id sid tid token lemma pos cord-018208-sc8j1ate 1 1 key key NN cord-018208-sc8j1ate 1 2 : : : cord-018208-sc8j1ate 1 3 cord-018208-sc8j1ate cord-018208-sc8j1ate NN cord-018208-sc8j1ate 1 4 authors author NNS cord-018208-sc8j1ate 1 5 : : : cord-018208-sc8j1ate 1 6 Qu Qu NNP cord-018208-sc8j1ate 1 7 , , , cord-018208-sc8j1ate 1 8 Bo Bo NNP cord-018208-sc8j1ate 1 9 ; ; : cord-018208-sc8j1ate 1 10 Wang Wang NNP cord-018208-sc8j1ate 2 1 , , , cord-018208-sc8j1ate 2 2 Huijuan Huijuan NNP cord-018208-sc8j1ate 2 3 title title NN cord-018208-sc8j1ate 2 4 : : : cord-018208-sc8j1ate 3 1 The the DT cord-018208-sc8j1ate 3 2 Accuracy Accuracy NNP cord-018208-sc8j1ate 3 3 of of IN cord-018208-sc8j1ate 3 4 Mean Mean NNP cord-018208-sc8j1ate 3 5 - - HYPH cord-018208-sc8j1ate 3 6 Field field NN cord-018208-sc8j1ate 3 7 Approximation approximation NN cord-018208-sc8j1ate 3 8 for for IN cord-018208-sc8j1ate 3 9 Susceptible susceptible JJ cord-018208-sc8j1ate 3 10 - - HYPH cord-018208-sc8j1ate 3 11 Infected infected JJ cord-018208-sc8j1ate 3 12 - - HYPH cord-018208-sc8j1ate 3 13 Susceptible susceptible JJ cord-018208-sc8j1ate 3 14 Epidemic epidemic NN cord-018208-sc8j1ate 3 15 Spreading spread VBG cord-018208-sc8j1ate 3 16 with with IN cord-018208-sc8j1ate 3 17 Heterogeneous heterogeneous JJ cord-018208-sc8j1ate 3 18 Infection infection NN cord-018208-sc8j1ate 3 19 Rates Rates NNPS cord-018208-sc8j1ate 3 20 date date NN cord-018208-sc8j1ate 3 21 : : : cord-018208-sc8j1ate 3 22 2016 2016 CD cord-018208-sc8j1ate 3 23 - - HYPH cord-018208-sc8j1ate 3 24 11 11 CD cord-018208-sc8j1ate 3 25 - - HYPH cord-018208-sc8j1ate 3 26 09 09 CD cord-018208-sc8j1ate 3 27 journal journal NN cord-018208-sc8j1ate 3 28 : : : cord-018208-sc8j1ate 3 29 Complex Complex NNP cord-018208-sc8j1ate 3 30 Networks Networks NNPS cord-018208-sc8j1ate 3 31 & & CC cord-018208-sc8j1ate 3 32 Their -PRON- PRP$ cord-018208-sc8j1ate 3 33 Applications application NNS cord-018208-sc8j1ate 3 34 V v NN cord-018208-sc8j1ate 3 35 DOI doi NN cord-018208-sc8j1ate 3 36 : : : cord-018208-sc8j1ate 3 37 10.1007/978 10.1007/978 CD cord-018208-sc8j1ate 3 38 - - HYPH cord-018208-sc8j1ate 3 39 3 3 CD cord-018208-sc8j1ate 3 40 - - HYPH cord-018208-sc8j1ate 3 41 319 319 CD cord-018208-sc8j1ate 3 42 - - HYPH cord-018208-sc8j1ate 3 43 50901 50901 CD cord-018208-sc8j1ate 3 44 - - HYPH cord-018208-sc8j1ate 3 45 3_40 3_40 CD cord-018208-sc8j1ate 3 46 sha sha NNP cord-018208-sc8j1ate 3 47 : : : cord-018208-sc8j1ate 3 48 56b88702d63277beff4ebef2c1bd01b6a50b017c 56b88702d63277beff4ebef2c1bd01b6a50b017c CD cord-018208-sc8j1ate 3 49 doc_id doc_id CD cord-018208-sc8j1ate 3 50 : : : cord-018208-sc8j1ate 3 51 18208 18208 CD cord-018208-sc8j1ate 3 52 cord_uid cord_uid FW cord-018208-sc8j1ate 3 53 : : : cord-018208-sc8j1ate 4 1 sc8j1ate sc8j1ate NNP cord-018208-sc8j1ate 4 2 The the DT cord-018208-sc8j1ate 4 3 epidemic epidemic NN cord-018208-sc8j1ate 4 4 spreading spread VBG cord-018208-sc8j1ate 4 5 over over IN cord-018208-sc8j1ate 4 6 a a DT cord-018208-sc8j1ate 4 7 network network NN cord-018208-sc8j1ate 4 8 has have VBZ cord-018208-sc8j1ate 4 9 been be VBN cord-018208-sc8j1ate 4 10 studied study VBN cord-018208-sc8j1ate 4 11 for for IN cord-018208-sc8j1ate 4 12 years year NNS cord-018208-sc8j1ate 4 13 by by IN cord-018208-sc8j1ate 4 14 applying apply VBG cord-018208-sc8j1ate 4 15 the the DT cord-018208-sc8j1ate 4 16 mean mean JJ cord-018208-sc8j1ate 4 17 - - HYPH cord-018208-sc8j1ate 4 18 field field NN cord-018208-sc8j1ate 4 19 approach approach NN cord-018208-sc8j1ate 4 20 in in IN cord-018208-sc8j1ate 4 21 both both CC cord-018208-sc8j1ate 4 22 homogeneous homogeneous JJ cord-018208-sc8j1ate 4 23 case case NN cord-018208-sc8j1ate 4 24 , , , cord-018208-sc8j1ate 4 25 where where WRB cord-018208-sc8j1ate 4 26 each each DT cord-018208-sc8j1ate 4 27 node node NN cord-018208-sc8j1ate 4 28 may may MD cord-018208-sc8j1ate 4 29 get get VB cord-018208-sc8j1ate 4 30 infected infect VBN cord-018208-sc8j1ate 4 31 by by IN cord-018208-sc8j1ate 4 32 an an DT cord-018208-sc8j1ate 4 33 infected infected JJ cord-018208-sc8j1ate 4 34 neighbor neighbor NN cord-018208-sc8j1ate 4 35 with with IN cord-018208-sc8j1ate 4 36 the the DT cord-018208-sc8j1ate 4 37 same same JJ cord-018208-sc8j1ate 4 38 rate rate NN cord-018208-sc8j1ate 4 39 , , , cord-018208-sc8j1ate 4 40 and and CC cord-018208-sc8j1ate 4 41 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 4 42 case case NN cord-018208-sc8j1ate 4 43 , , , cord-018208-sc8j1ate 4 44 where where WRB cord-018208-sc8j1ate 4 45 the the DT cord-018208-sc8j1ate 4 46 infection infection NN cord-018208-sc8j1ate 4 47 rates rate NNS cord-018208-sc8j1ate 4 48 between between IN cord-018208-sc8j1ate 4 49 different different JJ cord-018208-sc8j1ate 4 50 pairs pair NNS cord-018208-sc8j1ate 4 51 of of IN cord-018208-sc8j1ate 4 52 nodes node NNS cord-018208-sc8j1ate 4 53 are be VBP cord-018208-sc8j1ate 4 54 also also RB cord-018208-sc8j1ate 4 55 different different JJ cord-018208-sc8j1ate 4 56 . . . cord-018208-sc8j1ate 5 1 Researchers researcher NNS cord-018208-sc8j1ate 5 2 have have VBP cord-018208-sc8j1ate 5 3 discussed discuss VBN cord-018208-sc8j1ate 5 4 whether whether IN cord-018208-sc8j1ate 5 5 the the DT cord-018208-sc8j1ate 5 6 mean mean JJ cord-018208-sc8j1ate 5 7 - - HYPH cord-018208-sc8j1ate 5 8 field field NN cord-018208-sc8j1ate 5 9 approaches approach NNS cord-018208-sc8j1ate 5 10 could could MD cord-018208-sc8j1ate 5 11 accurately accurately RB cord-018208-sc8j1ate 5 12 describe describe VB cord-018208-sc8j1ate 5 13 the the DT cord-018208-sc8j1ate 5 14 epidemic epidemic NN cord-018208-sc8j1ate 5 15 spreading spread VBG cord-018208-sc8j1ate 5 16 for for IN cord-018208-sc8j1ate 5 17 the the DT cord-018208-sc8j1ate 5 18 homogeneous homogeneous JJ cord-018208-sc8j1ate 5 19 cases case NNS cord-018208-sc8j1ate 5 20 but but CC cord-018208-sc8j1ate 5 21 not not RB cord-018208-sc8j1ate 5 22 for for IN cord-018208-sc8j1ate 5 23 the the DT cord-018208-sc8j1ate 5 24 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 5 25 cases case NNS cord-018208-sc8j1ate 5 26 . . . cord-018208-sc8j1ate 6 1 In in IN cord-018208-sc8j1ate 6 2 this this DT cord-018208-sc8j1ate 6 3 paper paper NN cord-018208-sc8j1ate 6 4 , , , cord-018208-sc8j1ate 6 5 we -PRON- PRP cord-018208-sc8j1ate 6 6 explore explore VBP cord-018208-sc8j1ate 6 7 if if IN cord-018208-sc8j1ate 6 8 and and CC cord-018208-sc8j1ate 6 9 under under IN cord-018208-sc8j1ate 6 10 what what WDT cord-018208-sc8j1ate 6 11 conditions condition NNS cord-018208-sc8j1ate 6 12 the the DT cord-018208-sc8j1ate 6 13 mean mean JJ cord-018208-sc8j1ate 6 14 - - HYPH cord-018208-sc8j1ate 6 15 field field NN cord-018208-sc8j1ate 6 16 approach approach NN cord-018208-sc8j1ate 6 17 could could MD cord-018208-sc8j1ate 6 18 perform perform VB cord-018208-sc8j1ate 6 19 well well RB cord-018208-sc8j1ate 6 20 when when WRB cord-018208-sc8j1ate 6 21 the the DT cord-018208-sc8j1ate 6 22 infection infection NN cord-018208-sc8j1ate 6 23 rates rate NNS cord-018208-sc8j1ate 6 24 are be VBP cord-018208-sc8j1ate 6 25 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 6 26 . . . cord-018208-sc8j1ate 7 1 In in IN cord-018208-sc8j1ate 7 2 particular particular JJ cord-018208-sc8j1ate 7 3 , , , cord-018208-sc8j1ate 7 4 we -PRON- PRP cord-018208-sc8j1ate 7 5 employ employ VBP cord-018208-sc8j1ate 7 6 the the DT cord-018208-sc8j1ate 7 7 Susceptible Susceptible NNP cord-018208-sc8j1ate 7 8 - - HYPH cord-018208-sc8j1ate 7 9 Infected infected JJ cord-018208-sc8j1ate 7 10 - - HYPH cord-018208-sc8j1ate 7 11 Susceptible susceptible JJ cord-018208-sc8j1ate 7 12 ( ( -LRB- cord-018208-sc8j1ate 7 13 SIS SIS NNP cord-018208-sc8j1ate 7 14 ) ) -RRB- cord-018208-sc8j1ate 7 15 model model NN cord-018208-sc8j1ate 7 16 and and CC cord-018208-sc8j1ate 7 17 compare compare VB cord-018208-sc8j1ate 7 18 the the DT cord-018208-sc8j1ate 7 19 average average JJ cord-018208-sc8j1ate 7 20 fraction fraction NN cord-018208-sc8j1ate 7 21 of of IN cord-018208-sc8j1ate 7 22 infected infected JJ cord-018208-sc8j1ate 7 23 nodes node NNS cord-018208-sc8j1ate 7 24 in in IN cord-018208-sc8j1ate 7 25 the the DT cord-018208-sc8j1ate 7 26 metastable metastable JJ cord-018208-sc8j1ate 7 27 state state NN cord-018208-sc8j1ate 7 28 , , , cord-018208-sc8j1ate 7 29 where where WRB cord-018208-sc8j1ate 7 30 the the DT cord-018208-sc8j1ate 7 31 fraction fraction NN cord-018208-sc8j1ate 7 32 of of IN cord-018208-sc8j1ate 7 33 infected infected JJ cord-018208-sc8j1ate 7 34 nodes node NNS cord-018208-sc8j1ate 7 35 remains remain VBZ cord-018208-sc8j1ate 7 36 stable stable JJ cord-018208-sc8j1ate 7 37 for for IN cord-018208-sc8j1ate 7 38 a a DT cord-018208-sc8j1ate 7 39 long long JJ cord-018208-sc8j1ate 7 40 time time NN cord-018208-sc8j1ate 7 41 , , , cord-018208-sc8j1ate 7 42 obtained obtain VBN cord-018208-sc8j1ate 7 43 by by IN cord-018208-sc8j1ate 7 44 the the DT cord-018208-sc8j1ate 7 45 continuous continuous JJ cord-018208-sc8j1ate 7 46 - - HYPH cord-018208-sc8j1ate 7 47 time time NN cord-018208-sc8j1ate 7 48 simulation simulation NN cord-018208-sc8j1ate 7 49 and and CC cord-018208-sc8j1ate 7 50 the the DT cord-018208-sc8j1ate 7 51 mean mean JJ cord-018208-sc8j1ate 7 52 - - HYPH cord-018208-sc8j1ate 7 53 field field NN cord-018208-sc8j1ate 7 54 approximation approximation NN cord-018208-sc8j1ate 7 55 . . . cord-018208-sc8j1ate 8 1 We -PRON- PRP cord-018208-sc8j1ate 8 2 concentrate concentrate VBP cord-018208-sc8j1ate 8 3 on on IN cord-018208-sc8j1ate 8 4 an an DT cord-018208-sc8j1ate 8 5 individual individual NN cord-018208-sc8j1ate 8 6 - - HYPH cord-018208-sc8j1ate 8 7 based base VBN cord-018208-sc8j1ate 8 8 mean mean NN cord-018208-sc8j1ate 8 9 - - HYPH cord-018208-sc8j1ate 8 10 field field NN cord-018208-sc8j1ate 8 11 approximation approximation NN cord-018208-sc8j1ate 8 12 called call VBN cord-018208-sc8j1ate 8 13 the the DT cord-018208-sc8j1ate 8 14 N n NN cord-018208-sc8j1ate 8 15 - - HYPH cord-018208-sc8j1ate 8 16 intertwined intertwine VBN cord-018208-sc8j1ate 8 17 Mean Mean NNP cord-018208-sc8j1ate 8 18 Field field NN cord-018208-sc8j1ate 8 19 Approximation approximation NN cord-018208-sc8j1ate 8 20 ( ( -LRB- cord-018208-sc8j1ate 8 21 NIMFA NIMFA NNP cord-018208-sc8j1ate 8 22 ) ) -RRB- cord-018208-sc8j1ate 8 23 , , , cord-018208-sc8j1ate 8 24 which which WDT cord-018208-sc8j1ate 8 25 is be VBZ cord-018208-sc8j1ate 8 26 an an DT cord-018208-sc8j1ate 8 27 advanced advanced JJ cord-018208-sc8j1ate 8 28 approach approach NN cord-018208-sc8j1ate 8 29 considered consider VBD cord-018208-sc8j1ate 8 30 the the DT cord-018208-sc8j1ate 8 31 underlying underlying JJ cord-018208-sc8j1ate 8 32 network network NN cord-018208-sc8j1ate 8 33 topology topology NN cord-018208-sc8j1ate 8 34 . . . cord-018208-sc8j1ate 9 1 Moreover moreover RB cord-018208-sc8j1ate 9 2 , , , cord-018208-sc8j1ate 9 3 for for IN cord-018208-sc8j1ate 9 4 the the DT cord-018208-sc8j1ate 9 5 heterogeneity heterogeneity NN cord-018208-sc8j1ate 9 6 of of IN cord-018208-sc8j1ate 9 7 the the DT cord-018208-sc8j1ate 9 8 infection infection NN cord-018208-sc8j1ate 9 9 rates rate NNS cord-018208-sc8j1ate 9 10 , , , cord-018208-sc8j1ate 9 11 we -PRON- PRP cord-018208-sc8j1ate 9 12 consider consider VBP cord-018208-sc8j1ate 9 13 not not RB cord-018208-sc8j1ate 9 14 only only RB cord-018208-sc8j1ate 9 15 the the DT cord-018208-sc8j1ate 9 16 independent independent JJ cord-018208-sc8j1ate 9 17 and and CC cord-018208-sc8j1ate 9 18 identically identically RB cord-018208-sc8j1ate 9 19 distributed distribute VBN cord-018208-sc8j1ate 9 20 ( ( -LRB- cord-018208-sc8j1ate 9 21 i.i.d i.i.d NN cord-018208-sc8j1ate 9 22 . . . cord-018208-sc8j1ate 9 23 ) ) -RRB- cord-018208-sc8j1ate 10 1 infection infection NN cord-018208-sc8j1ate 10 2 rate rate NN cord-018208-sc8j1ate 10 3 but but CC cord-018208-sc8j1ate 10 4 also also RB cord-018208-sc8j1ate 10 5 the the DT cord-018208-sc8j1ate 10 6 infection infection NN cord-018208-sc8j1ate 10 7 rate rate NN cord-018208-sc8j1ate 10 8 correlated correlate VBN cord-018208-sc8j1ate 10 9 with with IN cord-018208-sc8j1ate 10 10 the the DT cord-018208-sc8j1ate 10 11 degree degree NN cord-018208-sc8j1ate 10 12 of of IN cord-018208-sc8j1ate 10 13 the the DT cord-018208-sc8j1ate 10 14 two two CD cord-018208-sc8j1ate 10 15 end end NN cord-018208-sc8j1ate 10 16 nodes node NNS cord-018208-sc8j1ate 10 17 . . . cord-018208-sc8j1ate 11 1 We -PRON- PRP cord-018208-sc8j1ate 11 2 conclude conclude VBP cord-018208-sc8j1ate 11 3 that that IN cord-018208-sc8j1ate 11 4 NIMFA NIMFA NNP cord-018208-sc8j1ate 11 5 is be VBZ cord-018208-sc8j1ate 11 6 generally generally RB cord-018208-sc8j1ate 11 7 more more RBR cord-018208-sc8j1ate 11 8 accurate accurate JJ cord-018208-sc8j1ate 11 9 when when WRB cord-018208-sc8j1ate 11 10 the the DT cord-018208-sc8j1ate 11 11 prevalence prevalence NN cord-018208-sc8j1ate 11 12 of of IN cord-018208-sc8j1ate 11 13 the the DT cord-018208-sc8j1ate 11 14 epidemic epidemic NN cord-018208-sc8j1ate 11 15 is be VBZ cord-018208-sc8j1ate 11 16 higher high JJR cord-018208-sc8j1ate 11 17 . . . cord-018208-sc8j1ate 12 1 Given give VBN cord-018208-sc8j1ate 12 2 the the DT cord-018208-sc8j1ate 12 3 same same JJ cord-018208-sc8j1ate 12 4 effective effective JJ cord-018208-sc8j1ate 12 5 infection infection NN cord-018208-sc8j1ate 12 6 rate rate NN cord-018208-sc8j1ate 12 7 , , , cord-018208-sc8j1ate 12 8 NIMFA NIMFA NNP cord-018208-sc8j1ate 12 9 is be VBZ cord-018208-sc8j1ate 12 10 less less RBR cord-018208-sc8j1ate 12 11 accurate accurate JJ cord-018208-sc8j1ate 12 12 when when WRB cord-018208-sc8j1ate 12 13 the the DT cord-018208-sc8j1ate 12 14 variance variance NN cord-018208-sc8j1ate 12 15 of of IN cord-018208-sc8j1ate 12 16 the the DT cord-018208-sc8j1ate 12 17 i.i.d i.i.d NN cord-018208-sc8j1ate 12 18 . . . cord-018208-sc8j1ate 12 19 infection infection NN cord-018208-sc8j1ate 12 20 rate rate NN cord-018208-sc8j1ate 12 21 or or CC cord-018208-sc8j1ate 12 22 the the DT cord-018208-sc8j1ate 12 23 correlation correlation NN cord-018208-sc8j1ate 12 24 between between IN cord-018208-sc8j1ate 12 25 the the DT cord-018208-sc8j1ate 12 26 infection infection NN cord-018208-sc8j1ate 12 27 rate rate NN cord-018208-sc8j1ate 12 28 and and CC cord-018208-sc8j1ate 12 29 the the DT cord-018208-sc8j1ate 12 30 nodal nodal JJ cord-018208-sc8j1ate 12 31 degree degree NN cord-018208-sc8j1ate 12 32 leads lead VBZ cord-018208-sc8j1ate 12 33 to to IN cord-018208-sc8j1ate 12 34 a a DT cord-018208-sc8j1ate 12 35 lower low JJR cord-018208-sc8j1ate 12 36 prevalence prevalence NN cord-018208-sc8j1ate 12 37 . . . cord-018208-sc8j1ate 13 1 Moreover moreover RB cord-018208-sc8j1ate 13 2 , , , cord-018208-sc8j1ate 13 3 given give VBN cord-018208-sc8j1ate 13 4 the the DT cord-018208-sc8j1ate 13 5 same same JJ cord-018208-sc8j1ate 13 6 actual actual JJ cord-018208-sc8j1ate 13 7 prevalence prevalence NN cord-018208-sc8j1ate 13 8 , , , cord-018208-sc8j1ate 13 9 NIMFA NIMFA NNP cord-018208-sc8j1ate 13 10 performs perform VBZ cord-018208-sc8j1ate 13 11 better well RBR cord-018208-sc8j1ate 13 12 in in IN cord-018208-sc8j1ate 13 13 the the DT cord-018208-sc8j1ate 13 14 cases case NNS cord-018208-sc8j1ate 13 15 : : : cord-018208-sc8j1ate 13 16 1 1 LS cord-018208-sc8j1ate 13 17 ) ) -RRB- cord-018208-sc8j1ate 13 18 when when WRB cord-018208-sc8j1ate 13 19 the the DT cord-018208-sc8j1ate 13 20 variance variance NN cord-018208-sc8j1ate 13 21 of of IN cord-018208-sc8j1ate 13 22 the the DT cord-018208-sc8j1ate 13 23 i.i.d i.i.d NN cord-018208-sc8j1ate 13 24 . . . cord-018208-sc8j1ate 13 25 infection infection NN cord-018208-sc8j1ate 13 26 rates rate NNS cord-018208-sc8j1ate 13 27 is be VBZ cord-018208-sc8j1ate 13 28 smaller small JJR cord-018208-sc8j1ate 13 29 ( ( -LRB- cord-018208-sc8j1ate 13 30 while while IN cord-018208-sc8j1ate 13 31 the the DT cord-018208-sc8j1ate 13 32 average average NN cord-018208-sc8j1ate 13 33 is be VBZ cord-018208-sc8j1ate 13 34 unchanged unchanged JJ cord-018208-sc8j1ate 13 35 ) ) -RRB- cord-018208-sc8j1ate 13 36 ; ; : cord-018208-sc8j1ate 13 37 2 2 LS cord-018208-sc8j1ate 13 38 ) ) -RRB- cord-018208-sc8j1ate 13 39 when when WRB cord-018208-sc8j1ate 13 40 the the DT cord-018208-sc8j1ate 13 41 correlation correlation NN cord-018208-sc8j1ate 13 42 between between IN cord-018208-sc8j1ate 13 43 the the DT cord-018208-sc8j1ate 13 44 infection infection NN cord-018208-sc8j1ate 13 45 rate rate NN cord-018208-sc8j1ate 13 46 and and CC cord-018208-sc8j1ate 13 47 the the DT cord-018208-sc8j1ate 13 48 nodal nodal JJ cord-018208-sc8j1ate 13 49 degree degree NN cord-018208-sc8j1ate 13 50 is be VBZ cord-018208-sc8j1ate 13 51 positive positive JJ cord-018208-sc8j1ate 13 52 . . . cord-018208-sc8j1ate 14 1 Our -PRON- PRP$ cord-018208-sc8j1ate 14 2 work work NN cord-018208-sc8j1ate 14 3 suggests suggest VBZ cord-018208-sc8j1ate 14 4 the the DT cord-018208-sc8j1ate 14 5 conditions condition NNS cord-018208-sc8j1ate 14 6 when when WRB cord-018208-sc8j1ate 14 7 the the DT cord-018208-sc8j1ate 14 8 mean mean JJ cord-018208-sc8j1ate 14 9 - - HYPH cord-018208-sc8j1ate 14 10 field field NN cord-018208-sc8j1ate 14 11 approach approach NN cord-018208-sc8j1ate 14 12 , , , cord-018208-sc8j1ate 14 13 in in IN cord-018208-sc8j1ate 14 14 particular particular JJ cord-018208-sc8j1ate 14 15 NIMFA NIMFA NNP cord-018208-sc8j1ate 14 16 , , , cord-018208-sc8j1ate 14 17 is be VBZ cord-018208-sc8j1ate 14 18 more more RBR cord-018208-sc8j1ate 14 19 accurate accurate JJ cord-018208-sc8j1ate 14 20 in in IN cord-018208-sc8j1ate 14 21 the the DT cord-018208-sc8j1ate 14 22 approximation approximation NN cord-018208-sc8j1ate 14 23 of of IN cord-018208-sc8j1ate 14 24 the the DT cord-018208-sc8j1ate 14 25 SIS SIS NNP cord-018208-sc8j1ate 14 26 epidemic epidemic NN cord-018208-sc8j1ate 14 27 with with IN cord-018208-sc8j1ate 14 28 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 14 29 infection infection NN cord-018208-sc8j1ate 14 30 rates rate NNS cord-018208-sc8j1ate 14 31 . . . cord-018208-sc8j1ate 15 1 By by IN cord-018208-sc8j1ate 15 2 considering consider VBG cord-018208-sc8j1ate 15 3 the the DT cord-018208-sc8j1ate 15 4 system system NN cord-018208-sc8j1ate 15 5 components component NNS cord-018208-sc8j1ate 15 6 as as IN cord-018208-sc8j1ate 15 7 nodes node NNS cord-018208-sc8j1ate 15 8 and and CC cord-018208-sc8j1ate 15 9 the the DT cord-018208-sc8j1ate 15 10 interactions interaction NNS cord-018208-sc8j1ate 15 11 or or CC cord-018208-sc8j1ate 15 12 relations relation NNS cord-018208-sc8j1ate 15 13 in in IN cord-018208-sc8j1ate 15 14 between between IN cord-018208-sc8j1ate 15 15 nodes node NNS cord-018208-sc8j1ate 15 16 as as IN cord-018208-sc8j1ate 15 17 links link NNS cord-018208-sc8j1ate 15 18 , , , cord-018208-sc8j1ate 15 19 networks network NNS cord-018208-sc8j1ate 15 20 have have VBP cord-018208-sc8j1ate 15 21 been be VBN cord-018208-sc8j1ate 15 22 used use VBN cord-018208-sc8j1ate 15 23 to to TO cord-018208-sc8j1ate 15 24 describe describe VB cord-018208-sc8j1ate 15 25 the the DT cord-018208-sc8j1ate 15 26 biological biological JJ cord-018208-sc8j1ate 15 27 , , , cord-018208-sc8j1ate 15 28 social social JJ cord-018208-sc8j1ate 15 29 and and CC cord-018208-sc8j1ate 15 30 communication communication NN cord-018208-sc8j1ate 15 31 systems system NNS cord-018208-sc8j1ate 15 32 . . . cord-018208-sc8j1ate 16 1 On on IN cord-018208-sc8j1ate 16 2 such such JJ cord-018208-sc8j1ate 16 3 networks network NNS cord-018208-sc8j1ate 16 4 or or CC cord-018208-sc8j1ate 16 5 complex complex JJ cord-018208-sc8j1ate 16 6 systems system NNS cord-018208-sc8j1ate 16 7 , , , cord-018208-sc8j1ate 16 8 viral viral JJ cord-018208-sc8j1ate 16 9 spreading spreading NN cord-018208-sc8j1ate 16 10 models model NNS cord-018208-sc8j1ate 16 11 have have VBP cord-018208-sc8j1ate 16 12 been be VBN cord-018208-sc8j1ate 16 13 used use VBN cord-018208-sc8j1ate 16 14 to to TO cord-018208-sc8j1ate 16 15 describe describe VB cord-018208-sc8j1ate 16 16 processes process NNS cord-018208-sc8j1ate 16 17 e.g. e.g. RB cord-018208-sc8j1ate 16 18 epidemic epidemic NN cord-018208-sc8j1ate 16 19 spreading spreading NN cord-018208-sc8j1ate 16 20 and and CC cord-018208-sc8j1ate 16 21 information information NN cord-018208-sc8j1ate 16 22 propagation propagation NN cord-018208-sc8j1ate 16 23 [ [ -LRB- cord-018208-sc8j1ate 16 24 8 8 CD cord-018208-sc8j1ate 16 25 , , , cord-018208-sc8j1ate 16 26 10 10 CD cord-018208-sc8j1ate 16 27 , , , cord-018208-sc8j1ate 16 28 13 13 CD cord-018208-sc8j1ate 16 29 , , , cord-018208-sc8j1ate 16 30 20 20 CD cord-018208-sc8j1ate 16 31 ] ] -RRB- cord-018208-sc8j1ate 16 32 . . . cord-018208-sc8j1ate 17 1 The the DT cord-018208-sc8j1ate 17 2 Susceptible susceptible JJ cord-018208-sc8j1ate 17 3 - - HYPH cord-018208-sc8j1ate 17 4 Infected infected JJ cord-018208-sc8j1ate 17 5 - - HYPH cord-018208-sc8j1ate 17 6 Susceptible susceptible JJ cord-018208-sc8j1ate 17 7 ( ( -LRB- cord-018208-sc8j1ate 17 8 SIS SIS NNP cord-018208-sc8j1ate 17 9 ) ) -RRB- cord-018208-sc8j1ate 17 10 model model NN cord-018208-sc8j1ate 17 11 is be VBZ cord-018208-sc8j1ate 17 12 one one CD cord-018208-sc8j1ate 17 13 of of IN cord-018208-sc8j1ate 17 14 the the DT cord-018208-sc8j1ate 17 15 most most RBS cord-018208-sc8j1ate 17 16 studied study VBN cord-018208-sc8j1ate 17 17 models model NNS cord-018208-sc8j1ate 17 18 . . . cord-018208-sc8j1ate 18 1 In in IN cord-018208-sc8j1ate 18 2 the the DT cord-018208-sc8j1ate 18 3 SIS SIS NNP cord-018208-sc8j1ate 18 4 model model NN cord-018208-sc8j1ate 18 5 , , , cord-018208-sc8j1ate 18 6 each each DT cord-018208-sc8j1ate 18 7 infected infect VBN cord-018208-sc8j1ate 18 8 node node NN cord-018208-sc8j1ate 18 9 infects infect VBZ cord-018208-sc8j1ate 18 10 each each DT cord-018208-sc8j1ate 18 11 of of IN cord-018208-sc8j1ate 18 12 its -PRON- PRP$ cord-018208-sc8j1ate 18 13 susceptible susceptible JJ cord-018208-sc8j1ate 18 14 neighbors neighbor NNS cord-018208-sc8j1ate 18 15 with with IN cord-018208-sc8j1ate 18 16 an an DT cord-018208-sc8j1ate 18 17 infection infection NN cord-018208-sc8j1ate 18 18 rate rate NN cord-018208-sc8j1ate 18 19 β β NN cord-018208-sc8j1ate 18 20 . . . cord-018208-sc8j1ate 19 1 The the DT cord-018208-sc8j1ate 19 2 infected infected JJ cord-018208-sc8j1ate 19 3 node node NN cord-018208-sc8j1ate 19 4 can can MD cord-018208-sc8j1ate 19 5 be be VB cord-018208-sc8j1ate 19 6 recovered recover VBN cord-018208-sc8j1ate 19 7 with with IN cord-018208-sc8j1ate 19 8 a a DT cord-018208-sc8j1ate 19 9 recovery recovery NN cord-018208-sc8j1ate 19 10 rate rate NN cord-018208-sc8j1ate 19 11 δ δ NN cord-018208-sc8j1ate 19 12 . . . cord-018208-sc8j1ate 20 1 Both both DT cord-018208-sc8j1ate 20 2 processes process NNS cord-018208-sc8j1ate 20 3 are be VBP cord-018208-sc8j1ate 20 4 independent independent JJ cord-018208-sc8j1ate 20 5 Poisson Poisson NNP cord-018208-sc8j1ate 20 6 processes process NNS cord-018208-sc8j1ate 20 7 . . . cord-018208-sc8j1ate 21 1 The the DT cord-018208-sc8j1ate 21 2 ratio ratio NN cord-018208-sc8j1ate 22 1 τ τ NN cord-018208-sc8j1ate 22 2 β β NNP cord-018208-sc8j1ate 22 3 /δ /δ NN cord-018208-sc8j1ate 22 4 is be VBZ cord-018208-sc8j1ate 22 5 called call VBN cord-018208-sc8j1ate 22 6 effective effective JJ cord-018208-sc8j1ate 22 7 infection infection NN cord-018208-sc8j1ate 22 8 rate rate NN cord-018208-sc8j1ate 22 9 , , , cord-018208-sc8j1ate 22 10 and and CC cord-018208-sc8j1ate 22 11 when when WRB cord-018208-sc8j1ate 22 12 τ τ NN cord-018208-sc8j1ate 22 13 is be VBZ cord-018208-sc8j1ate 22 14 larger large JJR cord-018208-sc8j1ate 22 15 than than IN cord-018208-sc8j1ate 22 16 the the DT cord-018208-sc8j1ate 22 17 epidemic epidemic NN cord-018208-sc8j1ate 22 18 threshold threshold NN cord-018208-sc8j1ate 22 19 τ τ NN cord-018208-sc8j1ate 22 20 c c NN cord-018208-sc8j1ate 22 21 , , , cord-018208-sc8j1ate 22 22 the the DT cord-018208-sc8j1ate 22 23 epidemic epidemic NN cord-018208-sc8j1ate 22 24 spreads spread VBZ cord-018208-sc8j1ate 22 25 out out RP cord-018208-sc8j1ate 22 26 with with IN cord-018208-sc8j1ate 22 27 a a DT cord-018208-sc8j1ate 22 28 nonzero nonzero JJ cord-018208-sc8j1ate 22 29 fraction fraction NN cord-018208-sc8j1ate 22 30 of of IN cord-018208-sc8j1ate 22 31 infected infected JJ cord-018208-sc8j1ate 22 32 nodes node NNS cord-018208-sc8j1ate 22 33 in in IN cord-018208-sc8j1ate 22 34 the the DT cord-018208-sc8j1ate 22 35 metastable metastable JJ cord-018208-sc8j1ate 22 36 state state NN cord-018208-sc8j1ate 22 37 . . . cord-018208-sc8j1ate 23 1 The the DT cord-018208-sc8j1ate 23 2 average average JJ cord-018208-sc8j1ate 23 3 fraction fraction NN cord-018208-sc8j1ate 23 4 of of IN cord-018208-sc8j1ate 23 5 infected infected JJ cord-018208-sc8j1ate 23 6 nodes node NNS cord-018208-sc8j1ate 23 7 y y NNP cord-018208-sc8j1ate 23 8 ∞ ∞ NNP cord-018208-sc8j1ate 23 9 in in IN cord-018208-sc8j1ate 23 10 the the DT cord-018208-sc8j1ate 23 11 metastable metastable JJ cord-018208-sc8j1ate 23 12 state state NN cord-018208-sc8j1ate 23 13 , , , cord-018208-sc8j1ate 23 14 ranging range VBG cord-018208-sc8j1ate 23 15 in in IN cord-018208-sc8j1ate 23 16 [ [ -LRB- cord-018208-sc8j1ate 23 17 0 0 CD cord-018208-sc8j1ate 23 18 , , , cord-018208-sc8j1ate 23 19 1 1 CD cord-018208-sc8j1ate 23 20 ] ] -RRB- cord-018208-sc8j1ate 24 1 , , , cord-018208-sc8j1ate 24 2 indicates indicate VBZ cord-018208-sc8j1ate 24 3 how how WRB cord-018208-sc8j1ate 24 4 severe severe JJ cord-018208-sc8j1ate 24 5 the the DT cord-018208-sc8j1ate 24 6 influence influence NN cord-018208-sc8j1ate 24 7 of of IN cord-018208-sc8j1ate 24 8 the the DT cord-018208-sc8j1ate 24 9 virus virus NN cord-018208-sc8j1ate 24 10 is be VBZ cord-018208-sc8j1ate 24 11 : : : cord-018208-sc8j1ate 25 1 the the DT cord-018208-sc8j1ate 25 2 larger large JJR cord-018208-sc8j1ate 25 3 the the DT cord-018208-sc8j1ate 25 4 fraction fraction NN cord-018208-sc8j1ate 26 1 y y NNP cord-018208-sc8j1ate 27 1 ∞ ∞ NNP cord-018208-sc8j1ate 27 2 is be VBZ cord-018208-sc8j1ate 27 3 , , , cord-018208-sc8j1ate 27 4 the the DT cord-018208-sc8j1ate 27 5 more more RBR cord-018208-sc8j1ate 27 6 severely severely RB cord-018208-sc8j1ate 27 7 the the DT cord-018208-sc8j1ate 27 8 network network NN cord-018208-sc8j1ate 27 9 is be VBZ cord-018208-sc8j1ate 27 10 infected infect VBN cord-018208-sc8j1ate 27 11 . . . cord-018208-sc8j1ate 28 1 In in IN cord-018208-sc8j1ate 28 2 this this DT cord-018208-sc8j1ate 28 3 paper paper NN cord-018208-sc8j1ate 28 4 , , , cord-018208-sc8j1ate 28 5 we -PRON- PRP cord-018208-sc8j1ate 28 6 concentrate concentrate VBP cord-018208-sc8j1ate 28 7 on on IN cord-018208-sc8j1ate 28 8 deriving derive VBG cord-018208-sc8j1ate 28 9 the the DT cord-018208-sc8j1ate 28 10 average average JJ cord-018208-sc8j1ate 28 11 fraction fraction NN cord-018208-sc8j1ate 29 1 y y NNP cord-018208-sc8j1ate 29 2 ∞ ∞ NNP cord-018208-sc8j1ate 29 3 of of IN cord-018208-sc8j1ate 29 4 infected infected JJ cord-018208-sc8j1ate 29 5 nodes node NNS cord-018208-sc8j1ate 29 6 in in IN cord-018208-sc8j1ate 29 7 the the DT cord-018208-sc8j1ate 29 8 metastable metastable JJ cord-018208-sc8j1ate 29 9 state state NN cord-018208-sc8j1ate 29 10 . . . cord-018208-sc8j1ate 30 1 Although although IN cord-018208-sc8j1ate 30 2 the the DT cord-018208-sc8j1ate 30 3 continuous continuous JJ cord-018208-sc8j1ate 30 4 - - HYPH cord-018208-sc8j1ate 30 5 time time NN cord-018208-sc8j1ate 30 6 Markov Markov NNP cord-018208-sc8j1ate 30 7 theory theory NN cord-018208-sc8j1ate 30 8 can can MD cord-018208-sc8j1ate 30 9 be be VB cord-018208-sc8j1ate 30 10 used use VBN cord-018208-sc8j1ate 30 11 to to TO cord-018208-sc8j1ate 30 12 obtain obtain VB cord-018208-sc8j1ate 30 13 the the DT cord-018208-sc8j1ate 30 14 exact exact JJ cord-018208-sc8j1ate 30 15 value value NN cord-018208-sc8j1ate 30 16 of of IN cord-018208-sc8j1ate 30 17 y y NNP cord-018208-sc8j1ate 30 18 ∞ ∞ NNP cord-018208-sc8j1ate 30 19 , , , cord-018208-sc8j1ate 30 20 the the DT cord-018208-sc8j1ate 30 21 number number NN cord-018208-sc8j1ate 30 22 of of IN cord-018208-sc8j1ate 30 23 states state NNS cord-018208-sc8j1ate 30 24 is be VBZ cord-018208-sc8j1ate 30 25 too too RB cord-018208-sc8j1ate 30 26 large large JJ cord-018208-sc8j1ate 30 27 to to TO cord-018208-sc8j1ate 30 28 be be VB cord-018208-sc8j1ate 30 29 solved solve VBN cord-018208-sc8j1ate 30 30 in in IN cord-018208-sc8j1ate 30 31 a a DT cord-018208-sc8j1ate 30 32 large large JJ cord-018208-sc8j1ate 30 33 network network NN cord-018208-sc8j1ate 30 34 [ [ -LRB- cord-018208-sc8j1ate 30 35 12 12 CD cord-018208-sc8j1ate 30 36 ] ] -RRB- cord-018208-sc8j1ate 30 37 . . . cord-018208-sc8j1ate 31 1 Hence hence RB cord-018208-sc8j1ate 31 2 , , , cord-018208-sc8j1ate 31 3 the the DT cord-018208-sc8j1ate 31 4 derivation derivation NN cord-018208-sc8j1ate 31 5 of of IN cord-018208-sc8j1ate 31 6 the the DT cord-018208-sc8j1ate 31 7 average average JJ cord-018208-sc8j1ate 31 8 fraction fraction NN cord-018208-sc8j1ate 31 9 y y NNP cord-018208-sc8j1ate 31 10 ∞ ∞ NNP cord-018208-sc8j1ate 31 11 of of IN cord-018208-sc8j1ate 31 12 infected infected JJ cord-018208-sc8j1ate 31 13 nodes node NNS cord-018208-sc8j1ate 31 14 in in IN cord-018208-sc8j1ate 31 15 the the DT cord-018208-sc8j1ate 31 16 metastable metastable JJ cord-018208-sc8j1ate 31 17 state state NN cord-018208-sc8j1ate 31 18 mostly mostly RB cord-018208-sc8j1ate 31 19 relies rely VBZ cord-018208-sc8j1ate 31 20 on on IN cord-018208-sc8j1ate 31 21 mean mean JJ cord-018208-sc8j1ate 31 22 - - HYPH cord-018208-sc8j1ate 31 23 field field NN cord-018208-sc8j1ate 31 24 theoretical theoretical JJ cord-018208-sc8j1ate 31 25 approaches approach NNS cord-018208-sc8j1ate 31 26 . . . cord-018208-sc8j1ate 32 1 The the DT cord-018208-sc8j1ate 32 2 first first JJ cord-018208-sc8j1ate 32 3 approach approach NN cord-018208-sc8j1ate 32 4 to to TO cord-018208-sc8j1ate 32 5 study study VB cord-018208-sc8j1ate 32 6 the the DT cord-018208-sc8j1ate 32 7 SIS SIS NNP cord-018208-sc8j1ate 32 8 model model NN cord-018208-sc8j1ate 32 9 in in IN cord-018208-sc8j1ate 32 10 complex complex JJ cord-018208-sc8j1ate 32 11 networks network NNS cord-018208-sc8j1ate 32 12 is be VBZ cord-018208-sc8j1ate 32 13 a a DT cord-018208-sc8j1ate 32 14 degree degree NN cord-018208-sc8j1ate 32 15 - - HYPH cord-018208-sc8j1ate 32 16 based base VBN cord-018208-sc8j1ate 32 17 mean mean NN cord-018208-sc8j1ate 32 18 - - HYPH cord-018208-sc8j1ate 32 19 field field NN cord-018208-sc8j1ate 32 20 ( ( -LRB- cord-018208-sc8j1ate 32 21 DBMF DBMF NNP cord-018208-sc8j1ate 32 22 ) ) -RRB- cord-018208-sc8j1ate 32 23 theory theory NN cord-018208-sc8j1ate 32 24 , , , cord-018208-sc8j1ate 32 25 also also RB cord-018208-sc8j1ate 32 26 called call VBN cord-018208-sc8j1ate 32 27 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 32 28 mean mean NN cord-018208-sc8j1ate 32 29 - - HYPH cord-018208-sc8j1ate 32 30 field field NN cord-018208-sc8j1ate 32 31 ( ( -LRB- cord-018208-sc8j1ate 32 32 HMF HMF NNP cord-018208-sc8j1ate 32 33 ) ) -RRB- cord-018208-sc8j1ate 32 34 approximation approximation NN cord-018208-sc8j1ate 32 35 , , , cord-018208-sc8j1ate 32 36 proposed propose VBN cord-018208-sc8j1ate 32 37 by by IN cord-018208-sc8j1ate 32 38 Pastor Pastor NNP cord-018208-sc8j1ate 32 39 - - HYPH cord-018208-sc8j1ate 32 40 Satorras Satorras NNP cord-018208-sc8j1ate 32 41 et et NNP cord-018208-sc8j1ate 32 42 al al NNP cord-018208-sc8j1ate 32 43 . . . cord-018208-sc8j1ate 33 1 [ [ -LRB- cord-018208-sc8j1ate 33 2 14 14 CD cord-018208-sc8j1ate 33 3 ] ] -RRB- cord-018208-sc8j1ate 33 4 , , , cord-018208-sc8j1ate 33 5 which which WDT cord-018208-sc8j1ate 33 6 assumes assume VBZ cord-018208-sc8j1ate 33 7 that that IN cord-018208-sc8j1ate 33 8 all all DT cord-018208-sc8j1ate 33 9 nodes node NNS cord-018208-sc8j1ate 33 10 with with IN cord-018208-sc8j1ate 33 11 the the DT cord-018208-sc8j1ate 33 12 same same JJ cord-018208-sc8j1ate 33 13 degree degree NN cord-018208-sc8j1ate 33 14 are be VBP cord-018208-sc8j1ate 33 15 statistically statistically RB cord-018208-sc8j1ate 33 16 equivalent equivalent JJ cord-018208-sc8j1ate 33 17 , , , cord-018208-sc8j1ate 33 18 i.e. i.e. FW cord-018208-sc8j1ate 33 19 the the DT cord-018208-sc8j1ate 33 20 infection infection NN cord-018208-sc8j1ate 33 21 probabilities probability NNS cord-018208-sc8j1ate 33 22 of of IN cord-018208-sc8j1ate 33 23 those those DT cord-018208-sc8j1ate 33 24 nodes node NNS cord-018208-sc8j1ate 33 25 are be VBP cord-018208-sc8j1ate 33 26 the the DT cord-018208-sc8j1ate 33 27 same same JJ cord-018208-sc8j1ate 33 28 . . . cord-018208-sc8j1ate 34 1 An an DT cord-018208-sc8j1ate 34 2 individual individual NN cord-018208-sc8j1ate 34 3 - - HYPH cord-018208-sc8j1ate 34 4 based base VBN cord-018208-sc8j1ate 34 5 mean mean NN cord-018208-sc8j1ate 34 6 - - HYPH cord-018208-sc8j1ate 34 7 field field NN cord-018208-sc8j1ate 34 8 ( ( -LRB- cord-018208-sc8j1ate 34 9 IBMF IBMF NNP cord-018208-sc8j1ate 34 10 ) ) -RRB- cord-018208-sc8j1ate 34 11 approximations approximation NNS cord-018208-sc8j1ate 34 12 , , , cord-018208-sc8j1ate 34 13 called call VBD cord-018208-sc8j1ate 34 14 the the DT cord-018208-sc8j1ate 34 15 N n NN cord-018208-sc8j1ate 34 16 - - HYPH cord-018208-sc8j1ate 34 17 Intertwined Intertwined NNP cord-018208-sc8j1ate 34 18 Mean Mean NNP cord-018208-sc8j1ate 34 19 - - HYPH cord-018208-sc8j1ate 34 20 Field field NN cord-018208-sc8j1ate 34 21 Approximation approximation NN cord-018208-sc8j1ate 34 22 ( ( -LRB- cord-018208-sc8j1ate 34 23 NIMFA NIMFA NNP cord-018208-sc8j1ate 34 24 ) ) -RRB- cord-018208-sc8j1ate 34 25 , , , cord-018208-sc8j1ate 34 26 of of IN cord-018208-sc8j1ate 34 27 the the DT cord-018208-sc8j1ate 34 28 SIS SIS NNP cord-018208-sc8j1ate 34 29 model model NN cord-018208-sc8j1ate 34 30 is be VBZ cord-018208-sc8j1ate 34 31 then then RB cord-018208-sc8j1ate 34 32 introduced introduce VBN cord-018208-sc8j1ate 34 33 [ [ -LRB- cord-018208-sc8j1ate 34 34 19 19 CD cord-018208-sc8j1ate 34 35 ] ] -RRB- cord-018208-sc8j1ate 34 36 with with IN cord-018208-sc8j1ate 34 37 the the DT cord-018208-sc8j1ate 34 38 only only JJ cord-018208-sc8j1ate 34 39 assumption assumption NN cord-018208-sc8j1ate 34 40 that that IN cord-018208-sc8j1ate 34 41 the the DT cord-018208-sc8j1ate 34 42 state state NN cord-018208-sc8j1ate 34 43 of of IN cord-018208-sc8j1ate 34 44 neighboring neighboring NN cord-018208-sc8j1ate 34 45 nodes node NNS cord-018208-sc8j1ate 34 46 is be VBZ cord-018208-sc8j1ate 34 47 statistically statistically RB cord-018208-sc8j1ate 34 48 independent independent JJ cord-018208-sc8j1ate 34 49 . . . cord-018208-sc8j1ate 35 1 NIMFA NIMFA NNP cord-018208-sc8j1ate 35 2 , , , cord-018208-sc8j1ate 35 3 taking take VBG cord-018208-sc8j1ate 35 4 the the DT cord-018208-sc8j1ate 35 5 network network NN cord-018208-sc8j1ate 35 6 topology topology NN cord-018208-sc8j1ate 35 7 into into IN cord-018208-sc8j1ate 35 8 account account NN cord-018208-sc8j1ate 35 9 , , , cord-018208-sc8j1ate 35 10 turns turn VBZ cord-018208-sc8j1ate 35 11 out out RP cord-018208-sc8j1ate 35 12 to to TO cord-018208-sc8j1ate 35 13 be be VB cord-018208-sc8j1ate 35 14 more more RBR cord-018208-sc8j1ate 35 15 precise precise JJ cord-018208-sc8j1ate 35 16 on on IN cord-018208-sc8j1ate 35 17 different different JJ cord-018208-sc8j1ate 35 18 types type NNS cord-018208-sc8j1ate 35 19 of of IN cord-018208-sc8j1ate 35 20 networks network NNS cord-018208-sc8j1ate 35 21 for for IN cord-018208-sc8j1ate 35 22 the the DT cord-018208-sc8j1ate 35 23 classic classic JJ cord-018208-sc8j1ate 35 24 SIS SIS NNP cord-018208-sc8j1ate 35 25 model model NN cord-018208-sc8j1ate 35 26 with with IN cord-018208-sc8j1ate 35 27 the the DT cord-018208-sc8j1ate 35 28 homogeneous homogeneous JJ cord-018208-sc8j1ate 35 29 infection infection NN cord-018208-sc8j1ate 35 30 rates rate NNS cord-018208-sc8j1ate 35 31 [ [ -LRB- cord-018208-sc8j1ate 35 32 7 7 CD cord-018208-sc8j1ate 35 33 ] ] -RRB- cord-018208-sc8j1ate 35 34 while while IN cord-018208-sc8j1ate 35 35 comparing compare VBG cord-018208-sc8j1ate 35 36 to to IN cord-018208-sc8j1ate 35 37 the the DT cord-018208-sc8j1ate 35 38 DBMF DBMF NNP cord-018208-sc8j1ate 35 39 approximation approximation NN cord-018208-sc8j1ate 35 40 . . . cord-018208-sc8j1ate 36 1 However however RB cord-018208-sc8j1ate 36 2 , , , cord-018208-sc8j1ate 36 3 as as IN cord-018208-sc8j1ate 36 4 discussed discuss VBN cord-018208-sc8j1ate 36 5 in in IN cord-018208-sc8j1ate 36 6 [ [ -LRB- cord-018208-sc8j1ate 36 7 4 4 CD cord-018208-sc8j1ate 36 8 , , , cord-018208-sc8j1ate 36 9 15 15 CD cord-018208-sc8j1ate 36 10 , , , cord-018208-sc8j1ate 36 11 22 22 CD cord-018208-sc8j1ate 36 12 ] ] -RRB- cord-018208-sc8j1ate 36 13 , , , cord-018208-sc8j1ate 36 14 the the DT cord-018208-sc8j1ate 36 15 infection infection NN cord-018208-sc8j1ate 36 16 rates rate NNS cord-018208-sc8j1ate 36 17 could could MD cord-018208-sc8j1ate 36 18 be be VB cord-018208-sc8j1ate 36 19 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 36 20 , , , cord-018208-sc8j1ate 36 21 i.e. i.e. FW cord-018208-sc8j1ate 36 22 the the DT cord-018208-sc8j1ate 36 23 infection infection NN cord-018208-sc8j1ate 36 24 rates rate NNS cord-018208-sc8j1ate 36 25 between between IN cord-018208-sc8j1ate 36 26 different different JJ cord-018208-sc8j1ate 36 27 pairs pair NNS cord-018208-sc8j1ate 36 28 of of IN cord-018208-sc8j1ate 36 29 nodes node NNS cord-018208-sc8j1ate 36 30 could could MD cord-018208-sc8j1ate 36 31 also also RB cord-018208-sc8j1ate 36 32 be be VB cord-018208-sc8j1ate 36 33 different different JJ cord-018208-sc8j1ate 36 34 . . . cord-018208-sc8j1ate 37 1 The the DT cord-018208-sc8j1ate 37 2 accuracy accuracy NN cord-018208-sc8j1ate 37 3 of of IN cord-018208-sc8j1ate 37 4 NIMFA NIMFA NNP cord-018208-sc8j1ate 37 5 with with IN cord-018208-sc8j1ate 37 6 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 37 7 infection infection NN cord-018208-sc8j1ate 37 8 rates rate NNS cord-018208-sc8j1ate 37 9 has have VBZ cord-018208-sc8j1ate 37 10 not not RB cord-018208-sc8j1ate 37 11 yet yet RB cord-018208-sc8j1ate 37 12 been be VBN cord-018208-sc8j1ate 37 13 discussed discuss VBN cord-018208-sc8j1ate 37 14 . . . cord-018208-sc8j1ate 38 1 In in IN cord-018208-sc8j1ate 38 2 this this DT cord-018208-sc8j1ate 38 3 paper paper NN cord-018208-sc8j1ate 38 4 , , , cord-018208-sc8j1ate 38 5 we -PRON- PRP cord-018208-sc8j1ate 38 6 explore explore VBP cord-018208-sc8j1ate 38 7 the the DT cord-018208-sc8j1ate 38 8 influence influence NN cord-018208-sc8j1ate 38 9 of of IN cord-018208-sc8j1ate 38 10 the the DT cord-018208-sc8j1ate 38 11 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 38 12 infection infection NN cord-018208-sc8j1ate 38 13 rates rate NNS cord-018208-sc8j1ate 38 14 on on IN cord-018208-sc8j1ate 38 15 the the DT cord-018208-sc8j1ate 38 16 precision precision NN cord-018208-sc8j1ate 38 17 of of IN cord-018208-sc8j1ate 38 18 NIMFA NIMFA NNP cord-018208-sc8j1ate 38 19 . . . cord-018208-sc8j1ate 39 1 In in IN cord-018208-sc8j1ate 39 2 particular particular JJ cord-018208-sc8j1ate 39 3 , , , cord-018208-sc8j1ate 39 4 we -PRON- PRP cord-018208-sc8j1ate 39 5 compare compare VBP cord-018208-sc8j1ate 39 6 the the DT cord-018208-sc8j1ate 39 7 average average JJ cord-018208-sc8j1ate 39 8 fraction fraction NN cord-018208-sc8j1ate 39 9 y y NNP cord-018208-sc8j1ate 39 10 ∞ ∞ NNP cord-018208-sc8j1ate 39 11 of of IN cord-018208-sc8j1ate 39 12 infected infected JJ cord-018208-sc8j1ate 39 13 nodes node NNS cord-018208-sc8j1ate 39 14 as as IN cord-018208-sc8j1ate 39 15 a a DT cord-018208-sc8j1ate 39 16 function function NN cord-018208-sc8j1ate 39 17 of of IN cord-018208-sc8j1ate 39 18 the the DT cord-018208-sc8j1ate 39 19 effective effective JJ cord-018208-sc8j1ate 39 20 infection infection NN cord-018208-sc8j1ate 39 21 rate rate NN cord-018208-sc8j1ate 39 22 τ τ NN cord-018208-sc8j1ate 39 23 computed compute VBN cord-018208-sc8j1ate 39 24 by by IN cord-018208-sc8j1ate 39 25 NIMFA NIMFA NNP cord-018208-sc8j1ate 39 26 to to IN cord-018208-sc8j1ate 39 27 that that DT cord-018208-sc8j1ate 39 28 obtained obtain VBN cord-018208-sc8j1ate 39 29 by by IN cord-018208-sc8j1ate 39 30 the the DT cord-018208-sc8j1ate 39 31 continuous continuous JJ cord-018208-sc8j1ate 39 32 - - HYPH cord-018208-sc8j1ate 39 33 time time NN cord-018208-sc8j1ate 39 34 simulations simulation NNS cord-018208-sc8j1ate 39 35 of of IN cord-018208-sc8j1ate 39 36 the the DT cord-018208-sc8j1ate 39 37 exact exact JJ cord-018208-sc8j1ate 39 38 SIS SIS NNP cord-018208-sc8j1ate 39 39 model model NN cord-018208-sc8j1ate 39 40 when when WRB cord-018208-sc8j1ate 39 41 the the DT cord-018208-sc8j1ate 39 42 infection infection NN cord-018208-sc8j1ate 39 43 rates rate NNS cord-018208-sc8j1ate 39 44 are be VBP cord-018208-sc8j1ate 39 45 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 39 46 but but CC cord-018208-sc8j1ate 39 47 the the DT cord-018208-sc8j1ate 39 48 recovery recovery NN cord-018208-sc8j1ate 39 49 rate rate NN cord-018208-sc8j1ate 39 50 is be VBZ cord-018208-sc8j1ate 39 51 the the DT cord-018208-sc8j1ate 39 52 same same JJ cord-018208-sc8j1ate 39 53 for for IN cord-018208-sc8j1ate 39 54 all all DT cord-018208-sc8j1ate 39 55 nodes node NNS cord-018208-sc8j1ate 39 56 . . . cord-018208-sc8j1ate 40 1 In in IN cord-018208-sc8j1ate 40 2 fact fact NN cord-018208-sc8j1ate 40 3 , , , cord-018208-sc8j1ate 40 4 the the DT cord-018208-sc8j1ate 40 5 effective effective JJ cord-018208-sc8j1ate 40 6 infection infection NN cord-018208-sc8j1ate 40 7 rate rate NN cord-018208-sc8j1ate 40 8 τ τ NN cord-018208-sc8j1ate 40 9 refers refer VBZ cord-018208-sc8j1ate 40 10 to to IN cord-018208-sc8j1ate 40 11 the the DT cord-018208-sc8j1ate 40 12 average average JJ cord-018208-sc8j1ate 40 13 infection infection NN cord-018208-sc8j1ate 40 14 rate rate NN cord-018208-sc8j1ate 40 15 divided divide VBN cord-018208-sc8j1ate 40 16 by by IN cord-018208-sc8j1ate 40 17 the the DT cord-018208-sc8j1ate 40 18 recovery recovery NN cord-018208-sc8j1ate 40 19 rate rate NN cord-018208-sc8j1ate 40 20 in in IN cord-018208-sc8j1ate 40 21 the the DT cord-018208-sc8j1ate 40 22 SIS SIS NNP cord-018208-sc8j1ate 40 23 model model NN cord-018208-sc8j1ate 40 24 with with IN cord-018208-sc8j1ate 40 25 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 40 26 infection infection NN cord-018208-sc8j1ate 40 27 rates rate NNS cord-018208-sc8j1ate 40 28 . . . cord-018208-sc8j1ate 41 1 We -PRON- PRP cord-018208-sc8j1ate 41 2 set set VBD cord-018208-sc8j1ate 41 3 the the DT cord-018208-sc8j1ate 41 4 average average JJ cord-018208-sc8j1ate 41 5 infection infection NN cord-018208-sc8j1ate 41 6 rate rate NN cord-018208-sc8j1ate 41 7 to to IN cord-018208-sc8j1ate 41 8 1 1 CD cord-018208-sc8j1ate 41 9 and and CC cord-018208-sc8j1ate 41 10 tune tune VB cord-018208-sc8j1ate 41 11 the the DT cord-018208-sc8j1ate 41 12 recovery recovery NN cord-018208-sc8j1ate 41 13 rate rate NN cord-018208-sc8j1ate 41 14 δ δ NN cord-018208-sc8j1ate 41 15 to to TO cord-018208-sc8j1ate 41 16 control control VB cord-018208-sc8j1ate 41 17 the the DT cord-018208-sc8j1ate 41 18 effective effective JJ cord-018208-sc8j1ate 41 19 infection infection NN cord-018208-sc8j1ate 41 20 rate rate NN cord-018208-sc8j1ate 41 21 τ τ NN cord-018208-sc8j1ate 41 22 . . . cord-018208-sc8j1ate 42 1 We -PRON- PRP cord-018208-sc8j1ate 42 2 consider consider VBP cord-018208-sc8j1ate 42 3 both both CC cord-018208-sc8j1ate 42 4 the the DT cord-018208-sc8j1ate 42 5 independent independent JJ cord-018208-sc8j1ate 42 6 and and CC cord-018208-sc8j1ate 42 7 identically identically RB cord-018208-sc8j1ate 42 8 distributed distribute VBN cord-018208-sc8j1ate 42 9 ( ( -LRB- cord-018208-sc8j1ate 42 10 i.i.d i.i.d NN cord-018208-sc8j1ate 42 11 . . . cord-018208-sc8j1ate 42 12 ) ) -RRB- cord-018208-sc8j1ate 42 13 and and CC cord-018208-sc8j1ate 42 14 the the DT cord-018208-sc8j1ate 42 15 correlated correlate VBN cord-018208-sc8j1ate 42 16 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 42 17 infection infection NN cord-018208-sc8j1ate 42 18 rates rate NNS cord-018208-sc8j1ate 42 19 in in IN cord-018208-sc8j1ate 42 20 different different JJ cord-018208-sc8j1ate 42 21 network network NN cord-018208-sc8j1ate 42 22 topologies topology NNS cord-018208-sc8j1ate 42 23 . . . cord-018208-sc8j1ate 43 1 The the DT cord-018208-sc8j1ate 43 2 N N NNP cord-018208-sc8j1ate 43 3 - - HYPH cord-018208-sc8j1ate 43 4 Intertwined Intertwined NNP cord-018208-sc8j1ate 43 5 Mean Mean NNP cord-018208-sc8j1ate 43 6 - - HYPH cord-018208-sc8j1ate 43 7 Field field NN cord-018208-sc8j1ate 43 8 Approximation approximation NN cord-018208-sc8j1ate 43 9 ( ( -LRB- cord-018208-sc8j1ate 43 10 NIMFA NIMFA NNP cord-018208-sc8j1ate 43 11 ) ) -RRB- cord-018208-sc8j1ate 43 12 is be VBZ cord-018208-sc8j1ate 43 13 so so RB cord-018208-sc8j1ate 43 14 far far RB cord-018208-sc8j1ate 43 15 one one CD cord-018208-sc8j1ate 43 16 of of IN cord-018208-sc8j1ate 43 17 the the DT cord-018208-sc8j1ate 43 18 most most RBS cord-018208-sc8j1ate 43 19 accurate accurate JJ cord-018208-sc8j1ate 43 20 approximations approximation NNS cord-018208-sc8j1ate 43 21 of of IN cord-018208-sc8j1ate 43 22 the the DT cord-018208-sc8j1ate 43 23 SIS SIS NNP cord-018208-sc8j1ate 43 24 model model NN cord-018208-sc8j1ate 43 25 that that WDT cord-018208-sc8j1ate 43 26 takes take VBZ cord-018208-sc8j1ate 43 27 into into IN cord-018208-sc8j1ate 43 28 account account NN cord-018208-sc8j1ate 43 29 the the DT cord-018208-sc8j1ate 43 30 influence influence NN cord-018208-sc8j1ate 43 31 of of IN cord-018208-sc8j1ate 43 32 the the DT cord-018208-sc8j1ate 43 33 network network NN cord-018208-sc8j1ate 43 34 topology topology NN cord-018208-sc8j1ate 43 35 . . . cord-018208-sc8j1ate 44 1 For for IN cord-018208-sc8j1ate 44 2 the the DT cord-018208-sc8j1ate 44 3 classic classic JJ cord-018208-sc8j1ate 44 4 SIS SIS NNP cord-018208-sc8j1ate 44 5 model model NN cord-018208-sc8j1ate 44 6 with with IN cord-018208-sc8j1ate 44 7 the the DT cord-018208-sc8j1ate 44 8 homogeneous homogeneous JJ cord-018208-sc8j1ate 44 9 infection infection NN cord-018208-sc8j1ate 44 10 rate rate NN cord-018208-sc8j1ate 44 11 β β NN cord-018208-sc8j1ate 44 12 and and CC cord-018208-sc8j1ate 44 13 recovery recovery NN cord-018208-sc8j1ate 44 14 rate rate NN cord-018208-sc8j1ate 44 15 δ δ NN cord-018208-sc8j1ate 44 16 . . . cord-018208-sc8j1ate 45 1 The the DT cord-018208-sc8j1ate 45 2 single single JJ cord-018208-sc8j1ate 45 3 governing govern VBG cord-018208-sc8j1ate 45 4 equation equation NN cord-018208-sc8j1ate 45 5 for for IN cord-018208-sc8j1ate 45 6 a a DT cord-018208-sc8j1ate 45 7 node node NN cord-018208-sc8j1ate 46 1 i i PRP cord-018208-sc8j1ate 46 2 in in IN cord-018208-sc8j1ate 46 3 NIMFA NIMFA NNP cord-018208-sc8j1ate 46 4 is be VBZ cord-018208-sc8j1ate 46 5 where where WRB cord-018208-sc8j1ate 46 6 v v NNP cord-018208-sc8j1ate 46 7 i i PRP cord-018208-sc8j1ate 46 8 ( ( -LRB- cord-018208-sc8j1ate 46 9 t t NN cord-018208-sc8j1ate 46 10 ) ) -RRB- cord-018208-sc8j1ate 46 11 is be VBZ cord-018208-sc8j1ate 46 12 the the DT cord-018208-sc8j1ate 46 13 infection infection NN cord-018208-sc8j1ate 46 14 probability probability NN cord-018208-sc8j1ate 46 15 of of IN cord-018208-sc8j1ate 46 16 node node NN cord-018208-sc8j1ate 46 17 i i PRP cord-018208-sc8j1ate 46 18 at at IN cord-018208-sc8j1ate 46 19 time time NN cord-018208-sc8j1ate 46 20 t t NNP cord-018208-sc8j1ate 46 21 , , , cord-018208-sc8j1ate 46 22 and and CC cord-018208-sc8j1ate 47 1 a a DT cord-018208-sc8j1ate 47 2 i i NNP cord-018208-sc8j1ate 47 3 j j NNP cord-018208-sc8j1ate 47 4 = = SYM cord-018208-sc8j1ate 47 5 1 1 CD cord-018208-sc8j1ate 47 6 or or CC cord-018208-sc8j1ate 47 7 0 0 NFP cord-018208-sc8j1ate 47 8 denotes denote VBZ cord-018208-sc8j1ate 47 9 if if IN cord-018208-sc8j1ate 47 10 there there EX cord-018208-sc8j1ate 47 11 is be VBZ cord-018208-sc8j1ate 47 12 a a DT cord-018208-sc8j1ate 47 13 link link NN cord-018208-sc8j1ate 47 14 or or CC cord-018208-sc8j1ate 47 15 not not RB cord-018208-sc8j1ate 47 16 between between IN cord-018208-sc8j1ate 47 17 node node NN cord-018208-sc8j1ate 47 18 i i PRP cord-018208-sc8j1ate 47 19 and and CC cord-018208-sc8j1ate 47 20 node node NN cord-018208-sc8j1ate 48 1 j. j. NNP cord-018208-sc8j1ate 48 2 The the DT cord-018208-sc8j1ate 48 3 governing govern VBG cord-018208-sc8j1ate 48 4 equation equation NN cord-018208-sc8j1ate 48 5 ( ( -LRB- cord-018208-sc8j1ate 48 6 1 1 CD cord-018208-sc8j1ate 48 7 ) ) -RRB- cord-018208-sc8j1ate 48 8 can can MD cord-018208-sc8j1ate 48 9 be be VB cord-018208-sc8j1ate 48 10 extended extend VBN cord-018208-sc8j1ate 48 11 to to IN cord-018208-sc8j1ate 48 12 the the DT cord-018208-sc8j1ate 48 13 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 48 14 case case NN cord-018208-sc8j1ate 48 15 : : : cord-018208-sc8j1ate 48 16 where where WRB cord-018208-sc8j1ate 48 17 β β NN cord-018208-sc8j1ate 48 18 i i NN cord-018208-sc8j1ate 48 19 j j NNP cord-018208-sc8j1ate 48 20 = = SYM cord-018208-sc8j1ate 48 21 β β NNP cord-018208-sc8j1ate 48 22 ji ji NNP cord-018208-sc8j1ate 48 23 is be VBZ cord-018208-sc8j1ate 48 24 the the DT cord-018208-sc8j1ate 48 25 infection infection NN cord-018208-sc8j1ate 48 26 rate rate NN cord-018208-sc8j1ate 48 27 between between IN cord-018208-sc8j1ate 48 28 node node NN cord-018208-sc8j1ate 48 29 i i PRP cord-018208-sc8j1ate 48 30 and and CC cord-018208-sc8j1ate 48 31 j. j. NNP cord-018208-sc8j1ate 49 1 In in IN cord-018208-sc8j1ate 49 2 the the DT cord-018208-sc8j1ate 49 3 steady steady JJ cord-018208-sc8j1ate 49 4 state state NN cord-018208-sc8j1ate 49 5 , , , cord-018208-sc8j1ate 49 6 defined define VBN cord-018208-sc8j1ate 49 7 by by IN cord-018208-sc8j1ate 49 8 dV dV NNP cord-018208-sc8j1ate 49 9 ( ( -LRB- cord-018208-sc8j1ate 49 10 t t NN cord-018208-sc8j1ate 49 11 ) ) -RRB- cord-018208-sc8j1ate 49 12 where where WRB cord-018208-sc8j1ate 49 13 A a DT cord-018208-sc8j1ate 49 14 is be VBZ cord-018208-sc8j1ate 49 15 the the DT cord-018208-sc8j1ate 49 16 N N NNP cord-018208-sc8j1ate 49 17 × × NNP cord-018208-sc8j1ate 49 18 N N NNP cord-018208-sc8j1ate 49 19 adjacency adjacency NN cord-018208-sc8j1ate 49 20 matrix matrix NN cord-018208-sc8j1ate 49 21 with with IN cord-018208-sc8j1ate 49 22 elements element NNS cord-018208-sc8j1ate 49 23 α α NNP cord-018208-sc8j1ate 49 24 i i NNP cord-018208-sc8j1ate 49 25 j j NNP cord-018208-sc8j1ate 49 26 , , , cord-018208-sc8j1ate 49 27 I -PRON- PRP cord-018208-sc8j1ate 49 28 is be VBZ cord-018208-sc8j1ate 49 29 the the DT cord-018208-sc8j1ate 49 30 N N NNP cord-018208-sc8j1ate 49 31 × × NNP cord-018208-sc8j1ate 49 32 N n CD cord-018208-sc8j1ate 49 33 identity identity NN cord-018208-sc8j1ate 49 34 matrix matrix NN cord-018208-sc8j1ate 49 35 , , , cord-018208-sc8j1ate 49 36 diag(v diag(v NNP cord-018208-sc8j1ate 49 37 i i PRP cord-018208-sc8j1ate 49 38 ( ( -LRB- cord-018208-sc8j1ate 49 39 t t NN cord-018208-sc8j1ate 49 40 ) ) -RRB- cord-018208-sc8j1ate 49 41 ) ) -RRB- cord-018208-sc8j1ate 49 42 is be VBZ cord-018208-sc8j1ate 49 43 the the DT cord-018208-sc8j1ate 49 44 diagonal diagonal JJ cord-018208-sc8j1ate 49 45 matrix matrix NN cord-018208-sc8j1ate 49 46 with with IN cord-018208-sc8j1ate 49 47 elements element NNS cord-018208-sc8j1ate 49 48 v v NNP cord-018208-sc8j1ate 49 49 1 1 CD cord-018208-sc8j1ate 49 50 ( ( -LRB- cord-018208-sc8j1ate 49 51 t t NN cord-018208-sc8j1ate 49 52 ) ) -RRB- cord-018208-sc8j1ate 49 53 , , . cord-018208-sc8j1ate 50 1 v v LS cord-018208-sc8j1ate 50 2 2 2 CD cord-018208-sc8j1ate 50 3 ( ( -LRB- cord-018208-sc8j1ate 50 4 t t NN cord-018208-sc8j1ate 50 5 ) ) -RRB- cord-018208-sc8j1ate 50 6 , , , cord-018208-sc8j1ate 50 7 .... .... . cord-018208-sc8j1ate 51 1 , , , cord-018208-sc8j1ate 51 2 v v NNP cord-018208-sc8j1ate 51 3 N N NNP cord-018208-sc8j1ate 51 4 ( ( -LRB- cord-018208-sc8j1ate 51 5 t t NN cord-018208-sc8j1ate 51 6 ) ) -RRB- cord-018208-sc8j1ate 51 7 and and CC cord-018208-sc8j1ate 51 8 B B NNP cord-018208-sc8j1ate 51 9 is be VBZ cord-018208-sc8j1ate 51 10 the the DT cord-018208-sc8j1ate 51 11 infection infection NN cord-018208-sc8j1ate 51 12 rate rate NN cord-018208-sc8j1ate 51 13 matrix matrix NN cord-018208-sc8j1ate 51 14 with with IN cord-018208-sc8j1ate 51 15 elements element NNS cord-018208-sc8j1ate 51 16 β β NNP cord-018208-sc8j1ate 51 17 i i NNP cord-018208-sc8j1ate 51 18 j j NNP cord-018208-sc8j1ate 51 19 . . . cord-018208-sc8j1ate 52 1 The the DT cord-018208-sc8j1ate 52 2 trivial trivial JJ cord-018208-sc8j1ate 52 3 , , , cord-018208-sc8j1ate 52 4 i.e. i.e. FW cord-018208-sc8j1ate 52 5 all all DT cord-018208-sc8j1ate 52 6 - - HYPH cord-018208-sc8j1ate 52 7 zero zero CD cord-018208-sc8j1ate 52 8 , , , cord-018208-sc8j1ate 52 9 solution solution NN cord-018208-sc8j1ate 52 10 of of IN cord-018208-sc8j1ate 52 11 ( ( -LRB- cord-018208-sc8j1ate 52 12 3 3 CD cord-018208-sc8j1ate 52 13 ) ) -RRB- cord-018208-sc8j1ate 52 14 indicates indicate VBZ cord-018208-sc8j1ate 52 15 the the DT cord-018208-sc8j1ate 52 16 absorbing absorb VBG cord-018208-sc8j1ate 52 17 state state NN cord-018208-sc8j1ate 52 18 where where WRB cord-018208-sc8j1ate 52 19 all all DT cord-018208-sc8j1ate 52 20 nodes node NNS cord-018208-sc8j1ate 52 21 are be VBP cord-018208-sc8j1ate 52 22 susceptible susceptible JJ cord-018208-sc8j1ate 52 23 . . . cord-018208-sc8j1ate 53 1 The the DT cord-018208-sc8j1ate 53 2 non non JJ cord-018208-sc8j1ate 53 3 - - JJ cord-018208-sc8j1ate 53 4 zero zero JJ cord-018208-sc8j1ate 53 5 solution solution NN cord-018208-sc8j1ate 53 6 of of IN cord-018208-sc8j1ate 53 7 V V NNP cord-018208-sc8j1ate 53 8 ∞ ∞ NNP cord-018208-sc8j1ate 53 9 in in IN cord-018208-sc8j1ate 53 10 ( ( -LRB- cord-018208-sc8j1ate 53 11 3 3 CD cord-018208-sc8j1ate 53 12 ) ) -RRB- cord-018208-sc8j1ate 53 13 , , , cord-018208-sc8j1ate 53 14 if if IN cord-018208-sc8j1ate 53 15 exists exist VBZ cord-018208-sc8j1ate 53 16 , , , cord-018208-sc8j1ate 53 17 points point VBZ cord-018208-sc8j1ate 53 18 to to IN cord-018208-sc8j1ate 53 19 the the DT cord-018208-sc8j1ate 53 20 existence existence NN cord-018208-sc8j1ate 53 21 of of IN cord-018208-sc8j1ate 53 22 a a DT cord-018208-sc8j1ate 53 23 metastable metastable JJ cord-018208-sc8j1ate 53 24 state state NN cord-018208-sc8j1ate 53 25 with with IN cord-018208-sc8j1ate 53 26 a a DT cord-018208-sc8j1ate 53 27 non non JJ cord-018208-sc8j1ate 53 28 - - JJ cord-018208-sc8j1ate 53 29 zero zero JJ cord-018208-sc8j1ate 53 30 fraction fraction NN cord-018208-sc8j1ate 53 31 of of IN cord-018208-sc8j1ate 53 32 infected infected JJ cord-018208-sc8j1ate 53 33 nodes node NNS cord-018208-sc8j1ate 53 34 . . . cord-018208-sc8j1ate 54 1 Or or CC cord-018208-sc8j1ate 54 2 else else RB cord-018208-sc8j1ate 54 3 , , , cord-018208-sc8j1ate 54 4 the the DT cord-018208-sc8j1ate 54 5 metastable metastable JJ cord-018208-sc8j1ate 54 6 state state NN cord-018208-sc8j1ate 54 7 can can MD cord-018208-sc8j1ate 54 8 be be VB cord-018208-sc8j1ate 54 9 figured figure VBN cord-018208-sc8j1ate 54 10 as as IN cord-018208-sc8j1ate 54 11 0 0 CD cord-018208-sc8j1ate 54 12 or or CC cord-018208-sc8j1ate 54 13 not not RB cord-018208-sc8j1ate 54 14 existing exist VBG cord-018208-sc8j1ate 54 15 . . . cord-018208-sc8j1ate 55 1 We -PRON- PRP cord-018208-sc8j1ate 55 2 are be VBP cord-018208-sc8j1ate 55 3 interested interested JJ cord-018208-sc8j1ate 55 4 in in IN cord-018208-sc8j1ate 55 5 actually actually RB cord-018208-sc8j1ate 55 6 the the DT cord-018208-sc8j1ate 55 7 metastable metastable JJ cord-018208-sc8j1ate 55 8 state state NN cord-018208-sc8j1ate 55 9 in in IN cord-018208-sc8j1ate 55 10 this this DT cord-018208-sc8j1ate 55 11 paper paper NN cord-018208-sc8j1ate 55 12 . . . cord-018208-sc8j1ate 56 1 In in IN cord-018208-sc8j1ate 56 2 this this DT cord-018208-sc8j1ate 56 3 paper paper NN cord-018208-sc8j1ate 56 4 , , , cord-018208-sc8j1ate 56 5 we -PRON- PRP cord-018208-sc8j1ate 56 6 keep keep VBP cord-018208-sc8j1ate 56 7 the the DT cord-018208-sc8j1ate 56 8 average average JJ cord-018208-sc8j1ate 56 9 infection infection NN cord-018208-sc8j1ate 56 10 rate rate NN cord-018208-sc8j1ate 56 11 to to IN cord-018208-sc8j1ate 56 12 1 1 CD cord-018208-sc8j1ate 56 13 and and CC cord-018208-sc8j1ate 56 14 tune tune VB cord-018208-sc8j1ate 56 15 the the DT cord-018208-sc8j1ate 56 16 recovery recovery NN cord-018208-sc8j1ate 56 17 rate rate NN cord-018208-sc8j1ate 56 18 δ δ NN cord-018208-sc8j1ate 56 19 to to TO cord-018208-sc8j1ate 56 20 control control VB cord-018208-sc8j1ate 56 21 the the DT cord-018208-sc8j1ate 56 22 effective effective JJ cord-018208-sc8j1ate 56 23 infection infection NN cord-018208-sc8j1ate 56 24 rate rate NN cord-018208-sc8j1ate 56 25 τ τ NN cord-018208-sc8j1ate 56 26 . . . cord-018208-sc8j1ate 57 1 In in IN cord-018208-sc8j1ate 57 2 the the DT cord-018208-sc8j1ate 57 3 case case NN cord-018208-sc8j1ate 57 4 of of IN cord-018208-sc8j1ate 57 5 the the DT cord-018208-sc8j1ate 57 6 i.i.d i.i.d NN cord-018208-sc8j1ate 57 7 . . . cord-018208-sc8j1ate 57 8 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 57 9 infection infection NN cord-018208-sc8j1ate 57 10 rates rate NNS cord-018208-sc8j1ate 57 11 , , , cord-018208-sc8j1ate 57 12 we -PRON- PRP cord-018208-sc8j1ate 57 13 aim aim VBP cord-018208-sc8j1ate 57 14 to to TO cord-018208-sc8j1ate 57 15 explore explore VB cord-018208-sc8j1ate 57 16 how how WRB cord-018208-sc8j1ate 57 17 the the DT cord-018208-sc8j1ate 57 18 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 57 19 infection infection NN cord-018208-sc8j1ate 57 20 rates rate NNS cord-018208-sc8j1ate 57 21 influence influence VBP cord-018208-sc8j1ate 57 22 the the DT cord-018208-sc8j1ate 57 23 accuracy accuracy NN cord-018208-sc8j1ate 57 24 of of IN cord-018208-sc8j1ate 57 25 NIMFA NIMFA NNP cord-018208-sc8j1ate 57 26 when when WRB cord-018208-sc8j1ate 57 27 the the DT cord-018208-sc8j1ate 57 28 variance variance NN cord-018208-sc8j1ate 57 29 of of IN cord-018208-sc8j1ate 57 30 the the DT cord-018208-sc8j1ate 57 31 infection infection NN cord-018208-sc8j1ate 57 32 rate rate NN cord-018208-sc8j1ate 57 33 varies vary VBZ cord-018208-sc8j1ate 57 34 . . . cord-018208-sc8j1ate 58 1 We -PRON- PRP cord-018208-sc8j1ate 58 2 choose choose VBP cord-018208-sc8j1ate 58 3 the the DT cord-018208-sc8j1ate 58 4 infection infection NN cord-018208-sc8j1ate 58 5 - - HYPH cord-018208-sc8j1ate 58 6 rate rate NN cord-018208-sc8j1ate 58 7 distribution distribution NN cord-018208-sc8j1ate 58 8 that that WDT cord-018208-sc8j1ate 58 9 is be VBZ cord-018208-sc8j1ate 58 10 frequently frequently RB cord-018208-sc8j1ate 58 11 observed observe VBN cord-018208-sc8j1ate 58 12 in in IN cord-018208-sc8j1ate 58 13 real real JJ cord-018208-sc8j1ate 58 14 - - HYPH cord-018208-sc8j1ate 58 15 world world NN cord-018208-sc8j1ate 58 16 and and CC cord-018208-sc8j1ate 58 17 importantly importantly RB cord-018208-sc8j1ate 58 18 the the DT cord-018208-sc8j1ate 58 19 variance variance NN cord-018208-sc8j1ate 58 20 is be VBZ cord-018208-sc8j1ate 58 21 tunable tunable JJ cord-018208-sc8j1ate 58 22 with with IN cord-018208-sc8j1ate 58 23 a a DT cord-018208-sc8j1ate 58 24 fixed fix VBN cord-018208-sc8j1ate 58 25 mean mean NN cord-018208-sc8j1ate 58 26 so so IN cord-018208-sc8j1ate 58 27 that that IN cord-018208-sc8j1ate 58 28 we -PRON- PRP cord-018208-sc8j1ate 58 29 can can MD cord-018208-sc8j1ate 58 30 systematically systematically RB cord-018208-sc8j1ate 58 31 explore explore VB cord-018208-sc8j1ate 58 32 how how WRB cord-018208-sc8j1ate 58 33 the the DT cord-018208-sc8j1ate 58 34 accuracy accuracy NN cord-018208-sc8j1ate 58 35 of of IN cord-018208-sc8j1ate 58 36 NIMFA NIMFA NNP cord-018208-sc8j1ate 58 37 changes change NNS cord-018208-sc8j1ate 58 38 with with IN cord-018208-sc8j1ate 58 39 the the DT cord-018208-sc8j1ate 58 40 broadness broadness NN cord-018208-sc8j1ate 58 41 of of IN cord-018208-sc8j1ate 58 42 the the DT cord-018208-sc8j1ate 58 43 i.i.d i.i.d NN cord-018208-sc8j1ate 58 44 . . . cord-018208-sc8j1ate 58 45 infection infection NN cord-018208-sc8j1ate 58 46 rate rate NN cord-018208-sc8j1ate 58 47 . . . cord-018208-sc8j1ate 59 1 We -PRON- PRP cord-018208-sc8j1ate 59 2 consider consider VBP cord-018208-sc8j1ate 59 3 the the DT cord-018208-sc8j1ate 59 4 log log NN cord-018208-sc8j1ate 59 5 - - HYPH cord-018208-sc8j1ate 59 6 normal normal JJ cord-018208-sc8j1ate 59 7 distribution distribution NN cord-018208-sc8j1ate 59 8 , , , cord-018208-sc8j1ate 59 9 of of IN cord-018208-sc8j1ate 59 10 which which WDT cord-018208-sc8j1ate 59 11 we -PRON- PRP cord-018208-sc8j1ate 59 12 can can MD cord-018208-sc8j1ate 59 13 keep keep VB cord-018208-sc8j1ate 59 14 the the DT cord-018208-sc8j1ate 59 15 mean mean NN cord-018208-sc8j1ate 59 16 unchanged unchanged JJ cord-018208-sc8j1ate 59 17 and and CC cord-018208-sc8j1ate 59 18 tune tune VB cord-018208-sc8j1ate 59 19 the the DT cord-018208-sc8j1ate 59 20 variance variance NN cord-018208-sc8j1ate 59 21 in in IN cord-018208-sc8j1ate 59 22 a a DT cord-018208-sc8j1ate 59 23 large large JJ cord-018208-sc8j1ate 59 24 range range NN cord-018208-sc8j1ate 59 25 . . . cord-018208-sc8j1ate 60 1 The the DT cord-018208-sc8j1ate 60 2 log log NN cord-018208-sc8j1ate 60 3 - - HYPH cord-018208-sc8j1ate 60 4 normal normal JJ cord-018208-sc8j1ate 60 5 distribution distribution NN cord-018208-sc8j1ate 60 6 [ [ -LRB- cord-018208-sc8j1ate 60 7 18 18 CD cord-018208-sc8j1ate 60 8 ] ] -RRB- cord-018208-sc8j1ate 60 9 B B NNP cord-018208-sc8j1ate 60 10 ∼ ∼ NNP cord-018208-sc8j1ate 60 11 Log Log NNP cord-018208-sc8j1ate 60 12 - - HYPH cord-018208-sc8j1ate 60 13 N(β N(β NNP cord-018208-sc8j1ate 60 14 ; ; : cord-018208-sc8j1ate 60 15 µ µ NN cord-018208-sc8j1ate 60 16 , , , cord-018208-sc8j1ate 60 17 σ σ NNP cord-018208-sc8j1ate 60 18 ) ) -RRB- cord-018208-sc8j1ate 60 19 , , , cord-018208-sc8j1ate 60 20 of of IN cord-018208-sc8j1ate 60 21 which which WDT cord-018208-sc8j1ate 60 22 the the DT cord-018208-sc8j1ate 60 23 probability probability NN cord-018208-sc8j1ate 60 24 density density NN cord-018208-sc8j1ate 60 25 function function NN cord-018208-sc8j1ate 60 26 ( ( -LRB- cord-018208-sc8j1ate 60 27 PDF PDF NNP cord-018208-sc8j1ate 60 28 ) ) -RRB- cord-018208-sc8j1ate 60 29 is be VBZ cord-018208-sc8j1ate 60 30 , , , cord-018208-sc8j1ate 60 31 for for IN cord-018208-sc8j1ate 60 32 β β NN cord-018208-sc8j1ate 60 33 > > XX cord-018208-sc8j1ate 60 34 0 0 NFP cord-018208-sc8j1ate 60 35 has have VBZ cord-018208-sc8j1ate 60 36 a a DT cord-018208-sc8j1ate 60 37 power power NN cord-018208-sc8j1ate 60 38 - - HYPH cord-018208-sc8j1ate 60 39 law law NN cord-018208-sc8j1ate 60 40 tail tail NN cord-018208-sc8j1ate 60 41 for for IN cord-018208-sc8j1ate 60 42 a a DT cord-018208-sc8j1ate 60 43 large large JJ cord-018208-sc8j1ate 60 44 range range NN cord-018208-sc8j1ate 60 45 of of IN cord-018208-sc8j1ate 60 46 β β NN cord-018208-sc8j1ate 60 47 provided provide VBD cord-018208-sc8j1ate 60 48 σ σ NNP cord-018208-sc8j1ate 60 49 is be VBZ cord-018208-sc8j1ate 60 50 sufficiently sufficiently RB cord-018208-sc8j1ate 60 51 large large JJ cord-018208-sc8j1ate 60 52 . . . cord-018208-sc8j1ate 61 1 The the DT cord-018208-sc8j1ate 61 2 log log NN cord-018208-sc8j1ate 61 3 - - HYPH cord-018208-sc8j1ate 61 4 normal normal JJ cord-018208-sc8j1ate 61 5 distribution distribution NN cord-018208-sc8j1ate 61 6 has have VBZ cord-018208-sc8j1ate 61 7 been be VBN cord-018208-sc8j1ate 61 8 widely widely RB cord-018208-sc8j1ate 61 9 observed observe VBN cord-018208-sc8j1ate 61 10 in in IN cord-018208-sc8j1ate 61 11 real real JJ cord-018208-sc8j1ate 61 12 - - HYPH cord-018208-sc8j1ate 61 13 world world NN cord-018208-sc8j1ate 61 14 , , , cord-018208-sc8j1ate 61 15 where where WRB cord-018208-sc8j1ate 61 16 interaction interaction NN cord-018208-sc8j1ate 61 17 frequencies frequency NNS cord-018208-sc8j1ate 61 18 between between IN cord-018208-sc8j1ate 61 19 nodes node NNS cord-018208-sc8j1ate 61 20 are be VBP cord-018208-sc8j1ate 61 21 usually usually RB cord-018208-sc8j1ate 61 22 considered consider VBN cord-018208-sc8j1ate 61 23 as as IN cord-018208-sc8j1ate 61 24 infection infection NN cord-018208-sc8j1ate 61 25 rates rate NNS cord-018208-sc8j1ate 61 26 . . . cord-018208-sc8j1ate 62 1 Wang Wang NNP cord-018208-sc8j1ate 62 2 et et NNP cord-018208-sc8j1ate 62 3 al al NNP cord-018208-sc8j1ate 62 4 . . . cord-018208-sc8j1ate 63 1 [ [ -LRB- cord-018208-sc8j1ate 63 2 21 21 CD cord-018208-sc8j1ate 63 3 ] ] -RRB- cord-018208-sc8j1ate 63 4 find find VBP cord-018208-sc8j1ate 63 5 that that IN cord-018208-sc8j1ate 63 6 by by IN cord-018208-sc8j1ate 63 7 employing employ VBG cord-018208-sc8j1ate 63 8 the the DT cord-018208-sc8j1ate 63 9 log log NN cord-018208-sc8j1ate 63 10 - - HYPH cord-018208-sc8j1ate 63 11 normal normal JJ cord-018208-sc8j1ate 63 12 distributed distribute VBN cord-018208-sc8j1ate 63 13 infection infection NN cord-018208-sc8j1ate 63 14 rates rate NNS cord-018208-sc8j1ate 63 15 , , , cord-018208-sc8j1ate 63 16 their -PRON- PRP$ cord-018208-sc8j1ate 63 17 epidemic epidemic NN cord-018208-sc8j1ate 63 18 model model NN cord-018208-sc8j1ate 63 19 can can MD cord-018208-sc8j1ate 63 20 accurately accurately RB cord-018208-sc8j1ate 63 21 fit fit VB cord-018208-sc8j1ate 63 22 the the DT cord-018208-sc8j1ate 63 23 infection infection NN cord-018208-sc8j1ate 63 24 data datum NNS cord-018208-sc8j1ate 63 25 of of IN cord-018208-sc8j1ate 63 26 2003 2003 CD cord-018208-sc8j1ate 63 27 SARS SARS NNP cord-018208-sc8j1ate 63 28 ; ; : cord-018208-sc8j1ate 63 29 we -PRON- PRP cord-018208-sc8j1ate 63 30 also also RB cord-018208-sc8j1ate 63 31 find find VBP cord-018208-sc8j1ate 63 32 that that IN cord-018208-sc8j1ate 63 33 the the DT cord-018208-sc8j1ate 63 34 infection infection NN cord-018208-sc8j1ate 63 35 rates rate NNS cord-018208-sc8j1ate 63 36 in in IN cord-018208-sc8j1ate 63 37 an an DT cord-018208-sc8j1ate 63 38 airline airline NN cord-018208-sc8j1ate 63 39 network network NN cord-018208-sc8j1ate 63 40 follow follow VB cord-018208-sc8j1ate 63 41 the the DT cord-018208-sc8j1ate 63 42 log log NN cord-018208-sc8j1ate 63 43 - - HYPH cord-018208-sc8j1ate 63 44 normal normal JJ cord-018208-sc8j1ate 63 45 distribution distribution NN cord-018208-sc8j1ate 63 46 [ [ -LRB- cord-018208-sc8j1ate 63 47 15 15 CD cord-018208-sc8j1ate 63 48 ] ] -RRB- cord-018208-sc8j1ate 63 49 . . . cord-018208-sc8j1ate 64 1 In in IN cord-018208-sc8j1ate 64 2 [ [ -LRB- cord-018208-sc8j1ate 64 3 15 15 CD cord-018208-sc8j1ate 64 4 ] ] -RRB- cord-018208-sc8j1ate 64 5 , , , cord-018208-sc8j1ate 64 6 we -PRON- PRP cord-018208-sc8j1ate 64 7 find find VBP cord-018208-sc8j1ate 64 8 that that IN cord-018208-sc8j1ate 64 9 , , , cord-018208-sc8j1ate 64 10 if if IN cord-018208-sc8j1ate 64 11 the the DT cord-018208-sc8j1ate 64 12 epidemic epidemic NN cord-018208-sc8j1ate 64 13 does do VBZ cord-018208-sc8j1ate 64 14 not not RB cord-018208-sc8j1ate 64 15 die die VB cord-018208-sc8j1ate 64 16 out out RP cord-018208-sc8j1ate 64 17 , , , cord-018208-sc8j1ate 64 18 the the DT cord-018208-sc8j1ate 64 19 larger large JJR cord-018208-sc8j1ate 64 20 the the DT cord-018208-sc8j1ate 64 21 variance variance NN cord-018208-sc8j1ate 64 22 of of IN cord-018208-sc8j1ate 64 23 the the DT cord-018208-sc8j1ate 64 24 i.i.d i.i.d NN cord-018208-sc8j1ate 64 25 . . . cord-018208-sc8j1ate 64 26 infection infection NN cord-018208-sc8j1ate 64 27 rate rate NN cord-018208-sc8j1ate 64 28 is be VBZ cord-018208-sc8j1ate 64 29 , , , cord-018208-sc8j1ate 64 30 the the DT cord-018208-sc8j1ate 64 31 smaller small JJR cord-018208-sc8j1ate 64 32 the the DT cord-018208-sc8j1ate 64 33 average average JJ cord-018208-sc8j1ate 64 34 fraction fraction NN cord-018208-sc8j1ate 65 1 y y NNP cord-018208-sc8j1ate 65 2 ∞ ∞ NNP cord-018208-sc8j1ate 65 3 of of IN cord-018208-sc8j1ate 65 4 infected infected JJ cord-018208-sc8j1ate 65 5 nodes node NNS cord-018208-sc8j1ate 65 6 is be VBZ cord-018208-sc8j1ate 65 7 . . . cord-018208-sc8j1ate 66 1 We -PRON- PRP cord-018208-sc8j1ate 66 2 will will MD cord-018208-sc8j1ate 66 3 show show VB cord-018208-sc8j1ate 66 4 that that IN cord-018208-sc8j1ate 66 5 this this DT cord-018208-sc8j1ate 66 6 conclusion conclusion NN cord-018208-sc8j1ate 66 7 can can MD cord-018208-sc8j1ate 66 8 actually actually RB cord-018208-sc8j1ate 66 9 explain explain VB cord-018208-sc8j1ate 66 10 the the DT cord-018208-sc8j1ate 66 11 observation observation NN cord-018208-sc8j1ate 66 12 about about IN cord-018208-sc8j1ate 66 13 how how WRB cord-018208-sc8j1ate 66 14 the the DT cord-018208-sc8j1ate 66 15 accuracy accuracy NN cord-018208-sc8j1ate 66 16 of of IN cord-018208-sc8j1ate 66 17 NIMFA NIMFA NNP cord-018208-sc8j1ate 66 18 changes change NNS cord-018208-sc8j1ate 66 19 with with IN cord-018208-sc8j1ate 66 20 the the DT cord-018208-sc8j1ate 66 21 variance variance NN cord-018208-sc8j1ate 66 22 of of IN cord-018208-sc8j1ate 66 23 the the DT cord-018208-sc8j1ate 66 24 i.i.d i.i.d NN cord-018208-sc8j1ate 66 25 . . . cord-018208-sc8j1ate 66 26 infection infection NN cord-018208-sc8j1ate 66 27 rates rate NNS cord-018208-sc8j1ate 66 28 at at IN cord-018208-sc8j1ate 66 29 a a DT cord-018208-sc8j1ate 66 30 given give VBN cord-018208-sc8j1ate 66 31 effective effective JJ cord-018208-sc8j1ate 66 32 infection infection NN cord-018208-sc8j1ate 66 33 rate rate NN cord-018208-sc8j1ate 66 34 τ τ NN cord-018208-sc8j1ate 66 35 in in IN cord-018208-sc8j1ate 66 36 this this DT cord-018208-sc8j1ate 66 37 paper paper NN cord-018208-sc8j1ate 66 38 . . . cord-018208-sc8j1ate 67 1 For for IN cord-018208-sc8j1ate 67 2 correlated correlate VBN cord-018208-sc8j1ate 67 3 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 67 4 infection infection NN cord-018208-sc8j1ate 67 5 rates rate NNS cord-018208-sc8j1ate 67 6 , , , cord-018208-sc8j1ate 67 7 we -PRON- PRP cord-018208-sc8j1ate 67 8 build build VBP cord-018208-sc8j1ate 67 9 a a DT cord-018208-sc8j1ate 67 10 correlated correlate VBN cord-018208-sc8j1ate 67 11 infection infection NN cord-018208-sc8j1ate 67 12 - - HYPH cord-018208-sc8j1ate 67 13 rate rate NN cord-018208-sc8j1ate 67 14 scenario scenario NN cord-018208-sc8j1ate 67 15 and and CC cord-018208-sc8j1ate 67 16 a a DT cord-018208-sc8j1ate 67 17 reference reference NN cord-018208-sc8j1ate 67 18 one one CD cord-018208-sc8j1ate 67 19 . . . cord-018208-sc8j1ate 68 1 In in IN cord-018208-sc8j1ate 68 2 the the DT cord-018208-sc8j1ate 68 3 correlated correlate VBN cord-018208-sc8j1ate 68 4 infection infection NN cord-018208-sc8j1ate 68 5 - - HYPH cord-018208-sc8j1ate 68 6 rate rate NN cord-018208-sc8j1ate 68 7 scenario scenario NN cord-018208-sc8j1ate 68 8 , , , cord-018208-sc8j1ate 68 9 we -PRON- PRP cord-018208-sc8j1ate 68 10 assume assume VBP cord-018208-sc8j1ate 68 11 where where WRB cord-018208-sc8j1ate 68 12 d d NNP cord-018208-sc8j1ate 68 13 i i NN cord-018208-sc8j1ate 68 14 and and CC cord-018208-sc8j1ate 68 15 d d NNP cord-018208-sc8j1ate 68 16 j j NNP cord-018208-sc8j1ate 68 17 are be VBP cord-018208-sc8j1ate 68 18 the the DT cord-018208-sc8j1ate 68 19 degree degree NN cord-018208-sc8j1ate 68 20 of of IN cord-018208-sc8j1ate 68 21 node node NN cord-018208-sc8j1ate 68 22 i i PRP cord-018208-sc8j1ate 68 23 and and CC cord-018208-sc8j1ate 68 24 node node NN cord-018208-sc8j1ate 68 25 j j NNP cord-018208-sc8j1ate 68 26 respectively respectively RB cord-018208-sc8j1ate 68 27 , , , cord-018208-sc8j1ate 68 28 c c NNP cord-018208-sc8j1ate 68 29 is be VBZ cord-018208-sc8j1ate 68 30 selected select VBN cord-018208-sc8j1ate 68 31 so so IN cord-018208-sc8j1ate 68 32 that that IN cord-018208-sc8j1ate 68 33 the the DT cord-018208-sc8j1ate 68 34 average average JJ cord-018208-sc8j1ate 68 35 infection infection NN cord-018208-sc8j1ate 68 36 rate rate NN cord-018208-sc8j1ate 68 37 is be VBZ cord-018208-sc8j1ate 68 38 1 1 CD cord-018208-sc8j1ate 68 39 and and CC cord-018208-sc8j1ate 68 40 α α NN cord-018208-sc8j1ate 68 41 indicates indicate VBZ cord-018208-sc8j1ate 68 42 the the DT cord-018208-sc8j1ate 68 43 correlation correlation NN cord-018208-sc8j1ate 68 44 strength strength NN cord-018208-sc8j1ate 68 45 . . . cord-018208-sc8j1ate 69 1 As as IN cord-018208-sc8j1ate 69 2 discussed discuss VBN cord-018208-sc8j1ate 69 3 in in IN cord-018208-sc8j1ate 69 4 [ [ -LRB- cord-018208-sc8j1ate 69 5 17 17 CD cord-018208-sc8j1ate 69 6 ] ] -RRB- cord-018208-sc8j1ate 69 7 , , , cord-018208-sc8j1ate 69 8 such such PDT cord-018208-sc8j1ate 69 9 a a DT cord-018208-sc8j1ate 69 10 correlation correlation NN cord-018208-sc8j1ate 69 11 between between IN cord-018208-sc8j1ate 69 12 the the DT cord-018208-sc8j1ate 69 13 infection infection NN cord-018208-sc8j1ate 69 14 rate rate NN cord-018208-sc8j1ate 69 15 and and CC cord-018208-sc8j1ate 69 16 the the DT cord-018208-sc8j1ate 69 17 nodal nodal JJ cord-018208-sc8j1ate 69 18 degree degree NN cord-018208-sc8j1ate 69 19 is be VBZ cord-018208-sc8j1ate 69 20 motivated motivate VBN cord-018208-sc8j1ate 69 21 by by IN cord-018208-sc8j1ate 69 22 the the DT cord-018208-sc8j1ate 69 23 real real JJ cord-018208-sc8j1ate 69 24 - - HYPH cord-018208-sc8j1ate 69 25 world world NN cord-018208-sc8j1ate 69 26 datasets dataset NNS cord-018208-sc8j1ate 69 27 . . . cord-018208-sc8j1ate 70 1 In in IN cord-018208-sc8j1ate 70 2 this this DT cord-018208-sc8j1ate 70 3 case case NN cord-018208-sc8j1ate 70 4 , , , cord-018208-sc8j1ate 70 5 the the DT cord-018208-sc8j1ate 70 6 infection infection NN cord-018208-sc8j1ate 70 7 rate rate NN cord-018208-sc8j1ate 70 8 of of IN cord-018208-sc8j1ate 70 9 each each DT cord-018208-sc8j1ate 70 10 link link NN cord-018208-sc8j1ate 70 11 is be VBZ cord-018208-sc8j1ate 70 12 determined determine VBN cord-018208-sc8j1ate 70 13 by by IN cord-018208-sc8j1ate 70 14 the the DT cord-018208-sc8j1ate 70 15 given give VBN cord-018208-sc8j1ate 70 16 network network NN cord-018208-sc8j1ate 70 17 topology topology NN cord-018208-sc8j1ate 70 18 and and CC cord-018208-sc8j1ate 70 19 α α NN cord-018208-sc8j1ate 70 20 . . . cord-018208-sc8j1ate 71 1 For for IN cord-018208-sc8j1ate 71 2 the the DT cord-018208-sc8j1ate 71 3 reference reference NN cord-018208-sc8j1ate 71 4 scenario scenario NN cord-018208-sc8j1ate 71 5 , , , cord-018208-sc8j1ate 71 6 we -PRON- PRP cord-018208-sc8j1ate 71 7 shuffle shuffle VBP cord-018208-sc8j1ate 71 8 the the DT cord-018208-sc8j1ate 71 9 infection infection NN cord-018208-sc8j1ate 71 10 rates rate NNS cord-018208-sc8j1ate 71 11 from from IN cord-018208-sc8j1ate 71 12 all all PDT cord-018208-sc8j1ate 71 13 the the DT cord-018208-sc8j1ate 71 14 links link NNS cord-018208-sc8j1ate 71 15 as as IN cord-018208-sc8j1ate 71 16 generated generate VBN cord-018208-sc8j1ate 71 17 in in IN cord-018208-sc8j1ate 71 18 the the DT cord-018208-sc8j1ate 71 19 first first JJ cord-018208-sc8j1ate 71 20 scenario scenario NN cord-018208-sc8j1ate 71 21 and and CC cord-018208-sc8j1ate 71 22 redistribute redistribute VB cord-018208-sc8j1ate 71 23 them -PRON- PRP cord-018208-sc8j1ate 71 24 randomly randomly RB cord-018208-sc8j1ate 71 25 to to IN cord-018208-sc8j1ate 71 26 all all PDT cord-018208-sc8j1ate 71 27 the the DT cord-018208-sc8j1ate 71 28 links link NNS cord-018208-sc8j1ate 71 29 . . . cord-018208-sc8j1ate 72 1 In in IN cord-018208-sc8j1ate 72 2 this this DT cord-018208-sc8j1ate 72 3 way way NN cord-018208-sc8j1ate 72 4 , , , cord-018208-sc8j1ate 72 5 we -PRON- PRP cord-018208-sc8j1ate 72 6 keep keep VBP cord-018208-sc8j1ate 72 7 the the DT cord-018208-sc8j1ate 72 8 distribution distribution NN cord-018208-sc8j1ate 72 9 of of IN cord-018208-sc8j1ate 72 10 infection infection NN cord-018208-sc8j1ate 72 11 rates rate NNS cord-018208-sc8j1ate 72 12 but but CC cord-018208-sc8j1ate 72 13 effectively effectively RB cord-018208-sc8j1ate 72 14 remove remove VB cord-018208-sc8j1ate 72 15 the the DT cord-018208-sc8j1ate 72 16 correlation correlation NN cord-018208-sc8j1ate 72 17 between between IN cord-018208-sc8j1ate 72 18 the the DT cord-018208-sc8j1ate 72 19 infection infection NN cord-018208-sc8j1ate 72 20 rates rate NNS cord-018208-sc8j1ate 72 21 and and CC cord-018208-sc8j1ate 72 22 nodal nodal JJ cord-018208-sc8j1ate 72 23 degrees degree NNS cord-018208-sc8j1ate 72 24 . . . cord-018208-sc8j1ate 73 1 For for IN cord-018208-sc8j1ate 73 2 simplicity simplicity NN cord-018208-sc8j1ate 73 3 , , , cord-018208-sc8j1ate 73 4 we -PRON- PRP cord-018208-sc8j1ate 73 5 name name VBP cord-018208-sc8j1ate 73 6 this this DT cord-018208-sc8j1ate 73 7 reference reference NN cord-018208-sc8j1ate 73 8 scenario scenario NN cord-018208-sc8j1ate 73 9 as as IN cord-018208-sc8j1ate 73 10 the the DT cord-018208-sc8j1ate 73 11 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 73 12 infection infection NN cord-018208-sc8j1ate 73 13 - - HYPH cord-018208-sc8j1ate 73 14 rate rate NN cord-018208-sc8j1ate 73 15 scenario scenario NN cord-018208-sc8j1ate 73 16 . . . cord-018208-sc8j1ate 74 1 Though though IN cord-018208-sc8j1ate 74 2 the the DT cord-018208-sc8j1ate 74 3 i.i.d i.i.d NN cord-018208-sc8j1ate 74 4 . . . cord-018208-sc8j1ate 74 5 infection infection NN cord-018208-sc8j1ate 74 6 rates rate NNS cord-018208-sc8j1ate 74 7 are be VBP cord-018208-sc8j1ate 74 8 also also RB cord-018208-sc8j1ate 74 9 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 74 10 , , , cord-018208-sc8j1ate 74 11 we -PRON- PRP cord-018208-sc8j1ate 74 12 can can MD cord-018208-sc8j1ate 74 13 tune tune VB cord-018208-sc8j1ate 74 14 the the DT cord-018208-sc8j1ate 74 15 variance variance NN cord-018208-sc8j1ate 74 16 of of IN cord-018208-sc8j1ate 74 17 the the DT cord-018208-sc8j1ate 74 18 infection infection NN cord-018208-sc8j1ate 74 19 rate rate NN cord-018208-sc8j1ate 74 20 in in IN cord-018208-sc8j1ate 74 21 the the DT cord-018208-sc8j1ate 74 22 case case NN cord-018208-sc8j1ate 74 23 of of IN cord-018208-sc8j1ate 74 24 the the DT cord-018208-sc8j1ate 74 25 i.i.d i.i.d NN cord-018208-sc8j1ate 74 26 . . . cord-018208-sc8j1ate 74 27 infection infection NN cord-018208-sc8j1ate 74 28 rates rate NNS cord-018208-sc8j1ate 74 29 while while IN cord-018208-sc8j1ate 74 30 keeping keep VBG cord-018208-sc8j1ate 74 31 the the DT cord-018208-sc8j1ate 74 32 distribution distribution NN cord-018208-sc8j1ate 74 33 and and CC cord-018208-sc8j1ate 74 34 the the DT cord-018208-sc8j1ate 74 35 mean mean NN cord-018208-sc8j1ate 74 36 of of IN cord-018208-sc8j1ate 74 37 the the DT cord-018208-sc8j1ate 74 38 infection infection NN cord-018208-sc8j1ate 74 39 rates rate NNS cord-018208-sc8j1ate 74 40 . . . cord-018208-sc8j1ate 75 1 However however RB cord-018208-sc8j1ate 75 2 , , , cord-018208-sc8j1ate 75 3 in in IN cord-018208-sc8j1ate 75 4 the the DT cord-018208-sc8j1ate 75 5 scenario scenario NN cord-018208-sc8j1ate 75 6 of of IN cord-018208-sc8j1ate 75 7 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 75 8 infection infection NN cord-018208-sc8j1ate 75 9 rates rate NNS cord-018208-sc8j1ate 75 10 in in IN cord-018208-sc8j1ate 75 11 this this DT cord-018208-sc8j1ate 75 12 paper paper NN cord-018208-sc8j1ate 75 13 , , , cord-018208-sc8j1ate 75 14 the the DT cord-018208-sc8j1ate 75 15 distribution distribution NN cord-018208-sc8j1ate 75 16 of of IN cord-018208-sc8j1ate 75 17 the the DT cord-018208-sc8j1ate 75 18 infection infection NN cord-018208-sc8j1ate 75 19 rate rate NN cord-018208-sc8j1ate 75 20 changes change NNS cord-018208-sc8j1ate 75 21 with with IN cord-018208-sc8j1ate 75 22 the the DT cord-018208-sc8j1ate 75 23 parameter parameter NN cord-018208-sc8j1ate 75 24 α α NN cord-018208-sc8j1ate 75 25 , , , cord-018208-sc8j1ate 75 26 hence hence RB cord-018208-sc8j1ate 75 27 the the DT cord-018208-sc8j1ate 75 28 variance variance NN cord-018208-sc8j1ate 75 29 of of IN cord-018208-sc8j1ate 75 30 the the DT cord-018208-sc8j1ate 75 31 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 75 32 infection infection NN cord-018208-sc8j1ate 75 33 rates rate NNS cord-018208-sc8j1ate 75 34 can can MD cord-018208-sc8j1ate 75 35 not not RB cord-018208-sc8j1ate 75 36 be be VB cord-018208-sc8j1ate 75 37 systematically systematically RB cord-018208-sc8j1ate 75 38 tuned tune VBN cord-018208-sc8j1ate 75 39 . . . cord-018208-sc8j1ate 76 1 A a DT cord-018208-sc8j1ate 76 2 positive positive JJ cord-018208-sc8j1ate 76 3 α α NN cord-018208-sc8j1ate 76 4 > > XX cord-018208-sc8j1ate 76 5 0 0 NFP cord-018208-sc8j1ate 76 6 ( ( -LRB- cord-018208-sc8j1ate 76 7 or or CC cord-018208-sc8j1ate 76 8 negative negative JJ cord-018208-sc8j1ate 76 9 α α XX cord-018208-sc8j1ate 76 10 < < XX cord-018208-sc8j1ate 76 11 0 0 CD cord-018208-sc8j1ate 76 12 ) ) -RRB- cord-018208-sc8j1ate 76 13 , , , cord-018208-sc8j1ate 76 14 suggests suggest VBZ cord-018208-sc8j1ate 76 15 a a DT cord-018208-sc8j1ate 76 16 positive positive JJ cord-018208-sc8j1ate 76 17 ( ( -LRB- cord-018208-sc8j1ate 76 18 or or CC cord-018208-sc8j1ate 76 19 negative negative JJ cord-018208-sc8j1ate 76 20 ) ) -RRB- cord-018208-sc8j1ate 76 21 correlation correlation NN cord-018208-sc8j1ate 76 22 between between IN cord-018208-sc8j1ate 76 23 infection infection NN cord-018208-sc8j1ate 76 24 rates rate NNS cord-018208-sc8j1ate 76 25 and and CC cord-018208-sc8j1ate 76 26 nodal nodal JJ cord-018208-sc8j1ate 76 27 degrees degree NNS cord-018208-sc8j1ate 76 28 . . . cord-018208-sc8j1ate 77 1 Too too RB cord-018208-sc8j1ate 77 2 large large JJ cord-018208-sc8j1ate 77 3 or or CC cord-018208-sc8j1ate 77 4 small small JJ cord-018208-sc8j1ate 77 5 values value NNS cord-018208-sc8j1ate 77 6 of of IN cord-018208-sc8j1ate 77 7 α α NN cord-018208-sc8j1ate 77 8 could could MD cord-018208-sc8j1ate 77 9 not not RB cord-018208-sc8j1ate 77 10 be be VB cord-018208-sc8j1ate 77 11 realistic realistic JJ cord-018208-sc8j1ate 77 12 . . . cord-018208-sc8j1ate 78 1 For for IN cord-018208-sc8j1ate 78 2 example example NN cord-018208-sc8j1ate 78 3 , , , cord-018208-sc8j1ate 78 4 [ [ -LRB- cord-018208-sc8j1ate 78 5 3 3 CD cord-018208-sc8j1ate 78 6 , , , cord-018208-sc8j1ate 78 7 9 9 CD cord-018208-sc8j1ate 78 8 , , , cord-018208-sc8j1ate 78 9 11 11 CD cord-018208-sc8j1ate 78 10 ] ] -RRB- cord-018208-sc8j1ate 78 11 suggest suggest VBP cord-018208-sc8j1ate 78 12 that that IN cord-018208-sc8j1ate 78 13 α α NN cord-018208-sc8j1ate 78 14 is be VBZ cord-018208-sc8j1ate 78 15 around around RB cord-018208-sc8j1ate 78 16 0.5 0.5 CD cord-018208-sc8j1ate 78 17 or or CC cord-018208-sc8j1ate 78 18 0.8 0.8 CD cord-018208-sc8j1ate 78 19 in in IN cord-018208-sc8j1ate 78 20 their -PRON- PRP$ cord-018208-sc8j1ate 78 21 datasets dataset NNS cord-018208-sc8j1ate 78 22 . . . cord-018208-sc8j1ate 79 1 Hence hence RB cord-018208-sc8j1ate 79 2 , , , cord-018208-sc8j1ate 79 3 we -PRON- PRP cord-018208-sc8j1ate 79 4 select select VBP cord-018208-sc8j1ate 79 5 α α NN cord-018208-sc8j1ate 79 6 = = SYM cord-018208-sc8j1ate 79 7 −0.25 −0.25 NNP cord-018208-sc8j1ate 79 8 , , , cord-018208-sc8j1ate 79 9 −0.5 −0.5 CD cord-018208-sc8j1ate 79 10 , , , cord-018208-sc8j1ate 79 11 −1 −1 NNP cord-018208-sc8j1ate 79 12 for for IN cord-018208-sc8j1ate 79 13 the the DT cord-018208-sc8j1ate 79 14 negative negative JJ cord-018208-sc8j1ate 79 15 correlation correlation NN cord-018208-sc8j1ate 79 16 and and CC cord-018208-sc8j1ate 79 17 α α NN cord-018208-sc8j1ate 79 18 = = SYM cord-018208-sc8j1ate 79 19 0.25 0.25 CD cord-018208-sc8j1ate 79 20 , , , cord-018208-sc8j1ate 79 21 0.5 0.5 CD cord-018208-sc8j1ate 79 22 , , , cord-018208-sc8j1ate 79 23 1 1 CD cord-018208-sc8j1ate 79 24 for for IN cord-018208-sc8j1ate 79 25 the the DT cord-018208-sc8j1ate 79 26 positive positive JJ cord-018208-sc8j1ate 79 27 correlation correlation NN cord-018208-sc8j1ate 79 28 . . . cord-018208-sc8j1ate 80 1 Different different JJ cord-018208-sc8j1ate 80 2 values value NNS cord-018208-sc8j1ate 80 3 of of IN cord-018208-sc8j1ate 80 4 α α NN cord-018208-sc8j1ate 80 5 also also RB cord-018208-sc8j1ate 80 6 offer offer VBP cord-018208-sc8j1ate 80 7 the the DT cord-018208-sc8j1ate 80 8 possibility possibility NN cord-018208-sc8j1ate 80 9 to to TO cord-018208-sc8j1ate 80 10 explore explore VB cord-018208-sc8j1ate 80 11 how how WRB cord-018208-sc8j1ate 80 12 NIMFA NIMFA NNP cord-018208-sc8j1ate 80 13 performs perform VBZ cord-018208-sc8j1ate 80 14 with with IN cord-018208-sc8j1ate 80 15 different different JJ cord-018208-sc8j1ate 80 16 correlation correlation NN cord-018208-sc8j1ate 80 17 strengths strength NNS cord-018208-sc8j1ate 80 18 . . . cord-018208-sc8j1ate 81 1 In in IN cord-018208-sc8j1ate 81 2 this this DT cord-018208-sc8j1ate 81 3 paper paper NN cord-018208-sc8j1ate 81 4 , , , cord-018208-sc8j1ate 81 5 we -PRON- PRP cord-018208-sc8j1ate 81 6 aim aim VBP cord-018208-sc8j1ate 81 7 to to TO cord-018208-sc8j1ate 81 8 understand understand VB cord-018208-sc8j1ate 81 9 how how WRB cord-018208-sc8j1ate 81 10 the the DT cord-018208-sc8j1ate 81 11 correlation correlation NN cord-018208-sc8j1ate 81 12 influences influence VBZ cord-018208-sc8j1ate 81 13 the the DT cord-018208-sc8j1ate 81 14 accuracy accuracy NN cord-018208-sc8j1ate 81 15 of of IN cord-018208-sc8j1ate 81 16 NIMFA NIMFA NNP cord-018208-sc8j1ate 81 17 by by IN cord-018208-sc8j1ate 81 18 comparing compare VBG cord-018208-sc8j1ate 81 19 the the DT cord-018208-sc8j1ate 81 20 average average JJ cord-018208-sc8j1ate 81 21 fraction fraction NN cord-018208-sc8j1ate 82 1 y y NNP cord-018208-sc8j1ate 82 2 ∞ ∞ NNP cord-018208-sc8j1ate 82 3 of of IN cord-018208-sc8j1ate 82 4 infected infected JJ cord-018208-sc8j1ate 82 5 nodes node NNS cord-018208-sc8j1ate 82 6 obtained obtain VBN cord-018208-sc8j1ate 82 7 by by IN cord-018208-sc8j1ate 82 8 NIMFA NIMFA NNP cord-018208-sc8j1ate 82 9 and and CC cord-018208-sc8j1ate 82 10 the the DT cord-018208-sc8j1ate 82 11 simulations simulation NNS cord-018208-sc8j1ate 82 12 of of IN cord-018208-sc8j1ate 82 13 the the DT cord-018208-sc8j1ate 82 14 exact exact JJ cord-018208-sc8j1ate 82 15 SIS SIS NNP cord-018208-sc8j1ate 82 16 model model NN cord-018208-sc8j1ate 82 17 . . . cord-018208-sc8j1ate 83 1 In in IN cord-018208-sc8j1ate 83 2 [ [ -LRB- cord-018208-sc8j1ate 83 3 17 17 CD cord-018208-sc8j1ate 83 4 ] ] -RRB- cord-018208-sc8j1ate 83 5 , , , cord-018208-sc8j1ate 83 6 we -PRON- PRP cord-018208-sc8j1ate 83 7 explored explore VBD cord-018208-sc8j1ate 83 8 the the DT cord-018208-sc8j1ate 83 9 influence influence NN cord-018208-sc8j1ate 83 10 of of IN cord-018208-sc8j1ate 83 11 the the DT cord-018208-sc8j1ate 83 12 correlation correlation NN cord-018208-sc8j1ate 83 13 between between IN cord-018208-sc8j1ate 83 14 the the DT cord-018208-sc8j1ate 83 15 infection infection NN cord-018208-sc8j1ate 83 16 rate rate NN cord-018208-sc8j1ate 83 17 and and CC cord-018208-sc8j1ate 83 18 the the DT cord-018208-sc8j1ate 83 19 nodal nodal JJ cord-018208-sc8j1ate 83 20 degree degree NN cord-018208-sc8j1ate 83 21 on on IN cord-018208-sc8j1ate 83 22 the the DT cord-018208-sc8j1ate 83 23 prevalence prevalence NN cord-018208-sc8j1ate 83 24 of of IN cord-018208-sc8j1ate 83 25 epidemic epidemic NN cord-018208-sc8j1ate 83 26 , , , cord-018208-sc8j1ate 83 27 which which WDT cord-018208-sc8j1ate 83 28 can can MD cord-018208-sc8j1ate 83 29 be be VB cord-018208-sc8j1ate 83 30 used use VBN cord-018208-sc8j1ate 83 31 to to TO cord-018208-sc8j1ate 83 32 partially partially RB cord-018208-sc8j1ate 83 33 explain explain VB cord-018208-sc8j1ate 83 34 the the DT cord-018208-sc8j1ate 83 35 conclusions conclusion NNS cord-018208-sc8j1ate 83 36 in in IN cord-018208-sc8j1ate 83 37 this this DT cord-018208-sc8j1ate 83 38 paper paper NN cord-018208-sc8j1ate 83 39 . . . cord-018208-sc8j1ate 84 1 As as IN cord-018208-sc8j1ate 84 2 in in IN cord-018208-sc8j1ate 84 3 our -PRON- PRP$ cord-018208-sc8j1ate 84 4 previous previous JJ cord-018208-sc8j1ate 84 5 work work NN cord-018208-sc8j1ate 84 6 [ [ -LRB- cord-018208-sc8j1ate 84 7 15 15 CD cord-018208-sc8j1ate 84 8 , , , cord-018208-sc8j1ate 84 9 17 17 CD cord-018208-sc8j1ate 84 10 ] ] -RRB- cord-018208-sc8j1ate 84 11 , , , cord-018208-sc8j1ate 84 12 we -PRON- PRP cord-018208-sc8j1ate 84 13 perform perform VBP cord-018208-sc8j1ate 84 14 the the DT cord-018208-sc8j1ate 84 15 continuous continuous JJ cord-018208-sc8j1ate 84 16 - - HYPH cord-018208-sc8j1ate 84 17 time time NN cord-018208-sc8j1ate 84 18 simulations simulation NNS cord-018208-sc8j1ate 84 19 of of IN cord-018208-sc8j1ate 84 20 the the DT cord-018208-sc8j1ate 84 21 SIS SIS NNP cord-018208-sc8j1ate 84 22 model model NN cord-018208-sc8j1ate 84 23 . . . cord-018208-sc8j1ate 85 1 We -PRON- PRP cord-018208-sc8j1ate 85 2 consider consider VBP cord-018208-sc8j1ate 85 3 both both CC cord-018208-sc8j1ate 85 4 the the DT cord-018208-sc8j1ate 85 5 scale scale NN cord-018208-sc8j1ate 85 6 - - HYPH cord-018208-sc8j1ate 85 7 free free JJ cord-018208-sc8j1ate 85 8 ( ( -LRB- cord-018208-sc8j1ate 85 9 SF SF NNP cord-018208-sc8j1ate 85 10 ) ) -RRB- cord-018208-sc8j1ate 85 11 and and CC cord-018208-sc8j1ate 85 12 Erdös Erdös NNP cord-018208-sc8j1ate 85 13 - - HYPH cord-018208-sc8j1ate 85 14 Rényi Rényi NNP cord-018208-sc8j1ate 85 15 ( ( -LRB- cord-018208-sc8j1ate 85 16 ER ER NNP cord-018208-sc8j1ate 85 17 ) ) -RRB- cord-018208-sc8j1ate 85 18 models model NNS cord-018208-sc8j1ate 85 19 for for IN cord-018208-sc8j1ate 85 20 different different JJ cord-018208-sc8j1ate 85 21 network network NN cord-018208-sc8j1ate 85 22 topologies topology NNS cord-018208-sc8j1ate 85 23 . . . cord-018208-sc8j1ate 86 1 The the DT cord-018208-sc8j1ate 86 2 SF SF NNP cord-018208-sc8j1ate 86 3 model model NN cord-018208-sc8j1ate 86 4 has have VBZ cord-018208-sc8j1ate 86 5 been be VBN cord-018208-sc8j1ate 86 6 used use VBN cord-018208-sc8j1ate 86 7 to to TO cord-018208-sc8j1ate 86 8 capture capture VB cord-018208-sc8j1ate 86 9 the the DT cord-018208-sc8j1ate 86 10 scale scale NN cord-018208-sc8j1ate 86 11 - - HYPH cord-018208-sc8j1ate 86 12 free free JJ cord-018208-sc8j1ate 86 13 nature nature NN cord-018208-sc8j1ate 86 14 of of IN cord-018208-sc8j1ate 86 15 degree degree NN cord-018208-sc8j1ate 86 16 distribution distribution NN cord-018208-sc8j1ate 86 17 in in IN cord-018208-sc8j1ate 86 18 real real JJ cord-018208-sc8j1ate 86 19 - - HYPH cord-018208-sc8j1ate 86 20 world world NN cord-018208-sc8j1ate 86 21 networks network NNS cord-018208-sc8j1ate 86 22 such such JJ cord-018208-sc8j1ate 86 23 as as IN cord-018208-sc8j1ate 86 24 the the DT cord-018208-sc8j1ate 86 25 Internet internet NN cord-018208-sc8j1ate 86 26 [ [ -LRB- cord-018208-sc8j1ate 86 27 5 5 CD cord-018208-sc8j1ate 86 28 ] ] -RRB- cord-018208-sc8j1ate 86 29 and and CC cord-018208-sc8j1ate 86 30 World World NNP cord-018208-sc8j1ate 86 31 Wide Wide NNP cord-018208-sc8j1ate 86 32 Web Web NNP cord-018208-sc8j1ate 86 33 [ [ -LRB- cord-018208-sc8j1ate 86 34 1 1 CD cord-018208-sc8j1ate 86 35 ] ] -RRB- cord-018208-sc8j1ate 86 36 : : : cord-018208-sc8j1ate 86 37 where where WRB cord-018208-sc8j1ate 86 38 d d NNP cord-018208-sc8j1ate 86 39 min min NNP cord-018208-sc8j1ate 86 40 is be VBZ cord-018208-sc8j1ate 86 41 the the DT cord-018208-sc8j1ate 86 42 smallest small JJS cord-018208-sc8j1ate 86 43 degree degree NN cord-018208-sc8j1ate 86 44 , , , cord-018208-sc8j1ate 86 45 d d NNP cord-018208-sc8j1ate 86 46 max max NNP cord-018208-sc8j1ate 86 47 is be VBZ cord-018208-sc8j1ate 86 48 the the DT cord-018208-sc8j1ate 86 49 degree degree NN cord-018208-sc8j1ate 86 50 cutoff cutoff NN cord-018208-sc8j1ate 86 51 , , , cord-018208-sc8j1ate 86 52 and and CC cord-018208-sc8j1ate 86 53 λ λ NN cord-018208-sc8j1ate 86 54 > > XX cord-018208-sc8j1ate 86 55 0 0 NFP cord-018208-sc8j1ate 86 56 is be VBZ cord-018208-sc8j1ate 86 57 the the DT cord-018208-sc8j1ate 86 58 exponent exponent NN cord-018208-sc8j1ate 86 59 characterizing characterize VBG cord-018208-sc8j1ate 86 60 the the DT cord-018208-sc8j1ate 86 61 broadness broadness NN cord-018208-sc8j1ate 86 62 of of IN cord-018208-sc8j1ate 86 63 the the DT cord-018208-sc8j1ate 86 64 distribution distribution NN cord-018208-sc8j1ate 86 65 [ [ -LRB- cord-018208-sc8j1ate 86 66 2 2 CD cord-018208-sc8j1ate 86 67 ] ] -RRB- cord-018208-sc8j1ate 86 68 . . . cord-018208-sc8j1ate 87 1 In in IN cord-018208-sc8j1ate 87 2 real real JJ cord-018208-sc8j1ate 87 3 - - HYPH cord-018208-sc8j1ate 87 4 word word NN cord-018208-sc8j1ate 87 5 networks network NNS cord-018208-sc8j1ate 87 6 , , , cord-018208-sc8j1ate 87 7 the the DT cord-018208-sc8j1ate 87 8 exponent exponent NN cord-018208-sc8j1ate 87 9 λ λ NN cord-018208-sc8j1ate 87 10 is be VBZ cord-018208-sc8j1ate 87 11 usually usually RB cord-018208-sc8j1ate 87 12 in in IN cord-018208-sc8j1ate 87 13 the the DT cord-018208-sc8j1ate 87 14 range range NN cord-018208-sc8j1ate 87 15 [ [ -LRB- cord-018208-sc8j1ate 87 16 2 2 CD cord-018208-sc8j1ate 87 17 , , , cord-018208-sc8j1ate 87 18 3 3 CD cord-018208-sc8j1ate 87 19 ] ] -RRB- cord-018208-sc8j1ate 87 20 , , , cord-018208-sc8j1ate 87 21 thus thus RB cord-018208-sc8j1ate 87 22 we -PRON- PRP cord-018208-sc8j1ate 87 23 confine confine VBP cord-018208-sc8j1ate 87 24 the the DT cord-018208-sc8j1ate 87 25 exponent exponent NN cord-018208-sc8j1ate 87 26 λ λ NN cord-018208-sc8j1ate 87 27 = = SYM cord-018208-sc8j1ate 87 28 2.5 2.5 CD cord-018208-sc8j1ate 87 29 in in IN cord-018208-sc8j1ate 87 30 this this DT cord-018208-sc8j1ate 87 31 paper paper NN cord-018208-sc8j1ate 87 32 . . . cord-018208-sc8j1ate 88 1 We -PRON- PRP cord-018208-sc8j1ate 88 2 further further RB cord-018208-sc8j1ate 88 3 employ employ VBP cord-018208-sc8j1ate 88 4 the the DT cord-018208-sc8j1ate 88 5 smallest small JJS cord-018208-sc8j1ate 88 6 degree degree NN cord-018208-sc8j1ate 88 7 d d NN cord-018208-sc8j1ate 88 8 min min NN cord-018208-sc8j1ate 88 9 = = SYM cord-018208-sc8j1ate 88 10 2 2 CD cord-018208-sc8j1ate 88 11 , , , cord-018208-sc8j1ate 88 12 the the DT cord-018208-sc8j1ate 88 13 natural natural JJ cord-018208-sc8j1ate 88 14 degree degree NN cord-018208-sc8j1ate 88 15 cutoff cutoff NNP cord-018208-sc8j1ate 88 16 d d NNP cord-018208-sc8j1ate 88 17 max max NNP cord-018208-sc8j1ate 88 18 = = SYM cord-018208-sc8j1ate 88 19 N N NNP cord-018208-sc8j1ate 88 20 1/(λ 1/(λ CD cord-018208-sc8j1ate 88 21 −1 −1 NNP cord-018208-sc8j1ate 88 22 ) ) -RRB- cord-018208-sc8j1ate 88 23 as as IN cord-018208-sc8j1ate 88 24 in in IN cord-018208-sc8j1ate 88 25 [ [ -LRB- cord-018208-sc8j1ate 88 26 6 6 CD cord-018208-sc8j1ate 88 27 ] ] -RRB- cord-018208-sc8j1ate 88 28 , , , cord-018208-sc8j1ate 88 29 and and CC cord-018208-sc8j1ate 88 30 the the DT cord-018208-sc8j1ate 88 31 size size NN cord-018208-sc8j1ate 88 32 N n NN cord-018208-sc8j1ate 88 33 = = SYM cord-018208-sc8j1ate 88 34 1000 1000 CD cord-018208-sc8j1ate 88 35 . . . cord-018208-sc8j1ate 89 1 Hence hence RB cord-018208-sc8j1ate 89 2 , , , cord-018208-sc8j1ate 89 3 the the DT cord-018208-sc8j1ate 89 4 average average JJ cord-018208-sc8j1ate 89 5 degree degree NN cord-018208-sc8j1ate 89 6 is be VBZ cord-018208-sc8j1ate 89 7 approximately approximately RB cord-018208-sc8j1ate 89 8 4 4 CD cord-018208-sc8j1ate 89 9 . . . cord-018208-sc8j1ate 90 1 The the DT cord-018208-sc8j1ate 90 2 distribution distribution NN cord-018208-sc8j1ate 90 3 of of IN cord-018208-sc8j1ate 90 4 the the DT cord-018208-sc8j1ate 90 5 degree degree NN cord-018208-sc8j1ate 90 6 of of IN cord-018208-sc8j1ate 90 7 a a DT cord-018208-sc8j1ate 90 8 random random JJ cord-018208-sc8j1ate 90 9 node node NN cord-018208-sc8j1ate 90 10 in in IN cord-018208-sc8j1ate 90 11 ER ER NNP cord-018208-sc8j1ate 90 12 network network NN cord-018208-sc8j1ate 90 13 is be VBZ cord-018208-sc8j1ate 90 14 binomial binomial JJ cord-018208-sc8j1ate 90 15 : : : cord-018208-sc8j1ate 90 16 Given give VBN cord-018208-sc8j1ate 90 17 a a DT cord-018208-sc8j1ate 90 18 network network NN cord-018208-sc8j1ate 90 19 topology topology NN cord-018208-sc8j1ate 90 20 and and CC cord-018208-sc8j1ate 90 21 a a DT cord-018208-sc8j1ate 90 22 recovery recovery NN cord-018208-sc8j1ate 90 23 rate rate NN cord-018208-sc8j1ate 90 24 δ δ NN cord-018208-sc8j1ate 90 25 , , , cord-018208-sc8j1ate 90 26 we -PRON- PRP cord-018208-sc8j1ate 90 27 carry carry VBP cord-018208-sc8j1ate 90 28 out out RP cord-018208-sc8j1ate 90 29 100 100 CD cord-018208-sc8j1ate 90 30 iterations iteration NNS cord-018208-sc8j1ate 90 31 . . . cord-018208-sc8j1ate 91 1 In in IN cord-018208-sc8j1ate 91 2 each each DT cord-018208-sc8j1ate 91 3 iteration iteration NN cord-018208-sc8j1ate 91 4 , , , cord-018208-sc8j1ate 91 5 the the DT cord-018208-sc8j1ate 91 6 networks network NNS cord-018208-sc8j1ate 91 7 are be VBP cord-018208-sc8j1ate 91 8 constructed construct VBN cord-018208-sc8j1ate 91 9 as as IN cord-018208-sc8j1ate 91 10 described describe VBN cord-018208-sc8j1ate 91 11 above above IN cord-018208-sc8j1ate 91 12 and and CC cord-018208-sc8j1ate 91 13 the the DT cord-018208-sc8j1ate 91 14 infection infection NN cord-018208-sc8j1ate 91 15 rates rate NNS cord-018208-sc8j1ate 91 16 are be VBP cord-018208-sc8j1ate 91 17 generated generate VBN cord-018208-sc8j1ate 91 18 as as IN cord-018208-sc8j1ate 91 19 described describe VBN cord-018208-sc8j1ate 91 20 in in IN cord-018208-sc8j1ate 91 21 Section section NN cord-018208-sc8j1ate 91 22 2.2 2.2 CD cord-018208-sc8j1ate 91 23 and and CC cord-018208-sc8j1ate 91 24 2.3 2.3 CD cord-018208-sc8j1ate 91 25 . . . cord-018208-sc8j1ate 92 1 Initially initially RB cord-018208-sc8j1ate 92 2 , , , cord-018208-sc8j1ate 92 3 10 10 CD cord-018208-sc8j1ate 92 4 % % NN cord-018208-sc8j1ate 92 5 of of IN cord-018208-sc8j1ate 92 6 the the DT cord-018208-sc8j1ate 92 7 nodes node NNS cord-018208-sc8j1ate 92 8 are be VBP cord-018208-sc8j1ate 92 9 randomly randomly RB cord-018208-sc8j1ate 92 10 infected infect VBN cord-018208-sc8j1ate 92 11 . . . cord-018208-sc8j1ate 93 1 Then then RB cord-018208-sc8j1ate 93 2 the the DT cord-018208-sc8j1ate 93 3 infection infection NN cord-018208-sc8j1ate 93 4 and and CC cord-018208-sc8j1ate 93 5 recovery recovery NN cord-018208-sc8j1ate 93 6 processes process NNS cord-018208-sc8j1ate 93 7 of of IN cord-018208-sc8j1ate 93 8 SIS SIS NNP cord-018208-sc8j1ate 93 9 model model NN cord-018208-sc8j1ate 93 10 are be VBP cord-018208-sc8j1ate 93 11 simulated simulate VBN cord-018208-sc8j1ate 93 12 until until IN cord-018208-sc8j1ate 93 13 the the DT cord-018208-sc8j1ate 93 14 system system NN cord-018208-sc8j1ate 93 15 reaches reach VBZ cord-018208-sc8j1ate 93 16 the the DT cord-018208-sc8j1ate 93 17 metastable metastable JJ cord-018208-sc8j1ate 93 18 state state NN cord-018208-sc8j1ate 93 19 where where WRB cord-018208-sc8j1ate 93 20 the the DT cord-018208-sc8j1ate 93 21 fraction fraction NN cord-018208-sc8j1ate 93 22 of of IN cord-018208-sc8j1ate 93 23 infected infected JJ cord-018208-sc8j1ate 93 24 nodes node NNS cord-018208-sc8j1ate 93 25 is be VBZ cord-018208-sc8j1ate 93 26 nonzero nonzero JJ cord-018208-sc8j1ate 93 27 and and CC cord-018208-sc8j1ate 93 28 unchanged unchanged JJ cord-018208-sc8j1ate 93 29 for for IN cord-018208-sc8j1ate 93 30 a a DT cord-018208-sc8j1ate 93 31 long long JJ cord-018208-sc8j1ate 93 32 time time NN cord-018208-sc8j1ate 93 33 if if IN cord-018208-sc8j1ate 93 34 the the DT cord-018208-sc8j1ate 93 35 epidemic epidemic NN cord-018208-sc8j1ate 93 36 spreads spread VBZ cord-018208-sc8j1ate 93 37 out out RP cord-018208-sc8j1ate 93 38 , , , cord-018208-sc8j1ate 93 39 or or CC cord-018208-sc8j1ate 93 40 the the DT cord-018208-sc8j1ate 93 41 fraction fraction NN cord-018208-sc8j1ate 93 42 is be VBZ cord-018208-sc8j1ate 93 43 zero zero CD cord-018208-sc8j1ate 93 44 if if IN cord-018208-sc8j1ate 93 45 the the DT cord-018208-sc8j1ate 93 46 epidemic epidemic NN cord-018208-sc8j1ate 93 47 dies die VBZ cord-018208-sc8j1ate 93 48 out out RP cord-018208-sc8j1ate 93 49 . . . cord-018208-sc8j1ate 94 1 The the DT cord-018208-sc8j1ate 94 2 average average JJ cord-018208-sc8j1ate 94 3 fraction fraction NN cord-018208-sc8j1ate 94 4 y y NNP cord-018208-sc8j1ate 94 5 ∞ ∞ NNP cord-018208-sc8j1ate 94 6 of of IN cord-018208-sc8j1ate 94 7 infected infected JJ cord-018208-sc8j1ate 94 8 nodes node NNS cord-018208-sc8j1ate 94 9 is be VBZ cord-018208-sc8j1ate 94 10 obtained obtain VBN cord-018208-sc8j1ate 94 11 over over IN cord-018208-sc8j1ate 94 12 100 100 CD cord-018208-sc8j1ate 94 13 iterations iteration NNS cord-018208-sc8j1ate 94 14 ( ( -LRB- cord-018208-sc8j1ate 94 15 no no RB cord-018208-sc8j1ate 94 16 matter matter RB cord-018208-sc8j1ate 94 17 the the DT cord-018208-sc8j1ate 94 18 epidemic epidemic NN cord-018208-sc8j1ate 94 19 dies die VBZ cord-018208-sc8j1ate 94 20 out out RP cord-018208-sc8j1ate 94 21 or or CC cord-018208-sc8j1ate 94 22 not not RB cord-018208-sc8j1ate 94 23 ) ) -RRB- cord-018208-sc8j1ate 94 24 . . . cord-018208-sc8j1ate 95 1 In in IN cord-018208-sc8j1ate 95 2 this this DT cord-018208-sc8j1ate 95 3 section section NN cord-018208-sc8j1ate 95 4 , , , cord-018208-sc8j1ate 95 5 we -PRON- PRP cord-018208-sc8j1ate 95 6 first first RB cord-018208-sc8j1ate 95 7 explore explore VBP cord-018208-sc8j1ate 95 8 the the DT cord-018208-sc8j1ate 95 9 accuracy accuracy NN cord-018208-sc8j1ate 95 10 of of IN cord-018208-sc8j1ate 95 11 NIMFA NIMFA NNP cord-018208-sc8j1ate 95 12 with with IN cord-018208-sc8j1ate 95 13 the the DT cord-018208-sc8j1ate 95 14 i.i.d i.i.d NN cord-018208-sc8j1ate 95 15 . . . cord-018208-sc8j1ate 95 16 infection infection NN cord-018208-sc8j1ate 95 17 rates rate NNS cord-018208-sc8j1ate 95 18 , , , cord-018208-sc8j1ate 95 19 and and CC cord-018208-sc8j1ate 95 20 particularly particularly RB cord-018208-sc8j1ate 95 21 how how WRB cord-018208-sc8j1ate 95 22 NIMFA NIMFA NNP cord-018208-sc8j1ate 95 23 performs perform VBZ cord-018208-sc8j1ate 95 24 when when WRB cord-018208-sc8j1ate 95 25 the the DT cord-018208-sc8j1ate 95 26 variance variance NN cord-018208-sc8j1ate 95 27 Var[B var[b NN cord-018208-sc8j1ate 95 28 ] ] -RRB- cord-018208-sc8j1ate 95 29 of of IN cord-018208-sc8j1ate 95 30 the the DT cord-018208-sc8j1ate 95 31 infection infection NN cord-018208-sc8j1ate 95 32 rate rate NN cord-018208-sc8j1ate 95 33 B b NN cord-018208-sc8j1ate 95 34 varies vary VBZ cord-018208-sc8j1ate 95 35 . . . cord-018208-sc8j1ate 96 1 Then then RB cord-018208-sc8j1ate 96 2 we -PRON- PRP cord-018208-sc8j1ate 96 3 explore explore VBP cord-018208-sc8j1ate 96 4 the the DT cord-018208-sc8j1ate 96 5 influence influence NN cord-018208-sc8j1ate 96 6 of of IN cord-018208-sc8j1ate 96 7 the the DT cord-018208-sc8j1ate 96 8 correlated correlate VBN cord-018208-sc8j1ate 96 9 infection infection NN cord-018208-sc8j1ate 96 10 rates rate NNS cord-018208-sc8j1ate 96 11 on on IN cord-018208-sc8j1ate 96 12 NIMFA NIMFA NNP cord-018208-sc8j1ate 96 13 . . . cord-018208-sc8j1ate 97 1 We -PRON- PRP cord-018208-sc8j1ate 97 2 aim aim VBP cord-018208-sc8j1ate 97 3 to to TO cord-018208-sc8j1ate 97 4 understand understand VB cord-018208-sc8j1ate 97 5 the the DT cord-018208-sc8j1ate 97 6 precision precision NN cord-018208-sc8j1ate 97 7 of of IN cord-018208-sc8j1ate 97 8 NIMFA NIMFA NNP cord-018208-sc8j1ate 97 9 under under IN cord-018208-sc8j1ate 97 10 different different JJ cord-018208-sc8j1ate 97 11 effective effective JJ cord-018208-sc8j1ate 97 12 infection infection NN cord-018208-sc8j1ate 97 13 rates rate NNS cord-018208-sc8j1ate 97 14 , , , cord-018208-sc8j1ate 97 15 different different JJ cord-018208-sc8j1ate 97 16 variances variance NNS cord-018208-sc8j1ate 97 17 of of IN cord-018208-sc8j1ate 97 18 infection infection NN cord-018208-sc8j1ate 97 19 rates rate NNS cord-018208-sc8j1ate 97 20 and and CC cord-018208-sc8j1ate 97 21 different different JJ cord-018208-sc8j1ate 97 22 network network NN cord-018208-sc8j1ate 97 23 topologies topology NNS cord-018208-sc8j1ate 97 24 : : : cord-018208-sc8j1ate 97 25 we -PRON- PRP cord-018208-sc8j1ate 97 26 set set VBP cord-018208-sc8j1ate 97 27 the the DT cord-018208-sc8j1ate 97 28 average average JJ cord-018208-sc8j1ate 97 29 infection infection NN cord-018208-sc8j1ate 97 30 rate rate NN cord-018208-sc8j1ate 97 31 to to IN cord-018208-sc8j1ate 97 32 1 1 CD cord-018208-sc8j1ate 97 33 and and CC cord-018208-sc8j1ate 97 34 tune tune VB cord-018208-sc8j1ate 97 35 the the DT cord-018208-sc8j1ate 97 36 recovery recovery NN cord-018208-sc8j1ate 97 37 rate rate NN cord-018208-sc8j1ate 97 38 δ δ NN cord-018208-sc8j1ate 97 39 to to TO cord-018208-sc8j1ate 97 40 control control VB cord-018208-sc8j1ate 97 41 the the DT cord-018208-sc8j1ate 97 42 effective effective JJ cord-018208-sc8j1ate 97 43 infection infection NN cord-018208-sc8j1ate 97 44 rate rate NN cord-018208-sc8j1ate 97 45 τ τ NN cord-018208-sc8j1ate 97 46 ; ; : cord-018208-sc8j1ate 97 47 we -PRON- PRP cord-018208-sc8j1ate 97 48 change change VBP cord-018208-sc8j1ate 97 49 the the DT cord-018208-sc8j1ate 97 50 variance variance NN cord-018208-sc8j1ate 97 51 of of IN cord-018208-sc8j1ate 97 52 infection infection NN cord-018208-sc8j1ate 97 53 rates rate NNS cord-018208-sc8j1ate 97 54 which which WDT cord-018208-sc8j1ate 97 55 follow follow VBP cord-018208-sc8j1ate 97 56 the the DT cord-018208-sc8j1ate 97 57 lognormal lognormal JJ cord-018208-sc8j1ate 97 58 distribution distribution NN cord-018208-sc8j1ate 97 59 ; ; : cord-018208-sc8j1ate 97 60 we -PRON- PRP cord-018208-sc8j1ate 97 61 consider consider VBP cord-018208-sc8j1ate 97 62 both both CC cord-018208-sc8j1ate 97 63 ER ER NNP cord-018208-sc8j1ate 97 64 and and CC cord-018208-sc8j1ate 97 65 SF SF NNP cord-018208-sc8j1ate 97 66 networks network NNS cord-018208-sc8j1ate 97 67 to to TO cord-018208-sc8j1ate 97 68 represent represent VB cord-018208-sc8j1ate 97 69 different different JJ cord-018208-sc8j1ate 97 70 topologies topology NNS cord-018208-sc8j1ate 97 71 . . . cord-018208-sc8j1ate 98 1 For for IN cord-018208-sc8j1ate 98 2 each each DT cord-018208-sc8j1ate 98 3 value value NN cord-018208-sc8j1ate 98 4 of of IN cord-018208-sc8j1ate 98 5 the the DT cord-018208-sc8j1ate 98 6 variance variance NN cord-018208-sc8j1ate 98 7 of of IN cord-018208-sc8j1ate 98 8 the the DT cord-018208-sc8j1ate 98 9 infection infection NN cord-018208-sc8j1ate 98 10 rate rate NN cord-018208-sc8j1ate 98 11 , , , cord-018208-sc8j1ate 98 12 we -PRON- PRP cord-018208-sc8j1ate 98 13 obtain obtain VBP cord-018208-sc8j1ate 98 14 the the DT cord-018208-sc8j1ate 98 15 average average JJ cord-018208-sc8j1ate 98 16 fraction fraction NN cord-018208-sc8j1ate 98 17 y y NNP cord-018208-sc8j1ate 98 18 ∞ ∞ NNP cord-018208-sc8j1ate 98 19 of of IN cord-018208-sc8j1ate 98 20 infected infected JJ cord-018208-sc8j1ate 98 21 nodes node NNS cord-018208-sc8j1ate 98 22 as as IN cord-018208-sc8j1ate 98 23 a a DT cord-018208-sc8j1ate 98 24 function function NN cord-018208-sc8j1ate 98 25 of of IN cord-018208-sc8j1ate 98 26 the the DT cord-018208-sc8j1ate 98 27 effective effective JJ cord-018208-sc8j1ate 98 28 infection infection NN cord-018208-sc8j1ate 98 29 rate rate NN cord-018208-sc8j1ate 98 30 τ τ NN cord-018208-sc8j1ate 98 31 for for IN cord-018208-sc8j1ate 98 32 NIMFA NIMFA NNP cord-018208-sc8j1ate 98 33 by by IN cord-018208-sc8j1ate 98 34 numerically numerically RB cord-018208-sc8j1ate 98 35 solving solve VBG cord-018208-sc8j1ate 98 36 ( ( -LRB- cord-018208-sc8j1ate 98 37 3 3 CD cord-018208-sc8j1ate 98 38 ) ) -RRB- cord-018208-sc8j1ate 98 39 and and CC cord-018208-sc8j1ate 98 40 compare compare VB cord-018208-sc8j1ate 98 41 with with IN cord-018208-sc8j1ate 98 42 that that DT cord-018208-sc8j1ate 98 43 by by IN cord-018208-sc8j1ate 98 44 the the DT cord-018208-sc8j1ate 98 45 continuous continuous JJ cord-018208-sc8j1ate 98 46 - - HYPH cord-018208-sc8j1ate 98 47 time time NN cord-018208-sc8j1ate 98 48 simulations simulation NNS cord-018208-sc8j1ate 98 49 . . . cord-018208-sc8j1ate 99 1 As as IN cord-018208-sc8j1ate 99 2 shown show VBN cord-018208-sc8j1ate 99 3 in in IN cord-018208-sc8j1ate 99 4 Fig Fig NNP cord-018208-sc8j1ate 99 5 . . . cord-018208-sc8j1ate 100 1 1a 1a LS cord-018208-sc8j1ate 100 2 , , , cord-018208-sc8j1ate 100 3 no no RB cord-018208-sc8j1ate 100 4 matter matter RB cord-018208-sc8j1ate 100 5 what what WP cord-018208-sc8j1ate 100 6 the the DT cord-018208-sc8j1ate 100 7 variance variance NN cord-018208-sc8j1ate 100 8 of of IN cord-018208-sc8j1ate 100 9 the the DT cord-018208-sc8j1ate 100 10 infection infection NN cord-018208-sc8j1ate 100 11 rate rate NN cord-018208-sc8j1ate 100 12 is be VBZ cord-018208-sc8j1ate 100 13 , , , cord-018208-sc8j1ate 100 14 the the DT cord-018208-sc8j1ate 100 15 curve curve NN cord-018208-sc8j1ate 100 16 of of IN cord-018208-sc8j1ate 100 17 y y NNP cord-018208-sc8j1ate 100 18 ∞ ∞ NNP cord-018208-sc8j1ate 100 19 vs. vs. IN cord-018208-sc8j1ate 100 20 τ τ NN cord-018208-sc8j1ate 100 21 obtained obtain VBN cord-018208-sc8j1ate 100 22 by by IN cord-018208-sc8j1ate 100 23 NIMFA NIMFA NNP cord-018208-sc8j1ate 100 24 for for IN cord-018208-sc8j1ate 100 25 ER ER NNP cord-018208-sc8j1ate 100 26 networks network NNS cord-018208-sc8j1ate 100 27 is be VBZ cord-018208-sc8j1ate 100 28 close close JJ cord-018208-sc8j1ate 100 29 to to IN cord-018208-sc8j1ate 100 30 that that DT cord-018208-sc8j1ate 100 31 obtained obtain VBN cord-018208-sc8j1ate 100 32 by by IN cord-018208-sc8j1ate 100 33 simulations simulation NNS cord-018208-sc8j1ate 100 34 when when WRB cord-018208-sc8j1ate 100 35 the the DT cord-018208-sc8j1ate 100 36 actual actual JJ cord-018208-sc8j1ate 100 37 prevalence prevalence NN cord-018208-sc8j1ate 100 38 of of IN cord-018208-sc8j1ate 100 39 the the DT cord-018208-sc8j1ate 100 40 epidemic epidemic NN cord-018208-sc8j1ate 100 41 is be VBZ cord-018208-sc8j1ate 100 42 high high JJ cord-018208-sc8j1ate 100 43 , , , cord-018208-sc8j1ate 100 44 i.e. i.e. FW cord-018208-sc8j1ate 100 45 the the DT cord-018208-sc8j1ate 100 46 effective effective JJ cord-018208-sc8j1ate 100 47 infection infection NN cord-018208-sc8j1ate 100 48 rate rate NN cord-018208-sc8j1ate 100 49 τ τ NN cord-018208-sc8j1ate 100 50 is be VBZ cord-018208-sc8j1ate 100 51 large large JJ cord-018208-sc8j1ate 100 52 . . . cord-018208-sc8j1ate 101 1 In in IN cord-018208-sc8j1ate 101 2 order order NN cord-018208-sc8j1ate 101 3 to to TO cord-018208-sc8j1ate 101 4 quantify quantify VB cord-018208-sc8j1ate 101 5 the the DT cord-018208-sc8j1ate 101 6 difference difference NN cord-018208-sc8j1ate 101 7 between between IN cord-018208-sc8j1ate 101 8 the the DT cord-018208-sc8j1ate 101 9 two two CD cord-018208-sc8j1ate 101 10 curves curve NNS cord-018208-sc8j1ate 101 11 obtained obtain VBN cord-018208-sc8j1ate 101 12 by by IN cord-018208-sc8j1ate 101 13 NIMFA NIMFA NNP cord-018208-sc8j1ate 101 14 and and CC cord-018208-sc8j1ate 101 15 simulations simulation NNS cord-018208-sc8j1ate 101 16 , , , cord-018208-sc8j1ate 101 17 we -PRON- PRP cord-018208-sc8j1ate 101 18 define define VBP cord-018208-sc8j1ate 101 19 the the DT cord-018208-sc8j1ate 101 20 variable variable NN cord-018208-sc8j1ate 101 21 ζ ζ NN cord-018208-sc8j1ate 101 22 : : : cord-018208-sc8j1ate 101 23 where where WRB cord-018208-sc8j1ate 101 24 y y NNP cord-018208-sc8j1ate 101 25 ∞,N ∞,N NNP cord-018208-sc8j1ate 101 26 ( ( -LRB- cord-018208-sc8j1ate 101 27 τ τ NN cord-018208-sc8j1ate 101 28 ) ) -RRB- cord-018208-sc8j1ate 102 1 > > XX cord-018208-sc8j1ate 102 2 0 0 NFP cord-018208-sc8j1ate 103 1 and and CC cord-018208-sc8j1ate 103 2 y y NNP cord-018208-sc8j1ate 103 3 ∞,S ∞,S NNP cord-018208-sc8j1ate 103 4 ( ( -LRB- cord-018208-sc8j1ate 103 5 τ τ NN cord-018208-sc8j1ate 103 6 ) ) -RRB- cord-018208-sc8j1ate 103 7 > > NFP cord-018208-sc8j1ate 103 8 0 0 NFP cord-018208-sc8j1ate 103 9 denote denote VBP cord-018208-sc8j1ate 103 10 the the DT cord-018208-sc8j1ate 103 11 average average JJ cord-018208-sc8j1ate 103 12 fraction fraction NN cord-018208-sc8j1ate 103 13 of of IN cord-018208-sc8j1ate 103 14 infected infected JJ cord-018208-sc8j1ate 103 15 nodes node NNS cord-018208-sc8j1ate 103 16 obtained obtain VBN cord-018208-sc8j1ate 103 17 by by IN cord-018208-sc8j1ate 103 18 NIMFA NIMFA NNP cord-018208-sc8j1ate 103 19 and and CC cord-018208-sc8j1ate 103 20 simulations simulation NNS cord-018208-sc8j1ate 103 21 respectively respectively RB cord-018208-sc8j1ate 103 22 . . . cord-018208-sc8j1ate 104 1 The the DT cord-018208-sc8j1ate 104 2 larger large JJR cord-018208-sc8j1ate 104 3 the the DT cord-018208-sc8j1ate 104 4 value value NN cord-018208-sc8j1ate 104 5 of of IN cord-018208-sc8j1ate 104 6 ζ ζ NN cord-018208-sc8j1ate 104 7 ( ( -LRB- cord-018208-sc8j1ate 104 8 τ τ NN cord-018208-sc8j1ate 104 9 ) ) -RRB- cord-018208-sc8j1ate 104 10 is be VBZ cord-018208-sc8j1ate 104 11 , , , cord-018208-sc8j1ate 104 12 the the DT cord-018208-sc8j1ate 104 13 less less RBR cord-018208-sc8j1ate 104 14 accurate accurate JJ cord-018208-sc8j1ate 104 15 NIMFA NIMFA NNP cord-018208-sc8j1ate 104 16 is be VBZ cord-018208-sc8j1ate 104 17 at at IN cord-018208-sc8j1ate 104 18 the the DT cord-018208-sc8j1ate 104 19 corresponding correspond VBG cord-018208-sc8j1ate 104 20 τ τ NN cord-018208-sc8j1ate 104 21 . . . cord-018208-sc8j1ate 105 1 In in IN cord-018208-sc8j1ate 105 2 Fig Fig NNP cord-018208-sc8j1ate 105 3 . . . cord-018208-sc8j1ate 106 1 1b 1b LS cord-018208-sc8j1ate 106 2 , , , cord-018208-sc8j1ate 106 3 the the DT cord-018208-sc8j1ate 106 4 plot plot NN cord-018208-sc8j1ate 106 5 of of IN cord-018208-sc8j1ate 106 6 ζ ζ NN cord-018208-sc8j1ate 106 7 vs. vs. IN cord-018208-sc8j1ate 106 8 τ τ NN cord-018208-sc8j1ate 106 9 is be VBZ cord-018208-sc8j1ate 106 10 shown show VBN cord-018208-sc8j1ate 106 11 for for IN cord-018208-sc8j1ate 106 12 ER ER NNP cord-018208-sc8j1ate 106 13 networks network NNS cord-018208-sc8j1ate 106 14 . . . cord-018208-sc8j1ate 107 1 We -PRON- PRP cord-018208-sc8j1ate 107 2 find find VBP cord-018208-sc8j1ate 107 3 that that IN cord-018208-sc8j1ate 107 4 , , , cord-018208-sc8j1ate 107 5 for for IN cord-018208-sc8j1ate 107 6 a a DT cord-018208-sc8j1ate 107 7 given give VBN cord-018208-sc8j1ate 107 8 effective effective JJ cord-018208-sc8j1ate 107 9 infection infection NN cord-018208-sc8j1ate 107 10 rate rate NN cord-018208-sc8j1ate 107 11 τ τ NN cord-018208-sc8j1ate 107 12 , , , cord-018208-sc8j1ate 107 13 NIMFA NIMFA NNP cord-018208-sc8j1ate 107 14 becomes become VBZ cord-018208-sc8j1ate 107 15 less less RBR cord-018208-sc8j1ate 107 16 accurate accurate JJ cord-018208-sc8j1ate 107 17 when when WRB cord-018208-sc8j1ate 107 18 the the DT cord-018208-sc8j1ate 107 19 variance variance NN cord-018208-sc8j1ate 107 20 of of IN cord-018208-sc8j1ate 107 21 the the DT cord-018208-sc8j1ate 107 22 i.i.d i.i.d NN cord-018208-sc8j1ate 107 23 . . . cord-018208-sc8j1ate 107 24 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 107 25 infection infection NN cord-018208-sc8j1ate 107 26 rates rate NNS cord-018208-sc8j1ate 107 27 increases increase VBZ cord-018208-sc8j1ate 107 28 . . . cord-018208-sc8j1ate 108 1 This this DT cord-018208-sc8j1ate 108 2 observation observation NN cord-018208-sc8j1ate 108 3 can can MD cord-018208-sc8j1ate 108 4 be be VB cord-018208-sc8j1ate 108 5 to to IN cord-018208-sc8j1ate 108 6 a a DT cord-018208-sc8j1ate 108 7 large large JJ cord-018208-sc8j1ate 108 8 extent extent NN cord-018208-sc8j1ate 108 9 explained explain VBN cord-018208-sc8j1ate 108 10 by by IN cord-018208-sc8j1ate 108 11 : : : cord-018208-sc8j1ate 108 12 1 1 LS cord-018208-sc8j1ate 108 13 ) ) -RRB- cord-018208-sc8j1ate 108 14 our -PRON- PRP$ cord-018208-sc8j1ate 108 15 finding finding NN cord-018208-sc8j1ate 108 16 in in IN cord-018208-sc8j1ate 108 17 Fig Fig NNP cord-018208-sc8j1ate 108 18 . . . cord-018208-sc8j1ate 108 19 1a 1a CD cord-018208-sc8j1ate 108 20 that that IN cord-018208-sc8j1ate 108 21 NIMFA NIMFA NNP cord-018208-sc8j1ate 108 22 is be VBZ cord-018208-sc8j1ate 108 23 more more RBR cord-018208-sc8j1ate 108 24 accurate accurate JJ cord-018208-sc8j1ate 108 25 when when WRB cord-018208-sc8j1ate 108 26 the the DT cord-018208-sc8j1ate 108 27 prevalence prevalence NN cord-018208-sc8j1ate 108 28 is be VBZ cord-018208-sc8j1ate 108 29 higher high JJR cord-018208-sc8j1ate 108 30 ; ; : cord-018208-sc8j1ate 108 31 2 2 LS cord-018208-sc8j1ate 108 32 ) ) -RRB- cord-018208-sc8j1ate 108 33 that that WDT cord-018208-sc8j1ate 108 34 given give VBN cord-018208-sc8j1ate 108 35 an an DT cord-018208-sc8j1ate 108 36 effective effective JJ cord-018208-sc8j1ate 108 37 infection infection NN cord-018208-sc8j1ate 108 38 rate rate NN cord-018208-sc8j1ate 108 39 τ τ NN cord-018208-sc8j1ate 108 40 a a DT cord-018208-sc8j1ate 108 41 smaller small JJR cord-018208-sc8j1ate 108 42 variance variance NN cord-018208-sc8j1ate 108 43 of of IN cord-018208-sc8j1ate 108 44 the the DT cord-018208-sc8j1ate 108 45 i.i.d i.i.d NN cord-018208-sc8j1ate 108 46 . . . cord-018208-sc8j1ate 108 47 infection infection NN cord-018208-sc8j1ate 108 48 rates rate VBZ cord-018208-sc8j1ate 108 49 leads lead VBZ cord-018208-sc8j1ate 108 50 to to IN cord-018208-sc8j1ate 108 51 a a DT cord-018208-sc8j1ate 108 52 higher high JJR cord-018208-sc8j1ate 108 53 prevalence prevalence NN cord-018208-sc8j1ate 108 54 [ [ -LRB- cord-018208-sc8j1ate 108 55 15 15 CD cord-018208-sc8j1ate 108 56 ] ] -RRB- cord-018208-sc8j1ate 108 57 . . . cord-018208-sc8j1ate 109 1 We -PRON- PRP cord-018208-sc8j1ate 109 2 observe observe VBP cord-018208-sc8j1ate 109 3 the the DT cord-018208-sc8j1ate 109 4 same same JJ cord-018208-sc8j1ate 109 5 in in IN cord-018208-sc8j1ate 109 6 SF SF NNP cord-018208-sc8j1ate 109 7 networks network NNS cord-018208-sc8j1ate 109 8 , , , cord-018208-sc8j1ate 109 9 and and CC cord-018208-sc8j1ate 109 10 the the DT cord-018208-sc8j1ate 109 11 figures figure NNS cord-018208-sc8j1ate 109 12 , , , cord-018208-sc8j1ate 109 13 which which WDT cord-018208-sc8j1ate 109 14 can can MD cord-018208-sc8j1ate 109 15 be be VB cord-018208-sc8j1ate 109 16 found find VBN cord-018208-sc8j1ate 109 17 in in IN cord-018208-sc8j1ate 109 18 [ [ -LRB- cord-018208-sc8j1ate 109 19 16 16 CD cord-018208-sc8j1ate 109 20 ] ] -RRB- cord-018208-sc8j1ate 109 21 , , , cord-018208-sc8j1ate 109 22 are be VBP cord-018208-sc8j1ate 109 23 not not RB cord-018208-sc8j1ate 109 24 shown show VBN cord-018208-sc8j1ate 109 25 here here RB cord-018208-sc8j1ate 109 26 due due IN cord-018208-sc8j1ate 109 27 to to IN cord-018208-sc8j1ate 109 28 the the DT cord-018208-sc8j1ate 109 29 page page NN cord-018208-sc8j1ate 109 30 limit limit NN cord-018208-sc8j1ate 109 31 . . . cord-018208-sc8j1ate 110 1 We -PRON- PRP cord-018208-sc8j1ate 110 2 further further RB cord-018208-sc8j1ate 110 3 explore explore VBP cord-018208-sc8j1ate 110 4 how how WRB cord-018208-sc8j1ate 110 5 the the DT cord-018208-sc8j1ate 110 6 variance variance NN cord-018208-sc8j1ate 110 7 of of IN cord-018208-sc8j1ate 110 8 the the DT cord-018208-sc8j1ate 110 9 infection infection NN cord-018208-sc8j1ate 110 10 rates rate VBZ cord-018208-sc8j1ate 110 11 influences influence VBZ cord-018208-sc8j1ate 110 12 the the DT cord-018208-sc8j1ate 110 13 accuracy accuracy NN cord-018208-sc8j1ate 110 14 of of IN cord-018208-sc8j1ate 110 15 NIMFA NIMFA NNP cord-018208-sc8j1ate 110 16 if if IN cord-018208-sc8j1ate 110 17 the the DT cord-018208-sc8j1ate 110 18 actual actual JJ cord-018208-sc8j1ate 110 19 prevalence prevalence NN cord-018208-sc8j1ate 110 20 y y NNP cord-018208-sc8j1ate 110 21 ∞,S ∞,s NN cord-018208-sc8j1ate 110 22 ( ( -LRB- cord-018208-sc8j1ate 110 23 τ τ NN cord-018208-sc8j1ate 110 24 ) ) -RRB- cord-018208-sc8j1ate 110 25 of of IN cord-018208-sc8j1ate 110 26 epidemic epidemic NN cord-018208-sc8j1ate 110 27 is be VBZ cord-018208-sc8j1ate 110 28 similar similar JJ cord-018208-sc8j1ate 110 29 . . . cord-018208-sc8j1ate 111 1 We -PRON- PRP cord-018208-sc8j1ate 111 2 plot plot VBP cord-018208-sc8j1ate 111 3 the the DT cord-018208-sc8j1ate 111 4 variable variable NN cord-018208-sc8j1ate 111 5 ζ ζ NN cord-018208-sc8j1ate 111 6 in in IN cord-018208-sc8j1ate 111 7 ( ( -LRB- cord-018208-sc8j1ate 111 8 6 6 CD cord-018208-sc8j1ate 111 9 ) ) -RRB- cord-018208-sc8j1ate 111 10 as as IN cord-018208-sc8j1ate 111 11 a a DT cord-018208-sc8j1ate 111 12 function function NN cord-018208-sc8j1ate 111 13 of of IN cord-018208-sc8j1ate 111 14 the the DT cord-018208-sc8j1ate 111 15 actual actual JJ cord-018208-sc8j1ate 111 16 average average JJ cord-018208-sc8j1ate 111 17 fraction fraction NN cord-018208-sc8j1ate 111 18 of of IN cord-018208-sc8j1ate 111 19 infected infected JJ cord-018208-sc8j1ate 111 20 nodes node NNS cord-018208-sc8j1ate 111 21 obtained obtain VBN cord-018208-sc8j1ate 111 22 by by IN cord-018208-sc8j1ate 111 23 simulations simulation NNS cord-018208-sc8j1ate 111 24 in in IN cord-018208-sc8j1ate 111 25 Fig Fig NNP cord-018208-sc8j1ate 111 26 . . . cord-018208-sc8j1ate 112 1 2 2 LS cord-018208-sc8j1ate 112 2 . . . cord-018208-sc8j1ate 113 1 We -PRON- PRP cord-018208-sc8j1ate 113 2 find find VBP cord-018208-sc8j1ate 113 3 that that IN cord-018208-sc8j1ate 113 4 though though IN cord-018208-sc8j1ate 113 5 it -PRON- PRP cord-018208-sc8j1ate 113 6 is be VBZ cord-018208-sc8j1ate 113 7 less less RBR cord-018208-sc8j1ate 113 8 evident evident JJ cord-018208-sc8j1ate 113 9 for for IN cord-018208-sc8j1ate 113 10 ER ER NNP cord-018208-sc8j1ate 113 11 networks network NNS cord-018208-sc8j1ate 113 12 in in IN cord-018208-sc8j1ate 113 13 Fig Fig NNP cord-018208-sc8j1ate 113 14 . . . cord-018208-sc8j1ate 114 1 2a 2a LS cord-018208-sc8j1ate 114 2 , , , cord-018208-sc8j1ate 114 3 the the DT cord-018208-sc8j1ate 114 4 difference difference NN cord-018208-sc8j1ate 114 5 ζ ζ NN cord-018208-sc8j1ate 114 6 in in IN cord-018208-sc8j1ate 114 7 ( ( -LRB- cord-018208-sc8j1ate 114 8 6 6 CD cord-018208-sc8j1ate 114 9 ) ) -RRB- cord-018208-sc8j1ate 114 10 is be VBZ cord-018208-sc8j1ate 114 11 actually actually RB cord-018208-sc8j1ate 114 12 larger large JJR cord-018208-sc8j1ate 114 13 if if IN cord-018208-sc8j1ate 114 14 the the DT cord-018208-sc8j1ate 114 15 variance variance NN cord-018208-sc8j1ate 114 16 of of IN cord-018208-sc8j1ate 114 17 the the DT cord-018208-sc8j1ate 114 18 infection infection NN cord-018208-sc8j1ate 114 19 rate rate NN cord-018208-sc8j1ate 114 20 is be VBZ cord-018208-sc8j1ate 114 21 larger large JJR cord-018208-sc8j1ate 114 22 as as IN cord-018208-sc8j1ate 114 23 shown show VBN cord-018208-sc8j1ate 114 24 in in IN cord-018208-sc8j1ate 114 25 Fig Fig NNP cord-018208-sc8j1ate 114 26 . . . cord-018208-sc8j1ate 115 1 2b 2b NNP cord-018208-sc8j1ate 115 2 for for IN cord-018208-sc8j1ate 115 3 SF SF NNP cord-018208-sc8j1ate 115 4 networks network NNS cord-018208-sc8j1ate 115 5 when when WRB cord-018208-sc8j1ate 115 6 the the DT cord-018208-sc8j1ate 115 7 prevalence prevalence NN cord-018208-sc8j1ate 115 8 is be VBZ cord-018208-sc8j1ate 115 9 the the DT cord-018208-sc8j1ate 115 10 same same JJ cord-018208-sc8j1ate 115 11 . . . cord-018208-sc8j1ate 116 1 Hence hence RB cord-018208-sc8j1ate 116 2 , , , cord-018208-sc8j1ate 116 3 the the DT cord-018208-sc8j1ate 116 4 higher high JJR cord-018208-sc8j1ate 116 5 heterogeneity heterogeneity NN cord-018208-sc8j1ate 116 6 , , , cord-018208-sc8j1ate 116 7 i.e. i.e. FW cord-018208-sc8j1ate 116 8 the the DT cord-018208-sc8j1ate 116 9 larger large JJR cord-018208-sc8j1ate 116 10 variance variance NN cord-018208-sc8j1ate 116 11 , , , cord-018208-sc8j1ate 116 12 of of IN cord-018208-sc8j1ate 116 13 the the DT cord-018208-sc8j1ate 116 14 i.i.d i.i.d NN cord-018208-sc8j1ate 116 15 . . . cord-018208-sc8j1ate 116 16 infection infection NN cord-018208-sc8j1ate 116 17 rates rate NNS cord-018208-sc8j1ate 116 18 tends tend VBZ cord-018208-sc8j1ate 116 19 to to TO cord-018208-sc8j1ate 116 20 lower lower VB cord-018208-sc8j1ate 116 21 down down RP cord-018208-sc8j1ate 116 22 more more RBR cord-018208-sc8j1ate 116 23 the the DT cord-018208-sc8j1ate 116 24 accuracy accuracy NN cord-018208-sc8j1ate 116 25 of of IN cord-018208-sc8j1ate 116 26 NIMFA NIMFA NNP cord-018208-sc8j1ate 116 27 . . . cord-018208-sc8j1ate 117 1 Overall overall RB cord-018208-sc8j1ate 117 2 , , , cord-018208-sc8j1ate 117 3 we -PRON- PRP cord-018208-sc8j1ate 117 4 conclude conclude VBP cord-018208-sc8j1ate 117 5 that that IN cord-018208-sc8j1ate 117 6 the the DT cord-018208-sc8j1ate 117 7 prevalence prevalence NN cord-018208-sc8j1ate 117 8 of of IN cord-018208-sc8j1ate 117 9 the the DT cord-018208-sc8j1ate 117 10 epidemic epidemic NN cord-018208-sc8j1ate 117 11 mainly mainly RB cord-018208-sc8j1ate 117 12 affects affect VBZ cord-018208-sc8j1ate 117 13 the the DT cord-018208-sc8j1ate 117 14 accuracy accuracy NN cord-018208-sc8j1ate 117 15 of of IN cord-018208-sc8j1ate 117 16 NIMFA NIMFA NNP cord-018208-sc8j1ate 117 17 , , , cord-018208-sc8j1ate 117 18 i.e. i.e. FW cord-018208-sc8j1ate 117 19 the the DT cord-018208-sc8j1ate 117 20 higher high JJR cord-018208-sc8j1ate 117 21 the the DT cord-018208-sc8j1ate 117 22 prevalence prevalence NN cord-018208-sc8j1ate 117 23 is be VBZ cord-018208-sc8j1ate 117 24 , , , cord-018208-sc8j1ate 117 25 the the DT cord-018208-sc8j1ate 117 26 more more RBR cord-018208-sc8j1ate 117 27 accurate accurate JJ cord-018208-sc8j1ate 117 28 NIMFA NIMFA NNP cord-018208-sc8j1ate 117 29 tends tend VBZ cord-018208-sc8j1ate 117 30 to to TO cord-018208-sc8j1ate 117 31 be be VB cord-018208-sc8j1ate 117 32 , , , cord-018208-sc8j1ate 117 33 and and CC cord-018208-sc8j1ate 117 34 given give VBN cord-018208-sc8j1ate 117 35 the the DT cord-018208-sc8j1ate 117 36 same same JJ cord-018208-sc8j1ate 117 37 prevalence prevalence NN cord-018208-sc8j1ate 117 38 , , , cord-018208-sc8j1ate 117 39 a a DT cord-018208-sc8j1ate 117 40 larger large JJR cord-018208-sc8j1ate 117 41 variance variance NN cord-018208-sc8j1ate 117 42 of of IN cord-018208-sc8j1ate 117 43 the the DT cord-018208-sc8j1ate 117 44 i.i.d i.i.d NN cord-018208-sc8j1ate 117 45 . . . cord-018208-sc8j1ate 117 46 infection infection NN cord-018208-sc8j1ate 117 47 rates rate NNS cord-018208-sc8j1ate 117 48 tends tend VBZ cord-018208-sc8j1ate 117 49 to to TO cord-018208-sc8j1ate 117 50 lower lower VB cord-018208-sc8j1ate 117 51 down down IN cord-018208-sc8j1ate 117 52 the the DT cord-018208-sc8j1ate 117 53 accuracy accuracy NN cord-018208-sc8j1ate 117 54 of of IN cord-018208-sc8j1ate 117 55 NIMFA NIMFA NNP cord-018208-sc8j1ate 117 56 . . . cord-018208-sc8j1ate 117 57 _SP cord-018208-sc8j1ate 118 1 In in IN cord-018208-sc8j1ate 118 2 this this DT cord-018208-sc8j1ate 118 3 subsection subsection NN cord-018208-sc8j1ate 118 4 , , , cord-018208-sc8j1ate 118 5 we -PRON- PRP cord-018208-sc8j1ate 118 6 aim aim VBP cord-018208-sc8j1ate 118 7 to to TO cord-018208-sc8j1ate 118 8 understand understand VB cord-018208-sc8j1ate 118 9 how how WRB cord-018208-sc8j1ate 118 10 the the DT cord-018208-sc8j1ate 118 11 correlation correlation NN cord-018208-sc8j1ate 118 12 between between IN cord-018208-sc8j1ate 118 13 the the DT cord-018208-sc8j1ate 118 14 infection infection NN cord-018208-sc8j1ate 118 15 rate rate NN cord-018208-sc8j1ate 118 16 and and CC cord-018208-sc8j1ate 118 17 the the DT cord-018208-sc8j1ate 118 18 nodal nodal JJ cord-018208-sc8j1ate 118 19 degree degree NN cord-018208-sc8j1ate 118 20 as as IN cord-018208-sc8j1ate 118 21 shown show VBN cord-018208-sc8j1ate 118 22 in in IN cord-018208-sc8j1ate 118 23 ( ( -LRB- cord-018208-sc8j1ate 118 24 5 5 CD cord-018208-sc8j1ate 118 25 ) ) -RRB- cord-018208-sc8j1ate 118 26 influences influence VBZ cord-018208-sc8j1ate 118 27 the the DT cord-018208-sc8j1ate 118 28 accuracy accuracy NN cord-018208-sc8j1ate 118 29 of of IN cord-018208-sc8j1ate 118 30 NIMFA NIMFA NNP cord-018208-sc8j1ate 118 31 . . . cord-018208-sc8j1ate 119 1 We -PRON- PRP cord-018208-sc8j1ate 119 2 first first RB cord-018208-sc8j1ate 119 3 employ employ VBP cord-018208-sc8j1ate 119 4 ER ER NNP cord-018208-sc8j1ate 119 5 networks network NNS cord-018208-sc8j1ate 119 6 as as IN cord-018208-sc8j1ate 119 7 an an DT cord-018208-sc8j1ate 119 8 example example NN cord-018208-sc8j1ate 119 9 and and CC cord-018208-sc8j1ate 119 10 discuss discuss VB cord-018208-sc8j1ate 119 11 the the DT cord-018208-sc8j1ate 119 12 case case NN cord-018208-sc8j1ate 119 13 when when WRB cord-018208-sc8j1ate 119 14 the the DT cord-018208-sc8j1ate 119 15 correlation correlation NN cord-018208-sc8j1ate 119 16 is be VBZ cord-018208-sc8j1ate 119 17 positive positive JJ cord-018208-sc8j1ate 119 18 . . . cord-018208-sc8j1ate 120 1 Afterwards afterwards RB cord-018208-sc8j1ate 120 2 we -PRON- PRP cord-018208-sc8j1ate 120 3 explore explore VBP cord-018208-sc8j1ate 120 4 the the DT cord-018208-sc8j1ate 120 5 influence influence NN cord-018208-sc8j1ate 120 6 of of IN cord-018208-sc8j1ate 120 7 the the DT cord-018208-sc8j1ate 120 8 negative negative JJ cord-018208-sc8j1ate 120 9 correlation correlation NN cord-018208-sc8j1ate 120 10 . . . cord-018208-sc8j1ate 121 1 As as IN cord-018208-sc8j1ate 121 2 mentioned mention VBN cord-018208-sc8j1ate 121 3 in in IN cord-018208-sc8j1ate 121 4 Section section NN cord-018208-sc8j1ate 121 5 2.3 2.3 CD cord-018208-sc8j1ate 121 6 , , , cord-018208-sc8j1ate 121 7 we -PRON- PRP cord-018208-sc8j1ate 121 8 build build VBP cord-018208-sc8j1ate 121 9 the the DT cord-018208-sc8j1ate 121 10 scenario scenario NN cord-018208-sc8j1ate 121 11 of of IN cord-018208-sc8j1ate 121 12 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 121 13 infection infection NN cord-018208-sc8j1ate 121 14 rates rate NNS cord-018208-sc8j1ate 121 15 as as IN cord-018208-sc8j1ate 121 16 a a DT cord-018208-sc8j1ate 121 17 reference reference NN cord-018208-sc8j1ate 121 18 to to TO cord-018208-sc8j1ate 121 19 study study VB cord-018208-sc8j1ate 121 20 the the DT cord-018208-sc8j1ate 121 21 influence influence NN cord-018208-sc8j1ate 121 22 of of IN cord-018208-sc8j1ate 121 23 the the DT cord-018208-sc8j1ate 121 24 correlation correlation NN cord-018208-sc8j1ate 121 25 between between IN cord-018208-sc8j1ate 121 26 the the DT cord-018208-sc8j1ate 121 27 infection infection NN cord-018208-sc8j1ate 121 28 rate rate NN cord-018208-sc8j1ate 121 29 and and CC cord-018208-sc8j1ate 121 30 the the DT cord-018208-sc8j1ate 121 31 nodal nodal JJ cord-018208-sc8j1ate 121 32 degree degree NN cord-018208-sc8j1ate 121 33 by by IN cord-018208-sc8j1ate 121 34 shuffling shuffle VBG cord-018208-sc8j1ate 121 35 the the DT cord-018208-sc8j1ate 121 36 infection infection NN cord-018208-sc8j1ate 121 37 rates rate NNS cord-018208-sc8j1ate 121 38 from from IN cord-018208-sc8j1ate 121 39 all all PDT cord-018208-sc8j1ate 121 40 the the DT cord-018208-sc8j1ate 121 41 links link NNS cord-018208-sc8j1ate 121 42 as as IN cord-018208-sc8j1ate 121 43 generated generate VBN cord-018208-sc8j1ate 121 44 in in IN cord-018208-sc8j1ate 121 45 the the DT cord-018208-sc8j1ate 121 46 scenario scenario NN cord-018208-sc8j1ate 121 47 of of IN cord-018208-sc8j1ate 121 48 correlated correlate VBN cord-018208-sc8j1ate 121 49 infection infection NN cord-018208-sc8j1ate 121 50 rates rate NNS cord-018208-sc8j1ate 121 51 and and CC cord-018208-sc8j1ate 121 52 redistributing redistribute VBG cord-018208-sc8j1ate 121 53 them -PRON- PRP cord-018208-sc8j1ate 121 54 randomly randomly RB cord-018208-sc8j1ate 121 55 to to IN cord-018208-sc8j1ate 121 56 all all PDT cord-018208-sc8j1ate 121 57 the the DT cord-018208-sc8j1ate 121 58 links link NNS cord-018208-sc8j1ate 121 59 . . . cord-018208-sc8j1ate 122 1 As as IN cord-018208-sc8j1ate 122 2 shown show VBN cord-018208-sc8j1ate 122 3 in in IN cord-018208-sc8j1ate 122 4 Fig Fig NNP cord-018208-sc8j1ate 122 5 . . . cord-018208-sc8j1ate 123 1 3a 3a NNP cord-018208-sc8j1ate 123 2 , , , cord-018208-sc8j1ate 123 3 we -PRON- PRP cord-018208-sc8j1ate 123 4 compare compare VBP cord-018208-sc8j1ate 123 5 the the DT cord-018208-sc8j1ate 123 6 difference difference NN cord-018208-sc8j1ate 123 7 ζ ζ NN cord-018208-sc8j1ate 123 8 between between IN cord-018208-sc8j1ate 123 9 NIMFA NIMFA NNP cord-018208-sc8j1ate 123 10 and and CC cord-018208-sc8j1ate 123 11 simulations simulation NNS cord-018208-sc8j1ate 123 12 in in IN cord-018208-sc8j1ate 123 13 the the DT cord-018208-sc8j1ate 123 14 scenario scenario NN cord-018208-sc8j1ate 123 15 of of IN cord-018208-sc8j1ate 123 16 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 123 17 and and CC cord-018208-sc8j1ate 123 18 correlated correlated JJ cord-018208-sc8j1ate 123 19 infection infection NN cord-018208-sc8j1ate 123 20 rates rate NNS cord-018208-sc8j1ate 123 21 for for IN cord-018208-sc8j1ate 123 22 both both CC cord-018208-sc8j1ate 123 23 α α NN cord-018208-sc8j1ate 123 24 = = SYM cord-018208-sc8j1ate 123 25 0.25 0.25 CD cord-018208-sc8j1ate 123 26 and and CC cord-018208-sc8j1ate 123 27 α α NN cord-018208-sc8j1ate 123 28 = = SYM cord-018208-sc8j1ate 123 29 1 1 CD cord-018208-sc8j1ate 123 30 , , , cord-018208-sc8j1ate 123 31 and and CC cord-018208-sc8j1ate 123 32 find find VB cord-018208-sc8j1ate 123 33 that that DT cord-018208-sc8j1ate 123 34 ζ ζ NN cord-018208-sc8j1ate 123 35 is be VBZ cord-018208-sc8j1ate 123 36 smaller small JJR cord-018208-sc8j1ate 123 37 in in IN cord-018208-sc8j1ate 123 38 the the DT cord-018208-sc8j1ate 123 39 scenario scenario NN cord-018208-sc8j1ate 123 40 of of IN cord-018208-sc8j1ate 123 41 correlated correlate VBN cord-018208-sc8j1ate 123 42 infection infection NN cord-018208-sc8j1ate 123 43 rates rate NNS cord-018208-sc8j1ate 123 44 , , , cord-018208-sc8j1ate 123 45 i.e. i.e. FW cord-018208-sc8j1ate 123 46 NIMFA NIMFA NNP cord-018208-sc8j1ate 123 47 is be VBZ cord-018208-sc8j1ate 123 48 more more RBR cord-018208-sc8j1ate 123 49 accurate accurate JJ cord-018208-sc8j1ate 123 50 at at IN cord-018208-sc8j1ate 123 51 a a DT cord-018208-sc8j1ate 123 52 given give VBN cord-018208-sc8j1ate 123 53 effective effective JJ cord-018208-sc8j1ate 123 54 infection infection NN cord-018208-sc8j1ate 123 55 rate rate NN cord-018208-sc8j1ate 123 56 τ τ NN cord-018208-sc8j1ate 123 57 when when WRB cord-018208-sc8j1ate 123 58 the the DT cord-018208-sc8j1ate 123 59 correlation correlation NN cord-018208-sc8j1ate 123 60 between between IN cord-018208-sc8j1ate 123 61 the the DT cord-018208-sc8j1ate 123 62 infection infection NN cord-018208-sc8j1ate 123 63 rate rate NN cord-018208-sc8j1ate 123 64 and and CC cord-018208-sc8j1ate 123 65 the the DT cord-018208-sc8j1ate 123 66 nodal nodal JJ cord-018208-sc8j1ate 123 67 degree degree NN cord-018208-sc8j1ate 123 68 is be VBZ cord-018208-sc8j1ate 123 69 positive positive JJ cord-018208-sc8j1ate 123 70 comparing compare VBG cord-018208-sc8j1ate 123 71 to to IN cord-018208-sc8j1ate 123 72 the the DT cord-018208-sc8j1ate 123 73 scenario scenario NN cord-018208-sc8j1ate 123 74 of of IN cord-018208-sc8j1ate 123 75 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 123 76 infection infection NN cord-018208-sc8j1ate 123 77 rates rate NNS cord-018208-sc8j1ate 123 78 . . . cord-018208-sc8j1ate 124 1 The the DT cord-018208-sc8j1ate 124 2 observations observation NNS cord-018208-sc8j1ate 124 3 are be VBP cord-018208-sc8j1ate 124 4 also also RB cord-018208-sc8j1ate 124 5 consistent consistent JJ cord-018208-sc8j1ate 124 6 with with IN cord-018208-sc8j1ate 124 7 our -PRON- PRP$ cord-018208-sc8j1ate 124 8 conclusion conclusion NN cord-018208-sc8j1ate 124 9 that that IN cord-018208-sc8j1ate 124 10 NIMFA NIMFA NNP cord-018208-sc8j1ate 124 11 is be VBZ cord-018208-sc8j1ate 124 12 more more RBR cord-018208-sc8j1ate 124 13 accurate accurate JJ cord-018208-sc8j1ate 124 14 when when WRB cord-018208-sc8j1ate 124 15 the the DT cord-018208-sc8j1ate 124 16 prevalence prevalence NN cord-018208-sc8j1ate 124 17 is be VBZ cord-018208-sc8j1ate 124 18 higher high JJR cord-018208-sc8j1ate 124 19 : : : cord-018208-sc8j1ate 124 20 the the DT cord-018208-sc8j1ate 124 21 positive positive JJ cord-018208-sc8j1ate 124 22 correlation correlation NN cord-018208-sc8j1ate 124 23 tends tend VBZ cord-018208-sc8j1ate 124 24 to to TO cord-018208-sc8j1ate 124 25 increase increase VB cord-018208-sc8j1ate 124 26 the the DT cord-018208-sc8j1ate 124 27 average average JJ cord-018208-sc8j1ate 124 28 fraction fraction NN cord-018208-sc8j1ate 124 29 of of IN cord-018208-sc8j1ate 124 30 infected infected JJ cord-018208-sc8j1ate 124 31 nodes node NNS cord-018208-sc8j1ate 124 32 [ [ -LRB- cord-018208-sc8j1ate 124 33 17 17 CD cord-018208-sc8j1ate 124 34 ] ] -RRB- cord-018208-sc8j1ate 124 35 , , , cord-018208-sc8j1ate 124 36 and and CC cord-018208-sc8j1ate 124 37 thus thus RB cord-018208-sc8j1ate 124 38 the the DT cord-018208-sc8j1ate 124 39 accuracy accuracy NN cord-018208-sc8j1ate 124 40 of of IN cord-018208-sc8j1ate 124 41 NIMFA NIMFA NNP cord-018208-sc8j1ate 124 42 , , , cord-018208-sc8j1ate 124 43 when when WRB cord-018208-sc8j1ate 124 44 the the DT cord-018208-sc8j1ate 124 45 effective effective JJ cord-018208-sc8j1ate 124 46 infection infection NN cord-018208-sc8j1ate 124 47 rate rate NN cord-018208-sc8j1ate 124 48 τ τ NN cord-018208-sc8j1ate 124 49 is be VBZ cord-018208-sc8j1ate 124 50 small small JJ cord-018208-sc8j1ate 124 51 ; ; : cord-018208-sc8j1ate 124 52 however however RB cord-018208-sc8j1ate 124 53 , , , cord-018208-sc8j1ate 124 54 when when WRB cord-018208-sc8j1ate 124 55 the the DT cord-018208-sc8j1ate 124 56 effective effective JJ cord-018208-sc8j1ate 124 57 infection infection NN cord-018208-sc8j1ate 124 58 rate rate NN cord-018208-sc8j1ate 124 59 τ τ NN cord-018208-sc8j1ate 124 60 is be VBZ cord-018208-sc8j1ate 124 61 large large JJ cord-018208-sc8j1ate 124 62 , , , cord-018208-sc8j1ate 124 63 though though IN cord-018208-sc8j1ate 124 64 the the DT cord-018208-sc8j1ate 124 65 positive positive JJ cord-018208-sc8j1ate 124 66 correlate correlate VBP cord-018208-sc8j1ate 124 67 may may MD cord-018208-sc8j1ate 124 68 lower lower VB cord-018208-sc8j1ate 124 69 down down IN cord-018208-sc8j1ate 124 70 a a DT cord-018208-sc8j1ate 124 71 bit bit NN cord-018208-sc8j1ate 124 72 the the DT cord-018208-sc8j1ate 124 73 average average JJ cord-018208-sc8j1ate 124 74 fraction fraction NN cord-018208-sc8j1ate 124 75 y y NNP cord-018208-sc8j1ate 124 76 ∞ ∞ NNP cord-018208-sc8j1ate 124 77 of of IN cord-018208-sc8j1ate 124 78 infected infected JJ cord-018208-sc8j1ate 124 79 nodes node NNS cord-018208-sc8j1ate 124 80 , , , cord-018208-sc8j1ate 124 81 the the DT cord-018208-sc8j1ate 124 82 prevalence prevalence NN cord-018208-sc8j1ate 124 83 in in IN cord-018208-sc8j1ate 124 84 both both DT cord-018208-sc8j1ate 124 85 scenarios scenario NNS cord-018208-sc8j1ate 124 86 is be VBZ cord-018208-sc8j1ate 124 87 high high JJ cord-018208-sc8j1ate 124 88 , , , cord-018208-sc8j1ate 124 89 i.e. i.e. FW cord-018208-sc8j1ate 124 90 NIMFA NIMFA NNP cord-018208-sc8j1ate 124 91 is be VBZ cord-018208-sc8j1ate 124 92 relatively relatively RB cord-018208-sc8j1ate 124 93 accurate accurate JJ cord-018208-sc8j1ate 124 94 , , , cord-018208-sc8j1ate 124 95 and and CC cord-018208-sc8j1ate 124 96 the the DT cord-018208-sc8j1ate 124 97 difference difference NN cord-018208-sc8j1ate 124 98 of of IN cord-018208-sc8j1ate 124 99 the the DT cord-018208-sc8j1ate 124 100 accuracy accuracy NN cord-018208-sc8j1ate 124 101 of of IN cord-018208-sc8j1ate 124 102 NIMFA NIMFA NNP cord-018208-sc8j1ate 124 103 in in IN cord-018208-sc8j1ate 124 104 the the DT cord-018208-sc8j1ate 124 105 two two CD cord-018208-sc8j1ate 124 106 scenarios scenario NNS cord-018208-sc8j1ate 124 107 is be VBZ cord-018208-sc8j1ate 124 108 not not RB cord-018208-sc8j1ate 124 109 obvious obvious JJ cord-018208-sc8j1ate 124 110 . . . cord-018208-sc8j1ate 125 1 As as IN cord-018208-sc8j1ate 125 2 the the DT cord-018208-sc8j1ate 125 3 correlation correlation NN cord-018208-sc8j1ate 125 4 strength strength NN cord-018208-sc8j1ate 125 5 α α NN cord-018208-sc8j1ate 125 6 increases increase NNS cord-018208-sc8j1ate 125 7 in in IN cord-018208-sc8j1ate 125 8 Fig Fig NNP cord-018208-sc8j1ate 125 9 . . . cord-018208-sc8j1ate 126 1 3b 3b NNP cord-018208-sc8j1ate 126 2 , , , cord-018208-sc8j1ate 126 3 the the DT cord-018208-sc8j1ate 126 4 difference difference NN cord-018208-sc8j1ate 126 5 ζ ζ NN cord-018208-sc8j1ate 126 6 decreases decrease VBZ cord-018208-sc8j1ate 126 7 at at IN cord-018208-sc8j1ate 126 8 a a DT cord-018208-sc8j1ate 126 9 given give VBN cord-018208-sc8j1ate 126 10 τ τ NN cord-018208-sc8j1ate 126 11 . . . cord-018208-sc8j1ate 127 1 That that DT cord-018208-sc8j1ate 127 2 is be VBZ cord-018208-sc8j1ate 127 3 to to TO cord-018208-sc8j1ate 127 4 say say VB cord-018208-sc8j1ate 127 5 , , , cord-018208-sc8j1ate 127 6 NIMFA NIMFA NNP cord-018208-sc8j1ate 127 7 tends tend VBZ cord-018208-sc8j1ate 127 8 to to TO cord-018208-sc8j1ate 127 9 be be VB cord-018208-sc8j1ate 127 10 more more RBR cord-018208-sc8j1ate 127 11 accurate accurate JJ cord-018208-sc8j1ate 127 12 when when WRB cord-018208-sc8j1ate 127 13 the the DT cord-018208-sc8j1ate 127 14 positive positive JJ cord-018208-sc8j1ate 127 15 correlation correlation NN cord-018208-sc8j1ate 127 16 becomes become VBZ cord-018208-sc8j1ate 127 17 stronger strong JJR cord-018208-sc8j1ate 127 18 . . . cord-018208-sc8j1ate 128 1 We -PRON- PRP cord-018208-sc8j1ate 128 2 further further RB cord-018208-sc8j1ate 128 3 consider consider VBP cord-018208-sc8j1ate 128 4 the the DT cord-018208-sc8j1ate 128 5 influence influence NN cord-018208-sc8j1ate 128 6 of of IN cord-018208-sc8j1ate 128 7 the the DT cord-018208-sc8j1ate 128 8 positive positive JJ cord-018208-sc8j1ate 128 9 correlation correlation NN cord-018208-sc8j1ate 128 10 on on IN cord-018208-sc8j1ate 128 11 the the DT cord-018208-sc8j1ate 128 12 accuracy accuracy NN cord-018208-sc8j1ate 128 13 of of IN cord-018208-sc8j1ate 128 14 NIMFA NIMFA NNP cord-018208-sc8j1ate 128 15 when when WRB cord-018208-sc8j1ate 128 16 the the DT cord-018208-sc8j1ate 128 17 prevalence prevalence NN cord-018208-sc8j1ate 128 18 is be VBZ cord-018208-sc8j1ate 128 19 the the DT cord-018208-sc8j1ate 128 20 same same JJ cord-018208-sc8j1ate 128 21 . . . cord-018208-sc8j1ate 129 1 The the DT cord-018208-sc8j1ate 129 2 plots plot NNS cord-018208-sc8j1ate 129 3 of of IN cord-018208-sc8j1ate 129 4 the the DT cord-018208-sc8j1ate 129 5 difference difference NN cord-018208-sc8j1ate 129 6 ζ ζ NN cord-018208-sc8j1ate 129 7 as as IN cord-018208-sc8j1ate 129 8 a a DT cord-018208-sc8j1ate 129 9 function function NN cord-018208-sc8j1ate 129 10 of of IN cord-018208-sc8j1ate 129 11 the the DT cord-018208-sc8j1ate 129 12 average average JJ cord-018208-sc8j1ate 129 13 fraction fraction NN cord-018208-sc8j1ate 130 1 y y NNP cord-018208-sc8j1ate 130 2 ∞ ∞ NNP cord-018208-sc8j1ate 130 3 of of IN cord-018208-sc8j1ate 130 4 infected infected JJ cord-018208-sc8j1ate 130 5 nodes node NNS cord-018208-sc8j1ate 130 6 are be VBP cord-018208-sc8j1ate 130 7 shown show VBN cord-018208-sc8j1ate 130 8 in in IN cord-018208-sc8j1ate 130 9 Fig Fig NNP cord-018208-sc8j1ate 130 10 . . . cord-018208-sc8j1ate 131 1 3c 3c NNP cord-018208-sc8j1ate 131 2 and and CC cord-018208-sc8j1ate 131 3 Fig Fig NNP cord-018208-sc8j1ate 131 4 . . NNP cord-018208-sc8j1ate 131 5 3d 3d NNP cord-018208-sc8j1ate 131 6 . . . cord-018208-sc8j1ate 132 1 Given give VBN cord-018208-sc8j1ate 132 2 the the DT cord-018208-sc8j1ate 132 3 prevalence prevalence NN cord-018208-sc8j1ate 132 4 of of IN cord-018208-sc8j1ate 132 5 epidemic epidemic NN cord-018208-sc8j1ate 132 6 , , , cord-018208-sc8j1ate 132 7 the the DT cord-018208-sc8j1ate 132 8 positive positive JJ cord-018208-sc8j1ate 132 9 correlation correlation NN cord-018208-sc8j1ate 132 10 is be VBZ cord-018208-sc8j1ate 132 11 more more RBR cord-018208-sc8j1ate 132 12 likely likely JJ cord-018208-sc8j1ate 132 13 to to TO cord-018208-sc8j1ate 132 14 increase increase VB cord-018208-sc8j1ate 132 15 the the DT cord-018208-sc8j1ate 132 16 precision precision NN cord-018208-sc8j1ate 132 17 of of IN cord-018208-sc8j1ate 132 18 NIMFA NIMFA NNP cord-018208-sc8j1ate 132 19 and and CC cord-018208-sc8j1ate 132 20 the the DT cord-018208-sc8j1ate 132 21 stronger strong JJR cord-018208-sc8j1ate 133 1 the the DT cord-018208-sc8j1ate 133 2 correlation correlation NN cord-018208-sc8j1ate 133 3 is be VBZ cord-018208-sc8j1ate 133 4 the the DT cord-018208-sc8j1ate 133 5 more more RBR cord-018208-sc8j1ate 133 6 accurate accurate JJ cord-018208-sc8j1ate 133 7 NIMFA NIMFA NNP cord-018208-sc8j1ate 133 8 is be VBZ cord-018208-sc8j1ate 133 9 . . . cord-018208-sc8j1ate 134 1 We -PRON- PRP cord-018208-sc8j1ate 134 2 observe observe VBP cord-018208-sc8j1ate 134 3 the the DT cord-018208-sc8j1ate 134 4 same same JJ cord-018208-sc8j1ate 134 5 on on IN cord-018208-sc8j1ate 134 6 SF SF NNP cord-018208-sc8j1ate 134 7 networks network NNS cord-018208-sc8j1ate 134 8 which which WDT cord-018208-sc8j1ate 134 9 is be VBZ cord-018208-sc8j1ate 134 10 though though IN cord-018208-sc8j1ate 134 11 not not RB cord-018208-sc8j1ate 134 12 shown show VBN cord-018208-sc8j1ate 134 13 here here RB cord-018208-sc8j1ate 134 14 . . . cord-018208-sc8j1ate 135 1 Regarding regard VBG cord-018208-sc8j1ate 135 2 to to IN cord-018208-sc8j1ate 135 3 the the DT cord-018208-sc8j1ate 135 4 influence influence NN cord-018208-sc8j1ate 135 5 of of IN cord-018208-sc8j1ate 135 6 the the DT cord-018208-sc8j1ate 135 7 negative negative JJ cord-018208-sc8j1ate 135 8 correlation correlation NN cord-018208-sc8j1ate 135 9 between between IN cord-018208-sc8j1ate 135 10 the the DT cord-018208-sc8j1ate 135 11 infection infection NN cord-018208-sc8j1ate 135 12 rate rate NN cord-018208-sc8j1ate 135 13 and and CC cord-018208-sc8j1ate 135 14 the the DT cord-018208-sc8j1ate 135 15 nodal nodal JJ cord-018208-sc8j1ate 135 16 degree degree NN cord-018208-sc8j1ate 135 17 on on IN cord-018208-sc8j1ate 135 18 the the DT cord-018208-sc8j1ate 135 19 accuracy accuracy NN cord-018208-sc8j1ate 135 20 of of IN cord-018208-sc8j1ate 135 21 NIMFA NIMFA NNP cord-018208-sc8j1ate 135 22 , , , cord-018208-sc8j1ate 135 23 we -PRON- PRP cord-018208-sc8j1ate 135 24 compare compare VBP cord-018208-sc8j1ate 135 25 the the DT cord-018208-sc8j1ate 135 26 variable variable NN cord-018208-sc8j1ate 135 27 ζ ζ NN cord-018208-sc8j1ate 135 28 in in IN cord-018208-sc8j1ate 135 29 the the DT cord-018208-sc8j1ate 135 30 scenario scenario NN cord-018208-sc8j1ate 135 31 of of IN cord-018208-sc8j1ate 135 32 correlated correlate VBN cord-018208-sc8j1ate 135 33 and and CC cord-018208-sc8j1ate 135 34 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 135 35 infection infection NN cord-018208-sc8j1ate 135 36 - - HYPH cord-018208-sc8j1ate 135 37 rate rate NN cord-018208-sc8j1ate 135 38 scenario scenario NN cord-018208-sc8j1ate 135 39 with with IN cord-018208-sc8j1ate 135 40 α α NN cord-018208-sc8j1ate 135 41 = = SYM cord-018208-sc8j1ate 135 42 −1 −1 NNP cord-018208-sc8j1ate 135 43 for for IN cord-018208-sc8j1ate 135 44 both both DT cord-018208-sc8j1ate 135 45 ER ER NNP cord-018208-sc8j1ate 135 46 and and CC cord-018208-sc8j1ate 135 47 SF SF NNP cord-018208-sc8j1ate 135 48 networks network NNS cord-018208-sc8j1ate 135 49 as as IN cord-018208-sc8j1ate 135 50 shown show VBN cord-018208-sc8j1ate 135 51 in in IN cord-018208-sc8j1ate 135 52 Fig Fig NNP cord-018208-sc8j1ate 135 53 . . . cord-018208-sc8j1ate 135 54 4a 4a CD cord-018208-sc8j1ate 135 55 . . . cord-018208-sc8j1ate 136 1 We -PRON- PRP cord-018208-sc8j1ate 136 2 find find VBP cord-018208-sc8j1ate 136 3 that that IN cord-018208-sc8j1ate 136 4 , , , cord-018208-sc8j1ate 136 5 in in IN cord-018208-sc8j1ate 136 6 general general JJ cord-018208-sc8j1ate 136 7 , , , cord-018208-sc8j1ate 136 8 the the DT cord-018208-sc8j1ate 136 9 negative negative JJ cord-018208-sc8j1ate 136 10 correlation correlation NN cord-018208-sc8j1ate 136 11 significantly significantly RB cord-018208-sc8j1ate 136 12 decreases decrease VBZ cord-018208-sc8j1ate 136 13 the the DT cord-018208-sc8j1ate 136 14 accuracy accuracy NN cord-018208-sc8j1ate 136 15 of of IN cord-018208-sc8j1ate 136 16 NIMFA NIMFA NNP cord-018208-sc8j1ate 136 17 when when WRB cord-018208-sc8j1ate 136 18 the the DT cord-018208-sc8j1ate 136 19 effective effective JJ cord-018208-sc8j1ate 136 20 infection infection NN cord-018208-sc8j1ate 136 21 rate rate NN cord-018208-sc8j1ate 136 22 τ τ NN cord-018208-sc8j1ate 136 23 is be VBZ cord-018208-sc8j1ate 136 24 small small JJ cord-018208-sc8j1ate 136 25 but but CC cord-018208-sc8j1ate 136 26 may may MD cord-018208-sc8j1ate 136 27 slightly slightly RB cord-018208-sc8j1ate 136 28 increase increase VB cord-018208-sc8j1ate 136 29 that that IN cord-018208-sc8j1ate 136 30 when when WRB cord-018208-sc8j1ate 136 31 τ τ NN cord-018208-sc8j1ate 136 32 is be VBZ cord-018208-sc8j1ate 136 33 large large JJ cord-018208-sc8j1ate 136 34 . . . cord-018208-sc8j1ate 137 1 Moreover moreover RB cord-018208-sc8j1ate 137 2 , , , cord-018208-sc8j1ate 137 3 NIMFA NIMFA NNP cord-018208-sc8j1ate 137 4 becomes become VBZ cord-018208-sc8j1ate 137 5 less less RBR cord-018208-sc8j1ate 137 6 accurate accurate JJ cord-018208-sc8j1ate 137 7 when when WRB cord-018208-sc8j1ate 137 8 the the DT cord-018208-sc8j1ate 137 9 negative negative JJ cord-018208-sc8j1ate 137 10 correlation correlation NN cord-018208-sc8j1ate 137 11 is be VBZ cord-018208-sc8j1ate 137 12 stronger strong JJR cord-018208-sc8j1ate 137 13 as as IN cord-018208-sc8j1ate 137 14 shown show VBN cord-018208-sc8j1ate 137 15 in in IN cord-018208-sc8j1ate 137 16 Fig Fig NNP cord-018208-sc8j1ate 137 17 . . . cord-018208-sc8j1ate 137 18 4b 4b CD cord-018208-sc8j1ate 137 19 . . . cord-018208-sc8j1ate 138 1 As as IN cord-018208-sc8j1ate 138 2 mentioned mention VBN cord-018208-sc8j1ate 138 3 in in IN cord-018208-sc8j1ate 138 4 Section section NN cord-018208-sc8j1ate 138 5 2.3 2.3 CD cord-018208-sc8j1ate 138 6 , , , cord-018208-sc8j1ate 138 7 the the DT cord-018208-sc8j1ate 138 8 negative negative JJ cord-018208-sc8j1ate 138 9 correlation correlation NN cord-018208-sc8j1ate 138 10 tends tend VBZ cord-018208-sc8j1ate 138 11 to to TO cord-018208-sc8j1ate 138 12 decrease decrease VB cord-018208-sc8j1ate 138 13 the the DT cord-018208-sc8j1ate 138 14 prevalence prevalence NN cord-018208-sc8j1ate 138 15 when when WRB cord-018208-sc8j1ate 138 16 the the DT cord-018208-sc8j1ate 138 17 effective effective JJ cord-018208-sc8j1ate 138 18 infection infection NN cord-018208-sc8j1ate 138 19 rate rate NN cord-018208-sc8j1ate 138 20 τ τ NN cord-018208-sc8j1ate 138 21 is be VBZ cord-018208-sc8j1ate 138 22 small small JJ cord-018208-sc8j1ate 138 23 while while IN cord-018208-sc8j1ate 138 24 increase increase VB cord-018208-sc8j1ate 138 25 the the DT cord-018208-sc8j1ate 138 26 prevalence prevalence NN cord-018208-sc8j1ate 138 27 when when WRB cord-018208-sc8j1ate 138 28 τ τ NN cord-018208-sc8j1ate 138 29 is be VBZ cord-018208-sc8j1ate 138 30 large large JJ cord-018208-sc8j1ate 138 31 . . . cord-018208-sc8j1ate 139 1 Hence hence RB cord-018208-sc8j1ate 139 2 , , , cord-018208-sc8j1ate 139 3 the the DT cord-018208-sc8j1ate 139 4 influence influence NN cord-018208-sc8j1ate 139 5 of of IN cord-018208-sc8j1ate 139 6 prevalence prevalence NN cord-018208-sc8j1ate 139 7 on on IN cord-018208-sc8j1ate 139 8 the the DT cord-018208-sc8j1ate 139 9 precision precision NN cord-018208-sc8j1ate 139 10 of of IN cord-018208-sc8j1ate 139 11 NIMFA NIMFA NNP cord-018208-sc8j1ate 139 12 could could MD cord-018208-sc8j1ate 139 13 largely largely RB cord-018208-sc8j1ate 139 14 explain explain VB cord-018208-sc8j1ate 139 15 our -PRON- PRP$ cord-018208-sc8j1ate 139 16 observations observation NNS cord-018208-sc8j1ate 139 17 here here RB cord-018208-sc8j1ate 139 18 . . . cord-018208-sc8j1ate 140 1 When when WRB cord-018208-sc8j1ate 140 2 the the DT cord-018208-sc8j1ate 140 3 prevalence prevalence NN cord-018208-sc8j1ate 140 4 of of IN cord-018208-sc8j1ate 140 5 epidemic epidemic NN cord-018208-sc8j1ate 140 6 is be VBZ cord-018208-sc8j1ate 140 7 the the DT cord-018208-sc8j1ate 140 8 same same JJ cord-018208-sc8j1ate 140 9 , , , cord-018208-sc8j1ate 140 10 the the DT cord-018208-sc8j1ate 140 11 influence influence NN cord-018208-sc8j1ate 140 12 of of IN cord-018208-sc8j1ate 140 13 the the DT cord-018208-sc8j1ate 140 14 negative negative JJ cord-018208-sc8j1ate 140 15 correlation correlation NN cord-018208-sc8j1ate 140 16 on on IN cord-018208-sc8j1ate 140 17 NIMFA NIMFA NNP cord-018208-sc8j1ate 140 18 's 's POS cord-018208-sc8j1ate 140 19 accuracy accuracy NN cord-018208-sc8j1ate 140 20 is be VBZ cord-018208-sc8j1ate 140 21 shown show VBN cord-018208-sc8j1ate 140 22 in in IN cord-018208-sc8j1ate 140 23 Fig Fig NNP cord-018208-sc8j1ate 140 24 . . . cord-018208-sc8j1ate 141 1 4c 4c LS cord-018208-sc8j1ate 141 2 and and CC cord-018208-sc8j1ate 141 3 Fig Fig NNP cord-018208-sc8j1ate 141 4 . . NNP cord-018208-sc8j1ate 141 5 4d 4d CD cord-018208-sc8j1ate 141 6 . . . cord-018208-sc8j1ate 142 1 We -PRON- PRP cord-018208-sc8j1ate 142 2 find find VBP cord-018208-sc8j1ate 142 3 that that IN cord-018208-sc8j1ate 142 4 , , , cord-018208-sc8j1ate 142 5 in in IN cord-018208-sc8j1ate 142 6 general general JJ cord-018208-sc8j1ate 142 7 , , , cord-018208-sc8j1ate 142 8 1 1 CD cord-018208-sc8j1ate 142 9 ) ) -RRB- cord-018208-sc8j1ate 142 10 NIMFA NIMFA NNP cord-018208-sc8j1ate 142 11 is be VBZ cord-018208-sc8j1ate 142 12 less less RBR cord-018208-sc8j1ate 142 13 accurate accurate JJ cord-018208-sc8j1ate 142 14 with with IN cord-018208-sc8j1ate 142 15 the the DT cord-018208-sc8j1ate 142 16 negative negative JJ cord-018208-sc8j1ate 142 17 correlation correlation NN cord-018208-sc8j1ate 142 18 comparing compare VBG cord-018208-sc8j1ate 142 19 to to IN cord-018208-sc8j1ate 142 20 the the DT cord-018208-sc8j1ate 142 21 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 142 22 scenario scenario NN cord-018208-sc8j1ate 142 23 especially especially RB cord-018208-sc8j1ate 142 24 when when WRB cord-018208-sc8j1ate 142 25 the the DT cord-018208-sc8j1ate 142 26 prevalence prevalence NN cord-018208-sc8j1ate 142 27 is be VBZ cord-018208-sc8j1ate 142 28 low low JJ cord-018208-sc8j1ate 142 29 as as IN cord-018208-sc8j1ate 142 30 shown show VBN cord-018208-sc8j1ate 142 31 in in IN cord-018208-sc8j1ate 142 32 Fig Fig NNP cord-018208-sc8j1ate 142 33 . . NNP cord-018208-sc8j1ate 142 34 4c 4c CD cord-018208-sc8j1ate 142 35 ; ; : cord-018208-sc8j1ate 142 36 2 2 LS cord-018208-sc8j1ate 142 37 ) ) -RRB- cord-018208-sc8j1ate 142 38 NIMFA NIMFA NNP cord-018208-sc8j1ate 142 39 becomes become VBZ cord-018208-sc8j1ate 142 40 even even RB cord-018208-sc8j1ate 142 41 less less RBR cord-018208-sc8j1ate 142 42 accurate accurate JJ cord-018208-sc8j1ate 142 43 if if IN cord-018208-sc8j1ate 142 44 the the DT cord-018208-sc8j1ate 142 45 negative negative JJ cord-018208-sc8j1ate 142 46 correlation correlation NN cord-018208-sc8j1ate 142 47 becomes become VBZ cord-018208-sc8j1ate 142 48 stronger strong JJR cord-018208-sc8j1ate 142 49 as as IN cord-018208-sc8j1ate 142 50 shown show VBN cord-018208-sc8j1ate 142 51 in in IN cord-018208-sc8j1ate 142 52 Fig Fig NNP cord-018208-sc8j1ate 142 53 . . . cord-018208-sc8j1ate 143 1 4d 4d NNP cord-018208-sc8j1ate 143 2 . . . cord-018208-sc8j1ate 144 1 In in IN cord-018208-sc8j1ate 144 2 this this DT cord-018208-sc8j1ate 144 3 section section NN cord-018208-sc8j1ate 144 4 , , , cord-018208-sc8j1ate 144 5 we -PRON- PRP cord-018208-sc8j1ate 144 6 choose choose VBP cord-018208-sc8j1ate 144 7 the the DT cord-018208-sc8j1ate 144 8 airline airline NN cord-018208-sc8j1ate 144 9 network network NN cord-018208-sc8j1ate 144 10 from from IN cord-018208-sc8j1ate 144 11 the the DT cord-018208-sc8j1ate 144 12 real real JJ cord-018208-sc8j1ate 144 13 world world NN cord-018208-sc8j1ate 144 14 as as IN cord-018208-sc8j1ate 144 15 an an DT cord-018208-sc8j1ate 144 16 example example NN cord-018208-sc8j1ate 144 17 to to TO cord-018208-sc8j1ate 144 18 illustrate illustrate VB cord-018208-sc8j1ate 144 19 how how WRB cord-018208-sc8j1ate 144 20 its -PRON- PRP$ cord-018208-sc8j1ate 144 21 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 144 22 infection infection NN cord-018208-sc8j1ate 144 23 rates rate NNS cord-018208-sc8j1ate 144 24 affect affect VBP cord-018208-sc8j1ate 144 25 the the DT cord-018208-sc8j1ate 144 26 accuracy accuracy NN cord-018208-sc8j1ate 144 27 of of IN cord-018208-sc8j1ate 144 28 NIMFA NIMFA NNP cord-018208-sc8j1ate 144 29 of of IN cord-018208-sc8j1ate 144 30 SIS SIS NNP cord-018208-sc8j1ate 144 31 epidemics epidemic NNS cord-018208-sc8j1ate 144 32 on on IN cord-018208-sc8j1ate 144 33 the the DT cord-018208-sc8j1ate 144 34 network network NN cord-018208-sc8j1ate 144 35 . . . cord-018208-sc8j1ate 145 1 In in IN cord-018208-sc8j1ate 145 2 the the DT cord-018208-sc8j1ate 145 3 airline airline NN cord-018208-sc8j1ate 145 4 network network NN cord-018208-sc8j1ate 145 5 , , , cord-018208-sc8j1ate 145 6 the the DT cord-018208-sc8j1ate 145 7 nodes node NNS cord-018208-sc8j1ate 145 8 are be VBP cord-018208-sc8j1ate 145 9 the the DT cord-018208-sc8j1ate 145 10 airports airport NNS cord-018208-sc8j1ate 145 11 , , , cord-018208-sc8j1ate 145 12 the the DT cord-018208-sc8j1ate 145 13 link link NN cord-018208-sc8j1ate 145 14 between between IN cord-018208-sc8j1ate 145 15 two two CD cord-018208-sc8j1ate 145 16 nodes node NNS cord-018208-sc8j1ate 145 17 indicates indicate VBZ cord-018208-sc8j1ate 145 18 that that IN cord-018208-sc8j1ate 145 19 there there EX cord-018208-sc8j1ate 145 20 's be VBZ cord-018208-sc8j1ate 145 21 at at RB cord-018208-sc8j1ate 145 22 least least RBS cord-018208-sc8j1ate 145 23 one one CD cord-018208-sc8j1ate 145 24 flight flight NN cord-018208-sc8j1ate 145 25 between between IN cord-018208-sc8j1ate 145 26 these these DT cord-018208-sc8j1ate 145 27 two two CD cord-018208-sc8j1ate 145 28 airports airport NNS cord-018208-sc8j1ate 145 29 , , , cord-018208-sc8j1ate 145 30 and and CC cord-018208-sc8j1ate 145 31 the the DT cord-018208-sc8j1ate 145 32 infection infection NN cord-018208-sc8j1ate 145 33 rate rate NN cord-018208-sc8j1ate 145 34 along along IN cord-018208-sc8j1ate 145 35 a a DT cord-018208-sc8j1ate 145 36 link link NN cord-018208-sc8j1ate 145 37 is be VBZ cord-018208-sc8j1ate 145 38 the the DT cord-018208-sc8j1ate 145 39 number number NN cord-018208-sc8j1ate 145 40 of of IN cord-018208-sc8j1ate 145 41 flights flight NNS cord-018208-sc8j1ate 145 42 between between IN cord-018208-sc8j1ate 145 43 the the DT cord-018208-sc8j1ate 145 44 two two CD cord-018208-sc8j1ate 145 45 airports airport NNS cord-018208-sc8j1ate 145 46 . . . cord-018208-sc8j1ate 146 1 We -PRON- PRP cord-018208-sc8j1ate 146 2 construct construct VBP cord-018208-sc8j1ate 146 3 this this DT cord-018208-sc8j1ate 146 4 network network NN cord-018208-sc8j1ate 146 5 and and CC cord-018208-sc8j1ate 146 6 its -PRON- PRP$ cord-018208-sc8j1ate 146 7 infection infection NN cord-018208-sc8j1ate 146 8 rates rate NNS cord-018208-sc8j1ate 146 9 from from IN cord-018208-sc8j1ate 146 10 the the DT cord-018208-sc8j1ate 146 11 dataset dataset NN cord-018208-sc8j1ate 146 12 of of IN cord-018208-sc8j1ate 146 13 openFlights openflight NNS cord-018208-sc8j1ate 146 14 1 1 CD cord-018208-sc8j1ate 146 15 . . . cord-018208-sc8j1ate 147 1 As as IN cord-018208-sc8j1ate 147 2 shown show VBN cord-018208-sc8j1ate 147 3 in in IN cord-018208-sc8j1ate 147 4 [ [ -LRB- cord-018208-sc8j1ate 147 5 17 17 CD cord-018208-sc8j1ate 147 6 ] ] -RRB- cord-018208-sc8j1ate 147 7 , , , cord-018208-sc8j1ate 147 8 the the DT cord-018208-sc8j1ate 147 9 airline airline NN cord-018208-sc8j1ate 147 10 network network NN cord-018208-sc8j1ate 147 11 possess possess VBP cord-018208-sc8j1ate 147 12 roughly roughly RB cord-018208-sc8j1ate 147 13 a a DT cord-018208-sc8j1ate 147 14 power power NN cord-018208-sc8j1ate 147 15 - - HYPH cord-018208-sc8j1ate 147 16 law law NN cord-018208-sc8j1ate 147 17 degree degree NN cord-018208-sc8j1ate 147 18 distribution distribution NN cord-018208-sc8j1ate 147 19 . . . cord-018208-sc8j1ate 148 1 The the DT cord-018208-sc8j1ate 148 2 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 148 3 infection infection NN cord-018208-sc8j1ate 148 4 rates rate NNS cord-018208-sc8j1ate 148 5 from from IN cord-018208-sc8j1ate 148 6 the the DT cord-018208-sc8j1ate 148 7 dataset dataset NN cord-018208-sc8j1ate 148 8 are be VBP cord-018208-sc8j1ate 148 9 normalized normalize VBN cord-018208-sc8j1ate 148 10 by by IN cord-018208-sc8j1ate 148 11 the the DT cord-018208-sc8j1ate 148 12 average average NN cord-018208-sc8j1ate 148 13 so so IN cord-018208-sc8j1ate 148 14 that that IN cord-018208-sc8j1ate 148 15 the the DT cord-018208-sc8j1ate 148 16 average average NN cord-018208-sc8j1ate 148 17 is be VBZ cord-018208-sc8j1ate 148 18 1 1 CD cord-018208-sc8j1ate 148 19 . . . cord-018208-sc8j1ate 149 1 We -PRON- PRP cord-018208-sc8j1ate 149 2 compare compare VBP cord-018208-sc8j1ate 149 3 the the DT cord-018208-sc8j1ate 149 4 difference difference NN cord-018208-sc8j1ate 149 5 ζ ζ NN cord-018208-sc8j1ate 149 6 between between IN cord-018208-sc8j1ate 149 7 NIMFA NIMFA NNP cord-018208-sc8j1ate 149 8 and and CC cord-018208-sc8j1ate 149 9 the the DT cord-018208-sc8j1ate 149 10 simulations simulation NNS cord-018208-sc8j1ate 149 11 of of IN cord-018208-sc8j1ate 149 12 the the DT cord-018208-sc8j1ate 149 13 exact exact JJ cord-018208-sc8j1ate 149 14 SIS SIS NNP cord-018208-sc8j1ate 149 15 model model NN cord-018208-sc8j1ate 149 16 in in IN cord-018208-sc8j1ate 149 17 three three CD cord-018208-sc8j1ate 149 18 scenarios scenario NNS cord-018208-sc8j1ate 149 19 : : : cord-018208-sc8j1ate 149 20 1 1 LS cord-018208-sc8j1ate 149 21 ) ) -RRB- cord-018208-sc8j1ate 149 22 the the DT cord-018208-sc8j1ate 149 23 network network NN cord-018208-sc8j1ate 149 24 is be VBZ cord-018208-sc8j1ate 149 25 equipped equip VBN cord-018208-sc8j1ate 149 26 with with IN cord-018208-sc8j1ate 149 27 its -PRON- PRP$ cord-018208-sc8j1ate 149 28 normalized normalized JJ cord-018208-sc8j1ate 149 29 original original JJ cord-018208-sc8j1ate 149 30 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 149 31 infection infection NN cord-018208-sc8j1ate 149 32 rates rate NNS cord-018208-sc8j1ate 149 33 ( ( -LRB- cord-018208-sc8j1ate 149 34 correlated correlate VBN cord-018208-sc8j1ate 149 35 ) ) -RRB- cord-018208-sc8j1ate 149 36 as as IN cord-018208-sc8j1ate 149 37 given give VBN cord-018208-sc8j1ate 149 38 in in IN cord-018208-sc8j1ate 149 39 the the DT cord-018208-sc8j1ate 149 40 dataset dataset NN cord-018208-sc8j1ate 149 41 ; ; : cord-018208-sc8j1ate 149 42 2 2 LS cord-018208-sc8j1ate 149 43 ) ) -RRB- cord-018208-sc8j1ate 149 44 the the DT cord-018208-sc8j1ate 149 45 network network NN cord-018208-sc8j1ate 149 46 is be VBZ cord-018208-sc8j1ate 149 47 equipped equip VBN cord-018208-sc8j1ate 149 48 with with IN cord-018208-sc8j1ate 149 49 the the DT cord-018208-sc8j1ate 149 50 infection infection NN cord-018208-sc8j1ate 149 51 rates rate NNS cord-018208-sc8j1ate 149 52 in in IN cord-018208-sc8j1ate 149 53 the the DT cord-018208-sc8j1ate 149 54 normalized normalized JJ cord-018208-sc8j1ate 149 55 original original JJ cord-018208-sc8j1ate 149 56 dataset dataset NN cord-018208-sc8j1ate 149 57 but but CC cord-018208-sc8j1ate 149 58 randomly randomly RB cord-018208-sc8j1ate 149 59 shuffled shuffle VBD cord-018208-sc8j1ate 149 60 ( ( -LRB- cord-018208-sc8j1ate 149 61 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 149 62 ) ) -RRB- cord-018208-sc8j1ate 149 63 ; ; : cord-018208-sc8j1ate 149 64 3 3 LS cord-018208-sc8j1ate 149 65 ) ) -RRB- cord-018208-sc8j1ate 149 66 the the DT cord-018208-sc8j1ate 149 67 network network NN cord-018208-sc8j1ate 149 68 is be VBZ cord-018208-sc8j1ate 149 69 equipped equip VBN cord-018208-sc8j1ate 149 70 with with IN cord-018208-sc8j1ate 149 71 a a DT cord-018208-sc8j1ate 149 72 constant constant JJ cord-018208-sc8j1ate 149 73 infection infection NN cord-018208-sc8j1ate 149 74 rate rate NN cord-018208-sc8j1ate 149 75 ( ( -LRB- cord-018208-sc8j1ate 149 76 homogeneous homogeneous JJ cord-018208-sc8j1ate 149 77 ) ) -RRB- cord-018208-sc8j1ate 149 78 which which WDT cord-018208-sc8j1ate 149 79 equals equal VBZ cord-018208-sc8j1ate 149 80 to to IN cord-018208-sc8j1ate 149 81 1 1 CD cord-018208-sc8j1ate 149 82 . . . cord-018208-sc8j1ate 150 1 The the DT cord-018208-sc8j1ate 150 2 original original JJ cord-018208-sc8j1ate 150 3 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 150 4 infection infection NN cord-018208-sc8j1ate 150 5 rate rate NN cord-018208-sc8j1ate 150 6 between between IN cord-018208-sc8j1ate 150 7 a a DT cord-018208-sc8j1ate 150 8 pair pair NN cord-018208-sc8j1ate 150 9 of of IN cord-018208-sc8j1ate 150 10 nodes node NNS cord-018208-sc8j1ate 150 11 are be VBP cord-018208-sc8j1ate 150 12 approximately approximately RB cord-018208-sc8j1ate 150 13 correlated correlate VBN cord-018208-sc8j1ate 150 14 with with IN cord-018208-sc8j1ate 150 15 the the DT cord-018208-sc8j1ate 150 16 degrees degree NNS cord-018208-sc8j1ate 150 17 of of IN cord-018208-sc8j1ate 150 18 the the DT cord-018208-sc8j1ate 150 19 two two CD cord-018208-sc8j1ate 150 20 nodes node NNS cord-018208-sc8j1ate 150 21 as as IN cord-018208-sc8j1ate 150 22 the the DT cord-018208-sc8j1ate 150 23 relationship relationship NN cord-018208-sc8j1ate 150 24 ( ( -LRB- cord-018208-sc8j1ate 150 25 5 5 CD cord-018208-sc8j1ate 150 26 ) ) -RRB- cord-018208-sc8j1ate 150 27 , , , cord-018208-sc8j1ate 150 28 and and CC cord-018208-sc8j1ate 151 1 the the DT cord-018208-sc8j1ate 151 2 parameter parameter NN cord-018208-sc8j1ate 151 3 α α NNP cord-018208-sc8j1ate 151 4 ≈ ≈ NNP cord-018208-sc8j1ate 151 5 0.14 0.14 CD cord-018208-sc8j1ate 151 6 indicates indicate VBZ cord-018208-sc8j1ate 151 7 a a DT cord-018208-sc8j1ate 151 8 positive positive JJ cord-018208-sc8j1ate 151 9 correlation correlation NN cord-018208-sc8j1ate 151 10 [ [ -LRB- cord-018208-sc8j1ate 151 11 17 17 CD cord-018208-sc8j1ate 151 12 ] ] -RRB- cord-018208-sc8j1ate 151 13 . . . cord-018208-sc8j1ate 152 1 We -PRON- PRP cord-018208-sc8j1ate 152 2 show show VBP cord-018208-sc8j1ate 152 3 the the DT cord-018208-sc8j1ate 152 4 difference difference NN cord-018208-sc8j1ate 152 5 ζ ζ NN cord-018208-sc8j1ate 152 6 as as IN cord-018208-sc8j1ate 152 7 a a DT cord-018208-sc8j1ate 152 8 function function NN cord-018208-sc8j1ate 152 9 of of IN cord-018208-sc8j1ate 152 10 the the DT cord-018208-sc8j1ate 152 11 effective effective JJ cord-018208-sc8j1ate 152 12 infection infection NN cord-018208-sc8j1ate 152 13 rate rate NN cord-018208-sc8j1ate 152 14 τ τ NN cord-018208-sc8j1ate 152 15 in in IN cord-018208-sc8j1ate 152 16 Fig Fig NNP cord-018208-sc8j1ate 152 17 . . . cord-018208-sc8j1ate 153 1 5a 5a CD cord-018208-sc8j1ate 153 2 for for IN cord-018208-sc8j1ate 153 3 the the DT cord-018208-sc8j1ate 153 4 3 3 CD cord-018208-sc8j1ate 153 5 scenarios scenario NNS cord-018208-sc8j1ate 153 6 defined define VBN cord-018208-sc8j1ate 153 7 as as IN cord-018208-sc8j1ate 153 8 above above RB cord-018208-sc8j1ate 153 9 . . . cord-018208-sc8j1ate 154 1 We -PRON- PRP cord-018208-sc8j1ate 154 2 find find VBP cord-018208-sc8j1ate 154 3 that that IN cord-018208-sc8j1ate 154 4 NIMFA NIMFA NNP cord-018208-sc8j1ate 154 5 is be VBZ cord-018208-sc8j1ate 154 6 generally generally RB cord-018208-sc8j1ate 154 7 more more RBR cord-018208-sc8j1ate 154 8 accurate accurate JJ cord-018208-sc8j1ate 154 9 when when WRB cord-018208-sc8j1ate 154 10 the the DT cord-018208-sc8j1ate 154 11 effective effective JJ cord-018208-sc8j1ate 154 12 infection infection NN cord-018208-sc8j1ate 154 13 rate rate NN cord-018208-sc8j1ate 154 14 τ τ NN cord-018208-sc8j1ate 154 15 is be VBZ cord-018208-sc8j1ate 154 16 larger large JJR cord-018208-sc8j1ate 154 17 , , , cord-018208-sc8j1ate 154 18 i.e. i.e. FW cord-018208-sc8j1ate 154 19 the the DT cord-018208-sc8j1ate 154 20 prevalence prevalence NN cord-018208-sc8j1ate 154 21 of of IN cord-018208-sc8j1ate 154 22 epidemic epidemic NN cord-018208-sc8j1ate 154 23 is be VBZ cord-018208-sc8j1ate 154 24 high high JJ cord-018208-sc8j1ate 154 25 . . . cord-018208-sc8j1ate 155 1 The the DT cord-018208-sc8j1ate 155 2 variable variable NN cord-018208-sc8j1ate 155 3 ζ ζ NN cord-018208-sc8j1ate 155 4 is be VBZ cord-018208-sc8j1ate 155 5 smaller small JJR cord-018208-sc8j1ate 155 6 in in IN cord-018208-sc8j1ate 155 7 the the DT cord-018208-sc8j1ate 155 8 scenario scenario NN cord-018208-sc8j1ate 155 9 of of IN cord-018208-sc8j1ate 155 10 homogeneous homogeneous JJ cord-018208-sc8j1ate 155 11 infection infection NN cord-018208-sc8j1ate 155 12 rates rate NNS cord-018208-sc8j1ate 155 13 than than IN cord-018208-sc8j1ate 155 14 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 155 15 infection infection NN cord-018208-sc8j1ate 155 16 rates rate NNS cord-018208-sc8j1ate 155 17 with with IN cord-018208-sc8j1ate 155 18 any any DT cord-018208-sc8j1ate 155 19 effective effective JJ cord-018208-sc8j1ate 155 20 infection infection NN cord-018208-sc8j1ate 155 21 rate rate NN cord-018208-sc8j1ate 155 22 . . . cord-018208-sc8j1ate 156 1 This this DT cord-018208-sc8j1ate 156 2 is be VBZ cord-018208-sc8j1ate 156 3 because because IN cord-018208-sc8j1ate 156 4 the the DT cord-018208-sc8j1ate 156 5 i.i.d i.i.d NN cord-018208-sc8j1ate 156 6 . . . cord-018208-sc8j1ate 156 7 infection infection NN cord-018208-sc8j1ate 156 8 rates rate VBZ cord-018208-sc8j1ate 156 9 with with IN cord-018208-sc8j1ate 156 10 a a DT cord-018208-sc8j1ate 156 11 non non JJ cord-018208-sc8j1ate 156 12 - - JJ cord-018208-sc8j1ate 156 13 zero zero JJ cord-018208-sc8j1ate 156 14 variance variance NN cord-018208-sc8j1ate 156 15 tends tend VBZ cord-018208-sc8j1ate 156 16 to to TO cord-018208-sc8j1ate 156 17 decrease decrease VB cord-018208-sc8j1ate 156 18 the the DT cord-018208-sc8j1ate 156 19 prevalence prevalence NN cord-018208-sc8j1ate 156 20 , , , cord-018208-sc8j1ate 156 21 and and CC cord-018208-sc8j1ate 156 22 thus thus RB cord-018208-sc8j1ate 156 23 lower lower VB cord-018208-sc8j1ate 156 24 down down IN cord-018208-sc8j1ate 156 25 the the DT cord-018208-sc8j1ate 156 26 accuracy accuracy NN cord-018208-sc8j1ate 156 27 of of IN cord-018208-sc8j1ate 156 28 NIMFA NIMFA NNP cord-018208-sc8j1ate 156 29 at at IN cord-018208-sc8j1ate 156 30 a a DT cord-018208-sc8j1ate 156 31 given give VBN cord-018208-sc8j1ate 156 32 effective effective JJ cord-018208-sc8j1ate 156 33 infection infection NN cord-018208-sc8j1ate 156 34 rate rate NN cord-018208-sc8j1ate 156 35 τ τ NN cord-018208-sc8j1ate 156 36 . . . cord-018208-sc8j1ate 157 1 NIMFA NIMFA NNP cord-018208-sc8j1ate 157 2 is be VBZ cord-018208-sc8j1ate 157 3 more more RBR cord-018208-sc8j1ate 157 4 accurate accurate JJ cord-018208-sc8j1ate 157 5 with with IN cord-018208-sc8j1ate 157 6 the the DT cord-018208-sc8j1ate 157 7 positive positive JJ cord-018208-sc8j1ate 157 8 correlation correlation NN cord-018208-sc8j1ate 157 9 by by IN cord-018208-sc8j1ate 157 10 comparing compare VBG cord-018208-sc8j1ate 157 11 the the DT cord-018208-sc8j1ate 157 12 difference difference NN cord-018208-sc8j1ate 157 13 ζ ζ NN cord-018208-sc8j1ate 157 14 in in IN cord-018208-sc8j1ate 157 15 the the DT cord-018208-sc8j1ate 157 16 scenario scenario NN cord-018208-sc8j1ate 157 17 of of IN cord-018208-sc8j1ate 157 18 correlated correlate VBN cord-018208-sc8j1ate 157 19 infection infection NN cord-018208-sc8j1ate 157 20 rates rate NNS cord-018208-sc8j1ate 157 21 and and CC cord-018208-sc8j1ate 157 22 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 157 23 infection infection NN cord-018208-sc8j1ate 157 24 rates rate NNS cord-018208-sc8j1ate 157 25 . . . cord-018208-sc8j1ate 158 1 Furthermore furthermore RB cord-018208-sc8j1ate 158 2 , , , cord-018208-sc8j1ate 158 3 Fig Fig NNP cord-018208-sc8j1ate 158 4 . . . cord-018208-sc8j1ate 159 1 5b 5b NN cord-018208-sc8j1ate 159 2 shows show VBZ cord-018208-sc8j1ate 159 3 that that IN cord-018208-sc8j1ate 159 4 , , , cord-018208-sc8j1ate 159 5 given give VBN cord-018208-sc8j1ate 159 6 the the DT cord-018208-sc8j1ate 159 7 same same JJ cord-018208-sc8j1ate 159 8 actual actual JJ cord-018208-sc8j1ate 159 9 prevalence prevalence NN cord-018208-sc8j1ate 159 10 , , , cord-018208-sc8j1ate 159 11 i.e. i.e. FW cord-018208-sc8j1ate 159 12 the the DT cord-018208-sc8j1ate 159 13 average average JJ cord-018208-sc8j1ate 159 14 fraction fraction NN cord-018208-sc8j1ate 159 15 y y NNP cord-018208-sc8j1ate 159 16 ∞ ∞ NNP cord-018208-sc8j1ate 159 17 of of IN cord-018208-sc8j1ate 159 18 infected infected JJ cord-018208-sc8j1ate 159 19 nodes node NNS cord-018208-sc8j1ate 159 20 obtained obtain VBN cord-018208-sc8j1ate 159 21 by by IN cord-018208-sc8j1ate 159 22 simulations simulation NNS cord-018208-sc8j1ate 159 23 , , , cord-018208-sc8j1ate 159 24 NIFMA NIFMA NNP cord-018208-sc8j1ate 159 25 is be VBZ cord-018208-sc8j1ate 159 26 more more RBR cord-018208-sc8j1ate 159 27 accurate accurate JJ cord-018208-sc8j1ate 159 28 : : : cord-018208-sc8j1ate 159 29 1 1 LS cord-018208-sc8j1ate 159 30 ) ) -RRB- cord-018208-sc8j1ate 159 31 in in IN cord-018208-sc8j1ate 159 32 the the DT cord-018208-sc8j1ate 159 33 homogeneous homogeneous JJ cord-018208-sc8j1ate 159 34 scenario scenario NN cord-018208-sc8j1ate 159 35 than than IN cord-018208-sc8j1ate 159 36 in in IN cord-018208-sc8j1ate 159 37 the the DT cord-018208-sc8j1ate 159 38 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 159 39 scenario scenario NN cord-018208-sc8j1ate 159 40 ; ; : cord-018208-sc8j1ate 159 41 2 2 LS cord-018208-sc8j1ate 159 42 ) ) -RRB- cord-018208-sc8j1ate 159 43 in in IN cord-018208-sc8j1ate 159 44 the the DT cord-018208-sc8j1ate 159 45 correlated correlate VBN cord-018208-sc8j1ate 159 46 scenario scenario NN cord-018208-sc8j1ate 159 47 than than IN cord-018208-sc8j1ate 159 48 in in IN cord-018208-sc8j1ate 159 49 the the DT cord-018208-sc8j1ate 159 50 uncorrelated uncorrelated JJ cord-018208-sc8j1ate 159 51 scenario scenario NN cord-018208-sc8j1ate 159 52 . . . cord-018208-sc8j1ate 160 1 All all PDT cord-018208-sc8j1ate 160 2 the the DT cord-018208-sc8j1ate 160 3 observations observation NNS cord-018208-sc8j1ate 160 4 agree agree VBP cord-018208-sc8j1ate 160 5 with with IN cord-018208-sc8j1ate 160 6 our -PRON- PRP$ cord-018208-sc8j1ate 160 7 previous previous JJ cord-018208-sc8j1ate 160 8 observations observation NNS cord-018208-sc8j1ate 160 9 and and CC cord-018208-sc8j1ate 160 10 explanations explanation NNS cord-018208-sc8j1ate 160 11 about about IN cord-018208-sc8j1ate 160 12 how how WRB cord-018208-sc8j1ate 160 13 the the DT cord-018208-sc8j1ate 160 14 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 160 15 infection infection NN cord-018208-sc8j1ate 160 16 rate rate NN cord-018208-sc8j1ate 160 17 influences influence VBZ cord-018208-sc8j1ate 160 18 the the DT cord-018208-sc8j1ate 160 19 accuracy accuracy NN cord-018208-sc8j1ate 160 20 of of IN cord-018208-sc8j1ate 160 21 NIMFA NIMFA NNP cord-018208-sc8j1ate 160 22 in in IN cord-018208-sc8j1ate 160 23 network network NN cord-018208-sc8j1ate 160 24 models model NNS cord-018208-sc8j1ate 160 25 . . . cord-018208-sc8j1ate 161 1 In in IN cord-018208-sc8j1ate 161 2 this this DT cord-018208-sc8j1ate 161 3 paper paper NN cord-018208-sc8j1ate 161 4 , , , cord-018208-sc8j1ate 161 5 we -PRON- PRP cord-018208-sc8j1ate 161 6 study study VBP cord-018208-sc8j1ate 161 7 how how WRB cord-018208-sc8j1ate 161 8 the the DT cord-018208-sc8j1ate 161 9 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 161 10 infection infection NN cord-018208-sc8j1ate 161 11 rates rate NNS cord-018208-sc8j1ate 161 12 affect affect VBP cord-018208-sc8j1ate 161 13 the the DT cord-018208-sc8j1ate 161 14 accuracy accuracy NN cord-018208-sc8j1ate 161 15 of of IN cord-018208-sc8j1ate 161 16 NIMFA NIMFA NNP cord-018208-sc8j1ate 161 17 -an -an : cord-018208-sc8j1ate 161 18 advanced advanced JJ cord-018208-sc8j1ate 161 19 mean mean JJ cord-018208-sc8j1ate 161 20 - - HYPH cord-018208-sc8j1ate 161 21 field field NN cord-018208-sc8j1ate 161 22 approximation approximation NN cord-018208-sc8j1ate 161 23 of of IN cord-018208-sc8j1ate 161 24 SIS SIS NNP cord-018208-sc8j1ate 161 25 model model NN cord-018208-sc8j1ate 161 26 that that WDT cord-018208-sc8j1ate 161 27 takes take VBZ cord-018208-sc8j1ate 161 28 the the DT cord-018208-sc8j1ate 161 29 underly underly JJ cord-018208-sc8j1ate 161 30 network network NN cord-018208-sc8j1ate 161 31 topology topology NN cord-018208-sc8j1ate 161 32 into into IN cord-018208-sc8j1ate 161 33 account account NN cord-018208-sc8j1ate 161 34 . . . cord-018208-sc8j1ate 162 1 By by IN cord-018208-sc8j1ate 162 2 comparing compare VBG cord-018208-sc8j1ate 162 3 NIMFA NIMFA NNP cord-018208-sc8j1ate 162 4 with with IN cord-018208-sc8j1ate 162 5 the the DT cord-018208-sc8j1ate 162 6 continuous continuous JJ cord-018208-sc8j1ate 162 7 - - HYPH cord-018208-sc8j1ate 162 8 time time NN cord-018208-sc8j1ate 162 9 simulations simulation NNS cord-018208-sc8j1ate 162 10 of of IN cord-018208-sc8j1ate 162 11 the the DT cord-018208-sc8j1ate 162 12 exact exact JJ cord-018208-sc8j1ate 162 13 SIS SIS NNP cord-018208-sc8j1ate 162 14 model model NN cord-018208-sc8j1ate 162 15 at at IN cord-018208-sc8j1ate 162 16 a a DT cord-018208-sc8j1ate 162 17 give give JJ cord-018208-sc8j1ate 162 18 effective effective JJ cord-018208-sc8j1ate 162 19 infection infection NN cord-018208-sc8j1ate 162 20 rate rate NN cord-018208-sc8j1ate 162 21 τ τ NN cord-018208-sc8j1ate 162 22 , , , cord-018208-sc8j1ate 162 23 we -PRON- PRP cord-018208-sc8j1ate 162 24 find find VBP cord-018208-sc8j1ate 162 25 that that IN cord-018208-sc8j1ate 162 26 the the DT cord-018208-sc8j1ate 162 27 prevalence prevalence NN cord-018208-sc8j1ate 162 28 of of IN cord-018208-sc8j1ate 162 29 epidemic epidemic NN cord-018208-sc8j1ate 162 30 could could MD cord-018208-sc8j1ate 162 31 largely largely RB cord-018208-sc8j1ate 162 32 characterize characterize VB cord-018208-sc8j1ate 162 33 the the DT cord-018208-sc8j1ate 162 34 accuracy accuracy NN cord-018208-sc8j1ate 162 35 of of IN cord-018208-sc8j1ate 162 36 NIMFA NIMFA NNP cord-018208-sc8j1ate 162 37 which which WDT cord-018208-sc8j1ate 162 38 is be VBZ cord-018208-sc8j1ate 162 39 reflected reflect VBN cord-018208-sc8j1ate 162 40 in in IN cord-018208-sc8j1ate 162 41 two two CD cord-018208-sc8j1ate 162 42 aspects aspect NNS cord-018208-sc8j1ate 162 43 : : : cord-018208-sc8j1ate 162 44 1 1 LS cord-018208-sc8j1ate 162 45 ) ) -RRB- cord-018208-sc8j1ate 162 46 NIFMA NIFMA NNP cord-018208-sc8j1ate 162 47 is be VBZ cord-018208-sc8j1ate 162 48 generally generally RB cord-018208-sc8j1ate 162 49 more more RBR cord-018208-sc8j1ate 162 50 accurate accurate JJ cord-018208-sc8j1ate 162 51 when when WRB cord-018208-sc8j1ate 162 52 the the DT cord-018208-sc8j1ate 162 53 effective effective JJ cord-018208-sc8j1ate 162 54 infection infection NN cord-018208-sc8j1ate 162 55 rate rate NN cord-018208-sc8j1ate 162 56 τ τ NN cord-018208-sc8j1ate 162 57 is be VBZ cord-018208-sc8j1ate 162 58 larger large JJR cord-018208-sc8j1ate 162 59 , , , cord-018208-sc8j1ate 162 60 i.e. i.e. FW cord-018208-sc8j1ate 162 61 the the DT cord-018208-sc8j1ate 162 62 prevalence prevalence NN cord-018208-sc8j1ate 162 63 of of IN cord-018208-sc8j1ate 162 64 epidemic epidemic NN cord-018208-sc8j1ate 162 65 is be VBZ cord-018208-sc8j1ate 162 66 higher high JJR cord-018208-sc8j1ate 162 67 ; ; : cord-018208-sc8j1ate 162 68 2 2 LS cord-018208-sc8j1ate 162 69 ) ) -RRB- cord-018208-sc8j1ate 162 70 when when WRB cord-018208-sc8j1ate 162 71 the the DT cord-018208-sc8j1ate 162 72 variance variance NN cord-018208-sc8j1ate 162 73 of of IN cord-018208-sc8j1ate 162 74 the the DT cord-018208-sc8j1ate 162 75 i.i.d i.i.d NN cord-018208-sc8j1ate 162 76 . . . cord-018208-sc8j1ate 162 77 infection infection NN cord-018208-sc8j1ate 162 78 rates rate NNS cord-018208-sc8j1ate 162 79 or or CC cord-018208-sc8j1ate 162 80 the the DT cord-018208-sc8j1ate 162 81 correlation correlation NN cord-018208-sc8j1ate 162 82 between between IN cord-018208-sc8j1ate 162 83 the the DT cord-018208-sc8j1ate 162 84 infection infection NN cord-018208-sc8j1ate 162 85 rate rate NN cord-018208-sc8j1ate 162 86 and and CC cord-018208-sc8j1ate 162 87 the the DT cord-018208-sc8j1ate 162 88 nodal nodal JJ cord-018208-sc8j1ate 162 89 degree degree NN cord-018208-sc8j1ate 162 90 decreases decrease VBZ cord-018208-sc8j1ate 162 91 the the DT cord-018208-sc8j1ate 162 92 prevalence prevalence NN cord-018208-sc8j1ate 162 93 at at IN cord-018208-sc8j1ate 162 94 a a DT cord-018208-sc8j1ate 162 95 given give VBN cord-018208-sc8j1ate 162 96 τ τ NN cord-018208-sc8j1ate 162 97 , , , cord-018208-sc8j1ate 162 98 NIMFA NIMFA NNP cord-018208-sc8j1ate 162 99 tends tend VBZ cord-018208-sc8j1ate 162 100 to to TO cord-018208-sc8j1ate 162 101 become become VB cord-018208-sc8j1ate 162 102 less less RBR cord-018208-sc8j1ate 162 103 accurate accurate JJ cord-018208-sc8j1ate 162 104 as as RB cord-018208-sc8j1ate 162 105 well well RB cord-018208-sc8j1ate 162 106 . . . cord-018208-sc8j1ate 163 1 Moreover moreover RB cord-018208-sc8j1ate 163 2 , , , cord-018208-sc8j1ate 163 3 we -PRON- PRP cord-018208-sc8j1ate 163 4 also also RB cord-018208-sc8j1ate 163 5 explore explore VBP cord-018208-sc8j1ate 163 6 the the DT cord-018208-sc8j1ate 163 7 influence influence NN cord-018208-sc8j1ate 163 8 of of IN cord-018208-sc8j1ate 163 9 the the DT cord-018208-sc8j1ate 163 10 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 163 11 infection infection NN cord-018208-sc8j1ate 163 12 rates rate NNS cord-018208-sc8j1ate 163 13 on on IN cord-018208-sc8j1ate 163 14 the the DT cord-018208-sc8j1ate 163 15 accuracy accuracy NN cord-018208-sc8j1ate 163 16 of of IN cord-018208-sc8j1ate 163 17 NIMFA NIMFA NNP cord-018208-sc8j1ate 163 18 at at IN cord-018208-sc8j1ate 163 19 a a DT cord-018208-sc8j1ate 163 20 given give VBN cord-018208-sc8j1ate 163 21 prevalence prevalence NN cord-018208-sc8j1ate 163 22 , , , cord-018208-sc8j1ate 163 23 i.e. i.e. FW cord-018208-sc8j1ate 163 24 when when WRB cord-018208-sc8j1ate 163 25 the the DT cord-018208-sc8j1ate 163 26 average average JJ cord-018208-sc8j1ate 163 27 fraction fraction NN cord-018208-sc8j1ate 163 28 y y NNP cord-018208-sc8j1ate 163 29 ∞ ∞ NNP cord-018208-sc8j1ate 163 30 of of IN cord-018208-sc8j1ate 163 31 infected infected JJ cord-018208-sc8j1ate 163 32 nodes node NNS cord-018208-sc8j1ate 163 33 obtained obtain VBN cord-018208-sc8j1ate 163 34 by by IN cord-018208-sc8j1ate 163 35 simulations simulation NNS cord-018208-sc8j1ate 163 36 is be VBZ cord-018208-sc8j1ate 163 37 given give VBN cord-018208-sc8j1ate 163 38 . . . cord-018208-sc8j1ate 164 1 Regarding regard VBG cord-018208-sc8j1ate 164 2 to to IN cord-018208-sc8j1ate 164 3 the the DT cord-018208-sc8j1ate 164 4 i.i.d i.i.d NN cord-018208-sc8j1ate 164 5 . . . cord-018208-sc8j1ate 164 6 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 164 7 infection infection NN cord-018208-sc8j1ate 164 8 rates rate NNS cord-018208-sc8j1ate 164 9 , , , cord-018208-sc8j1ate 164 10 the the DT cord-018208-sc8j1ate 164 11 accuracy accuracy NN cord-018208-sc8j1ate 164 12 of of IN cord-018208-sc8j1ate 164 13 NIMFA NIMFA NNP cord-018208-sc8j1ate 164 14 tends tend VBZ cord-018208-sc8j1ate 164 15 to to TO cord-018208-sc8j1ate 164 16 decrease decrease VB cord-018208-sc8j1ate 164 17 as as IN cord-018208-sc8j1ate 164 18 the the DT cord-018208-sc8j1ate 164 19 variance variance NN cord-018208-sc8j1ate 164 20 of of IN cord-018208-sc8j1ate 164 21 infection infection NN cord-018208-sc8j1ate 164 22 rates rate NNS cord-018208-sc8j1ate 164 23 increases increase VBZ cord-018208-sc8j1ate 164 24 . . . cord-018208-sc8j1ate 165 1 In in IN cord-018208-sc8j1ate 165 2 the the DT cord-018208-sc8j1ate 165 3 scenario scenario NN cord-018208-sc8j1ate 165 4 of of IN cord-018208-sc8j1ate 165 5 correlated correlate VBN cord-018208-sc8j1ate 165 6 infection infection NN cord-018208-sc8j1ate 165 7 rates rate NNS cord-018208-sc8j1ate 165 8 , , , cord-018208-sc8j1ate 165 9 the the DT cord-018208-sc8j1ate 165 10 positive positive JJ cord-018208-sc8j1ate 165 11 correlation correlation NN cord-018208-sc8j1ate 165 12 between between IN cord-018208-sc8j1ate 165 13 the the DT cord-018208-sc8j1ate 165 14 nodal nodal JJ cord-018208-sc8j1ate 165 15 degree degree NN cord-018208-sc8j1ate 165 16 and and CC cord-018208-sc8j1ate 165 17 the the DT cord-018208-sc8j1ate 165 18 infection infection NN cord-018208-sc8j1ate 165 19 rate rate NN cord-018208-sc8j1ate 165 20 is be VBZ cord-018208-sc8j1ate 165 21 more more RBR cord-018208-sc8j1ate 165 22 likely likely JJ cord-018208-sc8j1ate 165 23 to to TO cord-018208-sc8j1ate 165 24 increase increase VB cord-018208-sc8j1ate 165 25 the the DT cord-018208-sc8j1ate 165 26 accuracy accuracy NN cord-018208-sc8j1ate 165 27 of of IN cord-018208-sc8j1ate 165 28 NIMFA NIMFA NNP cord-018208-sc8j1ate 165 29 whereas whereas IN cord-018208-sc8j1ate 165 30 the the DT cord-018208-sc8j1ate 165 31 negative negative JJ cord-018208-sc8j1ate 165 32 correlation correlation NN cord-018208-sc8j1ate 165 33 tends tend VBZ cord-018208-sc8j1ate 165 34 to to TO cord-018208-sc8j1ate 165 35 lower lower VB cord-018208-sc8j1ate 165 36 down down IN cord-018208-sc8j1ate 165 37 the the DT cord-018208-sc8j1ate 165 38 accuracy accuracy NN cord-018208-sc8j1ate 165 39 especially especially RB cord-018208-sc8j1ate 165 40 when when WRB cord-018208-sc8j1ate 165 41 the the DT cord-018208-sc8j1ate 165 42 effective effective JJ cord-018208-sc8j1ate 165 43 infection infection NN cord-018208-sc8j1ate 165 44 rate rate NN cord-018208-sc8j1ate 165 45 τ τ NN cord-018208-sc8j1ate 165 46 is be VBZ cord-018208-sc8j1ate 165 47 small small JJ cord-018208-sc8j1ate 165 48 . . . cord-018208-sc8j1ate 166 1 Note note VB cord-018208-sc8j1ate 166 2 that that IN cord-018208-sc8j1ate 166 3 we -PRON- PRP cord-018208-sc8j1ate 166 4 discuss discuss VBP cord-018208-sc8j1ate 166 5 the the DT cord-018208-sc8j1ate 166 6 conditions condition NNS cord-018208-sc8j1ate 166 7 when when WRB cord-018208-sc8j1ate 166 8 NIMFA NIMFA NNP cord-018208-sc8j1ate 166 9 is be VBZ cord-018208-sc8j1ate 166 10 accurate accurate JJ cord-018208-sc8j1ate 166 11 but but CC cord-018208-sc8j1ate 166 12 the the DT cord-018208-sc8j1ate 166 13 cases case NNS cord-018208-sc8j1ate 166 14 where where WRB cord-018208-sc8j1ate 166 15 NIMFA NIMFA NNP cord-018208-sc8j1ate 166 16 is be VBZ cord-018208-sc8j1ate 166 17 far far RB cord-018208-sc8j1ate 166 18 from from IN cord-018208-sc8j1ate 166 19 the the DT cord-018208-sc8j1ate 166 20 simulations simulation NNS cord-018208-sc8j1ate 166 21 are be VBP cord-018208-sc8j1ate 166 22 still still RB cord-018208-sc8j1ate 166 23 unexplored unexplored JJ cord-018208-sc8j1ate 166 24 . . . cord-018208-sc8j1ate 167 1 Our -PRON- PRP$ cord-018208-sc8j1ate 167 2 work work NN cord-018208-sc8j1ate 167 3 sheds shed VBZ cord-018208-sc8j1ate 167 4 light light NN cord-018208-sc8j1ate 167 5 on on IN cord-018208-sc8j1ate 167 6 the the DT cord-018208-sc8j1ate 167 7 conditions condition NNS cord-018208-sc8j1ate 167 8 when when WRB cord-018208-sc8j1ate 167 9 we -PRON- PRP cord-018208-sc8j1ate 167 10 the the DT cord-018208-sc8j1ate 167 11 mean mean JJ cord-018208-sc8j1ate 167 12 - - HYPH cord-018208-sc8j1ate 167 13 field field NN cord-018208-sc8j1ate 167 14 approximation approximation NN cord-018208-sc8j1ate 167 15 of of IN cord-018208-sc8j1ate 167 16 the the DT cord-018208-sc8j1ate 167 17 SIS SIS NNP cord-018208-sc8j1ate 167 18 model model NN cord-018208-sc8j1ate 167 19 with with IN cord-018208-sc8j1ate 167 20 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 167 21 infection infection NN cord-018208-sc8j1ate 167 22 rates rate NNS cord-018208-sc8j1ate 167 23 is be VBZ cord-018208-sc8j1ate 167 24 accurate accurate JJ cord-018208-sc8j1ate 167 25 . . . cord-018208-sc8j1ate 168 1 Internet internet NN cord-018208-sc8j1ate 168 2 : : : cord-018208-sc8j1ate 169 1 Diameter diameter NN cord-018208-sc8j1ate 169 2 of of IN cord-018208-sc8j1ate 169 3 the the DT cord-018208-sc8j1ate 169 4 world world NN cord-018208-sc8j1ate 169 5 - - HYPH cord-018208-sc8j1ate 169 6 wide wide JJ cord-018208-sc8j1ate 169 7 web web NN cord-018208-sc8j1ate 169 8 Emergence emergence NN cord-018208-sc8j1ate 169 9 of of IN cord-018208-sc8j1ate 169 10 scaling scale VBG cord-018208-sc8j1ate 169 11 in in IN cord-018208-sc8j1ate 169 12 random random JJ cord-018208-sc8j1ate 169 13 networks network NNS cord-018208-sc8j1ate 170 1 The the DT cord-018208-sc8j1ate 170 2 architecture architecture NN cord-018208-sc8j1ate 170 3 of of IN cord-018208-sc8j1ate 170 4 complex complex JJ cord-018208-sc8j1ate 170 5 weighted weight VBN cord-018208-sc8j1ate 170 6 networks network NNS cord-018208-sc8j1ate 170 7 Slow slow JJ cord-018208-sc8j1ate 170 8 epidemic epidemic JJ cord-018208-sc8j1ate 170 9 extinction extinction NN cord-018208-sc8j1ate 170 10 in in IN cord-018208-sc8j1ate 170 11 populations population NNS cord-018208-sc8j1ate 170 12 with with IN cord-018208-sc8j1ate 170 13 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 170 14 infection infection NN cord-018208-sc8j1ate 170 15 rates rate NNS cord-018208-sc8j1ate 171 1 The the DT cord-018208-sc8j1ate 171 2 fractal fractal JJ cord-018208-sc8j1ate 171 3 properties property NNS cord-018208-sc8j1ate 171 4 of of IN cord-018208-sc8j1ate 171 5 internet internet NN cord-018208-sc8j1ate 171 6 Resilience resilience NN cord-018208-sc8j1ate 171 7 of of IN cord-018208-sc8j1ate 171 8 the the DT cord-018208-sc8j1ate 171 9 internet internet NN cord-018208-sc8j1ate 171 10 to to TO cord-018208-sc8j1ate 171 11 random random JJ cord-018208-sc8j1ate 171 12 breakdowns breakdown NNS cord-018208-sc8j1ate 171 13 Susceptible susceptible JJ cord-018208-sc8j1ate 171 14 - - HYPH cord-018208-sc8j1ate 171 15 infected infect VBN cord-018208-sc8j1ate 171 16 - - HYPH cord-018208-sc8j1ate 171 17 susceptible susceptible JJ cord-018208-sc8j1ate 171 18 model model NN cord-018208-sc8j1ate 171 19 : : : cord-018208-sc8j1ate 171 20 A a DT cord-018208-sc8j1ate 171 21 comparison comparison NN cord-018208-sc8j1ate 171 22 of of IN cord-018208-sc8j1ate 171 23 n n RB cord-018208-sc8j1ate 171 24 - - HYPH cord-018208-sc8j1ate 171 25 intertwined intertwined JJ cord-018208-sc8j1ate 171 26 and and CC cord-018208-sc8j1ate 171 27 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 171 28 mean mean NN cord-018208-sc8j1ate 171 29 - - HYPH cord-018208-sc8j1ate 171 30 field field NN cord-018208-sc8j1ate 171 31 approximations approximation NNS cord-018208-sc8j1ate 171 32 Epidemics epidemic NNS cord-018208-sc8j1ate 171 33 on on IN cord-018208-sc8j1ate 171 34 interconnected interconnect VBN cord-018208-sc8j1ate 171 35 lattices lattice NNS cord-018208-sc8j1ate 171 36 . . . cord-018208-sc8j1ate 172 1 EPL EPL NNP cord-018208-sc8j1ate 173 1 ( ( -LRB- cord-018208-sc8j1ate 173 2 Europhysics Europhysics NNP cord-018208-sc8j1ate 173 3 Letters Letters NNPS cord-018208-sc8j1ate 173 4 ) ) -RRB- cord-018208-sc8j1ate 173 5 105 105 CD cord-018208-sc8j1ate 173 6 Statistical statistical JJ cord-018208-sc8j1ate 173 7 analysis analysis NN cord-018208-sc8j1ate 173 8 of of IN cord-018208-sc8j1ate 173 9 airport airport NN cord-018208-sc8j1ate 173 10 network network NN cord-018208-sc8j1ate 173 11 of of IN cord-018208-sc8j1ate 173 12 china china NNP cord-018208-sc8j1ate 173 13 Epidemics Epidemics NNP cord-018208-sc8j1ate 173 14 in in IN cord-018208-sc8j1ate 173 15 interconnected interconnected JJ cord-018208-sc8j1ate 173 16 small small JJ cord-018208-sc8j1ate 173 17 - - HYPH cord-018208-sc8j1ate 173 18 world world NN cord-018208-sc8j1ate 173 19 networks network NNS cord-018208-sc8j1ate 173 20 Minimum minimum JJ cord-018208-sc8j1ate 173 21 spanning span VBG cord-018208-sc8j1ate 173 22 trees tree NNS cord-018208-sc8j1ate 173 23 of of IN cord-018208-sc8j1ate 173 24 weighted weighted JJ cord-018208-sc8j1ate 173 25 scale scale NN cord-018208-sc8j1ate 173 26 - - HYPH cord-018208-sc8j1ate 173 27 free free JJ cord-018208-sc8j1ate 173 28 networks network NNS cord-018208-sc8j1ate 173 29 Epidemic epidemic NN cord-018208-sc8j1ate 173 30 processes process NNS cord-018208-sc8j1ate 173 31 in in IN cord-018208-sc8j1ate 173 32 complex complex JJ cord-018208-sc8j1ate 173 33 networks network NNS cord-018208-sc8j1ate 173 34 Epidemic epidemic NN cord-018208-sc8j1ate 173 35 dynamics dynamic NNS cord-018208-sc8j1ate 173 36 and and CC cord-018208-sc8j1ate 173 37 endemic endemic JJ cord-018208-sc8j1ate 173 38 states state NNS cord-018208-sc8j1ate 173 39 in in IN cord-018208-sc8j1ate 173 40 complex complex JJ cord-018208-sc8j1ate 173 41 networks network NNS cord-018208-sc8j1ate 173 42 Epidemic epidemic NN cord-018208-sc8j1ate 173 43 spreading spread VBG cord-018208-sc8j1ate 173 44 in in IN cord-018208-sc8j1ate 173 45 scale scale NN cord-018208-sc8j1ate 173 46 - - HYPH cord-018208-sc8j1ate 173 47 free free JJ cord-018208-sc8j1ate 173 48 networks network NNS cord-018208-sc8j1ate 173 49 SIS SIS NNP cord-018208-sc8j1ate 173 50 epidemic epidemic NN cord-018208-sc8j1ate 173 51 spreading spread VBG cord-018208-sc8j1ate 173 52 with with IN cord-018208-sc8j1ate 173 53 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 173 54 infection infection NN cord-018208-sc8j1ate 173 55 rates rate NNS cord-018208-sc8j1ate 174 1 The the DT cord-018208-sc8j1ate 174 2 accuracy accuracy NN cord-018208-sc8j1ate 174 3 of of IN cord-018208-sc8j1ate 174 4 mean mean JJ cord-018208-sc8j1ate 174 5 - - HYPH cord-018208-sc8j1ate 174 6 field field NN cord-018208-sc8j1ate 174 7 approximation approximation NN cord-018208-sc8j1ate 174 8 for for IN cord-018208-sc8j1ate 174 9 susceptible susceptible JJ cord-018208-sc8j1ate 174 10 - - HYPH cord-018208-sc8j1ate 174 11 infectedsusceptible infectedsusceptible JJ cord-018208-sc8j1ate 174 12 epidemic epidemic NN cord-018208-sc8j1ate 174 13 spreading spread VBG cord-018208-sc8j1ate 174 14 SIS SIS NNP cord-018208-sc8j1ate 174 15 epidemic epidemic NN cord-018208-sc8j1ate 174 16 spreading spread VBG cord-018208-sc8j1ate 174 17 with with IN cord-018208-sc8j1ate 174 18 correlated correlate VBN cord-018208-sc8j1ate 174 19 heterogeneous heterogeneous JJ cord-018208-sc8j1ate 174 20 infection infection NN cord-018208-sc8j1ate 174 21 rates rate NNS cord-018208-sc8j1ate 174 22 Performance Performance NNP cord-018208-sc8j1ate 174 23 analysis analysis NN cord-018208-sc8j1ate 174 24 of of IN cord-018208-sc8j1ate 174 25 communications communication NNS cord-018208-sc8j1ate 174 26 networks network NNS cord-018208-sc8j1ate 174 27 and and CC cord-018208-sc8j1ate 174 28 systems system NNS cord-018208-sc8j1ate 174 29 Virus Virus NNP cord-018208-sc8j1ate 174 30 spread spread VBD cord-018208-sc8j1ate 174 31 in in IN cord-018208-sc8j1ate 174 32 networks network NNS cord-018208-sc8j1ate 174 33 Effect effect NN cord-018208-sc8j1ate 174 34 of of IN cord-018208-sc8j1ate 174 35 the the DT cord-018208-sc8j1ate 174 36 interconnected interconnected JJ cord-018208-sc8j1ate 174 37 network network NN cord-018208-sc8j1ate 174 38 structure structure NN cord-018208-sc8j1ate 174 39 on on IN cord-018208-sc8j1ate 174 40 the the DT cord-018208-sc8j1ate 174 41 epidemic epidemic NN cord-018208-sc8j1ate 174 42 threshold threshold NN cord-018208-sc8j1ate 174 43 Modelling model VBG cord-018208-sc8j1ate 174 44 the the DT cord-018208-sc8j1ate 174 45 spreading spread VBG cord-018208-sc8j1ate 174 46 rate rate NN cord-018208-sc8j1ate 174 47 of of IN cord-018208-sc8j1ate 174 48 controlled control VBN cord-018208-sc8j1ate 174 49 communicable communicable JJ cord-018208-sc8j1ate 174 50 epidemics epidemic NNS cord-018208-sc8j1ate 174 51 through through IN cord-018208-sc8j1ate 174 52 an an DT cord-018208-sc8j1ate 174 53 entropy entropy NN cord-018208-sc8j1ate 174 54 - - HYPH cord-018208-sc8j1ate 174 55 based base VBN cord-018208-sc8j1ate 174 56 thermodynamic thermodynamic JJ cord-018208-sc8j1ate 174 57 model model NN cord-018208-sc8j1ate 174 58 Epidemic epidemic NN cord-018208-sc8j1ate 174 59 spreading spread VBG cord-018208-sc8j1ate 174 60 in in IN cord-018208-sc8j1ate 174 61 weighted weighted JJ cord-018208-sc8j1ate 174 62 networks network NNS cord-018208-sc8j1ate 174 63 : : : cord-018208-sc8j1ate 174 64 an an DT cord-018208-sc8j1ate 174 65 edge edge NN cord-018208-sc8j1ate 174 66 - - HYPH cord-018208-sc8j1ate 174 67 based base VBN cord-018208-sc8j1ate 174 68 mean mean NN cord-018208-sc8j1ate 174 69 - - HYPH cord-018208-sc8j1ate 174 70 field field NN cord-018208-sc8j1ate 174 71 solution solution NN