id sid tid token lemma pos cord-258032-buh1e4tm 1 1 key key NNP cord-258032-buh1e4tm 1 2 : : : cord-258032-buh1e4tm 1 3 cord-258032-buh1e4tm cord-258032-buh1e4tm CD cord-258032-buh1e4tm 1 4 authors author NNS cord-258032-buh1e4tm 1 5 : : : cord-258032-buh1e4tm 1 6 Tang Tang NNP cord-258032-buh1e4tm 1 7 , , , cord-258032-buh1e4tm 1 8 Siming Siming NNP cord-258032-buh1e4tm 1 9 ; ; : cord-258032-buh1e4tm 1 10 Ma Ma NNP cord-258032-buh1e4tm 1 11 , , , cord-258032-buh1e4tm 1 12 Wanbiao Wanbiao NNP cord-258032-buh1e4tm 1 13 ; ; , cord-258032-buh1e4tm 1 14 Bai Bai NNP cord-258032-buh1e4tm 2 1 , , , cord-258032-buh1e4tm 2 2 Peifan Peifan NNP cord-258032-buh1e4tm 2 3 title title NN cord-258032-buh1e4tm 2 4 : : : cord-258032-buh1e4tm 2 5 A a DT cord-258032-buh1e4tm 2 6 Novel Novel NNP cord-258032-buh1e4tm 2 7 Dynamic Dynamic NNP cord-258032-buh1e4tm 2 8 Model model NN cord-258032-buh1e4tm 2 9 Describing describe VBG cord-258032-buh1e4tm 2 10 the the DT cord-258032-buh1e4tm 2 11 Spread spread NN cord-258032-buh1e4tm 2 12 of of IN cord-258032-buh1e4tm 2 13 the the DT cord-258032-buh1e4tm 2 14 MERS MERS NNP cord-258032-buh1e4tm 2 15 - - HYPH cord-258032-buh1e4tm 2 16 CoV CoV NNP cord-258032-buh1e4tm 2 17 and and CC cord-258032-buh1e4tm 2 18 the the DT cord-258032-buh1e4tm 2 19 Expression expression NN cord-258032-buh1e4tm 2 20 of of IN cord-258032-buh1e4tm 2 21 Dipeptidyl Dipeptidyl NNP cord-258032-buh1e4tm 2 22 Peptidase Peptidase NNP cord-258032-buh1e4tm 2 23 4 4 CD cord-258032-buh1e4tm 2 24 date date NN cord-258032-buh1e4tm 2 25 : : : cord-258032-buh1e4tm 2 26 2017 2017 CD cord-258032-buh1e4tm 2 27 - - HYPH cord-258032-buh1e4tm 2 28 08 08 CD cord-258032-buh1e4tm 2 29 - - SYM cord-258032-buh1e4tm 2 30 15 15 CD cord-258032-buh1e4tm 2 31 journal journal NN cord-258032-buh1e4tm 2 32 : : : cord-258032-buh1e4tm 2 33 Comput Comput NNP cord-258032-buh1e4tm 2 34 Math Math NNP cord-258032-buh1e4tm 2 35 Methods method NNS cord-258032-buh1e4tm 3 1 Med Med NNP cord-258032-buh1e4tm 3 2 DOI DOI NNP cord-258032-buh1e4tm 3 3 : : : cord-258032-buh1e4tm 3 4 10.1155/2017/5285810 10.1155/2017/5285810 CD cord-258032-buh1e4tm 3 5 sha sha NNP cord-258032-buh1e4tm 3 6 : : : cord-258032-buh1e4tm 3 7 bd5e22fa122a78846797a754e1dcb12887036229 bd5e22fa122a78846797a754e1dcb12887036229 NNP cord-258032-buh1e4tm 3 8 doc_id doc_id CD cord-258032-buh1e4tm 3 9 : : : cord-258032-buh1e4tm 3 10 258032 258032 CD cord-258032-buh1e4tm 3 11 cord_uid cord_uid NNS cord-258032-buh1e4tm 3 12 : : : cord-258032-buh1e4tm 4 1 buh1e4tm buh1e4tm RB cord-258032-buh1e4tm 4 2 The the DT cord-258032-buh1e4tm 4 3 Middle Middle NNP cord-258032-buh1e4tm 4 4 East East NNP cord-258032-buh1e4tm 4 5 respiratory respiratory JJ cord-258032-buh1e4tm 4 6 syndrome syndrome NN cord-258032-buh1e4tm 4 7 ( ( -LRB- cord-258032-buh1e4tm 4 8 MERS MERS NNP cord-258032-buh1e4tm 4 9 ) ) -RRB- cord-258032-buh1e4tm 4 10 coronavirus coronavirus NN cord-258032-buh1e4tm 4 11 , , , cord-258032-buh1e4tm 4 12 a a DT cord-258032-buh1e4tm 4 13 newly newly RB cord-258032-buh1e4tm 4 14 identified identify VBN cord-258032-buh1e4tm 4 15 pathogen pathogen NN cord-258032-buh1e4tm 4 16 , , , cord-258032-buh1e4tm 4 17 causes cause VBZ cord-258032-buh1e4tm 4 18 severe severe JJ cord-258032-buh1e4tm 4 19 pneumonia pneumonia NN cord-258032-buh1e4tm 4 20 in in IN cord-258032-buh1e4tm 4 21 humans human NNS cord-258032-buh1e4tm 4 22 . . . cord-258032-buh1e4tm 5 1 MERS MERS NNP cord-258032-buh1e4tm 5 2 is be VBZ cord-258032-buh1e4tm 5 3 caused cause VBN cord-258032-buh1e4tm 5 4 by by IN cord-258032-buh1e4tm 5 5 a a DT cord-258032-buh1e4tm 5 6 coronavirus coronavirus NN cord-258032-buh1e4tm 5 7 known know VBN cord-258032-buh1e4tm 5 8 as as IN cord-258032-buh1e4tm 5 9 MERS MERS NNP cord-258032-buh1e4tm 5 10 - - HYPH cord-258032-buh1e4tm 5 11 CoV CoV NNP cord-258032-buh1e4tm 5 12 , , , cord-258032-buh1e4tm 5 13 which which WDT cord-258032-buh1e4tm 5 14 attacks attack VBZ cord-258032-buh1e4tm 5 15 the the DT cord-258032-buh1e4tm 5 16 respiratory respiratory JJ cord-258032-buh1e4tm 5 17 system system NN cord-258032-buh1e4tm 5 18 . . . cord-258032-buh1e4tm 6 1 The the DT cord-258032-buh1e4tm 6 2 recently recently RB cord-258032-buh1e4tm 6 3 defined define VBN cord-258032-buh1e4tm 6 4 receptor receptor NN cord-258032-buh1e4tm 6 5 for for IN cord-258032-buh1e4tm 6 6 MERS MERS NNP cord-258032-buh1e4tm 6 7 - - HYPH cord-258032-buh1e4tm 6 8 CoV CoV NNP cord-258032-buh1e4tm 6 9 , , , cord-258032-buh1e4tm 6 10 dipeptidyl dipeptidyl JJ cord-258032-buh1e4tm 6 11 peptidase peptidase NN cord-258032-buh1e4tm 6 12 4 4 CD cord-258032-buh1e4tm 6 13 ( ( -LRB- cord-258032-buh1e4tm 6 14 DPP4 DPP4 NNP cord-258032-buh1e4tm 6 15 ) ) -RRB- cord-258032-buh1e4tm 6 16 , , , cord-258032-buh1e4tm 6 17 is be VBZ cord-258032-buh1e4tm 6 18 generally generally RB cord-258032-buh1e4tm 6 19 expressed express VBN cord-258032-buh1e4tm 6 20 in in IN cord-258032-buh1e4tm 6 21 endothelial endothelial JJ cord-258032-buh1e4tm 6 22 and and CC cord-258032-buh1e4tm 6 23 epithelial epithelial JJ cord-258032-buh1e4tm 6 24 cells cell NNS cord-258032-buh1e4tm 6 25 and and CC cord-258032-buh1e4tm 6 26 has have VBZ cord-258032-buh1e4tm 6 27 been be VBN cord-258032-buh1e4tm 6 28 shown show VBN cord-258032-buh1e4tm 6 29 to to TO cord-258032-buh1e4tm 6 30 be be VB cord-258032-buh1e4tm 6 31 present present JJ cord-258032-buh1e4tm 6 32 on on IN cord-258032-buh1e4tm 6 33 cultured cultured JJ cord-258032-buh1e4tm 6 34 human human JJ cord-258032-buh1e4tm 6 35 nonciliated nonciliate VBN cord-258032-buh1e4tm 6 36 bronchiolar bronchiolar NNP cord-258032-buh1e4tm 6 37 epithelium epithelium NN cord-258032-buh1e4tm 6 38 cells cell NNS cord-258032-buh1e4tm 6 39 . . . cord-258032-buh1e4tm 7 1 In in IN cord-258032-buh1e4tm 7 2 this this DT cord-258032-buh1e4tm 7 3 paper paper NN cord-258032-buh1e4tm 7 4 , , , cord-258032-buh1e4tm 7 5 a a DT cord-258032-buh1e4tm 7 6 class class NN cord-258032-buh1e4tm 7 7 of of IN cord-258032-buh1e4tm 7 8 novel novel JJ cord-258032-buh1e4tm 7 9 four four CD cord-258032-buh1e4tm 7 10 - - HYPH cord-258032-buh1e4tm 7 11 dimensional dimensional JJ cord-258032-buh1e4tm 7 12 dynamic dynamic JJ cord-258032-buh1e4tm 7 13 model model NN cord-258032-buh1e4tm 7 14 describing describe VBG cord-258032-buh1e4tm 7 15 the the DT cord-258032-buh1e4tm 7 16 infection infection NN cord-258032-buh1e4tm 7 17 of of IN cord-258032-buh1e4tm 7 18 MERS MERS NNP cord-258032-buh1e4tm 7 19 - - HYPH cord-258032-buh1e4tm 7 20 CoV CoV NNP cord-258032-buh1e4tm 7 21 is be VBZ cord-258032-buh1e4tm 7 22 given give VBN cord-258032-buh1e4tm 7 23 , , , cord-258032-buh1e4tm 7 24 and and CC cord-258032-buh1e4tm 7 25 then then RB cord-258032-buh1e4tm 7 26 global global JJ cord-258032-buh1e4tm 7 27 stability stability NN cord-258032-buh1e4tm 7 28 of of IN cord-258032-buh1e4tm 7 29 the the DT cord-258032-buh1e4tm 7 30 equilibria equilibrium NNS cord-258032-buh1e4tm 7 31 of of IN cord-258032-buh1e4tm 7 32 the the DT cord-258032-buh1e4tm 7 33 model model NN cord-258032-buh1e4tm 7 34 is be VBZ cord-258032-buh1e4tm 7 35 discussed discuss VBN cord-258032-buh1e4tm 7 36 . . . cord-258032-buh1e4tm 8 1 Our -PRON- PRP$ cord-258032-buh1e4tm 8 2 results result NNS cord-258032-buh1e4tm 8 3 show show VBP cord-258032-buh1e4tm 8 4 that that IN cord-258032-buh1e4tm 8 5 the the DT cord-258032-buh1e4tm 8 6 spread spread NN cord-258032-buh1e4tm 8 7 of of IN cord-258032-buh1e4tm 8 8 MERS MERS NNP cord-258032-buh1e4tm 8 9 - - HYPH cord-258032-buh1e4tm 8 10 CoV CoV NNP cord-258032-buh1e4tm 8 11 can can MD cord-258032-buh1e4tm 8 12 also also RB cord-258032-buh1e4tm 8 13 be be VB cord-258032-buh1e4tm 8 14 controlled control VBN cord-258032-buh1e4tm 8 15 by by IN cord-258032-buh1e4tm 8 16 decreasing decrease VBG cord-258032-buh1e4tm 8 17 the the DT cord-258032-buh1e4tm 8 18 expression expression NN cord-258032-buh1e4tm 8 19 rate rate NN cord-258032-buh1e4tm 8 20 of of IN cord-258032-buh1e4tm 8 21 DPP4 DPP4 NNP cord-258032-buh1e4tm 8 22 . . . cord-258032-buh1e4tm 9 1 The the DT cord-258032-buh1e4tm 9 2 Middle Middle NNP cord-258032-buh1e4tm 9 3 East East NNP cord-258032-buh1e4tm 9 4 respiratory respiratory JJ cord-258032-buh1e4tm 9 5 syndrome syndrome NN cord-258032-buh1e4tm 9 6 ( ( -LRB- cord-258032-buh1e4tm 9 7 MERS MERS NNP cord-258032-buh1e4tm 9 8 ) ) -RRB- cord-258032-buh1e4tm 9 9 coronavirus coronavirus NN cord-258032-buh1e4tm 9 10 , , , cord-258032-buh1e4tm 9 11 a a DT cord-258032-buh1e4tm 9 12 newly newly RB cord-258032-buh1e4tm 9 13 identified identify VBN cord-258032-buh1e4tm 9 14 pathogen pathogen NN cord-258032-buh1e4tm 9 15 , , , cord-258032-buh1e4tm 9 16 causes cause VBZ cord-258032-buh1e4tm 9 17 severe severe JJ cord-258032-buh1e4tm 9 18 pneumonia pneumonia NN cord-258032-buh1e4tm 9 19 in in IN cord-258032-buh1e4tm 9 20 humans human NNS cord-258032-buh1e4tm 9 21 , , , cord-258032-buh1e4tm 9 22 with with IN cord-258032-buh1e4tm 9 23 a a DT cord-258032-buh1e4tm 9 24 mortality mortality NN cord-258032-buh1e4tm 9 25 of of IN cord-258032-buh1e4tm 9 26 nearly nearly RB cord-258032-buh1e4tm 9 27 44 44 CD cord-258032-buh1e4tm 9 28 % % NN cord-258032-buh1e4tm 9 29 . . . cord-258032-buh1e4tm 10 1 Human human NN cord-258032-buh1e4tm 10 2 - - HYPH cord-258032-buh1e4tm 10 3 to to IN cord-258032-buh1e4tm 10 4 - - HYPH cord-258032-buh1e4tm 10 5 human human JJ cord-258032-buh1e4tm 10 6 spread spread NN cord-258032-buh1e4tm 10 7 has have VBZ cord-258032-buh1e4tm 10 8 been be VBN cord-258032-buh1e4tm 10 9 demonstrated demonstrate VBN cord-258032-buh1e4tm 10 10 , , , cord-258032-buh1e4tm 10 11 raising raise VBG cord-258032-buh1e4tm 10 12 the the DT cord-258032-buh1e4tm 10 13 possibility possibility NN cord-258032-buh1e4tm 10 14 that that IN cord-258032-buh1e4tm 10 15 the the DT cord-258032-buh1e4tm 10 16 infection infection NN cord-258032-buh1e4tm 10 17 could could MD cord-258032-buh1e4tm 10 18 become become VB cord-258032-buh1e4tm 10 19 pandemic pandemic JJ cord-258032-buh1e4tm 10 20 [ [ -LRB- cord-258032-buh1e4tm 10 21 1 1 CD cord-258032-buh1e4tm 10 22 ] ] -RRB- cord-258032-buh1e4tm 10 23 . . . cord-258032-buh1e4tm 11 1 A a DT cord-258032-buh1e4tm 11 2 colorized colorize VBN cord-258032-buh1e4tm 11 3 electron electron NN cord-258032-buh1e4tm 11 4 micrograph micrograph NN cord-258032-buh1e4tm 11 5 shows show VBZ cord-258032-buh1e4tm 11 6 the the DT cord-258032-buh1e4tm 11 7 coronavirus coronavirus NN cord-258032-buh1e4tm 11 8 MERS MERS NNP cord-258032-buh1e4tm 11 9 - - HYPH cord-258032-buh1e4tm 11 10 CoV cov NN cord-258032-buh1e4tm 11 11 acute acute JJ cord-258032-buh1e4tm 11 12 viral viral JJ cord-258032-buh1e4tm 11 13 respiratory respiratory JJ cord-258032-buh1e4tm 11 14 illness illness NN cord-258032-buh1e4tm 11 15 that that WDT cord-258032-buh1e4tm 11 16 is be VBZ cord-258032-buh1e4tm 11 17 characterized characterize VBN cord-258032-buh1e4tm 11 18 primarily primarily RB cord-258032-buh1e4tm 11 19 by by IN cord-258032-buh1e4tm 11 20 cough cough NN cord-258032-buh1e4tm 11 21 , , , cord-258032-buh1e4tm 11 22 fever fever NN cord-258032-buh1e4tm 11 23 , , , cord-258032-buh1e4tm 11 24 and and CC cord-258032-buh1e4tm 11 25 shortness shortness NN cord-258032-buh1e4tm 11 26 of of IN cord-258032-buh1e4tm 11 27 breath breath NN cord-258032-buh1e4tm 11 28 and and CC cord-258032-buh1e4tm 11 29 is be VBZ cord-258032-buh1e4tm 11 30 sometimes sometimes RB cord-258032-buh1e4tm 11 31 associated associate VBN cord-258032-buh1e4tm 11 32 with with IN cord-258032-buh1e4tm 11 33 severe severe JJ cord-258032-buh1e4tm 11 34 and and CC cord-258032-buh1e4tm 11 35 potentially potentially RB cord-258032-buh1e4tm 11 36 fatal fatal JJ cord-258032-buh1e4tm 11 37 complications complication NNS cord-258032-buh1e4tm 11 38 such such JJ cord-258032-buh1e4tm 11 39 as as IN cord-258032-buh1e4tm 11 40 pneumonia pneumonia NN cord-258032-buh1e4tm 11 41 and and CC cord-258032-buh1e4tm 11 42 kidney kidney NN cord-258032-buh1e4tm 11 43 failure failure NN cord-258032-buh1e4tm 11 44 . . . cord-258032-buh1e4tm 12 1 The the DT cord-258032-buh1e4tm 12 2 illness illness NN cord-258032-buh1e4tm 12 3 was be VBD cord-258032-buh1e4tm 12 4 first first RB cord-258032-buh1e4tm 12 5 observed observe VBN cord-258032-buh1e4tm 12 6 in in IN cord-258032-buh1e4tm 12 7 June June NNP cord-258032-buh1e4tm 12 8 2012 2012 CD cord-258032-buh1e4tm 12 9 in in IN cord-258032-buh1e4tm 12 10 Jiddah Jiddah NNP cord-258032-buh1e4tm 12 11 , , , cord-258032-buh1e4tm 12 12 Saudi Saudi NNP cord-258032-buh1e4tm 12 13 Arabia Arabia NNP cord-258032-buh1e4tm 12 14 , , , cord-258032-buh1e4tm 12 15 and and CC cord-258032-buh1e4tm 12 16 soon soon RB cord-258032-buh1e4tm 12 17 afterward afterward RB cord-258032-buh1e4tm 12 18 it -PRON- PRP cord-258032-buh1e4tm 12 19 was be VBD cord-258032-buh1e4tm 12 20 reported report VBN cord-258032-buh1e4tm 12 21 in in IN cord-258032-buh1e4tm 12 22 other other JJ cord-258032-buh1e4tm 12 23 countries country NNS cord-258032-buh1e4tm 12 24 in in IN cord-258032-buh1e4tm 12 25 the the DT cord-258032-buh1e4tm 12 26 Middle Middle NNP cord-258032-buh1e4tm 12 27 East East NNP cord-258032-buh1e4tm 12 28 , , , cord-258032-buh1e4tm 12 29 including include VBG cord-258032-buh1e4tm 12 30 Jordan Jordan NNP cord-258032-buh1e4tm 12 31 , , , cord-258032-buh1e4tm 12 32 Qatar Qatar NNP cord-258032-buh1e4tm 12 33 , , , cord-258032-buh1e4tm 12 34 and and CC cord-258032-buh1e4tm 12 35 the the DT cord-258032-buh1e4tm 12 36 United United NNP cord-258032-buh1e4tm 12 37 Arab Arab NNP cord-258032-buh1e4tm 12 38 Emirates Emirates NNPS cord-258032-buh1e4tm 12 39 ( ( -LRB- cord-258032-buh1e4tm 12 40 UAE UAE NNP cord-258032-buh1e4tm 12 41 ) ) -RRB- cord-258032-buh1e4tm 12 42 . . . cord-258032-buh1e4tm 13 1 It -PRON- PRP cord-258032-buh1e4tm 13 2 later later RB cord-258032-buh1e4tm 13 3 was be VBD cord-258032-buh1e4tm 13 4 detected detect VBN cord-258032-buh1e4tm 13 5 in in IN cord-258032-buh1e4tm 13 6 Europe Europe NNP cord-258032-buh1e4tm 13 7 , , , cord-258032-buh1e4tm 13 8 including include VBG cord-258032-buh1e4tm 13 9 cases case NNS cord-258032-buh1e4tm 13 10 in in IN cord-258032-buh1e4tm 13 11 France France NNP cord-258032-buh1e4tm 13 12 , , , cord-258032-buh1e4tm 13 13 Germany Germany NNP cord-258032-buh1e4tm 13 14 , , , cord-258032-buh1e4tm 13 15 Italy Italy NNP cord-258032-buh1e4tm 13 16 , , , cord-258032-buh1e4tm 13 17 and and CC cord-258032-buh1e4tm 13 18 the the DT cord-258032-buh1e4tm 13 19 United United NNP cord-258032-buh1e4tm 13 20 Kingdom Kingdom NNP cord-258032-buh1e4tm 13 21 ; ; : cord-258032-buh1e4tm 13 22 in in IN cord-258032-buh1e4tm 13 23 the the DT cord-258032-buh1e4tm 13 24 North north JJ cord-258032-buh1e4tm 13 25 African african JJ cord-258032-buh1e4tm 13 26 country country NN cord-258032-buh1e4tm 13 27 of of IN cord-258032-buh1e4tm 13 28 Tunisia Tunisia NNP cord-258032-buh1e4tm 13 29 ; ; : cord-258032-buh1e4tm 13 30 and and CC cord-258032-buh1e4tm 13 31 in in IN cord-258032-buh1e4tm 13 32 countries country NNS cord-258032-buh1e4tm 13 33 more more RBR cord-258032-buh1e4tm 13 34 distant distant JJ cord-258032-buh1e4tm 13 35 from from IN cord-258032-buh1e4tm 13 36 the the DT cord-258032-buh1e4tm 13 37 Middle Middle NNP cord-258032-buh1e4tm 13 38 East East NNP cord-258032-buh1e4tm 13 39 , , , cord-258032-buh1e4tm 13 40 including include VBG cord-258032-buh1e4tm 13 41 China China NNP cord-258032-buh1e4tm 13 42 , , , cord-258032-buh1e4tm 13 43 Malaysia Malaysia NNP cord-258032-buh1e4tm 13 44 , , , cord-258032-buh1e4tm 13 45 South South NNP cord-258032-buh1e4tm 13 46 Korea Korea NNP cord-258032-buh1e4tm 13 47 , , , cord-258032-buh1e4tm 13 48 and and CC cord-258032-buh1e4tm 13 49 the the DT cord-258032-buh1e4tm 13 50 United United NNP cord-258032-buh1e4tm 13 51 States States NNP cord-258032-buh1e4tm 13 52 . . . cord-258032-buh1e4tm 14 1 The the DT cord-258032-buh1e4tm 14 2 largest large JJS cord-258032-buh1e4tm 14 3 MERS MERS NNP cord-258032-buh1e4tm 14 4 outbreak outbreak NN cord-258032-buh1e4tm 14 5 outside outside IN cord-258032-buh1e4tm 14 6 Saudi Saudi NNP cord-258032-buh1e4tm 14 7 Arabia Arabia NNP cord-258032-buh1e4tm 14 8 occurred occur VBD cord-258032-buh1e4tm 14 9 in in IN cord-258032-buh1e4tm 14 10 2015 2015 CD cord-258032-buh1e4tm 14 11 , , , cord-258032-buh1e4tm 14 12 when when WRB cord-258032-buh1e4tm 14 13 an an DT cord-258032-buh1e4tm 14 14 individual individual NN cord-258032-buh1e4tm 14 15 who who WP cord-258032-buh1e4tm 14 16 had have VBD cord-258032-buh1e4tm 14 17 recently recently RB cord-258032-buh1e4tm 14 18 traveled travel VBN cord-258032-buh1e4tm 14 19 to to IN cord-258032-buh1e4tm 14 20 the the DT cord-258032-buh1e4tm 14 21 Middle Middle NNP cord-258032-buh1e4tm 14 22 East East NNP cord-258032-buh1e4tm 14 23 subsequently subsequently RB cord-258032-buh1e4tm 14 24 fell fall VBD cord-258032-buh1e4tm 14 25 ill ill JJ cord-258032-buh1e4tm 14 26 in in IN cord-258032-buh1e4tm 14 27 South South NNP cord-258032-buh1e4tm 14 28 Korea Korea NNP cord-258032-buh1e4tm 14 29 , , , cord-258032-buh1e4tm 14 30 transmitting transmit VBG cord-258032-buh1e4tm 14 31 the the DT cord-258032-buh1e4tm 14 32 disease disease NN cord-258032-buh1e4tm 14 33 to to TO cord-258032-buh1e4tm 14 34 close close VB cord-258032-buh1e4tm 14 35 contacts contact NNS cord-258032-buh1e4tm 14 36 . . . cord-258032-buh1e4tm 15 1 The the DT cord-258032-buh1e4tm 15 2 dissemination dissemination NN cord-258032-buh1e4tm 15 3 of of IN cord-258032-buh1e4tm 15 4 the the DT cord-258032-buh1e4tm 15 5 disease disease NN cord-258032-buh1e4tm 15 6 by by IN cord-258032-buh1e4tm 15 7 infected infected JJ cord-258032-buh1e4tm 15 8 travelers traveler NNS cord-258032-buh1e4tm 15 9 leaving leave VBG cord-258032-buh1e4tm 15 10 the the DT cord-258032-buh1e4tm 15 11 Middle Middle NNP cord-258032-buh1e4tm 15 12 East East NNP cord-258032-buh1e4tm 15 13 suggested suggest VBD cord-258032-buh1e4tm 15 14 that that IN cord-258032-buh1e4tm 15 15 MERS MERS NNP cord-258032-buh1e4tm 15 16 had have VBD cord-258032-buh1e4tm 15 17 the the DT cord-258032-buh1e4tm 15 18 potential potential NN cord-258032-buh1e4tm 15 19 to to TO cord-258032-buh1e4tm 15 20 escalate escalate VB cord-258032-buh1e4tm 15 21 into into IN cord-258032-buh1e4tm 15 22 an an DT cord-258032-buh1e4tm 15 23 international international JJ cord-258032-buh1e4tm 15 24 public public JJ cord-258032-buh1e4tm 15 25 health health NN cord-258032-buh1e4tm 15 26 emergency emergency NN cord-258032-buh1e4tm 15 27 . . . cord-258032-buh1e4tm 16 1 The the DT cord-258032-buh1e4tm 16 2 possibility possibility NN cord-258032-buh1e4tm 16 3 of of IN cord-258032-buh1e4tm 16 4 a a DT cord-258032-buh1e4tm 16 5 pandemic pandemic NN cord-258032-buh1e4tm 16 6 was be VBD cord-258032-buh1e4tm 16 7 thought think VBN cord-258032-buh1e4tm 16 8 to to TO cord-258032-buh1e4tm 16 9 be be VB cord-258032-buh1e4tm 16 10 impeded impede VBN cord-258032-buh1e4tm 16 11 , , , cord-258032-buh1e4tm 16 12 however however RB cord-258032-buh1e4tm 16 13 , , , cord-258032-buh1e4tm 16 14 by by IN cord-258032-buh1e4tm 16 15 the the DT cord-258032-buh1e4tm 16 16 limited limited JJ cord-258032-buh1e4tm 16 17 ability ability NN cord-258032-buh1e4tm 16 18 of of IN cord-258032-buh1e4tm 16 19 the the DT cord-258032-buh1e4tm 16 20 disease disease NN cord-258032-buh1e4tm 16 21 to to TO cord-258032-buh1e4tm 16 22 be be VB cord-258032-buh1e4tm 16 23 passed pass VBN cord-258032-buh1e4tm 16 24 from from IN cord-258032-buh1e4tm 16 25 one one CD cord-258032-buh1e4tm 16 26 person person NN cord-258032-buh1e4tm 16 27 to to IN cord-258032-buh1e4tm 16 28 another another DT cord-258032-buh1e4tm 16 29 . . . cord-258032-buh1e4tm 17 1 MERS MERS NNP cord-258032-buh1e4tm 17 2 is be VBZ cord-258032-buh1e4tm 17 3 caused cause VBN cord-258032-buh1e4tm 17 4 by by IN cord-258032-buh1e4tm 17 5 a a DT cord-258032-buh1e4tm 17 6 coronavirus coronavirus NN cord-258032-buh1e4tm 17 7 known know VBN cord-258032-buh1e4tm 17 8 as as IN cord-258032-buh1e4tm 17 9 MERS MERS NNP cord-258032-buh1e4tm 17 10 - - HYPH cord-258032-buh1e4tm 17 11 CoV CoV NNP cord-258032-buh1e4tm 17 12 , , , cord-258032-buh1e4tm 17 13 which which WDT cord-258032-buh1e4tm 17 14 attacks attack VBZ cord-258032-buh1e4tm 17 15 the the DT cord-258032-buh1e4tm 17 16 respiratory respiratory JJ cord-258032-buh1e4tm 17 17 system system NN cord-258032-buh1e4tm 17 18 . . . cord-258032-buh1e4tm 18 1 The the DT cord-258032-buh1e4tm 18 2 recently recently RB cord-258032-buh1e4tm 18 3 defined define VBN cord-258032-buh1e4tm 18 4 receptor receptor NN cord-258032-buh1e4tm 18 5 for for IN cord-258032-buh1e4tm 18 6 MERS MERS NNP cord-258032-buh1e4tm 18 7 - - HYPH cord-258032-buh1e4tm 18 8 CoV CoV NNP cord-258032-buh1e4tm 18 9 , , , cord-258032-buh1e4tm 18 10 dipeptidyl dipeptidyl JJ cord-258032-buh1e4tm 18 11 peptidase peptidase NN cord-258032-buh1e4tm 18 12 4 4 CD cord-258032-buh1e4tm 18 13 ( ( -LRB- cord-258032-buh1e4tm 18 14 DPP4 DPP4 NNP cord-258032-buh1e4tm 18 15 ) ) -RRB- cord-258032-buh1e4tm 18 16 , , , cord-258032-buh1e4tm 18 17 is be VBZ cord-258032-buh1e4tm 18 18 generally generally RB cord-258032-buh1e4tm 18 19 expressed express VBN cord-258032-buh1e4tm 18 20 in in IN cord-258032-buh1e4tm 18 21 endothelial endothelial JJ cord-258032-buh1e4tm 18 22 and and CC cord-258032-buh1e4tm 18 23 epithelial epithelial JJ cord-258032-buh1e4tm 18 24 cells cell NNS cord-258032-buh1e4tm 18 25 and and CC cord-258032-buh1e4tm 18 26 has have VBZ cord-258032-buh1e4tm 18 27 been be VBN cord-258032-buh1e4tm 18 28 shown show VBN cord-258032-buh1e4tm 18 29 to to TO cord-258032-buh1e4tm 18 30 be be VB cord-258032-buh1e4tm 18 31 present present JJ cord-258032-buh1e4tm 18 32 on on IN cord-258032-buh1e4tm 18 33 cultured cultured JJ cord-258032-buh1e4tm 18 34 human human JJ cord-258032-buh1e4tm 18 35 nonciliated nonciliate VBN cord-258032-buh1e4tm 18 36 bronchiolar bronchiolar NNP cord-258032-buh1e4tm 18 37 epithelium epithelium NN cord-258032-buh1e4tm 18 38 cells cell NNS cord-258032-buh1e4tm 18 39 , , , cord-258032-buh1e4tm 18 40 providing provide VBG cord-258032-buh1e4tm 18 41 further further JJ cord-258032-buh1e4tm 18 42 information information NN cord-258032-buh1e4tm 18 43 on on IN cord-258032-buh1e4tm 18 44 the the DT cord-258032-buh1e4tm 18 45 respiratory respiratory JJ cord-258032-buh1e4tm 18 46 tropism tropism NN cord-258032-buh1e4tm 18 47 of of IN cord-258032-buh1e4tm 18 48 MERS MERS NNP cord-258032-buh1e4tm 18 49 - - HYPH cord-258032-buh1e4tm 18 50 CoV CoV NNP cord-258032-buh1e4tm 18 51 [ [ -LRB- cord-258032-buh1e4tm 18 52 2 2 CD cord-258032-buh1e4tm 18 53 ] ] -RRB- cord-258032-buh1e4tm 18 54 . . . cord-258032-buh1e4tm 19 1 Symptoms symptom NNS cord-258032-buh1e4tm 19 2 of of IN cord-258032-buh1e4tm 19 3 illness illness NN cord-258032-buh1e4tm 19 4 appear appear VBP cord-258032-buh1e4tm 19 5 anytime anytime RB cord-258032-buh1e4tm 19 6 from from IN cord-258032-buh1e4tm 19 7 2 2 CD cord-258032-buh1e4tm 19 8 to to TO cord-258032-buh1e4tm 19 9 14 14 CD cord-258032-buh1e4tm 19 10 days day NNS cord-258032-buh1e4tm 19 11 following follow VBG cord-258032-buh1e4tm 19 12 infection infection NN cord-258032-buh1e4tm 19 13 . . . cord-258032-buh1e4tm 20 1 Cough cough NN cord-258032-buh1e4tm 20 2 , , , cord-258032-buh1e4tm 20 3 fever fever NN cord-258032-buh1e4tm 20 4 , , , cord-258032-buh1e4tm 20 5 and and CC cord-258032-buh1e4tm 20 6 shortness shortness NN cord-258032-buh1e4tm 20 7 of of IN cord-258032-buh1e4tm 20 8 breath breath NN cord-258032-buh1e4tm 20 9 are be VBP cord-258032-buh1e4tm 20 10 the the DT cord-258032-buh1e4tm 20 11 primary primary JJ cord-258032-buh1e4tm 20 12 symptoms symptom NNS cord-258032-buh1e4tm 20 13 , , , cord-258032-buh1e4tm 20 14 but but CC cord-258032-buh1e4tm 20 15 others other NNS cord-258032-buh1e4tm 20 16 such such JJ cord-258032-buh1e4tm 20 17 as as IN cord-258032-buh1e4tm 20 18 diarrhea diarrhea NN cord-258032-buh1e4tm 20 19 , , , cord-258032-buh1e4tm 20 20 nausea nausea NN cord-258032-buh1e4tm 20 21 , , , cord-258032-buh1e4tm 20 22 vomiting vomit VBG cord-258032-buh1e4tm 20 23 , , , cord-258032-buh1e4tm 20 24 and and CC cord-258032-buh1e4tm 20 25 myalgia myalgia NN cord-258032-buh1e4tm 20 26 ( ( -LRB- cord-258032-buh1e4tm 20 27 muscle muscle NN cord-258032-buh1e4tm 20 28 pain pain NN cord-258032-buh1e4tm 20 29 ) ) -RRB- cord-258032-buh1e4tm 20 30 can can MD cord-258032-buh1e4tm 20 31 also also RB cord-258032-buh1e4tm 20 32 occur occur VB cord-258032-buh1e4tm 20 33 . . . cord-258032-buh1e4tm 21 1 In in IN cord-258032-buh1e4tm 21 2 some some DT cord-258032-buh1e4tm 21 3 persons person NNS cord-258032-buh1e4tm 21 4 , , , cord-258032-buh1e4tm 21 5 infection infection NN cord-258032-buh1e4tm 21 6 produces produce VBZ cord-258032-buh1e4tm 21 7 no no DT cord-258032-buh1e4tm 21 8 symptoms symptom NNS cord-258032-buh1e4tm 21 9 or or CC cord-258032-buh1e4tm 21 10 only only RB cord-258032-buh1e4tm 21 11 mild mild JJ cord-258032-buh1e4tm 21 12 cold cold JJ cord-258032-buh1e4tm 21 13 - - HYPH cord-258032-buh1e4tm 21 14 like like JJ cord-258032-buh1e4tm 21 15 symptoms symptom NNS cord-258032-buh1e4tm 21 16 , , , cord-258032-buh1e4tm 21 17 whereas whereas IN cord-258032-buh1e4tm 21 18 in in IN cord-258032-buh1e4tm 21 19 others other NNS cord-258032-buh1e4tm 21 20 , , , cord-258032-buh1e4tm 21 21 particularly particularly RB cord-258032-buh1e4tm 21 22 in in IN cord-258032-buh1e4tm 21 23 persons person NNS cord-258032-buh1e4tm 21 24 with with IN cord-258032-buh1e4tm 21 25 underlying underlying JJ cord-258032-buh1e4tm 21 26 medical medical JJ cord-258032-buh1e4tm 21 27 conditions condition NNS cord-258032-buh1e4tm 21 28 , , , cord-258032-buh1e4tm 21 29 infection infection NN cord-258032-buh1e4tm 21 30 can can MD cord-258032-buh1e4tm 21 31 produce produce VB cord-258032-buh1e4tm 21 32 severe severe JJ cord-258032-buh1e4tm 21 33 illness illness NN cord-258032-buh1e4tm 21 34 [ [ -LRB- cord-258032-buh1e4tm 21 35 3 3 CD cord-258032-buh1e4tm 21 36 ] ] -RRB- cord-258032-buh1e4tm 21 37 . . . cord-258032-buh1e4tm 22 1 It -PRON- PRP cord-258032-buh1e4tm 22 2 is be VBZ cord-258032-buh1e4tm 22 3 well well RB cord-258032-buh1e4tm 22 4 - - HYPH cord-258032-buh1e4tm 22 5 known know VBN cord-258032-buh1e4tm 22 6 that that IN cord-258032-buh1e4tm 22 7 dynamic dynamic JJ cord-258032-buh1e4tm 22 8 models model NNS cord-258032-buh1e4tm 22 9 are be VBP cord-258032-buh1e4tm 22 10 still still RB cord-258032-buh1e4tm 22 11 playing play VBG cord-258032-buh1e4tm 22 12 important important JJ cord-258032-buh1e4tm 22 13 roles role NNS cord-258032-buh1e4tm 22 14 in in IN cord-258032-buh1e4tm 22 15 describing describe VBG cord-258032-buh1e4tm 22 16 the the DT cord-258032-buh1e4tm 22 17 interactions interaction NNS cord-258032-buh1e4tm 22 18 among among IN cord-258032-buh1e4tm 22 19 uninfected uninfected JJ cord-258032-buh1e4tm 22 20 cells cell NNS cord-258032-buh1e4tm 22 21 , , , cord-258032-buh1e4tm 22 22 free free JJ cord-258032-buh1e4tm 22 23 viruses virus NNS cord-258032-buh1e4tm 22 24 , , , cord-258032-buh1e4tm 22 25 and and CC cord-258032-buh1e4tm 22 26 immune immune JJ cord-258032-buh1e4tm 22 27 responses response NNS cord-258032-buh1e4tm 22 28 ( ( -LRB- cord-258032-buh1e4tm 22 29 see see VB cord-258032-buh1e4tm 22 30 , , , cord-258032-buh1e4tm 22 31 e.g. e.g. RB cord-258032-buh1e4tm 22 32 , , , cord-258032-buh1e4tm 22 33 [ [ -LRB- cord-258032-buh1e4tm 22 34 4 4 CD cord-258032-buh1e4tm 22 35 ] ] -RRB- cord-258032-buh1e4tm 23 1 [ [ -LRB- cord-258032-buh1e4tm 23 2 5 5 CD cord-258032-buh1e4tm 23 3 ] ] -RRB- cord-258032-buh1e4tm 23 4 [ [ -LRB- cord-258032-buh1e4tm 23 5 6 6 CD cord-258032-buh1e4tm 23 6 ] ] -RRB- cord-258032-buh1e4tm 23 7 [ [ -LRB- cord-258032-buh1e4tm 23 8 7 7 CD cord-258032-buh1e4tm 23 9 ] ] -RRB- cord-258032-buh1e4tm 23 10 ) ) -RRB- cord-258032-buh1e4tm 23 11 . . . cord-258032-buh1e4tm 24 1 A a DT cord-258032-buh1e4tm 24 2 three three CD cord-258032-buh1e4tm 24 3 - - HYPH cord-258032-buh1e4tm 24 4 dimensional dimensional JJ cord-258032-buh1e4tm 24 5 dynamic dynamic JJ cord-258032-buh1e4tm 24 6 model model NN cord-258032-buh1e4tm 24 7 for for IN cord-258032-buh1e4tm 24 8 viral viral JJ cord-258032-buh1e4tm 24 9 infection infection NN cord-258032-buh1e4tm 24 10 is be VBZ cord-258032-buh1e4tm 24 11 proposed propose VBN cord-258032-buh1e4tm 24 12 by by IN cord-258032-buh1e4tm 24 13 Nowak Nowak NNP cord-258032-buh1e4tm 24 14 et et NNP cord-258032-buh1e4tm 24 15 al al NNP cord-258032-buh1e4tm 24 16 . . . cord-258032-buh1e4tm 25 1 ( ( -LRB- cord-258032-buh1e4tm 25 2 see see VB cord-258032-buh1e4tm 25 3 , , , cord-258032-buh1e4tm 25 4 e.g. e.g. RB cord-258032-buh1e4tm 25 5 , , , cord-258032-buh1e4tm 25 6 [ [ -LRB- cord-258032-buh1e4tm 25 7 5 5 CD cord-258032-buh1e4tm 25 8 ] ] -RRB- cord-258032-buh1e4tm 25 9 [ [ -LRB- cord-258032-buh1e4tm 25 10 6 6 CD cord-258032-buh1e4tm 25 11 ] ] -RRB- cord-258032-buh1e4tm 25 12 [ [ -LRB- cord-258032-buh1e4tm 25 13 7 7 CD cord-258032-buh1e4tm 25 14 ] ] -RRB- cord-258032-buh1e4tm 25 15 ) ) -RRB- cord-258032-buh1e4tm 25 16 . . . cord-258032-buh1e4tm 26 1 ( ( -LRB- cord-258032-buh1e4tm 26 2 1 1 CD cord-258032-buh1e4tm 26 3 ) ) -RRB- cord-258032-buh1e4tm 27 1 In in IN cord-258032-buh1e4tm 27 2 model model NN cord-258032-buh1e4tm 27 3 ( ( -LRB- cord-258032-buh1e4tm 27 4 1 1 CD cord-258032-buh1e4tm 27 5 ) ) -RRB- cord-258032-buh1e4tm 27 6 , , , cord-258032-buh1e4tm 27 7 ( ( -LRB- cord-258032-buh1e4tm 27 8 ) ) -RRB- cord-258032-buh1e4tm 27 9 , , , cord-258032-buh1e4tm 27 10 ( ( -LRB- cord-258032-buh1e4tm 27 11 ) ) -RRB- cord-258032-buh1e4tm 27 12 , , , cord-258032-buh1e4tm 27 13 and and CC cord-258032-buh1e4tm 27 14 V V NNP cord-258032-buh1e4tm 27 15 ( ( -LRB- cord-258032-buh1e4tm 27 16 ) ) -RRB- cord-258032-buh1e4tm 27 17 denote denote VB cord-258032-buh1e4tm 27 18 the the DT cord-258032-buh1e4tm 27 19 concentration concentration NN cord-258032-buh1e4tm 27 20 of of IN cord-258032-buh1e4tm 27 21 uninfected uninfected JJ cord-258032-buh1e4tm 27 22 cells cell NNS cord-258032-buh1e4tm 27 23 , , , cord-258032-buh1e4tm 27 24 infected infected JJ cord-258032-buh1e4tm 27 25 cells cell NNS cord-258032-buh1e4tm 27 26 , , , cord-258032-buh1e4tm 27 27 and and CC cord-258032-buh1e4tm 27 28 free free JJ cord-258032-buh1e4tm 27 29 viruses virus NNS cord-258032-buh1e4tm 27 30 at at IN cord-258032-buh1e4tm 27 31 time time NN cord-258032-buh1e4tm 27 32 , , , cord-258032-buh1e4tm 27 33 respectively respectively RB cord-258032-buh1e4tm 27 34 . . . cord-258032-buh1e4tm 28 1 The the DT cord-258032-buh1e4tm 28 2 constant constant JJ cord-258032-buh1e4tm 28 3 > > XX cord-258032-buh1e4tm 28 4 0 0 NFP cord-258032-buh1e4tm 28 5 is be VBZ cord-258032-buh1e4tm 28 6 the the DT cord-258032-buh1e4tm 28 7 rate rate NN cord-258032-buh1e4tm 28 8 at at IN cord-258032-buh1e4tm 28 9 which which WDT cord-258032-buh1e4tm 28 10 new new JJ cord-258032-buh1e4tm 28 11 uninfected uninfected JJ cord-258032-buh1e4tm 28 12 cells cell NNS cord-258032-buh1e4tm 28 13 are be VBP cord-258032-buh1e4tm 28 14 generated generate VBN cord-258032-buh1e4tm 28 15 ( ( -LRB- cord-258032-buh1e4tm 28 16 from from IN cord-258032-buh1e4tm 28 17 a a DT cord-258032-buh1e4tm 28 18 pool pool NN cord-258032-buh1e4tm 28 19 of of IN cord-258032-buh1e4tm 28 20 precursor precursor NN cord-258032-buh1e4tm 28 21 cells cell NNS cord-258032-buh1e4tm 28 22 ) ) -RRB- cord-258032-buh1e4tm 28 23 . . . cord-258032-buh1e4tm 29 1 The the DT cord-258032-buh1e4tm 29 2 constants constant NNS cord-258032-buh1e4tm 29 3 > > XX cord-258032-buh1e4tm 29 4 0 0 CD cord-258032-buh1e4tm 29 5 and and CC cord-258032-buh1e4tm 29 6 ≥ ≥ CD cord-258032-buh1e4tm 29 7 0 0 CD cord-258032-buh1e4tm 29 8 are be VBP cord-258032-buh1e4tm 29 9 the the DT cord-258032-buh1e4tm 29 10 death death NN cord-258032-buh1e4tm 29 11 rate rate NN cord-258032-buh1e4tm 29 12 of of IN cord-258032-buh1e4tm 29 13 uninfected uninfected JJ cord-258032-buh1e4tm 29 14 cells cell NNS cord-258032-buh1e4tm 29 15 and and CC cord-258032-buh1e4tm 29 16 the the DT cord-258032-buh1e4tm 29 17 rate rate NN cord-258032-buh1e4tm 29 18 constant constant NN cord-258032-buh1e4tm 29 19 characterizing characterize VBG cord-258032-buh1e4tm 29 20 infection infection NN cord-258032-buh1e4tm 29 21 of of IN cord-258032-buh1e4tm 29 22 the the DT cord-258032-buh1e4tm 29 23 cells cell NNS cord-258032-buh1e4tm 29 24 , , , cord-258032-buh1e4tm 29 25 respectively respectively RB cord-258032-buh1e4tm 29 26 . . . cord-258032-buh1e4tm 30 1 The the DT cord-258032-buh1e4tm 30 2 constant constant JJ cord-258032-buh1e4tm 30 3 1 1 CD cord-258032-buh1e4tm 30 4 > > SYM cord-258032-buh1e4tm 30 5 0 0 NFP cord-258032-buh1e4tm 30 6 is be VBZ cord-258032-buh1e4tm 30 7 the the DT cord-258032-buh1e4tm 30 8 death death NN cord-258032-buh1e4tm 30 9 rate rate NN cord-258032-buh1e4tm 30 10 of of IN cord-258032-buh1e4tm 30 11 the the DT cord-258032-buh1e4tm 30 12 infected infected JJ cord-258032-buh1e4tm 30 13 cells cell NNS cord-258032-buh1e4tm 30 14 due due IN cord-258032-buh1e4tm 30 15 to to IN cord-258032-buh1e4tm 30 16 either either CC cord-258032-buh1e4tm 30 17 viruses virus NNS cord-258032-buh1e4tm 30 18 or or CC cord-258032-buh1e4tm 30 19 immune immune JJ cord-258032-buh1e4tm 30 20 responses response NNS cord-258032-buh1e4tm 30 21 . . . cord-258032-buh1e4tm 31 1 The the DT cord-258032-buh1e4tm 31 2 infected infected JJ cord-258032-buh1e4tm 31 3 cells cell NNS cord-258032-buh1e4tm 31 4 produce produce VBP cord-258032-buh1e4tm 31 5 new new JJ cord-258032-buh1e4tm 31 6 viruses virus NNS cord-258032-buh1e4tm 31 7 at at IN cord-258032-buh1e4tm 31 8 the the DT cord-258032-buh1e4tm 31 9 rate rate NN cord-258032-buh1e4tm 31 10 1 1 CD cord-258032-buh1e4tm 31 11 during during IN cord-258032-buh1e4tm 31 12 their -PRON- PRP$ cord-258032-buh1e4tm 31 13 life life NN cord-258032-buh1e4tm 31 14 , , , cord-258032-buh1e4tm 31 15 on on IN cord-258032-buh1e4tm 31 16 average average JJ cord-258032-buh1e4tm 31 17 having have VBG cord-258032-buh1e4tm 31 18 the the DT cord-258032-buh1e4tm 31 19 length length NN cord-258032-buh1e4tm 31 20 1/ 1/ CD cord-258032-buh1e4tm 31 21 1 1 CD cord-258032-buh1e4tm 31 22 , , , cord-258032-buh1e4tm 31 23 where where WRB cord-258032-buh1e4tm 31 24 > > XX cord-258032-buh1e4tm 31 25 0 0 NFP cord-258032-buh1e4tm 31 26 is be VBZ cord-258032-buh1e4tm 31 27 some some DT cord-258032-buh1e4tm 31 28 integer integ JJR cord-258032-buh1e4tm 31 29 number number NN cord-258032-buh1e4tm 31 30 . . . cord-258032-buh1e4tm 32 1 The the DT cord-258032-buh1e4tm 32 2 constant constant JJ cord-258032-buh1e4tm 32 3 > > XX cord-258032-buh1e4tm 32 4 0 0 NFP cord-258032-buh1e4tm 32 5 is be VBZ cord-258032-buh1e4tm 32 6 the the DT cord-258032-buh1e4tm 32 7 rate rate NN cord-258032-buh1e4tm 32 8 at at IN cord-258032-buh1e4tm 32 9 which which WDT cord-258032-buh1e4tm 32 10 the the DT cord-258032-buh1e4tm 32 11 viruses virus NNS cord-258032-buh1e4tm 32 12 are be VBP cord-258032-buh1e4tm 32 13 cleared clear VBN cord-258032-buh1e4tm 32 14 , , , cord-258032-buh1e4tm 32 15 and and CC cord-258032-buh1e4tm 32 16 the the DT cord-258032-buh1e4tm 32 17 average average JJ cord-258032-buh1e4tm 32 18 lifetime lifetime NN cord-258032-buh1e4tm 32 19 of of IN cord-258032-buh1e4tm 32 20 a a DT cord-258032-buh1e4tm 32 21 free free JJ cord-258032-buh1e4tm 32 22 virus virus NN cord-258032-buh1e4tm 32 23 is be VBZ cord-258032-buh1e4tm 32 24 1/ 1/ CD cord-258032-buh1e4tm 32 25 . . . cord-258032-buh1e4tm 33 1 Figure figure NN cord-258032-buh1e4tm 33 2 1 1 CD cord-258032-buh1e4tm 33 3 shows show VBZ cord-258032-buh1e4tm 33 4 a a DT cord-258032-buh1e4tm 33 5 interaction interaction NN cord-258032-buh1e4tm 33 6 procedure procedure NN cord-258032-buh1e4tm 33 7 between between IN cord-258032-buh1e4tm 33 8 uninfected uninfected JJ cord-258032-buh1e4tm 33 9 cells cell NNS cord-258032-buh1e4tm 33 10 and and CC cord-258032-buh1e4tm 33 11 MERS MERS NNP cord-258032-buh1e4tm 33 12 - - HYPH cord-258032-buh1e4tm 33 13 CoV cov NN cord-258032-buh1e4tm 33 14 mediated mediate VBN cord-258032-buh1e4tm 33 15 by by IN cord-258032-buh1e4tm 33 16 DPP4 DPP4 NNP cord-258032-buh1e4tm 33 17 receptors receptor NNS cord-258032-buh1e4tm 33 18 . . . cord-258032-buh1e4tm 34 1 Based base VBN cord-258032-buh1e4tm 34 2 on on IN cord-258032-buh1e4tm 34 3 basic basic JJ cord-258032-buh1e4tm 34 4 dynamic dynamic JJ cord-258032-buh1e4tm 34 5 model model NN cord-258032-buh1e4tm 34 6 ( ( -LRB- cord-258032-buh1e4tm 34 7 1 1 CD cord-258032-buh1e4tm 34 8 ) ) -RRB- cord-258032-buh1e4tm 34 9 and and CC cord-258032-buh1e4tm 34 10 Figure Figure NNP cord-258032-buh1e4tm 34 11 1 1 CD cord-258032-buh1e4tm 34 12 , , , cord-258032-buh1e4tm 34 13 we -PRON- PRP cord-258032-buh1e4tm 34 14 propose propose VBP cord-258032-buh1e4tm 34 15 the the DT cord-258032-buh1e4tm 34 16 following following JJ cord-258032-buh1e4tm 34 17 novel novel JJ cord-258032-buh1e4tm 34 18 four four CD cord-258032-buh1e4tm 34 19 - - HYPH cord-258032-buh1e4tm 34 20 dimensional dimensional JJ cord-258032-buh1e4tm 34 21 dynamic dynamic JJ cord-258032-buh1e4tm 34 22 model model NN cord-258032-buh1e4tm 34 23 which which WDT cord-258032-buh1e4tm 34 24 describes describe VBZ cord-258032-buh1e4tm 34 25 the the DT cord-258032-buh1e4tm 34 26 spread spread NN cord-258032-buh1e4tm 34 27 of of IN cord-258032-buh1e4tm 34 28 the the DT cord-258032-buh1e4tm 34 29 MERS MERS NNP cord-258032-buh1e4tm 34 30 - - HYPH cord-258032-buh1e4tm 34 31 CoV CoV NNP cord-258032-buh1e4tm 34 32 and and CC cord-258032-buh1e4tm 34 33 the the DT cord-258032-buh1e4tm 34 34 expression expression NN cord-258032-buh1e4tm 34 35 of of IN cord-258032-buh1e4tm 34 36 DPP4:̇= DPP4:̇= NNP cord-258032-buh1e4tm 35 1 In in IN cord-258032-buh1e4tm 35 2 model model NN cord-258032-buh1e4tm 35 3 ( ( -LRB- cord-258032-buh1e4tm 35 4 2 2 CD cord-258032-buh1e4tm 35 5 ) ) -RRB- cord-258032-buh1e4tm 35 6 , , , cord-258032-buh1e4tm 35 7 ( ( -LRB- cord-258032-buh1e4tm 35 8 ) ) -RRB- cord-258032-buh1e4tm 35 9 represents represent VBZ cord-258032-buh1e4tm 35 10 the the DT cord-258032-buh1e4tm 35 11 concentration concentration NN cord-258032-buh1e4tm 35 12 of of IN cord-258032-buh1e4tm 35 13 DPP4 DPP4 NNP cord-258032-buh1e4tm 35 14 on on IN cord-258032-buh1e4tm 35 15 the the DT cord-258032-buh1e4tm 35 16 surface surface NN cord-258032-buh1e4tm 35 17 of of IN cord-258032-buh1e4tm 35 18 uninfected uninfected JJ cord-258032-buh1e4tm 35 19 cells cell NNS cord-258032-buh1e4tm 35 20 , , , cord-258032-buh1e4tm 35 21 which which WDT cord-258032-buh1e4tm 35 22 can can MD cord-258032-buh1e4tm 35 23 be be VB cord-258032-buh1e4tm 35 24 recognized recognize VBN cord-258032-buh1e4tm 35 25 by by IN cord-258032-buh1e4tm 35 26 surface surface NN cord-258032-buh1e4tm 35 27 spike spike NN cord-258032-buh1e4tm 35 28 ( ( -LRB- cord-258032-buh1e4tm 35 29 S s NN cord-258032-buh1e4tm 35 30 ) ) -RRB- cord-258032-buh1e4tm 35 31 protein protein NN cord-258032-buh1e4tm 35 32 of of IN cord-258032-buh1e4tm 35 33 MERS MERS NNP cord-258032-buh1e4tm 35 34 - - HYPH cord-258032-buh1e4tm 35 35 CoV CoV NNP cord-258032-buh1e4tm 35 36 ( ( -LRB- cord-258032-buh1e4tm 35 37 see see UH cord-258032-buh1e4tm 35 38 , , , cord-258032-buh1e4tm 35 39 e.g. e.g. RB cord-258032-buh1e4tm 35 40 , , , cord-258032-buh1e4tm 35 41 [ [ -LRB- cord-258032-buh1e4tm 35 42 8 8 CD cord-258032-buh1e4tm 35 43 ] ] -RRB- cord-258032-buh1e4tm 35 44 ) ) -RRB- cord-258032-buh1e4tm 35 45 . . . cord-258032-buh1e4tm 36 1 Infected infected JJ cord-258032-buh1e4tm 36 2 cells cell NNS cord-258032-buh1e4tm 36 3 are be VBP cord-258032-buh1e4tm 36 4 produced produce VBN cord-258032-buh1e4tm 36 5 from from IN cord-258032-buh1e4tm 36 6 uninfected uninfected JJ cord-258032-buh1e4tm 36 7 cells cell NNS cord-258032-buh1e4tm 36 8 and and CC cord-258032-buh1e4tm 36 9 free free JJ cord-258032-buh1e4tm 36 10 viruses virus NNS cord-258032-buh1e4tm 36 11 at at IN cord-258032-buh1e4tm 36 12 the the DT cord-258032-buh1e4tm 36 13 rate rate NN cord-258032-buh1e4tm 36 14 ( ( -LRB- cord-258032-buh1e4tm 36 15 ( ( -LRB- cord-258032-buh1e4tm 36 16 ) ) -RRB- cord-258032-buh1e4tm 37 1 ) ) -RRB- cord-258032-buh1e4tm 37 2 V v NN cord-258032-buh1e4tm 37 3 ( ( -LRB- cord-258032-buh1e4tm 37 4 ) ) -RRB- cord-258032-buh1e4tm 37 5 ( ( -LRB- cord-258032-buh1e4tm 37 6 ) ) -RRB- cord-258032-buh1e4tm 37 7 . . . cord-258032-buh1e4tm 38 1 It -PRON- PRP cord-258032-buh1e4tm 38 2 is be VBZ cord-258032-buh1e4tm 38 3 assumed assume VBN cord-258032-buh1e4tm 38 4 that that IN cord-258032-buh1e4tm 38 5 DPP4 DPP4 NNP cord-258032-buh1e4tm 38 6 is be VBZ cord-258032-buh1e4tm 38 7 produced produce VBN cord-258032-buh1e4tm 38 8 from from IN cord-258032-buh1e4tm 38 9 the the DT cord-258032-buh1e4tm 38 10 surface surface NN cord-258032-buh1e4tm 38 11 of of IN cord-258032-buh1e4tm 38 12 uninfected uninfected JJ cord-258032-buh1e4tm 38 13 cells cell NNS cord-258032-buh1e4tm 38 14 at at IN cord-258032-buh1e4tm 38 15 the the DT cord-258032-buh1e4tm 38 16 constant constant JJ cord-258032-buh1e4tm 38 17 rate rate NN cord-258032-buh1e4tm 38 18 1 1 CD cord-258032-buh1e4tm 38 19 > > SYM cord-258032-buh1e4tm 38 20 0 0 CD cord-258032-buh1e4tm 38 21 . . . cord-258032-buh1e4tm 39 1 DPP4 DPP4 NNP cord-258032-buh1e4tm 39 2 is be VBZ cord-258032-buh1e4tm 39 3 destroyed destroy VBN cord-258032-buh1e4tm 39 4 , , , cord-258032-buh1e4tm 39 5 when when WRB cord-258032-buh1e4tm 39 6 free free JJ cord-258032-buh1e4tm 39 7 viruses virus NNS cord-258032-buh1e4tm 39 8 try try VBP cord-258032-buh1e4tm 39 9 to to TO cord-258032-buh1e4tm 39 10 infect infect VB cord-258032-buh1e4tm 39 11 uninfected uninfected JJ cord-258032-buh1e4tm 39 12 cells cell NNS cord-258032-buh1e4tm 39 13 , , , cord-258032-buh1e4tm 39 14 at at IN cord-258032-buh1e4tm 39 15 the the DT cord-258032-buh1e4tm 39 16 rate rate NN cord-258032-buh1e4tm 39 17 1 1 CD cord-258032-buh1e4tm 39 18 ( ( -LRB- cord-258032-buh1e4tm 39 19 ( ( -LRB- cord-258032-buh1e4tm 39 20 ) ) -RRB- cord-258032-buh1e4tm 40 1 ) ) -RRB- cord-258032-buh1e4tm 40 2 V v NN cord-258032-buh1e4tm 40 3 ( ( -LRB- cord-258032-buh1e4tm 40 4 ) ) -RRB- cord-258032-buh1e4tm 40 5 ( ( -LRB- cord-258032-buh1e4tm 40 6 ) ) -RRB- cord-258032-buh1e4tm 40 7 , , , cord-258032-buh1e4tm 40 8 and and CC cord-258032-buh1e4tm 40 9 is be VBZ cord-258032-buh1e4tm 40 10 hydrolyzed hydrolyze VBN cord-258032-buh1e4tm 40 11 at at IN cord-258032-buh1e4tm 40 12 the the DT cord-258032-buh1e4tm 40 13 rate rate NN cord-258032-buh1e4tm 40 14 ( ( -LRB- cord-258032-buh1e4tm 40 15 ) ) -RRB- cord-258032-buh1e4tm 40 16 . . . cord-258032-buh1e4tm 41 1 Here here RB cord-258032-buh1e4tm 41 2 , , , cord-258032-buh1e4tm 41 3 1 1 CD cord-258032-buh1e4tm 41 4 ≥ ≥ CD cord-258032-buh1e4tm 41 5 0 0 CD cord-258032-buh1e4tm 41 6 and and CC cord-258032-buh1e4tm 41 7 > > XX cord-258032-buh1e4tm 41 8 0 0 CD cord-258032-buh1e4tm 41 9 are be VBP cord-258032-buh1e4tm 41 10 constants constant NNS cord-258032-buh1e4tm 41 11 . . . cord-258032-buh1e4tm 42 1 It -PRON- PRP cord-258032-buh1e4tm 42 2 is be VBZ cord-258032-buh1e4tm 42 3 assumed assume VBN cord-258032-buh1e4tm 42 4 that that IN cord-258032-buh1e4tm 42 5 there there EX cord-258032-buh1e4tm 42 6 is be VBZ cord-258032-buh1e4tm 42 7 no no DT cord-258032-buh1e4tm 42 8 undestroyed undestroyed JJ cord-258032-buh1e4tm 42 9 DPP4 DPP4 NNP cord-258032-buh1e4tm 42 10 on on IN cord-258032-buh1e4tm 42 11 the the DT cord-258032-buh1e4tm 42 12 surface surface NN cord-258032-buh1e4tm 42 13 of of IN cord-258032-buh1e4tm 42 14 infected infected JJ cord-258032-buh1e4tm 42 15 cells cell NNS cord-258032-buh1e4tm 42 16 . . . cord-258032-buh1e4tm 43 1 All all DT cord-258032-buh1e4tm 43 2 other other JJ cord-258032-buh1e4tm 43 3 parameters parameter NNS cord-258032-buh1e4tm 43 4 in in IN cord-258032-buh1e4tm 43 5 model model NN cord-258032-buh1e4tm 43 6 ( ( -LRB- cord-258032-buh1e4tm 43 7 2 2 LS cord-258032-buh1e4tm 43 8 ) ) -RRB- cord-258032-buh1e4tm 43 9 have have VBP cord-258032-buh1e4tm 43 10 similar similar JJ cord-258032-buh1e4tm 43 11 biological biological JJ cord-258032-buh1e4tm 43 12 meanings meaning NNS cord-258032-buh1e4tm 43 13 to to IN cord-258032-buh1e4tm 43 14 that that DT cord-258032-buh1e4tm 43 15 in in IN cord-258032-buh1e4tm 43 16 model model NN cord-258032-buh1e4tm 43 17 ( ( -LRB- cord-258032-buh1e4tm 43 18 1 1 CD cord-258032-buh1e4tm 43 19 ) ) -RRB- cord-258032-buh1e4tm 43 20 . . . cord-258032-buh1e4tm 44 1 The the DT cord-258032-buh1e4tm 44 2 initial initial JJ cord-258032-buh1e4tm 44 3 condition condition NN cord-258032-buh1e4tm 44 4 of of IN cord-258032-buh1e4tm 44 5 model model NN cord-258032-buh1e4tm 44 6 ( ( -LRB- cord-258032-buh1e4tm 44 7 2 2 LS cord-258032-buh1e4tm 44 8 ) ) -RRB- cord-258032-buh1e4tm 44 9 is be VBZ cord-258032-buh1e4tm 44 10 given give VBN cord-258032-buh1e4tm 44 11 as as IN cord-258032-buh1e4tm 44 12 ( ( -LRB- cord-258032-buh1e4tm 44 13 0 0 NFP cord-258032-buh1e4tm 45 1 ) ) -RRB- cord-258032-buh1e4tm 45 2 ≥ ≥ CD cord-258032-buh1e4tm 45 3 0 0 CD cord-258032-buh1e4tm 45 4 , , , cord-258032-buh1e4tm 45 5 ( ( -LRB- cord-258032-buh1e4tm 45 6 0 0 NFP cord-258032-buh1e4tm 45 7 ) ) -RRB- cord-258032-buh1e4tm 45 8 ≥ ≥ CD cord-258032-buh1e4tm 45 9 0 0 CD cord-258032-buh1e4tm 45 10 , , , cord-258032-buh1e4tm 45 11 V(0 V(0 NNP cord-258032-buh1e4tm 45 12 ) ) -RRB- cord-258032-buh1e4tm 45 13 ≥ ≥ CD cord-258032-buh1e4tm 45 14 0 0 CD cord-258032-buh1e4tm 45 15 , , , cord-258032-buh1e4tm 45 16 and and CC cord-258032-buh1e4tm 45 17 ( ( -LRB- cord-258032-buh1e4tm 45 18 0 0 NFP cord-258032-buh1e4tm 45 19 ) ) -RRB- cord-258032-buh1e4tm 46 1 ≥ ≥ CD cord-258032-buh1e4tm 46 2 0 0 CD cord-258032-buh1e4tm 46 3 . . . cord-258032-buh1e4tm 47 1 It -PRON- PRP cord-258032-buh1e4tm 47 2 is be VBZ cord-258032-buh1e4tm 47 3 not not RB cord-258032-buh1e4tm 47 4 difficult difficult JJ cord-258032-buh1e4tm 47 5 to to TO cord-258032-buh1e4tm 47 6 show show VB cord-258032-buh1e4tm 47 7 that that IN cord-258032-buh1e4tm 47 8 the the DT cord-258032-buh1e4tm 47 9 solution solution NN cord-258032-buh1e4tm 47 10 ( ( -LRB- cord-258032-buh1e4tm 47 11 ( ( -LRB- cord-258032-buh1e4tm 47 12 ) ) -RRB- cord-258032-buh1e4tm 47 13 , , , cord-258032-buh1e4tm 47 14 ( ( -LRB- cord-258032-buh1e4tm 47 15 ) ) -RRB- cord-258032-buh1e4tm 47 16 , , , cord-258032-buh1e4tm 47 17 V V NNP cord-258032-buh1e4tm 47 18 ( ( -LRB- cord-258032-buh1e4tm 47 19 ) ) -RRB- cord-258032-buh1e4tm 47 20 , , , cord-258032-buh1e4tm 47 21 ( ( -LRB- cord-258032-buh1e4tm 47 22 ) ) -RRB- cord-258032-buh1e4tm 47 23 ) ) -RRB- cord-258032-buh1e4tm 47 24 with with IN cord-258032-buh1e4tm 47 25 the the DT cord-258032-buh1e4tm 47 26 initial initial JJ cord-258032-buh1e4tm 47 27 condition condition NN cord-258032-buh1e4tm 47 28 is be VBZ cord-258032-buh1e4tm 47 29 existent existent JJ cord-258032-buh1e4tm 47 30 , , , cord-258032-buh1e4tm 47 31 unique unique JJ cord-258032-buh1e4tm 47 32 , , , cord-258032-buh1e4tm 47 33 bounded bounded JJ cord-258032-buh1e4tm 47 34 , , , cord-258032-buh1e4tm 47 35 and and CC cord-258032-buh1e4tm 47 36 nonnegative nonnegative JJ cord-258032-buh1e4tm 47 37 for for IN cord-258032-buh1e4tm 47 38 all all DT cord-258032-buh1e4tm 47 39 ≥ ≥ CD cord-258032-buh1e4tm 47 40 0 0 CD cord-258032-buh1e4tm 47 41 ( ( -LRB- cord-258032-buh1e4tm 47 42 in in IN cord-258032-buh1e4tm 47 43 fact fact NN cord-258032-buh1e4tm 47 44 , , , cord-258032-buh1e4tm 47 45 it -PRON- PRP cord-258032-buh1e4tm 47 46 also also RB cord-258032-buh1e4tm 47 47 has have VBZ cord-258032-buh1e4tm 47 48 ( ( -LRB- cord-258032-buh1e4tm 47 49 ) ) -RRB- cord-258032-buh1e4tm 48 1 > > XX cord-258032-buh1e4tm 48 2 0 0 NFP cord-258032-buh1e4tm 48 3 and and CC cord-258032-buh1e4tm 49 1 ( ( -LRB- cord-258032-buh1e4tm 49 2 ) ) -RRB- cord-258032-buh1e4tm 49 3 > > NFP cord-258032-buh1e4tm 49 4 0 0 NFP cord-258032-buh1e4tm 49 5 for for IN cord-258032-buh1e4tm 49 6 all all DT cord-258032-buh1e4tm 49 7 > > XX cord-258032-buh1e4tm 49 8 0 0 CD cord-258032-buh1e4tm 49 9 ) ) -RRB- cord-258032-buh1e4tm 49 10 . . . cord-258032-buh1e4tm 50 1 If if IN cord-258032-buh1e4tm 50 2 ( ( -LRB- cord-258032-buh1e4tm 50 3 0 0 NFP cord-258032-buh1e4tm 50 4 ) ) -RRB- cord-258032-buh1e4tm 50 5 > > XX cord-258032-buh1e4tm 50 6 0 0 CD cord-258032-buh1e4tm 50 7 , , , cord-258032-buh1e4tm 50 8 ( ( -LRB- cord-258032-buh1e4tm 50 9 0 0 NFP cord-258032-buh1e4tm 50 10 ) ) -RRB- cord-258032-buh1e4tm 50 11 > > XX cord-258032-buh1e4tm 50 12 0 0 CD cord-258032-buh1e4tm 50 13 , , , cord-258032-buh1e4tm 50 14 V(0 V(0 NNP cord-258032-buh1e4tm 50 15 ) ) -RRB- cord-258032-buh1e4tm 50 16 > > XX cord-258032-buh1e4tm 50 17 0 0 CD cord-258032-buh1e4tm 50 18 , , , cord-258032-buh1e4tm 50 19 and and CC cord-258032-buh1e4tm 50 20 ( ( -LRB- cord-258032-buh1e4tm 50 21 0 0 NFP cord-258032-buh1e4tm 50 22 ) ) -RRB- cord-258032-buh1e4tm 50 23 > > XX cord-258032-buh1e4tm 50 24 0 0 NFP cord-258032-buh1e4tm 50 25 , , , cord-258032-buh1e4tm 50 26 it -PRON- PRP cord-258032-buh1e4tm 50 27 is be VBZ cord-258032-buh1e4tm 50 28 easily easily RB cord-258032-buh1e4tm 50 29 proven prove VBN cord-258032-buh1e4tm 50 30 that that IN cord-258032-buh1e4tm 50 31 the the DT cord-258032-buh1e4tm 50 32 corresponding corresponding JJ cord-258032-buh1e4tm 50 33 solution solution NN cord-258032-buh1e4tm 50 34 ( ( -LRB- cord-258032-buh1e4tm 50 35 ( ( -LRB- cord-258032-buh1e4tm 50 36 ) ) -RRB- cord-258032-buh1e4tm 50 37 , , , cord-258032-buh1e4tm 50 38 ( ( -LRB- cord-258032-buh1e4tm 50 39 ) ) -RRB- cord-258032-buh1e4tm 50 40 , , , cord-258032-buh1e4tm 50 41 V V NNP cord-258032-buh1e4tm 50 42 ( ( -LRB- cord-258032-buh1e4tm 50 43 ) ) -RRB- cord-258032-buh1e4tm 50 44 , , , cord-258032-buh1e4tm 50 45 ( ( -LRB- cord-258032-buh1e4tm 50 46 ) ) -RRB- cord-258032-buh1e4tm 50 47 ) ) -RRB- cord-258032-buh1e4tm 50 48 is be VBZ cord-258032-buh1e4tm 50 49 positive positive JJ cord-258032-buh1e4tm 50 50 for for IN cord-258032-buh1e4tm 50 51 all all DT cord-258032-buh1e4tm 50 52 ≥ ≥ CD cord-258032-buh1e4tm 50 53 0 0 CD cord-258032-buh1e4tm 50 54 . . . cord-258032-buh1e4tm 51 1 Furthermore furthermore RB cord-258032-buh1e4tm 51 2 , , , cord-258032-buh1e4tm 51 3 it -PRON- PRP cord-258032-buh1e4tm 51 4 can can MD cord-258032-buh1e4tm 51 5 be be VB cord-258032-buh1e4tm 51 6 easily easily RB cord-258032-buh1e4tm 51 7 shown show VBN cord-258032-buh1e4tm 51 8 that that IN cord-258032-buh1e4tm 51 9 the the DT cord-258032-buh1e4tm 51 10 set set NN cord-258032-buh1e4tm 51 11 is be VBZ cord-258032-buh1e4tm 51 12 attractive attractive JJ cord-258032-buh1e4tm 51 13 and and CC cord-258032-buh1e4tm 51 14 positively positively RB cord-258032-buh1e4tm 51 15 invariant invariant JJ cord-258032-buh1e4tm 51 16 with with IN cord-258032-buh1e4tm 51 17 respect respect NN cord-258032-buh1e4tm 51 18 to to IN cord-258032-buh1e4tm 51 19 model model NN cord-258032-buh1e4tm 51 20 ( ( -LRB- cord-258032-buh1e4tm 51 21 2 2 CD cord-258032-buh1e4tm 51 22 ) ) -RRB- cord-258032-buh1e4tm 51 23 , , , cord-258032-buh1e4tm 51 24 The the DT cord-258032-buh1e4tm 51 25 purpose purpose NN cord-258032-buh1e4tm 51 26 of of IN cord-258032-buh1e4tm 51 27 the the DT cord-258032-buh1e4tm 51 28 paper paper NN cord-258032-buh1e4tm 51 29 is be VBZ cord-258032-buh1e4tm 51 30 to to TO cord-258032-buh1e4tm 51 31 study study VB cord-258032-buh1e4tm 51 32 local local JJ cord-258032-buh1e4tm 51 33 and and CC cord-258032-buh1e4tm 51 34 global global JJ cord-258032-buh1e4tm 51 35 stability stability NN cord-258032-buh1e4tm 51 36 of of IN cord-258032-buh1e4tm 51 37 the the DT cord-258032-buh1e4tm 51 38 equilibria equilibrium NNS cord-258032-buh1e4tm 51 39 of of IN cord-258032-buh1e4tm 51 40 model model NN cord-258032-buh1e4tm 51 41 ( ( -LRB- cord-258032-buh1e4tm 51 42 2 2 CD cord-258032-buh1e4tm 51 43 ) ) -RRB- cord-258032-buh1e4tm 51 44 by by IN cord-258032-buh1e4tm 51 45 using use VBG cord-258032-buh1e4tm 51 46 Roth Roth NNP cord-258032-buh1e4tm 51 47 - - HYPH cord-258032-buh1e4tm 51 48 Hurwitz Hurwitz NNP cord-258032-buh1e4tm 51 49 criterion criterion NN cord-258032-buh1e4tm 51 50 and and CC cord-258032-buh1e4tm 51 51 constructing construct VBG cord-258032-buh1e4tm 51 52 suitable suitable JJ cord-258032-buh1e4tm 51 53 Lyapunov Lyapunov NNP cord-258032-buh1e4tm 51 54 function function NN cord-258032-buh1e4tm 51 55 ( ( -LRB- cord-258032-buh1e4tm 51 56 see see VB cord-258032-buh1e4tm 51 57 , , , cord-258032-buh1e4tm 52 1 e.g. e.g. RB cord-258032-buh1e4tm 52 2 , , , cord-258032-buh1e4tm 52 3 [ [ -LRB- cord-258032-buh1e4tm 52 4 9 9 CD cord-258032-buh1e4tm 52 5 ] ] -RRB- cord-258032-buh1e4tm 52 6 [ [ -LRB- cord-258032-buh1e4tm 52 7 10 10 CD cord-258032-buh1e4tm 52 8 ] ] -RRB- cord-258032-buh1e4tm 52 9 [ [ -LRB- cord-258032-buh1e4tm 52 10 11 11 CD cord-258032-buh1e4tm 52 11 ] ] -RRB- cord-258032-buh1e4tm 53 1 [ [ -LRB- cord-258032-buh1e4tm 53 2 12 12 CD cord-258032-buh1e4tm 53 3 ] ] -RRB- cord-258032-buh1e4tm 53 4 [ [ -LRB- cord-258032-buh1e4tm 53 5 13 13 CD cord-258032-buh1e4tm 53 6 ] ] -RRB- cord-258032-buh1e4tm 53 7 ) ) -RRB- cord-258032-buh1e4tm 53 8 . . . cord-258032-buh1e4tm 54 1 The the DT cord-258032-buh1e4tm 54 2 basic basic JJ cord-258032-buh1e4tm 54 3 reproductive reproductive JJ cord-258032-buh1e4tm 54 4 ratio ratio NN cord-258032-buh1e4tm 54 5 of of IN cord-258032-buh1e4tm 54 6 the the DT cord-258032-buh1e4tm 54 7 virus virus NN cord-258032-buh1e4tm 54 8 for for IN cord-258032-buh1e4tm 54 9 model model NN cord-258032-buh1e4tm 54 10 ( ( -LRB- cord-258032-buh1e4tm 54 11 2 2 LS cord-258032-buh1e4tm 54 12 ) ) -RRB- cord-258032-buh1e4tm 54 13 is be VBZ cord-258032-buh1e4tm 54 14 ( ( -LRB- cord-258032-buh1e4tm 54 15 2 2 LS cord-258032-buh1e4tm 54 16 ) ) -RRB- cord-258032-buh1e4tm 54 17 always always RB cord-258032-buh1e4tm 54 18 has have VBZ cord-258032-buh1e4tm 54 19 an an DT cord-258032-buh1e4tm 54 20 infection infection NN cord-258032-buh1e4tm 54 21 - - HYPH cord-258032-buh1e4tm 54 22 free free JJ cord-258032-buh1e4tm 54 23 equilibrium equilibrium NN cord-258032-buh1e4tm 54 24 0 0 CD cord-258032-buh1e4tm 54 25 = = NFP cord-258032-buh1e4tm 54 26 ( ( -LRB- cord-258032-buh1e4tm 54 27 0 0 CD cord-258032-buh1e4tm 54 28 , , , cord-258032-buh1e4tm 54 29 0 0 CD cord-258032-buh1e4tm 54 30 , , , cord-258032-buh1e4tm 54 31 0 0 CD cord-258032-buh1e4tm 54 32 , , , cord-258032-buh1e4tm 54 33 0 0 CD cord-258032-buh1e4tm 54 34 ) ) -RRB- cord-258032-buh1e4tm 54 35 = = NFP cord-258032-buh1e4tm 55 1 ( ( -LRB- cord-258032-buh1e4tm 55 2 / / SYM cord-258032-buh1e4tm 55 3 , , , cord-258032-buh1e4tm 55 4 0 0 CD cord-258032-buh1e4tm 55 5 , , , cord-258032-buh1e4tm 55 6 0 0 CD cord-258032-buh1e4tm 55 7 , , , cord-258032-buh1e4tm 55 8 1 1 CD cord-258032-buh1e4tm 55 9 / / SYM cord-258032-buh1e4tm 55 10 ) ) -RRB- cord-258032-buh1e4tm 55 11 . . . cord-258032-buh1e4tm 56 1 If if IN cord-258032-buh1e4tm 56 2 0 0 CD cord-258032-buh1e4tm 56 3 > > SYM cord-258032-buh1e4tm 56 4 1 1 CD cord-258032-buh1e4tm 56 5 , , , cord-258032-buh1e4tm 56 6 model model NN cord-258032-buh1e4tm 56 7 ( ( -LRB- cord-258032-buh1e4tm 56 8 2 2 LS cord-258032-buh1e4tm 56 9 ) ) -RRB- cord-258032-buh1e4tm 56 10 also also RB cord-258032-buh1e4tm 56 11 has have VBZ cord-258032-buh1e4tm 56 12 unique unique JJ cord-258032-buh1e4tm 56 13 infected infect VBN cord-258032-buh1e4tm 56 14 equilibrium equilibrium NN cord-258032-buh1e4tm 57 1 * * NFP cord-258032-buh1e4tm 57 2 = = NFP cord-258032-buh1e4tm 58 1 ( ( -LRB- cord-258032-buh1e4tm 58 2 * * NFP cord-258032-buh1e4tm 58 3 , , , cord-258032-buh1e4tm 58 4 * * NFP cord-258032-buh1e4tm 58 5 , , , cord-258032-buh1e4tm 58 6 V V NNP cord-258032-buh1e4tm 58 7 * * NFP cord-258032-buh1e4tm 58 8 , , , cord-258032-buh1e4tm 58 9 * * NFP cord-258032-buh1e4tm 58 10 ) ) -RRB- cord-258032-buh1e4tm 58 11 , , , cord-258032-buh1e4tm 58 12 where where WRB cord-258032-buh1e4tm 58 13 , , , cord-258032-buh1e4tm 58 14 for for IN cord-258032-buh1e4tm 58 15 First first RB cord-258032-buh1e4tm 58 16 , , , cord-258032-buh1e4tm 58 17 we -PRON- PRP cord-258032-buh1e4tm 58 18 have have VBP cord-258032-buh1e4tm 58 19 the the DT cord-258032-buh1e4tm 58 20 following following JJ cord-258032-buh1e4tm 58 21 result result NN cord-258032-buh1e4tm 58 22 . . . cord-258032-buh1e4tm 59 1 Proof proof NN cord-258032-buh1e4tm 59 2 . . . cord-258032-buh1e4tm 60 1 At at IN cord-258032-buh1e4tm 60 2 any any DT cord-258032-buh1e4tm 60 3 equilibrium equilibrium NN cord-258032-buh1e4tm 60 4 ( ( -LRB- cord-258032-buh1e4tm 60 5 , , , cord-258032-buh1e4tm 60 6 , , , cord-258032-buh1e4tm 60 7 V v NN cord-258032-buh1e4tm 60 8 , , , cord-258032-buh1e4tm 60 9 ) ) -RRB- cord-258032-buh1e4tm 60 10 , , , cord-258032-buh1e4tm 60 11 Jacobian jacobian JJ cord-258032-buh1e4tm 60 12 matrix matrix NN cord-258032-buh1e4tm 60 13 of of IN cord-258032-buh1e4tm 60 14 model model NN cord-258032-buh1e4tm 60 15 ( ( -LRB- cord-258032-buh1e4tm 60 16 2 2 CD cord-258032-buh1e4tm 60 17 ) ) -RRB- cord-258032-buh1e4tm 60 18 _SP cord-258032-buh1e4tm 61 1 By by IN cord-258032-buh1e4tm 61 2 simple simple JJ cord-258032-buh1e4tm 61 3 computations computation NNS cord-258032-buh1e4tm 61 4 , , , cord-258032-buh1e4tm 61 5 we -PRON- PRP cord-258032-buh1e4tm 61 6 can can MD cord-258032-buh1e4tm 61 7 get get VB cord-258032-buh1e4tm 61 8 that that IN cord-258032-buh1e4tm 61 9 the the DT cord-258032-buh1e4tm 61 10 characteristic characteristic JJ cord-258032-buh1e4tm 61 11 equation equation NN cord-258032-buh1e4tm 61 12 at at IN cord-258032-buh1e4tm 61 13 0 0 CD cord-258032-buh1e4tm 61 14 is be VBZ cord-258032-buh1e4tm 61 15 ( ( -LRB- cord-258032-buh1e4tm 61 16 ) ) -RRB- cord-258032-buh1e4tm 61 17 = = . cord-258032-buh1e4tm 62 1 ( ( -LRB- cord-258032-buh1e4tm 62 2 + + CC cord-258032-buh1e4tm 62 3 ) ) -RRB- cord-258032-buh1e4tm 62 4 ( ( -LRB- cord-258032-buh1e4tm 62 5 + + NFP cord-258032-buh1e4tm 62 6 ) ) -RRB- cord-258032-buh1e4tm 62 7 [ [ -LRB- cord-258032-buh1e4tm 62 8 2 2 CD cord-258032-buh1e4tm 62 9 + + SYM cord-258032-buh1e4tm 62 10 ( ( -LRB- cord-258032-buh1e4tm 62 11 + + CD cord-258032-buh1e4tm 62 12 1 1 CD cord-258032-buh1e4tm 62 13 ) ) -RRB- cord-258032-buh1e4tm 62 14 + + SYM cord-258032-buh1e4tm 62 15 1 1 CD cord-258032-buh1e4tm 62 16 ( ( -LRB- cord-258032-buh1e4tm 62 17 1 1 CD cord-258032-buh1e4tm 62 18 − − NN cord-258032-buh1e4tm 62 19 0 0 CD cord-258032-buh1e4tm 62 20 ) ) -RRB- cord-258032-buh1e4tm 62 21 ] ] -RRB- cord-258032-buh1e4tm 62 22 = = SYM cord-258032-buh1e4tm 62 23 0 0 CD cord-258032-buh1e4tm 62 24 . . . cord-258032-buh1e4tm 63 1 Clearly clearly RB cord-258032-buh1e4tm 63 2 , , , cord-258032-buh1e4tm 63 3 if if IN cord-258032-buh1e4tm 63 4 0 0 CD cord-258032-buh1e4tm 63 5 < < XX cord-258032-buh1e4tm 63 6 1 1 CD cord-258032-buh1e4tm 63 7 , , , cord-258032-buh1e4tm 63 8 all all DT cord-258032-buh1e4tm 63 9 roots root NNS cord-258032-buh1e4tm 63 10 of of IN cord-258032-buh1e4tm 63 11 ( ( -LRB- cord-258032-buh1e4tm 63 12 ) ) -RRB- cord-258032-buh1e4tm 63 13 = = SYM cord-258032-buh1e4tm 63 14 0 0 NFP cord-258032-buh1e4tm 63 15 have have VBP cord-258032-buh1e4tm 63 16 negative negative JJ cord-258032-buh1e4tm 63 17 real real JJ cord-258032-buh1e4tm 63 18 parts part NNS cord-258032-buh1e4tm 63 19 . . . cord-258032-buh1e4tm 64 1 Hence hence RB cord-258032-buh1e4tm 64 2 , , , cord-258032-buh1e4tm 64 3 0 0 NFP cord-258032-buh1e4tm 64 4 is be VBZ cord-258032-buh1e4tm 64 5 local local JJ cord-258032-buh1e4tm 64 6 asymptotic asymptotic JJ cord-258032-buh1e4tm 64 7 stability stability NN cord-258032-buh1e4tm 64 8 by by IN cord-258032-buh1e4tm 64 9 Routh Routh NNP cord-258032-buh1e4tm 64 10 - - HYPH cord-258032-buh1e4tm 64 11 Hurwitz Hurwitz NNP cord-258032-buh1e4tm 64 12 criterion criterion NN cord-258032-buh1e4tm 64 13 . . . cord-258032-buh1e4tm 65 1 If if IN cord-258032-buh1e4tm 65 2 0 0 CD cord-258032-buh1e4tm 65 3 = = SYM cord-258032-buh1e4tm 65 4 1 1 CD cord-258032-buh1e4tm 65 5 , , , cord-258032-buh1e4tm 65 6 ( ( -LRB- cord-258032-buh1e4tm 65 7 ) ) -RRB- cord-258032-buh1e4tm 65 8 = = SYM cord-258032-buh1e4tm 65 9 0 0 NFP cord-258032-buh1e4tm 65 10 has have VBZ cord-258032-buh1e4tm 65 11 the the DT cord-258032-buh1e4tm 65 12 zero zero CD cord-258032-buh1e4tm 65 13 root root NN cord-258032-buh1e4tm 65 14 = = SYM cord-258032-buh1e4tm 65 15 0 0 CD cord-258032-buh1e4tm 65 16 and and CC cord-258032-buh1e4tm 65 17 three three CD cord-258032-buh1e4tm 65 18 negative negative JJ cord-258032-buh1e4tm 65 19 roots root NNS cord-258032-buh1e4tm 65 20 . . . cord-258032-buh1e4tm 66 1 Hence hence RB cord-258032-buh1e4tm 66 2 , , , cord-258032-buh1e4tm 66 3 0 0 NFP cord-258032-buh1e4tm 66 4 is be VBZ cord-258032-buh1e4tm 66 5 linearly linearly RB cord-258032-buh1e4tm 66 6 stable stable JJ cord-258032-buh1e4tm 66 7 . . . cord-258032-buh1e4tm 67 1 Construct construct VB cord-258032-buh1e4tm 67 2 the the DT cord-258032-buh1e4tm 67 3 Lyapunov Lyapunov NNP cord-258032-buh1e4tm 67 4 function function NN cord-258032-buh1e4tm 67 5 as as IN cord-258032-buh1e4tm 67 6 follows follow VBZ cord-258032-buh1e4tm 67 7 : : : cord-258032-buh1e4tm 67 8 It -PRON- PRP cord-258032-buh1e4tm 67 9 is be VBZ cord-258032-buh1e4tm 67 10 clear clear JJ cord-258032-buh1e4tm 67 11 that that WDT cord-258032-buh1e4tm 67 12 is be VBZ cord-258032-buh1e4tm 67 13 continuous continuous JJ cord-258032-buh1e4tm 67 14 on on IN cord-258032-buh1e4tm 67 15 Ω Ω NNP cord-258032-buh1e4tm 67 16 1 1 CD cord-258032-buh1e4tm 67 17 and and CC cord-258032-buh1e4tm 67 18 positive positive JJ cord-258032-buh1e4tm 67 19 definite definite JJ cord-258032-buh1e4tm 67 20 with with IN cord-258032-buh1e4tm 67 21 respect respect NN cord-258032-buh1e4tm 67 22 to to IN cord-258032-buh1e4tm 67 23 0 0 CD cord-258032-buh1e4tm 67 24 and and CC cord-258032-buh1e4tm 67 25 satisfies satisfy VBZ cord-258032-buh1e4tm 67 26 condition condition NN cord-258032-buh1e4tm 67 27 ( ( -LRB- cord-258032-buh1e4tm 67 28 ii ii NN cord-258032-buh1e4tm 67 29 ) ) -RRB- cord-258032-buh1e4tm 67 30 of of IN cord-258032-buh1e4tm 67 31 Definition Definition NNP cord-258032-buh1e4tm 67 32 1.1 1.1 CD cord-258032-buh1e4tm 67 33 in in IN cord-258032-buh1e4tm 67 34 [ [ -LRB- cord-258032-buh1e4tm 67 35 14 14 CD cord-258032-buh1e4tm 67 36 ] ] -RRB- cord-258032-buh1e4tm 67 37 or or CC cord-258032-buh1e4tm 67 38 Lemma Lemma NNP cord-258032-buh1e4tm 67 39 3.1 3.1 CD cord-258032-buh1e4tm 67 40 in in IN cord-258032-buh1e4tm 67 41 [ [ -LRB- cord-258032-buh1e4tm 67 42 15 15 CD cord-258032-buh1e4tm 67 43 ] ] -RRB- cord-258032-buh1e4tm 67 44 on on IN cord-258032-buh1e4tm 67 45 Ω ω NN cord-258032-buh1e4tm 67 46 = = SYM cord-258032-buh1e4tm 67 47 Ω ω NN cord-258032-buh1e4tm 67 48 \ \ NN cord-258032-buh1e4tm 67 49 Ω ω NN cord-258032-buh1e4tm 67 50 1 1 CD cord-258032-buh1e4tm 67 51 . . . cord-258032-buh1e4tm 68 1 Calculating calculate VBG cord-258032-buh1e4tm 68 2 the the DT cord-258032-buh1e4tm 68 3 derivative derivative NN cord-258032-buh1e4tm 68 4 of of IN cord-258032-buh1e4tm 68 5 along along IN cord-258032-buh1e4tm 68 6 the the DT cord-258032-buh1e4tm 68 7 solutions solution NNS cord-258032-buh1e4tm 68 8 of of IN cord-258032-buh1e4tm 68 9 model model NN cord-258032-buh1e4tm 68 10 ( ( -LRB- cord-258032-buh1e4tm 68 11 2 2 CD cord-258032-buh1e4tm 68 12 ) ) -RRB- cord-258032-buh1e4tm 68 13 , , , cord-258032-buh1e4tm 68 14 we -PRON- PRP cord-258032-buh1e4tm 68 15 have have VBP cord-258032-buh1e4tm 68 16 , , , cord-258032-buh1e4tm 68 17 for for IN cord-258032-buh1e4tm 68 18 ≥ ≥ CD cord-258032-buh1e4tm 68 19 0 0 CD cord-258032-buh1e4tm 68 20 , , , cord-258032-buh1e4tm 68 21 Clearly clearly RB cord-258032-buh1e4tm 68 22 , , , cord-258032-buh1e4tm 68 23 / / SYM cord-258032-buh1e4tm 68 24 ≤ ≤ NN cord-258032-buh1e4tm 68 25 0 0 CD cord-258032-buh1e4tm 68 26 on on IN cord-258032-buh1e4tm 68 27 Ω Ω NNP cord-258032-buh1e4tm 68 28 1 1 CD cord-258032-buh1e4tm 68 29 by by IN cord-258032-buh1e4tm 68 30 0 0 CD cord-258032-buh1e4tm 68 31 ≤ ≤ NN cord-258032-buh1e4tm 68 32 1 1 CD cord-258032-buh1e4tm 68 33 . . . cord-258032-buh1e4tm 69 1 Define define VB cord-258032-buh1e4tm 69 2 = = NN cord-258032-buh1e4tm 69 3 { { -LRB- cord-258032-buh1e4tm 69 4 / / SYM cord-258032-buh1e4tm 69 5 = = SYM cord-258032-buh1e4tm 69 6 0 0 CD cord-258032-buh1e4tm 69 7 | | NNP cord-258032-buh1e4tm 69 8 ( ( -LRB- cord-258032-buh1e4tm 69 9 , , , cord-258032-buh1e4tm 69 10 , , , cord-258032-buh1e4tm 69 11 V v NN cord-258032-buh1e4tm 69 12 , , , cord-258032-buh1e4tm 69 13 ) ) -RRB- cord-258032-buh1e4tm 70 1 ∈ ∈ NNP cord-258032-buh1e4tm 70 2 Ω Ω NNP cord-258032-buh1e4tm 70 3 , , , cord-258032-buh1e4tm 70 4 ( ( -LRB- cord-258032-buh1e4tm 70 5 , , , cord-258032-buh1e4tm 70 6 , , , cord-258032-buh1e4tm 70 7 V v NN cord-258032-buh1e4tm 70 8 , , , cord-258032-buh1e4tm 70 9 ) ) -RRB- cord-258032-buh1e4tm 71 1 < < XX cord-258032-buh1e4tm 71 2 + + CC cord-258032-buh1e4tm 71 3 ∞ ∞ NNP cord-258032-buh1e4tm 71 4 } } -RRB- cord-258032-buh1e4tm 71 5 . . . cord-258032-buh1e4tm 72 1 Let let VB cord-258032-buh1e4tm 72 2 be be VB cord-258032-buh1e4tm 72 3 the the DT cord-258032-buh1e4tm 72 4 largest large JJS cord-258032-buh1e4tm 72 5 subset subset JJ cord-258032-buh1e4tm 72 6 in in IN cord-258032-buh1e4tm 72 7 which which WDT cord-258032-buh1e4tm 72 8 is be VBZ cord-258032-buh1e4tm 72 9 invariant invariant JJ cord-258032-buh1e4tm 72 10 with with IN cord-258032-buh1e4tm 72 11 respect respect NN cord-258032-buh1e4tm 72 12 to to IN cord-258032-buh1e4tm 72 13 the the DT cord-258032-buh1e4tm 72 14 set set NN cord-258032-buh1e4tm 72 15 model model NN cord-258032-buh1e4tm 72 16 ( ( -LRB- cord-258032-buh1e4tm 72 17 2 2 CD cord-258032-buh1e4tm 72 18 ) ) -RRB- cord-258032-buh1e4tm 72 19 . . . cord-258032-buh1e4tm 73 1 Hence hence RB cord-258032-buh1e4tm 73 2 , , , cord-258032-buh1e4tm 73 3 we -PRON- PRP cord-258032-buh1e4tm 73 4 have have VBP cord-258032-buh1e4tm 73 5 that that DT cord-258032-buh1e4tm 73 6 ⊂ ⊂ NN cord-258032-buh1e4tm 73 7 ⊂ ⊂ NN cord-258032-buh1e4tm 73 8 { { -LRB- cord-258032-buh1e4tm 73 9 ( ( -LRB- cord-258032-buh1e4tm 73 10 , , , cord-258032-buh1e4tm 73 11 , , , cord-258032-buh1e4tm 73 12 V v NN cord-258032-buh1e4tm 73 13 , , , cord-258032-buh1e4tm 73 14 ) ) -RRB- cord-258032-buh1e4tm 73 15 | | NNP cord-258032-buh1e4tm 73 16 ( ( -LRB- cord-258032-buh1e4tm 73 17 , , , cord-258032-buh1e4tm 73 18 , , , cord-258032-buh1e4tm 73 19 V v NN cord-258032-buh1e4tm 73 20 , , , cord-258032-buh1e4tm 73 21 ) ) -RRB- cord-258032-buh1e4tm 73 22 ∈ ∈ NN cord-258032-buh1e4tm 73 23 Ω ω NN cord-258032-buh1e4tm 73 24 , , , cord-258032-buh1e4tm 73 25 = = SYM cord-258032-buh1e4tm 73 26 0 0 CD cord-258032-buh1e4tm 73 27 , , , cord-258032-buh1e4tm 73 28 = = SYM cord-258032-buh1e4tm 73 29 0 0 CD cord-258032-buh1e4tm 73 30 } } -RRB- cord-258032-buh1e4tm 73 31 . . . cord-258032-buh1e4tm 74 1 From from IN cord-258032-buh1e4tm 74 2 the the DT cord-258032-buh1e4tm 74 3 invariance invariance NN cord-258032-buh1e4tm 74 4 of of IN cord-258032-buh1e4tm 74 5 and and CC cord-258032-buh1e4tm 74 6 model model NN cord-258032-buh1e4tm 74 7 ( ( -LRB- cord-258032-buh1e4tm 74 8 2 2 CD cord-258032-buh1e4tm 74 9 ) ) -RRB- cord-258032-buh1e4tm 74 10 , , , cord-258032-buh1e4tm 74 11 we -PRON- PRP cord-258032-buh1e4tm 74 12 can can MD cord-258032-buh1e4tm 74 13 easily easily RB cord-258032-buh1e4tm 74 14 show show VB cord-258032-buh1e4tm 74 15 that that IN cord-258032-buh1e4tm 74 16 = = NFP cord-258032-buh1e4tm 74 17 { { -LRB- cord-258032-buh1e4tm 74 18 0 0 CD cord-258032-buh1e4tm 74 19 } } -RRB- cord-258032-buh1e4tm 74 20 . . . cord-258032-buh1e4tm 75 1 Therefore therefore RB cord-258032-buh1e4tm 75 2 , , , cord-258032-buh1e4tm 75 3 it -PRON- PRP cord-258032-buh1e4tm 75 4 follows follow VBZ cord-258032-buh1e4tm 75 5 from from IN cord-258032-buh1e4tm 75 6 Theorem Theorem NNP cord-258032-buh1e4tm 75 7 1.2 1.2 CD cord-258032-buh1e4tm 75 8 in in IN cord-258032-buh1e4tm 75 9 [ [ -LRB- cord-258032-buh1e4tm 75 10 14 14 CD cord-258032-buh1e4tm 75 11 ] ] -RRB- cord-258032-buh1e4tm 75 12 or or CC cord-258032-buh1e4tm 75 13 Lemma Lemma NNP cord-258032-buh1e4tm 75 14 3.1 3.1 CD cord-258032-buh1e4tm 75 15 in in IN cord-258032-buh1e4tm 75 16 [ [ -LRB- cord-258032-buh1e4tm 75 17 15 15 CD cord-258032-buh1e4tm 75 18 ] ] -RRB- cord-258032-buh1e4tm 76 1 that that DT cord-258032-buh1e4tm 76 2 0 0 CD cord-258032-buh1e4tm 76 3 is be VBZ cord-258032-buh1e4tm 76 4 globally globally RB cord-258032-buh1e4tm 76 5 attractive attractive JJ cord-258032-buh1e4tm 76 6 . . . cord-258032-buh1e4tm 77 1 This this DT cord-258032-buh1e4tm 77 2 completes complete VBZ cord-258032-buh1e4tm 77 3 the the DT cord-258032-buh1e4tm 77 4 proof proof NN cord-258032-buh1e4tm 77 5 . . . cord-258032-buh1e4tm 78 1 For for IN cord-258032-buh1e4tm 78 2 local local JJ cord-258032-buh1e4tm 78 3 and and CC cord-258032-buh1e4tm 78 4 global global JJ cord-258032-buh1e4tm 78 5 stability stability NN cord-258032-buh1e4tm 78 6 of of IN cord-258032-buh1e4tm 78 7 the the DT cord-258032-buh1e4tm 78 8 infected infected JJ cord-258032-buh1e4tm 78 9 equilibrium equilibrium NN cord-258032-buh1e4tm 78 10 * * NFP cord-258032-buh1e4tm 78 11 , , , cord-258032-buh1e4tm 78 12 we -PRON- PRP cord-258032-buh1e4tm 78 13 have have VBP cord-258032-buh1e4tm 78 14 the the DT cord-258032-buh1e4tm 78 15 following following JJ cord-258032-buh1e4tm 78 16 result result NN cord-258032-buh1e4tm 78 17 . . . cord-258032-buh1e4tm 78 18 _SP cord-258032-buh1e4tm 79 1 where where WRB cord-258032-buh1e4tm 79 2 It -PRON- PRP cord-258032-buh1e4tm 79 3 is be VBZ cord-258032-buh1e4tm 79 4 obvious obvious JJ cord-258032-buh1e4tm 79 5 that that IN cord-258032-buh1e4tm 79 6 > > XX cord-258032-buh1e4tm 79 7 0 0 NFP cord-258032-buh1e4tm 79 8 ( ( -LRB- cord-258032-buh1e4tm 79 9 = = SYM cord-258032-buh1e4tm 79 10 0 0 CD cord-258032-buh1e4tm 79 11 , , , cord-258032-buh1e4tm 79 12 1 1 CD cord-258032-buh1e4tm 79 13 , , , cord-258032-buh1e4tm 79 14 2 2 CD cord-258032-buh1e4tm 79 15 , , , cord-258032-buh1e4tm 79 16 3 3 CD cord-258032-buh1e4tm 79 17 ) ) -RRB- cord-258032-buh1e4tm 79 18 . . . cord-258032-buh1e4tm 80 1 Furthermore furthermore RB cord-258032-buh1e4tm 80 2 , , , cord-258032-buh1e4tm 80 3 by by IN cord-258032-buh1e4tm 80 4 using use VBG cord-258032-buh1e4tm 80 5 Matlab Matlab NNP cord-258032-buh1e4tm 80 6 program program NN cord-258032-buh1e4tm 80 7 , , , cord-258032-buh1e4tm 80 8 it -PRON- PRP cord-258032-buh1e4tm 80 9 can can MD cord-258032-buh1e4tm 80 10 been be VBN cord-258032-buh1e4tm 80 11 shown show VBN cord-258032-buh1e4tm 80 12 that that IN cord-258032-buh1e4tm 80 13 Δ δ NN cord-258032-buh1e4tm 80 14 3 3 CD cord-258032-buh1e4tm 80 15 = = SYM cord-258032-buh1e4tm 80 16 1 1 CD cord-258032-buh1e4tm 80 17 2 2 CD cord-258032-buh1e4tm 80 18 3 3 CD cord-258032-buh1e4tm 80 19 − − NN cord-258032-buh1e4tm 80 20 2 2 CD cord-258032-buh1e4tm 80 21 1 1 CD cord-258032-buh1e4tm 80 22 − − CD cord-258032-buh1e4tm 80 23 2 2 CD cord-258032-buh1e4tm 80 24 3 3 CD cord-258032-buh1e4tm 80 25 0 0 CD cord-258032-buh1e4tm 80 26 has have VBZ cord-258032-buh1e4tm 80 27 200 200 CD cord-258032-buh1e4tm 80 28 items item NNS cord-258032-buh1e4tm 80 29 in in IN cord-258032-buh1e4tm 80 30 which which WDT cord-258032-buh1e4tm 80 31 all all DT cord-258032-buh1e4tm 80 32 items item NNS cord-258032-buh1e4tm 80 33 are be VBP cord-258032-buh1e4tm 80 34 positive positive JJ cord-258032-buh1e4tm 80 35 . . . cord-258032-buh1e4tm 81 1 Hence hence RB cord-258032-buh1e4tm 81 2 , , , cord-258032-buh1e4tm 81 3 * * NFP cord-258032-buh1e4tm 81 4 is be VBZ cord-258032-buh1e4tm 81 5 local local JJ cord-258032-buh1e4tm 81 6 asymptotic asymptotic JJ cord-258032-buh1e4tm 81 7 stability stability NN cord-258032-buh1e4tm 81 8 by by IN cord-258032-buh1e4tm 81 9 Routh Routh NNP cord-258032-buh1e4tm 81 10 - - HYPH cord-258032-buh1e4tm 81 11 Hurwitz Hurwitz NNP cord-258032-buh1e4tm 81 12 criterion criterion NN cord-258032-buh1e4tm 81 13 . . . cord-258032-buh1e4tm 82 1 Construct construct VB cord-258032-buh1e4tm 82 2 the the DT cord-258032-buh1e4tm 82 3 Lyapunov Lyapunov NNP cord-258032-buh1e4tm 82 4 function function NN cord-258032-buh1e4tm 82 5 as as IN cord-258032-buh1e4tm 82 6 follows follow VBZ cord-258032-buh1e4tm 82 7 : : : cord-258032-buh1e4tm 82 8 It -PRON- PRP cord-258032-buh1e4tm 82 9 is be VBZ cord-258032-buh1e4tm 82 10 clear clear JJ cord-258032-buh1e4tm 82 11 that that WDT cord-258032-buh1e4tm 82 12 is be VBZ cord-258032-buh1e4tm 82 13 continuous continuous JJ cord-258032-buh1e4tm 82 14 on on IN cord-258032-buh1e4tm 82 15 Ω Ω NNP cord-258032-buh1e4tm 82 16 2 2 CD cord-258032-buh1e4tm 82 17 and and CC cord-258032-buh1e4tm 82 18 positive positive JJ cord-258032-buh1e4tm 82 19 definite definite JJ cord-258032-buh1e4tm 82 20 with with IN cord-258032-buh1e4tm 82 21 respect respect NN cord-258032-buh1e4tm 82 22 to to IN cord-258032-buh1e4tm 82 23 * * NFP cord-258032-buh1e4tm 82 24 and and CC cord-258032-buh1e4tm 82 25 satisfies satisfy VBZ cord-258032-buh1e4tm 82 26 condition condition NN cord-258032-buh1e4tm 82 27 ( ( -LRB- cord-258032-buh1e4tm 82 28 ii ii NN cord-258032-buh1e4tm 82 29 ) ) -RRB- cord-258032-buh1e4tm 82 30 of of IN cord-258032-buh1e4tm 82 31 Definition Definition NNP cord-258032-buh1e4tm 82 32 1.1 1.1 CD cord-258032-buh1e4tm 82 33 in in IN cord-258032-buh1e4tm 82 34 [ [ -LRB- cord-258032-buh1e4tm 82 35 14 14 CD cord-258032-buh1e4tm 82 36 ] ] -RRB- cord-258032-buh1e4tm 82 37 or or CC cord-258032-buh1e4tm 82 38 Lemma Lemma NNP cord-258032-buh1e4tm 82 39 3.1 3.1 CD cord-258032-buh1e4tm 82 40 in in IN cord-258032-buh1e4tm 82 41 [ [ -LRB- cord-258032-buh1e4tm 82 42 15 15 CD cord-258032-buh1e4tm 82 43 ] ] -RRB- cord-258032-buh1e4tm 82 44 on on IN cord-258032-buh1e4tm 82 45 Ω ω NN cord-258032-buh1e4tm 82 46 = = SYM cord-258032-buh1e4tm 82 47 Ω ω NN cord-258032-buh1e4tm 82 48 \ \ NN cord-258032-buh1e4tm 82 49 Ω Ω NNP cord-258032-buh1e4tm 82 50 2 2 CD cord-258032-buh1e4tm 82 51 . . . cord-258032-buh1e4tm 83 1 Calculating calculate VBG cord-258032-buh1e4tm 83 2 the the DT cord-258032-buh1e4tm 83 3 derivative derivative NN cord-258032-buh1e4tm 83 4 of of IN cord-258032-buh1e4tm 83 5 along along IN cord-258032-buh1e4tm 83 6 the the DT cord-258032-buh1e4tm 83 7 solutions solution NNS cord-258032-buh1e4tm 83 8 of of IN cord-258032-buh1e4tm 83 9 model model NN cord-258032-buh1e4tm 83 10 ( ( -LRB- cord-258032-buh1e4tm 83 11 2 2 CD cord-258032-buh1e4tm 83 12 ) ) -RRB- cord-258032-buh1e4tm 83 13 , , , cord-258032-buh1e4tm 83 14 we -PRON- PRP cord-258032-buh1e4tm 83 15 have have VBP cord-258032-buh1e4tm 83 16 , , , cord-258032-buh1e4tm 83 17 for for IN cord-258032-buh1e4tm 83 18 ≥ ≥ CD cord-258032-buh1e4tm 83 19 0 0 CD cord-258032-buh1e4tm 83 20 , , , cord-258032-buh1e4tm 83 21 Since since IN cord-258032-buh1e4tm 83 22 the the DT cord-258032-buh1e4tm 83 23 arithmetical arithmetical JJ cord-258032-buh1e4tm 83 24 mean mean NN cord-258032-buh1e4tm 83 25 is be VBZ cord-258032-buh1e4tm 83 26 greater great JJR cord-258032-buh1e4tm 83 27 than than IN cord-258032-buh1e4tm 83 28 or or CC cord-258032-buh1e4tm 83 29 equal equal JJ cord-258032-buh1e4tm 83 30 to to IN cord-258032-buh1e4tm 83 31 the the DT cord-258032-buh1e4tm 83 32 geometrical geometrical JJ cord-258032-buh1e4tm 83 33 mean mean NN cord-258032-buh1e4tm 83 34 , , , cord-258032-buh1e4tm 83 35 we -PRON- PRP cord-258032-buh1e4tm 83 36 have have VBP cord-258032-buh1e4tm 83 37 that that DT cord-258032-buh1e4tm 84 1 * * NFP cord-258032-buh1e4tm 84 2 / / NFP cord-258032-buh1e4tm 85 1 + + CC cord-258032-buh1e4tm 86 1 * * NFP cord-258032-buh1e4tm 86 2 / / SYM cord-258032-buh1e4tm 86 3 + + CC cord-258032-buh1e4tm 87 1 V V NNP cord-258032-buh1e4tm 88 1 * * NFP cord-258032-buh1e4tm 88 2 / / NFP cord-258032-buh1e4tm 89 1 * * NFP cord-258032-buh1e4tm 89 2 V v NN cord-258032-buh1e4tm 89 3 * * NFP cord-258032-buh1e4tm 89 4 * * NFP cord-258032-buh1e4tm 89 5 + + . cord-258032-buh1e4tm 90 1 V V NNP cord-258032-buh1e4tm 90 2 * * NFP cord-258032-buh1e4tm 90 3 / / . cord-258032-buh1e4tm 91 1 * * NFP cord-258032-buh1e4tm 91 2 V V NNP cord-258032-buh1e4tm 91 3 − − NN cord-258032-buh1e4tm 91 4 4 4 CD cord-258032-buh1e4tm 91 5 ≤ ≤ NN cord-258032-buh1e4tm 91 6 0 0 CD cord-258032-buh1e4tm 91 7 , , , cord-258032-buh1e4tm 91 8 for for IN cord-258032-buh1e4tm 91 9 any any DT cord-258032-buh1e4tm 91 10 , , , cord-258032-buh1e4tm 91 11 , , , cord-258032-buh1e4tm 91 12 V v NN cord-258032-buh1e4tm 91 13 , , , cord-258032-buh1e4tm 91 14 > > XX cord-258032-buh1e4tm 91 15 0 0 CD cord-258032-buh1e4tm 91 16 , , , cord-258032-buh1e4tm 91 17 and and CC cord-258032-buh1e4tm 92 1 that that DT cord-258032-buh1e4tm 92 2 * * NFP cord-258032-buh1e4tm 92 3 / / SYM cord-258032-buh1e4tm 92 4 + + CC cord-258032-buh1e4tm 92 5 On on IN cord-258032-buh1e4tm 92 6 the the DT cord-258032-buh1e4tm 92 7 other other JJ cord-258032-buh1e4tm 92 8 hand hand NN cord-258032-buh1e4tm 92 9 , , , cord-258032-buh1e4tm 92 10 notice notice VB cord-258032-buh1e4tm 92 11 the the DT cord-258032-buh1e4tm 92 12 inequality inequality NN cord-258032-buh1e4tm 92 13 in in IN cord-258032-buh1e4tm 92 14 [ [ -LRB- cord-258032-buh1e4tm 92 15 16 16 CD cord-258032-buh1e4tm 92 16 ] ] -RRB- cord-258032-buh1e4tm 92 17 : : : cord-258032-buh1e4tm 92 18 We -PRON- PRP cord-258032-buh1e4tm 92 19 have have VBP cord-258032-buh1e4tm 92 20 ( ( -LRB- cord-258032-buh1e4tm 92 21 2 2 CD cord-258032-buh1e4tm 92 22 ) ) -RRB- cord-258032-buh1e4tm 92 23 , , , cord-258032-buh1e4tm 92 24 we -PRON- PRP cord-258032-buh1e4tm 92 25 can can MD cord-258032-buh1e4tm 92 26 also also RB cord-258032-buh1e4tm 92 27 show show VB cord-258032-buh1e4tm 92 28 that that IN cord-258032-buh1e4tm 92 29 = = NFP cord-258032-buh1e4tm 92 30 { { -LRB- cord-258032-buh1e4tm 93 1 * * NFP cord-258032-buh1e4tm 93 2 } } -RRB- cord-258032-buh1e4tm 93 3 . . . cord-258032-buh1e4tm 94 1 Hence hence RB cord-258032-buh1e4tm 94 2 , , , cord-258032-buh1e4tm 94 3 it -PRON- PRP cord-258032-buh1e4tm 94 4 follows follow VBZ cord-258032-buh1e4tm 94 5 from from IN cord-258032-buh1e4tm 94 6 Theorem Theorem NNP cord-258032-buh1e4tm 94 7 1.2 1.2 CD cord-258032-buh1e4tm 94 8 in in IN cord-258032-buh1e4tm 94 9 [ [ -LRB- cord-258032-buh1e4tm 94 10 14 14 CD cord-258032-buh1e4tm 94 11 ] ] -RRB- cord-258032-buh1e4tm 94 12 or or CC cord-258032-buh1e4tm 94 13 Lemma Lemma NNP cord-258032-buh1e4tm 94 14 3.1 3.1 CD cord-258032-buh1e4tm 94 15 in in IN cord-258032-buh1e4tm 94 16 [ [ -LRB- cord-258032-buh1e4tm 94 17 15 15 CD cord-258032-buh1e4tm 94 18 ] ] -RRB- cord-258032-buh1e4tm 95 1 that that DT cord-258032-buh1e4tm 95 2 * * NFP cord-258032-buh1e4tm 95 3 is be VBZ cord-258032-buh1e4tm 95 4 globally globally RB cord-258032-buh1e4tm 95 5 attractive attractive JJ cord-258032-buh1e4tm 95 6 . . . cord-258032-buh1e4tm 96 1 This this DT cord-258032-buh1e4tm 96 2 completes complete VBZ cord-258032-buh1e4tm 96 3 the the DT cord-258032-buh1e4tm 96 4 proof proof NN cord-258032-buh1e4tm 96 5 . . . cord-258032-buh1e4tm 97 1 Let let VB cord-258032-buh1e4tm 97 2 us -PRON- PRP cord-258032-buh1e4tm 97 3 first first RB cord-258032-buh1e4tm 97 4 give give VB cord-258032-buh1e4tm 97 5 some some DT cord-258032-buh1e4tm 97 6 numerical numerical JJ cord-258032-buh1e4tm 97 7 simulations simulation NNS cord-258032-buh1e4tm 97 8 on on IN cord-258032-buh1e4tm 97 9 the the DT cord-258032-buh1e4tm 97 10 orbits orbit NNS cord-258032-buh1e4tm 97 11 of of IN cord-258032-buh1e4tm 97 12 model model NN cord-258032-buh1e4tm 97 13 ( ( -LRB- cord-258032-buh1e4tm 97 14 2 2 CD cord-258032-buh1e4tm 97 15 ) ) -RRB- cord-258032-buh1e4tm 97 16 . . . cord-258032-buh1e4tm 98 1 Take take VB cord-258032-buh1e4tm 98 2 the the DT cord-258032-buh1e4tm 98 3 following follow VBG cord-258032-buh1e4tm 98 4 a a DT cord-258032-buh1e4tm 98 5 set set NN cord-258032-buh1e4tm 98 6 of of IN cord-258032-buh1e4tm 98 7 parameters parameter NNS cord-258032-buh1e4tm 98 8 , , , cord-258032-buh1e4tm 98 9 = = SYM cord-258032-buh1e4tm 98 10 1 1 CD cord-258032-buh1e4tm 98 11 = = SYM cord-258032-buh1e4tm 98 12 1 1 CD cord-258032-buh1e4tm 98 13 , , , cord-258032-buh1e4tm 98 14 = = SYM cord-258032-buh1e4tm 98 15 0.001 0.001 CD cord-258032-buh1e4tm 98 16 , , , cord-258032-buh1e4tm 98 17 = = SYM cord-258032-buh1e4tm 98 18 1 1 CD cord-258032-buh1e4tm 98 19 = = SYM cord-258032-buh1e4tm 98 20 0.05 0.05 CD cord-258032-buh1e4tm 98 21 , , , cord-258032-buh1e4tm 98 22 = = NFP cord-258032-buh1e4tm 99 1 1 1 CD cord-258032-buh1e4tm 99 2 , , , cord-258032-buh1e4tm 99 3 = = SYM cord-258032-buh1e4tm 99 4 0.2 0.2 CD cord-258032-buh1e4tm 99 5 , , , cord-258032-buh1e4tm 99 6 1 1 CD cord-258032-buh1e4tm 99 7 = = SYM cord-258032-buh1e4tm 99 8 1 1 CD cord-258032-buh1e4tm 99 9 , , , cord-258032-buh1e4tm 99 10 and and CC cord-258032-buh1e4tm 100 1 = = SYM cord-258032-buh1e4tm 100 2 0.11 0.11 CD cord-258032-buh1e4tm 100 3 . . . cord-258032-buh1e4tm 101 1 We -PRON- PRP cord-258032-buh1e4tm 101 2 can can MD cord-258032-buh1e4tm 101 3 compute compute VB cord-258032-buh1e4tm 101 4 the the DT cord-258032-buh1e4tm 101 5 values value NNS cord-258032-buh1e4tm 101 6 of of IN cord-258032-buh1e4tm 101 7 the the DT cord-258032-buh1e4tm 101 8 infectionfree infectionfree NNP cord-258032-buh1e4tm 101 9 equilibrium equilibrium NNP cord-258032-buh1e4tm 101 10 0 0 NFP cord-258032-buh1e4tm 101 11 and and CC cord-258032-buh1e4tm 101 12 the the DT cord-258032-buh1e4tm 101 13 basic basic JJ cord-258032-buh1e4tm 101 14 reproductive reproductive JJ cord-258032-buh1e4tm 101 15 ratio ratio NN cord-258032-buh1e4tm 101 16 , , , cord-258032-buh1e4tm 101 17 0 0 CD cord-258032-buh1e4tm 101 18 = = NFP cord-258032-buh1e4tm 101 19 ( ( -LRB- cord-258032-buh1e4tm 101 20 20 20 CD cord-258032-buh1e4tm 101 21 , , , cord-258032-buh1e4tm 101 22 0 0 CD cord-258032-buh1e4tm 101 23 , , , cord-258032-buh1e4tm 101 24 0 0 CD cord-258032-buh1e4tm 101 25 , , , cord-258032-buh1e4tm 101 26 9.0909 9.0909 CD cord-258032-buh1e4tm 101 27 ) ) -RRB- cord-258032-buh1e4tm 101 28 and and CC cord-258032-buh1e4tm 101 29 0 0 CD cord-258032-buh1e4tm 101 30 = = SYM cord-258032-buh1e4tm 101 31 0.90909 0.90909 CD cord-258032-buh1e4tm 101 32 < < SYM cord-258032-buh1e4tm 101 33 1 1 CD cord-258032-buh1e4tm 101 34 . . . cord-258032-buh1e4tm 102 1 Figure figure NN cord-258032-buh1e4tm 102 2 2(a 2(a CD cord-258032-buh1e4tm 102 3 ) ) -RRB- cord-258032-buh1e4tm 102 4 shows show VBZ cord-258032-buh1e4tm 102 5 the the DT cord-258032-buh1e4tm 102 6 trajectory trajectory NN cord-258032-buh1e4tm 102 7 of of IN cord-258032-buh1e4tm 102 8 model model NN cord-258032-buh1e4tm 102 9 ( ( -LRB- cord-258032-buh1e4tm 102 10 2 2 LS cord-258032-buh1e4tm 102 11 ) ) -RRB- cord-258032-buh1e4tm 102 12 with with IN cord-258032-buh1e4tm 102 13 suitable suitable JJ cord-258032-buh1e4tm 102 14 initial initial JJ cord-258032-buh1e4tm 102 15 condition condition NN cord-258032-buh1e4tm 102 16 , , , cord-258032-buh1e4tm 102 17 which which WDT cord-258032-buh1e4tm 102 18 shows show VBZ cord-258032-buh1e4tm 102 19 that that IN cord-258032-buh1e4tm 102 20 the the DT cord-258032-buh1e4tm 102 21 infection infection NN cord-258032-buh1e4tm 102 22 - - HYPH cord-258032-buh1e4tm 102 23 free free JJ cord-258032-buh1e4tm 102 24 equilibrium equilibrium NN cord-258032-buh1e4tm 102 25 0 0 NFP cord-258032-buh1e4tm 102 26 is be VBZ cord-258032-buh1e4tm 102 27 asymptotically asymptotically RB cord-258032-buh1e4tm 102 28 stable stable JJ cord-258032-buh1e4tm 102 29 . . . cord-258032-buh1e4tm 103 1 Let let VB cord-258032-buh1e4tm 103 2 us -PRON- PRP cord-258032-buh1e4tm 103 3 take take VB cord-258032-buh1e4tm 103 4 = = SYM cord-258032-buh1e4tm 103 5 0.05 0.05 CD cord-258032-buh1e4tm 103 6 , , , cord-258032-buh1e4tm 103 7 and and CC cord-258032-buh1e4tm 103 8 all all PDT cord-258032-buh1e4tm 103 9 the the DT cord-258032-buh1e4tm 103 10 other other JJ cord-258032-buh1e4tm 103 11 parameters parameter NNS cord-258032-buh1e4tm 103 12 are be VBP cord-258032-buh1e4tm 103 13 the the DT cord-258032-buh1e4tm 103 14 same same JJ cord-258032-buh1e4tm 103 15 as as IN cord-258032-buh1e4tm 103 16 above above RB cord-258032-buh1e4tm 103 17 . . . cord-258032-buh1e4tm 104 1 We -PRON- PRP cord-258032-buh1e4tm 104 2 can can MD cord-258032-buh1e4tm 104 3 also also RB cord-258032-buh1e4tm 104 4 compute compute VB cord-258032-buh1e4tm 104 5 the the DT cord-258032-buh1e4tm 104 6 values value NNS cord-258032-buh1e4tm 104 7 of of IN cord-258032-buh1e4tm 104 8 the the DT cord-258032-buh1e4tm 104 9 infection infection NN cord-258032-buh1e4tm 104 10 - - HYPH cord-258032-buh1e4tm 104 11 free free JJ cord-258032-buh1e4tm 104 12 equilibrium equilibrium NN cord-258032-buh1e4tm 104 13 0 0 NFP cord-258032-buh1e4tm 104 14 , , , cord-258032-buh1e4tm 104 15 the the DT cord-258032-buh1e4tm 104 16 infected infected JJ cord-258032-buh1e4tm 104 17 equilibrium equilibrium NN cord-258032-buh1e4tm 104 18 * * NFP cord-258032-buh1e4tm 104 19 , , , cord-258032-buh1e4tm 104 20 and and CC cord-258032-buh1e4tm 104 21 the the DT cord-258032-buh1e4tm 104 22 basic basic JJ cord-258032-buh1e4tm 104 23 reproductive reproductive JJ cord-258032-buh1e4tm 104 24 ratio ratio NN cord-258032-buh1e4tm 104 25 , , , cord-258032-buh1e4tm 104 26 0 0 CD cord-258032-buh1e4tm 104 27 = = NFP cord-258032-buh1e4tm 104 28 ( ( -LRB- cord-258032-buh1e4tm 104 29 20 20 CD cord-258032-buh1e4tm 104 30 , , , cord-258032-buh1e4tm 104 31 0 0 CD cord-258032-buh1e4tm 104 32 , , , cord-258032-buh1e4tm 104 33 0 0 CD cord-258032-buh1e4tm 104 34 , , , cord-258032-buh1e4tm 104 35 20 20 CD cord-258032-buh1e4tm 104 36 ) ) -RRB- cord-258032-buh1e4tm 104 37 , , , cord-258032-buh1e4tm 104 38 * * NFP cord-258032-buh1e4tm 104 39 = = NFP cord-258032-buh1e4tm 104 40 ( ( -LRB- cord-258032-buh1e4tm 104 41 14.142 14.142 CD cord-258032-buh1e4tm 104 42 , , , cord-258032-buh1e4tm 104 43 5.8579 5.8579 CD cord-258032-buh1e4tm 104 44 , , , cord-258032-buh1e4tm 104 45 1.4645 1.4645 CD cord-258032-buh1e4tm 104 46 , , , cord-258032-buh1e4tm 104 47 14.142 14.142 CD cord-258032-buh1e4tm 104 48 ) ) -RRB- cord-258032-buh1e4tm 104 49 , , , cord-258032-buh1e4tm 104 50 and and CC cord-258032-buh1e4tm 104 51 0 0 CD cord-258032-buh1e4tm 104 52 = = SYM cord-258032-buh1e4tm 104 53 2 2 CD cord-258032-buh1e4tm 104 54 > > SYM cord-258032-buh1e4tm 104 55 1 1 CD cord-258032-buh1e4tm 104 56 . . . cord-258032-buh1e4tm 105 1 Figure figure NN cord-258032-buh1e4tm 105 2 2 2 CD cord-258032-buh1e4tm 105 3 ( ( -LRB- cord-258032-buh1e4tm 105 4 b b NN cord-258032-buh1e4tm 105 5 ) ) -RRB- cord-258032-buh1e4tm 105 6 shows show VBZ cord-258032-buh1e4tm 105 7 orbits orbit NNS cord-258032-buh1e4tm 105 8 of of IN cord-258032-buh1e4tm 105 9 model model NN cord-258032-buh1e4tm 105 10 ( ( -LRB- cord-258032-buh1e4tm 105 11 2 2 LS cord-258032-buh1e4tm 105 12 ) ) -RRB- cord-258032-buh1e4tm 105 13 with with IN cord-258032-buh1e4tm 105 14 suitable suitable JJ cord-258032-buh1e4tm 105 15 initial initial JJ cord-258032-buh1e4tm 105 16 conditions condition NNS cord-258032-buh1e4tm 105 17 , , , cord-258032-buh1e4tm 105 18 which which WDT cord-258032-buh1e4tm 105 19 shows show VBZ cord-258032-buh1e4tm 105 20 that that IN cord-258032-buh1e4tm 105 21 the the DT cord-258032-buh1e4tm 105 22 infected infected JJ cord-258032-buh1e4tm 105 23 equilibrium equilibrium NN cord-258032-buh1e4tm 105 24 * * NFP cord-258032-buh1e4tm 105 25 is be VBZ cord-258032-buh1e4tm 105 26 asymptotically asymptotically RB cord-258032-buh1e4tm 105 27 stable stable JJ cord-258032-buh1e4tm 105 28 . . . cord-258032-buh1e4tm 106 1 We -PRON- PRP cord-258032-buh1e4tm 106 2 would would MD cord-258032-buh1e4tm 106 3 like like VB cord-258032-buh1e4tm 106 4 to to TO cord-258032-buh1e4tm 106 5 point point VB cord-258032-buh1e4tm 106 6 out out RP cord-258032-buh1e4tm 106 7 here here RB cord-258032-buh1e4tm 106 8 that that IN cord-258032-buh1e4tm 106 9 , , , cord-258032-buh1e4tm 106 10 based base VBN cord-258032-buh1e4tm 106 11 on on IN cord-258032-buh1e4tm 106 12 the the DT cord-258032-buh1e4tm 106 13 numerical numerical JJ cord-258032-buh1e4tm 106 14 simulations simulation NNS cord-258032-buh1e4tm 106 15 , , , cord-258032-buh1e4tm 106 16 the the DT cord-258032-buh1e4tm 106 17 condition condition NN cord-258032-buh1e4tm 106 18 ( ( -LRB- cord-258032-buh1e4tm 106 19 2 2 CD cord-258032-buh1e4tm 106 20 ) ) -RRB- cord-258032-buh1e4tm 106 21 2 2 CD cord-258032-buh1e4tm 106 22 ≥ ≥ CD cord-258032-buh1e4tm 106 23 1 1 CD cord-258032-buh1e4tm 106 24 2 2 CD cord-258032-buh1e4tm 106 25 1 1 CD cord-258032-buh1e4tm 106 26 3 3 CD cord-258032-buh1e4tm 106 27 2 2 CD cord-258032-buh1e4tm 106 28 may may MD cord-258032-buh1e4tm 106 29 be be VB cord-258032-buh1e4tm 106 30 further further RB cord-258032-buh1e4tm 106 31 weakened weaken VBN cord-258032-buh1e4tm 106 32 or or CC cord-258032-buh1e4tm 106 33 even even RB cord-258032-buh1e4tm 106 34 removed remove VBN cord-258032-buh1e4tm 106 35 . . . cord-258032-buh1e4tm 107 1 Finally finally RB cord-258032-buh1e4tm 107 2 , , , cord-258032-buh1e4tm 107 3 by by IN cord-258032-buh1e4tm 107 4 using use VBG cord-258032-buh1e4tm 107 5 the the DT cord-258032-buh1e4tm 107 6 basic basic JJ cord-258032-buh1e4tm 107 7 reproductive reproductive JJ cord-258032-buh1e4tm 107 8 ratio ratio NN cord-258032-buh1e4tm 107 9 0 0 CD cord-258032-buh1e4tm 107 10 = = SYM cord-258032-buh1e4tm 107 11 1 1 CD cord-258032-buh1e4tm 107 12 / / SYM cord-258032-buh1e4tm 107 13 , , , cord-258032-buh1e4tm 107 14 let let VB cord-258032-buh1e4tm 107 15 us -PRON- PRP cord-258032-buh1e4tm 107 16 give give VB cord-258032-buh1e4tm 107 17 some some DT cord-258032-buh1e4tm 107 18 simple simple JJ cord-258032-buh1e4tm 107 19 discussions discussion NNS cord-258032-buh1e4tm 107 20 on on IN cord-258032-buh1e4tm 107 21 the the DT cord-258032-buh1e4tm 107 22 interactions interaction NNS cord-258032-buh1e4tm 107 23 between between IN cord-258032-buh1e4tm 107 24 the the DT cord-258032-buh1e4tm 107 25 protein protein NN cord-258032-buh1e4tm 107 26 DPP4 DPP4 NNP cord-258032-buh1e4tm 107 27 and and CC cord-258032-buh1e4tm 107 28 the the DT cord-258032-buh1e4tm 107 29 virus virus NN cord-258032-buh1e4tm 107 30 infection infection NN cord-258032-buh1e4tm 107 31 . . . cord-258032-buh1e4tm 108 1 Usually usually RB cord-258032-buh1e4tm 108 2 , , , cord-258032-buh1e4tm 108 3 in in IN cord-258032-buh1e4tm 108 4 the the DT cord-258032-buh1e4tm 108 5 absence absence NN cord-258032-buh1e4tm 108 6 of of IN cord-258032-buh1e4tm 108 7 any any DT cord-258032-buh1e4tm 108 8 drug drug NN cord-258032-buh1e4tm 108 9 treatment treatment NN cord-258032-buh1e4tm 108 10 , , , cord-258032-buh1e4tm 108 11 all all PDT cord-258032-buh1e4tm 108 12 the the DT cord-258032-buh1e4tm 108 13 parameters parameter NNS cord-258032-buh1e4tm 108 14 in in IN cord-258032-buh1e4tm 108 15 model model NN cord-258032-buh1e4tm 108 16 ( ( -LRB- cord-258032-buh1e4tm 108 17 2 2 CD cord-258032-buh1e4tm 108 18 ) ) -RRB- cord-258032-buh1e4tm 108 19 and and CC cord-258032-buh1e4tm 108 20 the the DT cord-258032-buh1e4tm 108 21 corresponding corresponding JJ cord-258032-buh1e4tm 108 22 basic basic JJ cord-258032-buh1e4tm 108 23 reproductive reproductive JJ cord-258032-buh1e4tm 108 24 ratio ratio NN cord-258032-buh1e4tm 108 25 0 0 CD cord-258032-buh1e4tm 108 26 can can MD cord-258032-buh1e4tm 108 27 be be VB cord-258032-buh1e4tm 108 28 regarded regard VBN cord-258032-buh1e4tm 108 29 as as IN cord-258032-buh1e4tm 108 30 relatively relatively RB cord-258032-buh1e4tm 108 31 fixed fix VBN cord-258032-buh1e4tm 108 32 constants constant NNS cord-258032-buh1e4tm 108 33 . . . cord-258032-buh1e4tm 109 1 If if IN cord-258032-buh1e4tm 109 2 some some DT cord-258032-buh1e4tm 109 3 drug drug NN cord-258032-buh1e4tm 109 4 treatment treatment NN cord-258032-buh1e4tm 109 5 measures measure NNS cord-258032-buh1e4tm 109 6 are be VBP cord-258032-buh1e4tm 109 7 taken take VBN cord-258032-buh1e4tm 109 8 , , , cord-258032-buh1e4tm 109 9 the the DT cord-258032-buh1e4tm 109 10 effectiveness effectiveness NN cord-258032-buh1e4tm 109 11 of of IN cord-258032-buh1e4tm 109 12 the the DT cord-258032-buh1e4tm 109 13 treatment treatment NN cord-258032-buh1e4tm 109 14 can can MD cord-258032-buh1e4tm 109 15 be be VB cord-258032-buh1e4tm 109 16 reflected reflect VBN cord-258032-buh1e4tm 109 17 in in IN cord-258032-buh1e4tm 109 18 the the DT cord-258032-buh1e4tm 109 19 regulation regulation NN cord-258032-buh1e4tm 109 20 of of IN cord-258032-buh1e4tm 109 21 the the DT cord-258032-buh1e4tm 109 22 parameter parameter NN cord-258032-buh1e4tm 109 23 . . . cord-258032-buh1e4tm 110 1 For for IN cord-258032-buh1e4tm 110 2 example example NN cord-258032-buh1e4tm 110 3 , , , cord-258032-buh1e4tm 110 4 by by IN cord-258032-buh1e4tm 110 5 increasing increase VBG cord-258032-buh1e4tm 110 6 the the DT cord-258032-buh1e4tm 110 7 value value NN cord-258032-buh1e4tm 110 8 of of IN cord-258032-buh1e4tm 110 9 , , , cord-258032-buh1e4tm 110 10 the the DT cord-258032-buh1e4tm 110 11 value value NN cord-258032-buh1e4tm 110 12 of of IN cord-258032-buh1e4tm 110 13 the the DT cord-258032-buh1e4tm 110 14 basic basic JJ cord-258032-buh1e4tm 110 15 reproductive reproductive JJ cord-258032-buh1e4tm 110 16 ratio ratio NN cord-258032-buh1e4tm 110 17 of of IN cord-258032-buh1e4tm 110 18 0 0 CD cord-258032-buh1e4tm 110 19 can can MD cord-258032-buh1e4tm 110 20 be be VB cord-258032-buh1e4tm 110 21 changed change VBN cord-258032-buh1e4tm 110 22 from from IN cord-258032-buh1e4tm 110 23 greater great JJR cord-258032-buh1e4tm 110 24 than than IN cord-258032-buh1e4tm 110 25 1 1 CD cord-258032-buh1e4tm 110 26 to to IN cord-258032-buh1e4tm 110 27 less less JJR cord-258032-buh1e4tm 110 28 than than IN cord-258032-buh1e4tm 110 29 1 1 CD cord-258032-buh1e4tm 110 30 . . . cord-258032-buh1e4tm 111 1 In in IN cord-258032-buh1e4tm 111 2 the the DT cord-258032-buh1e4tm 111 3 numerical numerical JJ cord-258032-buh1e4tm 111 4 simulations simulation NNS cord-258032-buh1e4tm 111 5 in in IN cord-258032-buh1e4tm 111 6 this this DT cord-258032-buh1e4tm 111 7 section section NN cord-258032-buh1e4tm 111 8 , , , cord-258032-buh1e4tm 111 9 Figure figure NN cord-258032-buh1e4tm 111 10 2 2 CD cord-258032-buh1e4tm 111 11 ( ( -LRB- cord-258032-buh1e4tm 111 12 b b NN cord-258032-buh1e4tm 111 13 ) ) -RRB- cord-258032-buh1e4tm 111 14 shows show VBZ cord-258032-buh1e4tm 111 15 that that IN cord-258032-buh1e4tm 111 16 the the DT cord-258032-buh1e4tm 111 17 virus virus NN cord-258032-buh1e4tm 111 18 infection infection NN cord-258032-buh1e4tm 111 19 will will MD cord-258032-buh1e4tm 111 20 be be VB cord-258032-buh1e4tm 111 21 persistent persistent JJ cord-258032-buh1e4tm 111 22 , , , cord-258032-buh1e4tm 111 23 when when WRB cord-258032-buh1e4tm 111 24 = = SYM cord-258032-buh1e4tm 111 25 0.05 0.05 CD cord-258032-buh1e4tm 111 26 and and CC cord-258032-buh1e4tm 111 27 0 0 CD cord-258032-buh1e4tm 111 28 = = SYM cord-258032-buh1e4tm 111 29 2 2 CD cord-258032-buh1e4tm 111 30 > > SYM cord-258032-buh1e4tm 111 31 1 1 CD cord-258032-buh1e4tm 111 32 . . . cord-258032-buh1e4tm 112 1 If if IN cord-258032-buh1e4tm 112 2 increasing increase VBG cord-258032-buh1e4tm 112 3 from from IN cord-258032-buh1e4tm 112 4 = = SYM cord-258032-buh1e4tm 112 5 0.05 0.05 CD cord-258032-buh1e4tm 112 6 to to IN cord-258032-buh1e4tm 112 7 = = SYM cord-258032-buh1e4tm 112 8 0.11 0.11 CD cord-258032-buh1e4tm 112 9 , , , cord-258032-buh1e4tm 112 10 Figure figure NN cord-258032-buh1e4tm 112 11 2 2 CD cord-258032-buh1e4tm 112 12 ( ( -LRB- cord-258032-buh1e4tm 112 13 a a NN cord-258032-buh1e4tm 112 14 ) ) -RRB- cord-258032-buh1e4tm 112 15 shows show VBZ cord-258032-buh1e4tm 112 16 that that IN cord-258032-buh1e4tm 112 17 the the DT cord-258032-buh1e4tm 112 18 virus virus NN cord-258032-buh1e4tm 112 19 infection infection NN cord-258032-buh1e4tm 112 20 can can MD cord-258032-buh1e4tm 112 21 be be VB cord-258032-buh1e4tm 112 22 controlled control VBN cord-258032-buh1e4tm 112 23 , , , cord-258032-buh1e4tm 112 24 since since IN cord-258032-buh1e4tm 112 25 0 0 CD cord-258032-buh1e4tm 112 26 = = SYM cord-258032-buh1e4tm 112 27 0.9090 0.9090 CD cord-258032-buh1e4tm 112 28 < < XX cord-258032-buh1e4tm 112 29 1 1 CD cord-258032-buh1e4tm 112 30 . . . cord-258032-buh1e4tm 113 1 The the DT cord-258032-buh1e4tm 113 2 authors author NNS cord-258032-buh1e4tm 113 3 declare declare VBP cord-258032-buh1e4tm 113 4 that that IN cord-258032-buh1e4tm 113 5 they -PRON- PRP cord-258032-buh1e4tm 113 6 have have VBP cord-258032-buh1e4tm 113 7 no no DT cord-258032-buh1e4tm 113 8 conflicts conflict NNS cord-258032-buh1e4tm 113 9 of of IN cord-258032-buh1e4tm 113 10 interest interest NN cord-258032-buh1e4tm 113 11 . . . cord-258032-buh1e4tm 114 1 Rapid rapid JJ cord-258032-buh1e4tm 114 2 generation generation NN cord-258032-buh1e4tm 114 3 of of IN cord-258032-buh1e4tm 114 4 a a DT cord-258032-buh1e4tm 114 5 mouse mouse NN cord-258032-buh1e4tm 114 6 model model NN cord-258032-buh1e4tm 114 7 for for IN cord-258032-buh1e4tm 114 8 Middle Middle NNP cord-258032-buh1e4tm 114 9 East East NNP cord-258032-buh1e4tm 114 10 respiratory respiratory JJ cord-258032-buh1e4tm 114 11 syndrome syndrome NN cord-258032-buh1e4tm 114 12 Middle Middle NNP cord-258032-buh1e4tm 114 13 East East NNP cord-258032-buh1e4tm 114 14 respiratory respiratory JJ cord-258032-buh1e4tm 114 15 syndrome syndrome NN cord-258032-buh1e4tm 114 16 coronavirus coronavirus NN cord-258032-buh1e4tm 114 17 ( ( -LRB- cord-258032-buh1e4tm 114 18 MERSCoV MERSCoV NFP cord-258032-buh1e4tm 114 19 ) ) -RRB- cord-258032-buh1e4tm 114 20 causes cause VBZ cord-258032-buh1e4tm 114 21 transient transient JJ cord-258032-buh1e4tm 114 22 lower low JJR cord-258032-buh1e4tm 114 23 respiratory respiratory JJ cord-258032-buh1e4tm 114 24 tract tract NN cord-258032-buh1e4tm 114 25 infection infection NN cord-258032-buh1e4tm 114 26 in in IN cord-258032-buh1e4tm 114 27 rhesus rhesu NNS cord-258032-buh1e4tm 114 28 macaques macaque NNS cord-258032-buh1e4tm 114 29 MERSE MERSE NNP cord-258032-buh1e4tm 114 30 Infectious infectious JJ cord-258032-buh1e4tm 114 31 Diseases Diseases NNPS cord-258032-buh1e4tm 114 32 of of IN cord-258032-buh1e4tm 114 33 Humans human NNS cord-258032-buh1e4tm 114 34 : : : cord-258032-buh1e4tm 115 1 Dynamics dynamic NNS cord-258032-buh1e4tm 115 2 and and CC cord-258032-buh1e4tm 115 3 Control Control NNP cord-258032-buh1e4tm 115 4 Population Population NNP cord-258032-buh1e4tm 115 5 dynamics dynamic NNS cord-258032-buh1e4tm 115 6 of of IN cord-258032-buh1e4tm 115 7 immune immune JJ cord-258032-buh1e4tm 115 8 responses response NNS cord-258032-buh1e4tm 115 9 to to IN cord-258032-buh1e4tm 115 10 persistent persistent JJ cord-258032-buh1e4tm 115 11 viruses virus NNS cord-258032-buh1e4tm 115 12 Virus Virus NNP cord-258032-buh1e4tm 115 13 Dynamics Dynamics NNPS cord-258032-buh1e4tm 115 14 : : : cord-258032-buh1e4tm 115 15 Mathematics Mathematics NNP cord-258032-buh1e4tm 115 16 Principles Principles NNPS cord-258032-buh1e4tm 115 17 of of IN cord-258032-buh1e4tm 115 18 Immunology Immunology NNP cord-258032-buh1e4tm 115 19 and and CC cord-258032-buh1e4tm 115 20 Virology Virology NNP cord-258032-buh1e4tm 115 21 Mathematical Mathematical NNP cord-258032-buh1e4tm 115 22 analysis analysis NN cord-258032-buh1e4tm 115 23 of of IN cord-258032-buh1e4tm 115 24 HIV-1 HIV-1 NNP cord-258032-buh1e4tm 115 25 dynamics dynamic NNS cord-258032-buh1e4tm 115 26 in in IN cord-258032-buh1e4tm 115 27 vivo vivo NNP cord-258032-buh1e4tm 115 28 Host host NN cord-258032-buh1e4tm 115 29 cell cell NN cord-258032-buh1e4tm 115 30 entry entry NN cord-258032-buh1e4tm 115 31 of of IN cord-258032-buh1e4tm 115 32 Middle Middle NNP cord-258032-buh1e4tm 115 33 East East NNP cord-258032-buh1e4tm 115 34 respiratory respiratory JJ cord-258032-buh1e4tm 115 35 syndrome syndrome NN cord-258032-buh1e4tm 115 36 coronavirus coronavirus NN cord-258032-buh1e4tm 115 37 after after IN cord-258032-buh1e4tm 115 38 two two CD cord-258032-buh1e4tm 115 39 - - HYPH cord-258032-buh1e4tm 115 40 step step NN cord-258032-buh1e4tm 115 41 , , , cord-258032-buh1e4tm 115 42 furinmediated furinmediated JJ cord-258032-buh1e4tm 115 43 activation activation NN cord-258032-buh1e4tm 115 44 of of IN cord-258032-buh1e4tm 115 45 the the DT cord-258032-buh1e4tm 115 46 spike spike NN cord-258032-buh1e4tm 115 47 protein protein NN cord-258032-buh1e4tm 115 48 Global global JJ cord-258032-buh1e4tm 115 49 properties property NNS cord-258032-buh1e4tm 115 50 of of IN cord-258032-buh1e4tm 115 51 basic basic JJ cord-258032-buh1e4tm 115 52 virus virus NN cord-258032-buh1e4tm 115 53 dynamics dynamic NNS cord-258032-buh1e4tm 115 54 models model NNS cord-258032-buh1e4tm 116 1 Global global JJ cord-258032-buh1e4tm 116 2 asymptotic asymptotic JJ cord-258032-buh1e4tm 116 3 properties property NNS cord-258032-buh1e4tm 116 4 of of IN cord-258032-buh1e4tm 116 5 virus virus NN cord-258032-buh1e4tm 116 6 dynamics dynamic NNS cord-258032-buh1e4tm 116 7 models model NNS cord-258032-buh1e4tm 116 8 with with IN cord-258032-buh1e4tm 116 9 dose dose NN cord-258032-buh1e4tm 116 10 - - HYPH cord-258032-buh1e4tm 116 11 dependent dependent JJ cord-258032-buh1e4tm 116 12 parasite parasite NN cord-258032-buh1e4tm 116 13 reproduction reproduction NN cord-258032-buh1e4tm 116 14 and and CC cord-258032-buh1e4tm 116 15 virulence virulence NN cord-258032-buh1e4tm 116 16 and and CC cord-258032-buh1e4tm 116 17 non non JJ cord-258032-buh1e4tm 116 18 - - JJ cord-258032-buh1e4tm 116 19 linear linear JJ cord-258032-buh1e4tm 116 20 incidence incidence NN cord-258032-buh1e4tm 116 21 rate rate NN cord-258032-buh1e4tm 117 1 Complete complete JJ cord-258032-buh1e4tm 117 2 global global JJ cord-258032-buh1e4tm 117 3 stability stability NN cord-258032-buh1e4tm 117 4 for for IN cord-258032-buh1e4tm 117 5 an an DT cord-258032-buh1e4tm 117 6 SIR SIR NNP cord-258032-buh1e4tm 117 7 epidemic epidemic NN cord-258032-buh1e4tm 117 8 model model NN cord-258032-buh1e4tm 117 9 with with IN cord-258032-buh1e4tm 117 10 delay delay NN cord-258032-buh1e4tm 117 11 - - HYPH cord-258032-buh1e4tm 117 12 distributed distribute VBN cord-258032-buh1e4tm 117 13 or or CC cord-258032-buh1e4tm 117 14 discrete discrete JJ cord-258032-buh1e4tm 117 15 Global global JJ cord-258032-buh1e4tm 117 16 properties property NNS cord-258032-buh1e4tm 117 17 for for IN cord-258032-buh1e4tm 117 18 virus virus NN cord-258032-buh1e4tm 117 19 dynamics dynamic NNS cord-258032-buh1e4tm 117 20 model model NN cord-258032-buh1e4tm 117 21 with with IN cord-258032-buh1e4tm 117 22 Beddington Beddington NNP cord-258032-buh1e4tm 117 23 - - HYPH cord-258032-buh1e4tm 117 24 DeAngelis DeAngelis NNP cord-258032-buh1e4tm 117 25 functional functional JJ cord-258032-buh1e4tm 117 26 response response NN cord-258032-buh1e4tm 117 27 Stability stability NN cord-258032-buh1e4tm 117 28 and and CC cord-258032-buh1e4tm 117 29 Hopf Hopf NNP cord-258032-buh1e4tm 117 30 bifurcation bifurcation NN cord-258032-buh1e4tm 117 31 in in IN cord-258032-buh1e4tm 117 32 a a DT cord-258032-buh1e4tm 117 33 delayed delay VBN cord-258032-buh1e4tm 117 34 HIV HIV NNP cord-258032-buh1e4tm 117 35 infection infection NN cord-258032-buh1e4tm 117 36 model model NN cord-258032-buh1e4tm 117 37 with with IN cord-258032-buh1e4tm 117 38 general general JJ cord-258032-buh1e4tm 117 39 incidence incidence NN cord-258032-buh1e4tm 117 40 rate rate NN cord-258032-buh1e4tm 117 41 and and CC cord-258032-buh1e4tm 117 42 immune immune JJ cord-258032-buh1e4tm 117 43 impairment impairment NN cord-258032-buh1e4tm 117 44 Global global JJ cord-258032-buh1e4tm 117 45 dynamics dynamic NNS cord-258032-buh1e4tm 117 46 of of IN cord-258032-buh1e4tm 117 47 a a DT cord-258032-buh1e4tm 117 48 mathematical mathematical JJ cord-258032-buh1e4tm 117 49 model model NN cord-258032-buh1e4tm 117 50 of of IN cord-258032-buh1e4tm 117 51 competition competition NN cord-258032-buh1e4tm 117 52 in in IN cord-258032-buh1e4tm 117 53 the the DT cord-258032-buh1e4tm 117 54 chemostat chemostat NNP cord-258032-buh1e4tm 117 55 : : : cord-258032-buh1e4tm 117 56 general general JJ cord-258032-buh1e4tm 117 57 response response NN cord-258032-buh1e4tm 117 58 functions function NNS cord-258032-buh1e4tm 117 59 and and CC cord-258032-buh1e4tm 117 60 differential differential JJ cord-258032-buh1e4tm 117 61 death death NN cord-258032-buh1e4tm 117 62 rates rate NNS cord-258032-buh1e4tm 118 1 Necessary necessary JJ cord-258032-buh1e4tm 118 2 and and CC cord-258032-buh1e4tm 118 3 sufficient sufficient JJ cord-258032-buh1e4tm 118 4 conditions condition NNS cord-258032-buh1e4tm 118 5 for for IN cord-258032-buh1e4tm 118 6 permanence permanence NN cord-258032-buh1e4tm 118 7 and and CC cord-258032-buh1e4tm 118 8 global global JJ cord-258032-buh1e4tm 118 9 stability stability NN cord-258032-buh1e4tm 118 10 of of IN cord-258032-buh1e4tm 118 11 a a DT cord-258032-buh1e4tm 118 12 Lotka Lotka NNP cord-258032-buh1e4tm 118 13 - - HYPH cord-258032-buh1e4tm 118 14 Volterra Volterra NNP cord-258032-buh1e4tm 118 15 system system NN cord-258032-buh1e4tm 118 16 with with IN cord-258032-buh1e4tm 118 17 two two CD cord-258032-buh1e4tm 118 18 delays delay NNS cord-258032-buh1e4tm 118 19 Theory theory NN cord-258032-buh1e4tm 118 20 of of IN cord-258032-buh1e4tm 118 21 Motion Motion NNP cord-258032-buh1e4tm 118 22 Stability Stability NNP cord-258032-buh1e4tm 118 23 and and CC cord-258032-buh1e4tm 118 24 Their -PRON- PRP$ cord-258032-buh1e4tm 118 25 Applications application NNS cord-258032-buh1e4tm 119 1 The the DT cord-258032-buh1e4tm 119 2 authors author NNS cord-258032-buh1e4tm 119 3 are be VBP cord-258032-buh1e4tm 119 4 grateful grateful JJ cord-258032-buh1e4tm 119 5 to to IN cord-258032-buh1e4tm 119 6 Drs Drs NNP cord-258032-buh1e4tm 119 7 . . . cord-258032-buh1e4tm 120 1 Songbai Songbai NNP cord-258032-buh1e4tm 120 2 Guo Guo NNP cord-258032-buh1e4tm 120 3 and and CC cord-258032-buh1e4tm 120 4 Ke Ke NNP cord-258032-buh1e4tm 120 5 Guo Guo NNP cord-258032-buh1e4tm 120 6 for for IN cord-258032-buh1e4tm 120 7 their -PRON- PRP$ cord-258032-buh1e4tm 120 8 valuable valuable JJ cord-258032-buh1e4tm 120 9 suggestions suggestion NNS cord-258032-buh1e4tm 120 10 . . . cord-258032-buh1e4tm 121 1 The the DT cord-258032-buh1e4tm 121 2 research research NN cord-258032-buh1e4tm 121 3 is be VBZ cord-258032-buh1e4tm 121 4 partly partly RB cord-258032-buh1e4tm 121 5 supported support VBN cord-258032-buh1e4tm 121 6 by by IN cord-258032-buh1e4tm 121 7 SRTP SRTP NNP cord-258032-buh1e4tm 121 8 of of IN cord-258032-buh1e4tm 121 9 USTB USTB NNP cord-258032-buh1e4tm 121 10 ( ( -LRB- cord-258032-buh1e4tm 121 11 for for IN cord-258032-buh1e4tm 121 12 S. S. NNP cord-258032-buh1e4tm 121 13 Tang Tang NNP cord-258032-buh1e4tm 121 14 and and CC cord-258032-buh1e4tm 121 15 P. P. NNP cord-258032-buh1e4tm 121 16 Bai Bai NNP cord-258032-buh1e4tm 121 17 ) ) -RRB- cord-258032-buh1e4tm 121 18 and and CC cord-258032-buh1e4tm 121 19 partly partly RB cord-258032-buh1e4tm 121 20 supported support VBN cord-258032-buh1e4tm 121 21 by by IN cord-258032-buh1e4tm 121 22 the the DT cord-258032-buh1e4tm 121 23 NNSF NNSF NNP cord-258032-buh1e4tm 121 24 of of IN cord-258032-buh1e4tm 121 25 China China NNP cord-258032-buh1e4tm 121 26 ( ( -LRB- cord-258032-buh1e4tm 121 27 11471034 11471034 CD cord-258032-buh1e4tm 121 28 ) ) -RRB- cord-258032-buh1e4tm 121 29 and and CC cord-258032-buh1e4tm 121 30 National National NNP cord-258032-buh1e4tm 121 31 Key Key NNP cord-258032-buh1e4tm 121 32 R&D R&D NNP cord-258032-buh1e4tm 121 33 Program Program NNP cord-258032-buh1e4tm 121 34 of of IN cord-258032-buh1e4tm 121 35 China China NNP cord-258032-buh1e4tm 121 36 ( ( -LRB- cord-258032-buh1e4tm 121 37 for for IN cord-258032-buh1e4tm 121 38 W. W. NNP cord-258032-buh1e4tm 121 39 Ma Ma NNP cord-258032-buh1e4tm 121 40 ) ) -RRB- cord-258032-buh1e4tm 121 41 . . . cord-258032-buh1e4tm 122 1 S. S. NNP cord-258032-buh1e4tm 122 2 Tang Tang NNP cord-258032-buh1e4tm 122 3 and and CC cord-258032-buh1e4tm 122 4 P. P. NNP cord-258032-buh1e4tm 122 5 Bai Bai NNP cord-258032-buh1e4tm 122 6 performed perform VBD cord-258032-buh1e4tm 122 7 local local JJ cord-258032-buh1e4tm 122 8 and and CC cord-258032-buh1e4tm 122 9 global global JJ cord-258032-buh1e4tm 122 10 stability stability NN cord-258032-buh1e4tm 122 11 analysis analysis NN cord-258032-buh1e4tm 122 12 and and CC cord-258032-buh1e4tm 122 13 the the DT cord-258032-buh1e4tm 122 14 numerical numerical JJ cord-258032-buh1e4tm 122 15 simulations simulation NNS cord-258032-buh1e4tm 122 16 and and CC cord-258032-buh1e4tm 122 17 wrote write VBD cord-258032-buh1e4tm 122 18 the the DT cord-258032-buh1e4tm 122 19 manuscript manuscript NN cord-258032-buh1e4tm 122 20 . . . cord-258032-buh1e4tm 123 1 W. W. NNP cord-258032-buh1e4tm 123 2 Ma Ma NNP cord-258032-buh1e4tm 123 3 designed design VBD cord-258032-buh1e4tm 123 4 the the DT cord-258032-buh1e4tm 123 5 study study NN cord-258032-buh1e4tm 123 6 , , , cord-258032-buh1e4tm 123 7 developed develop VBD cord-258032-buh1e4tm 123 8 the the DT cord-258032-buh1e4tm 123 9 methodology methodology NN cord-258032-buh1e4tm 123 10 of of IN cord-258032-buh1e4tm 123 11 invariance invariance NN cord-258032-buh1e4tm 123 12 principle principle NN cord-258032-buh1e4tm 123 13 , , , cord-258032-buh1e4tm 123 14 and and CC cord-258032-buh1e4tm 123 15 wrote write VBD cord-258032-buh1e4tm 123 16 the the DT cord-258032-buh1e4tm 123 17 manuscript manuscript NN cord-258032-buh1e4tm 123 18 . . . cord-258032-buh1e4tm 124 1 All all DT cord-258032-buh1e4tm 124 2 authors author NNS cord-258032-buh1e4tm 124 3 have have VBP cord-258032-buh1e4tm 124 4 read read VBN cord-258032-buh1e4tm 124 5 and and CC cord-258032-buh1e4tm 124 6 approved approve VBD cord-258032-buh1e4tm 124 7 the the DT cord-258032-buh1e4tm 124 8 final final JJ cord-258032-buh1e4tm 124 9 manuscript manuscript NN cord-258032-buh1e4tm 124 10 . . .