id sid tid token lemma pos cord-242132-fhepdgz9 1 1 key key NN cord-242132-fhepdgz9 1 2 : : : cord-242132-fhepdgz9 1 3 cord-242132-fhepdgz9 cord-242132-fhepdgz9 NN cord-242132-fhepdgz9 1 4 authors author NNS cord-242132-fhepdgz9 1 5 : : : cord-242132-fhepdgz9 1 6 Burlak Burlak NNP cord-242132-fhepdgz9 1 7 , , , cord-242132-fhepdgz9 1 8 Gennadiy Gennadiy NNP cord-242132-fhepdgz9 1 9 title title NN cord-242132-fhepdgz9 1 10 : : : cord-242132-fhepdgz9 1 11 Is be VBZ cord-242132-fhepdgz9 1 12 it -PRON- PRP cord-242132-fhepdgz9 1 13 possible possible JJ cord-242132-fhepdgz9 1 14 to to TO cord-242132-fhepdgz9 1 15 suspend suspend VB cord-242132-fhepdgz9 1 16 the the DT cord-242132-fhepdgz9 1 17 spread spread NN cord-242132-fhepdgz9 1 18 of of IN cord-242132-fhepdgz9 1 19 an an DT cord-242132-fhepdgz9 1 20 epidemic epidemic NN cord-242132-fhepdgz9 1 21 infection infection NN cord-242132-fhepdgz9 1 22 ? ? . cord-242132-fhepdgz9 2 1 The the DT cord-242132-fhepdgz9 2 2 dynamic dynamic JJ cord-242132-fhepdgz9 2 3 Monte Monte NNP cord-242132-fhepdgz9 2 4 Carlo Carlo NNP cord-242132-fhepdgz9 2 5 approach approach NN cord-242132-fhepdgz9 2 6 date date NN cord-242132-fhepdgz9 2 7 : : : cord-242132-fhepdgz9 2 8 2020 2020 CD cord-242132-fhepdgz9 2 9 - - HYPH cord-242132-fhepdgz9 2 10 05 05 CD cord-242132-fhepdgz9 2 11 - - HYPH cord-242132-fhepdgz9 2 12 28 28 CD cord-242132-fhepdgz9 2 13 journal journal NN cord-242132-fhepdgz9 2 14 : : : cord-242132-fhepdgz9 3 1 nan nan NNP cord-242132-fhepdgz9 3 2 DOI DOI NNP cord-242132-fhepdgz9 3 3 : : : cord-242132-fhepdgz9 4 1 nan nan NNP cord-242132-fhepdgz9 4 2 sha sha NNP cord-242132-fhepdgz9 4 3 : : : cord-242132-fhepdgz9 5 1 fa4c827c2dddc22fd77f95b2c9c981435765e808 fa4c827c2dddc22fd77f95b2c9c981435765e808 CD cord-242132-fhepdgz9 5 2 doc_id doc_id CD cord-242132-fhepdgz9 5 3 : : : cord-242132-fhepdgz9 6 1 242132 242132 CD cord-242132-fhepdgz9 6 2 cord_uid cord_uid NNS cord-242132-fhepdgz9 6 3 : : : cord-242132-fhepdgz9 7 1 fhepdgz9 fhepdgz9 NNP cord-242132-fhepdgz9 8 1 We -PRON- PRP cord-242132-fhepdgz9 8 2 study study VBP cord-242132-fhepdgz9 8 3 a a DT cord-242132-fhepdgz9 8 4 dynamics dynamic NNS cord-242132-fhepdgz9 8 5 of of IN cord-242132-fhepdgz9 8 6 the the DT cord-242132-fhepdgz9 8 7 epidemiological epidemiological JJ cord-242132-fhepdgz9 8 8 infection infection NN cord-242132-fhepdgz9 8 9 spreading spread VBG cord-242132-fhepdgz9 8 10 at at IN cord-242132-fhepdgz9 8 11 different different JJ cord-242132-fhepdgz9 8 12 values value NNS cord-242132-fhepdgz9 8 13 of of IN cord-242132-fhepdgz9 8 14 the the DT cord-242132-fhepdgz9 8 15 risk risk NN cord-242132-fhepdgz9 8 16 factor factor NN cord-242132-fhepdgz9 8 17 $ $ $ cord-242132-fhepdgz9 8 18 beta$ beta$ NN cord-242132-fhepdgz9 8 19 ( ( -LRB- cord-242132-fhepdgz9 8 20 a a DT cord-242132-fhepdgz9 8 21 control control NN cord-242132-fhepdgz9 8 22 parameter parameter NN cord-242132-fhepdgz9 8 23 ) ) -RRB- cord-242132-fhepdgz9 8 24 with with IN cord-242132-fhepdgz9 8 25 the the DT cord-242132-fhepdgz9 8 26 using using NN cord-242132-fhepdgz9 8 27 of of IN cord-242132-fhepdgz9 8 28 dynamic dynamic JJ cord-242132-fhepdgz9 8 29 Monte Monte NNP cord-242132-fhepdgz9 8 30 Carlo Carlo NNP cord-242132-fhepdgz9 8 31 approach approach NN cord-242132-fhepdgz9 8 32 ( ( -LRB- cord-242132-fhepdgz9 8 33 DMC DMC NNP cord-242132-fhepdgz9 8 34 ) ) -RRB- cord-242132-fhepdgz9 8 35 . . . cord-242132-fhepdgz9 9 1 In in IN cord-242132-fhepdgz9 9 2 our -PRON- PRP$ cord-242132-fhepdgz9 9 3 toy toy NN cord-242132-fhepdgz9 9 4 model model NN cord-242132-fhepdgz9 9 5 , , , cord-242132-fhepdgz9 9 6 the the DT cord-242132-fhepdgz9 9 7 infection infection NN cord-242132-fhepdgz9 9 8 transmits transmit VBZ cord-242132-fhepdgz9 9 9 due due IN cord-242132-fhepdgz9 9 10 to to IN cord-242132-fhepdgz9 9 11 contacts contact NNS cord-242132-fhepdgz9 9 12 of of IN cord-242132-fhepdgz9 9 13 randomly randomly RB cord-242132-fhepdgz9 9 14 moving move VBG cord-242132-fhepdgz9 9 15 individuals individual NNS cord-242132-fhepdgz9 9 16 . . . cord-242132-fhepdgz9 10 1 We -PRON- PRP cord-242132-fhepdgz9 10 2 show show VBP cord-242132-fhepdgz9 10 3 that that IN cord-242132-fhepdgz9 10 4 the the DT cord-242132-fhepdgz9 10 5 behavior behavior NN cord-242132-fhepdgz9 10 6 of of IN cord-242132-fhepdgz9 10 7 recovereds recovereds NNP cord-242132-fhepdgz9 10 8 critically critically RB cord-242132-fhepdgz9 10 9 depends depend VBZ cord-242132-fhepdgz9 10 10 on on IN cord-242132-fhepdgz9 10 11 the the DT cord-242132-fhepdgz9 10 12 $ $ $ cord-242132-fhepdgz9 10 13 beta$ beta$ NN cord-242132-fhepdgz9 10 14 value value NN cord-242132-fhepdgz9 10 15 . . . cord-242132-fhepdgz9 11 1 For for IN cord-242132-fhepdgz9 11 2 sub sub JJ cord-242132-fhepdgz9 11 3 - - JJ cord-242132-fhepdgz9 11 4 critical critical JJ cord-242132-fhepdgz9 11 5 values value NNS cord-242132-fhepdgz9 11 6 $ $ $ cord-242132-fhepdgz9 11 7 beta beta NN cord-242132-fhepdgz9 11 8 < < XX cord-242132-fhepdgz9 11 9 beta_{c}sim beta_{c}sim XX cord-242132-fhepdgz9 11 10 0.6 0.6 CD cord-242132-fhepdgz9 11 11 $ $ $ cord-242132-fhepdgz9 11 12 , , , cord-242132-fhepdgz9 11 13 the the DT cord-242132-fhepdgz9 11 14 number number NN cord-242132-fhepdgz9 11 15 of of IN cord-242132-fhepdgz9 11 16 infected infected JJ cord-242132-fhepdgz9 11 17 cases case NNS cord-242132-fhepdgz9 11 18 asymptotically asymptotically RB cord-242132-fhepdgz9 11 19 converges converge VBZ cord-242132-fhepdgz9 11 20 to to IN cord-242132-fhepdgz9 11 21 zero zero CD cord-242132-fhepdgz9 11 22 , , , cord-242132-fhepdgz9 11 23 such such JJ cord-242132-fhepdgz9 11 24 that that IN cord-242132-fhepdgz9 11 25 for for IN cord-242132-fhepdgz9 11 26 a a DT cord-242132-fhepdgz9 11 27 moderate moderate JJ cord-242132-fhepdgz9 11 28 risk risk NN cord-242132-fhepdgz9 11 29 factor factor NN cord-242132-fhepdgz9 11 30 the the DT cord-242132-fhepdgz9 11 31 infection infection NN cord-242132-fhepdgz9 11 32 may may MD cord-242132-fhepdgz9 11 33 disappear disappear VB cord-242132-fhepdgz9 11 34 with with IN cord-242132-fhepdgz9 11 35 time time NN cord-242132-fhepdgz9 11 36 . . . cord-242132-fhepdgz9 12 1 Our -PRON- PRP$ cord-242132-fhepdgz9 12 2 simulations simulation NNS cord-242132-fhepdgz9 12 3 shown show VBN cord-242132-fhepdgz9 12 4 that that IN cord-242132-fhepdgz9 12 5 over over IN cord-242132-fhepdgz9 12 6 time time NN cord-242132-fhepdgz9 12 7 , , , cord-242132-fhepdgz9 12 8 the the DT cord-242132-fhepdgz9 12 9 properties property NNS cord-242132-fhepdgz9 12 10 of of IN cord-242132-fhepdgz9 12 11 such such PDT cord-242132-fhepdgz9 12 12 a a DT cord-242132-fhepdgz9 12 13 system system NN cord-242132-fhepdgz9 12 14 asymptotically asymptotically RB cord-242132-fhepdgz9 12 15 become become VBP cord-242132-fhepdgz9 12 16 close close JJ cord-242132-fhepdgz9 12 17 to to IN cord-242132-fhepdgz9 12 18 the the DT cord-242132-fhepdgz9 12 19 critical critical JJ cord-242132-fhepdgz9 12 20 transition transition NN cord-242132-fhepdgz9 12 21 in in IN cord-242132-fhepdgz9 12 22 2D 2D NNP cord-242132-fhepdgz9 12 23 percolation percolation NN cord-242132-fhepdgz9 12 24 system system NN cord-242132-fhepdgz9 12 25 . . . cord-242132-fhepdgz9 13 1 We -PRON- PRP cord-242132-fhepdgz9 13 2 also also RB cord-242132-fhepdgz9 13 3 analyzed analyze VBD cord-242132-fhepdgz9 13 4 an an DT cord-242132-fhepdgz9 13 5 extended extended JJ cord-242132-fhepdgz9 13 6 system system NN cord-242132-fhepdgz9 13 7 , , , cord-242132-fhepdgz9 13 8 which which WDT cord-242132-fhepdgz9 13 9 includes include VBZ cord-242132-fhepdgz9 13 10 two two CD cord-242132-fhepdgz9 13 11 additional additional JJ cord-242132-fhepdgz9 13 12 parameters parameter NNS cord-242132-fhepdgz9 13 13 : : : cord-242132-fhepdgz9 13 14 the the DT cord-242132-fhepdgz9 13 15 limits limit NNS cord-242132-fhepdgz9 13 16 of of IN cord-242132-fhepdgz9 13 17 taking take VBG cord-242132-fhepdgz9 13 18 on on RP cord-242132-fhepdgz9 13 19 / / SYM cord-242132-fhepdgz9 13 20 off off IN cord-242132-fhepdgz9 13 21 quarantine quarantine NN cord-242132-fhepdgz9 13 22 state state NN cord-242132-fhepdgz9 13 23 . . . cord-242132-fhepdgz9 14 1 It -PRON- PRP cord-242132-fhepdgz9 14 2 is be VBZ cord-242132-fhepdgz9 14 3 found find VBN cord-242132-fhepdgz9 14 4 that that IN cord-242132-fhepdgz9 14 5 the the DT cord-242132-fhepdgz9 14 6 early early JJ cord-242132-fhepdgz9 14 7 quarantine quarantine NN cord-242132-fhepdgz9 14 8 off off RP cord-242132-fhepdgz9 14 9 does do VBZ cord-242132-fhepdgz9 14 10 result result VB cord-242132-fhepdgz9 14 11 in in IN cord-242132-fhepdgz9 14 12 the the DT cord-242132-fhepdgz9 14 13 irregular irregular JJ cord-242132-fhepdgz9 14 14 ( ( -LRB- cord-242132-fhepdgz9 14 15 with with IN cord-242132-fhepdgz9 14 16 positive positive JJ cord-242132-fhepdgz9 14 17 Lyapunov Lyapunov NNP cord-242132-fhepdgz9 14 18 exponent exponent NN cord-242132-fhepdgz9 14 19 ) ) -RRB- cord-242132-fhepdgz9 14 20 oscillatory oscillatory JJ cord-242132-fhepdgz9 14 21 dynamics dynamic NNS cord-242132-fhepdgz9 14 22 of of IN cord-242132-fhepdgz9 14 23 infection infection NN cord-242132-fhepdgz9 14 24 . . . cord-242132-fhepdgz9 15 1 If if IN cord-242132-fhepdgz9 15 2 the the DT cord-242132-fhepdgz9 15 3 lower low JJR cord-242132-fhepdgz9 15 4 limit limit NN cord-242132-fhepdgz9 15 5 of of IN cord-242132-fhepdgz9 15 6 the the DT cord-242132-fhepdgz9 15 7 quarantine quarantine NN cord-242132-fhepdgz9 15 8 off off RP cord-242132-fhepdgz9 15 9 is be VBZ cord-242132-fhepdgz9 15 10 small small JJ cord-242132-fhepdgz9 15 11 enough enough RB cord-242132-fhepdgz9 15 12 , , , cord-242132-fhepdgz9 15 13 the the DT cord-242132-fhepdgz9 15 14 recovery recovery NN cord-242132-fhepdgz9 15 15 dynamics dynamic NNS cord-242132-fhepdgz9 15 16 acquirers acquirer NNS cord-242132-fhepdgz9 15 17 a a DT cord-242132-fhepdgz9 15 18 characteristic characteristic JJ cord-242132-fhepdgz9 15 19 nonmonotonic nonmonotonic JJ cord-242132-fhepdgz9 15 20 shape shape NN cord-242132-fhepdgz9 15 21 with with IN cord-242132-fhepdgz9 15 22 several several JJ cord-242132-fhepdgz9 15 23 damped damp VBN cord-242132-fhepdgz9 15 24 peaks peak NNS cord-242132-fhepdgz9 15 25 . . . cord-242132-fhepdgz9 16 1 The the DT cord-242132-fhepdgz9 16 2 dynamics dynamic NNS cord-242132-fhepdgz9 16 3 of of IN cord-242132-fhepdgz9 16 4 infection infection NN cord-242132-fhepdgz9 16 5 spreading spread VBG cord-242132-fhepdgz9 16 6 in in IN cord-242132-fhepdgz9 16 7 case case NN cord-242132-fhepdgz9 16 8 of of IN cord-242132-fhepdgz9 16 9 the the DT cord-242132-fhepdgz9 16 10 individuals individual NNS cord-242132-fhepdgz9 16 11 with with IN cord-242132-fhepdgz9 16 12 immunity immunity NN cord-242132-fhepdgz9 16 13 is be VBZ cord-242132-fhepdgz9 16 14 studied study VBN cord-242132-fhepdgz9 16 15 too too RB cord-242132-fhepdgz9 16 16 . . . cord-242132-fhepdgz9 17 1 We -PRON- PRP cord-242132-fhepdgz9 17 2 study study VBP cord-242132-fhepdgz9 17 3 a a DT cord-242132-fhepdgz9 17 4 dynamics dynamic NNS cord-242132-fhepdgz9 17 5 of of IN cord-242132-fhepdgz9 17 6 the the DT cord-242132-fhepdgz9 17 7 epidemiological epidemiological JJ cord-242132-fhepdgz9 17 8 infection infection NN cord-242132-fhepdgz9 17 9 spreading spread VBG cord-242132-fhepdgz9 17 10 at at IN cord-242132-fhepdgz9 17 11 different different JJ cord-242132-fhepdgz9 17 12 values value NNS cord-242132-fhepdgz9 17 13 of of IN cord-242132-fhepdgz9 17 14 the the DT cord-242132-fhepdgz9 17 15 risk risk NN cord-242132-fhepdgz9 17 16 factor factor NN cord-242132-fhepdgz9 17 17 β β NNP cord-242132-fhepdgz9 17 18 ( ( -LRB- cord-242132-fhepdgz9 17 19 a a DT cord-242132-fhepdgz9 17 20 control control NN cord-242132-fhepdgz9 17 21 parameter parameter NN cord-242132-fhepdgz9 17 22 ) ) -RRB- cord-242132-fhepdgz9 17 23 with with IN cord-242132-fhepdgz9 17 24 the the DT cord-242132-fhepdgz9 17 25 using using NN cord-242132-fhepdgz9 17 26 of of IN cord-242132-fhepdgz9 17 27 dynamic dynamic JJ cord-242132-fhepdgz9 17 28 Monte Monte NNP cord-242132-fhepdgz9 17 29 Carlo Carlo NNP cord-242132-fhepdgz9 17 30 approach approach NN cord-242132-fhepdgz9 17 31 ( ( -LRB- cord-242132-fhepdgz9 17 32 DMC DMC NNP cord-242132-fhepdgz9 17 33 ) ) -RRB- cord-242132-fhepdgz9 17 34 . . . cord-242132-fhepdgz9 18 1 In in IN cord-242132-fhepdgz9 18 2 our -PRON- PRP$ cord-242132-fhepdgz9 18 3 toy toy NN cord-242132-fhepdgz9 18 4 model model NN cord-242132-fhepdgz9 18 5 , , , cord-242132-fhepdgz9 18 6 the the DT cord-242132-fhepdgz9 18 7 infection infection NN cord-242132-fhepdgz9 18 8 transmits transmit VBZ cord-242132-fhepdgz9 18 9 due due IN cord-242132-fhepdgz9 18 10 to to IN cord-242132-fhepdgz9 18 11 contacts contact NNS cord-242132-fhepdgz9 18 12 of of IN cord-242132-fhepdgz9 18 13 randomly randomly RB cord-242132-fhepdgz9 18 14 moving move VBG cord-242132-fhepdgz9 18 15 individuals individual NNS cord-242132-fhepdgz9 18 16 . . . cord-242132-fhepdgz9 19 1 We -PRON- PRP cord-242132-fhepdgz9 19 2 show show VBP cord-242132-fhepdgz9 19 3 that that IN cord-242132-fhepdgz9 19 4 the the DT cord-242132-fhepdgz9 19 5 behavior behavior NN cord-242132-fhepdgz9 19 6 of of IN cord-242132-fhepdgz9 19 7 recovereds recovereds NNP cord-242132-fhepdgz9 19 8 critically critically RB cord-242132-fhepdgz9 19 9 depends depend VBZ cord-242132-fhepdgz9 19 10 on on IN cord-242132-fhepdgz9 19 11 the the DT cord-242132-fhepdgz9 19 12 β β NN cord-242132-fhepdgz9 19 13 value value NN cord-242132-fhepdgz9 19 14 . . . cord-242132-fhepdgz9 20 1 For for IN cord-242132-fhepdgz9 20 2 sub sub JJ cord-242132-fhepdgz9 20 3 - - JJ cord-242132-fhepdgz9 20 4 critical critical JJ cord-242132-fhepdgz9 20 5 values value NNS cord-242132-fhepdgz9 20 6 β β XX cord-242132-fhepdgz9 20 7 < < XX cord-242132-fhepdgz9 20 8 β β XX cord-242132-fhepdgz9 20 9 c c NNP cord-242132-fhepdgz9 20 10 ∼ ∼ NNP cord-242132-fhepdgz9 20 11 0.6 0.6 CD cord-242132-fhepdgz9 20 12 , , , cord-242132-fhepdgz9 20 13 the the DT cord-242132-fhepdgz9 20 14 number number NN cord-242132-fhepdgz9 20 15 of of IN cord-242132-fhepdgz9 20 16 infected infected JJ cord-242132-fhepdgz9 20 17 cases case NNS cord-242132-fhepdgz9 20 18 asymptotically asymptotically RB cord-242132-fhepdgz9 20 19 converges converge VBZ cord-242132-fhepdgz9 20 20 to to IN cord-242132-fhepdgz9 20 21 zero zero CD cord-242132-fhepdgz9 20 22 , , , cord-242132-fhepdgz9 20 23 such such JJ cord-242132-fhepdgz9 20 24 that that IN cord-242132-fhepdgz9 20 25 for for IN cord-242132-fhepdgz9 20 26 a a DT cord-242132-fhepdgz9 20 27 moderate moderate JJ cord-242132-fhepdgz9 20 28 risk risk NN cord-242132-fhepdgz9 20 29 factor factor NN cord-242132-fhepdgz9 20 30 the the DT cord-242132-fhepdgz9 20 31 infection infection NN cord-242132-fhepdgz9 20 32 may may MD cord-242132-fhepdgz9 20 33 disappear disappear VB cord-242132-fhepdgz9 20 34 with with IN cord-242132-fhepdgz9 20 35 time time NN cord-242132-fhepdgz9 20 36 . . . cord-242132-fhepdgz9 21 1 Our -PRON- PRP$ cord-242132-fhepdgz9 21 2 simulations simulation NNS cord-242132-fhepdgz9 21 3 shown show VBN cord-242132-fhepdgz9 21 4 that that IN cord-242132-fhepdgz9 21 5 over over IN cord-242132-fhepdgz9 21 6 time time NN cord-242132-fhepdgz9 21 7 , , , cord-242132-fhepdgz9 21 8 the the DT cord-242132-fhepdgz9 21 9 properties property NNS cord-242132-fhepdgz9 21 10 of of IN cord-242132-fhepdgz9 21 11 such such PDT cord-242132-fhepdgz9 21 12 a a DT cord-242132-fhepdgz9 21 13 system system NN cord-242132-fhepdgz9 21 14 asymptotically asymptotically RB cord-242132-fhepdgz9 21 15 become become VBP cord-242132-fhepdgz9 21 16 close close JJ cord-242132-fhepdgz9 21 17 to to IN cord-242132-fhepdgz9 21 18 the the DT cord-242132-fhepdgz9 21 19 critical critical JJ cord-242132-fhepdgz9 21 20 transition transition NN cord-242132-fhepdgz9 21 21 in in IN cord-242132-fhepdgz9 21 22 2D 2D NNP cord-242132-fhepdgz9 21 23 percolation percolation NN cord-242132-fhepdgz9 21 24 system system NN cord-242132-fhepdgz9 21 25 . . . cord-242132-fhepdgz9 22 1 We -PRON- PRP cord-242132-fhepdgz9 22 2 also also RB cord-242132-fhepdgz9 22 3 analyzed analyze VBD cord-242132-fhepdgz9 22 4 an an DT cord-242132-fhepdgz9 22 5 extended extended JJ cord-242132-fhepdgz9 22 6 system system NN cord-242132-fhepdgz9 22 7 , , , cord-242132-fhepdgz9 22 8 which which WDT cord-242132-fhepdgz9 22 9 includes include VBZ cord-242132-fhepdgz9 22 10 two two CD cord-242132-fhepdgz9 22 11 additional additional JJ cord-242132-fhepdgz9 22 12 parameters parameter NNS cord-242132-fhepdgz9 22 13 : : : cord-242132-fhepdgz9 22 14 the the DT cord-242132-fhepdgz9 22 15 limits limit NNS cord-242132-fhepdgz9 22 16 of of IN cord-242132-fhepdgz9 22 17 taking take VBG cord-242132-fhepdgz9 22 18 on on RP cord-242132-fhepdgz9 22 19 / / SYM cord-242132-fhepdgz9 22 20 off off IN cord-242132-fhepdgz9 22 21 quarantine quarantine NN cord-242132-fhepdgz9 22 22 state state NN cord-242132-fhepdgz9 22 23 . . . cord-242132-fhepdgz9 23 1 It -PRON- PRP cord-242132-fhepdgz9 23 2 is be VBZ cord-242132-fhepdgz9 23 3 found find VBN cord-242132-fhepdgz9 23 4 that that IN cord-242132-fhepdgz9 23 5 the the DT cord-242132-fhepdgz9 23 6 early early JJ cord-242132-fhepdgz9 23 7 quarantine quarantine NN cord-242132-fhepdgz9 23 8 off off RP cord-242132-fhepdgz9 23 9 does do VBZ cord-242132-fhepdgz9 23 10 result result VB cord-242132-fhepdgz9 23 11 in in IN cord-242132-fhepdgz9 23 12 the the DT cord-242132-fhepdgz9 23 13 irregular irregular JJ cord-242132-fhepdgz9 23 14 ( ( -LRB- cord-242132-fhepdgz9 23 15 with with IN cord-242132-fhepdgz9 23 16 positive positive JJ cord-242132-fhepdgz9 23 17 Lyapunov Lyapunov NNP cord-242132-fhepdgz9 23 18 exponent exponent NN cord-242132-fhepdgz9 23 19 ) ) -RRB- cord-242132-fhepdgz9 23 20 oscillatory oscillatory JJ cord-242132-fhepdgz9 23 21 dynamics dynamic NNS cord-242132-fhepdgz9 23 22 of of IN cord-242132-fhepdgz9 23 23 infection infection NN cord-242132-fhepdgz9 23 24 . . . cord-242132-fhepdgz9 24 1 If if IN cord-242132-fhepdgz9 24 2 the the DT cord-242132-fhepdgz9 24 3 lower low JJR cord-242132-fhepdgz9 24 4 limit limit NN cord-242132-fhepdgz9 24 5 of of IN cord-242132-fhepdgz9 24 6 the the DT cord-242132-fhepdgz9 24 7 quarantine quarantine NN cord-242132-fhepdgz9 24 8 off off RP cord-242132-fhepdgz9 24 9 is be VBZ cord-242132-fhepdgz9 24 10 small small JJ cord-242132-fhepdgz9 24 11 enough enough RB cord-242132-fhepdgz9 24 12 , , , cord-242132-fhepdgz9 24 13 the the DT cord-242132-fhepdgz9 24 14 recovery recovery NN cord-242132-fhepdgz9 24 15 dynamics dynamic NNS cord-242132-fhepdgz9 24 16 acquirers acquirer NNS cord-242132-fhepdgz9 24 17 a a DT cord-242132-fhepdgz9 24 18 characteristic characteristic JJ cord-242132-fhepdgz9 24 19 nonmonotonic nonmonotonic JJ cord-242132-fhepdgz9 24 20 shape shape NN cord-242132-fhepdgz9 24 21 with with IN cord-242132-fhepdgz9 24 22 several several JJ cord-242132-fhepdgz9 24 23 damped damp VBN cord-242132-fhepdgz9 24 24 peaks peak NNS cord-242132-fhepdgz9 24 25 . . . cord-242132-fhepdgz9 25 1 The the DT cord-242132-fhepdgz9 25 2 dynamics dynamic NNS cord-242132-fhepdgz9 25 3 of of IN cord-242132-fhepdgz9 25 4 infection infection NN cord-242132-fhepdgz9 25 5 spreading spread VBG cord-242132-fhepdgz9 25 6 in in IN cord-242132-fhepdgz9 25 7 case case NN cord-242132-fhepdgz9 25 8 of of IN cord-242132-fhepdgz9 25 9 the the DT cord-242132-fhepdgz9 25 10 individuals individual NNS cord-242132-fhepdgz9 25 11 with with IN cord-242132-fhepdgz9 25 12 immunity immunity NN cord-242132-fhepdgz9 25 13 is be VBZ cord-242132-fhepdgz9 25 14 studied study VBN cord-242132-fhepdgz9 25 15 too too RB cord-242132-fhepdgz9 25 16 . . . cord-242132-fhepdgz9 26 1 The the DT cord-242132-fhepdgz9 26 2 dangerous dangerous JJ cord-242132-fhepdgz9 26 3 trends trend NNS cord-242132-fhepdgz9 26 4 of of IN cord-242132-fhepdgz9 26 5 the the DT cord-242132-fhepdgz9 26 6 coronavirus coronavirus NN cord-242132-fhepdgz9 26 7 spreading spread VBG cord-242132-fhepdgz9 26 8 throughout throughout IN cord-242132-fhepdgz9 26 9 the the DT cord-242132-fhepdgz9 26 10 world world NN cord-242132-fhepdgz9 26 11 gives give VBZ cord-242132-fhepdgz9 26 12 rise rise NN cord-242132-fhepdgz9 26 13 to to IN cord-242132-fhepdgz9 26 14 numerous numerous JJ cord-242132-fhepdgz9 26 15 investigations investigation NNS cord-242132-fhepdgz9 26 16 in in IN cord-242132-fhepdgz9 26 17 wide wide JJ cord-242132-fhepdgz9 26 18 scientific scientific JJ cord-242132-fhepdgz9 26 19 spectrum spectrum NN cord-242132-fhepdgz9 26 20 . . . cord-242132-fhepdgz9 27 1 We -PRON- PRP cord-242132-fhepdgz9 27 2 study study VBP cord-242132-fhepdgz9 27 3 the the DT cord-242132-fhepdgz9 27 4 spread spread NN cord-242132-fhepdgz9 27 5 of of IN cord-242132-fhepdgz9 27 6 epidemiological epidemiological JJ cord-242132-fhepdgz9 27 7 infection infection NN cord-242132-fhepdgz9 27 8 at at IN cord-242132-fhepdgz9 27 9 different different JJ cord-242132-fhepdgz9 27 10 values value NNS cord-242132-fhepdgz9 27 11 of of IN cord-242132-fhepdgz9 27 12 the the DT cord-242132-fhepdgz9 27 13 risk risk NN cord-242132-fhepdgz9 27 14 factors factor NNS cord-242132-fhepdgz9 27 15 beta beta VBP cord-242132-fhepdgz9 27 16 with with IN cord-242132-fhepdgz9 27 17 the the DT cord-242132-fhepdgz9 27 18 use use NN cord-242132-fhepdgz9 27 19 of of IN cord-242132-fhepdgz9 27 20 the the DT cord-242132-fhepdgz9 27 21 dynamic dynamic JJ cord-242132-fhepdgz9 27 22 Monte Monte NNP cord-242132-fhepdgz9 27 23 Carlo Carlo NNP cord-242132-fhepdgz9 27 24 ( ( -LRB- cord-242132-fhepdgz9 27 25 DMC DMC NNP cord-242132-fhepdgz9 27 26 ) ) -RRB- cord-242132-fhepdgz9 27 27 method method NN cord-242132-fhepdgz9 27 28 . . . cord-242132-fhepdgz9 28 1 In in IN cord-242132-fhepdgz9 28 2 such such PDT cord-242132-fhepdgz9 28 3 a a DT cord-242132-fhepdgz9 28 4 model model NN cord-242132-fhepdgz9 28 5 , , , cord-242132-fhepdgz9 28 6 it -PRON- PRP cord-242132-fhepdgz9 28 7 is be VBZ cord-242132-fhepdgz9 28 8 accepted accept VBN cord-242132-fhepdgz9 28 9 that that IN cord-242132-fhepdgz9 28 10 the the DT cord-242132-fhepdgz9 28 11 infection infection NN cord-242132-fhepdgz9 28 12 is be VBZ cord-242132-fhepdgz9 28 13 transmitted transmit VBN cord-242132-fhepdgz9 28 14 through through IN cord-242132-fhepdgz9 28 15 the the DT cord-242132-fhepdgz9 28 16 contacts contact NNS cord-242132-fhepdgz9 28 17 of of IN cord-242132-fhepdgz9 28 18 randomly randomly RB cord-242132-fhepdgz9 28 19 moving move VBG cord-242132-fhepdgz9 28 20 individuals individual NNS cord-242132-fhepdgz9 28 21 . . . cord-242132-fhepdgz9 29 1 We -PRON- PRP cord-242132-fhepdgz9 29 2 show show VBP cord-242132-fhepdgz9 29 3 that that IN cord-242132-fhepdgz9 29 4 the the DT cord-242132-fhepdgz9 29 5 quantity quantity NN cord-242132-fhepdgz9 29 6 of of IN cord-242132-fhepdgz9 29 7 recovered recover VBN cord-242132-fhepdgz9 29 8 critically critically RB cord-242132-fhepdgz9 29 9 dependent dependent JJ cord-242132-fhepdgz9 29 10 on on IN cord-242132-fhepdgz9 29 11 the the DT cord-242132-fhepdgz9 29 12 value value NN cord-242132-fhepdgz9 29 13 β β NN cord-242132-fhepdgz9 29 14 . . . cord-242132-fhepdgz9 30 1 It -PRON- PRP cord-242132-fhepdgz9 30 2 is be VBZ cord-242132-fhepdgz9 30 3 remarkably remarkably RB cord-242132-fhepdgz9 30 4 that that IN cord-242132-fhepdgz9 30 5 for for IN cord-242132-fhepdgz9 30 6 sub sub JJ cord-242132-fhepdgz9 30 7 - - JJ cord-242132-fhepdgz9 30 8 critical critical JJ cord-242132-fhepdgz9 30 9 values value NNS cord-242132-fhepdgz9 30 10 β β XX cord-242132-fhepdgz9 30 11 < < XX cord-242132-fhepdgz9 30 12 β β XX cord-242132-fhepdgz9 30 13 c c NN cord-242132-fhepdgz9 30 14 ∼ ∼ NNP cord-242132-fhepdgz9 30 15 0.6 0.6 CD cord-242132-fhepdgz9 30 16 the the DT cord-242132-fhepdgz9 30 17 number number NN cord-242132-fhepdgz9 30 18 of of IN cord-242132-fhepdgz9 30 19 infected infected JJ cord-242132-fhepdgz9 30 20 cases case NNS cord-242132-fhepdgz9 30 21 asymptotically asymptotically RB cord-242132-fhepdgz9 30 22 converges converge VBZ cord-242132-fhepdgz9 30 23 to to IN cord-242132-fhepdgz9 30 24 zero zero CD cord-242132-fhepdgz9 30 25 , , , cord-242132-fhepdgz9 30 26 so so IN cord-242132-fhepdgz9 30 27 that that IN cord-242132-fhepdgz9 30 28 for for IN cord-242132-fhepdgz9 30 29 a a DT cord-242132-fhepdgz9 30 30 moderate moderate JJ cord-242132-fhepdgz9 30 31 risk risk NN cord-242132-fhepdgz9 30 32 factor factor NN cord-242132-fhepdgz9 30 33 , , , cord-242132-fhepdgz9 30 34 the the DT cord-242132-fhepdgz9 30 35 infection infection NN cord-242132-fhepdgz9 30 36 can can MD cord-242132-fhepdgz9 30 37 quickly quickly RB cord-242132-fhepdgz9 30 38 disappear disappear VB cord-242132-fhepdgz9 30 39 . . . cord-242132-fhepdgz9 31 1 Our -PRON- PRP$ cord-242132-fhepdgz9 31 2 calculations calculation NNS cord-242132-fhepdgz9 31 3 showed show VBD cord-242132-fhepdgz9 31 4 that that IN cord-242132-fhepdgz9 31 5 such such PDT cord-242132-fhepdgz9 31 6 a a DT cord-242132-fhepdgz9 31 7 dynamic dynamic JJ cord-242132-fhepdgz9 31 8 property property NN cord-242132-fhepdgz9 31 9 of of IN cord-242132-fhepdgz9 31 10 the the DT cord-242132-fhepdgz9 31 11 system system NN cord-242132-fhepdgz9 31 12 ( ( -LRB- cord-242132-fhepdgz9 31 13 asymptotically asymptotically RB cord-242132-fhepdgz9 31 14 ) ) -RRB- cord-242132-fhepdgz9 31 15 is be VBZ cord-242132-fhepdgz9 31 16 associated associate VBN cord-242132-fhepdgz9 31 17 with with IN cord-242132-fhepdgz9 31 18 the the DT cord-242132-fhepdgz9 31 19 critical critical JJ cord-242132-fhepdgz9 31 20 behavior behavior NN cord-242132-fhepdgz9 31 21 in in IN cord-242132-fhepdgz9 31 22 2D 2D NNP cord-242132-fhepdgz9 31 23 percolation percolation NN cord-242132-fhepdgz9 31 24 medium medium NN cord-242132-fhepdgz9 31 25 . . . cord-242132-fhepdgz9 32 1 We -PRON- PRP cord-242132-fhepdgz9 32 2 also also RB cord-242132-fhepdgz9 32 3 analyze analyze VBP cord-242132-fhepdgz9 32 4 an an DT cord-242132-fhepdgz9 32 5 extended extended JJ cord-242132-fhepdgz9 32 6 system system NN cord-242132-fhepdgz9 32 7 , , , cord-242132-fhepdgz9 32 8 which which WDT cord-242132-fhepdgz9 32 9 is be VBZ cord-242132-fhepdgz9 32 10 currently currently RB cord-242132-fhepdgz9 32 11 widely widely RB cord-242132-fhepdgz9 32 12 used use VBN cord-242132-fhepdgz9 32 13 to to TO cord-242132-fhepdgz9 32 14 prevent prevent VB cord-242132-fhepdgz9 32 15 the the DT cord-242132-fhepdgz9 32 16 spread spread NN cord-242132-fhepdgz9 32 17 of of IN cord-242132-fhepdgz9 32 18 the the DT cord-242132-fhepdgz9 32 19 virus virus NN cord-242132-fhepdgz9 32 20 and and CC cord-242132-fhepdgz9 32 21 includes include VBZ cord-242132-fhepdgz9 32 22 quarantine quarantine NN cord-242132-fhepdgz9 32 23 on on IN cord-242132-fhepdgz9 32 24 / / SYM cord-242132-fhepdgz9 32 25 off off IN cord-242132-fhepdgz9 32 26 settings setting NNS cord-242132-fhepdgz9 32 27 . . . cord-242132-fhepdgz9 33 1 It -PRON- PRP cord-242132-fhepdgz9 33 2 was be VBD cord-242132-fhepdgz9 33 3 revealed reveal VBN cord-242132-fhepdgz9 33 4 that that IN cord-242132-fhepdgz9 33 5 early early JJ cord-242132-fhepdgz9 33 6 exit exit NN cord-242132-fhepdgz9 33 7 from from IN cord-242132-fhepdgz9 33 8 the the DT cord-242132-fhepdgz9 33 9 quarantine quarantine NN cord-242132-fhepdgz9 33 10 state state NN cord-242132-fhepdgz9 33 11 leads lead VBZ cord-242132-fhepdgz9 33 12 to to IN cord-242132-fhepdgz9 33 13 irregular irregular JJ cord-242132-fhepdgz9 33 14 oscillatory oscillatory JJ cord-242132-fhepdgz9 33 15 dynamics dynamic NNS cord-242132-fhepdgz9 33 16 of of IN cord-242132-fhepdgz9 33 17 infection infection NN cord-242132-fhepdgz9 33 18 . . . cord-242132-fhepdgz9 34 1 However however RB cord-242132-fhepdgz9 34 2 , , , cord-242132-fhepdgz9 34 3 when when WRB cord-242132-fhepdgz9 34 4 the the DT cord-242132-fhepdgz9 34 5 lower low JJR cord-242132-fhepdgz9 34 6 limit limit NN cord-242132-fhepdgz9 34 7 of of IN cord-242132-fhepdgz9 34 8 quarantine quarantine NN cord-242132-fhepdgz9 34 9 off off RP cord-242132-fhepdgz9 34 10 is be VBZ cord-242132-fhepdgz9 34 11 small small JJ cord-242132-fhepdgz9 34 12 enough enough RB cord-242132-fhepdgz9 34 13 , , , cord-242132-fhepdgz9 34 14 the the DT cord-242132-fhepdgz9 34 15 dynamics dynamic NNS cord-242132-fhepdgz9 34 16 of of IN cord-242132-fhepdgz9 34 17 infection infection NN cord-242132-fhepdgz9 34 18 acquires acquire VBZ cord-242132-fhepdgz9 34 19 a a DT cord-242132-fhepdgz9 34 20 characteristic characteristic JJ cord-242132-fhepdgz9 34 21 non non JJ cord-242132-fhepdgz9 34 22 - - JJ cord-242132-fhepdgz9 34 23 monotonic monotonic JJ cord-242132-fhepdgz9 34 24 shape shape NN cord-242132-fhepdgz9 34 25 with with IN cord-242132-fhepdgz9 34 26 several several JJ cord-242132-fhepdgz9 34 27 damped damp VBN cord-242132-fhepdgz9 34 28 peaks peak NNS cord-242132-fhepdgz9 34 29 . . . cord-242132-fhepdgz9 35 1 Comparison comparison NN cord-242132-fhepdgz9 35 2 of of IN cord-242132-fhepdgz9 35 3 quarantine quarantine NN cord-242132-fhepdgz9 35 4 and and CC cord-242132-fhepdgz9 35 5 immunity immunity NN cord-242132-fhepdgz9 35 6 factors factor NNS cord-242132-fhepdgz9 35 7 shows show VBZ cord-242132-fhepdgz9 35 8 that that IN cord-242132-fhepdgz9 35 9 in in IN cord-242132-fhepdgz9 35 10 the the DT cord-242132-fhepdgz9 35 11 case case NN cord-242132-fhepdgz9 35 12 of of IN cord-242132-fhepdgz9 35 13 immunity immunity NN cord-242132-fhepdgz9 35 14 , , , cord-242132-fhepdgz9 35 15 the the DT cord-242132-fhepdgz9 35 16 complete complete JJ cord-242132-fhepdgz9 35 17 recovery recovery NN cord-242132-fhepdgz9 35 18 occurs occur VBZ cord-242132-fhepdgz9 35 19 faster fast RBR cord-242132-fhepdgz9 35 20 than than IN cord-242132-fhepdgz9 35 21 in in IN cord-242132-fhepdgz9 35 22 a a DT cord-242132-fhepdgz9 35 23 quarantine quarantine NN cord-242132-fhepdgz9 35 24 mode mode NN cord-242132-fhepdgz9 35 25 . . . cord-242132-fhepdgz9 36 1 The the DT cord-242132-fhepdgz9 36 2 dangerous dangerous JJ cord-242132-fhepdgz9 36 3 dynamics dynamic NNS cord-242132-fhepdgz9 36 4 of of IN cord-242132-fhepdgz9 36 5 the the DT cord-242132-fhepdgz9 36 6 coronavirus coronavirus NN cord-242132-fhepdgz9 36 7 spread spread VBD cord-242132-fhepdgz9 36 8 throughout throughout IN cord-242132-fhepdgz9 36 9 the the DT cord-242132-fhepdgz9 36 10 world world NN cord-242132-fhepdgz9 36 11 gives give VBZ cord-242132-fhepdgz9 36 12 rise rise NN cord-242132-fhepdgz9 36 13 to to IN cord-242132-fhepdgz9 36 14 numerous numerous JJ cord-242132-fhepdgz9 36 15 studies study NNS cord-242132-fhepdgz9 36 16 in in IN cord-242132-fhepdgz9 36 17 a a DT cord-242132-fhepdgz9 36 18 wide wide JJ cord-242132-fhepdgz9 36 19 scientific scientific JJ cord-242132-fhepdgz9 36 20 spectrum spectrum NN cord-242132-fhepdgz9 36 21 . . . cord-242132-fhepdgz9 37 1 Improving improve VBG cord-242132-fhepdgz9 37 2 known know VBN cord-242132-fhepdgz9 37 3 epidemic epidemic NN cord-242132-fhepdgz9 37 4 models model NNS cord-242132-fhepdgz9 37 5 and and CC cord-242132-fhepdgz9 37 6 developing develop VBG cord-242132-fhepdgz9 37 7 new new JJ cord-242132-fhepdgz9 37 8 models model NNS cord-242132-fhepdgz9 37 9 are be VBP cord-242132-fhepdgz9 37 10 complicated complicated JJ cord-242132-fhepdgz9 37 11 tasks task NNS cord-242132-fhepdgz9 37 12 because because IN cord-242132-fhepdgz9 37 13 the the DT cord-242132-fhepdgz9 37 14 lack lack NN cord-242132-fhepdgz9 37 15 of of IN cord-242132-fhepdgz9 37 16 verified verify VBN cord-242132-fhepdgz9 37 17 statistics statistic NNS cord-242132-fhepdgz9 37 18 on on IN cord-242132-fhepdgz9 37 19 the the DT cord-242132-fhepdgz9 37 20 infection infection NN cord-242132-fhepdgz9 37 21 spread spread NN cord-242132-fhepdgz9 37 22 and and CC cord-242132-fhepdgz9 37 23 disease disease NN cord-242132-fhepdgz9 37 24 dynamics dynamic NNS cord-242132-fhepdgz9 37 25 . . . cord-242132-fhepdgz9 38 1 Unstable unstable JJ cord-242132-fhepdgz9 38 2 predictability predictability NN cord-242132-fhepdgz9 38 3 of of IN cord-242132-fhepdgz9 38 4 infection infection NN cord-242132-fhepdgz9 38 5 , , , cord-242132-fhepdgz9 38 6 ambiguity ambiguity NN cord-242132-fhepdgz9 38 7 with with IN cord-242132-fhepdgz9 38 8 drugs drug NNS cord-242132-fhepdgz9 38 9 1 1 CD cord-242132-fhepdgz9 38 10 , , , cord-242132-fhepdgz9 38 11 uncertainty uncertainty NN cord-242132-fhepdgz9 38 12 regarding regard VBG cord-242132-fhepdgz9 38 13 the the DT cord-242132-fhepdgz9 38 14 immunity immunity NN cord-242132-fhepdgz9 38 15 of of IN cord-242132-fhepdgz9 38 16 disease disease NN cord-242132-fhepdgz9 38 17 2 2 CD cord-242132-fhepdgz9 38 18 , , , cord-242132-fhepdgz9 38 19 and and CC cord-242132-fhepdgz9 38 20 other other JJ cord-242132-fhepdgz9 38 21 factors factor NNS cord-242132-fhepdgz9 38 22 ( ( -LRB- cord-242132-fhepdgz9 38 23 such such JJ cord-242132-fhepdgz9 38 24 as as IN cord-242132-fhepdgz9 38 25 a a DT cord-242132-fhepdgz9 38 26 viral viral JJ cord-242132-fhepdgz9 38 27 mutation mutation NN cord-242132-fhepdgz9 38 28 ) ) -RRB- cord-242132-fhepdgz9 38 29 make make VB cord-242132-fhepdgz9 38 30 it -PRON- PRP cord-242132-fhepdgz9 38 31 difficult difficult JJ cord-242132-fhepdgz9 38 32 to to TO cord-242132-fhepdgz9 38 33 predict predict VB cord-242132-fhepdgz9 38 34 the the DT cord-242132-fhepdgz9 38 35 dynamics dynamic NNS cord-242132-fhepdgz9 38 36 of of IN cord-242132-fhepdgz9 38 37 pandemic pandemic NN cord-242132-fhepdgz9 38 38 . . . cord-242132-fhepdgz9 39 1 This this DT cord-242132-fhepdgz9 39 2 may may MD cord-242132-fhepdgz9 39 3 relay relay VB cord-242132-fhepdgz9 39 4 to to IN cord-242132-fhepdgz9 39 5 some some DT cord-242132-fhepdgz9 39 6 mathematical mathematical JJ cord-242132-fhepdgz9 39 7 models model NNS cord-242132-fhepdgz9 39 8 , , , cord-242132-fhepdgz9 39 9 which which WDT cord-242132-fhepdgz9 39 10 depend depend VBP cord-242132-fhepdgz9 39 11 on on IN cord-242132-fhepdgz9 39 12 a a DT cord-242132-fhepdgz9 39 13 significant significant JJ cord-242132-fhepdgz9 39 14 number number NN cord-242132-fhepdgz9 39 15 of of IN cord-242132-fhepdgz9 39 16 free free JJ cord-242132-fhepdgz9 39 17 ( ( -LRB- cord-242132-fhepdgz9 39 18 statistically statistically RB cord-242132-fhepdgz9 39 19 - - HYPH cord-242132-fhepdgz9 39 20 driven drive VBN cord-242132-fhepdgz9 39 21 ) ) -RRB- cord-242132-fhepdgz9 39 22 parameters parameter NNS cord-242132-fhepdgz9 39 23 . . . cord-242132-fhepdgz9 40 1 The the DT cord-242132-fhepdgz9 40 2 known know VBN cord-242132-fhepdgz9 40 3 models model NNS cord-242132-fhepdgz9 40 4 of of IN cord-242132-fhepdgz9 40 5 the the DT cord-242132-fhepdgz9 40 6 SIR SIR NNP cord-242132-fhepdgz9 40 7 family family NN cord-242132-fhepdgz9 40 8 give give VB cord-242132-fhepdgz9 40 9 solutions solution NNS cord-242132-fhepdgz9 40 10 in in IN cord-242132-fhepdgz9 40 11 a a DT cord-242132-fhepdgz9 40 12 form form NN cord-242132-fhepdgz9 40 13 of of IN cord-242132-fhepdgz9 40 14 smooth smooth JJ cord-242132-fhepdgz9 40 15 functions function NNS cord-242132-fhepdgz9 40 16 3 3 CD cord-242132-fhepdgz9 40 17 ( ( -LRB- cord-242132-fhepdgz9 40 18 solutions solution NNS cord-242132-fhepdgz9 40 19 of of IN cord-242132-fhepdgz9 40 20 differential differential JJ cord-242132-fhepdgz9 40 21 equations equation NNS cord-242132-fhepdgz9 40 22 ) ) -RRB- cord-242132-fhepdgz9 40 23 that that IN cord-242132-fhepdgz9 40 24 only only RB cord-242132-fhepdgz9 40 25 indirectly indirectly RB cord-242132-fhepdgz9 40 26 include include VBP cord-242132-fhepdgz9 40 27 important important JJ cord-242132-fhepdgz9 40 28 random random JJ cord-242132-fhepdgz9 40 29 factors factor NNS cord-242132-fhepdgz9 40 30 . . . cord-242132-fhepdgz9 41 1 Naturally naturally RB cord-242132-fhepdgz9 41 2 , , , cord-242132-fhepdgz9 41 3 that that IN cord-242132-fhepdgz9 41 4 in in IN cord-242132-fhepdgz9 41 5 such such PDT cord-242132-fhepdgz9 41 6 a a DT cord-242132-fhepdgz9 41 7 situation situation NN cord-242132-fhepdgz9 41 8 , , , cord-242132-fhepdgz9 41 9 most most RBS cord-242132-fhepdgz9 41 10 statistically statistically RB cord-242132-fhepdgz9 41 11 reliable reliable JJ cord-242132-fhepdgz9 41 12 forecasts forecast NNS cord-242132-fhepdgz9 41 13 are be VBP cord-242132-fhepdgz9 41 14 obtained obtain VBN cord-242132-fhepdgz9 41 15 by by IN cord-242132-fhepdgz9 41 16 methods method NNS cord-242132-fhepdgz9 41 17 based base VBN cord-242132-fhepdgz9 41 18 on on IN cord-242132-fhepdgz9 41 19 the the DT cord-242132-fhepdgz9 41 20 direct direct JJ cord-242132-fhepdgz9 41 21 application application NN cord-242132-fhepdgz9 41 22 of of IN cord-242132-fhepdgz9 41 23 the the DT cord-242132-fhepdgz9 41 24 central central JJ cord-242132-fhepdgz9 41 25 limit limit NN cord-242132-fhepdgz9 41 26 theorem theorem NN cord-242132-fhepdgz9 41 27 with with IN cord-242132-fhepdgz9 41 28 a a DT cord-242132-fhepdgz9 41 29 predicted predict VBN cord-242132-fhepdgz9 41 30 error error NN cord-242132-fhepdgz9 41 31 of of IN cord-242132-fhepdgz9 41 32 1/ 1/ CD cord-242132-fhepdgz9 41 33 √ √ NNP cord-242132-fhepdgz9 41 34 N N NNP cord-242132-fhepdgz9 41 35 , , , cord-242132-fhepdgz9 41 36 see see VBP cord-242132-fhepdgz9 41 37 4 4 CD cord-242132-fhepdgz9 41 38 , , , cord-242132-fhepdgz9 41 39 5 5 CD cord-242132-fhepdgz9 41 40 , , , cord-242132-fhepdgz9 41 41 6 6 CD cord-242132-fhepdgz9 41 42 and and CC cord-242132-fhepdgz9 41 43 references reference NNS cord-242132-fhepdgz9 41 44 therein therein RB cord-242132-fhepdgz9 41 45 . . . cord-242132-fhepdgz9 42 1 In in IN cord-242132-fhepdgz9 42 2 this this DT cord-242132-fhepdgz9 42 3 paper paper NN cord-242132-fhepdgz9 42 4 , , , cord-242132-fhepdgz9 42 5 we -PRON- PRP cord-242132-fhepdgz9 42 6 propose propose VBP cord-242132-fhepdgz9 42 7 the the DT cord-242132-fhepdgz9 42 8 use use NN cord-242132-fhepdgz9 42 9 of of IN cord-242132-fhepdgz9 42 10 the the DT cord-242132-fhepdgz9 42 11 dynamic dynamic JJ cord-242132-fhepdgz9 42 12 Monte Monte NNP cord-242132-fhepdgz9 42 13 Carlo Carlo NNP cord-242132-fhepdgz9 42 14 ( ( -LRB- cord-242132-fhepdgz9 42 15 DMC DMC NNP cord-242132-fhepdgz9 42 16 ) ) -RRB- cord-242132-fhepdgz9 42 17 method method NN cord-242132-fhepdgz9 42 18 that that WDT cord-242132-fhepdgz9 42 19 self self NN cord-242132-fhepdgz9 42 20 - - : cord-242132-fhepdgz9 42 21 consistently consistently RB cord-242132-fhepdgz9 42 22 includes include VBZ cord-242132-fhepdgz9 42 23 various various JJ cord-242132-fhepdgz9 42 24 dynamic dynamic JJ cord-242132-fhepdgz9 42 25 random random JJ cord-242132-fhepdgz9 42 26 factors factor NNS cord-242132-fhepdgz9 42 27 . . . cord-242132-fhepdgz9 43 1 Such such JJ cord-242132-fhepdgz9 43 2 a a DT cord-242132-fhepdgz9 43 3 technique technique NN cord-242132-fhepdgz9 43 4 was be VBD cord-242132-fhepdgz9 43 5 previously previously RB cord-242132-fhepdgz9 43 6 used use VBN cord-242132-fhepdgz9 43 7 to to TO cord-242132-fhepdgz9 43 8 study study VB cord-242132-fhepdgz9 43 9 the the DT cord-242132-fhepdgz9 43 10 processes process NNS cord-242132-fhepdgz9 43 11 associated associate VBN cord-242132-fhepdgz9 43 12 with with IN cord-242132-fhepdgz9 43 13 aggregation aggregation NN cord-242132-fhepdgz9 43 14 , , , cord-242132-fhepdgz9 43 15 viscous viscous JJ cord-242132-fhepdgz9 43 16 flow flow NN cord-242132-fhepdgz9 43 17 properties property NNS cord-242132-fhepdgz9 43 18 , , , cord-242132-fhepdgz9 43 19 the the DT cord-242132-fhepdgz9 43 20 formation formation NN cord-242132-fhepdgz9 43 21 of of IN cord-242132-fhepdgz9 43 22 biological biological JJ cord-242132-fhepdgz9 43 23 structures structure NNS cord-242132-fhepdgz9 43 24 , , , cord-242132-fhepdgz9 43 25 and and CC cord-242132-fhepdgz9 43 26 allows allow VBZ cord-242132-fhepdgz9 43 27 to to TO cord-242132-fhepdgz9 43 28 scale scale VB cord-242132-fhepdgz9 43 29 the the DT cord-242132-fhepdgz9 43 30 associated associate VBN cord-242132-fhepdgz9 43 31 geometric geometric JJ cord-242132-fhepdgz9 43 32 and and CC cord-242132-fhepdgz9 43 33 dynamic dynamic JJ cord-242132-fhepdgz9 43 34 quantities quantity NNS cord-242132-fhepdgz9 43 35 that that WDT cord-242132-fhepdgz9 43 36 characterize characterize VBP cord-242132-fhepdgz9 43 37 these these DT cord-242132-fhepdgz9 43 38 phenomena phenomena JJ cord-242132-fhepdgz9 43 39 7 7 CD cord-242132-fhepdgz9 43 40 , , , cord-242132-fhepdgz9 43 41 8 8 CD cord-242132-fhepdgz9 43 42 , , , cord-242132-fhepdgz9 43 43 9 9 CD cord-242132-fhepdgz9 43 44 . . . cord-242132-fhepdgz9 44 1 In in IN cord-242132-fhepdgz9 44 2 our -PRON- PRP$ cord-242132-fhepdgz9 44 3 study study NN cord-242132-fhepdgz9 44 4 , , , cord-242132-fhepdgz9 44 5 as as IN cord-242132-fhepdgz9 44 6 a a DT cord-242132-fhepdgz9 44 7 control control NN cord-242132-fhepdgz9 44 8 ( ( -LRB- cord-242132-fhepdgz9 44 9 free free JJ cord-242132-fhepdgz9 44 10 ) ) -RRB- cord-242132-fhepdgz9 44 11 parameter parameter NN cord-242132-fhepdgz9 44 12 , , , cord-242132-fhepdgz9 44 13 we -PRON- PRP cord-242132-fhepdgz9 44 14 use use VBP cord-242132-fhepdgz9 44 15 the the DT cord-242132-fhepdgz9 44 16 generalized generalized JJ cord-242132-fhepdgz9 44 17 risk risk NN cord-242132-fhepdgz9 44 18 factor factor NN cord-242132-fhepdgz9 44 19 β β NNP cord-242132-fhepdgz9 44 20 , , , cord-242132-fhepdgz9 44 21 which which WDT cord-242132-fhepdgz9 44 22 includes include VBZ cord-242132-fhepdgz9 44 23 some some DT cord-242132-fhepdgz9 44 24 of of IN cord-242132-fhepdgz9 44 25 the the DT cord-242132-fhepdgz9 44 26 factors factor NNS cord-242132-fhepdgz9 44 27 mentioned mention VBN cord-242132-fhepdgz9 44 28 above above RB cord-242132-fhepdgz9 44 29 in in IN cord-242132-fhepdgz9 44 30 an an DT cord-242132-fhepdgz9 44 31 integral integral JJ cord-242132-fhepdgz9 44 32 form form NN cord-242132-fhepdgz9 44 33 . . . cord-242132-fhepdgz9 45 1 In in IN cord-242132-fhepdgz9 45 2 our -PRON- PRP$ cord-242132-fhepdgz9 45 3 2D 2d NN cord-242132-fhepdgz9 45 4 toy toy NN cord-242132-fhepdgz9 45 5 model model NN cord-242132-fhepdgz9 45 6 , , , cord-242132-fhepdgz9 45 7 the the DT cord-242132-fhepdgz9 45 8 transmission transmission NN cord-242132-fhepdgz9 45 9 of of IN cord-242132-fhepdgz9 45 10 infection infection NN cord-242132-fhepdgz9 45 11 occurs occur VBZ cord-242132-fhepdgz9 45 12 due due IN cord-242132-fhepdgz9 45 13 to to IN cord-242132-fhepdgz9 45 14 contacts contact NNS cord-242132-fhepdgz9 45 15 of of IN cord-242132-fhepdgz9 45 16 randomly randomly RB cord-242132-fhepdgz9 45 17 moving move VBG cord-242132-fhepdgz9 45 18 individuals individual NNS cord-242132-fhepdgz9 45 19 , , , cord-242132-fhepdgz9 45 20 that that WDT cord-242132-fhepdgz9 45 21 determines determine VBZ cord-242132-fhepdgz9 45 22 the the DT cord-242132-fhepdgz9 45 23 complex complex JJ cord-242132-fhepdgz9 45 24 dynamics dynamic NNS cord-242132-fhepdgz9 45 25 of of IN cord-242132-fhepdgz9 45 26 the the DT cord-242132-fhepdgz9 45 27 infection infection NN cord-242132-fhepdgz9 45 28 spread spread VBD cord-242132-fhepdgz9 45 29 and and CC cord-242132-fhepdgz9 45 30 various various JJ cord-242132-fhepdgz9 45 31 critical critical JJ cord-242132-fhepdgz9 45 32 aspects aspect NNS cord-242132-fhepdgz9 45 33 of of IN cord-242132-fhepdgz9 45 34 such such PDT cord-242132-fhepdgz9 45 35 a a DT cord-242132-fhepdgz9 45 36 dynamics dynamic NNS cord-242132-fhepdgz9 45 37 . . . cord-242132-fhepdgz9 46 1 The the DT cord-242132-fhepdgz9 46 2 paper paper NN cord-242132-fhepdgz9 46 3 is be VBZ cord-242132-fhepdgz9 46 4 organized organize VBN cord-242132-fhepdgz9 46 5 as as IN cord-242132-fhepdgz9 46 6 follows follow NNS cord-242132-fhepdgz9 46 7 . . . cord-242132-fhepdgz9 47 1 In in IN cord-242132-fhepdgz9 47 2 Section section NN cord-242132-fhepdgz9 47 3 2 2 CD cord-242132-fhepdgz9 47 4 , , , cord-242132-fhepdgz9 47 5 we -PRON- PRP cord-242132-fhepdgz9 47 6 formulate formulate VBP cord-242132-fhepdgz9 47 7 our -PRON- PRP$ cord-242132-fhepdgz9 47 8 approach approach NN cord-242132-fhepdgz9 47 9 and and CC cord-242132-fhepdgz9 47 10 examine examine VB cord-242132-fhepdgz9 47 11 the the DT cord-242132-fhepdgz9 47 12 behavior behavior NN cord-242132-fhepdgz9 47 13 of of IN cord-242132-fhepdgz9 47 14 infected infected JJ cord-242132-fhepdgz9 47 15 individuals individual NNS cord-242132-fhepdgz9 47 16 ( ( -LRB- cord-242132-fhepdgz9 47 17 order order NN cord-242132-fhepdgz9 47 18 parameter parameter NN cord-242132-fhepdgz9 47 19 A(t A(t NNP cord-242132-fhepdgz9 47 20 , , , cord-242132-fhepdgz9 47 21 β β NN cord-242132-fhepdgz9 47 22 ) ) -RRB- cord-242132-fhepdgz9 47 23 ) ) -RRB- cord-242132-fhepdgz9 47 24 , , , cord-242132-fhepdgz9 47 25 which which WDT cord-242132-fhepdgz9 47 26 , , , cord-242132-fhepdgz9 47 27 as as IN cord-242132-fhepdgz9 47 28 it -PRON- PRP cord-242132-fhepdgz9 47 29 turns turn VBZ cord-242132-fhepdgz9 47 30 out out RP cord-242132-fhepdgz9 47 31 latter latter RB cord-242132-fhepdgz9 47 32 , , , cord-242132-fhepdgz9 47 33 critically critically RB cord-242132-fhepdgz9 47 34 depends depend VBZ cord-242132-fhepdgz9 47 35 on on IN cord-242132-fhepdgz9 47 36 the the DT cord-242132-fhepdgz9 47 37 value value NN cord-242132-fhepdgz9 47 38 β β NN cord-242132-fhepdgz9 47 39 . . . cord-242132-fhepdgz9 48 1 It -PRON- PRP cord-242132-fhepdgz9 48 2 also also RB cord-242132-fhepdgz9 48 3 is be VBZ cord-242132-fhepdgz9 48 4 discussed discuss VBN cord-242132-fhepdgz9 48 5 the the DT cord-242132-fhepdgz9 48 6 similarity similarity NN cord-242132-fhepdgz9 48 7 of of IN cord-242132-fhepdgz9 48 8 the the DT cord-242132-fhepdgz9 48 9 asymptotic asymptotic JJ cord-242132-fhepdgz9 48 10 behavior behavior NN cord-242132-fhepdgz9 48 11 of of IN cord-242132-fhepdgz9 48 12 the the DT cord-242132-fhepdgz9 48 13 infection infection NN cord-242132-fhepdgz9 48 14 dynamics dynamic NNS cord-242132-fhepdgz9 48 15 with with IN cord-242132-fhepdgz9 48 16 the the DT cord-242132-fhepdgz9 48 17 critical critical JJ cord-242132-fhepdgz9 48 18 phase phase NN cord-242132-fhepdgz9 48 19 transition transition NN cord-242132-fhepdgz9 48 20 in in IN cord-242132-fhepdgz9 48 21 a a DT cord-242132-fhepdgz9 48 22 two two CD cord-242132-fhepdgz9 48 23 - - HYPH cord-242132-fhepdgz9 48 24 dimensional dimensional JJ cord-242132-fhepdgz9 48 25 ( ( -LRB- cord-242132-fhepdgz9 48 26 2D 2D NNP cord-242132-fhepdgz9 48 27 ) ) -RRB- cord-242132-fhepdgz9 48 28 percolation percolation NN cord-242132-fhepdgz9 48 29 system system NN cord-242132-fhepdgz9 48 30 . . . cord-242132-fhepdgz9 49 1 In in IN cord-242132-fhepdgz9 49 2 the the DT cord-242132-fhepdgz9 49 3 next next JJ cord-242132-fhepdgz9 49 4 Section section NN cord-242132-fhepdgz9 49 5 , , , cord-242132-fhepdgz9 49 6 we -PRON- PRP cord-242132-fhepdgz9 49 7 analyze analyze VBP cord-242132-fhepdgz9 49 8 the the DT cord-242132-fhepdgz9 49 9 dynamic dynamic JJ cord-242132-fhepdgz9 49 10 properties property NNS cord-242132-fhepdgz9 49 11 of of IN cord-242132-fhepdgz9 49 12 the the DT cord-242132-fhepdgz9 49 13 extended extended JJ cord-242132-fhepdgz9 49 14 system system NN cord-242132-fhepdgz9 49 15 , , , cord-242132-fhepdgz9 49 16 where where WRB cord-242132-fhepdgz9 49 17 we -PRON- PRP cord-242132-fhepdgz9 49 18 deal deal VBP cord-242132-fhepdgz9 49 19 with with IN cord-242132-fhepdgz9 49 20 two two CD cord-242132-fhepdgz9 49 21 additional additional JJ cord-242132-fhepdgz9 49 22 parameters parameter NNS cord-242132-fhepdgz9 49 23 which which WDT cord-242132-fhepdgz9 49 24 allow allow VBP cord-242132-fhepdgz9 49 25 to to IN cord-242132-fhepdgz9 49 26 on on IN cord-242132-fhepdgz9 49 27 / / SYM cord-242132-fhepdgz9 49 28 off off IN cord-242132-fhepdgz9 49 29 the the DT cord-242132-fhepdgz9 49 30 quarantine quarantine NN cord-242132-fhepdgz9 49 31 state state NN cord-242132-fhepdgz9 49 32 . . . cord-242132-fhepdgz9 50 1 The the DT cord-242132-fhepdgz9 50 2 next next JJ cord-242132-fhepdgz9 50 3 Section section NN cord-242132-fhepdgz9 50 4 , , , cord-242132-fhepdgz9 50 5 contains contain VBZ cord-242132-fhepdgz9 50 6 the the DT cord-242132-fhepdgz9 50 7 study study NN cord-242132-fhepdgz9 50 8 of of IN cord-242132-fhepdgz9 50 9 dynamics dynamic NNS cord-242132-fhepdgz9 50 10 of of IN cord-242132-fhepdgz9 50 11 the the DT cord-242132-fhepdgz9 50 12 infection infection NN cord-242132-fhepdgz9 50 13 spreading spread VBG cord-242132-fhepdgz9 50 14 and and CC cord-242132-fhepdgz9 50 15 the the DT cord-242132-fhepdgz9 50 16 formation formation NN cord-242132-fhepdgz9 50 17 of of IN cord-242132-fhepdgz9 50 18 immunity immunity NN cord-242132-fhepdgz9 50 19 for for IN cord-242132-fhepdgz9 50 20 infected infected JJ cord-242132-fhepdgz9 50 21 individuals individual NNS cord-242132-fhepdgz9 50 22 . . . cord-242132-fhepdgz9 51 1 The the DT cord-242132-fhepdgz9 51 2 last last JJ cord-242132-fhepdgz9 51 3 Section section NN cord-242132-fhepdgz9 51 4 summarizes summarize VBZ cord-242132-fhepdgz9 51 5 our -PRON- PRP$ cord-242132-fhepdgz9 51 6 conclusions conclusion NNS cord-242132-fhepdgz9 51 7 . . . cord-242132-fhepdgz9 52 1 First first RB cord-242132-fhepdgz9 52 2 we -PRON- PRP cord-242132-fhepdgz9 52 3 explain explain VBP cord-242132-fhepdgz9 52 4 which which WDT cord-242132-fhepdgz9 52 5 the the DT cord-242132-fhepdgz9 52 6 properties property NNS cord-242132-fhepdgz9 52 7 of of IN cord-242132-fhepdgz9 52 8 dynamic dynamic JJ cord-242132-fhepdgz9 52 9 Monte Monte NNP cord-242132-fhepdgz9 52 10 Carlo Carlo NNP cord-242132-fhepdgz9 52 11 ( ( -LRB- cord-242132-fhepdgz9 52 12 DMC DMC NNP cord-242132-fhepdgz9 52 13 ) ) -RRB- cord-242132-fhepdgz9 52 14 approach approach NN cord-242132-fhepdgz9 52 15 we -PRON- PRP cord-242132-fhepdgz9 52 16 deal deal VBP cord-242132-fhepdgz9 52 17 with with IN cord-242132-fhepdgz9 52 18 . . . cord-242132-fhepdgz9 53 1 In in IN cord-242132-fhepdgz9 53 2 order order NN cord-242132-fhepdgz9 53 3 to to TO cord-242132-fhepdgz9 53 4 study study VB cord-242132-fhepdgz9 53 5 the the DT cord-242132-fhepdgz9 53 6 infection infection NN cord-242132-fhepdgz9 53 7 dynamic dynamic JJ cord-242132-fhepdgz9 53 8 in in IN cord-242132-fhepdgz9 53 9 epidemiological epidemiological JJ cord-242132-fhepdgz9 53 10 system system NN cord-242132-fhepdgz9 53 11 ( ( -LRB- cord-242132-fhepdgz9 53 12 that that DT cord-242132-fhepdgz9 53 13 is be VBZ cord-242132-fhepdgz9 53 14 far far RB cord-242132-fhepdgz9 53 15 from from IN cord-242132-fhepdgz9 53 16 equilibrium equilibrium NN cord-242132-fhepdgz9 53 17 ) ) -RRB- cord-242132-fhepdgz9 54 1 the the DT cord-242132-fhepdgz9 54 2 DMC DMC NNP cord-242132-fhepdgz9 54 3 method method NN cord-242132-fhepdgz9 54 4 is be VBZ cord-242132-fhepdgz9 54 5 used use VBN cord-242132-fhepdgz9 54 6 , , , cord-242132-fhepdgz9 54 7 that that DT cord-242132-fhepdgz9 54 8 allows allow VBZ cord-242132-fhepdgz9 54 9 investigation investigation NN cord-242132-fhepdgz9 54 10 both both CC cord-242132-fhepdgz9 54 11 temporal temporal JJ cord-242132-fhepdgz9 54 12 and and CC cord-242132-fhepdgz9 54 13 spatial spatial JJ cord-242132-fhepdgz9 54 14 properties property NNS cord-242132-fhepdgz9 54 15 by by IN cord-242132-fhepdgz9 54 16 the the DT cord-242132-fhepdgz9 54 17 numerical numerical JJ cord-242132-fhepdgz9 54 18 simulations simulation NNS cord-242132-fhepdgz9 54 19 . . . cord-242132-fhepdgz9 55 1 As as IN cord-242132-fhepdgz9 55 2 a a DT cord-242132-fhepdgz9 55 3 toy toy NN cord-242132-fhepdgz9 55 4 model model NN cord-242132-fhepdgz9 55 5 , , , cord-242132-fhepdgz9 55 6 we -PRON- PRP cord-242132-fhepdgz9 55 7 choose choose VBP cord-242132-fhepdgz9 55 8 a a DT cord-242132-fhepdgz9 55 9 2D 2d NN cord-242132-fhepdgz9 55 10 L L NNP cord-242132-fhepdgz9 55 11 × × NNP cord-242132-fhepdgz9 55 12 L L NNP cord-242132-fhepdgz9 55 13 ( ( -LRB- cord-242132-fhepdgz9 55 14 where where WRB cord-242132-fhepdgz9 55 15 L L NNP cord-242132-fhepdgz9 55 16 is be VBZ cord-242132-fhepdgz9 55 17 size size NN cord-242132-fhepdgz9 55 18 ) ) -RRB- cord-242132-fhepdgz9 55 19 bounded bound VBN cord-242132-fhepdgz9 55 20 system system NN cord-242132-fhepdgz9 55 21 that that WDT cord-242132-fhepdgz9 55 22 contains contain VBZ cord-242132-fhepdgz9 55 23 a a DT cord-242132-fhepdgz9 55 24 disordered disordered JJ cord-242132-fhepdgz9 55 25 population population NN cord-242132-fhepdgz9 55 26 of of IN cord-242132-fhepdgz9 55 27 N n CD cord-242132-fhepdgz9 55 28 individuals individual NNS cord-242132-fhepdgz9 55 29 . . . cord-242132-fhepdgz9 56 1 Following follow VBG cord-242132-fhepdgz9 56 2 the the DT cord-242132-fhepdgz9 56 3 classifications classification NNS cord-242132-fhepdgz9 56 4 commonly commonly RB cord-242132-fhepdgz9 56 5 known know VBN cord-242132-fhepdgz9 56 6 from from IN cord-242132-fhepdgz9 56 7 SIR SIR NNP cord-242132-fhepdgz9 56 8 model model NN cord-242132-fhepdgz9 56 9 3 3 CD cord-242132-fhepdgz9 56 10 in in IN cord-242132-fhepdgz9 56 11 our -PRON- PRP$ cord-242132-fhepdgz9 56 12 DMC DMC NNP cord-242132-fhepdgz9 56 13 model model NN cord-242132-fhepdgz9 56 14 we -PRON- PRP cord-242132-fhepdgz9 56 15 divide divide VBP cord-242132-fhepdgz9 56 16 the the DT cord-242132-fhepdgz9 56 17 host host NN cord-242132-fhepdgz9 56 18 population population NN cord-242132-fhepdgz9 56 19 into into IN cord-242132-fhepdgz9 56 20 a a DT cord-242132-fhepdgz9 56 21 set set NN cord-242132-fhepdgz9 56 22 of of IN cord-242132-fhepdgz9 56 23 distinct distinct JJ cord-242132-fhepdgz9 56 24 categories category NNS cord-242132-fhepdgz9 56 25 , , , cord-242132-fhepdgz9 56 26 according accord VBG cord-242132-fhepdgz9 56 27 to to IN cord-242132-fhepdgz9 56 28 its -PRON- PRP$ cord-242132-fhepdgz9 56 29 epidemiological epidemiological JJ cord-242132-fhepdgz9 56 30 status status NN cord-242132-fhepdgz9 56 31 , , , cord-242132-fhepdgz9 56 32 that that WDT cord-242132-fhepdgz9 56 33 are be VBP cord-242132-fhepdgz9 56 34 susceptible susceptible JJ cord-242132-fhepdgz9 56 35 ( ( -LRB- cord-242132-fhepdgz9 56 36 S S NNP cord-242132-fhepdgz9 56 37 ) ) -RRB- cord-242132-fhepdgz9 56 38 , , , cord-242132-fhepdgz9 56 39 currently currently RB cord-242132-fhepdgz9 56 40 infectious infectious JJ cord-242132-fhepdgz9 56 41 ( ( -LRB- cord-242132-fhepdgz9 56 42 I i NN cord-242132-fhepdgz9 56 43 ) ) -RRB- cord-242132-fhepdgz9 56 44 , , , cord-242132-fhepdgz9 56 45 and and CC cord-242132-fhepdgz9 56 46 recovered recover VBN cord-242132-fhepdgz9 56 47 ( ( -LRB- cord-242132-fhepdgz9 56 48 R r NN cord-242132-fhepdgz9 56 49 ) ) -RRB- cord-242132-fhepdgz9 56 50 . . . cord-242132-fhepdgz9 57 1 The the DT cord-242132-fhepdgz9 57 2 total total JJ cord-242132-fhepdgz9 57 3 size size NN cord-242132-fhepdgz9 57 4 of of IN cord-242132-fhepdgz9 57 5 the the DT cord-242132-fhepdgz9 57 6 host host NN cord-242132-fhepdgz9 57 7 population population NN cord-242132-fhepdgz9 57 8 is be VBZ cord-242132-fhepdgz9 57 9 then then RB cord-242132-fhepdgz9 57 10 N n CD cord-242132-fhepdgz9 57 11 = = SYM cord-242132-fhepdgz9 57 12 S+I S+I NNP cord-242132-fhepdgz9 57 13 + + CC cord-242132-fhepdgz9 57 14 R r NN cord-242132-fhepdgz9 57 15 and and CC cord-242132-fhepdgz9 58 1 all all PDT cord-242132-fhepdgz9 58 2 the the DT cord-242132-fhepdgz9 58 3 individuals individual NNS cord-242132-fhepdgz9 58 4 are be VBP cord-242132-fhepdgz9 58 5 born bear VBN cord-242132-fhepdgz9 58 6 in in IN cord-242132-fhepdgz9 58 7 the the DT cord-242132-fhepdgz9 58 8 susceptible susceptible JJ cord-242132-fhepdgz9 58 9 category category NN cord-242132-fhepdgz9 58 10 3 3 CD cord-242132-fhepdgz9 58 11 . . . cord-242132-fhepdgz9 59 1 Following follow VBG cord-242132-fhepdgz9 59 2 the the DT cord-242132-fhepdgz9 59 3 actual actual JJ cord-242132-fhepdgz9 59 4 situations situation NNS cord-242132-fhepdgz9 59 5 we -PRON- PRP cord-242132-fhepdgz9 59 6 assume assume VBP cord-242132-fhepdgz9 59 7 that that IN cord-242132-fhepdgz9 59 8 initially initially RB cord-242132-fhepdgz9 59 9 the the DT cord-242132-fhepdgz9 59 10 maternally maternally RB cord-242132-fhepdgz9 59 11 derived derive VBN cord-242132-fhepdgz9 59 12 immunity immunity NN cord-242132-fhepdgz9 59 13 is be VBZ cord-242132-fhepdgz9 59 14 clear clear JJ cord-242132-fhepdgz9 59 15 . . . cord-242132-fhepdgz9 60 1 ( ( -LRB- cord-242132-fhepdgz9 60 2 The the DT cord-242132-fhepdgz9 60 3 effect effect NN cord-242132-fhepdgz9 60 4 of of IN cord-242132-fhepdgz9 60 5 immunity immunity NN cord-242132-fhepdgz9 60 6 is be VBZ cord-242132-fhepdgz9 60 7 studied study VBN cord-242132-fhepdgz9 60 8 in in IN cord-242132-fhepdgz9 60 9 the the DT cord-242132-fhepdgz9 60 10 following follow VBG cord-242132-fhepdgz9 60 11 sections section NNS cord-242132-fhepdgz9 60 12 ) ) -RRB- cord-242132-fhepdgz9 60 13 . . . cord-242132-fhepdgz9 61 1 Upon upon IN cord-242132-fhepdgz9 61 2 contact contact NN cord-242132-fhepdgz9 61 3 with with IN cord-242132-fhepdgz9 61 4 infectious infectious JJ cord-242132-fhepdgz9 61 5 individuals individual NNS cord-242132-fhepdgz9 61 6 , , , cord-242132-fhepdgz9 61 7 the the DT cord-242132-fhepdgz9 61 8 susceptibles susceptible NNS cord-242132-fhepdgz9 61 9 may may MD cord-242132-fhepdgz9 61 10 get get VB cord-242132-fhepdgz9 61 11 infected infect VBN cord-242132-fhepdgz9 61 12 and and CC cord-242132-fhepdgz9 61 13 move move VB cord-242132-fhepdgz9 61 14 into into IN cord-242132-fhepdgz9 61 15 the the DT cord-242132-fhepdgz9 61 16 infectious infectious JJ cord-242132-fhepdgz9 61 17 category category NN cord-242132-fhepdgz9 61 18 . . . cord-242132-fhepdgz9 62 1 To to TO cord-242132-fhepdgz9 62 2 apply apply VB cord-242132-fhepdgz9 62 3 the the DT cord-242132-fhepdgz9 62 4 DMC DMC NNP cord-242132-fhepdgz9 62 5 approach approach NN cord-242132-fhepdgz9 62 6 it -PRON- PRP cord-242132-fhepdgz9 62 7 is be VBZ cord-242132-fhepdgz9 62 8 constructed construct VBN cord-242132-fhepdgz9 62 9 the the DT cord-242132-fhepdgz9 62 10 Person Person NNP cord-242132-fhepdgz9 62 11 class class NN cord-242132-fhepdgz9 62 12 ( ( -LRB- cord-242132-fhepdgz9 62 13 individual individual NN cord-242132-fhepdgz9 62 14 , , , cord-242132-fhepdgz9 62 15 alias alias NN cord-242132-fhepdgz9 62 16 object object NN cord-242132-fhepdgz9 62 17 ) ) -RRB- cord-242132-fhepdgz9 62 18 that that WDT cord-242132-fhepdgz9 62 19 encapsulates encapsulate VBZ cord-242132-fhepdgz9 62 20 properties property NNS cord-242132-fhepdgz9 62 21 of of IN cord-242132-fhepdgz9 62 22 a a DT cord-242132-fhepdgz9 62 23 randomly randomly RB cord-242132-fhepdgz9 62 24 placed place VBN cord-242132-fhepdgz9 62 25 and and CC cord-242132-fhepdgz9 62 26 moving move VBG cord-242132-fhepdgz9 62 27 individual individual NN cord-242132-fhepdgz9 62 28 and and CC cord-242132-fhepdgz9 62 29 contains contain VBZ cord-242132-fhepdgz9 62 30 the the DT cord-242132-fhepdgz9 62 31 following follow VBG cord-242132-fhepdgz9 62 32 significant significant JJ cord-242132-fhepdgz9 62 33 attributes attribute NNS cord-242132-fhepdgz9 62 34 where where WRB cord-242132-fhepdgz9 62 35 x x NNP cord-242132-fhepdgz9 62 36 , , , cord-242132-fhepdgz9 62 37 y y NNP cord-242132-fhepdgz9 62 38 are be VBP cord-242132-fhepdgz9 62 39 the the DT cord-242132-fhepdgz9 62 40 components component NNS cord-242132-fhepdgz9 62 41 of of IN cord-242132-fhepdgz9 62 42 position position NN cord-242132-fhepdgz9 62 43 , , , cord-242132-fhepdgz9 62 44 v v NNP cord-242132-fhepdgz9 62 45 x x NN cord-242132-fhepdgz9 62 46 , , , cord-242132-fhepdgz9 62 47 v v NNP cord-242132-fhepdgz9 62 48 y y NNP cord-242132-fhepdgz9 62 49 are be VBP cord-242132-fhepdgz9 62 50 the the DT cord-242132-fhepdgz9 62 51 components component NNS cord-242132-fhepdgz9 62 52 of of IN cord-242132-fhepdgz9 62 53 velocity velocity NN cord-242132-fhepdgz9 62 54 , , , cord-242132-fhepdgz9 62 55 the the DT cord-242132-fhepdgz9 62 56 parameters parameter NNS cord-242132-fhepdgz9 62 57 I -PRON- PRP cord-242132-fhepdgz9 62 58 , , , cord-242132-fhepdgz9 62 59 M M NNP cord-242132-fhepdgz9 62 60 describe describe VBP cord-242132-fhepdgz9 62 61 the the DT cord-242132-fhepdgz9 62 62 states state NNS cord-242132-fhepdgz9 62 63 : : : cord-242132-fhepdgz9 62 64 infected infect VBN cord-242132-fhepdgz9 62 65 / / SYM cord-242132-fhepdgz9 62 66 uninfected uninfected JJ cord-242132-fhepdgz9 62 67 and and CC cord-242132-fhepdgz9 62 68 immunized immunize VBN cord-242132-fhepdgz9 62 69 / / SYM cord-242132-fhepdgz9 62 70 nonimmunized nonimmunize VBN cord-242132-fhepdgz9 62 71 , , , cord-242132-fhepdgz9 62 72 respectively respectively RB cord-242132-fhepdgz9 62 73 . . . cord-242132-fhepdgz9 63 1 The the DT cord-242132-fhepdgz9 63 2 list list NN cord-242132-fhepdgz9 63 3 of of IN cord-242132-fhepdgz9 63 4 Persons person NNS cord-242132-fhepdgz9 63 5 that that WDT cord-242132-fhepdgz9 63 6 represents represent VBZ cord-242132-fhepdgz9 63 7 a a DT cord-242132-fhepdgz9 63 8 total total JJ cord-242132-fhepdgz9 63 9 host host NN cord-242132-fhepdgz9 63 10 population population NN cord-242132-fhepdgz9 63 11 is be VBZ cord-242132-fhepdgz9 63 12 used use VBN cord-242132-fhepdgz9 63 13 in in IN cord-242132-fhepdgz9 63 14 our -PRON- PRP$ cord-242132-fhepdgz9 63 15 DMC DMC NNP cord-242132-fhepdgz9 63 16 simulations simulation NNS cord-242132-fhepdgz9 63 17 . . . cord-242132-fhepdgz9 64 1 One one CD cord-242132-fhepdgz9 64 2 of of IN cord-242132-fhepdgz9 64 3 the the DT cord-242132-fhepdgz9 64 4 underlying underlie VBG cord-242132-fhepdgz9 64 5 reasons reason NNS cord-242132-fhepdgz9 64 6 why why WRB cord-242132-fhepdgz9 64 7 epidemiological epidemiological JJ cord-242132-fhepdgz9 64 8 systems system NNS cord-242132-fhepdgz9 64 9 exhibit exhibit NN cord-242132-fhepdgz9 64 10 variation variation NN cord-242132-fhepdgz9 64 11 is be VBZ cord-242132-fhepdgz9 64 12 due due JJ cord-242132-fhepdgz9 64 13 to to IN cord-242132-fhepdgz9 64 14 a a DT cord-242132-fhepdgz9 64 15 different different JJ cord-242132-fhepdgz9 64 16 way way NN cord-242132-fhepdgz9 64 17 that that IN cord-242132-fhepdgz9 64 18 the the DT cord-242132-fhepdgz9 64 19 individuals individual NNS cord-242132-fhepdgz9 64 20 in in IN cord-242132-fhepdgz9 64 21 a a DT cord-242132-fhepdgz9 64 22 population population NN cord-242132-fhepdgz9 64 23 have have VBP cord-242132-fhepdgz9 64 24 contact contact NN cord-242132-fhepdgz9 64 25 with with IN cord-242132-fhepdgz9 64 26 each each DT cord-242132-fhepdgz9 64 27 other other JJ cord-242132-fhepdgz9 64 28 . . . cord-242132-fhepdgz9 65 1 In in IN cord-242132-fhepdgz9 65 2 our -PRON- PRP$ cord-242132-fhepdgz9 65 3 DMC DMC NNP cord-242132-fhepdgz9 65 4 simulation simulation NN cord-242132-fhepdgz9 65 5 we -PRON- PRP cord-242132-fhepdgz9 65 6 assume assume VBP cord-242132-fhepdgz9 65 7 that that IN cord-242132-fhepdgz9 65 8 the the DT cord-242132-fhepdgz9 65 9 spreading spread VBG cord-242132-fhepdgz9 65 10 ( ( -LRB- cord-242132-fhepdgz9 65 11 transmission transmission NN cord-242132-fhepdgz9 65 12 ) ) -RRB- cord-242132-fhepdgz9 65 13 of of IN cord-242132-fhepdgz9 65 14 the the DT cord-242132-fhepdgz9 65 15 infection infection NN cord-242132-fhepdgz9 65 16 occurs occur VBZ cord-242132-fhepdgz9 65 17 because because IN cord-242132-fhepdgz9 65 18 of of IN cord-242132-fhepdgz9 65 19 random random JJ cord-242132-fhepdgz9 65 20 contacts contact NNS cord-242132-fhepdgz9 65 21 for for IN cord-242132-fhepdgz9 65 22 moving move VBG cord-242132-fhepdgz9 65 23 individuals individual NNS cord-242132-fhepdgz9 65 24 . . . cord-242132-fhepdgz9 66 1 To to TO cord-242132-fhepdgz9 66 2 do do VB cord-242132-fhepdgz9 66 3 that that DT cord-242132-fhepdgz9 66 4 in in IN cord-242132-fhepdgz9 66 5 DMC DMC NNP cord-242132-fhepdgz9 66 6 simulations simulation NNS cord-242132-fhepdgz9 66 7 we -PRON- PRP cord-242132-fhepdgz9 66 8 use use VBP cord-242132-fhepdgz9 66 9 the the DT cord-242132-fhepdgz9 66 10 following follow VBG cord-242132-fhepdgz9 66 11 strategy strategy NN cord-242132-fhepdgz9 66 12 . . . cord-242132-fhepdgz9 67 1 ( ( -LRB- cord-242132-fhepdgz9 67 2 i i NN cord-242132-fhepdgz9 67 3 ) ) -RRB- cord-242132-fhepdgz9 68 1 Any any DT cord-242132-fhepdgz9 68 2 contact contact NN cord-242132-fhepdgz9 68 3 can can MD cord-242132-fhepdgz9 68 4 occur occur VB cord-242132-fhepdgz9 68 5 only only RB cord-242132-fhepdgz9 68 6 between between IN cord-242132-fhepdgz9 68 7 two two CD cord-242132-fhepdgz9 68 8 nearest near JJS cord-242132-fhepdgz9 68 9 individuals individual NNS cord-242132-fhepdgz9 68 10 . . . cord-242132-fhepdgz9 69 1 ( ( -LRB- cord-242132-fhepdgz9 69 2 ii ii NN cord-242132-fhepdgz9 69 3 ) ) -RRB- cord-242132-fhepdgz9 70 1 At at IN cord-242132-fhepdgz9 70 2 any any DT cord-242132-fhepdgz9 70 3 contact contact NN cord-242132-fhepdgz9 70 4 , , , cord-242132-fhepdgz9 70 5 the the DT cord-242132-fhepdgz9 70 6 state state NN cord-242132-fhepdgz9 70 7 of of IN cord-242132-fhepdgz9 70 8 an an DT cord-242132-fhepdgz9 70 9 infected infected JJ cord-242132-fhepdgz9 70 10 transmits transmit VBZ cord-242132-fhepdgz9 70 11 to to IN cord-242132-fhepdgz9 70 12 the the DT cord-242132-fhepdgz9 70 13 other other JJ cord-242132-fhepdgz9 70 14 contact contact NN cord-242132-fhepdgz9 70 15 person person NN cord-242132-fhepdgz9 70 16 . . . cord-242132-fhepdgz9 71 1 But but CC cord-242132-fhepdgz9 71 2 the the DT cord-242132-fhepdgz9 71 3 infected infected JJ cord-242132-fhepdgz9 71 4 one one NN cord-242132-fhepdgz9 71 5 can can MD cord-242132-fhepdgz9 71 6 still still RB cord-242132-fhepdgz9 71 7 be be VB cord-242132-fhepdgz9 71 8 recovered recover VBN cord-242132-fhepdgz9 71 9 with with IN cord-242132-fhepdgz9 71 10 probability probability NN cord-242132-fhepdgz9 71 11 1 1 CD cord-242132-fhepdgz9 71 12 − − NN cord-242132-fhepdgz9 71 13 β β NN cord-242132-fhepdgz9 71 14 ( ( -LRB- cord-242132-fhepdgz9 71 15 recall recall VB cord-242132-fhepdgz9 71 16 that that IN cord-242132-fhepdgz9 71 17 β β NN cord-242132-fhepdgz9 71 18 ∈ ∈ VB cord-242132-fhepdgz9 71 19 [ [ -LRB- cord-242132-fhepdgz9 71 20 0 0 CD cord-242132-fhepdgz9 71 21 , , , cord-242132-fhepdgz9 71 22 1 1 CD cord-242132-fhepdgz9 71 23 ] ] -RRB- cord-242132-fhepdgz9 71 24 is be VBZ cord-242132-fhepdgz9 71 25 a a DT cord-242132-fhepdgz9 71 26 risk risk NN cord-242132-fhepdgz9 71 27 factor factor NN cord-242132-fhepdgz9 71 28 ) ) -RRB- cord-242132-fhepdgz9 71 29 . . . cord-242132-fhepdgz9 72 1 This this DT cord-242132-fhepdgz9 72 2 means mean VBZ cord-242132-fhepdgz9 72 3 that that IN cord-242132-fhepdgz9 72 4 if if IN cord-242132-fhepdgz9 72 5 β β NN cord-242132-fhepdgz9 72 6 1 1 CD cord-242132-fhepdgz9 72 7 , , , cord-242132-fhepdgz9 72 8 the the DT cord-242132-fhepdgz9 72 9 probability probability NN cord-242132-fhepdgz9 72 10 to to IN cord-242132-fhepdgz9 72 11 a a DT cord-242132-fhepdgz9 72 12 recovery recovery NN cord-242132-fhepdgz9 72 13 is be VBZ cord-242132-fhepdgz9 72 14 small small JJ cord-242132-fhepdgz9 72 15 . . . cord-242132-fhepdgz9 73 1 To to TO cord-242132-fhepdgz9 73 2 take take VB cord-242132-fhepdgz9 73 3 an an DT cord-242132-fhepdgz9 73 4 advantage advantage NN cord-242132-fhepdgz9 73 5 of of IN cord-242132-fhepdgz9 73 6 the the DT cord-242132-fhepdgz9 73 7 visualizations visualization NNS cord-242132-fhepdgz9 73 8 at at IN cord-242132-fhepdgz9 73 9 applying apply VBG cord-242132-fhepdgz9 73 10 the the DT cord-242132-fhepdgz9 73 11 DMC DMC NNP cord-242132-fhepdgz9 73 12 technique technique NN cord-242132-fhepdgz9 73 13 , , , cord-242132-fhepdgz9 73 14 we -PRON- PRP cord-242132-fhepdgz9 73 15 allow allow VBP cord-242132-fhepdgz9 73 16 each each DT cord-242132-fhepdgz9 73 17 object object NN cord-242132-fhepdgz9 73 18 to to TO cord-242132-fhepdgz9 73 19 have have VB cord-242132-fhepdgz9 73 20 a a DT cord-242132-fhepdgz9 73 21 visual visual JJ cord-242132-fhepdgz9 73 22 representation representation NN cord-242132-fhepdgz9 73 23 , , , cord-242132-fhepdgz9 73 24 which which WDT cord-242132-fhepdgz9 73 25 is be VBZ cord-242132-fhepdgz9 73 26 a a DT cord-242132-fhepdgz9 73 27 yellow yellow JJ cord-242132-fhepdgz9 73 28 circle circle NN cord-242132-fhepdgz9 73 29 ( ( -LRB- cord-242132-fhepdgz9 73 30 nonimmunized nonimmunize VBN cord-242132-fhepdgz9 73 31 individual individual NN cord-242132-fhepdgz9 73 32 ) ) -RRB- cord-242132-fhepdgz9 73 33 , , , cord-242132-fhepdgz9 73 34 a a DT cord-242132-fhepdgz9 73 35 green green JJ cord-242132-fhepdgz9 73 36 circle circle NN cord-242132-fhepdgz9 73 37 ( ( -LRB- cord-242132-fhepdgz9 73 38 immunized immunize VBN cord-242132-fhepdgz9 73 39 but but CC cord-242132-fhepdgz9 73 40 not not RB cord-242132-fhepdgz9 73 41 infected infect VBN cord-242132-fhepdgz9 73 42 individual individual NN cord-242132-fhepdgz9 73 43 ) ) -RRB- cord-242132-fhepdgz9 73 44 and and CC cord-242132-fhepdgz9 73 45 a a DT cord-242132-fhepdgz9 73 46 red red JJ cord-242132-fhepdgz9 73 47 circle circle NN cord-242132-fhepdgz9 73 48 ( ( -LRB- cord-242132-fhepdgz9 73 49 infected infect VBN cord-242132-fhepdgz9 73 50 individual individual NN cord-242132-fhepdgz9 73 51 ) ) -RRB- cord-242132-fhepdgz9 73 52 , , , cord-242132-fhepdgz9 73 53 see see VB cord-242132-fhepdgz9 73 54 Fig.1 fig.1 NN cord-242132-fhepdgz9 73 55 . . . cord-242132-fhepdgz9 74 1 We -PRON- PRP cord-242132-fhepdgz9 74 2 used use VBD cord-242132-fhepdgz9 74 3 the the DT cord-242132-fhepdgz9 74 4 interaction interaction NN cord-242132-fhepdgz9 74 5 radius radius NN cord-242132-fhepdgz9 74 6 r r NN cord-242132-fhepdgz9 74 7 as as IN cord-242132-fhepdgz9 74 8 the the DT cord-242132-fhepdgz9 74 9 unit unit NN cord-242132-fhepdgz9 74 10 scale scale NN cord-242132-fhepdgz9 74 11 to to TO cord-242132-fhepdgz9 74 12 measure measure VB cord-242132-fhepdgz9 74 13 distances distance NNS cord-242132-fhepdgz9 74 14 ( ( -LRB- cord-242132-fhepdgz9 74 15 used use VBN cord-242132-fhepdgz9 74 16 r r NN cord-242132-fhepdgz9 74 17 = = SYM cord-242132-fhepdgz9 74 18 6 6 CD cord-242132-fhepdgz9 74 19 , , , cord-242132-fhepdgz9 74 20 see see VB cord-242132-fhepdgz9 74 21 Fig.1 Fig.1 NNP cord-242132-fhepdgz9 74 22 ) ) -RRB- cord-242132-fhepdgz9 74 23 between between IN cord-242132-fhepdgz9 74 24 the the DT cord-242132-fhepdgz9 74 25 individuals individual NNS cord-242132-fhepdgz9 74 26 , , , cord-242132-fhepdgz9 74 27 while while IN cord-242132-fhepdgz9 74 28 the the DT cord-242132-fhepdgz9 74 29 time time NN cord-242132-fhepdgz9 74 30 unit unit NN cord-242132-fhepdgz9 74 31 ∆t ∆t NN cord-242132-fhepdgz9 74 32 = = SYM cord-242132-fhepdgz9 74 33 1 1 CD cord-242132-fhepdgz9 74 34 was be VBD cord-242132-fhepdgz9 74 35 the the DT cord-242132-fhepdgz9 74 36 time time NN cord-242132-fhepdgz9 74 37 interval interval NN cord-242132-fhepdgz9 74 38 between between IN cord-242132-fhepdgz9 74 39 two two CD cord-242132-fhepdgz9 74 40 updatings updating NNS cord-242132-fhepdgz9 74 41 of of IN cord-242132-fhepdgz9 74 42 the the DT cord-242132-fhepdgz9 74 43 directions direction NNS cord-242132-fhepdgz9 74 44 and and CC cord-242132-fhepdgz9 74 45 positions position NNS cord-242132-fhepdgz9 74 46 . . . cord-242132-fhepdgz9 75 1 In in IN cord-242132-fhepdgz9 75 2 our -PRON- PRP$ cord-242132-fhepdgz9 75 3 simulations simulation NNS cord-242132-fhepdgz9 75 4 we -PRON- PRP cord-242132-fhepdgz9 75 5 used use VBD cord-242132-fhepdgz9 75 6 the the DT cord-242132-fhepdgz9 75 7 simplest simple JJS cord-242132-fhepdgz9 75 8 initial initial JJ cord-242132-fhepdgz9 75 9 conditions condition NNS cord-242132-fhepdgz9 75 10 : : : cord-242132-fhepdgz9 75 11 at at IN cord-242132-fhepdgz9 75 12 time time NN cord-242132-fhepdgz9 75 13 t t NNP cord-242132-fhepdgz9 75 14 = = SYM cord-242132-fhepdgz9 75 15 0 0 NFP cord-242132-fhepdgz9 75 16 the the DT cord-242132-fhepdgz9 75 17 positions position NNS cord-242132-fhepdgz9 75 18 and and CC cord-242132-fhepdgz9 75 19 velocities velocity NNS cord-242132-fhepdgz9 75 20 for for IN cord-242132-fhepdgz9 75 21 all all PDT cord-242132-fhepdgz9 75 22 the the DT cord-242132-fhepdgz9 75 23 N n CD cord-242132-fhepdgz9 75 24 individuals individual NNS cord-242132-fhepdgz9 75 25 are be VBP cord-242132-fhepdgz9 75 26 randomly randomly RB cord-242132-fhepdgz9 75 27 distributed distribute VBN cord-242132-fhepdgz9 75 28 . . . cord-242132-fhepdgz9 76 1 We -PRON- PRP cord-242132-fhepdgz9 76 2 use use VBP cord-242132-fhepdgz9 76 3 the the DT cord-242132-fhepdgz9 76 4 velocity velocity NN cord-242132-fhepdgz9 76 5 scale scale NN cord-242132-fhepdgz9 76 6 such such JJ cord-242132-fhepdgz9 76 7 that that IN cord-242132-fhepdgz9 76 8 random random JJ cord-242132-fhepdgz9 76 9 v v NN cord-242132-fhepdgz9 77 1 x x NNP cord-242132-fhepdgz9 77 2 , , , cord-242132-fhepdgz9 77 3 v v NNP cord-242132-fhepdgz9 77 4 y y NN cord-242132-fhepdgz9 77 5 ∈ ∈ NNP cord-242132-fhepdgz9 77 6 [ [ -LRB- cord-242132-fhepdgz9 77 7 2 2 CD cord-242132-fhepdgz9 77 8 , , , cord-242132-fhepdgz9 77 9 10 10 CD cord-242132-fhepdgz9 77 10 ] ] -RRB- cord-242132-fhepdgz9 77 11 for for IN cord-242132-fhepdgz9 77 12 which which WDT cord-242132-fhepdgz9 77 13 the the DT cord-242132-fhepdgz9 77 14 individuals individual NNS cord-242132-fhepdgz9 77 15 always always RB cord-242132-fhepdgz9 77 16 interact interact VBP cord-242132-fhepdgz9 77 17 with with IN cord-242132-fhepdgz9 77 18 their -PRON- PRP$ cord-242132-fhepdgz9 77 19 actual actual JJ cord-242132-fhepdgz9 77 20 neighbors neighbor NNS cord-242132-fhepdgz9 77 21 and and CC cord-242132-fhepdgz9 77 22 move move VB cord-242132-fhepdgz9 77 23 fast fast RB cord-242132-fhepdgz9 77 24 enough enough RB cord-242132-fhepdgz9 77 25 to to TO cord-242132-fhepdgz9 77 26 change change VB cord-242132-fhepdgz9 77 27 the the DT cord-242132-fhepdgz9 77 28 configuration configuration NN cord-242132-fhepdgz9 77 29 after after IN cord-242132-fhepdgz9 77 30 a a DT cord-242132-fhepdgz9 77 31 few few JJ cord-242132-fhepdgz9 77 32 updates update NNS cord-242132-fhepdgz9 77 33 . . . cord-242132-fhepdgz9 78 1 According accord VBG cord-242132-fhepdgz9 78 2 to to IN cord-242132-fhepdgz9 78 3 our -PRON- PRP$ cord-242132-fhepdgz9 78 4 simulations simulation NNS cord-242132-fhepdgz9 78 5 , , , cord-242132-fhepdgz9 78 6 the the DT cord-242132-fhepdgz9 78 7 variation variation NN cord-242132-fhepdgz9 78 8 of of IN cord-242132-fhepdgz9 78 9 actual actual JJ cord-242132-fhepdgz9 78 10 interval interval NN cord-242132-fhepdgz9 78 11 of of IN cord-242132-fhepdgz9 78 12 values value NNS cord-242132-fhepdgz9 78 13 of of IN cord-242132-fhepdgz9 78 14 v v NN cord-242132-fhepdgz9 78 15 x x NN cord-242132-fhepdgz9 78 16 , , , cord-242132-fhepdgz9 78 17 v v NNP cord-242132-fhepdgz9 78 18 y y NNP cord-242132-fhepdgz9 78 19 does do VBZ cord-242132-fhepdgz9 78 20 not not RB cord-242132-fhepdgz9 78 21 affect affect VB cord-242132-fhepdgz9 78 22 the the DT cord-242132-fhepdgz9 78 23 results result NNS cord-242132-fhepdgz9 78 24 . . . cord-242132-fhepdgz9 79 1 We -PRON- PRP cord-242132-fhepdgz9 79 2 also also RB cord-242132-fhepdgz9 79 3 investigated investigate VBD cord-242132-fhepdgz9 79 4 the the DT cord-242132-fhepdgz9 79 5 cases case NNS cord-242132-fhepdgz9 79 6 when when WRB cord-242132-fhepdgz9 79 7 the the DT cord-242132-fhepdgz9 79 8 basic basic JJ cord-242132-fhepdgz9 79 9 parameter parameter NN cord-242132-fhepdgz9 79 10 of of IN cord-242132-fhepdgz9 79 11 the the DT cord-242132-fhepdgz9 79 12 model model NN cord-242132-fhepdgz9 79 13 , , , cord-242132-fhepdgz9 79 14 the the DT cord-242132-fhepdgz9 79 15 density density NN cord-242132-fhepdgz9 79 16 ρ ρ NN cord-242132-fhepdgz9 79 17 = = SYM cord-242132-fhepdgz9 79 18 N N NNP cord-242132-fhepdgz9 79 19 / / SYM cord-242132-fhepdgz9 79 20 L L NNP cord-242132-fhepdgz9 79 21 2 2 CD cord-242132-fhepdgz9 79 22 is be VBZ cord-242132-fhepdgz9 79 23 slightly slightly RB cord-242132-fhepdgz9 79 24 varied varied JJ cord-242132-fhepdgz9 79 25 . . . cord-242132-fhepdgz9 80 1 When when WRB cord-242132-fhepdgz9 80 2 the the DT cord-242132-fhepdgz9 80 3 simulation simulation NN cord-242132-fhepdgz9 80 4 time time NN cord-242132-fhepdgz9 80 5 runs run VBZ cord-242132-fhepdgz9 80 6 a a DT cord-242132-fhepdgz9 80 7 lot lot NN cord-242132-fhepdgz9 80 8 contacts contact NNS cord-242132-fhepdgz9 80 9 occur occur VBP cord-242132-fhepdgz9 80 10 between between IN cord-242132-fhepdgz9 80 11 nearest near JJS cord-242132-fhepdgz9 80 12 randomly randomly RB cord-242132-fhepdgz9 80 13 moving move VBG cord-242132-fhepdgz9 80 14 persons person NNS cord-242132-fhepdgz9 80 15 that that WDT cord-242132-fhepdgz9 80 16 leads lead VBZ cord-242132-fhepdgz9 80 17 to to TO cord-242132-fhepdgz9 80 18 fast fast VB cord-242132-fhepdgz9 80 19 and and CC cord-242132-fhepdgz9 80 20 uncontrollable uncontrollable JJ cord-242132-fhepdgz9 80 21 transfer transfer NN cord-242132-fhepdgz9 80 22 of of IN cord-242132-fhepdgz9 80 23 infection infection NN cord-242132-fhepdgz9 80 24 between between IN cord-242132-fhepdgz9 80 25 many many JJ cord-242132-fhepdgz9 80 26 individuals individual NNS cord-242132-fhepdgz9 80 27 , , , cord-242132-fhepdgz9 80 28 see see VB cord-242132-fhepdgz9 80 29 Fig Fig NNP cord-242132-fhepdgz9 80 30 . . . cord-242132-fhepdgz9 81 1 1 1 LS cord-242132-fhepdgz9 81 2 . . . cord-242132-fhepdgz9 82 1 It -PRON- PRP cord-242132-fhepdgz9 82 2 is be VBZ cord-242132-fhepdgz9 82 3 of of IN cord-242132-fhepdgz9 82 4 great great JJ cord-242132-fhepdgz9 82 5 interest interest NN cord-242132-fhepdgz9 82 6 to to TO cord-242132-fhepdgz9 82 7 investigate investigate VB cord-242132-fhepdgz9 82 8 the the DT cord-242132-fhepdgz9 82 9 temporal temporal JJ cord-242132-fhepdgz9 82 10 infection infection NN cord-242132-fhepdgz9 82 11 dynamics dynamic NNS cord-242132-fhepdgz9 82 12 at at IN cord-242132-fhepdgz9 82 13 various various JJ cord-242132-fhepdgz9 82 14 risk risk NN cord-242132-fhepdgz9 82 15 factors factor NNS cord-242132-fhepdgz9 82 16 β β NN cord-242132-fhepdgz9 82 17 . . . cord-242132-fhepdgz9 83 1 Such such JJ cord-242132-fhepdgz9 83 2 a a DT cord-242132-fhepdgz9 83 3 dynamics dynamic NNS cord-242132-fhepdgz9 83 4 of of IN cord-242132-fhepdgz9 83 5 the the DT cord-242132-fhepdgz9 83 6 infections infection NNS cord-242132-fhepdgz9 83 7 spreading spread VBG cord-242132-fhepdgz9 83 8 ( ( -LRB- cord-242132-fhepdgz9 83 9 coefficient coefficient NN cord-242132-fhepdgz9 83 10 A(t A(t NNP cord-242132-fhepdgz9 83 11 ) ) -RRB- cord-242132-fhepdgz9 83 12 = = NFP cord-242132-fhepdgz9 84 1 I(t)/N i(t)/n NN cord-242132-fhepdgz9 84 2 ) ) -RRB- cord-242132-fhepdgz9 85 1 as as IN cord-242132-fhepdgz9 85 2 function function NN cord-242132-fhepdgz9 85 3 of of IN cord-242132-fhepdgz9 85 4 time time NN cord-242132-fhepdgz9 85 5 t t NNP cord-242132-fhepdgz9 85 6 is be VBZ cord-242132-fhepdgz9 85 7 displayed display VBN cord-242132-fhepdgz9 85 8 in in IN cord-242132-fhepdgz9 85 9 Fig.2 Fig.2 NNP cord-242132-fhepdgz9 85 10 . . . cord-242132-fhepdgz9 86 1 Since since IN cord-242132-fhepdgz9 86 2 A(t A(t NNP cord-242132-fhepdgz9 86 3 ) ) -RRB- cord-242132-fhepdgz9 86 4 is be VBZ cord-242132-fhepdgz9 86 5 a a DT cord-242132-fhepdgz9 86 6 random random JJ cord-242132-fhepdgz9 86 7 - - HYPH cord-242132-fhepdgz9 86 8 valued value VBN cord-242132-fhepdgz9 86 9 function function NN cord-242132-fhepdgz9 86 10 we -PRON- PRP cord-242132-fhepdgz9 86 11 will will MD cord-242132-fhepdgz9 86 12 fit fit VB cord-242132-fhepdgz9 86 13 ( ( -LRB- cord-242132-fhepdgz9 86 14 see see VB cord-242132-fhepdgz9 86 15 10 10 CD cord-242132-fhepdgz9 86 16 ) ) -RRB- cord-242132-fhepdgz9 86 17 A(t a(t CD cord-242132-fhepdgz9 86 18 ) ) -RRB- cord-242132-fhepdgz9 86 19 by by IN cord-242132-fhepdgz9 86 20 a a DT cord-242132-fhepdgz9 86 21 suitable suitable JJ cord-242132-fhepdgz9 86 22 fitting fitting JJ cord-242132-fhepdgz9 86 23 function function NN cord-242132-fhepdgz9 86 24 that that WDT cord-242132-fhepdgz9 86 25 is be VBZ cord-242132-fhepdgz9 86 26 chosen choose VBN cord-242132-fhepdgz9 86 27 as as IN cord-242132-fhepdgz9 86 28 where where WRB cord-242132-fhepdgz9 86 29 a a DT cord-242132-fhepdgz9 86 30 0,1,2 0,1,2 CD cord-242132-fhepdgz9 86 31 are be VBP cord-242132-fhepdgz9 86 32 the the DT cord-242132-fhepdgz9 86 33 fitting fitting JJ cord-242132-fhepdgz9 86 34 coefficients coefficient NNS cord-242132-fhepdgz9 86 35 . . . cord-242132-fhepdgz9 87 1 We -PRON- PRP cord-242132-fhepdgz9 87 2 found find VBD cord-242132-fhepdgz9 87 3 that that IN cord-242132-fhepdgz9 87 4 a a DT cord-242132-fhepdgz9 87 5 1 1 CD cord-242132-fhepdgz9 87 6 is be VBZ cord-242132-fhepdgz9 87 7 very very RB cord-242132-fhepdgz9 87 8 small small JJ cord-242132-fhepdgz9 87 9 ∼ ∼ NN cord-242132-fhepdgz9 87 10 10 10 CD cord-242132-fhepdgz9 87 11 −5 −5 NNS cord-242132-fhepdgz9 87 12 and and CC cord-242132-fhepdgz9 87 13 a a DT cord-242132-fhepdgz9 87 14 2 2 CD cord-242132-fhepdgz9 87 15 2 2 CD cord-242132-fhepdgz9 87 16 for for IN cord-242132-fhepdgz9 87 17 all all PDT cord-242132-fhepdgz9 87 18 the the DT cord-242132-fhepdgz9 87 19 cases case NNS cord-242132-fhepdgz9 87 20 , , , cord-242132-fhepdgz9 87 21 but but CC cord-242132-fhepdgz9 87 22 the the DT cord-242132-fhepdgz9 87 23 amplitude amplitude NN cord-242132-fhepdgz9 87 24 a a DT cord-242132-fhepdgz9 87 25 0 0 CD cord-242132-fhepdgz9 87 26 changes change NNS cord-242132-fhepdgz9 87 27 considerably considerably RB cord-242132-fhepdgz9 87 28 at at IN cord-242132-fhepdgz9 87 29 the the DT cord-242132-fhepdgz9 87 30 β β NNP cord-242132-fhepdgz9 87 31 variation variation NN cord-242132-fhepdgz9 87 32 . . . cord-242132-fhepdgz9 88 1 In in IN cord-242132-fhepdgz9 88 2 Fig.2 Fig.2 NNP cord-242132-fhepdgz9 88 3 the the DT cord-242132-fhepdgz9 88 4 blue blue JJ cord-242132-fhepdgz9 88 5 lines line NNS cord-242132-fhepdgz9 88 6 show show VBP cord-242132-fhepdgz9 88 7 the the DT cord-242132-fhepdgz9 88 8 numerical numerical JJ cord-242132-fhepdgz9 88 9 simulations simulation NNS cord-242132-fhepdgz9 88 10 ( ( -LRB- cord-242132-fhepdgz9 88 11 DMC DMC NNP cord-242132-fhepdgz9 88 12 ) ) -RRB- cord-242132-fhepdgz9 88 13 data datum NNS cord-242132-fhepdgz9 88 14 , , , cord-242132-fhepdgz9 88 15 while while IN cord-242132-fhepdgz9 88 16 the the DT cord-242132-fhepdgz9 88 17 red red JJ cord-242132-fhepdgz9 88 18 lines line NNS cord-242132-fhepdgz9 88 19 display display VBP cord-242132-fhepdgz9 88 20 the the DT cord-242132-fhepdgz9 88 21 fitting fitting JJ cord-242132-fhepdgz9 88 22 function function NN cord-242132-fhepdgz9 88 23 f f NNP cord-242132-fhepdgz9 88 24 ( ( -LRB- cord-242132-fhepdgz9 88 25 t t NN cord-242132-fhepdgz9 88 26 ) ) -RRB- cord-242132-fhepdgz9 88 27 . . . cord-242132-fhepdgz9 89 1 Fig.2 Fig.2 NNP cord-242132-fhepdgz9 90 1 ( ( -LRB- cord-242132-fhepdgz9 90 2 a a LS cord-242132-fhepdgz9 90 3 ) ) -RRB- cord-242132-fhepdgz9 90 4 shows show VBZ cord-242132-fhepdgz9 90 5 the the DT cord-242132-fhepdgz9 90 6 case case NN cord-242132-fhepdgz9 90 7 β β XX cord-242132-fhepdgz9 91 1 = = SYM cord-242132-fhepdgz9 91 2 0.99 0.99 CD cord-242132-fhepdgz9 91 3 , , , cord-242132-fhepdgz9 91 4 ( ( -LRB- cord-242132-fhepdgz9 91 5 b b NN cord-242132-fhepdgz9 91 6 ) ) -RRB- cord-242132-fhepdgz9 91 7 β β NN cord-242132-fhepdgz9 91 8 = = SYM cord-242132-fhepdgz9 91 9 0.90 0.90 CD cord-242132-fhepdgz9 91 10 , , , cord-242132-fhepdgz9 92 1 ( ( -LRB- cord-242132-fhepdgz9 92 2 c c NN cord-242132-fhepdgz9 92 3 ) ) -RRB- cord-242132-fhepdgz9 92 4 β β NN cord-242132-fhepdgz9 92 5 = = SYM cord-242132-fhepdgz9 92 6 0.80 0.80 CD cord-242132-fhepdgz9 92 7 , , , cord-242132-fhepdgz9 93 1 ( ( -LRB- cord-242132-fhepdgz9 93 2 d d NNP cord-242132-fhepdgz9 93 3 ) ) -RRB- cord-242132-fhepdgz9 93 4 β β NN cord-242132-fhepdgz9 93 5 = = SYM cord-242132-fhepdgz9 93 6 0.60 0.60 CD cord-242132-fhepdgz9 93 7 . . . cord-242132-fhepdgz9 94 1 We -PRON- PRP cord-242132-fhepdgz9 94 2 indicate indicate VBP cord-242132-fhepdgz9 94 3 a a DT cord-242132-fhepdgz9 94 4 remarkable remarkable JJ cord-242132-fhepdgz9 94 5 observation observation NN cord-242132-fhepdgz9 94 6 that that IN cord-242132-fhepdgz9 94 7 for for IN cord-242132-fhepdgz9 94 8 β β NN cord-242132-fhepdgz9 94 9 < < XX cord-242132-fhepdgz9 94 10 0.60 0.60 CD cord-242132-fhepdgz9 94 11 the the DT cord-242132-fhepdgz9 94 12 system system NN cord-242132-fhepdgz9 94 13 asymptotically asymptotically RB cord-242132-fhepdgz9 94 14 converges converge VBZ cord-242132-fhepdgz9 94 15 to to IN cord-242132-fhepdgz9 94 16 a a DT cord-242132-fhepdgz9 94 17 trivial trivial JJ cord-242132-fhepdgz9 94 18 solution solution NN cord-242132-fhepdgz9 94 19 with with IN cord-242132-fhepdgz9 94 20 A a DT cord-242132-fhepdgz9 94 21 a a DT cord-242132-fhepdgz9 94 22 0 0 CD cord-242132-fhepdgz9 94 23 = = SYM cord-242132-fhepdgz9 94 24 0 0 NFP cord-242132-fhepdgz9 94 25 already already RB cord-242132-fhepdgz9 94 26 for for IN cord-242132-fhepdgz9 94 27 t t NNP cord-242132-fhepdgz9 94 28 6 6 CD cord-242132-fhepdgz9 94 29 . . . cord-242132-fhepdgz9 95 1 Such such JJ cord-242132-fhepdgz9 95 2 observation observation NN cord-242132-fhepdgz9 95 3 leads lead VBZ cord-242132-fhepdgz9 95 4 to to IN cord-242132-fhepdgz9 95 5 an an DT cord-242132-fhepdgz9 95 6 interesting interesting JJ cord-242132-fhepdgz9 95 7 assumption assumption NN cord-242132-fhepdgz9 95 8 that that IN cord-242132-fhepdgz9 95 9 the the DT cord-242132-fhepdgz9 95 10 studied study VBN cord-242132-fhepdgz9 95 11 dynamics dynamic NNS cord-242132-fhepdgz9 95 12 of of IN cord-242132-fhepdgz9 95 13 the the DT cord-242132-fhepdgz9 95 14 infection infection NN cord-242132-fhepdgz9 95 15 spread spread NN cord-242132-fhepdgz9 95 16 can can MD cord-242132-fhepdgz9 95 17 ( ( -LRB- cord-242132-fhepdgz9 95 18 asymptotically asymptotically RB cord-242132-fhepdgz9 95 19 ) ) -RRB- cord-242132-fhepdgz9 95 20 be be VB cord-242132-fhepdgz9 95 21 associated associate VBN cord-242132-fhepdgz9 95 22 with with IN cord-242132-fhepdgz9 95 23 a a DT cord-242132-fhepdgz9 95 24 critical critical JJ cord-242132-fhepdgz9 95 25 transition transition NN cord-242132-fhepdgz9 95 26 in in IN cord-242132-fhepdgz9 95 27 the the DT cord-242132-fhepdgz9 95 28 two two CD cord-242132-fhepdgz9 95 29 - - HYPH cord-242132-fhepdgz9 95 30 dimensional dimensional JJ cord-242132-fhepdgz9 95 31 ( ( -LRB- cord-242132-fhepdgz9 95 32 2D 2D NNP cord-242132-fhepdgz9 95 33 ) ) -RRB- cord-242132-fhepdgz9 95 34 percolation percolation NN cord-242132-fhepdgz9 95 35 system system NN cord-242132-fhepdgz9 95 36 , , , cord-242132-fhepdgz9 95 37 that that DT cord-242132-fhepdgz9 95 38 occurs occur VBZ cord-242132-fhepdgz9 95 39 when when WRB cord-242132-fhepdgz9 95 40 the the DT cord-242132-fhepdgz9 95 41 occupation occupation NN cord-242132-fhepdgz9 95 42 probability probability NN cord-242132-fhepdgz9 95 43 of of IN cord-242132-fhepdgz9 95 44 defects defect NNS cord-242132-fhepdgz9 95 45 is be VBZ cord-242132-fhepdgz9 95 46 p p NN cord-242132-fhepdgz9 95 47 c c NN cord-242132-fhepdgz9 95 48 = = SYM cord-242132-fhepdgz9 95 49 0.594 0.594 CD cord-242132-fhepdgz9 95 50 12 12 CD cord-242132-fhepdgz9 95 51 , , , cord-242132-fhepdgz9 95 52 11 11 CD cord-242132-fhepdgz9 95 53 , , , cord-242132-fhepdgz9 95 54 13 13 CD cord-242132-fhepdgz9 95 55 , , , cord-242132-fhepdgz9 95 56 14 14 CD cord-242132-fhepdgz9 95 57 , , , cord-242132-fhepdgz9 95 58 15 15 CD cord-242132-fhepdgz9 95 59 see see VBP cord-242132-fhepdgz9 95 60 Fig.3 Fig.3 NNS cord-242132-fhepdgz9 95 61 . . . cord-242132-fhepdgz9 96 1 Such such PDT cord-242132-fhepdgz9 96 2 an an DT cord-242132-fhepdgz9 96 3 assumption assumption NN cord-242132-fhepdgz9 96 4 is be VBZ cord-242132-fhepdgz9 96 5 studied study VBN cord-242132-fhepdgz9 96 6 in in IN cord-242132-fhepdgz9 96 7 the the DT cord-242132-fhepdgz9 96 8 following follow VBG cord-242132-fhepdgz9 96 9 Section section NN cord-242132-fhepdgz9 96 10 . . . cord-242132-fhepdgz9 97 1 Fig Fig NNP cord-242132-fhepdgz9 97 2 . . . cord-242132-fhepdgz9 98 1 3 3 LS cord-242132-fhepdgz9 98 2 displays display VBZ cord-242132-fhepdgz9 98 3 a a DT cord-242132-fhepdgz9 98 4 comparison comparison NN cord-242132-fhepdgz9 98 5 of of IN cord-242132-fhepdgz9 98 6 above above RB cord-242132-fhepdgz9 98 7 mentioned mention VBN cord-242132-fhepdgz9 98 8 dependencies dependency NNS cord-242132-fhepdgz9 98 9 . . . cord-242132-fhepdgz9 99 1 In in IN cord-242132-fhepdgz9 99 2 Fig Fig NNP cord-242132-fhepdgz9 99 3 . . . cord-242132-fhepdgz9 100 1 3 3 LS cord-242132-fhepdgz9 101 1 the the DT cord-242132-fhepdgz9 101 2 red red JJ cord-242132-fhepdgz9 101 3 line line NN cord-242132-fhepdgz9 101 4 shows show VBZ cord-242132-fhepdgz9 101 5 the the DT cord-242132-fhepdgz9 101 6 dependence dependence NN cord-242132-fhepdgz9 102 1 a a LS cord-242132-fhepdgz9 102 2 0 0 CD cord-242132-fhepdgz9 102 3 ( ( -LRB- cord-242132-fhepdgz9 102 4 β β NN cord-242132-fhepdgz9 102 5 ) ) -RRB- cord-242132-fhepdgz9 102 6 ( ( -LRB- cord-242132-fhepdgz9 102 7 see see VB cord-242132-fhepdgz9 102 8 Fig.2 Fig.2 NNP cord-242132-fhepdgz9 102 9 ) ) -RRB- cord-242132-fhepdgz9 103 1 associated associate VBN cord-242132-fhepdgz9 103 2 with with IN cord-242132-fhepdgz9 103 3 the the DT cord-242132-fhepdgz9 103 4 infecting infect VBG cord-242132-fhepdgz9 103 5 parameter parameter NN cord-242132-fhepdgz9 103 6 A(β a(β NN cord-242132-fhepdgz9 103 7 ) ) -RRB- cord-242132-fhepdgz9 104 1 = = NFP cord-242132-fhepdgz9 105 1 I I NNP cord-242132-fhepdgz9 105 2 / / SYM cord-242132-fhepdgz9 105 3 N N NNP cord-242132-fhepdgz9 105 4 , , , cord-242132-fhepdgz9 105 5 and and CC cord-242132-fhepdgz9 105 6 the the DT cord-242132-fhepdgz9 105 7 blue blue JJ cord-242132-fhepdgz9 105 8 line line NN cord-242132-fhepdgz9 105 9 shows show VBZ cord-242132-fhepdgz9 105 10 the the DT cord-242132-fhepdgz9 105 11 percolating percolate VBG cord-242132-fhepdgz9 105 12 order order NN cord-242132-fhepdgz9 105 13 parameters parameter NNS cord-242132-fhepdgz9 105 14 P p NN cord-242132-fhepdgz9 105 15 ( ( -LRB- cord-242132-fhepdgz9 105 16 p p NN cord-242132-fhepdgz9 105 17 ) ) -RRB- cord-242132-fhepdgz9 105 18 as as IN cord-242132-fhepdgz9 105 19 function function NN cord-242132-fhepdgz9 105 20 of of IN cord-242132-fhepdgz9 105 21 the the DT cord-242132-fhepdgz9 105 22 occupation occupation NN cord-242132-fhepdgz9 105 23 defect defect NN cord-242132-fhepdgz9 105 24 probability probability NN cord-242132-fhepdgz9 105 25 p. p. NN cord-242132-fhepdgz9 106 1 We -PRON- PRP cord-242132-fhepdgz9 106 2 observe observe VBP cord-242132-fhepdgz9 106 3 that that IN cord-242132-fhepdgz9 106 4 both both DT cord-242132-fhepdgz9 106 5 dependencies dependency NNS cord-242132-fhepdgz9 106 6 are be VBP cord-242132-fhepdgz9 106 7 in in IN cord-242132-fhepdgz9 106 8 excellent excellent JJ cord-242132-fhepdgz9 106 9 agreement agreement NN cord-242132-fhepdgz9 106 10 and and CC cord-242132-fhepdgz9 106 11 at at IN cord-242132-fhepdgz9 106 12 β β NNP cord-242132-fhepdgz9 106 13 c c NN cord-242132-fhepdgz9 106 14 p p NN cord-242132-fhepdgz9 106 15 c c NN cord-242132-fhepdgz9 106 16 0.6 0.6 CD cord-242132-fhepdgz9 106 17 the the DT cord-242132-fhepdgz9 106 18 phase phase NN cord-242132-fhepdgz9 106 19 transition transition NN cord-242132-fhepdgz9 106 20 to to IN cord-242132-fhepdgz9 106 21 infected infect VBN cord-242132-fhepdgz9 106 22 / / SYM cord-242132-fhepdgz9 106 23 percolating percolate VBG cord-242132-fhepdgz9 106 24 state state NN cord-242132-fhepdgz9 106 25 occurs occur VBZ cord-242132-fhepdgz9 106 26 . . . cord-242132-fhepdgz9 107 1 From from IN cord-242132-fhepdgz9 107 2 Fig Fig NNP cord-242132-fhepdgz9 107 3 . . . cord-242132-fhepdgz9 108 1 3 3 LS cord-242132-fhepdgz9 108 2 we -PRON- PRP cord-242132-fhepdgz9 108 3 can can MD cord-242132-fhepdgz9 108 4 assume assume VB cord-242132-fhepdgz9 108 5 that that IN cord-242132-fhepdgz9 108 6 the the DT cord-242132-fhepdgz9 108 7 parameter parameter NN cord-242132-fhepdgz9 108 8 A(β a(β NN cord-242132-fhepdgz9 108 9 ) ) -RRB- cord-242132-fhepdgz9 108 10 can can MD cord-242132-fhepdgz9 108 11 be be VB cord-242132-fhepdgz9 108 12 mentioned mention VBN cord-242132-fhepdgz9 108 13 further further RB cord-242132-fhepdgz9 108 14 as as IN cord-242132-fhepdgz9 108 15 an an DT cord-242132-fhepdgz9 108 16 order order NN cord-242132-fhepdgz9 108 17 parameter parameter NN cord-242132-fhepdgz9 108 18 ( ( -LRB- cord-242132-fhepdgz9 108 19 similarly similarly RB cord-242132-fhepdgz9 108 20 P p NN cord-242132-fhepdgz9 108 21 ( ( -LRB- cord-242132-fhepdgz9 108 22 p p NN cord-242132-fhepdgz9 108 23 ) ) -RRB- cord-242132-fhepdgz9 108 24 ) ) -RRB- cord-242132-fhepdgz9 108 25 . . . cord-242132-fhepdgz9 109 1 This this DT cord-242132-fhepdgz9 109 2 results result VBZ cord-242132-fhepdgz9 109 3 that that IN cord-242132-fhepdgz9 109 4 the the DT cord-242132-fhepdgz9 109 5 formalism formalism NN cord-242132-fhepdgz9 109 6 of of IN cord-242132-fhepdgz9 109 7 the the DT cord-242132-fhepdgz9 109 8 percolation percolation NN cord-242132-fhepdgz9 109 9 critical critical JJ cord-242132-fhepdgz9 109 10 percolating percolate VBG cord-242132-fhepdgz9 109 11 phase phase NN cord-242132-fhepdgz9 109 12 transition transition NN cord-242132-fhepdgz9 109 13 12 12 CD cord-242132-fhepdgz9 109 14 , , , cord-242132-fhepdgz9 109 15 11 11 CD cord-242132-fhepdgz9 109 16 , , , cord-242132-fhepdgz9 109 17 13 13 CD cord-242132-fhepdgz9 109 18 can can MD cord-242132-fhepdgz9 109 19 be be VB cord-242132-fhepdgz9 109 20 applied apply VBN cord-242132-fhepdgz9 109 21 to to IN cord-242132-fhepdgz9 109 22 investigation investigation NN cord-242132-fhepdgz9 109 23 the the DT cord-242132-fhepdgz9 109 24 asymptotic asymptotic JJ cord-242132-fhepdgz9 109 25 of of IN cord-242132-fhepdgz9 109 26 infection infection NN cord-242132-fhepdgz9 109 27 spreading spread VBG cord-242132-fhepdgz9 109 28 at at IN cord-242132-fhepdgz9 109 29 11 11 CD cord-242132-fhepdgz9 109 30 . . . cord-242132-fhepdgz9 110 1 Red red JJ cord-242132-fhepdgz9 110 2 line line NN cord-242132-fhepdgz9 110 3 shows show VBZ cord-242132-fhepdgz9 110 4 the the DT cord-242132-fhepdgz9 110 5 dependence dependence NN cord-242132-fhepdgz9 110 6 of of IN cord-242132-fhepdgz9 110 7 ( ( -LRB- cord-242132-fhepdgz9 110 8 slightly slightly RB cord-242132-fhepdgz9 110 9 tailored tailor VBN cord-242132-fhepdgz9 110 10 ) ) -RRB- cord-242132-fhepdgz9 110 11 amplitude amplitude NN cord-242132-fhepdgz9 110 12 parameter parameter NN cord-242132-fhepdgz9 110 13 the the DT cord-242132-fhepdgz9 110 14 fitting fitting JJ cord-242132-fhepdgz9 110 15 function function NN cord-242132-fhepdgz9 111 1 a0 a0 NNP cord-242132-fhepdgz9 111 2 corresponding correspond VBG cord-242132-fhepdgz9 111 3 to to IN cord-242132-fhepdgz9 111 4 A a NN cord-242132-fhepdgz9 112 1 = = NFP cord-242132-fhepdgz9 112 2 I I NNP cord-242132-fhepdgz9 112 3 / / SYM cord-242132-fhepdgz9 112 4 N n CC cord-242132-fhepdgz9 112 5 at at IN cord-242132-fhepdgz9 112 6 fixed fix VBN cord-242132-fhepdgz9 112 7 time time NN cord-242132-fhepdgz9 112 8 t t NN cord-242132-fhepdgz9 112 9 = = SYM cord-242132-fhepdgz9 112 10 8 8 CD cord-242132-fhepdgz9 113 1 as as IN cord-242132-fhepdgz9 113 2 function function NN cord-242132-fhepdgz9 113 3 of of IN cord-242132-fhepdgz9 113 4 the the DT cord-242132-fhepdgz9 113 5 risk risk NN cord-242132-fhepdgz9 113 6 factor factor NN cord-242132-fhepdgz9 113 7 β β NNP cord-242132-fhepdgz9 113 8 . . . cord-242132-fhepdgz9 114 1 Blue blue JJ cord-242132-fhepdgz9 114 2 line line NN cord-242132-fhepdgz9 114 3 shows show VBZ cord-242132-fhepdgz9 114 4 the the DT cord-242132-fhepdgz9 114 5 dependence dependence NN cord-242132-fhepdgz9 114 6 of of IN cord-242132-fhepdgz9 114 7 the the DT cord-242132-fhepdgz9 114 8 order order NN cord-242132-fhepdgz9 114 9 parameters parameter VBZ cord-242132-fhepdgz9 114 10 P p NN cord-242132-fhepdgz9 114 11 ( ( -LRB- cord-242132-fhepdgz9 114 12 p p NN cord-242132-fhepdgz9 114 13 ) ) -RRB- cord-242132-fhepdgz9 114 14 for for IN cord-242132-fhepdgz9 114 15 2D 2D NNP cord-242132-fhepdgz9 114 16 percolating percolate VBG cord-242132-fhepdgz9 114 17 material material NN cord-242132-fhepdgz9 114 18 as as IN cord-242132-fhepdgz9 114 19 function function NN cord-242132-fhepdgz9 114 20 of of IN cord-242132-fhepdgz9 114 21 the the DT cord-242132-fhepdgz9 114 22 occupation occupation NN cord-242132-fhepdgz9 114 23 probability probability NN cord-242132-fhepdgz9 115 1 p. p. NN cord-242132-fhepdgz9 116 1 We -PRON- PRP cord-242132-fhepdgz9 116 2 observe observe VBP cord-242132-fhepdgz9 116 3 that that IN cord-242132-fhepdgz9 116 4 both both DT cord-242132-fhepdgz9 116 5 curves curve NNS cord-242132-fhepdgz9 116 6 are be VBP cord-242132-fhepdgz9 116 7 very very RB cord-242132-fhepdgz9 116 8 close close JJ cord-242132-fhepdgz9 116 9 and and CC cord-242132-fhepdgz9 116 10 the the DT cord-242132-fhepdgz9 116 11 phase phase NN cord-242132-fhepdgz9 116 12 transitions transition NNS cord-242132-fhepdgz9 116 13 to to IN cord-242132-fhepdgz9 116 14 infected infect VBN cord-242132-fhepdgz9 116 15 / / SYM cord-242132-fhepdgz9 116 16 percolating percolate VBG cord-242132-fhepdgz9 116 17 state state NN cord-242132-fhepdgz9 116 18 occurs occur VBZ cord-242132-fhepdgz9 116 19 similarly similarly RB cord-242132-fhepdgz9 116 20 at at IN cord-242132-fhepdgz9 116 21 βc βc XX cord-242132-fhepdgz9 116 22 pc pc NN cord-242132-fhepdgz9 116 23 0.6 0.6 CD cord-242132-fhepdgz9 116 24 for for IN cord-242132-fhepdgz9 116 25 both both DT cord-242132-fhepdgz9 116 26 cases case NNS cord-242132-fhepdgz9 116 27 . . . cord-242132-fhepdgz9 117 1 various various JJ cord-242132-fhepdgz9 117 2 β β XX cord-242132-fhepdgz9 117 3 . . . cord-242132-fhepdgz9 118 1 On on IN cord-242132-fhepdgz9 118 2 the the DT cord-242132-fhepdgz9 118 3 other other JJ cord-242132-fhepdgz9 118 4 hand hand NN cord-242132-fhepdgz9 118 5 , , , cord-242132-fhepdgz9 118 6 good good JJ cord-242132-fhepdgz9 118 7 agreement agreement NN cord-242132-fhepdgz9 118 8 between between IN cord-242132-fhepdgz9 118 9 the the DT cord-242132-fhepdgz9 118 10 results result NNS cord-242132-fhepdgz9 118 11 of of IN cord-242132-fhepdgz9 118 12 DMC DMC NNP cord-242132-fhepdgz9 118 13 modeling modeling NN cord-242132-fhepdgz9 118 14 and and CC cord-242132-fhepdgz9 118 15 the the DT cord-242132-fhepdgz9 118 16 critical critical JJ cord-242132-fhepdgz9 118 17 transition transition NN cord-242132-fhepdgz9 118 18 in in IN cord-242132-fhepdgz9 118 19 2D 2D NNP cord-242132-fhepdgz9 118 20 percolation percolation NN cord-242132-fhepdgz9 118 21 system system NN cord-242132-fhepdgz9 118 22 shows show VBZ cord-242132-fhepdgz9 118 23 the the DT cord-242132-fhepdgz9 118 24 general general JJ cord-242132-fhepdgz9 118 25 applicability applicability NN cord-242132-fhepdgz9 118 26 of of IN cord-242132-fhepdgz9 118 27 DMC DMC NNP cord-242132-fhepdgz9 118 28 approach approach NN cord-242132-fhepdgz9 118 29 to to TO cord-242132-fhepdgz9 118 30 analyze analyze VB cord-242132-fhepdgz9 118 31 the the DT cord-242132-fhepdgz9 118 32 dynamics dynamic NNS cord-242132-fhepdgz9 118 33 of of IN cord-242132-fhepdgz9 118 34 infection infection NN cord-242132-fhepdgz9 118 35 spread spread VBD cord-242132-fhepdgz9 118 36 in in IN cord-242132-fhepdgz9 118 37 the the DT cord-242132-fhepdgz9 118 38 epidemiological epidemiological JJ cord-242132-fhepdgz9 118 39 system system NN cord-242132-fhepdgz9 118 40 . . . cord-242132-fhepdgz9 119 1 Fig Fig NNP cord-242132-fhepdgz9 119 2 . . . cord-242132-fhepdgz9 120 1 1 1 CD cord-242132-fhepdgz9 120 2 is be VBZ cord-242132-fhepdgz9 120 3 an an DT cord-242132-fhepdgz9 120 4 extremely extremely RB cord-242132-fhepdgz9 120 5 dangerous dangerous JJ cord-242132-fhepdgz9 120 6 and and CC cord-242132-fhepdgz9 120 7 highly highly RB cord-242132-fhepdgz9 120 8 undesirable undesirable JJ cord-242132-fhepdgz9 120 9 scenario scenario NN cord-242132-fhepdgz9 120 10 for for IN cord-242132-fhepdgz9 120 11 the the DT cord-242132-fhepdgz9 120 12 development development NN cord-242132-fhepdgz9 120 13 of of IN cord-242132-fhepdgz9 120 14 epidemiological epidemiological JJ cord-242132-fhepdgz9 120 15 situation situation NN cord-242132-fhepdgz9 120 16 . . . cord-242132-fhepdgz9 121 1 This this DT cord-242132-fhepdgz9 121 2 Section section NN cord-242132-fhepdgz9 121 3 discusses discuss VBZ cord-242132-fhepdgz9 121 4 the the DT cord-242132-fhepdgz9 121 5 extension extension NN cord-242132-fhepdgz9 121 6 of of IN cord-242132-fhepdgz9 121 7 the the DT cord-242132-fhepdgz9 121 8 model model NN cord-242132-fhepdgz9 121 9 , , , cord-242132-fhepdgz9 121 10 which which WDT cord-242132-fhepdgz9 121 11 in in IN cord-242132-fhepdgz9 121 12 principle principle NN cord-242132-fhepdgz9 121 13 allows allow VBZ cord-242132-fhepdgz9 121 14 suspending suspend VBG cord-242132-fhepdgz9 121 15 this this DT cord-242132-fhepdgz9 121 16 trend trend NN cord-242132-fhepdgz9 121 17 . . . cord-242132-fhepdgz9 122 1 One one CD cord-242132-fhepdgz9 122 2 of of IN cord-242132-fhepdgz9 122 3 the the DT cord-242132-fhepdgz9 122 4 simple simple JJ cord-242132-fhepdgz9 122 5 solutions solution NNS cord-242132-fhepdgz9 122 6 proposed propose VBN cord-242132-fhepdgz9 122 7 recently recently RB cord-242132-fhepdgz9 122 8 is be VBZ cord-242132-fhepdgz9 122 9 introducing introduce VBG cord-242132-fhepdgz9 122 10 the the DT cord-242132-fhepdgz9 122 11 quarantine quarantine NN cord-242132-fhepdgz9 122 12 by by IN cord-242132-fhepdgz9 122 13 localizing localize VBG cord-242132-fhepdgz9 122 14 of of IN cord-242132-fhepdgz9 122 15 infected infected JJ cord-242132-fhepdgz9 122 16 individuals individual NNS cord-242132-fhepdgz9 122 17 in in IN cord-242132-fhepdgz9 122 18 order order NN cord-242132-fhepdgz9 122 19 to to TO cord-242132-fhepdgz9 122 20 significantly significantly RB cord-242132-fhepdgz9 122 21 reduce reduce VB cord-242132-fhepdgz9 122 22 the the DT cord-242132-fhepdgz9 122 23 number number NN cord-242132-fhepdgz9 122 24 of of IN cord-242132-fhepdgz9 122 25 contacts contact NNS cord-242132-fhepdgz9 122 26 that that WDT cord-242132-fhepdgz9 122 27 leads lead VBZ cord-242132-fhepdgz9 122 28 to to IN cord-242132-fhepdgz9 122 29 the the DT cord-242132-fhepdgz9 122 30 transmission transmission NN cord-242132-fhepdgz9 122 31 of of IN cord-242132-fhepdgz9 122 32 infection infection NN cord-242132-fhepdgz9 122 33 . . . cord-242132-fhepdgz9 123 1 This this DT cord-242132-fhepdgz9 123 2 can can MD cord-242132-fhepdgz9 123 3 be be VB cord-242132-fhepdgz9 123 4 modeled model VBN cord-242132-fhepdgz9 123 5 by by IN cord-242132-fhepdgz9 123 6 setting set VBG cord-242132-fhepdgz9 123 7 v v NN cord-242132-fhepdgz9 124 1 x x LS cord-242132-fhepdgz9 124 2 = = SYM cord-242132-fhepdgz9 124 3 v v NN cord-242132-fhepdgz9 125 1 y y NNP cord-242132-fhepdgz9 126 1 = = SYM cord-242132-fhepdgz9 126 2 0 0 CD cord-242132-fhepdgz9 126 3 for for IN cord-242132-fhepdgz9 126 4 infected infected JJ cord-242132-fhepdgz9 126 5 individuals individual NNS cord-242132-fhepdgz9 126 6 and and CC cord-242132-fhepdgz9 126 7 ignoring ignore VBG cord-242132-fhepdgz9 126 8 all all PDT cord-242132-fhepdgz9 126 9 the the DT cord-242132-fhepdgz9 126 10 contacts contact NNS cord-242132-fhepdgz9 126 11 with with IN cord-242132-fhepdgz9 126 12 them -PRON- PRP cord-242132-fhepdgz9 126 13 in in IN cord-242132-fhepdgz9 126 14 our -PRON- PRP$ cord-242132-fhepdgz9 126 15 approach approach NN cord-242132-fhepdgz9 126 16 . . . cord-242132-fhepdgz9 127 1 We -PRON- PRP cord-242132-fhepdgz9 127 2 call call VBP cord-242132-fhepdgz9 127 3 such such PDT cord-242132-fhepdgz9 127 4 a a DT cord-242132-fhepdgz9 127 5 regime regime NN cord-242132-fhepdgz9 127 6 of of IN cord-242132-fhepdgz9 127 7 simulation simulation NN cord-242132-fhepdgz9 127 8 as as IN cord-242132-fhepdgz9 127 9 a a DT cord-242132-fhepdgz9 127 10 quarantine quarantine NN cord-242132-fhepdgz9 127 11 mode mode NN cord-242132-fhepdgz9 127 12 . . . cord-242132-fhepdgz9 128 1 In in IN cord-242132-fhepdgz9 128 2 order order NN cord-242132-fhepdgz9 128 3 to to TO cord-242132-fhepdgz9 128 4 do do VB cord-242132-fhepdgz9 128 5 this this DT cord-242132-fhepdgz9 128 6 we -PRON- PRP cord-242132-fhepdgz9 128 7 introduce introduce VBP cord-242132-fhepdgz9 128 8 two two CD cord-242132-fhepdgz9 128 9 new new JJ cord-242132-fhepdgz9 128 10 parameters parameter NNS cord-242132-fhepdgz9 128 11 into into IN cord-242132-fhepdgz9 128 12 the the DT cord-242132-fhepdgz9 128 13 model model NN cord-242132-fhepdgz9 128 14 , , , cord-242132-fhepdgz9 128 15 A a DT cord-242132-fhepdgz9 128 16 max max NN cord-242132-fhepdgz9 128 17 ( ( -LRB- cord-242132-fhepdgz9 128 18 the the DT cord-242132-fhepdgz9 128 19 infection infection NN cord-242132-fhepdgz9 128 20 level level NN cord-242132-fhepdgz9 128 21 when when WRB cord-242132-fhepdgz9 128 22 the the DT cord-242132-fhepdgz9 128 23 quarantine quarantine NN cord-242132-fhepdgz9 128 24 is be VBZ cord-242132-fhepdgz9 128 25 automatically automatically RB cord-242132-fhepdgz9 128 26 turned turn VBN cord-242132-fhepdgz9 128 27 on on RP cord-242132-fhepdgz9 128 28 ) ) -RRB- cord-242132-fhepdgz9 128 29 , , , cord-242132-fhepdgz9 128 30 and and CC cord-242132-fhepdgz9 128 31 A a DT cord-242132-fhepdgz9 128 32 min min NN cord-242132-fhepdgz9 128 33 ( ( -LRB- cord-242132-fhepdgz9 128 34 the the DT cord-242132-fhepdgz9 128 35 infection infection NN cord-242132-fhepdgz9 128 36 level level NN cord-242132-fhepdgz9 128 37 when when WRB cord-242132-fhepdgz9 128 38 the the DT cord-242132-fhepdgz9 128 39 quarantine quarantine NN cord-242132-fhepdgz9 128 40 is be VBZ cord-242132-fhepdgz9 128 41 turned turn VBN cord-242132-fhepdgz9 128 42 off off RP cord-242132-fhepdgz9 128 43 ) ) -RRB- cord-242132-fhepdgz9 128 44 . . . cord-242132-fhepdgz9 129 1 Fig.4 Fig.4 NNP cord-242132-fhepdgz9 129 2 we -PRON- PRP cord-242132-fhepdgz9 129 3 observe observe VBP cord-242132-fhepdgz9 129 4 that that IN cord-242132-fhepdgz9 129 5 the the DT cord-242132-fhepdgz9 129 6 system system NN cord-242132-fhepdgz9 129 7 transmits transmit VBZ cord-242132-fhepdgz9 129 8 to to IN cord-242132-fhepdgz9 129 9 unexpected unexpected JJ cord-242132-fhepdgz9 129 10 dynamic dynamic JJ cord-242132-fhepdgz9 129 11 state state NN cord-242132-fhepdgz9 129 12 : : : cord-242132-fhepdgz9 129 13 the the DT cord-242132-fhepdgz9 129 14 generation generation NN cord-242132-fhepdgz9 129 15 of of IN cord-242132-fhepdgz9 129 16 irregular irregular JJ cord-242132-fhepdgz9 129 17 oscillations oscillation NNS cord-242132-fhepdgz9 129 18 of of IN cord-242132-fhepdgz9 129 19 A a DT cord-242132-fhepdgz9 129 20 with with IN cord-242132-fhepdgz9 129 21 large large JJ cord-242132-fhepdgz9 129 22 amplitudes amplitude NNS cord-242132-fhepdgz9 129 23 between between IN cord-242132-fhepdgz9 129 24 A a DT cord-242132-fhepdgz9 129 25 max max NN cord-242132-fhepdgz9 129 26 and and CC cord-242132-fhepdgz9 129 27 A a DT cord-242132-fhepdgz9 129 28 min min NN cord-242132-fhepdgz9 129 29 . . . cord-242132-fhepdgz9 130 1 We -PRON- PRP cord-242132-fhepdgz9 130 2 have have VBP cord-242132-fhepdgz9 130 3 calculated calculate VBN cord-242132-fhepdgz9 130 4 ( ( -LRB- cord-242132-fhepdgz9 130 5 by by IN cord-242132-fhepdgz9 130 6 the the DT cord-242132-fhepdgz9 130 7 method method NN cord-242132-fhepdgz9 130 8 16 16 CD cord-242132-fhepdgz9 130 9 ) ) -RRB- cord-242132-fhepdgz9 130 10 that that IN cord-242132-fhepdgz9 130 11 the the DT cord-242132-fhepdgz9 130 12 Lyapunov Lyapunov NNP cord-242132-fhepdgz9 130 13 exponent exponent NN cord-242132-fhepdgz9 130 14 for for IN cord-242132-fhepdgz9 130 15 such such JJ cord-242132-fhepdgz9 130 16 irregular irregular JJ cord-242132-fhepdgz9 130 17 oscillations oscillation NNS cord-242132-fhepdgz9 130 18 is be VBZ cord-242132-fhepdgz9 130 19 about about RB cord-242132-fhepdgz9 130 20 0.3 0.3 CD cord-242132-fhepdgz9 130 21 . . . cord-242132-fhepdgz9 131 1 This this DT cord-242132-fhepdgz9 131 2 means mean VBZ cord-242132-fhepdgz9 131 3 that that IN cord-242132-fhepdgz9 131 4 if if IN cord-242132-fhepdgz9 131 5 quarantine quarantine NN cord-242132-fhepdgz9 131 6 is be VBZ cord-242132-fhepdgz9 131 7 turned turn VBN cord-242132-fhepdgz9 131 8 off off RP cord-242132-fhepdgz9 131 9 too too RB cord-242132-fhepdgz9 131 10 early early RB cord-242132-fhepdgz9 131 11 , , , cord-242132-fhepdgz9 131 12 the the DT cord-242132-fhepdgz9 131 13 growth growth NN cord-242132-fhepdgz9 131 14 of of IN cord-242132-fhepdgz9 131 15 infections infection NNS cord-242132-fhepdgz9 131 16 suppressed suppress VBN cord-242132-fhepdgz9 131 17 , , , cord-242132-fhepdgz9 131 18 but but CC cord-242132-fhepdgz9 131 19 the the DT cord-242132-fhepdgz9 131 20 system system NN cord-242132-fhepdgz9 131 21 goes go VBZ cord-242132-fhepdgz9 131 22 into into IN cord-242132-fhepdgz9 131 23 dynamic dynamic JJ cord-242132-fhepdgz9 131 24 mode mode NN cord-242132-fhepdgz9 131 25 with with IN cord-242132-fhepdgz9 131 26 irregular irregular JJ cord-242132-fhepdgz9 131 27 oscillations oscillation NNS cord-242132-fhepdgz9 131 28 . . . cord-242132-fhepdgz9 132 1 In in IN cord-242132-fhepdgz9 132 2 this this DT cord-242132-fhepdgz9 132 3 case case NN cord-242132-fhepdgz9 132 4 , , , cord-242132-fhepdgz9 132 5 a a DT cord-242132-fhepdgz9 132 6 significant significant JJ cord-242132-fhepdgz9 132 7 number number NN cord-242132-fhepdgz9 132 8 of of IN cord-242132-fhepdgz9 132 9 infected infected JJ cord-242132-fhepdgz9 132 10 and and CC cord-242132-fhepdgz9 132 11 recovered recover VBN cord-242132-fhepdgz9 132 12 individuals individual NNS cord-242132-fhepdgz9 132 13 can can MD cord-242132-fhepdgz9 132 14 be be VB cord-242132-fhepdgz9 132 15 re re VBN cord-242132-fhepdgz9 132 16 - - VBN cord-242132-fhepdgz9 132 17 infected infect VBN cord-242132-fhepdgz9 132 18 , , , cord-242132-fhepdgz9 132 19 therefore therefore RB cord-242132-fhepdgz9 132 20 , , , cord-242132-fhepdgz9 132 21 a a DT cord-242132-fhepdgz9 132 22 full full JJ cord-242132-fhepdgz9 132 23 recovery recovery NN cord-242132-fhepdgz9 132 24 does do VBZ cord-242132-fhepdgz9 132 25 not not RB cord-242132-fhepdgz9 132 26 occur occur VB cord-242132-fhepdgz9 132 27 . . . cord-242132-fhepdgz9 133 1 Fig.5 Fig.5 NNP cord-242132-fhepdgz9 133 2 shows show VBZ cord-242132-fhepdgz9 133 3 the the DT cord-242132-fhepdgz9 133 4 infections infection NNS cord-242132-fhepdgz9 133 5 dynamics dynamic NNS cord-242132-fhepdgz9 133 6 A(t A(t NNP cord-242132-fhepdgz9 133 7 ) ) -RRB- cord-242132-fhepdgz9 133 8 in in IN cord-242132-fhepdgz9 133 9 the the DT cord-242132-fhepdgz9 133 10 quarantine quarantine NN cord-242132-fhepdgz9 133 11 mode mode NN cord-242132-fhepdgz9 133 12 but but CC cord-242132-fhepdgz9 134 1 for for IN cord-242132-fhepdgz9 134 2 large large JJ cord-242132-fhepdgz9 134 3 the the DT cord-242132-fhepdgz9 134 4 risk risk NN cord-242132-fhepdgz9 134 5 factors factor NNS cord-242132-fhepdgz9 134 6 β β NNP cord-242132-fhepdgz9 134 7 : : : cord-242132-fhepdgz9 134 8 ( ( -LRB- cord-242132-fhepdgz9 134 9 a a LS cord-242132-fhepdgz9 134 10 ) ) -RRB- cord-242132-fhepdgz9 134 11 β β NN cord-242132-fhepdgz9 134 12 = = SYM cord-242132-fhepdgz9 134 13 0.88 0.88 CD cord-242132-fhepdgz9 134 14 , , , cord-242132-fhepdgz9 135 1 ( ( -LRB- cord-242132-fhepdgz9 135 2 b b NN cord-242132-fhepdgz9 135 3 ) ) -RRB- cord-242132-fhepdgz9 135 4 β β NN cord-242132-fhepdgz9 135 5 = = SYM cord-242132-fhepdgz9 135 6 0.90 0.90 CD cord-242132-fhepdgz9 135 7 , , , cord-242132-fhepdgz9 136 1 ( ( -LRB- cord-242132-fhepdgz9 136 2 c c NN cord-242132-fhepdgz9 136 3 ) ) -RRB- cord-242132-fhepdgz9 136 4 β β NN cord-242132-fhepdgz9 136 5 = = SYM cord-242132-fhepdgz9 136 6 0.92 0.92 CD cord-242132-fhepdgz9 137 1 , , , cord-242132-fhepdgz9 137 2 ( ( -LRB- cord-242132-fhepdgz9 137 3 d d NN cord-242132-fhepdgz9 137 4 ) ) -RRB- cord-242132-fhepdgz9 137 5 β β NN cord-242132-fhepdgz9 137 6 = = SYM cord-242132-fhepdgz9 137 7 0.88 0.88 CD cord-242132-fhepdgz9 137 8 . . . cord-242132-fhepdgz9 138 1 We -PRON- PRP cord-242132-fhepdgz9 138 2 observe observe VBP cord-242132-fhepdgz9 138 3 that that IN cord-242132-fhepdgz9 138 4 for for IN cord-242132-fhepdgz9 138 5 large large JJ cord-242132-fhepdgz9 138 6 β β NN cord-242132-fhepdgz9 138 7 the the DT cord-242132-fhepdgz9 138 8 evolution evolution NN cord-242132-fhepdgz9 138 9 of of IN cord-242132-fhepdgz9 138 10 the the DT cord-242132-fhepdgz9 138 11 infections infection NNS cord-242132-fhepdgz9 138 12 has have VBZ cord-242132-fhepdgz9 138 13 monotonic monotonic JJ cord-242132-fhepdgz9 138 14 shape shape NN cord-242132-fhepdgz9 138 15 ( ( -LRB- cord-242132-fhepdgz9 138 16 with with IN cord-242132-fhepdgz9 138 17 small small JJ cord-242132-fhepdgz9 138 18 random random JJ cord-242132-fhepdgz9 138 19 variations variation NNS cord-242132-fhepdgz9 138 20 ) ) -RRB- cord-242132-fhepdgz9 139 1 but but CC cord-242132-fhepdgz9 139 2 without without IN cord-242132-fhepdgz9 139 3 the the DT cord-242132-fhepdgz9 139 4 oscillations oscillation NNS cord-242132-fhepdgz9 139 5 as as IN cord-242132-fhepdgz9 139 6 in in IN cord-242132-fhepdgz9 139 7 Fig.4 Fig.4 NNP cord-242132-fhepdgz9 139 8 . . . cord-242132-fhepdgz9 140 1 However however RB cord-242132-fhepdgz9 140 2 the the DT cord-242132-fhepdgz9 140 3 dynamics dynamic NNS cord-242132-fhepdgz9 140 4 A(t A(t NNP cord-242132-fhepdgz9 140 5 ) ) -RRB- cord-242132-fhepdgz9 140 6 in in IN cord-242132-fhepdgz9 140 7 ( ( -LRB- cord-242132-fhepdgz9 140 8 b b NN cord-242132-fhepdgz9 140 9 ) ) -RRB- cord-242132-fhepdgz9 140 10 for for IN cord-242132-fhepdgz9 140 11 β β NN cord-242132-fhepdgz9 141 1 = = SYM cord-242132-fhepdgz9 141 2 0.90 0.90 CD cord-242132-fhepdgz9 141 3 is be VBZ cord-242132-fhepdgz9 141 4 already already RB cord-242132-fhepdgz9 141 5 suppressed suppress VBN cord-242132-fhepdgz9 141 6 and and CC cord-242132-fhepdgz9 141 7 strongly strongly RB cord-242132-fhepdgz9 141 8 differs differ VBZ cord-242132-fhepdgz9 141 9 with with IN cord-242132-fhepdgz9 141 10 respect respect NN cord-242132-fhepdgz9 141 11 to to IN cord-242132-fhepdgz9 141 12 a a DT cord-242132-fhepdgz9 141 13 case case NN cord-242132-fhepdgz9 141 14 without without IN cord-242132-fhepdgz9 141 15 the the DT cord-242132-fhepdgz9 141 16 quarantine quarantine NN cord-242132-fhepdgz9 141 17 shown show VBN cord-242132-fhepdgz9 141 18 in in IN cord-242132-fhepdgz9 141 19 Fig.2 Fig.2 NNP cord-242132-fhepdgz9 141 20 ( ( -LRB- cord-242132-fhepdgz9 141 21 b b NN cord-242132-fhepdgz9 141 22 ) ) -RRB- cord-242132-fhepdgz9 141 23 . . . cord-242132-fhepdgz9 142 1 Although although IN cord-242132-fhepdgz9 142 2 actually actually RB cord-242132-fhepdgz9 142 3 there there EX cord-242132-fhepdgz9 142 4 are be VBP cord-242132-fhepdgz9 142 5 no no DT cord-242132-fhepdgz9 142 6 reliable reliable JJ cord-242132-fhepdgz9 142 7 statistics statistic NNS cord-242132-fhepdgz9 142 8 for for IN cord-242132-fhepdgz9 142 9 the the DT cord-242132-fhepdgz9 142 10 congenital congenital JJ cord-242132-fhepdgz9 142 11 or or CC cord-242132-fhepdgz9 142 12 acquired acquire VBN cord-242132-fhepdgz9 142 13 immunity immunity NN cord-242132-fhepdgz9 142 14 for for IN cord-242132-fhepdgz9 142 15 persons person NNS cord-242132-fhepdgz9 142 16 ( ( -LRB- cord-242132-fhepdgz9 142 17 for for IN cord-242132-fhepdgz9 142 18 animals animal NNS cord-242132-fhepdgz9 142 19 see see VBP cord-242132-fhepdgz9 142 20 Ref Ref NNP cord-242132-fhepdgz9 142 21 . . . cord-242132-fhepdgz9 143 1 17 17 LS cord-242132-fhepdgz9 143 2 ) ) -RRB- cord-242132-fhepdgz9 143 3 , , , cord-242132-fhepdgz9 143 4 in in IN cord-242132-fhepdgz9 143 5 this this DT cord-242132-fhepdgz9 143 6 Section section NN cord-242132-fhepdgz9 143 7 we -PRON- PRP cord-242132-fhepdgz9 143 8 analyze analyze VBP cord-242132-fhepdgz9 143 9 this this DT cord-242132-fhepdgz9 143 10 aspect aspect NN cord-242132-fhepdgz9 144 1 We -PRON- PRP cord-242132-fhepdgz9 144 2 observe observe VBP cord-242132-fhepdgz9 144 3 that that IN cord-242132-fhepdgz9 144 4 for for IN cord-242132-fhepdgz9 144 5 large large JJ cord-242132-fhepdgz9 144 6 β β NN cord-242132-fhepdgz9 144 7 the the DT cord-242132-fhepdgz9 144 8 evolution evolution NN cord-242132-fhepdgz9 144 9 of of IN cord-242132-fhepdgz9 144 10 the the DT cord-242132-fhepdgz9 144 11 infections infection NNS cord-242132-fhepdgz9 144 12 has have VBZ cord-242132-fhepdgz9 144 13 monotonic monotonic JJ cord-242132-fhepdgz9 144 14 shape shape NN cord-242132-fhepdgz9 144 15 ( ( -LRB- cord-242132-fhepdgz9 144 16 with with IN cord-242132-fhepdgz9 144 17 small small JJ cord-242132-fhepdgz9 144 18 random random JJ cord-242132-fhepdgz9 144 19 variations variation NNS cord-242132-fhepdgz9 144 20 ) ) -RRB- cord-242132-fhepdgz9 145 1 but but CC cord-242132-fhepdgz9 145 2 without without IN cord-242132-fhepdgz9 145 3 the the DT cord-242132-fhepdgz9 145 4 large large JJ cord-242132-fhepdgz9 145 5 oscillations oscillation NNS cord-242132-fhepdgz9 145 6 shown show VBN cord-242132-fhepdgz9 145 7 in in IN cord-242132-fhepdgz9 145 8 Fig.4 Fig.4 NNP cord-242132-fhepdgz9 145 9 . . . cord-242132-fhepdgz9 146 1 One one PRP cord-242132-fhepdgz9 146 2 can can MD cord-242132-fhepdgz9 146 3 see see VB cord-242132-fhepdgz9 146 4 that that IN cord-242132-fhepdgz9 146 5 the the DT cord-242132-fhepdgz9 146 6 dynamics dynamic NNS cord-242132-fhepdgz9 146 7 A(t A(t NNP cord-242132-fhepdgz9 146 8 ) ) -RRB- cord-242132-fhepdgz9 146 9 in in IN cord-242132-fhepdgz9 146 10 ( ( -LRB- cord-242132-fhepdgz9 146 11 b b NN cord-242132-fhepdgz9 146 12 ) ) -RRB- cord-242132-fhepdgz9 146 13 for for IN cord-242132-fhepdgz9 146 14 β β NN cord-242132-fhepdgz9 146 15 = = SYM cord-242132-fhepdgz9 146 16 0.90 0.90 CD cord-242132-fhepdgz9 146 17 is be VBZ cord-242132-fhepdgz9 146 18 already already RB cord-242132-fhepdgz9 146 19 suppressed suppress VBN cord-242132-fhepdgz9 146 20 and and CC cord-242132-fhepdgz9 146 21 considerably considerably RB cord-242132-fhepdgz9 146 22 differs differ VBZ cord-242132-fhepdgz9 146 23 with with IN cord-242132-fhepdgz9 146 24 respect respect NN cord-242132-fhepdgz9 146 25 to to IN cord-242132-fhepdgz9 146 26 situation situation NN cord-242132-fhepdgz9 146 27 without without IN cord-242132-fhepdgz9 146 28 the the DT cord-242132-fhepdgz9 146 29 quarantine quarantine NN cord-242132-fhepdgz9 146 30 shown show VBN cord-242132-fhepdgz9 146 31 in in IN cord-242132-fhepdgz9 146 32 Fig.2 Fig.2 NNP cord-242132-fhepdgz9 146 33 _SP cord-242132-fhepdgz9 146 34 in in IN cord-242132-fhepdgz9 146 35 framework framework NN cord-242132-fhepdgz9 146 36 of of IN cord-242132-fhepdgz9 146 37 our -PRON- PRP$ cord-242132-fhepdgz9 146 38 model model NN cord-242132-fhepdgz9 146 39 . . . cord-242132-fhepdgz9 147 1 Following follow VBG cord-242132-fhepdgz9 147 2 the the DT cord-242132-fhepdgz9 147 3 Ref Ref NNP cord-242132-fhepdgz9 147 4 . . . cord-242132-fhepdgz9 148 1 3 3 LS cord-242132-fhepdgz9 148 2 , , , cord-242132-fhepdgz9 148 3 we -PRON- PRP cord-242132-fhepdgz9 148 4 assume assume VBP cord-242132-fhepdgz9 148 5 that that IN cord-242132-fhepdgz9 148 6 in in IN cord-242132-fhepdgz9 148 7 the the DT cord-242132-fhepdgz9 148 8 host host NN cord-242132-fhepdgz9 148 9 population population NN cord-242132-fhepdgz9 148 10 there there EX cord-242132-fhepdgz9 148 11 is be VBZ cord-242132-fhepdgz9 148 12 no no DT cord-242132-fhepdgz9 148 13 innate innate JJ cord-242132-fhepdgz9 148 14 immunity immunity NN cord-242132-fhepdgz9 148 15 to to IN cord-242132-fhepdgz9 148 16 the the DT cord-242132-fhepdgz9 148 17 virus virus NN cord-242132-fhepdgz9 148 18 . . . cord-242132-fhepdgz9 149 1 But but CC cord-242132-fhepdgz9 149 2 we -PRON- PRP cord-242132-fhepdgz9 149 3 suppose suppose VBP cord-242132-fhepdgz9 149 4 that that IN cord-242132-fhepdgz9 149 5 the the DT cord-242132-fhepdgz9 149 6 persons person NNS cord-242132-fhepdgz9 149 7 ( ( -LRB- cord-242132-fhepdgz9 149 8 at at IN cord-242132-fhepdgz9 149 9 least least JJS cord-242132-fhepdgz9 149 10 a a DT cord-242132-fhepdgz9 149 11 large large JJ cord-242132-fhepdgz9 149 12 majority majority NN cord-242132-fhepdgz9 149 13 ) ) -RRB- cord-242132-fhepdgz9 149 14 will will MD cord-242132-fhepdgz9 149 15 acquire acquire VB cord-242132-fhepdgz9 149 16 this this DT cord-242132-fhepdgz9 149 17 immunity immunity NN cord-242132-fhepdgz9 149 18 , , , cord-242132-fhepdgz9 149 19 as as IN cord-242132-fhepdgz9 149 20 is be VBZ cord-242132-fhepdgz9 149 21 usually usually RB cord-242132-fhepdgz9 149 22 the the DT cord-242132-fhepdgz9 149 23 case case NN cord-242132-fhepdgz9 149 24 . . . cord-242132-fhepdgz9 150 1 To to IN cord-242132-fhepdgz9 150 2 this this DT cord-242132-fhepdgz9 150 3 end end NN cord-242132-fhepdgz9 150 4 , , , cord-242132-fhepdgz9 150 5 in in IN cord-242132-fhepdgz9 150 6 our -PRON- PRP$ cord-242132-fhepdgz9 150 7 model model NN cord-242132-fhepdgz9 150 8 we -PRON- PRP cord-242132-fhepdgz9 150 9 use use VBP cord-242132-fhepdgz9 150 10 the the DT cord-242132-fhepdgz9 150 11 parameter parameter NN cord-242132-fhepdgz9 150 12 M M NNP cord-242132-fhepdgz9 150 13 , , , cord-242132-fhepdgz9 150 14 see see VB cord-242132-fhepdgz9 150 15 Eq Eq NNP cord-242132-fhepdgz9 150 16 . . . cord-242132-fhepdgz9 151 1 ( ( -LRB- cord-242132-fhepdgz9 151 2 1 1 CD cord-242132-fhepdgz9 151 3 ) ) -RRB- cord-242132-fhepdgz9 151 4 . . . cord-242132-fhepdgz9 152 1 Following follow VBG cord-242132-fhepdgz9 152 2 3 3 CD cord-242132-fhepdgz9 152 3 , , , cord-242132-fhepdgz9 152 4 we -PRON- PRP cord-242132-fhepdgz9 152 5 assume assume VBP cord-242132-fhepdgz9 152 6 that that IN cord-242132-fhepdgz9 152 7 this this DT cord-242132-fhepdgz9 152 8 parameter parameter NN cord-242132-fhepdgz9 152 9 acquires acquire VBZ cord-242132-fhepdgz9 152 10 a a DT cord-242132-fhepdgz9 152 11 non non JJ cord-242132-fhepdgz9 152 12 - - JJ cord-242132-fhepdgz9 152 13 zero zero CD cord-242132-fhepdgz9 152 14 value value NN cord-242132-fhepdgz9 152 15 ( ( -LRB- cord-242132-fhepdgz9 152 16 the the DT cord-242132-fhepdgz9 152 17 presence presence NN cord-242132-fhepdgz9 152 18 of of IN cord-242132-fhepdgz9 152 19 immunity immunity NN cord-242132-fhepdgz9 152 20 ) ) -RRB- cord-242132-fhepdgz9 152 21 only only RB cord-242132-fhepdgz9 152 22 after after IN cord-242132-fhepdgz9 152 23 first first JJ cord-242132-fhepdgz9 152 24 infection infection NN cord-242132-fhepdgz9 152 25 and and CC cord-242132-fhepdgz9 152 26 recovery recovery NN cord-242132-fhepdgz9 152 27 . . . cord-242132-fhepdgz9 153 1 Re Re NNS cord-242132-fhepdgz9 153 2 - - NN cord-242132-fhepdgz9 153 3 infection infection NN cord-242132-fhepdgz9 153 4 no no RB cord-242132-fhepdgz9 153 5 longer long RBR cord-242132-fhepdgz9 153 6 occurs occur VBZ cord-242132-fhepdgz9 153 7 even even RB cord-242132-fhepdgz9 153 8 at at IN cord-242132-fhepdgz9 153 9 contacts contact NNS cord-242132-fhepdgz9 153 10 with with IN cord-242132-fhepdgz9 153 11 infected infected JJ cord-242132-fhepdgz9 153 12 persons person NNS cord-242132-fhepdgz9 153 13 . . . cord-242132-fhepdgz9 154 1 Fig Fig NNP cord-242132-fhepdgz9 154 2 . . NNP cord-242132-fhepdgz9 154 3 6 6 CD cord-242132-fhepdgz9 154 4 shows show VBZ cord-242132-fhepdgz9 154 5 the the DT cord-242132-fhepdgz9 154 6 dynamics dynamic NNS cord-242132-fhepdgz9 154 7 of of IN cord-242132-fhepdgz9 154 8 recovery recovery NN cord-242132-fhepdgz9 154 9 at at IN cord-242132-fhepdgz9 154 10 presence presence NN cord-242132-fhepdgz9 154 11 of of IN cord-242132-fhepdgz9 154 12 immunity immunity NN cord-242132-fhepdgz9 154 13 in in IN cord-242132-fhepdgz9 154 14 the the DT cord-242132-fhepdgz9 154 15 quarantine quarantine NN cord-242132-fhepdgz9 154 16 mode mode NN cord-242132-fhepdgz9 154 17 for for IN cord-242132-fhepdgz9 154 18 fixed fix VBN cord-242132-fhepdgz9 154 19 parameters parameter NNS cord-242132-fhepdgz9 154 20 β β XX cord-242132-fhepdgz9 155 1 = = SYM cord-242132-fhepdgz9 155 2 0.94 0.94 CD cord-242132-fhepdgz9 155 3 and and CC cord-242132-fhepdgz9 155 4 A a DT cord-242132-fhepdgz9 155 5 max max NN cord-242132-fhepdgz9 155 6 = = SYM cord-242132-fhepdgz9 155 7 0.24 0.24 CD cord-242132-fhepdgz9 155 8 and and CC cord-242132-fhepdgz9 155 9 different different JJ cord-242132-fhepdgz9 156 1 A a DT cord-242132-fhepdgz9 156 2 min min NN cord-242132-fhepdgz9 156 3 = = SYM cord-242132-fhepdgz9 156 4 0.17 0.17 CD cord-242132-fhepdgz9 156 5 , , , cord-242132-fhepdgz9 156 6 0.1 0.1 CD cord-242132-fhepdgz9 156 7 , , , cord-242132-fhepdgz9 156 8 0.05 0.05 CD cord-242132-fhepdgz9 156 9 , , , cord-242132-fhepdgz9 156 10 0.02 0.02 CD cord-242132-fhepdgz9 156 11 , , , cord-242132-fhepdgz9 156 12 0.01 0.01 CD cord-242132-fhepdgz9 156 13 . . . cord-242132-fhepdgz9 157 1 One one PRP cord-242132-fhepdgz9 157 2 can can MD cord-242132-fhepdgz9 157 3 see see VB cord-242132-fhepdgz9 157 4 that that IN cord-242132-fhepdgz9 157 5 now now RB cord-242132-fhepdgz9 157 6 the the DT cord-242132-fhepdgz9 157 7 oscillations oscillation NNS cord-242132-fhepdgz9 157 8 shown show VBN cord-242132-fhepdgz9 157 9 in in IN cord-242132-fhepdgz9 157 10 Fig.6 fig.6 NN cord-242132-fhepdgz9 157 11 acquire acquire NN cord-242132-fhepdgz9 157 12 shape shape NN cord-242132-fhepdgz9 157 13 of of IN cord-242132-fhepdgz9 157 14 strongly strongly RB cord-242132-fhepdgz9 157 15 damped damp VBN cord-242132-fhepdgz9 157 16 picks pick NNS cord-242132-fhepdgz9 157 17 that that WDT cord-242132-fhepdgz9 157 18 results result VBZ cord-242132-fhepdgz9 157 19 the the DT cord-242132-fhepdgz9 157 20 number number NN cord-242132-fhepdgz9 157 21 of of IN cord-242132-fhepdgz9 157 22 infected infected JJ cord-242132-fhepdgz9 157 23 ( ( -LRB- cord-242132-fhepdgz9 157 24 order order NN cord-242132-fhepdgz9 157 25 parameter parameter NN cord-242132-fhepdgz9 157 26 A a NN cord-242132-fhepdgz9 157 27 ) ) -RRB- cord-242132-fhepdgz9 157 28 to to TO cord-242132-fhepdgz9 157 29 rapidly rapidly RB cord-242132-fhepdgz9 157 30 decrease decrease VB cord-242132-fhepdgz9 157 31 . . . cord-242132-fhepdgz9 158 1 This this DT cord-242132-fhepdgz9 158 2 allows allow VBZ cord-242132-fhepdgz9 158 3 to to TO cord-242132-fhepdgz9 158 4 predicts predicts VB cord-242132-fhepdgz9 158 5 that that IN cord-242132-fhepdgz9 158 6 after after IN cord-242132-fhepdgz9 158 7 the the DT cord-242132-fhepdgz9 158 8 first first JJ cord-242132-fhepdgz9 158 9 high high JJ cord-242132-fhepdgz9 158 10 pick pick NN cord-242132-fhepdgz9 158 11 of of IN cord-242132-fhepdgz9 158 12 infection infection NN cord-242132-fhepdgz9 158 13 ( ( -LRB- cord-242132-fhepdgz9 158 14 that that DT cord-242132-fhepdgz9 158 15 has have VBZ cord-242132-fhepdgz9 158 16 nearly nearly RB cord-242132-fhepdgz9 158 17 fixed fix VBN cord-242132-fhepdgz9 158 18 amplitude amplitude NN cord-242132-fhepdgz9 158 19 for for IN cord-242132-fhepdgz9 158 20 all all PDT cord-242132-fhepdgz9 158 21 the the DT cord-242132-fhepdgz9 158 22 cases case NNS cord-242132-fhepdgz9 158 23 ) ) -RRB- cord-242132-fhepdgz9 158 24 may may MD cord-242132-fhepdgz9 158 25 occur occur VB cord-242132-fhepdgz9 158 26 a a DT cord-242132-fhepdgz9 158 27 second second JJ cord-242132-fhepdgz9 158 28 pick pick NN cord-242132-fhepdgz9 158 29 but but CC cord-242132-fhepdgz9 158 30 with with IN cord-242132-fhepdgz9 158 31 lesser less JJR cord-242132-fhepdgz9 158 32 amplitude amplitude NN cord-242132-fhepdgz9 158 33 and and CC cord-242132-fhepdgz9 158 34 then then RB cord-242132-fhepdgz9 158 35 the the DT cord-242132-fhepdgz9 158 36 complete complete JJ cord-242132-fhepdgz9 158 37 recover recover NN cord-242132-fhepdgz9 158 38 may may MD cord-242132-fhepdgz9 158 39 become become VB cord-242132-fhepdgz9 158 40 . . . cord-242132-fhepdgz9 159 1 Now now RB cord-242132-fhepdgz9 159 2 we -PRON- PRP cord-242132-fhepdgz9 159 3 compare compare VBP cord-242132-fhepdgz9 159 4 the the DT cord-242132-fhepdgz9 159 5 effects effect NNS cord-242132-fhepdgz9 159 6 of of IN cord-242132-fhepdgz9 159 7 quarantine quarantine NN cord-242132-fhepdgz9 159 8 and and CC cord-242132-fhepdgz9 159 9 immunity immunity NN cord-242132-fhepdgz9 159 10 factors factor NNS cord-242132-fhepdgz9 159 11 for for IN cord-242132-fhepdgz9 159 12 recovery recovery NN cord-242132-fhepdgz9 159 13 . . . cord-242132-fhepdgz9 160 1 Fig.7 Fig.7 NNP cord-242132-fhepdgz9 160 2 shows show VBZ cord-242132-fhepdgz9 160 3 the the DT cord-242132-fhepdgz9 160 4 dynamics dynamic NNS cord-242132-fhepdgz9 160 5 of of IN cord-242132-fhepdgz9 160 6 infections infection NNS cord-242132-fhepdgz9 160 7 ( ( -LRB- cord-242132-fhepdgz9 160 8 order order NN cord-242132-fhepdgz9 160 9 parameter parameter NN cord-242132-fhepdgz9 160 10 A a NN cord-242132-fhepdgz9 160 11 ) ) -RRB- cord-242132-fhepdgz9 160 12 for for IN cord-242132-fhepdgz9 160 13 different different JJ cord-242132-fhepdgz9 160 14 values value NNS cord-242132-fhepdgz9 160 15 of of IN cord-242132-fhepdgz9 160 16 the the DT cord-242132-fhepdgz9 160 17 risk risk NN cord-242132-fhepdgz9 160 18 factor factor NN cord-242132-fhepdgz9 160 19 β β NNP cord-242132-fhepdgz9 160 20 = = SYM cord-242132-fhepdgz9 160 21 0.99 0.99 CD cord-242132-fhepdgz9 160 22 , , , cord-242132-fhepdgz9 160 23 0.94 0.94 CD cord-242132-fhepdgz9 160 24 , , , cord-242132-fhepdgz9 160 25 0.9 0.9 CD cord-242132-fhepdgz9 160 26 , , , cord-242132-fhepdgz9 160 27 0.8 0.8 CD cord-242132-fhepdgz9 160 28 at at IN cord-242132-fhepdgz9 160 29 situation situation NN cord-242132-fhepdgz9 160 30 without without IN cord-242132-fhepdgz9 160 31 the the DT cord-242132-fhepdgz9 160 32 quarantine quarantine NN cord-242132-fhepdgz9 161 1 when when WRB cord-242132-fhepdgz9 161 2 only only RB cord-242132-fhepdgz9 161 3 the the DT cord-242132-fhepdgz9 161 4 personal personal JJ cord-242132-fhepdgz9 161 5 immunity immunity NN cord-242132-fhepdgz9 161 6 M m NN cord-242132-fhepdgz9 161 7 > > XX cord-242132-fhepdgz9 162 1 0 0 NFP cord-242132-fhepdgz9 162 2 presents present VBZ cord-242132-fhepdgz9 162 3 ( ( -LRB- cord-242132-fhepdgz9 162 4 see see VB cord-242132-fhepdgz9 162 5 Eq Eq NNP cord-242132-fhepdgz9 162 6 . . . cord-242132-fhepdgz9 163 1 ( ( -LRB- cord-242132-fhepdgz9 163 2 1 1 LS cord-242132-fhepdgz9 163 3 ) ) -RRB- cord-242132-fhepdgz9 163 4 ) ) -RRB- cord-242132-fhepdgz9 163 5 . . . cord-242132-fhepdgz9 164 1 This this DT cord-242132-fhepdgz9 164 2 simulation simulation NN cord-242132-fhepdgz9 164 3 shows show VBZ cord-242132-fhepdgz9 164 4 that that IN cord-242132-fhepdgz9 164 5 in in IN cord-242132-fhepdgz9 164 6 such such JJ cord-242132-fhepdgz9 164 7 case case NN cord-242132-fhepdgz9 164 8 the the DT cord-242132-fhepdgz9 164 9 complete complete JJ cord-242132-fhepdgz9 164 10 recover recover NN cord-242132-fhepdgz9 164 11 can can MD cord-242132-fhepdgz9 164 12 occur occur VB cord-242132-fhepdgz9 164 13 even even RB cord-242132-fhepdgz9 164 14 for for IN cord-242132-fhepdgz9 164 15 a a DT cord-242132-fhepdgz9 164 16 lesser less JJR cord-242132-fhepdgz9 164 17 time time NN cord-242132-fhepdgz9 164 18 comparing compare VBG cord-242132-fhepdgz9 164 19 to to IN cord-242132-fhepdgz9 164 20 Fig.6 fig.6 NN cord-242132-fhepdgz9 164 21 . . . cord-242132-fhepdgz9 164 22 _SP cord-242132-fhepdgz9 165 1 We -PRON- PRP cord-242132-fhepdgz9 165 2 studied study VBD cord-242132-fhepdgz9 165 3 the the DT cord-242132-fhepdgz9 165 4 dynamics dynamic NNS cord-242132-fhepdgz9 165 5 of of IN cord-242132-fhepdgz9 165 6 the the DT cord-242132-fhepdgz9 165 7 infection infection NN cord-242132-fhepdgz9 165 8 spread spread VBD cord-242132-fhepdgz9 165 9 at at IN cord-242132-fhepdgz9 165 10 various various JJ cord-242132-fhepdgz9 165 11 values value NNS cord-242132-fhepdgz9 165 12 of of IN cord-242132-fhepdgz9 165 13 the the DT cord-242132-fhepdgz9 165 14 risk risk NN cord-242132-fhepdgz9 165 15 factors factor NNS cord-242132-fhepdgz9 165 16 β β NNP cord-242132-fhepdgz9 165 17 ( ( -LRB- cord-242132-fhepdgz9 165 18 control control NN cord-242132-fhepdgz9 165 19 parameter parameter NN cord-242132-fhepdgz9 165 20 ) ) -RRB- cord-242132-fhepdgz9 165 21 using use VBG cord-242132-fhepdgz9 165 22 the the DT cord-242132-fhepdgz9 165 23 dynamic dynamic JJ cord-242132-fhepdgz9 165 24 Monte Monte NNP cord-242132-fhepdgz9 165 25 Carlo Carlo NNP cord-242132-fhepdgz9 165 26 method method NN cord-242132-fhepdgz9 165 27 ( ( -LRB- cord-242132-fhepdgz9 165 28 DMC DMC NNP cord-242132-fhepdgz9 165 29 ) ) -RRB- cord-242132-fhepdgz9 165 30 . . . cord-242132-fhepdgz9 166 1 In in IN cord-242132-fhepdgz9 166 2 our -PRON- PRP$ cord-242132-fhepdgz9 166 3 model model NN cord-242132-fhepdgz9 166 4 , , , cord-242132-fhepdgz9 166 5 it -PRON- PRP cord-242132-fhepdgz9 166 6 is be VBZ cord-242132-fhepdgz9 166 7 accepted accept VBN cord-242132-fhepdgz9 166 8 that that IN cord-242132-fhepdgz9 166 9 the the DT cord-242132-fhepdgz9 166 10 infection infection NN cord-242132-fhepdgz9 166 11 is be VBZ cord-242132-fhepdgz9 166 12 transmitted transmit VBN cord-242132-fhepdgz9 166 13 through through IN cord-242132-fhepdgz9 166 14 the the DT cord-242132-fhepdgz9 166 15 contacts contact NNS cord-242132-fhepdgz9 166 16 of of IN cord-242132-fhepdgz9 166 17 randomly randomly RB cord-242132-fhepdgz9 166 18 moving move VBG cord-242132-fhepdgz9 166 19 individuals individual NNS cord-242132-fhepdgz9 166 20 . . . cord-242132-fhepdgz9 167 1 We -PRON- PRP cord-242132-fhepdgz9 167 2 show show VBP cord-242132-fhepdgz9 167 3 that that IN cord-242132-fhepdgz9 167 4 the the DT cord-242132-fhepdgz9 167 5 behavior behavior NN cord-242132-fhepdgz9 167 6 of of IN cord-242132-fhepdgz9 167 7 recovered recover VBN cord-242132-fhepdgz9 167 8 individuals individual NNS cord-242132-fhepdgz9 167 9 crit- crit- VBN cord-242132-fhepdgz9 167 10 ically ically RB cord-242132-fhepdgz9 167 11 dependents dependent NNS cord-242132-fhepdgz9 167 12 on on IN cord-242132-fhepdgz9 167 13 the the DT cord-242132-fhepdgz9 167 14 value value NN cord-242132-fhepdgz9 167 15 β β NN cord-242132-fhepdgz9 167 16 . . . cord-242132-fhepdgz9 168 1 For for IN cord-242132-fhepdgz9 168 2 sub sub JJ cord-242132-fhepdgz9 168 3 - - JJ cord-242132-fhepdgz9 168 4 critical critical JJ cord-242132-fhepdgz9 168 5 values value NNS cord-242132-fhepdgz9 168 6 β β XX cord-242132-fhepdgz9 168 7 < < XX cord-242132-fhepdgz9 168 8 β β XX cord-242132-fhepdgz9 168 9 c c NNP cord-242132-fhepdgz9 168 10 ∼ ∼ NNP cord-242132-fhepdgz9 168 11 0.6 0.6 CD cord-242132-fhepdgz9 168 12 , , , cord-242132-fhepdgz9 168 13 the the DT cord-242132-fhepdgz9 168 14 number number NN cord-242132-fhepdgz9 168 15 of of IN cord-242132-fhepdgz9 168 16 infected infected JJ cord-242132-fhepdgz9 168 17 cases case NNS cord-242132-fhepdgz9 168 18 ( ( -LRB- cord-242132-fhepdgz9 168 19 the the DT cord-242132-fhepdgz9 168 20 order order NN cord-242132-fhepdgz9 168 21 parameters parameter VBZ cord-242132-fhepdgz9 168 22 A(t A(t NNP cord-242132-fhepdgz9 168 23 ) ) -RRB- cord-242132-fhepdgz9 168 24 ) ) -RRB- cord-242132-fhepdgz9 168 25 asymptotically asymptotically RB cord-242132-fhepdgz9 168 26 converges converge VBZ cord-242132-fhepdgz9 168 27 to to IN cord-242132-fhepdgz9 168 28 zero zero CD cord-242132-fhepdgz9 168 29 , , , cord-242132-fhepdgz9 168 30 so so IN cord-242132-fhepdgz9 168 31 that that IN cord-242132-fhepdgz9 168 32 at at IN cord-242132-fhepdgz9 168 33 moderate moderate JJ cord-242132-fhepdgz9 168 34 risk risk NN cord-242132-fhepdgz9 168 35 factor factor NN cord-242132-fhepdgz9 168 36 , , , cord-242132-fhepdgz9 168 37 the the DT cord-242132-fhepdgz9 168 38 infection infection NN cord-242132-fhepdgz9 168 39 can can MD cord-242132-fhepdgz9 168 40 quickly quickly RB cord-242132-fhepdgz9 168 41 disappear disappear VB cord-242132-fhepdgz9 168 42 . . . cord-242132-fhepdgz9 169 1 However however RB cord-242132-fhepdgz9 169 2 such such PDT cord-242132-fhepdgz9 169 3 a a DT cord-242132-fhepdgz9 169 4 nontrivial nontrivial JJ cord-242132-fhepdgz9 169 5 behavior behavior NN cord-242132-fhepdgz9 169 6 has have VBZ cord-242132-fhepdgz9 169 7 to to TO cord-242132-fhepdgz9 169 8 be be VB cord-242132-fhepdgz9 169 9 confirmed confirm VBN cord-242132-fhepdgz9 169 10 by by IN cord-242132-fhepdgz9 169 11 direct direct JJ cord-242132-fhepdgz9 169 12 calculation calculation NN cord-242132-fhepdgz9 169 13 . . . cord-242132-fhepdgz9 170 1 Fig Fig NNP cord-242132-fhepdgz9 170 2 . . . cord-242132-fhepdgz9 171 1 8 8 CD cord-242132-fhepdgz9 171 2 shows show VBZ cord-242132-fhepdgz9 171 3 the the DT cord-242132-fhepdgz9 171 4 dynamics dynamic NNS cord-242132-fhepdgz9 171 5 of of IN cord-242132-fhepdgz9 171 6 infections infection NNS cord-242132-fhepdgz9 171 7 fraction fraction NN cord-242132-fhepdgz9 171 8 A(t A(t NNP cord-242132-fhepdgz9 171 9 , , , cord-242132-fhepdgz9 171 10 β β NN cord-242132-fhepdgz9 171 11 ) ) -RRB- cord-242132-fhepdgz9 171 12 with with IN cord-242132-fhepdgz9 171 13 time time NN cord-242132-fhepdgz9 171 14 for for IN cord-242132-fhepdgz9 171 15 different different JJ cord-242132-fhepdgz9 171 16 risk risk NN cord-242132-fhepdgz9 171 17 factors factor NNS cord-242132-fhepdgz9 171 18 β β XX cord-242132-fhepdgz9 171 19 near near IN cord-242132-fhepdgz9 171 20 the the DT cord-242132-fhepdgz9 171 21 critical critical JJ cord-242132-fhepdgz9 171 22 transition transition NN cord-242132-fhepdgz9 171 23 β β NNP cord-242132-fhepdgz9 171 24 ∼ ∼ NNP cord-242132-fhepdgz9 171 25 β β NNP cord-242132-fhepdgz9 171 26 c c NN cord-242132-fhepdgz9 171 27 = = SYM cord-242132-fhepdgz9 171 28 0.6 0.6 CD cord-242132-fhepdgz9 171 29 for for IN cord-242132-fhepdgz9 171 30 N n CD cord-242132-fhepdgz9 171 31 = = SYM cord-242132-fhepdgz9 171 32 1000 1000 CD cord-242132-fhepdgz9 171 33 and and CC cord-242132-fhepdgz9 171 34 rather rather RB cord-242132-fhepdgz9 171 35 large large JJ cord-242132-fhepdgz9 171 36 the the DT cord-242132-fhepdgz9 171 37 initial initial JJ cord-242132-fhepdgz9 171 38 number number NN cord-242132-fhepdgz9 171 39 of of IN cord-242132-fhepdgz9 171 40 infections infection NNS cord-242132-fhepdgz9 172 1 I -PRON- PRP cord-242132-fhepdgz9 172 2 0 0 CD cord-242132-fhepdgz9 172 3 = = SYM cord-242132-fhepdgz9 172 4 100 100 CD cord-242132-fhepdgz9 172 5 . . . cord-242132-fhepdgz9 173 1 We -PRON- PRP cord-242132-fhepdgz9 173 2 observe observe VBP cord-242132-fhepdgz9 173 3 that that DT cord-242132-fhepdgz9 173 4 really really RB cord-242132-fhepdgz9 173 5 for for IN cord-242132-fhepdgz9 173 6 β β NN cord-242132-fhepdgz9 173 7 0.58 0.58 CD cord-242132-fhepdgz9 173 8 the the DT cord-242132-fhepdgz9 173 9 number number NN cord-242132-fhepdgz9 173 10 of of IN cord-242132-fhepdgz9 173 11 infections infection NNS cord-242132-fhepdgz9 173 12 rapidly rapidly RB cord-242132-fhepdgz9 173 13 reach reach VBP cord-242132-fhepdgz9 173 14 zero zero CD cord-242132-fhepdgz9 173 15 . . . cord-242132-fhepdgz9 174 1 We -PRON- PRP cord-242132-fhepdgz9 174 2 also also RB cord-242132-fhepdgz9 174 3 analyzed analyze VBD cord-242132-fhepdgz9 174 4 the the DT cord-242132-fhepdgz9 174 5 extended extended JJ cord-242132-fhepdgz9 174 6 system system NN cord-242132-fhepdgz9 174 7 , , , cord-242132-fhepdgz9 174 8 which which WDT cord-242132-fhepdgz9 174 9 currently currently RB cord-242132-fhepdgz9 174 10 is be VBZ cord-242132-fhepdgz9 174 11 widely widely RB cord-242132-fhepdgz9 174 12 used use VBN cord-242132-fhepdgz9 174 13 to to TO cord-242132-fhepdgz9 174 14 prevent prevent VB cord-242132-fhepdgz9 174 15 the the DT cord-242132-fhepdgz9 174 16 spread spread NN cord-242132-fhepdgz9 174 17 of of IN cord-242132-fhepdgz9 174 18 the the DT cord-242132-fhepdgz9 174 19 virus virus NN cord-242132-fhepdgz9 174 20 . . . cord-242132-fhepdgz9 175 1 In in IN cord-242132-fhepdgz9 175 2 our -PRON- PRP$ cord-242132-fhepdgz9 175 3 approach approach NN cord-242132-fhepdgz9 175 4 such such PDT cord-242132-fhepdgz9 175 5 a a DT cord-242132-fhepdgz9 175 6 system system NN cord-242132-fhepdgz9 175 7 includes include VBZ cord-242132-fhepdgz9 175 8 two two CD cord-242132-fhepdgz9 175 9 additional additional JJ cord-242132-fhepdgz9 175 10 parameters parameter NNS cord-242132-fhepdgz9 175 11 on on IN cord-242132-fhepdgz9 175 12 / / SYM cord-242132-fhepdgz9 175 13 off off IN cord-242132-fhepdgz9 175 14 the the DT cord-242132-fhepdgz9 175 15 quarantine quarantine NN cord-242132-fhepdgz9 175 16 state state NN cord-242132-fhepdgz9 175 17 . . . cord-242132-fhepdgz9 176 1 It -PRON- PRP cord-242132-fhepdgz9 176 2 was be VBD cord-242132-fhepdgz9 176 3 revealed reveal VBN cord-242132-fhepdgz9 176 4 that that IN cord-242132-fhepdgz9 176 5 early early JJ cord-242132-fhepdgz9 176 6 exit exit NN cord-242132-fhepdgz9 176 7 from from IN cord-242132-fhepdgz9 176 8 the the DT cord-242132-fhepdgz9 176 9 quarantine quarantine NN cord-242132-fhepdgz9 176 10 leads lead VBZ cord-242132-fhepdgz9 176 11 to to IN cord-242132-fhepdgz9 176 12 irregular irregular JJ cord-242132-fhepdgz9 176 13 oscillating oscillating JJ cord-242132-fhepdgz9 176 14 dynamics dynamic NNS cord-242132-fhepdgz9 176 15 ( ( -LRB- cord-242132-fhepdgz9 176 16 with with IN cord-242132-fhepdgz9 176 17 positive positive JJ cord-242132-fhepdgz9 176 18 Lyapunov Lyapunov NNP cord-242132-fhepdgz9 176 19 exponent exponent NN cord-242132-fhepdgz9 176 20 ) ) -RRB- cord-242132-fhepdgz9 176 21 of of IN cord-242132-fhepdgz9 176 22 the the DT cord-242132-fhepdgz9 176 23 infection infection NN cord-242132-fhepdgz9 176 24 . . . cord-242132-fhepdgz9 177 1 However however RB cord-242132-fhepdgz9 177 2 when when WRB cord-242132-fhepdgz9 177 3 the the DT cord-242132-fhepdgz9 177 4 lower low JJR cord-242132-fhepdgz9 177 5 limit limit NN cord-242132-fhepdgz9 177 6 of of IN cord-242132-fhepdgz9 177 7 the the DT cord-242132-fhepdgz9 177 8 quarantine quarantine NN cord-242132-fhepdgz9 177 9 off off RP cord-242132-fhepdgz9 177 10 is be VBZ cord-242132-fhepdgz9 177 11 sufficiently sufficiently RB cord-242132-fhepdgz9 177 12 small small JJ cord-242132-fhepdgz9 177 13 , , , cord-242132-fhepdgz9 177 14 the the DT cord-242132-fhepdgz9 177 15 infection infection NN cord-242132-fhepdgz9 177 16 dynamics dynamic NNS cord-242132-fhepdgz9 177 17 acquires acquire VBZ cord-242132-fhepdgz9 177 18 a a DT cord-242132-fhepdgz9 177 19 characteristic characteristic JJ cord-242132-fhepdgz9 177 20 nonmonotonic nonmonotonic JJ cord-242132-fhepdgz9 177 21 shape shape NN cord-242132-fhepdgz9 177 22 with with IN cord-242132-fhepdgz9 177 23 several several JJ cord-242132-fhepdgz9 177 24 damped damp VBN cord-242132-fhepdgz9 177 25 peaks peak NNS cord-242132-fhepdgz9 177 26 . . . cord-242132-fhepdgz9 178 1 The the DT cord-242132-fhepdgz9 178 2 dynamics dynamic NNS cord-242132-fhepdgz9 178 3 of of IN cord-242132-fhepdgz9 178 4 the the DT cord-242132-fhepdgz9 178 5 infection infection NN cord-242132-fhepdgz9 178 6 spread spread VBD cord-242132-fhepdgz9 178 7 in in IN cord-242132-fhepdgz9 178 8 case case NN cord-242132-fhepdgz9 178 9 of of IN cord-242132-fhepdgz9 178 10 individuals individual NNS cord-242132-fhepdgz9 178 11 with with IN cord-242132-fhepdgz9 178 12 immunity immunity NN cord-242132-fhepdgz9 178 13 was be VBD cord-242132-fhepdgz9 178 14 studied study VBN cord-242132-fhepdgz9 178 15 too too RB cord-242132-fhepdgz9 178 16 . . . cord-242132-fhepdgz9 179 1 Our -PRON- PRP$ cord-242132-fhepdgz9 179 2 comparison comparison NN cord-242132-fhepdgz9 179 3 of of IN cord-242132-fhepdgz9 179 4 the the DT cord-242132-fhepdgz9 179 5 quarantine quarantine NN cord-242132-fhepdgz9 179 6 and and CC cord-242132-fhepdgz9 179 7 the the DT cord-242132-fhepdgz9 179 8 immunity immunity NN cord-242132-fhepdgz9 179 9 factors factor NNS cord-242132-fhepdgz9 179 10 on on IN cord-242132-fhepdgz9 179 11 a a DT cord-242132-fhepdgz9 179 12 recovery recovery NN cord-242132-fhepdgz9 179 13 shows show VBZ cord-242132-fhepdgz9 179 14 that that IN cord-242132-fhepdgz9 179 15 in in IN cord-242132-fhepdgz9 179 16 case case NN cord-242132-fhepdgz9 179 17 of of IN cord-242132-fhepdgz9 179 18 stable stable JJ cord-242132-fhepdgz9 179 19 immunity immunity NN cord-242132-fhepdgz9 179 20 a a DT cord-242132-fhepdgz9 179 21 complete complete JJ cord-242132-fhepdgz9 179 22 recovery recovery NN cord-242132-fhepdgz9 179 23 occurs occur VBZ cord-242132-fhepdgz9 179 24 faster fast RBR cord-242132-fhepdgz9 179 25 than than IN cord-242132-fhepdgz9 179 26 in in IN cord-242132-fhepdgz9 179 27 a a DT cord-242132-fhepdgz9 179 28 quarantine quarantine NN cord-242132-fhepdgz9 179 29 mode mode NN cord-242132-fhepdgz9 179 30 . . . cord-242132-fhepdgz9 180 1 This this DT cord-242132-fhepdgz9 180 2 work work NN cord-242132-fhepdgz9 180 3 was be VBD cord-242132-fhepdgz9 180 4 supported support VBN cord-242132-fhepdgz9 180 5 in in IN cord-242132-fhepdgz9 180 6 part part NN cord-242132-fhepdgz9 180 7 by by IN cord-242132-fhepdgz9 180 8 CONACYT CONACYT NNP cord-242132-fhepdgz9 180 9 ( ( -LRB- cord-242132-fhepdgz9 180 10 México México NNP cord-242132-fhepdgz9 180 11 ) ) -RRB- cord-242132-fhepdgz9 180 12 under under IN cord-242132-fhepdgz9 180 13 the the DT cord-242132-fhepdgz9 180 14 grant grant NN cord-242132-fhepdgz9 181 1 No no UH cord-242132-fhepdgz9 181 2 . . . cord-242132-fhepdgz9 182 1 A1-S-9201 A1-S-9201 NNP cord-242132-fhepdgz9 182 2 . . . cord-242132-fhepdgz9 183 1 A a DT cord-242132-fhepdgz9 183 2 strategic strategic JJ cord-242132-fhepdgz9 183 3 approach approach NN cord-242132-fhepdgz9 183 4 to to IN cord-242132-fhepdgz9 183 5 COVID-19 covid-19 JJ cord-242132-fhepdgz9 183 6 vaccine vaccine NN cord-242132-fhepdgz9 183 7 R&D r&d NN cord-242132-fhepdgz9 183 8 , , , cord-242132-fhepdgz9 183 9 Science Science NNP cord-242132-fhepdgz9 183 10 Coronavirus Coronavirus NNP cord-242132-fhepdgz9 183 11 research research NN cord-242132-fhepdgz9 183 12 updates update NNS cord-242132-fhepdgz9 183 13 : : : cord-242132-fhepdgz9 183 14 Potent potent JJ cord-242132-fhepdgz9 183 15 human human JJ cord-242132-fhepdgz9 183 16 antibodies antibody NNS cord-242132-fhepdgz9 183 17 could could MD cord-242132-fhepdgz9 183 18 inspire inspire VB cord-242132-fhepdgz9 183 19 a a DT cord-242132-fhepdgz9 183 20 vaccine vaccine NN cord-242132-fhepdgz9 183 21 Mathematical Mathematical NNP cord-242132-fhepdgz9 183 22 Modeling Modeling NNP cord-242132-fhepdgz9 183 23 of of IN cord-242132-fhepdgz9 183 24 Infectious Infectious NNP cord-242132-fhepdgz9 183 25 Diseases Diseases NNPS cord-242132-fhepdgz9 183 26 Dynamics Dynamics NNPS cord-242132-fhepdgz9 183 27 Estimating estimate VBG cord-242132-fhepdgz9 183 28 the the DT cord-242132-fhepdgz9 183 29 infection infection NN cord-242132-fhepdgz9 183 30 horizon horizon NN cord-242132-fhepdgz9 183 31 of of IN cord-242132-fhepdgz9 183 32 COVID-19 COVID-19 NNP cord-242132-fhepdgz9 183 33 in in IN cord-242132-fhepdgz9 183 34 eight eight CD cord-242132-fhepdgz9 183 35 countries country NNS cord-242132-fhepdgz9 183 36 with with IN cord-242132-fhepdgz9 183 37 a a DT cord-242132-fhepdgz9 183 38 data data NN cord-242132-fhepdgz9 183 39 - - HYPH cord-242132-fhepdgz9 183 40 driven drive VBN cord-242132-fhepdgz9 183 41 approach approach NN cord-242132-fhepdgz9 183 42 Estimation Estimation NNP cord-242132-fhepdgz9 183 43 of of IN cord-242132-fhepdgz9 183 44 COVID-19 COVID-19 NNP cord-242132-fhepdgz9 183 45 dynamics dynamic NNS cord-242132-fhepdgz9 183 46 " " '' cord-242132-fhepdgz9 183 47 on on IN cord-242132-fhepdgz9 183 48 a a DT cord-242132-fhepdgz9 183 49 back back JJ cord-242132-fhepdgz9 183 50 - - HYPH cord-242132-fhepdgz9 183 51 of of IN cord-242132-fhepdgz9 183 52 - - HYPH cord-242132-fhepdgz9 183 53 envelope envelope NN cord-242132-fhepdgz9 183 54 " " '' cord-242132-fhepdgz9 183 55 : : : cord-242132-fhepdgz9 183 56 Does do VBZ cord-242132-fhepdgz9 183 57 the the DT cord-242132-fhepdgz9 183 58 simplest simple JJS cord-242132-fhepdgz9 183 59 SIR SIR NNP cord-242132-fhepdgz9 183 60 model model NN cord-242132-fhepdgz9 183 61 provide provide VB cord-242132-fhepdgz9 183 62 quantitative quantitative JJ cord-242132-fhepdgz9 183 63 parameters parameter NNS cord-242132-fhepdgz9 183 64 and and CC cord-242132-fhepdgz9 183 65 predictions prediction NNS cord-242132-fhepdgz9 183 66 ? ? . cord-242132-fhepdgz9 184 1 Mathematical mathematical JJ cord-242132-fhepdgz9 184 2 modeling modeling NN cord-242132-fhepdgz9 184 3 of of IN cord-242132-fhepdgz9 184 4 COVID-19 covid-19 JJ cord-242132-fhepdgz9 184 5 transmission transmission NN cord-242132-fhepdgz9 184 6 dynamics dynamic NNS cord-242132-fhepdgz9 184 7 with with IN cord-242132-fhepdgz9 184 8 a a DT cord-242132-fhepdgz9 184 9 case case NN cord-242132-fhepdgz9 184 10 study study NN cord-242132-fhepdgz9 184 11 of of IN cord-242132-fhepdgz9 184 12 Wuhan Wuhan NNP cord-242132-fhepdgz9 184 13 Novel Novel NNP cord-242132-fhepdgz9 184 14 Type Type NNP cord-242132-fhepdgz9 184 15 of of IN cord-242132-fhepdgz9 184 16 Phase Phase NNP cord-242132-fhepdgz9 184 17 Transition Transition NNP cord-242132-fhepdgz9 184 18 in in IN cord-242132-fhepdgz9 184 19 a a DT cord-242132-fhepdgz9 184 20 System System NNP cord-242132-fhepdgz9 184 21 of of IN cord-242132-fhepdgz9 184 22 Self Self NNP cord-242132-fhepdgz9 184 23 - - HYPH cord-242132-fhepdgz9 184 24 Driven drive VBN cord-242132-fhepdgz9 184 25 Particles particle NNS cord-242132-fhepdgz9 184 26 From from IN cord-242132-fhepdgz9 184 27 Phase phase NN cord-242132-fhepdgz9 184 28 to to IN cord-242132-fhepdgz9 184 29 Microphase Microphase NNP cord-242132-fhepdgz9 184 30 Separation Separation NNP cord-242132-fhepdgz9 184 31 in in IN cord-242132-fhepdgz9 184 32 Flocking Flocking NNP cord-242132-fhepdgz9 184 33 Models model NNS cord-242132-fhepdgz9 184 34 : : : cord-242132-fhepdgz9 184 35 The the DT cord-242132-fhepdgz9 184 36 Essential essential JJ cord-242132-fhepdgz9 184 37 Role role NN cord-242132-fhepdgz9 184 38 of of IN cord-242132-fhepdgz9 184 39 Nonequilibrium Nonequilibrium NNP cord-242132-fhepdgz9 184 40 Fluctuations Fluctuations NNPS cord-242132-fhepdgz9 184 41 Flocking flock VBG cord-242132-fhepdgz9 184 42 with with IN cord-242132-fhepdgz9 184 43 discrete discrete JJ cord-242132-fhepdgz9 184 44 symmetry symmetry NN cord-242132-fhepdgz9 184 45 : : : cord-242132-fhepdgz9 184 46 The the DT cord-242132-fhepdgz9 184 47 two two CD cord-242132-fhepdgz9 184 48 - - HYPH cord-242132-fhepdgz9 184 49 dimensional dimensional JJ cord-242132-fhepdgz9 184 50 active active JJ cord-242132-fhepdgz9 184 51 Ising Ising NNP cord-242132-fhepdgz9 184 52 model model NN cord-242132-fhepdgz9 184 53 Numerical numerical JJ cord-242132-fhepdgz9 184 54 recipes recipe NNS cord-242132-fhepdgz9 184 55 in in IN cord-242132-fhepdgz9 184 56 C++ C++ NNP cord-242132-fhepdgz9 184 57 Percolation Percolation NNP cord-242132-fhepdgz9 184 58 Percolation Percolation NNP cord-242132-fhepdgz9 184 59 , , , cord-242132-fhepdgz9 184 60 statistical statistical JJ cord-242132-fhepdgz9 184 61 topography topography NN cord-242132-fhepdgz9 184 62 , , , cord-242132-fhepdgz9 184 63 and and CC cord-242132-fhepdgz9 184 64 transport transport NN cord-242132-fhepdgz9 184 65 in in IN cord-242132-fhepdgz9 184 66 random random JJ cord-242132-fhepdgz9 184 67 media medium NNS cord-242132-fhepdgz9 184 68 Introduction introduction NN cord-242132-fhepdgz9 184 69 toPercolation topercolation NN cord-242132-fhepdgz9 185 1 Theory theory NN cord-242132-fhepdgz9 185 2 Sec Sec NNP cord-242132-fhepdgz9 185 3 Optical optical JJ cord-242132-fhepdgz9 185 4 percolation percolation NN cord-242132-fhepdgz9 185 5 in in IN cord-242132-fhepdgz9 185 6 ceramics ceramic NNS cord-242132-fhepdgz9 185 7 assisted assist VBN cord-242132-fhepdgz9 185 8 by by IN cord-242132-fhepdgz9 185 9 porousclusters porouscluster NNS cord-242132-fhepdgz9 185 10 Mirrorless Mirrorless NNP cord-242132-fhepdgz9 185 11 lasing lase VBG cord-242132-fhepdgz9 185 12 from from IN cord-242132-fhepdgz9 185 13 light light JJ cord-242132-fhepdgz9 185 14 emitters emitter NNS cord-242132-fhepdgz9 185 15 in in IN cord-242132-fhepdgz9 185 16 percolating percolate VBG cord-242132-fhepdgz9 185 17 clusters cluster NNS cord-242132-fhepdgz9 185 18 Determining determine VBG cord-242132-fhepdgz9 185 19 Lyapunov Lyapunov NNP cord-242132-fhepdgz9 185 20 exponents exponent NNS cord-242132-fhepdgz9 185 21 from from IN cord-242132-fhepdgz9 185 22 a a DT cord-242132-fhepdgz9 185 23 time time NN cord-242132-fhepdgz9 185 24 series series NN cord-242132-fhepdgz9 185 25 SARS SARS NNP cord-242132-fhepdgz9 185 26 - - HYPH cord-242132-fhepdgz9 185 27 CoV-2 CoV-2 NNP cord-242132-fhepdgz9 185 28 infection infection NN cord-242132-fhepdgz9 185 29 protects protect VBZ cord-242132-fhepdgz9 185 30 against against IN cord-242132-fhepdgz9 185 31 rechallenge rechallenge NN cord-242132-fhepdgz9 185 32 in in IN cord-242132-fhepdgz9 185 33 rhesus rhesu NNS cord-242132-fhepdgz9 185 34 macaques macaque NNS