 Epidemiological Epidemiological NNP cord-340851-lnv8yi9l 352 2 Data Data NNP cord-340851-lnv8yi9l 352 3 from from IN cord-340851-lnv8yi9l 352 4 the the DT cord-340851-lnv8yi9l 352 5 nCoV-2019 ncov-2019 CD cord-340851-lnv8yi9l 352 6 Outbreak outbreak NN cord-340851-lnv8yi9l 352 7 : : : cord-340851-lnv8yi9l 352 8 Early early JJ cord-340851-lnv8yi9l 352 9 Descriptions description NNS cord-340851-lnv8yi9l 352 10 from from IN cord-340851-lnv8yi9l 352 11 Publicly publicly RB cord-340851-lnv8yi9l 352 12 Available Available NNP cord-340851-lnv8yi9l 352 13 Data datum NNS cord-340851-lnv8yi9l 352 14 Optimal Optimal NNP cord-340851-lnv8yi9l 352 15 control control NN cord-340851-lnv8yi9l 352 16 strategies strategy NNS cord-340851-lnv8yi9l 352 17 for for IN cord-340851-lnv8yi9l 352 18 dengue dengue NN cord-340851-lnv8yi9l 352 19 transmission transmission NN cord-340851-lnv8yi9l 352 20 in in IN cord-340851-lnv8yi9l 352 21 pakistan pakistan NNP cord-340851-lnv8yi9l 352 22 Non Non NNP cord-340851-lnv8yi9l 352 23 - - JJ cord-340851-lnv8yi9l 352 24 pharmaceutical pharmaceutical JJ cord-340851-lnv8yi9l 352 25 public public JJ cord-340851-lnv8yi9l 352 26 health health NN cord-340851-lnv8yi9l 352 27 interventions intervention NNS cord-340851-lnv8yi9l 352 28 for for IN cord-340851-lnv8yi9l 352 29 pandemic pandemic NN cord-340851-lnv8yi9l 352 30 influenza influenza NN cord-340851-lnv8yi9l 352 31 : : : cord-340851-lnv8yi9l 352 32 an an DT cord-340851-lnv8yi9l 352 33 evaluation evaluation NN cord-340851-lnv8yi9l 352 34 of of IN cord-340851-lnv8yi9l 352 35 the the DT cord-340851-lnv8yi9l 352 36 evidence evidence NN cord-340851-lnv8yi9l 352 37 base base NN cord-340851-lnv8yi9l 352 38 CNN CNN NNP cord-340851-lnv8yi9l 353 1 : : : cord-340851-lnv8yi9l 353 2 Lead lead VB cord-340851-lnv8yi9l 353 3 scientist scientist NN cord-340851-lnv8yi9l 353 4 says say VBZ cord-340851-lnv8yi9l 353 5 coronavirus coronavirus NN cord-340851-lnv8yi9l 353 6 vaccine vaccine NN cord-340851-lnv8yi9l 353 7 could could MD cord-340851-lnv8yi9l 353 8 be be VB cord-340851-lnv8yi9l 353 9 ready ready JJ cord-340851-lnv8yi9l 353 10 soon soon RB cord-340851-lnv8yi9l 354 1 Covid-19 Covid-19 NNP cord-340851-lnv8yi9l 354 2 : : : cord-340851-lnv8yi9l 354 3 towards towards IN cord-340851-lnv8yi9l 354 4 controlling control VBG cord-340851-lnv8yi9l 354 5 of of IN cord-340851-lnv8yi9l 354 6 a a DT cord-340851-lnv8yi9l 354 7 pandemic pandemic JJ cord-340851-lnv8yi9l 354 8 Backward backward JJ cord-340851-lnv8yi9l 354 9 bifurcation bifurcation NN cord-340851-lnv8yi9l 354 10 and and CC cord-340851-lnv8yi9l 354 11 optimal optimal JJ cord-340851-lnv8yi9l 354 12 control control NN cord-340851-lnv8yi9l 354 13 in in IN cord-340851-lnv8yi9l 354 14 transmission transmission NN cord-340851-lnv8yi9l 354 15 dynamics dynamic NNS cord-340851-lnv8yi9l 354 16 of of IN cord-340851-lnv8yi9l 354 17 west west NNP cord-340851-lnv8yi9l 354 18 nile nile NNP cord-340851-lnv8yi9l 354 19 virus virus NN cord-340851-lnv8yi9l 354 20 H1N1 H1N1 NNP cord-340851-lnv8yi9l 354 21 Flu Flu NNP cord-340851-lnv8yi9l 354 22 Vaccine Vaccine NNP cord-340851-lnv8yi9l 354 23 H1N1 H1N1 NNP cord-340851-lnv8yi9l 354 24 Pandemic Pandemic NNP cord-340851-lnv8yi9l 354 25 Timeline Timeline NNP cord-340851-lnv8yi9l 354 26 Control Control NNP cord-340851-lnv8yi9l 354 27 and and CC cord-340851-lnv8yi9l 354 28 Prevention Prevention NNP cord-340851-lnv8yi9l 354 29 : : : cord-340851-lnv8yi9l 354 30 Severe severe JJ cord-340851-lnv8yi9l 354 31 outcomes outcome NNS cord-340851-lnv8yi9l 354 32 among among IN cord-340851-lnv8yi9l 354 33 patients patient NNS cord-340851-lnv8yi9l 354 34 with with IN cord-340851-lnv8yi9l 354 35 coronavirus coronavirus NN cord-340851-lnv8yi9l 354 36 disease disease NN cord-340851-lnv8yi9l 354 37 2019 2019 CD cord-340851-lnv8yi9l 354 38 ( ( -LRB- cord-340851-lnv8yi9l 355 1 covid-19 covid-19 LS cord-340851-lnv8yi9l 355 2 ) ) -RRB- cord-340851-lnv8yi9l 355 3 -united -unite VBD cord-340851-lnv8yi9l 355 4 states state NNS cord-340851-lnv8yi9l 356 1 The the DT cord-340851-lnv8yi9l 356 2 effect effect NN cord-340851-lnv8yi9l 356 3 of of IN cord-340851-lnv8yi9l 356 4 travel travel NN cord-340851-lnv8yi9l 356 5 restrictions restriction NNS cord-340851-lnv8yi9l 356 6 on on IN cord-340851-lnv8yi9l 356 7 the the DT cord-340851-lnv8yi9l 356 8 spread spread NN cord-340851-lnv8yi9l 356 9 of of IN cord-340851-lnv8yi9l 356 10 the the DT cord-340851-lnv8yi9l 356 11 2019 2019 CD cord-340851-lnv8yi9l 356 12 novel novel NN cord-340851-lnv8yi9l 356 13 coronavirus coronavirus NN cord-340851-lnv8yi9l 356 14 ( ( -LRB- cord-340851-lnv8yi9l 356 15 covid-19 covid-19 NNP cord-340851-lnv8yi9l 356 16 ) ) -RRB- cord-340851-lnv8yi9l 356 17 outbreak outbreak NN cord-340851-lnv8yi9l 356 18 Optimal Optimal NNP cord-340851-lnv8yi9l 356 19 tuberculosis tuberculosis NN cord-340851-lnv8yi9l 356 20 prevention prevention NN cord-340851-lnv8yi9l 356 21 and and CC cord-340851-lnv8yi9l 356 22 control control NN cord-340851-lnv8yi9l 356 23 strategy strategy NN cord-340851-lnv8yi9l 356 24 from from IN cord-340851-lnv8yi9l 356 25 a a DT cord-340851-lnv8yi9l 356 26 mathematical mathematical JJ cord-340851-lnv8yi9l 356 27 model model NN cord-340851-lnv8yi9l 356 28 based base VBN cord-340851-lnv8yi9l 356 29 on on IN cord-340851-lnv8yi9l 356 30 real real JJ cord-340851-lnv8yi9l 356 31 data datum NNS cord-340851-lnv8yi9l 356 32 Impact impact NN cord-340851-lnv8yi9l 356 33 assessment assessment NN cord-340851-lnv8yi9l 356 34 of of IN cord-340851-lnv8yi9l 356 35 non non JJ cord-340851-lnv8yi9l 356 36 - - JJ cord-340851-lnv8yi9l 356 37 pharmaceutical pharmaceutical JJ cord-340851-lnv8yi9l 356 38 interventions intervention NNS cord-340851-lnv8yi9l 356 39 against against IN cord-340851-lnv8yi9l 356 40 coronavirus coronavirus NN cord-340851-lnv8yi9l 356 41 disease disease NN cord-340851-lnv8yi9l 356 42 2019 2019 CD cord-340851-lnv8yi9l 356 43 and and CC cord-340851-lnv8yi9l 356 44 influenza influenza NN cord-340851-lnv8yi9l 356 45 in in IN cord-340851-lnv8yi9l 356 46 hong hong NNP cord-340851-lnv8yi9l 356 47 kong kong NNP cord-340851-lnv8yi9l 356 48 : : : cord-340851-lnv8yi9l 356 49 an an DT cord-340851-lnv8yi9l 356 50 observational observational JJ cord-340851-lnv8yi9l 356 51 study study NN cord-340851-lnv8yi9l 356 52 The the DT cord-340851-lnv8yi9l 356 53 effect effect NN cord-340851-lnv8yi9l 356 54 of of IN cord-340851-lnv8yi9l 356 55 nonpharmaceutical nonpharmaceutical JJ cord-340851-lnv8yi9l 356 56 interventions intervention NNS cord-340851-lnv8yi9l 356 57 on on IN cord-340851-lnv8yi9l 356 58 COVID-19 covid-19 JJ cord-340851-lnv8yi9l 356 59 cases case NNS cord-340851-lnv8yi9l 356 60 , , , cord-340851-lnv8yi9l 356 61 deaths death NNS cord-340851-lnv8yi9l 356 62 and and CC cord-340851-lnv8yi9l 356 63 demand demand NN cord-340851-lnv8yi9l 356 64 for for IN cord-340851-lnv8yi9l 356 65 hospital hospital NN cord-340851-lnv8yi9l 356 66 services service NNS cord-340851-lnv8yi9l 356 67 in in IN cord-340851-lnv8yi9l 356 68 the the DT cord-340851-lnv8yi9l 356 69 UK UK NNP cord-340851-lnv8yi9l 356 70 : : : cord-340851-lnv8yi9l 356 71 a a DT cord-340851-lnv8yi9l 356 72 modeling modeling NN cord-340851-lnv8yi9l 356 73 study study NN cord-340851-lnv8yi9l 356 74 Optimal Optimal NNP cord-340851-lnv8yi9l 356 75 covid-19 covid-19 NNP cord-340851-lnv8yi9l 356 76 epidemic epidemic NN cord-340851-lnv8yi9l 356 77 control control NN cord-340851-lnv8yi9l 356 78 until until IN cord-340851-lnv8yi9l 356 79 vaccine vaccine NN cord-340851-lnv8yi9l 356 80 deployment deployment NN cord-340851-lnv8yi9l 356 81 . . . cord-340851-lnv8yi9l 357 1 medRxiv medRxiv NNS cord-340851-lnv8yi9l 358 1 Further further JJ cord-340851-lnv8yi9l 358 2 notes note NNS cord-340851-lnv8yi9l 358 3 on on IN cord-340851-lnv8yi9l 358 4 the the DT cord-340851-lnv8yi9l 358 5 basic basic JJ cord-340851-lnv8yi9l 358 6 reproduction reproduction NN cord-340851-lnv8yi9l 358 7 number number NN cord-340851-lnv8yi9l 358 8 Editorial editorial NN cord-340851-lnv8yi9l 358 9 : : : cord-340851-lnv8yi9l 358 10 Covid-19 covid-19 VB cord-340851-lnv8yi9l 358 11 in in IN cord-340851-lnv8yi9l 358 12 the the DT cord-340851-lnv8yi9l 358 13 usa usa NNP cord-340851-lnv8yi9l 358 14 : : : cord-340851-lnv8yi9l 358 15 a a DT cord-340851-lnv8yi9l 358 16 question question NN cord-340851-lnv8yi9l 358 17 of of IN cord-340851-lnv8yi9l 358 18 time time NN cord-340851-lnv8yi9l 358 19 Report Report NNP cord-340851-lnv8yi9l 358 20 9 9 CD cord-340851-lnv8yi9l 358 21 -Impact -Impact : cord-340851-lnv8yi9l 358 22 of of IN cord-340851-lnv8yi9l 358 23 non non JJ cord-340851-lnv8yi9l 358 24 - - JJ cord-340851-lnv8yi9l 358 25 pharmaceutical pharmaceutical JJ cord-340851-lnv8yi9l 358 26 interventions intervention NNS cord-340851-lnv8yi9l 358 27 ( ( -LRB- cord-340851-lnv8yi9l 358 28 NPIs NPIs NNP cord-340851-lnv8yi9l 358 29 ) ) -RRB- cord-340851-lnv8yi9l 358 30 to to TO cord-340851-lnv8yi9l 358 31 reduce reduce VB cord-340851-lnv8yi9l 358 32 COVID-19 covid-19 JJ cord-340851-lnv8yi9l 358 33 mortality mortality NN cord-340851-lnv8yi9l 358 34 and and CC cord-340851-lnv8yi9l 358 35 healthcare healthcare NN cord-340851-lnv8yi9l 358 36 demand demand NN cord-340851-lnv8yi9l 358 37 Report Report NNP cord-340851-lnv8yi9l 358 38 13 13 CD cord-340851-lnv8yi9l 359 1 -Estimating -estimate VBG cord-340851-lnv8yi9l 360 1 the the DT cord-340851-lnv8yi9l 360 2 number number NN cord-340851-lnv8yi9l 360 3 of of IN cord-340851-lnv8yi9l 360 4 infections infection NNS cord-340851-lnv8yi9l 360 5 and and CC cord-340851-lnv8yi9l 360 6 the the DT cord-340851-lnv8yi9l 360 7 impact impact NN cord-340851-lnv8yi9l 360 8 of of IN cord-340851-lnv8yi9l 360 9 nonpharmaceutical nonpharmaceutical JJ cord-340851-lnv8yi9l 360 10 interventions intervention NNS cord-340851-lnv8yi9l 360 11 on on IN cord-340851-lnv8yi9l 360 12 COVID-19 COVID-19 NNP cord-340851-lnv8yi9l 360 13 Preparedness Preparedness NNP cord-340851-lnv8yi9l 360 14 and and CC cord-340851-lnv8yi9l 360 15 vulnerability vulnerability NN cord-340851-lnv8yi9l 360 16 of of IN cord-340851-lnv8yi9l 360 17 african african JJ cord-340851-lnv8yi9l 360 18 countries country NNS cord-340851-lnv8yi9l 360 19 against against IN cord-340851-lnv8yi9l 360 20 importations importation NNS cord-340851-lnv8yi9l 360 21 of of IN cord-340851-lnv8yi9l 360 22 covid-19 covid-19 CD cord-340851-lnv8yi9l 360 23 : : : cord-340851-lnv8yi9l 360 24 a a DT cord-340851-lnv8yi9l 360 25 modelling modelling NN cord-340851-lnv8yi9l 360 26 study study NN cord-340851-lnv8yi9l 360 27 Estimation estimation NN cord-340851-lnv8yi9l 360 28 of of IN cord-340851-lnv8yi9l 360 29 country country NN cord-340851-lnv8yi9l 360 30 - - HYPH cord-340851-lnv8yi9l 360 31 level level NN cord-340851-lnv8yi9l 360 32 basic basic JJ cord-340851-lnv8yi9l 360 33 reproductive reproductive JJ cord-340851-lnv8yi9l 360 34 ratios ratio NNS cord-340851-lnv8yi9l 360 35 for for IN cord-340851-lnv8yi9l 360 36 novel novel JJ cord-340851-lnv8yi9l 360 37 coronavirus coronavirus NN cord-340851-lnv8yi9l 360 38 ( ( -LRB- cord-340851-lnv8yi9l 360 39 covid-19 covid-19 NN cord-340851-lnv8yi9l 360 40 ) ) -RRB- cord-340851-lnv8yi9l 360 41 using use VBG cord-340851-lnv8yi9l 360 42 synthetic synthetic JJ cord-340851-lnv8yi9l 360 43 contact contact NN cord-340851-lnv8yi9l 360 44 matrices matrix NNS cord-340851-lnv8yi9l 360 45 . . . cord-340851-lnv8yi9l 361 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 361 2 First first JJ cord-340851-lnv8yi9l 361 3 case case NN cord-340851-lnv8yi9l 361 4 of of IN cord-340851-lnv8yi9l 361 5 2019 2019 CD cord-340851-lnv8yi9l 361 6 novel novel JJ cord-340851-lnv8yi9l 361 7 coronavirus coronavirus NN cord-340851-lnv8yi9l 361 8 in in IN cord-340851-lnv8yi9l 361 9 the the DT cord-340851-lnv8yi9l 361 10 united united NNP cord-340851-lnv8yi9l 361 11 states states NNP cord-340851-lnv8yi9l 361 12 Quantifying quantify VBG cord-340851-lnv8yi9l 361 13 the the DT cord-340851-lnv8yi9l 361 14 impact impact NN cord-340851-lnv8yi9l 361 15 of of IN cord-340851-lnv8yi9l 361 16 physical physical JJ cord-340851-lnv8yi9l 361 17 distance distance NN cord-340851-lnv8yi9l 361 18 measures measure NNS cord-340851-lnv8yi9l 361 19 on on IN cord-340851-lnv8yi9l 361 20 the the DT cord-340851-lnv8yi9l 361 21 transmission transmission NN cord-340851-lnv8yi9l 361 22 of of IN cord-340851-lnv8yi9l 361 23 covid-19 covid-19 NN cord-340851-lnv8yi9l 361 24 in in IN cord-340851-lnv8yi9l 361 25 the the DT cord-340851-lnv8yi9l 361 26 uk uk NNP cord-340851-lnv8yi9l 361 27 Modeling Modeling NNP cord-340851-lnv8yi9l 361 28 Infectious Infectious NNP cord-340851-lnv8yi9l 361 29 Diseases Diseases NNPS cord-340851-lnv8yi9l 361 30 in in IN cord-340851-lnv8yi9l 361 31 Humans Humans NNPS cord-340851-lnv8yi9l 361 32 and and CC cord-340851-lnv8yi9l 361 33 Animals animal NNS cord-340851-lnv8yi9l 361 34 Projecting project VBG cord-340851-lnv8yi9l 361 35 the the DT cord-340851-lnv8yi9l 361 36 transmission transmission NN cord-340851-lnv8yi9l 361 37 dynamics dynamic NNS cord-340851-lnv8yi9l 361 38 of of IN cord-340851-lnv8yi9l 361 39 sars sars NNP cord-340851-lnv8yi9l 361 40 - - HYPH cord-340851-lnv8yi9l 361 41 cov-2 cov-2 NNP cord-340851-lnv8yi9l 361 42 through through IN cord-340851-lnv8yi9l 361 43 the the DT cord-340851-lnv8yi9l 361 44 postpandemic postpandemic JJ cord-340851-lnv8yi9l 361 45 period period NN cord-340851-lnv8yi9l 362 1 The the DT cord-340851-lnv8yi9l 362 2 effect effect NN cord-340851-lnv8yi9l 362 3 of of IN cord-340851-lnv8yi9l 362 4 human human JJ cord-340851-lnv8yi9l 362 5 mobility mobility NN cord-340851-lnv8yi9l 362 6 and and CC cord-340851-lnv8yi9l 362 7 control control NN cord-340851-lnv8yi9l 362 8 measures measure NNS cord-340851-lnv8yi9l 362 9 on on IN cord-340851-lnv8yi9l 362 10 the the DT cord-340851-lnv8yi9l 362 11 covid-19 covid-19 JJ cord-340851-lnv8yi9l 362 12 epidemic epidemic NN cord-340851-lnv8yi9l 362 13 in in IN cord-340851-lnv8yi9l 362 14 china china NNP cord-340851-lnv8yi9l 362 15 Effect Effect NNP cord-340851-lnv8yi9l 362 16 of of IN cord-340851-lnv8yi9l 362 17 non non JJ cord-340851-lnv8yi9l 362 18 - - JJ cord-340851-lnv8yi9l 362 19 pharmaceutical pharmaceutical JJ cord-340851-lnv8yi9l 362 20 interventions intervention NNS cord-340851-lnv8yi9l 362 21 for for IN cord-340851-lnv8yi9l 362 22 containing contain VBG cord-340851-lnv8yi9l 362 23 the the DT cord-340851-lnv8yi9l 362 24 covid-19 covid-19 CD cord-340851-lnv8yi9l 362 25 outbreak outbreak NN cord-340851-lnv8yi9l 362 26 in in IN cord-340851-lnv8yi9l 362 27 china china NNP cord-340851-lnv8yi9l 362 28 Optimal Optimal NNP cord-340851-lnv8yi9l 362 29 Control Control NNP cord-340851-lnv8yi9l 362 30 Applied apply VBD cord-340851-lnv8yi9l 362 31 to to IN cord-340851-lnv8yi9l 362 32 Biological Biological NNP cord-340851-lnv8yi9l 362 33 Models model NNS cord-340851-lnv8yi9l 363 1 An an DT cord-340851-lnv8yi9l 363 2 optimal optimal JJ cord-340851-lnv8yi9l 363 3 control control NN cord-340851-lnv8yi9l 363 4 theory theory NN cord-340851-lnv8yi9l 363 5 approach approach NN cord-340851-lnv8yi9l 363 6 to to IN cord-340851-lnv8yi9l 363 7 nonpharmaceutical nonpharmaceutical JJ cord-340851-lnv8yi9l 363 8 interventions intervention NNS cord-340851-lnv8yi9l 363 9 Developing develop VBG cord-340851-lnv8yi9l 363 10 covid-19 covid-19 CD cord-340851-lnv8yi9l 363 11 vaccines vaccine NNS cord-340851-lnv8yi9l 363 12 at at IN cord-340851-lnv8yi9l 363 13 pandemic pandemic NN cord-340851-lnv8yi9l 363 14 speed speed NN cord-340851-lnv8yi9l 364 1 Optimal optimal JJ cord-340851-lnv8yi9l 364 2 control control NN cord-340851-lnv8yi9l 364 3 applied apply VBD cord-340851-lnv8yi9l 364 4 to to IN cord-340851-lnv8yi9l 364 5 a a DT cord-340851-lnv8yi9l 364 6 seir seir JJ cord-340851-lnv8yi9l 364 7 model model NN cord-340851-lnv8yi9l 364 8 of of IN cord-340851-lnv8yi9l 364 9 2019-ncov 2019-ncov CD cord-340851-lnv8yi9l 364 10 with with IN cord-340851-lnv8yi9l 364 11 social social JJ cord-340851-lnv8yi9l 364 12 distancing distancing NN cord-340851-lnv8yi9l 364 13 . . . cord-340851-lnv8yi9l 365 1 medRxiv medRxiv NNS cord-340851-lnv8yi9l 365 2 Births birth NNS cord-340851-lnv8yi9l 365 3 : : : cord-340851-lnv8yi9l 365 4 Final final JJ cord-340851-lnv8yi9l 365 5 data datum NNS cord-340851-lnv8yi9l 365 6 for for IN cord-340851-lnv8yi9l 365 7 2018 2018 CD cord-340851-lnv8yi9l 366 1 Modeling model VBG cord-340851-lnv8yi9l 366 2 optimal optimal JJ cord-340851-lnv8yi9l 366 3 intervention intervention NN cord-340851-lnv8yi9l 366 4 strategies strategy NNS cord-340851-lnv8yi9l 366 5 for for IN cord-340851-lnv8yi9l 366 6 cholera cholera NN cord-340851-lnv8yi9l 366 7 Estimating estimate VBG cord-340851-lnv8yi9l 366 8 the the DT cord-340851-lnv8yi9l 366 9 asymptomatic asymptomatic JJ cord-340851-lnv8yi9l 366 10 proportion proportion NN cord-340851-lnv8yi9l 366 11 of of IN cord-340851-lnv8yi9l 366 12 coronavirus coronavirus NN cord-340851-lnv8yi9l 366 13 disease disease NN cord-340851-lnv8yi9l 366 14 2019 2019 CD cord-340851-lnv8yi9l 366 15 ( ( -LRB- cord-340851-lnv8yi9l 366 16 covid-19 covid-19 NNP cord-340851-lnv8yi9l 366 17 ) ) -RRB- cord-340851-lnv8yi9l 366 18 cases case NNS cord-340851-lnv8yi9l 366 19 on on IN cord-340851-lnv8yi9l 366 20 board board NN cord-340851-lnv8yi9l 366 21 the the DT cord-340851-lnv8yi9l 366 22 diamond diamond NNP cord-340851-lnv8yi9l 366 23 princess princess NNP cord-340851-lnv8yi9l 366 24 cruise cruise NN cord-340851-lnv8yi9l 366 25 ship ship NN cord-340851-lnv8yi9l 366 26 Optimal Optimal NNP cord-340851-lnv8yi9l 366 27 , , , cord-340851-lnv8yi9l 366 28 near near JJ cord-340851-lnv8yi9l 366 29 - - HYPH cord-340851-lnv8yi9l 366 30 optimal optimal JJ cord-340851-lnv8yi9l 366 31 , , , cord-340851-lnv8yi9l 366 32 and and CC cord-340851-lnv8yi9l 366 33 robust robust JJ cord-340851-lnv8yi9l 366 34 epidemic epidemic NN cord-340851-lnv8yi9l 366 35 control control NN cord-340851-lnv8yi9l 366 36 . . . cord-340851-lnv8yi9l 367 1 arXiv arXiv NNP cord-340851-lnv8yi9l 367 2 New New NNP cord-340851-lnv8yi9l 367 3 York York NNP cord-340851-lnv8yi9l 367 4 Times Times NNP cord-340851-lnv8yi9l 367 5 : : : cord-340851-lnv8yi9l 367 6 Coronavirus Coronavirus NNP cord-340851-lnv8yi9l 367 7 ( ( -LRB- cord-340851-lnv8yi9l 367 8 Covid-19 Covid-19 NNP cord-340851-lnv8yi9l 367 9 ) ) -RRB- cord-340851-lnv8yi9l 367 10 Data Data NNP cord-340851-lnv8yi9l 367 11 in in IN cord-340851-lnv8yi9l 367 12 the the DT cord-340851-lnv8yi9l 367 13 United United NNP cord-340851-lnv8yi9l 367 14 States States NNP cord-340851-lnv8yi9l 367 15 Mathematical Mathematical NNP cord-340851-lnv8yi9l 367 16 assessment assessment NN cord-340851-lnv8yi9l 367 17 of of IN cord-340851-lnv8yi9l 367 18 the the DT cord-340851-lnv8yi9l 367 19 impact impact NN cord-340851-lnv8yi9l 367 20 of of IN cord-340851-lnv8yi9l 367 21 non non JJ cord-340851-lnv8yi9l 367 22 - - JJ cord-340851-lnv8yi9l 367 23 pharmaceutical pharmaceutical JJ cord-340851-lnv8yi9l 367 24 interventions intervention NNS cord-340851-lnv8yi9l 367 25 on on IN cord-340851-lnv8yi9l 367 26 curtailing curtail VBG cord-340851-lnv8yi9l 367 27 the the DT cord-340851-lnv8yi9l 367 28 2019 2019 CD cord-340851-lnv8yi9l 367 29 novel novel NN cord-340851-lnv8yi9l 367 30 coronavirus coronavirus NN cord-340851-lnv8yi9l 367 31 Case case NN cord-340851-lnv8yi9l 367 32 - - HYPH cord-340851-lnv8yi9l 367 33 Fatality fatality NN cord-340851-lnv8yi9l 367 34 Rate rate NN cord-340851-lnv8yi9l 367 35 and and CC cord-340851-lnv8yi9l 367 36 Characteristics characteristic NNS cord-340851-lnv8yi9l 367 37 of of IN cord-340851-lnv8yi9l 367 38 Patients patient NNS cord-340851-lnv8yi9l 367 39 Dying die VBG cord-340851-lnv8yi9l 367 40 in in IN cord-340851-lnv8yi9l 367 41 Relation Relation NNP cord-340851-lnv8yi9l 367 42 to to TO cord-340851-lnv8yi9l 367 43 COVID-19 covid-19 VB cord-340851-lnv8yi9l 367 44 in in IN cord-340851-lnv8yi9l 367 45 Italy Italy NNP cord-340851-lnv8yi9l 367 46 Reconciling reconcile VBG cord-340851-lnv8yi9l 367 47 early early JJ cord-340851-lnv8yi9l 367 48 - - HYPH cord-340851-lnv8yi9l 367 49 outbreak outbreak NN cord-340851-lnv8yi9l 367 50 estimates estimate NNS cord-340851-lnv8yi9l 367 51 of of IN cord-340851-lnv8yi9l 367 52 the the DT cord-340851-lnv8yi9l 367 53 basic basic JJ cord-340851-lnv8yi9l 367 54 reproductive reproductive JJ cord-340851-lnv8yi9l 367 55 number number NN cord-340851-lnv8yi9l 367 56 and and CC cord-340851-lnv8yi9l 367 57 its -PRON- PRP$ cord-340851-lnv8yi9l 367 58 uncertainty uncertainty NN cord-340851-lnv8yi9l 367 59 : : : cord-340851-lnv8yi9l 367 60 framework framework NN cord-340851-lnv8yi9l 367 61 and and CC cord-340851-lnv8yi9l 367 62 applications application NNS cord-340851-lnv8yi9l 367 63 to to IN cord-340851-lnv8yi9l 367 64 the the DT cord-340851-lnv8yi9l 367 65 novel novel JJ cord-340851-lnv8yi9l 367 66 coronavirus coronavirus NN cord-340851-lnv8yi9l 367 67 ( ( -LRB- cord-340851-lnv8yi9l 367 68 sars sars NNP cord-340851-lnv8yi9l 367 69 - - HYPH cord-340851-lnv8yi9l 367 70 cov-2 cov-2 NNP cord-340851-lnv8yi9l 367 71 ) ) -RRB- cord-340851-lnv8yi9l 367 72 outbreak outbreak NN cord-340851-lnv8yi9l 367 73 . . . cord-340851-lnv8yi9l 368 1 medRxiv medRxiv NNS cord-340851-lnv8yi9l 368 2 Optimal Optimal NNP cord-340851-lnv8yi9l 368 3 timing timing NN cord-340851-lnv8yi9l 368 4 for for IN cord-340851-lnv8yi9l 368 5 social social JJ cord-340851-lnv8yi9l 368 6 distancing distancing NN cord-340851-lnv8yi9l 368 7 during during IN cord-340851-lnv8yi9l 368 8 an an DT cord-340851-lnv8yi9l 368 9 epidemic epidemic NN cord-340851-lnv8yi9l 368 10 . . . cord-340851-lnv8yi9l 369 1 medRxiv medRxiv NNS cord-340851-lnv8yi9l 369 2 ( ( -LRB- cord-340851-lnv8yi9l 369 3 2020 2020 CD cord-340851-lnv8yi9l 369 4 ) ) -RRB- cord-340851-lnv8yi9l 370 1 Estimating estimate VBG cord-340851-lnv8yi9l 370 2 unobserved unobserved JJ cord-340851-lnv8yi9l 370 3 sars sars NNP cord-340851-lnv8yi9l 370 4 - - HYPH cord-340851-lnv8yi9l 370 5 cov-2 cov-2 CD cord-340851-lnv8yi9l 370 6 infections infection NNS cord-340851-lnv8yi9l 370 7 in in IN cord-340851-lnv8yi9l 370 8 the the DT cord-340851-lnv8yi9l 370 9 united united NNP cord-340851-lnv8yi9l 370 10 states states NNP cord-340851-lnv8yi9l 371 1 Heterogeneous heterogeneous JJ cord-340851-lnv8yi9l 371 2 local local JJ cord-340851-lnv8yi9l 371 3 dynamics dynamic NNS cord-340851-lnv8yi9l 371 4 revealed reveal VBN cord-340851-lnv8yi9l 371 5 by by IN cord-340851-lnv8yi9l 371 6 classification classification NN cord-340851-lnv8yi9l 371 7 analysis analysis NN cord-340851-lnv8yi9l 371 8 of of IN cord-340851-lnv8yi9l 371 9 spatially spatially RB cord-340851-lnv8yi9l 371 10 disaggregated disaggregated JJ cord-340851-lnv8yi9l 371 11 time time NN cord-340851-lnv8yi9l 371 12 series series NNP cord-340851-lnv8yi9l 371 13 data datum NNS cord-340851-lnv8yi9l 371 14 Optimal Optimal NNP cord-340851-lnv8yi9l 371 15 covid-19 covid-19 NNP cord-340851-lnv8yi9l 371 16 quarantine quarantine NN cord-340851-lnv8yi9l 371 17 and and CC cord-340851-lnv8yi9l 371 18 testing testing NN cord-340851-lnv8yi9l 371 19 policies policy NNS cord-340851-lnv8yi9l 371 20 . . . cord-340851-lnv8yi9l 372 1 EIEF EIEF NNP cord-340851-lnv8yi9l 372 2 Working Working NNP cord-340851-lnv8yi9l 372 3 Papers Papers NNPS cord-340851-lnv8yi9l 372 4 Series Series NNP cord-340851-lnv8yi9l 373 1 The the DT cord-340851-lnv8yi9l 373 2 effect effect NN cord-340851-lnv8yi9l 373 3 of of IN cord-340851-lnv8yi9l 373 4 control control NN cord-340851-lnv8yi9l 373 5 strategies strategy NNS cord-340851-lnv8yi9l 373 6 to to TO cord-340851-lnv8yi9l 373 7 reduce reduce VB cord-340851-lnv8yi9l 373 8 social social JJ cord-340851-lnv8yi9l 373 9 mixing mixing NN cord-340851-lnv8yi9l 373 10 on on IN cord-340851-lnv8yi9l 373 11 outcomes outcome NNS cord-340851-lnv8yi9l 373 12 of of IN cord-340851-lnv8yi9l 373 13 the the DT cord-340851-lnv8yi9l 373 14 covid-19 covid-19 JJ cord-340851-lnv8yi9l 373 15 epidemic epidemic NN cord-340851-lnv8yi9l 373 16 in in IN cord-340851-lnv8yi9l 373 17 wuhan wuhan NNP cord-340851-lnv8yi9l 373 18 , , , cord-340851-lnv8yi9l 373 19 china china NNP cord-340851-lnv8yi9l 373 20 : : : cord-340851-lnv8yi9l 373 21 a a DT cord-340851-lnv8yi9l 373 22 modelling modelling NN cord-340851-lnv8yi9l 373 23 study study NN cord-340851-lnv8yi9l 373 24 Control control NN cord-340851-lnv8yi9l 373 25 strategies strategy NNS cord-340851-lnv8yi9l 373 26 to to TO cord-340851-lnv8yi9l 373 27 curtail curtail VB cord-340851-lnv8yi9l 373 28 transmission transmission NN cord-340851-lnv8yi9l 373 29 of of IN cord-340851-lnv8yi9l 373 30 covid-19 covid-19 NN cord-340851-lnv8yi9l 373 31 . . . cord-340851-lnv8yi9l 374 1 medRxiv medRxiv NNP cord-340851-lnv8yi9l 374 2 Optimal optimal JJ cord-340851-lnv8yi9l 374 3 strategies strategy NNS cord-340851-lnv8yi9l 374 4 of of IN cord-340851-lnv8yi9l 374 5 social social JJ cord-340851-lnv8yi9l 374 6 distancing distancing NN cord-340851-lnv8yi9l 374 7 and and CC cord-340851-lnv8yi9l 374 8 vaccination vaccination NN cord-340851-lnv8yi9l 374 9 against against IN cord-340851-lnv8yi9l 374 10 seasonal seasonal JJ cord-340851-lnv8yi9l 374 11 influenza influenza NN cord-340851-lnv8yi9l 374 12 Solving solve VBG cord-340851-lnv8yi9l 374 13 differential differential JJ cord-340851-lnv8yi9l 374 14 equations equation NNS cord-340851-lnv8yi9l 374 15 in in IN cord-340851-lnv8yi9l 374 16 r r NN cord-340851-lnv8yi9l 375 1 : : : cord-340851-lnv8yi9l 375 2 Package package NN cord-340851-lnv8yi9l 375 3 desolve desolve VB cord-340851-lnv8yi9l 375 4 Optimal Optimal NNP cord-340851-lnv8yi9l 375 5 control control NN cord-340851-lnv8yi9l 375 6 and and CC cord-340851-lnv8yi9l 375 7 sensitivity sensitivity NN cord-340851-lnv8yi9l 375 8 analysis analysis NN cord-340851-lnv8yi9l 375 9 of of IN cord-340851-lnv8yi9l 375 10 an an DT cord-340851-lnv8yi9l 375 11 influenza influenza NN cord-340851-lnv8yi9l 375 12 model model NN cord-340851-lnv8yi9l 375 13 with with IN cord-340851-lnv8yi9l 375 14 treatment treatment NN cord-340851-lnv8yi9l 375 15 and and CC cord-340851-lnv8yi9l 375 16 vaccination vaccination NN cord-340851-lnv8yi9l 375 17 Forecasting Forecasting NNP cord-340851-lnv8yi9l 375 18 covid-19 covid-19 NN cord-340851-lnv8yi9l 375 19 impact impact NN cord-340851-lnv8yi9l 375 20 on on IN cord-340851-lnv8yi9l 375 21 hospital hospital NN cord-340851-lnv8yi9l 375 22 bed bed NN cord-340851-lnv8yi9l 375 23 - - HYPH cord-340851-lnv8yi9l 375 24 days day NNS cord-340851-lnv8yi9l 375 25 , , , cord-340851-lnv8yi9l 375 26 icu icu NN cord-340851-lnv8yi9l 375 27 - - HYPH cord-340851-lnv8yi9l 375 28 days day NNS cord-340851-lnv8yi9l 375 29 , , , cord-340851-lnv8yi9l 375 30 ventilator ventilator NN cord-340851-lnv8yi9l 375 31 - - HYPH cord-340851-lnv8yi9l 375 32 days day NNS cord-340851-lnv8yi9l 375 33 and and CC cord-340851-lnv8yi9l 375 34 deaths death NNS cord-340851-lnv8yi9l 375 35 by by IN cord-340851-lnv8yi9l 375 36 us us NNP cord-340851-lnv8yi9l 375 37 state state NN cord-340851-lnv8yi9l 375 38 in in IN cord-340851-lnv8yi9l 375 39 the the DT cord-340851-lnv8yi9l 375 40 next next JJ cord-340851-lnv8yi9l 375 41 4 4 CD cord-340851-lnv8yi9l 375 42 months month NNS cord-340851-lnv8yi9l 376 1 Mathematical mathematical JJ cord-340851-lnv8yi9l 376 2 modelling modelling NN cord-340851-lnv8yi9l 376 3 of of IN cord-340851-lnv8yi9l 376 4 covid-19 covid-19 CD cord-340851-lnv8yi9l 376 5 transmission transmission NN cord-340851-lnv8yi9l 376 6 and and CC cord-340851-lnv8yi9l 376 7 mitigation mitigation NN cord-340851-lnv8yi9l 376 8 strategies strategy NNS cord-340851-lnv8yi9l 376 9 in in IN cord-340851-lnv8yi9l 376 10 the the DT cord-340851-lnv8yi9l 376 11 population population NN cord-340851-lnv8yi9l 376 12 of of IN cord-340851-lnv8yi9l 376 13 ontario ontario NNP cord-340851-lnv8yi9l 376 14 , , , cord-340851-lnv8yi9l 376 15 canada canada NNP cord-340851-lnv8yi9l 376 16 Time Time NNP cord-340851-lnv8yi9l 376 17 - - HYPH cord-340851-lnv8yi9l 376 18 variant variant NN cord-340851-lnv8yi9l 376 19 strategies strategy NNS cord-340851-lnv8yi9l 376 20 for for IN cord-340851-lnv8yi9l 376 21 optimizing optimize VBG cord-340851-lnv8yi9l 376 22 the the DT cord-340851-lnv8yi9l 376 23 performance performance NN cord-340851-lnv8yi9l 376 24 of of IN cord-340851-lnv8yi9l 376 25 nonpharmaceutical nonpharmaceutical JJ cord-340851-lnv8yi9l 376 26 interventions intervention NNS cord-340851-lnv8yi9l 376 27 ( ( -LRB- cord-340851-lnv8yi9l 376 28 npis npis NNP cord-340851-lnv8yi9l 376 29 ) ) -RRB- cord-340851-lnv8yi9l 376 30 in in IN cord-340851-lnv8yi9l 376 31 protecting protect VBG cord-340851-lnv8yi9l 376 32 lives life NNS cord-340851-lnv8yi9l 376 33 and and CC cord-340851-lnv8yi9l 376 34 livelihoods livelihood NNS cord-340851-lnv8yi9l 376 35 during during IN cord-340851-lnv8yi9l 376 36 the the DT cord-340851-lnv8yi9l 376 37 covid-19 covid-19 CD cord-340851-lnv8yi9l 376 38 pandemic pandemic NN cord-340851-lnv8yi9l 376 39 Acknowledgements acknowledgement NNS cord-340851-lnv8yi9l 377 1 Thanks thank NNS cord-340851-lnv8yi9l 377 2 to to IN cord-340851-lnv8yi9l 378 1 the the DT cord-340851-lnv8yi9l 378 2 University University NNP cord-340851-lnv8yi9l 378 3 of of IN cord-340851-lnv8yi9l 378 4 Notre Notre NNP cord-340851-lnv8yi9l 378 5 Dame Dame NNP cord-340851-lnv8yi9l 378 6 's 's POS cord-340851-lnv8yi9l 378 7 Center Center NNP cord-340851-lnv8yi9l 378 8 for for IN cord-340851-lnv8yi9l 378 9 Research Research NNP cord-340851-lnv8yi9l 378 10 Computing Computing NNP cord-340851-lnv8yi9l 378 11 for for IN cord-340851-lnv8yi9l 378 12 computing compute VBG cord-340851-lnv8yi9l 378 13 resources resource NNS cord-340851-lnv8yi9l 378 14 . . .