id sid tid token lemma pos american_scientific_journal-3424 1 1 1 1 NUM american_scientific_journal-3424 1 2 american american ADJ american_scientific_journal-3424 1 3 scientific scientific ADJ american_scientific_journal-3424 1 4 research research NOUN american_scientific_journal-3424 1 5 journal journal NOUN american_scientific_journal-3424 1 6 for for ADP american_scientific_journal-3424 1 7 engineering engineering NOUN american_scientific_journal-3424 1 8 , , PUNCT american_scientific_journal-3424 1 9 technology technology NOUN american_scientific_journal-3424 1 10 , , PUNCT american_scientific_journal-3424 1 11 and and CCONJ american_scientific_journal-3424 1 12 sciences science NOUN american_scientific_journal-3424 1 13 ( ( PUNCT american_scientific_journal-3424 1 14 asrjets asrjet NOUN american_scientific_journal-3424 1 15 ) ) PUNCT american_scientific_journal-3424 1 16 issn issn PROPN american_scientific_journal-3424 1 17 ( ( PUNCT american_scientific_journal-3424 1 18 print print NOUN american_scientific_journal-3424 1 19 ) ) PUNCT american_scientific_journal-3424 1 20 2313 2313 NUM american_scientific_journal-3424 1 21 - - SYM american_scientific_journal-3424 1 22 4410 4410 NUM american_scientific_journal-3424 1 23 , , PUNCT american_scientific_journal-3424 1 24 issn issn PROPN american_scientific_journal-3424 1 25 ( ( PUNCT american_scientific_journal-3424 1 26 online online ADJ american_scientific_journal-3424 1 27 ) ) PUNCT american_scientific_journal-3424 1 28 2313 2313 NUM american_scientific_journal-3424 1 29 - - SYM american_scientific_journal-3424 1 30 4402 4402 NUM american_scientific_journal-3424 1 31 Β© Β© PROPN american_scientific_journal-3424 1 32 global global ADJ american_scientific_journal-3424 1 33 society society NOUN american_scientific_journal-3424 1 34 of of ADP american_scientific_journal-3424 1 35 scientific scientific ADJ american_scientific_journal-3424 1 36 research research NOUN american_scientific_journal-3424 1 37 and and CCONJ american_scientific_journal-3424 1 38 researchers researcher NOUN american_scientific_journal-3424 1 39 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-3424 1 40 numerical numerical ADJ american_scientific_journal-3424 1 41 study study NOUN american_scientific_journal-3424 1 42 of of ADP american_scientific_journal-3424 1 43 kermack kermack NOUN american_scientific_journal-3424 1 44 - - PUNCT american_scientific_journal-3424 1 45 mckendrik mckendrik ADJ american_scientific_journal-3424 1 46 sir sir PROPN american_scientific_journal-3424 1 47 model model NOUN american_scientific_journal-3424 1 48 to to PART american_scientific_journal-3424 1 49 predict predict VERB american_scientific_journal-3424 1 50 the the DET american_scientific_journal-3424 1 51 outbreak outbreak NOUN american_scientific_journal-3424 1 52 of of ADP american_scientific_journal-3424 1 53 ebola ebola PROPN american_scientific_journal-3424 1 54 virus virus NOUN american_scientific_journal-3424 1 55 diseases disease NOUN american_scientific_journal-3424 1 56 using use VERB american_scientific_journal-3424 1 57 euler euler NOUN american_scientific_journal-3424 1 58 and and CCONJ american_scientific_journal-3424 1 59 fourth fourth ADJ american_scientific_journal-3424 1 60 order order NOUN american_scientific_journal-3424 1 61 runge runge NOUN american_scientific_journal-3424 1 62 - - PUNCT american_scientific_journal-3424 1 63 kutta kutta NOUN american_scientific_journal-3424 1 64 methods method NOUN american_scientific_journal-3424 1 65 md md PROPN american_scientific_journal-3424 1 66 . . PUNCT american_scientific_journal-3424 1 67 tareque tareque PROPN american_scientific_journal-3424 1 68 hossaina hossaina PROPN american_scientific_journal-3424 1 69 , , PUNCT american_scientific_journal-3424 1 70 md md PROPN american_scientific_journal-3424 1 71 . . PROPN american_scientific_journal-3424 1 72 musa musa PROPN american_scientific_journal-3424 1 73 miahb miahb PROPN american_scientific_journal-3424 1 74 * * PROPN american_scientific_journal-3424 1 75 , , PUNCT american_scientific_journal-3424 1 76 md md PROPN american_scientific_journal-3424 1 77 . . PROPN american_scientific_journal-3424 1 78 babul babul PROPN american_scientific_journal-3424 1 79 hossainc hossainc PROPN american_scientific_journal-3424 1 80 adepartment adepartment PROPN american_scientific_journal-3424 1 81 of of ADP american_scientific_journal-3424 1 82 textile textile NOUN american_scientific_journal-3424 1 83 engineering engineering NOUN american_scientific_journal-3424 1 84 , , PUNCT american_scientific_journal-3424 1 85 city city NOUN american_scientific_journal-3424 1 86 university university PROPN american_scientific_journal-3424 1 87 , , PUNCT american_scientific_journal-3424 1 88 birulia birulia PROPN american_scientific_journal-3424 1 89 , , PUNCT american_scientific_journal-3424 1 90 savar savar NOUN american_scientific_journal-3424 1 91 , , PUNCT american_scientific_journal-3424 1 92 dhaka dhaka PROPN american_scientific_journal-3424 1 93 , , PUNCT american_scientific_journal-3424 1 94 bangladesh bangladesh PROPN american_scientific_journal-3424 1 95 b b PROPN american_scientific_journal-3424 1 96 , , PUNCT american_scientific_journal-3424 1 97 cdepartment cdepartment NOUN american_scientific_journal-3424 1 98 of of ADP american_scientific_journal-3424 1 99 mathematics mathematic NOUN american_scientific_journal-3424 1 100 , , PUNCT american_scientific_journal-3424 1 101 mawlana mawlana NOUN american_scientific_journal-3424 1 102 bhashani bhashani VERB american_scientific_journal-3424 1 103 science science NOUN american_scientific_journal-3424 1 104 and and CCONJ american_scientific_journal-3424 1 105 technology technology NOUN american_scientific_journal-3424 1 106 university university PROPN american_scientific_journal-3424 1 107 , , PUNCT american_scientific_journal-3424 1 108 santosh santosh NOUN american_scientific_journal-3424 1 109 , , PUNCT american_scientific_journal-3424 1 110 tangail-1902 tangail-1902 NOUN american_scientific_journal-3424 1 111 , , PUNCT american_scientific_journal-3424 1 112 bangladesh bangladesh NOUN american_scientific_journal-3424 1 113 aemail aemail NOUN american_scientific_journal-3424 1 114 : : PUNCT american_scientific_journal-3424 1 115 tareque.ms@gmail.com tareque.ms@gmail.com PROPN american_scientific_journal-3424 1 116 , , PUNCT american_scientific_journal-3424 1 117 bemail bemail NOUN american_scientific_journal-3424 1 118 : : PUNCT american_scientific_journal-3424 1 119 musa_ju69@yahoo.com musa_ju69@yahoo.com PROPN american_scientific_journal-3424 1 120 , , PUNCT american_scientific_journal-3424 1 121 cemail cemail NOUN american_scientific_journal-3424 1 122 : : PUNCT american_scientific_journal-3424 1 123 babulhossainh@yahoo.com babulhossainh@yahoo.com X american_scientific_journal-3424 2 1 abstract abstract ADJ american_scientific_journal-3424 2 2 mathematical mathematical ADJ american_scientific_journal-3424 2 3 modeling modeling NOUN american_scientific_journal-3424 2 4 has have AUX american_scientific_journal-3424 2 5 emerged emerge VERB american_scientific_journal-3424 2 6 as as ADP american_scientific_journal-3424 2 7 a a DET american_scientific_journal-3424 2 8 vital vital ADJ american_scientific_journal-3424 2 9 tool tool NOUN american_scientific_journal-3424 2 10 for for ADP american_scientific_journal-3424 2 11 understanding understand VERB american_scientific_journal-3424 2 12 the the DET american_scientific_journal-3424 2 13 dynamics dynamic NOUN american_scientific_journal-3424 2 14 of of ADP american_scientific_journal-3424 2 15 the the DET american_scientific_journal-3424 2 16 spread spread NOUN american_scientific_journal-3424 2 17 of of ADP american_scientific_journal-3424 2 18 many many ADJ american_scientific_journal-3424 2 19 infectious infectious ADJ american_scientific_journal-3424 2 20 diseases disease NOUN american_scientific_journal-3424 2 21 , , PUNCT american_scientific_journal-3424 2 22 one one NUM american_scientific_journal-3424 2 23 amongst amongst ADV american_scientific_journal-3424 2 24 is be AUX american_scientific_journal-3424 2 25 ebola ebola PROPN american_scientific_journal-3424 2 26 virus virus NOUN american_scientific_journal-3424 2 27 . . PUNCT american_scientific_journal-3424 3 1 the the DET american_scientific_journal-3424 3 2 main main ADJ american_scientific_journal-3424 3 3 focus focus NOUN american_scientific_journal-3424 3 4 of of ADP american_scientific_journal-3424 3 5 this this DET american_scientific_journal-3424 3 6 paper paper NOUN american_scientific_journal-3424 3 7 is be AUX american_scientific_journal-3424 3 8 to to PART american_scientific_journal-3424 3 9 model model VERB american_scientific_journal-3424 3 10 mathematically mathematically ADV american_scientific_journal-3424 3 11 the the DET american_scientific_journal-3424 3 12 transmission transmission NOUN american_scientific_journal-3424 3 13 dynamics dynamic NOUN american_scientific_journal-3424 3 14 of of ADP american_scientific_journal-3424 3 15 ebola ebola PROPN american_scientific_journal-3424 3 16 virus virus NOUN american_scientific_journal-3424 3 17 . . PUNCT american_scientific_journal-3424 4 1 for for ADP american_scientific_journal-3424 4 2 this this DET american_scientific_journal-3424 4 3 purpose purpose NOUN american_scientific_journal-3424 4 4 we we PRON american_scientific_journal-3424 4 5 tend tend VERB american_scientific_journal-3424 4 6 to to PART american_scientific_journal-3424 4 7 use use VERB american_scientific_journal-3424 4 8 basic basic ADJ american_scientific_journal-3424 4 9 sir sir NOUN american_scientific_journal-3424 4 10 model model NOUN american_scientific_journal-3424 4 11 of of ADP american_scientific_journal-3424 4 12 ebola ebola PROPN american_scientific_journal-3424 4 13 virus virus NOUN american_scientific_journal-3424 4 14 to to PART american_scientific_journal-3424 4 15 predict predict VERB american_scientific_journal-3424 4 16 the the DET american_scientific_journal-3424 4 17 outbreak outbreak NOUN american_scientific_journal-3424 4 18 of of ADP american_scientific_journal-3424 4 19 the the DET american_scientific_journal-3424 4 20 diseases disease NOUN american_scientific_journal-3424 4 21 . . PUNCT american_scientific_journal-3424 5 1 as as SCONJ american_scientific_journal-3424 5 2 we we PRON american_scientific_journal-3424 5 3 can can AUX american_scientific_journal-3424 5 4 not not PART american_scientific_journal-3424 5 5 fully fully ADV american_scientific_journal-3424 5 6 solve solve VERB american_scientific_journal-3424 5 7 the the DET american_scientific_journal-3424 5 8 3 3 NUM american_scientific_journal-3424 5 9 basic basic ADJ american_scientific_journal-3424 5 10 equations equation NOUN american_scientific_journal-3424 5 11 of of ADP american_scientific_journal-3424 5 12 sir sir PROPN american_scientific_journal-3424 5 13 model model NOUN american_scientific_journal-3424 5 14 with with ADP american_scientific_journal-3424 5 15 a a DET american_scientific_journal-3424 5 16 certain certain ADJ american_scientific_journal-3424 5 17 formula formula NOUN american_scientific_journal-3424 5 18 solution solution NOUN american_scientific_journal-3424 5 19 , , PUNCT american_scientific_journal-3424 5 20 we we PRON american_scientific_journal-3424 5 21 introduce introduce VERB american_scientific_journal-3424 5 22 euler euler NOUN american_scientific_journal-3424 5 23 and and CCONJ american_scientific_journal-3424 5 24 fourth fourth ADJ american_scientific_journal-3424 5 25 - - PUNCT american_scientific_journal-3424 5 26 order order NOUN american_scientific_journal-3424 5 27 runge runge NOUN american_scientific_journal-3424 5 28 - - PUNCT american_scientific_journal-3424 5 29 kutta kutta NOUN american_scientific_journal-3424 5 30 methods method NOUN american_scientific_journal-3424 5 31 ( ( PUNCT american_scientific_journal-3424 5 32 rk4 rk4 NOUN american_scientific_journal-3424 5 33 ) ) PUNCT american_scientific_journal-3424 5 34 . . PUNCT american_scientific_journal-3424 6 1 these these DET american_scientific_journal-3424 6 2 two two NUM american_scientific_journal-3424 6 3 proposed propose VERB american_scientific_journal-3424 6 4 strategies strategy NOUN american_scientific_journal-3424 6 5 are be AUX american_scientific_journal-3424 6 6 quite quite ADV american_scientific_journal-3424 6 7 efficient efficient ADJ american_scientific_journal-3424 6 8 and and CCONJ american_scientific_journal-3424 6 9 practically practically ADV american_scientific_journal-3424 6 10 well well ADV american_scientific_journal-3424 6 11 suited suited ADJ american_scientific_journal-3424 6 12 for for ADP american_scientific_journal-3424 6 13 solving solve VERB american_scientific_journal-3424 6 14 initial initial ADJ american_scientific_journal-3424 6 15 value value NOUN american_scientific_journal-3424 6 16 problem problem NOUN american_scientific_journal-3424 6 17 ( ( PUNCT american_scientific_journal-3424 6 18 ivp ivp NOUN american_scientific_journal-3424 6 19 ) ) PUNCT american_scientific_journal-3424 6 20 for for ADP american_scientific_journal-3424 6 21 ordinary ordinary ADJ american_scientific_journal-3424 6 22 differential differential ADJ american_scientific_journal-3424 6 23 equations equation NOUN american_scientific_journal-3424 6 24 ( ( PUNCT american_scientific_journal-3424 6 25 ode).we ode).we NOUN american_scientific_journal-3424 6 26 discuss discuss VERB american_scientific_journal-3424 6 27 the the DET american_scientific_journal-3424 6 28 numerical numerical ADJ american_scientific_journal-3424 6 29 comparisons comparison NOUN american_scientific_journal-3424 6 30 between between ADP american_scientific_journal-3424 6 31 euler euler NOUN american_scientific_journal-3424 6 32 method method NOUN american_scientific_journal-3424 6 33 and and CCONJ american_scientific_journal-3424 6 34 runge runge NOUN american_scientific_journal-3424 6 35 - - PUNCT american_scientific_journal-3424 6 36 kutta kutta NOUN american_scientific_journal-3424 6 37 methods method NOUN american_scientific_journal-3424 6 38 and and CCONJ american_scientific_journal-3424 6 39 also also ADV american_scientific_journal-3424 6 40 discuss discuss VERB american_scientific_journal-3424 6 41 regarding regard VERB american_scientific_journal-3424 6 42 their their PRON american_scientific_journal-3424 6 43 performances performance NOUN american_scientific_journal-3424 6 44 with with ADP american_scientific_journal-3424 6 45 the the DET american_scientific_journal-3424 6 46 actual actual ADJ american_scientific_journal-3424 6 47 data datum NOUN american_scientific_journal-3424 6 48 . . PUNCT american_scientific_journal-3424 7 1 the the DET american_scientific_journal-3424 7 2 population population NOUN american_scientific_journal-3424 7 3 that that PRON american_scientific_journal-3424 7 4 we we PRON american_scientific_journal-3424 7 5 used use VERB american_scientific_journal-3424 7 6 for for ADP american_scientific_journal-3424 7 7 this this DET american_scientific_journal-3424 7 8 model model NOUN american_scientific_journal-3424 7 9 had have VERB american_scientific_journal-3424 7 10 roughly roughly ADV american_scientific_journal-3424 7 11 a a DET american_scientific_journal-3424 7 12 similar similar ADJ american_scientific_journal-3424 7 13 number number NOUN american_scientific_journal-3424 7 14 of of ADP american_scientific_journal-3424 7 15 individuals individual NOUN american_scientific_journal-3424 7 16 as as SCONJ american_scientific_journal-3424 7 17 the the DET american_scientific_journal-3424 7 18 number number NOUN american_scientific_journal-3424 7 19 was be AUX american_scientific_journal-3424 7 20 living live VERB american_scientific_journal-3424 7 21 in in ADP american_scientific_journal-3424 7 22 republic republic NOUN american_scientific_journal-3424 7 23 of of ADP american_scientific_journal-3424 7 24 liberia liberia PROPN american_scientific_journal-3424 7 25 during during ADP american_scientific_journal-3424 7 26 2014 2014 NUM american_scientific_journal-3424 7 27 . . PUNCT american_scientific_journal-3424 8 1 keywords keyword NOUN american_scientific_journal-3424 8 2 : : PUNCT american_scientific_journal-3424 8 3 ebola ebola NOUN american_scientific_journal-3424 8 4 ; ; PUNCT american_scientific_journal-3424 8 5 outbreak outbreak NOUN american_scientific_journal-3424 8 6 ; ; PUNCT american_scientific_journal-3424 8 7 evolution evolution NOUN american_scientific_journal-3424 8 8 ; ; PUNCT american_scientific_journal-3424 8 9 mathematical mathematical ADJ american_scientific_journal-3424 8 10 modeling modeling NOUN american_scientific_journal-3424 8 11 . . PUNCT american_scientific_journal-3424 9 1 1 1 X american_scientific_journal-3424 9 2 . . X american_scientific_journal-3424 9 3 introduction introduction NOUN american_scientific_journal-3424 9 4 mathematical mathematical ADJ american_scientific_journal-3424 9 5 models model NOUN american_scientific_journal-3424 9 6 are be AUX american_scientific_journal-3424 9 7 a a DET american_scientific_journal-3424 9 8 powerful powerful ADJ american_scientific_journal-3424 9 9 tool tool NOUN american_scientific_journal-3424 9 10 for for ADP american_scientific_journal-3424 9 11 investigating investigate VERB american_scientific_journal-3424 9 12 human human ADJ american_scientific_journal-3424 9 13 infectious infectious ADJ american_scientific_journal-3424 9 14 diseases disease NOUN american_scientific_journal-3424 9 15 , , PUNCT american_scientific_journal-3424 9 16 such such ADJ american_scientific_journal-3424 9 17 as as ADP american_scientific_journal-3424 9 18 ebola ebola PROPN american_scientific_journal-3424 9 19 virus virus NOUN american_scientific_journal-3424 9 20 , , PUNCT american_scientific_journal-3424 9 21 contributing contribute VERB american_scientific_journal-3424 9 22 to to ADP american_scientific_journal-3424 9 23 the the DET american_scientific_journal-3424 9 24 understanding understanding NOUN american_scientific_journal-3424 9 25 of of ADP american_scientific_journal-3424 9 26 the the DET american_scientific_journal-3424 9 27 dynamics dynamic NOUN american_scientific_journal-3424 9 28 of of ADP american_scientific_journal-3424 9 29 disease disease NOUN american_scientific_journal-3424 9 30 and and CCONJ american_scientific_journal-3424 9 31 providing provide VERB american_scientific_journal-3424 9 32 useful useful ADJ american_scientific_journal-3424 9 33 predictions prediction NOUN american_scientific_journal-3424 9 34 about about ADP american_scientific_journal-3424 9 35 the the DET american_scientific_journal-3424 9 36 potential potential ADJ american_scientific_journal-3424 9 37 transmission transmission NOUN american_scientific_journal-3424 9 38 of of ADP american_scientific_journal-3424 9 39 a a DET american_scientific_journal-3424 9 40 disease disease NOUN american_scientific_journal-3424 9 41 and and CCONJ american_scientific_journal-3424 9 42 the the DET american_scientific_journal-3424 9 43 effectiveness effectiveness NOUN american_scientific_journal-3424 9 44 of of ADP american_scientific_journal-3424 9 45 possible possible ADJ american_scientific_journal-3424 9 46 control control NOUN american_scientific_journal-3424 9 47 measures measure NOUN american_scientific_journal-3424 9 48 , , PUNCT american_scientific_journal-3424 9 49 which which PRON american_scientific_journal-3424 9 50 can can AUX american_scientific_journal-3424 9 51 provide provide VERB american_scientific_journal-3424 9 52 valuable valuable ADJ american_scientific_journal-3424 9 53 information information NOUN american_scientific_journal-3424 9 54 for for ADP american_scientific_journal-3424 9 55 public public ADJ american_scientific_journal-3424 9 56 health health NOUN american_scientific_journal-3424 9 57 policy policy NOUN american_scientific_journal-3424 9 58 makers maker NOUN american_scientific_journal-3424 9 59 . . PUNCT american_scientific_journal-3424 10 1 ----------------------------------------------------------------------- ----------------------------------------------------------------------- PUNCT american_scientific_journal-3424 11 1 * * PUNCT american_scientific_journal-3424 11 2 corresponding correspond VERB american_scientific_journal-3424 11 3 author author NOUN american_scientific_journal-3424 11 4 . . PUNCT american_scientific_journal-3424 12 1 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-3424 12 2 american american PROPN american_scientific_journal-3424 12 3 scientific scientific PROPN american_scientific_journal-3424 12 4 research research NOUN american_scientific_journal-3424 12 5 journal journal NOUN american_scientific_journal-3424 12 6 for for ADP american_scientific_journal-3424 12 7 engineering engineering NOUN american_scientific_journal-3424 12 8 , , PUNCT american_scientific_journal-3424 12 9 technology technology NOUN american_scientific_journal-3424 12 10 , , PUNCT american_scientific_journal-3424 12 11 and and CCONJ american_scientific_journal-3424 12 12 sciences science NOUN american_scientific_journal-3424 12 13 ( ( PUNCT american_scientific_journal-3424 12 14 asrjets asrjet NOUN american_scientific_journal-3424 12 15 ) ) PUNCT american_scientific_journal-3424 12 16 ( ( PUNCT american_scientific_journal-3424 12 17 2017 2017 NUM american_scientific_journal-3424 12 18 ) ) PUNCT american_scientific_journal-3424 12 19 volume volume NOUN american_scientific_journal-3424 12 20 37 37 NUM american_scientific_journal-3424 12 21 , , PUNCT american_scientific_journal-3424 12 22 no no DET american_scientific_journal-3424 12 23 1 1 NUM american_scientific_journal-3424 12 24 , , PUNCT american_scientific_journal-3424 12 25 pp pp ADV american_scientific_journal-3424 12 26 1 1 NUM american_scientific_journal-3424 12 27 - - SYM american_scientific_journal-3424 12 28 21 21 NUM american_scientific_journal-3424 12 29 2 2 NUM american_scientific_journal-3424 12 30 the the DET american_scientific_journal-3424 12 31 ebola ebola PROPN american_scientific_journal-3424 12 32 virus virus NOUN american_scientific_journal-3424 12 33 disease disease NOUN american_scientific_journal-3424 12 34 was be AUX american_scientific_journal-3424 12 35 first first ADV american_scientific_journal-3424 12 36 discovered discover VERB american_scientific_journal-3424 12 37 in in ADP american_scientific_journal-3424 12 38 1976 1976 NUM american_scientific_journal-3424 12 39 in in ADP american_scientific_journal-3424 12 40 the the DET american_scientific_journal-3424 12 41 present present ADJ american_scientific_journal-3424 12 42 democratic democratic PROPN american_scientific_journal-3424 12 43 republic republic PROPN american_scientific_journal-3424 12 44 of of ADP american_scientific_journal-3424 12 45 congo congo PROPN american_scientific_journal-3424 13 1 [ [ X american_scientific_journal-3424 13 2 1 1 NUM american_scientific_journal-3424 13 3 ] ] PUNCT american_scientific_journal-3424 13 4 . . PUNCT american_scientific_journal-3424 14 1 since since SCONJ american_scientific_journal-3424 14 2 then then ADV american_scientific_journal-3424 14 3 , , PUNCT american_scientific_journal-3424 14 4 there there PRON american_scientific_journal-3424 14 5 have have AUX american_scientific_journal-3424 14 6 been be AUX american_scientific_journal-3424 14 7 many many ADJ american_scientific_journal-3424 14 8 outbreaks outbreak NOUN american_scientific_journal-3424 14 9 ; ; PUNCT american_scientific_journal-3424 14 10 with with ADP american_scientific_journal-3424 14 11 the the DET american_scientific_journal-3424 14 12 greatest great ADJ american_scientific_journal-3424 14 13 was be AUX american_scientific_journal-3424 14 14 2014 2014 NUM american_scientific_journal-3424 14 15 outbreak outbreak NOUN american_scientific_journal-3424 14 16 [ [ X american_scientific_journal-3424 14 17 2 2 X american_scientific_journal-3424 14 18 ] ] PUNCT american_scientific_journal-3424 14 19 which which PRON american_scientific_journal-3424 14 20 has have AUX american_scientific_journal-3424 14 21 spread spread VERB american_scientific_journal-3424 14 22 through through ADP american_scientific_journal-3424 14 23 many many ADJ american_scientific_journal-3424 14 24 countries country NOUN american_scientific_journal-3424 14 25 . . PUNCT american_scientific_journal-3424 15 1 according accord VERB american_scientific_journal-3424 15 2 to to ADP american_scientific_journal-3424 15 3 bekoe bekoe PROPN american_scientific_journal-3424 15 4 ( ( PUNCT american_scientific_journal-3424 15 5 2015 2015 NUM american_scientific_journal-3424 15 6 ) ) PUNCT american_scientific_journal-3424 15 7 , , PUNCT american_scientific_journal-3424 15 8 from from ADP american_scientific_journal-3424 15 9 the the DET american_scientific_journal-3424 15 10 first first ADJ american_scientific_journal-3424 15 11 confirmed confirm VERB american_scientific_journal-3424 15 12 case case NOUN american_scientific_journal-3424 15 13 recorded record VERB american_scientific_journal-3424 15 14 on on ADP american_scientific_journal-3424 15 15 23 23 NUM american_scientific_journal-3424 15 16 march march NOUN american_scientific_journal-3424 15 17 2014 2014 NUM american_scientific_journal-3424 15 18 which which DET american_scientific_journal-3424 15 19 more more ADJ american_scientific_journal-3424 15 20 than than ADP american_scientific_journal-3424 15 21 18 18 NUM american_scientific_journal-3424 15 22 months month NOUN american_scientific_journal-3424 15 23 , , PUNCT american_scientific_journal-3424 15 24 at at ADP american_scientific_journal-3424 15 25 least least ADJ american_scientific_journal-3424 15 26 11,312 11,312 NUM american_scientific_journal-3424 15 27 people people NOUN american_scientific_journal-3424 15 28 have have AUX american_scientific_journal-3424 15 29 been be AUX american_scientific_journal-3424 15 30 reported report VERB american_scientific_journal-3424 15 31 died die VERB american_scientific_journal-3424 15 32 from from ADP american_scientific_journal-3424 15 33 the the DET american_scientific_journal-3424 15 34 disease disease NOUN american_scientific_journal-3424 15 35 in in ADP american_scientific_journal-3424 15 36 six six NUM american_scientific_journal-3424 15 37 countries country NOUN american_scientific_journal-3424 15 38 ; ; PUNCT american_scientific_journal-3424 15 39 liberia liberia PROPN american_scientific_journal-3424 15 40 , , PUNCT american_scientific_journal-3424 15 41 sierra sierra PROPN american_scientific_journal-3424 15 42 leone leone PROPN american_scientific_journal-3424 15 43 , , PUNCT american_scientific_journal-3424 15 44 guinea guinea NOUN american_scientific_journal-3424 15 45 , , PUNCT american_scientific_journal-3424 15 46 nigeria nigeria PROPN american_scientific_journal-3424 15 47 , , PUNCT american_scientific_journal-3424 15 48 mali mali PROPN american_scientific_journal-3424 15 49 and and CCONJ american_scientific_journal-3424 15 50 us we PRON american_scientific_journal-3424 15 51 . . PUNCT american_scientific_journal-3424 16 1 since since SCONJ american_scientific_journal-3424 16 2 the the DET american_scientific_journal-3424 16 3 virus virus NOUN american_scientific_journal-3424 16 4 keeps keep VERB american_scientific_journal-3424 16 5 spreading spread VERB american_scientific_journal-3424 16 6 through through ADP american_scientific_journal-3424 16 7 contacts contact NOUN american_scientific_journal-3424 16 8 and and CCONJ american_scientific_journal-3424 16 9 the the DET american_scientific_journal-3424 16 10 mortality mortality NOUN american_scientific_journal-3424 16 11 rate rate NOUN american_scientific_journal-3424 16 12 of of ADP american_scientific_journal-3424 16 13 0.7[3 0.7[3 NUM american_scientific_journal-3424 16 14 ] ] PUNCT american_scientific_journal-3424 16 15 , , PUNCT american_scientific_journal-3424 16 16 it it PRON american_scientific_journal-3424 16 17 is be AUX american_scientific_journal-3424 16 18 needed need VERB american_scientific_journal-3424 16 19 to to PART american_scientific_journal-3424 16 20 understand understand VERB american_scientific_journal-3424 16 21 the the DET american_scientific_journal-3424 16 22 patterns pattern NOUN american_scientific_journal-3424 16 23 and and CCONJ american_scientific_journal-3424 16 24 epidemiology epidemiology NOUN american_scientific_journal-3424 16 25 of of ADP american_scientific_journal-3424 16 26 the the DET american_scientific_journal-3424 16 27 disease disease NOUN american_scientific_journal-3424 16 28 . . PUNCT american_scientific_journal-3424 17 1 by by ADP american_scientific_journal-3424 17 2 these these DET american_scientific_journal-3424 17 3 conditions condition NOUN american_scientific_journal-3424 17 4 , , PUNCT american_scientific_journal-3424 17 5 mathematical mathematical ADJ american_scientific_journal-3424 17 6 model model NOUN american_scientific_journal-3424 17 7 of of ADP american_scientific_journal-3424 17 8 the the DET american_scientific_journal-3424 17 9 outbreaks outbreak NOUN american_scientific_journal-3424 17 10 of of ADP american_scientific_journal-3424 17 11 ebola ebola PROPN american_scientific_journal-3424 17 12 virus virus NOUN american_scientific_journal-3424 17 13 can can AUX american_scientific_journal-3424 17 14 be be AUX american_scientific_journal-3424 17 15 helpful helpful ADJ american_scientific_journal-3424 17 16 as as SCONJ american_scientific_journal-3424 17 17 it it PRON american_scientific_journal-3424 17 18 is be AUX american_scientific_journal-3424 17 19 a a DET american_scientific_journal-3424 17 20 platform platform NOUN american_scientific_journal-3424 17 21 for for ADP american_scientific_journal-3424 17 22 understanding understand VERB american_scientific_journal-3424 17 23 the the DET american_scientific_journal-3424 17 24 behavior behavior NOUN american_scientific_journal-3424 17 25 of of ADP american_scientific_journal-3424 17 26 a a DET american_scientific_journal-3424 17 27 dynamical dynamical ADJ american_scientific_journal-3424 17 28 system system NOUN american_scientific_journal-3424 17 29 . . PUNCT american_scientific_journal-3424 18 1 the the DET american_scientific_journal-3424 18 2 objectives objective NOUN american_scientific_journal-3424 18 3 are be AUX american_scientific_journal-3424 18 4 to to PART american_scientific_journal-3424 18 5 understand understand VERB american_scientific_journal-3424 18 6 better well ADJ american_scientific_journal-3424 18 7 the the DET american_scientific_journal-3424 18 8 mathematical mathematical ADJ american_scientific_journal-3424 18 9 dynamics dynamic NOUN american_scientific_journal-3424 18 10 of of ADP american_scientific_journal-3424 18 11 an an DET american_scientific_journal-3424 18 12 infected infected ADJ american_scientific_journal-3424 18 13 population population NOUN american_scientific_journal-3424 18 14 when when SCONJ american_scientific_journal-3424 18 15 an an DET american_scientific_journal-3424 18 16 outbreak outbreak NOUN american_scientific_journal-3424 18 17 occurs occur VERB american_scientific_journal-3424 18 18 . . PUNCT american_scientific_journal-3424 19 1 another another DET american_scientific_journal-3424 19 2 goal goal NOUN american_scientific_journal-3424 19 3 is be AUX american_scientific_journal-3424 19 4 to to PART american_scientific_journal-3424 19 5 use use VERB american_scientific_journal-3424 19 6 mathematical mathematical ADJ american_scientific_journal-3424 19 7 modeling modeling NOUN american_scientific_journal-3424 19 8 to to PART american_scientific_journal-3424 19 9 examine examine VERB american_scientific_journal-3424 19 10 and and CCONJ american_scientific_journal-3424 19 11 to to PART american_scientific_journal-3424 19 12 analyze analyze VERB american_scientific_journal-3424 19 13 the the DET american_scientific_journal-3424 19 14 viral viral ADJ american_scientific_journal-3424 19 15 dynamics dynamic NOUN american_scientific_journal-3424 19 16 of of ADP american_scientific_journal-3424 19 17 the the DET american_scientific_journal-3424 19 18 ebola ebola PROPN american_scientific_journal-3424 19 19 virus virus NOUN american_scientific_journal-3424 19 20 . . PUNCT american_scientific_journal-3424 20 1 to to PART american_scientific_journal-3424 20 2 model model VERB american_scientific_journal-3424 20 3 this this DET american_scientific_journal-3424 20 4 outbreak outbreak NOUN american_scientific_journal-3424 20 5 , , PUNCT american_scientific_journal-3424 20 6 the the DET american_scientific_journal-3424 20 7 systems system NOUN american_scientific_journal-3424 20 8 of of ADP american_scientific_journal-3424 20 9 differential differential ADJ american_scientific_journal-3424 20 10 equations equation NOUN american_scientific_journal-3424 20 11 are be AUX american_scientific_journal-3424 20 12 used use VERB american_scientific_journal-3424 20 13 . . PUNCT american_scientific_journal-3424 21 1 to to PART american_scientific_journal-3424 21 2 study study VERB american_scientific_journal-3424 21 3 the the DET american_scientific_journal-3424 21 4 known know VERB american_scientific_journal-3424 21 5 data datum NOUN american_scientific_journal-3424 21 6 , , PUNCT american_scientific_journal-3424 21 7 several several ADJ american_scientific_journal-3424 21 8 distinct distinct ADJ american_scientific_journal-3424 21 9 models model NOUN american_scientific_journal-3424 21 10 will will AUX american_scientific_journal-3424 21 11 be be AUX american_scientific_journal-3424 21 12 used use VERB american_scientific_journal-3424 21 13 and and CCONJ american_scientific_journal-3424 21 14 each each DET american_scientific_journal-3424 21 15 model model NOUN american_scientific_journal-3424 21 16 is be AUX american_scientific_journal-3424 21 17 different different ADJ american_scientific_journal-3424 21 18 depends depend VERB american_scientific_journal-3424 21 19 on on ADP american_scientific_journal-3424 21 20 the the DET american_scientific_journal-3424 21 21 parameters parameter NOUN american_scientific_journal-3424 21 22 acquired acquire VERB american_scientific_journal-3424 21 23 . . PUNCT american_scientific_journal-3424 22 1 i i PRON american_scientific_journal-3424 22 2 decided decide VERB american_scientific_journal-3424 22 3 to to PART american_scientific_journal-3424 22 4 model model VERB american_scientific_journal-3424 22 5 the the DET american_scientific_journal-3424 22 6 ebola ebola NOUN american_scientific_journal-3424 22 7 epidemics epidemic NOUN american_scientific_journal-3424 22 8 in in ADP american_scientific_journal-3424 22 9 liberia liberia PROPN american_scientific_journal-3424 22 10 in in ADP american_scientific_journal-3424 22 11 2014 2014 NUM american_scientific_journal-3424 22 12 and and CCONJ american_scientific_journal-3424 22 13 compare compare VERB american_scientific_journal-3424 22 14 their their PRON american_scientific_journal-3424 22 15 spread spread NOUN american_scientific_journal-3424 22 16 using use VERB american_scientific_journal-3424 22 17 an an DET american_scientific_journal-3424 22 18 sir sir NOUN american_scientific_journal-3424 22 19 model model NOUN american_scientific_journal-3424 22 20 . . PUNCT american_scientific_journal-3424 23 1 1.1 1.1 NUM american_scientific_journal-3424 23 2 objectives objective VERB american_scientific_journal-3424 23 3 the the DET american_scientific_journal-3424 23 4 purposes purpose NOUN american_scientific_journal-3424 23 5 of of ADP american_scientific_journal-3424 23 6 this this DET american_scientific_journal-3424 23 7 research research NOUN american_scientific_journal-3424 23 8 are be AUX american_scientific_journal-3424 23 9 1 1 NUM american_scientific_journal-3424 23 10 . . PUNCT american_scientific_journal-3424 23 11 to to PART american_scientific_journal-3424 23 12 apply apply VERB american_scientific_journal-3424 23 13 sir sir NOUN american_scientific_journal-3424 23 14 model model NOUN american_scientific_journal-3424 23 15 to to PART american_scientific_journal-3424 23 16 predict predict VERB american_scientific_journal-3424 23 17 the the DET american_scientific_journal-3424 23 18 outbreaks outbreak NOUN american_scientific_journal-3424 23 19 of of ADP american_scientific_journal-3424 23 20 ebola ebola PROPN american_scientific_journal-3424 23 21 virus virus NOUN american_scientific_journal-3424 23 22 . . PUNCT american_scientific_journal-3424 24 1 2 2 X american_scientific_journal-3424 24 2 . . PUNCT american_scientific_journal-3424 24 3 to to PART american_scientific_journal-3424 24 4 determine determine VERB american_scientific_journal-3424 24 5 the the DET american_scientific_journal-3424 24 6 effect effect NOUN american_scientific_journal-3424 24 7 of of ADP american_scientific_journal-3424 24 8 the the DET american_scientific_journal-3424 24 9 initial initial ADJ american_scientific_journal-3424 24 10 number number NOUN american_scientific_journal-3424 24 11 of of ADP american_scientific_journal-3424 24 12 infectives infective NOUN american_scientific_journal-3424 24 13 of of ADP american_scientific_journal-3424 24 14 the the DET american_scientific_journal-3424 24 15 population population NOUN american_scientific_journal-3424 24 16 . . PUNCT american_scientific_journal-3424 25 1 3 3 X american_scientific_journal-3424 25 2 . . X american_scientific_journal-3424 25 3 compare compare VERB american_scientific_journal-3424 25 4 with with ADP american_scientific_journal-3424 25 5 real real ADJ american_scientific_journal-3424 25 6 data datum NOUN american_scientific_journal-3424 25 7 and and CCONJ american_scientific_journal-3424 25 8 fit fit ADJ american_scientific_journal-3424 25 9 with with ADP american_scientific_journal-3424 25 10 model model NOUN american_scientific_journal-3424 25 11 . . PUNCT american_scientific_journal-3424 26 1 1.2 1.2 NUM american_scientific_journal-3424 26 2 scope scope NOUN american_scientific_journal-3424 26 3 in in ADP american_scientific_journal-3424 26 4 the the DET american_scientific_journal-3424 26 5 proposal proposal NOUN american_scientific_journal-3424 26 6 study study NOUN american_scientific_journal-3424 26 7 , , PUNCT american_scientific_journal-3424 26 8 we we PRON american_scientific_journal-3424 26 9 will will AUX american_scientific_journal-3424 26 10 only only ADV american_scientific_journal-3424 26 11 investigate investigate VERB american_scientific_journal-3424 26 12 the the DET american_scientific_journal-3424 26 13 outbreaks outbreak NOUN american_scientific_journal-3424 26 14 of of ADP american_scientific_journal-3424 26 15 ebola ebola PROPN american_scientific_journal-3424 26 16 virus virus NOUN american_scientific_journal-3424 26 17 by by ADP american_scientific_journal-3424 26 18 applying apply VERB american_scientific_journal-3424 26 19 the the DET american_scientific_journal-3424 26 20 mathematical mathematical ADJ american_scientific_journal-3424 26 21 model model NOUN american_scientific_journal-3424 26 22 . . PUNCT american_scientific_journal-3424 27 1 the the DET american_scientific_journal-3424 27 2 data datum NOUN american_scientific_journal-3424 27 3 has have AUX american_scientific_journal-3424 27 4 been be AUX american_scientific_journal-3424 27 5 collected collect VERB american_scientific_journal-3424 27 6 and and CCONJ american_scientific_journal-3424 27 7 it it PRON american_scientific_journal-3424 27 8 covers cover VERB american_scientific_journal-3424 27 9 the the DET american_scientific_journal-3424 27 10 area area NOUN american_scientific_journal-3424 27 11 in in ADP american_scientific_journal-3424 27 12 the the DET american_scientific_journal-3424 27 13 continent continent NOUN american_scientific_journal-3424 27 14 of of ADP american_scientific_journal-3424 27 15 africa africa PROPN american_scientific_journal-3424 27 16 , , PUNCT american_scientific_journal-3424 27 17 on on ADP american_scientific_journal-3424 27 18 liberia liberia PROPN american_scientific_journal-3424 27 19 that that PRON american_scientific_journal-3424 27 20 was be AUX american_scientific_journal-3424 27 21 recorded record VERB american_scientific_journal-3424 27 22 by by ADP american_scientific_journal-3424 27 23 cdc cdc PROPN american_scientific_journal-3424 28 1 [ [ X american_scientific_journal-3424 28 2 4 4 NUM american_scientific_journal-3424 28 3 ] ] PUNCT american_scientific_journal-3424 28 4 . . PUNCT american_scientific_journal-3424 29 1 the the DET american_scientific_journal-3424 29 2 calculation calculation NOUN american_scientific_journal-3424 29 3 will will AUX american_scientific_journal-3424 29 4 be be AUX american_scientific_journal-3424 29 5 done do VERB american_scientific_journal-3424 29 6 by by ADP american_scientific_journal-3424 29 7 using use VERB american_scientific_journal-3424 29 8 tools tool NOUN american_scientific_journal-3424 29 9 of of ADP american_scientific_journal-3424 29 10 matlab matlab PROPN american_scientific_journal-3424 29 11 software software NOUN american_scientific_journal-3424 29 12 . . PUNCT american_scientific_journal-3424 30 1 2 2 X american_scientific_journal-3424 30 2 . . X american_scientific_journal-3424 30 3 methodology methodology NOUN american_scientific_journal-3424 30 4 2.1 2.1 NUM american_scientific_journal-3424 30 5 formulation formulation NOUN american_scientific_journal-3424 30 6 of of ADP american_scientific_journal-3424 30 7 sir sir NOUN american_scientific_journal-3424 30 8 model model NOUN american_scientific_journal-3424 30 9 the the DET american_scientific_journal-3424 30 10 sir sir NOUN american_scientific_journal-3424 30 11 model model NOUN american_scientific_journal-3424 30 12 is be AUX american_scientific_journal-3424 30 13 used use VERB american_scientific_journal-3424 30 14 to to PART american_scientific_journal-3424 30 15 illustrate illustrate VERB american_scientific_journal-3424 30 16 the the DET american_scientific_journal-3424 30 17 transfer transfer NOUN american_scientific_journal-3424 30 18 of of ADP american_scientific_journal-3424 30 19 the the DET american_scientific_journal-3424 30 20 epidemic epidemic NOUN american_scientific_journal-3424 30 21 through through ADP american_scientific_journal-3424 30 22 the the DET american_scientific_journal-3424 30 23 interaction interaction NOUN american_scientific_journal-3424 30 24 of of ADP american_scientific_journal-3424 30 25 the the DET american_scientific_journal-3424 30 26 following follow VERB american_scientific_journal-3424 30 27 three three NUM american_scientific_journal-3424 30 28 different different ADJ american_scientific_journal-3424 30 29 variables variable NOUN american_scientific_journal-3424 30 30 : : PUNCT american_scientific_journal-3424 30 31 𝑆𝑆 𝑆𝑆 PROPN american_scientific_journal-3424 30 32 = = SYM american_scientific_journal-3424 30 33 number number NOUN american_scientific_journal-3424 30 34 of of ADP american_scientific_journal-3424 30 35 people people NOUN american_scientific_journal-3424 30 36 that that PRON american_scientific_journal-3424 30 37 are be AUX american_scientific_journal-3424 30 38 susceptible susceptible ADJ american_scientific_journal-3424 30 39 to to ADP american_scientific_journal-3424 30 40 ebola ebola PROPN american_scientific_journal-3424 30 41 𝐼𝐼 𝐼𝐼 PROPN american_scientific_journal-3424 30 42 = = PUNCT american_scientific_journal-3424 30 43 number number NOUN american_scientific_journal-3424 30 44 of of ADP american_scientific_journal-3424 30 45 people people NOUN american_scientific_journal-3424 30 46 infected infect VERB american_scientific_journal-3424 30 47 with with ADP american_scientific_journal-3424 30 48 ebola ebola PROPN american_scientific_journal-3424 30 49 𝑅𝑅 𝑅𝑅 PROPN american_scientific_journal-3424 30 50 = = PUNCT american_scientific_journal-3424 30 51 number number NOUN american_scientific_journal-3424 30 52 of of ADP american_scientific_journal-3424 30 53 people people NOUN american_scientific_journal-3424 30 54 recovered recover VERB american_scientific_journal-3424 30 55 american american ADJ american_scientific_journal-3424 30 56 scientific scientific ADJ american_scientific_journal-3424 30 57 research research NOUN american_scientific_journal-3424 30 58 journal journal NOUN american_scientific_journal-3424 30 59 for for ADP american_scientific_journal-3424 30 60 engineering engineering NOUN american_scientific_journal-3424 30 61 , , PUNCT american_scientific_journal-3424 30 62 technology technology NOUN american_scientific_journal-3424 30 63 , , PUNCT american_scientific_journal-3424 30 64 and and CCONJ american_scientific_journal-3424 30 65 sciences science NOUN american_scientific_journal-3424 30 66 ( ( PUNCT american_scientific_journal-3424 30 67 asrjets asrjet NOUN american_scientific_journal-3424 30 68 ) ) PUNCT american_scientific_journal-3424 30 69 ( ( PUNCT american_scientific_journal-3424 30 70 2017 2017 NUM american_scientific_journal-3424 30 71 ) ) PUNCT american_scientific_journal-3424 30 72 volume volume NOUN american_scientific_journal-3424 30 73 37 37 NUM american_scientific_journal-3424 30 74 , , PUNCT american_scientific_journal-3424 30 75 no no DET american_scientific_journal-3424 30 76 1 1 NUM american_scientific_journal-3424 30 77 , , PUNCT american_scientific_journal-3424 30 78 pp pp ADV american_scientific_journal-3424 30 79 1 1 NUM american_scientific_journal-3424 30 80 - - SYM american_scientific_journal-3424 30 81 21 21 NUM american_scientific_journal-3424 30 82 3 3 NUM american_scientific_journal-3424 30 83 from from ADP american_scientific_journal-3424 30 84 ebola ebola PROPN american_scientific_journal-3424 30 85 with with ADP american_scientific_journal-3424 30 86 total total ADJ american_scientific_journal-3424 30 87 immunity immunity NOUN american_scientific_journal-3424 30 88 it it PRON american_scientific_journal-3424 30 89 makes make VERB american_scientific_journal-3424 30 90 sense sense NOUN american_scientific_journal-3424 30 91 to to PART american_scientific_journal-3424 30 92 assume assume VERB american_scientific_journal-3424 30 93 that that SCONJ american_scientific_journal-3424 30 94 a a DET american_scientific_journal-3424 30 95 fixed fix VERB american_scientific_journal-3424 30 96 population population NOUN american_scientific_journal-3424 30 97 of of ADP american_scientific_journal-3424 30 98 𝑁𝑁 𝑁𝑁 PROPN american_scientific_journal-3424 30 99 people people NOUN american_scientific_journal-3424 30 100 , , PUNCT american_scientific_journal-3424 30 101 whereby whereby SCONJ american_scientific_journal-3424 30 102 there there PRON american_scientific_journal-3424 30 103 are be VERB american_scientific_journal-3424 30 104 no no DET american_scientific_journal-3424 30 105 births birth NOUN american_scientific_journal-3424 30 106 and and CCONJ american_scientific_journal-3424 30 107 deaths death NOUN american_scientific_journal-3424 30 108 by by ADP american_scientific_journal-3424 30 109 natural natural ADJ american_scientific_journal-3424 30 110 cause cause NOUN american_scientific_journal-3424 30 111 i.e. i.e. X american_scientific_journal-3424 30 112 𝑁𝑁 𝑁𝑁 PROPN american_scientific_journal-3424 30 113 = = SYM american_scientific_journal-3424 30 114 𝑆𝑆 𝑆𝑆 PROPN american_scientific_journal-3424 30 115 + + CCONJ american_scientific_journal-3424 30 116 𝐼𝐼 𝐼𝐼 PROPN american_scientific_journal-3424 30 117 + + CCONJ american_scientific_journal-3424 30 118 𝑅𝑅 𝑅𝑅 PROPN american_scientific_journal-3424 31 1 [ [ X american_scientific_journal-3424 31 2 5 5 NUM american_scientific_journal-3424 31 3 ] ] PUNCT american_scientific_journal-3424 31 4 this this PRON american_scientific_journal-3424 31 5 is be AUX american_scientific_journal-3424 31 6 because because SCONJ american_scientific_journal-3424 31 7 the the DET american_scientific_journal-3424 31 8 population population NOUN american_scientific_journal-3424 31 9 is be AUX american_scientific_journal-3424 31 10 fixed fix VERB american_scientific_journal-3424 31 11 and and CCONJ american_scientific_journal-3424 31 12 therefore therefore ADV american_scientific_journal-3424 31 13 , , PUNCT american_scientific_journal-3424 31 14 there there PRON american_scientific_journal-3424 31 15 are be VERB american_scientific_journal-3424 31 16 only only ADV american_scientific_journal-3424 31 17 three three NUM american_scientific_journal-3424 31 18 compartments compartment NOUN american_scientific_journal-3424 31 19 in in ADP american_scientific_journal-3424 31 20 which which PRON american_scientific_journal-3424 31 21 the the DET american_scientific_journal-3424 31 22 population population NOUN american_scientific_journal-3424 31 23 may may AUX american_scientific_journal-3424 31 24 fit fit VERB american_scientific_journal-3424 31 25 into into ADP american_scientific_journal-3424 31 26 . . PUNCT american_scientific_journal-3424 32 1 thus thus ADV american_scientific_journal-3424 32 2 , , PUNCT american_scientific_journal-3424 32 3 the the DET american_scientific_journal-3424 32 4 total total NOUN american_scientific_journal-3424 32 5 of of ADP american_scientific_journal-3424 32 6 the the DET american_scientific_journal-3424 32 7 number number NOUN american_scientific_journal-3424 32 8 of of ADP american_scientific_journal-3424 32 9 people people NOUN american_scientific_journal-3424 32 10 susceptible susceptible ADJ american_scientific_journal-3424 32 11 infected infect VERB american_scientific_journal-3424 32 12 and and CCONJ american_scientific_journal-3424 32 13 recovered recover VERB american_scientific_journal-3424 32 14 in in ADP american_scientific_journal-3424 32 15 equivalent equivalent NOUN american_scientific_journal-3424 32 16 to to ADP american_scientific_journal-3424 32 17 the the DET american_scientific_journal-3424 32 18 total total ADJ american_scientific_journal-3424 32 19 population population NOUN american_scientific_journal-3424 32 20 . . PUNCT american_scientific_journal-3424 33 1 the the DET american_scientific_journal-3424 33 2 assumption assumption NOUN american_scientific_journal-3424 33 3 that that SCONJ american_scientific_journal-3424 33 4 𝑁𝑁 𝑁𝑁 PROPN american_scientific_journal-3424 33 5 is be AUX american_scientific_journal-3424 33 6 fixed fix VERB american_scientific_journal-3424 33 7 , , PUNCT american_scientific_journal-3424 33 8 with with ADP american_scientific_journal-3424 33 9 no no DET american_scientific_journal-3424 33 10 births birth NOUN american_scientific_journal-3424 33 11 or or CCONJ american_scientific_journal-3424 33 12 deaths death NOUN american_scientific_journal-3424 33 13 , , PUNCT american_scientific_journal-3424 33 14 makes make VERB american_scientific_journal-3424 33 15 sense sense NOUN american_scientific_journal-3424 33 16 given give VERB american_scientific_journal-3424 33 17 60 60 NUM american_scientific_journal-3424 33 18 days day NOUN american_scientific_journal-3424 33 19 , , PUNCT american_scientific_journal-3424 33 20 although although SCONJ american_scientific_journal-3424 33 21 it it PRON american_scientific_journal-3424 33 22 is be AUX american_scientific_journal-3424 33 23 a a DET american_scientific_journal-3424 33 24 simplification simplification NOUN american_scientific_journal-3424 33 25 . . PUNCT american_scientific_journal-3424 34 1 these these DET american_scientific_journal-3424 34 2 variables variable NOUN american_scientific_journal-3424 34 3 change change VERB american_scientific_journal-3424 34 4 over over ADP american_scientific_journal-3424 34 5 time time NOUN american_scientific_journal-3424 34 6 , , PUNCT american_scientific_journal-3424 34 7 so so SCONJ american_scientific_journal-3424 34 8 we we PRON american_scientific_journal-3424 34 9 will will AUX american_scientific_journal-3424 34 10 define define VERB american_scientific_journal-3424 34 11 the the DET american_scientific_journal-3424 34 12 variable variable ADJ american_scientific_journal-3424 34 13 𝑑𝑑 𝑑𝑑 NOUN american_scientific_journal-3424 35 1 = = PUNCT american_scientific_journal-3424 36 1 time time NOUN american_scientific_journal-3424 36 2 in in ADP american_scientific_journal-3424 36 3 days day NOUN american_scientific_journal-3424 36 4 . . PUNCT american_scientific_journal-3424 37 1 we we PRON american_scientific_journal-3424 37 2 will will AUX american_scientific_journal-3424 37 3 set set VERB american_scientific_journal-3424 37 4 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-3424 37 5 = = SYM american_scientific_journal-3424 37 6 0 0 NUM american_scientific_journal-3424 37 7 at at ADP american_scientific_journal-3424 37 8 the the DET american_scientific_journal-3424 37 9 start start NOUN american_scientific_journal-3424 37 10 of of ADP american_scientific_journal-3424 37 11 august august PROPN american_scientific_journal-3424 37 12 2014 2014 NUM american_scientific_journal-3424 37 13 . . PUNCT american_scientific_journal-3424 38 1 the the DET american_scientific_journal-3424 38 2 model model NOUN american_scientific_journal-3424 38 3 uses use VERB american_scientific_journal-3424 38 4 two two NUM american_scientific_journal-3424 38 5 parameters parameter NOUN american_scientific_journal-3424 38 6 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 38 7 and and CCONJ american_scientific_journal-3424 38 8 𝛾𝛾 𝛾𝛾 ADV american_scientific_journal-3424 38 9 with with ADP american_scientific_journal-3424 38 10 𝛽𝛽 𝛽𝛽 NOUN american_scientific_journal-3424 38 11 , , PUNCT american_scientific_journal-3424 38 12 𝛾𝛾 𝛾𝛾 ADV american_scientific_journal-3424 38 13 > > X american_scientific_journal-3424 38 14 0 0 X american_scientific_journal-3424 38 15 . . PUNCT american_scientific_journal-3424 39 1 given give VERB american_scientific_journal-3424 39 2 these these DET american_scientific_journal-3424 39 3 parameters parameter NOUN american_scientific_journal-3424 39 4 , , PUNCT american_scientific_journal-3424 39 5 the the DET american_scientific_journal-3424 39 6 model model NOUN american_scientific_journal-3424 39 7 uses use VERB american_scientific_journal-3424 39 8 3 3 NUM american_scientific_journal-3424 39 9 differential differential ADJ american_scientific_journal-3424 39 10 equations equation NOUN american_scientific_journal-3424 39 11 . . PUNCT american_scientific_journal-3424 40 1 the the DET american_scientific_journal-3424 40 2 rate rate NOUN american_scientific_journal-3424 40 3 of of ADP american_scientific_journal-3424 40 4 change change NOUN american_scientific_journal-3424 40 5 of of ADP american_scientific_journal-3424 40 6 the the DET american_scientific_journal-3424 40 7 number number NOUN american_scientific_journal-3424 40 8 of of ADP american_scientific_journal-3424 40 9 people people NOUN american_scientific_journal-3424 40 10 susceptible susceptible ADJ american_scientific_journal-3424 40 11 to to ADP american_scientific_journal-3424 40 12 the the DET american_scientific_journal-3424 40 13 disease disease NOUN american_scientific_journal-3424 40 14 over over ADP american_scientific_journal-3424 40 15 time time NOUN american_scientific_journal-3424 40 16 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 40 17 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 41 1 = = PUNCT american_scientific_journal-3424 42 1 βˆ’ βˆ’ PROPN american_scientific_journal-3424 42 2 𝛽𝛽𝐼𝐼𝑆𝑆 𝛽𝛽𝐼𝐼𝑆𝑆 NOUN american_scientific_journal-3424 42 3 ( ( PUNCT american_scientific_journal-3424 42 4 1 1 NUM american_scientific_journal-3424 42 5 ) ) PUNCT american_scientific_journal-3424 42 6 the the DET american_scientific_journal-3424 42 7 rate rate NOUN american_scientific_journal-3424 42 8 of of ADP american_scientific_journal-3424 42 9 change change NOUN american_scientific_journal-3424 42 10 of of ADP american_scientific_journal-3424 42 11 the the DET american_scientific_journal-3424 42 12 number number NOUN american_scientific_journal-3424 42 13 of of ADP american_scientific_journal-3424 42 14 people people NOUN american_scientific_journal-3424 42 15 recovered recover VERB american_scientific_journal-3424 42 16 over over ADP american_scientific_journal-3424 42 17 time time NOUN american_scientific_journal-3424 42 18 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 42 19 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 43 1 = = PUNCT american_scientific_journal-3424 44 1 𝛾𝛾𝐼𝐼 𝛾𝛾𝐼𝐼 NOUN american_scientific_journal-3424 44 2 ( ( PUNCT american_scientific_journal-3424 44 3 2 2 NUM american_scientific_journal-3424 44 4 ) ) PUNCT american_scientific_journal-3424 44 5 the the DET american_scientific_journal-3424 44 6 rate rate NOUN american_scientific_journal-3424 44 7 of of ADP american_scientific_journal-3424 44 8 change change NOUN american_scientific_journal-3424 44 9 of of ADP american_scientific_journal-3424 44 10 the the DET american_scientific_journal-3424 44 11 number number NOUN american_scientific_journal-3424 44 12 of of ADP american_scientific_journal-3424 44 13 people people NOUN american_scientific_journal-3424 44 14 infected infect VERB american_scientific_journal-3424 44 15 . . PUNCT american_scientific_journal-3424 45 1 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 PROPN american_scientific_journal-3424 45 2 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 46 1 = = PUNCT american_scientific_journal-3424 46 2 𝛽𝛽𝐼𝐼𝑆𝑆 𝛽𝛽𝐼𝐼𝑆𝑆 PROPN american_scientific_journal-3424 46 3 βˆ’ βˆ’ PROPN american_scientific_journal-3424 46 4 𝛾𝛾𝐼𝐼 𝛾𝛾𝐼𝐼 NOUN american_scientific_journal-3424 46 5 ( ( PUNCT american_scientific_journal-3424 46 6 3 3 NUM american_scientific_journal-3424 46 7 ) ) PUNCT american_scientific_journal-3424 46 8 parameterization parameterization NOUN american_scientific_journal-3424 46 9 of of ADP american_scientific_journal-3424 46 10 the the DET american_scientific_journal-3424 46 11 model model NOUN american_scientific_journal-3424 46 12 in in ADP american_scientific_journal-3424 46 13 order order NOUN american_scientific_journal-3424 46 14 to to PART american_scientific_journal-3424 46 15 calculate calculate VERB american_scientific_journal-3424 46 16 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 46 17 ( ( PUNCT american_scientific_journal-3424 46 18 the the DET american_scientific_journal-3424 46 19 rate rate NOUN american_scientific_journal-3424 46 20 of of ADP american_scientific_journal-3424 46 21 infection infection NOUN american_scientific_journal-3424 46 22 ) ) PUNCT american_scientific_journal-3424 46 23 and and CCONJ american_scientific_journal-3424 46 24 𝛾𝛾 𝛾𝛾 ADV american_scientific_journal-3424 46 25 ( ( PUNCT american_scientific_journal-3424 46 26 the the DET american_scientific_journal-3424 46 27 rate rate NOUN american_scientific_journal-3424 46 28 of of ADP american_scientific_journal-3424 46 29 recovery recovery NOUN american_scientific_journal-3424 46 30 ) ) PUNCT american_scientific_journal-3424 47 1 , , PUNCT american_scientific_journal-3424 47 2 it it PRON american_scientific_journal-3424 47 3 helps help VERB american_scientific_journal-3424 47 4 to to PART american_scientific_journal-3424 47 5 define define VERB american_scientific_journal-3424 47 6 two two NUM american_scientific_journal-3424 47 7 more more ADJ american_scientific_journal-3424 47 8 parameters parameter NOUN american_scientific_journal-3424 47 9 . . PUNCT american_scientific_journal-3424 48 1 𝐷𝐷 𝐷𝐷 NOUN american_scientific_journal-3424 48 2 = = NOUN american_scientific_journal-3424 48 3 duration duration NOUN american_scientific_journal-3424 48 4 of of ADP american_scientific_journal-3424 48 5 disease disease NOUN american_scientific_journal-3424 48 6 for for ADP american_scientific_journal-3424 48 7 those those DET american_scientific_journal-3424 48 8 recovered recover VERB american_scientific_journal-3424 48 9 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-3424 48 10 = = NOUN american_scientific_journal-3424 48 11 mortality mortality NOUN american_scientific_journal-3424 48 12 rate rate NOUN american_scientific_journal-3424 48 13 for for ADP american_scientific_journal-3424 48 14 those those PRON american_scientific_journal-3424 48 15 who who PRON american_scientific_journal-3424 48 16 die die VERB american_scientific_journal-3424 48 17 per per ADP american_scientific_journal-3424 48 18 day day NOUN american_scientific_journal-3424 48 19 ( ( PUNCT american_scientific_journal-3424 48 20 0.7 0.7 NUM american_scientific_journal-3424 48 21 for for ADP american_scientific_journal-3424 48 22 ebola ebola NOUN american_scientific_journal-3424 48 23 ) ) PUNCT american_scientific_journal-3424 49 1 this this PRON american_scientific_journal-3424 49 2 leads lead VERB american_scientific_journal-3424 49 3 to to ADP american_scientific_journal-3424 49 4 two two NUM american_scientific_journal-3424 49 5 further further ADJ american_scientific_journal-3424 49 6 equations equation NOUN american_scientific_journal-3424 49 7 . . PUNCT american_scientific_journal-3424 50 1 american american ADJ american_scientific_journal-3424 50 2 scientific scientific ADJ american_scientific_journal-3424 50 3 research research PROPN american_scientific_journal-3424 50 4 journal journal NOUN american_scientific_journal-3424 50 5 for for ADP american_scientific_journal-3424 50 6 engineering engineering NOUN american_scientific_journal-3424 50 7 , , PUNCT american_scientific_journal-3424 50 8 technology technology NOUN american_scientific_journal-3424 50 9 , , PUNCT american_scientific_journal-3424 50 10 and and CCONJ american_scientific_journal-3424 50 11 sciences science NOUN american_scientific_journal-3424 50 12 ( ( PUNCT american_scientific_journal-3424 50 13 asrjets asrjet NOUN american_scientific_journal-3424 50 14 ) ) PUNCT american_scientific_journal-3424 50 15 ( ( PUNCT american_scientific_journal-3424 50 16 2017 2017 NUM american_scientific_journal-3424 50 17 ) ) PUNCT american_scientific_journal-3424 50 18 volume volume NOUN american_scientific_journal-3424 50 19 37 37 NUM american_scientific_journal-3424 50 20 , , PUNCT american_scientific_journal-3424 50 21 no no DET american_scientific_journal-3424 50 22 1 1 NUM american_scientific_journal-3424 50 23 , , PUNCT american_scientific_journal-3424 50 24 pp pp ADV american_scientific_journal-3424 50 25 1 1 NUM american_scientific_journal-3424 50 26 - - SYM american_scientific_journal-3424 50 27 21 21 NUM american_scientific_journal-3424 50 28 4 4 NUM american_scientific_journal-3424 50 29 the the DET american_scientific_journal-3424 50 30 rate rate NOUN american_scientific_journal-3424 50 31 at at ADP american_scientific_journal-3424 50 32 which which PRON american_scientific_journal-3424 50 33 the the DET american_scientific_journal-3424 50 34 disease disease NOUN american_scientific_journal-3424 50 35 is be AUX american_scientific_journal-3424 50 36 spread spread VERB american_scientific_journal-3424 50 37 𝛾𝛾 𝛾𝛾 ADV american_scientific_journal-3424 50 38 = = SYM american_scientific_journal-3424 50 39 1 1 NUM american_scientific_journal-3424 50 40 𝐷𝐷 𝐷𝐷 PROPN american_scientific_journal-3424 51 1 [ [ X american_scientific_journal-3424 51 2 6 6 NUM american_scientific_journal-3424 51 3 ] ] PUNCT american_scientific_journal-3424 51 4 ( ( PUNCT american_scientific_journal-3424 51 5 4 4 X american_scientific_journal-3424 51 6 ) ) PUNCT american_scientific_journal-3424 51 7 the the DET american_scientific_journal-3424 51 8 infection infection NOUN american_scientific_journal-3424 51 9 rate rate NOUN american_scientific_journal-3424 51 10 of of ADP american_scientific_journal-3424 51 11 the the DET american_scientific_journal-3424 51 12 disease disease NOUN american_scientific_journal-3424 51 13 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 51 14 = = SYM american_scientific_journal-3424 51 15 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-3424 51 16 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-3424 52 1 [ [ X american_scientific_journal-3424 52 2 7 7 NUM american_scientific_journal-3424 52 3 ] ] X american_scientific_journal-3424 52 4 ( ( PUNCT american_scientific_journal-3424 52 5 5 5 NUM american_scientific_journal-3424 52 6 ) ) PUNCT american_scientific_journal-3424 52 7 2.2 2.2 NUM american_scientific_journal-3424 52 8 transformation transformation NOUN american_scientific_journal-3424 52 9 of of ADP american_scientific_journal-3424 52 10 runge runge NOUN american_scientific_journal-3424 52 11 - - PUNCT american_scientific_journal-3424 52 12 kutta kutta NOUN american_scientific_journal-3424 52 13 equations equation NOUN american_scientific_journal-3424 52 14 for for ADP american_scientific_journal-3424 52 15 sir sir NOUN american_scientific_journal-3424 52 16 modeling model VERB american_scientific_journal-3424 52 17 rk4 rk4 PROPN american_scientific_journal-3424 52 18 is be AUX american_scientific_journal-3424 52 19 one one NUM american_scientific_journal-3424 52 20 of of ADP american_scientific_journal-3424 52 21 the the DET american_scientific_journal-3424 52 22 classic classic ADJ american_scientific_journal-3424 52 23 methods method NOUN american_scientific_journal-3424 52 24 for for ADP american_scientific_journal-3424 52 25 numerical numerical ADJ american_scientific_journal-3424 52 26 integration integration NOUN american_scientific_journal-3424 52 27 of of ADP american_scientific_journal-3424 52 28 ode ode ADJ american_scientific_journal-3424 52 29 models model NOUN american_scientific_journal-3424 52 30 . . PUNCT american_scientific_journal-3424 53 1 consider consider VERB american_scientific_journal-3424 53 2 the the DET american_scientific_journal-3424 53 3 following following ADJ american_scientific_journal-3424 53 4 initial initial ADJ american_scientific_journal-3424 53 5 problem problem NOUN american_scientific_journal-3424 53 6 of of ADP american_scientific_journal-3424 53 7 ode ode PROPN american_scientific_journal-3424 53 8 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 53 9 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 53 10 = = SYM american_scientific_journal-3424 53 11 𝑓𝑓(𝑑𝑑,𝑦𝑦 𝑓𝑓(𝑑𝑑,𝑦𝑦 PROPN american_scientific_journal-3424 53 12 ) ) PUNCT american_scientific_journal-3424 53 13 𝑦𝑦(π‘‘π‘‘π‘œπ‘œ 𝑦𝑦(π‘‘π‘‘π‘œπ‘œ PROPN american_scientific_journal-3424 53 14 ) ) PUNCT american_scientific_journal-3424 53 15 = = PUNCT american_scientific_journal-3424 54 1 π‘¦π‘¦π‘œπ‘œ π‘¦π‘¦π‘œπ‘œ ADJ american_scientific_journal-3424 54 2 where where SCONJ american_scientific_journal-3424 54 3 𝑦𝑦(𝑑𝑑 𝑦𝑦(𝑑𝑑 PROPN american_scientific_journal-3424 54 4 ) ) PUNCT american_scientific_journal-3424 54 5 is be AUX american_scientific_journal-3424 54 6 the the DET american_scientific_journal-3424 54 7 unknown unknown ADJ american_scientific_journal-3424 54 8 function function NOUN american_scientific_journal-3424 54 9 ( ( PUNCT american_scientific_journal-3424 54 10 scalar scalar ADJ american_scientific_journal-3424 54 11 or or CCONJ american_scientific_journal-3424 54 12 vector vector NOUN american_scientific_journal-3424 54 13 ) ) PUNCT american_scientific_journal-3424 54 14 which which PRON american_scientific_journal-3424 54 15 i i PRON american_scientific_journal-3424 54 16 would would AUX american_scientific_journal-3424 54 17 like like VERB american_scientific_journal-3424 54 18 to to PART american_scientific_journal-3424 54 19 approximate approximate VERB american_scientific_journal-3424 54 20 . . PUNCT american_scientific_journal-3424 55 1 the the DET american_scientific_journal-3424 55 2 iterative iterative NOUN american_scientific_journal-3424 55 3 formula formula NOUN american_scientific_journal-3424 55 4 of of ADP american_scientific_journal-3424 55 5 rk4 rk4 NOUN american_scientific_journal-3424 55 6 method method NOUN american_scientific_journal-3424 55 7 for for ADP american_scientific_journal-3424 55 8 solving solve VERB american_scientific_journal-3424 55 9 ode ode NOUN american_scientific_journal-3424 55 10 is be AUX american_scientific_journal-3424 55 11 as as SCONJ american_scientific_journal-3424 55 12 follows follow VERB american_scientific_journal-3424 55 13 π‘˜π‘˜1 π‘˜π‘˜1 NOUN american_scientific_journal-3424 55 14 = = SYM american_scientific_journal-3424 55 15 β„Žπ‘“π‘“(𝑑𝑑𝑛𝑛,𝑦𝑦𝑛𝑛 β„Žπ‘“π‘“(𝑑𝑑𝑛𝑛,𝑦𝑦𝑛𝑛 PROPN american_scientific_journal-3424 55 16 ) ) PUNCT american_scientific_journal-3424 55 17 π‘˜π‘˜2 π‘˜π‘˜2 PROPN american_scientific_journal-3424 55 18 = = SYM american_scientific_journal-3424 55 19 β„Žπ‘“π‘“ β„Žπ‘“π‘“ PROPN american_scientific_journal-3424 55 20 οΏ½ οΏ½ PROPN american_scientific_journal-3424 55 21 𝑑𝑑𝑛𝑛 𝑑𝑑𝑛𝑛 VERB american_scientific_journal-3424 55 22 + + CCONJ american_scientific_journal-3424 55 23 1 1 NUM american_scientific_journal-3424 55 24 2 2 NUM american_scientific_journal-3424 55 25 β„Ž,𝑦𝑦𝑛𝑛 β„Ž,𝑦𝑦𝑛𝑛 ADJ american_scientific_journal-3424 55 26 + + NUM american_scientific_journal-3424 55 27 1 1 NUM american_scientific_journal-3424 55 28 2 2 NUM american_scientific_journal-3424 55 29 π‘˜π‘˜1 π‘˜π‘˜1 NUM american_scientific_journal-3424 55 30 οΏ½ οΏ½ PROPN american_scientific_journal-3424 55 31 π‘˜π‘˜3 π‘˜π‘˜3 NOUN american_scientific_journal-3424 55 32 = = PROPN american_scientific_journal-3424 55 33 β„Žπ‘“π‘“ β„Žπ‘“π‘“ PROPN american_scientific_journal-3424 55 34 οΏ½ οΏ½ PROPN american_scientific_journal-3424 55 35 𝑑𝑑𝑛𝑛 𝑑𝑑𝑛𝑛 VERB american_scientific_journal-3424 55 36 + + CCONJ american_scientific_journal-3424 55 37 1 1 NUM american_scientific_journal-3424 55 38 2 2 NUM american_scientific_journal-3424 55 39 β„Ž,𝑦𝑦𝑛𝑛 β„Ž,𝑦𝑦𝑛𝑛 ADJ american_scientific_journal-3424 55 40 + + NOUN american_scientific_journal-3424 55 41 1 1 NUM american_scientific_journal-3424 55 42 2 2 NUM american_scientific_journal-3424 55 43 π‘˜π‘˜2 π‘˜π‘˜2 PROPN american_scientific_journal-3424 55 44 οΏ½ οΏ½ PROPN american_scientific_journal-3424 55 45 π‘˜π‘˜4 π‘˜π‘˜4 NOUN american_scientific_journal-3424 55 46 = = PUNCT american_scientific_journal-3424 55 47 β„Žπ‘“π‘“(𝑑𝑑𝑛𝑛 β„Žπ‘“π‘“(𝑑𝑑𝑛𝑛 NOUN american_scientific_journal-3424 55 48 + + CCONJ american_scientific_journal-3424 55 49 β„Ž,𝑦𝑦𝑛𝑛 β„Ž,𝑦𝑦𝑛𝑛 ADJ american_scientific_journal-3424 55 50 + + CCONJ american_scientific_journal-3424 55 51 π‘˜π‘˜3 π‘˜π‘˜3 NOUN american_scientific_journal-3424 55 52 ) ) PUNCT american_scientific_journal-3424 55 53 𝑦𝑦𝑛𝑛+1 𝑦𝑦𝑛𝑛+1 PROPN american_scientific_journal-3424 55 54 = = SYM american_scientific_journal-3424 55 55 𝑦𝑦𝑛𝑛 𝑦𝑦𝑛𝑛 NOUN american_scientific_journal-3424 55 56 + + CCONJ american_scientific_journal-3424 55 57 1 1 NUM american_scientific_journal-3424 55 58 6 6 NUM american_scientific_journal-3424 55 59 ( ( PUNCT american_scientific_journal-3424 55 60 π‘˜π‘˜1 π‘˜π‘˜1 X american_scientific_journal-3424 55 61 + + PUNCT american_scientific_journal-3424 55 62 2π‘˜π‘˜2 2π‘˜π‘˜2 NUM american_scientific_journal-3424 55 63 + + CCONJ american_scientific_journal-3424 55 64 2π‘˜π‘˜3 2π‘˜π‘˜3 NUM american_scientific_journal-3424 55 65 + + CCONJ american_scientific_journal-3424 55 66 π‘˜π‘˜4 π‘˜π‘˜4 NOUN american_scientific_journal-3424 55 67 ) ) PUNCT american_scientific_journal-3424 55 68 for for ADP american_scientific_journal-3424 55 69 simplicity simplicity NOUN american_scientific_journal-3424 55 70 , , PUNCT american_scientific_journal-3424 55 71 here here ADV american_scientific_journal-3424 55 72 we we PRON american_scientific_journal-3424 55 73 use use VERB american_scientific_journal-3424 55 74 the the DET american_scientific_journal-3424 55 75 simplest simple ADJ american_scientific_journal-3424 55 76 sir sir NOUN american_scientific_journal-3424 55 77 model model NOUN american_scientific_journal-3424 55 78 to to PART american_scientific_journal-3424 55 79 examine examine VERB american_scientific_journal-3424 55 80 whether whether SCONJ american_scientific_journal-3424 55 81 the the DET american_scientific_journal-3424 55 82 rk4 rk4 NOUN american_scientific_journal-3424 55 83 method method NOUN american_scientific_journal-3424 55 84 has have AUX american_scientific_journal-3424 55 85 been be AUX american_scientific_journal-3424 55 86 implemented implement VERB american_scientific_journal-3424 55 87 correctly correctly ADV american_scientific_journal-3424 55 88 . . PUNCT american_scientific_journal-3424 56 1 the the DET american_scientific_journal-3424 56 2 sir sir PROPN american_scientific_journal-3424 56 3 model model NOUN american_scientific_journal-3424 56 4 is be AUX american_scientific_journal-3424 56 5 defined define VERB american_scientific_journal-3424 56 6 as as SCONJ american_scientific_journal-3424 56 7 follows follow VERB american_scientific_journal-3424 56 8 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 PROPN american_scientific_journal-3424 56 9 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 57 1 = = PUNCT american_scientific_journal-3424 58 1 βˆ’ βˆ’ PROPN american_scientific_journal-3424 58 2 𝛽𝛽𝐼𝐼𝑆𝑆 𝛽𝛽𝐼𝐼𝑆𝑆 PROPN american_scientific_journal-3424 58 3 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 58 4 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 58 5 = = PUNCT american_scientific_journal-3424 58 6 𝛽𝛽𝐼𝐼𝑆𝑆 𝛽𝛽𝐼𝐼𝑆𝑆 PROPN american_scientific_journal-3424 58 7 βˆ’ βˆ’ PROPN american_scientific_journal-3424 58 8 𝛾𝛾𝐼𝐼 𝛾𝛾𝐼𝐼 NOUN american_scientific_journal-3424 58 9 american american ADJ american_scientific_journal-3424 58 10 scientific scientific ADJ american_scientific_journal-3424 58 11 research research NOUN american_scientific_journal-3424 58 12 journal journal NOUN american_scientific_journal-3424 58 13 for for ADP american_scientific_journal-3424 58 14 engineering engineering NOUN american_scientific_journal-3424 58 15 , , PUNCT american_scientific_journal-3424 58 16 technology technology NOUN american_scientific_journal-3424 58 17 , , PUNCT american_scientific_journal-3424 58 18 and and CCONJ american_scientific_journal-3424 58 19 sciences science NOUN american_scientific_journal-3424 58 20 ( ( PUNCT american_scientific_journal-3424 58 21 asrjets asrjet NOUN american_scientific_journal-3424 58 22 ) ) PUNCT american_scientific_journal-3424 58 23 ( ( PUNCT american_scientific_journal-3424 58 24 2017 2017 NUM american_scientific_journal-3424 58 25 ) ) PUNCT american_scientific_journal-3424 58 26 volume volume NOUN american_scientific_journal-3424 58 27 37 37 NUM american_scientific_journal-3424 58 28 , , PUNCT american_scientific_journal-3424 58 29 no no DET american_scientific_journal-3424 58 30 1 1 NUM american_scientific_journal-3424 58 31 , , PUNCT american_scientific_journal-3424 58 32 pp pp ADV american_scientific_journal-3424 58 33 1 1 NUM american_scientific_journal-3424 58 34 - - SYM american_scientific_journal-3424 58 35 21 21 NUM american_scientific_journal-3424 58 36 5 5 NUM american_scientific_journal-3424 58 37 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 58 38 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 58 39 = = NOUN american_scientific_journal-3424 58 40 𝛾𝛾𝐼𝐼 𝛾𝛾𝐼𝐼 NOUN american_scientific_journal-3424 58 41 where where SCONJ american_scientific_journal-3424 58 42 𝑆𝑆(𝑑𝑑 𝑆𝑆(𝑑𝑑 NOUN american_scientific_journal-3424 58 43 ) ) PUNCT american_scientific_journal-3424 58 44 is be AUX american_scientific_journal-3424 58 45 the the DET american_scientific_journal-3424 58 46 number number NOUN american_scientific_journal-3424 58 47 of of ADP american_scientific_journal-3424 58 48 susceptible susceptible ADJ american_scientific_journal-3424 58 49 people people NOUN american_scientific_journal-3424 58 50 in in ADP american_scientific_journal-3424 58 51 the the DET american_scientific_journal-3424 58 52 population population NOUN american_scientific_journal-3424 58 53 at at ADP american_scientific_journal-3424 58 54 time time NOUN american_scientific_journal-3424 58 55 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-3424 58 56 , , PUNCT american_scientific_journal-3424 58 57 𝐼𝐼(𝑑𝑑 𝐼𝐼(𝑑𝑑 NOUN american_scientific_journal-3424 58 58 ) ) PUNCT american_scientific_journal-3424 58 59 is be AUX american_scientific_journal-3424 58 60 the the DET american_scientific_journal-3424 58 61 number number NOUN american_scientific_journal-3424 58 62 of of ADP american_scientific_journal-3424 58 63 infectious infectious ADJ american_scientific_journal-3424 58 64 people people NOUN american_scientific_journal-3424 58 65 at at ADP american_scientific_journal-3424 58 66 time time NOUN american_scientific_journal-3424 58 67 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-3424 58 68 , , PUNCT american_scientific_journal-3424 58 69 𝑅𝑅(𝑑𝑑 𝑅𝑅(𝑑𝑑 PROPN american_scientific_journal-3424 58 70 ) ) PUNCT american_scientific_journal-3424 58 71 is be AUX american_scientific_journal-3424 58 72 the the DET american_scientific_journal-3424 58 73 number number NOUN american_scientific_journal-3424 58 74 of of ADP american_scientific_journal-3424 58 75 recovered recovered ADJ american_scientific_journal-3424 58 76 people people NOUN american_scientific_journal-3424 58 77 at at ADP american_scientific_journal-3424 58 78 time time NOUN american_scientific_journal-3424 58 79 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-3424 58 80 , , PUNCT american_scientific_journal-3424 58 81 𝛽𝛽 𝛽𝛽 X american_scientific_journal-3424 58 82 is be AUX american_scientific_journal-3424 58 83 the the DET american_scientific_journal-3424 58 84 transmission transmission NOUN american_scientific_journal-3424 58 85 rate rate NOUN american_scientific_journal-3424 58 86 , , PUNCT american_scientific_journal-3424 58 87 𝛾𝛾 𝛾𝛾 PROPN american_scientific_journal-3424 58 88 represents represent VERB american_scientific_journal-3424 58 89 the the DET american_scientific_journal-3424 58 90 recovery recovery NOUN american_scientific_journal-3424 58 91 rate rate NOUN american_scientific_journal-3424 58 92 , , PUNCT american_scientific_journal-3424 58 93 and and CCONJ american_scientific_journal-3424 58 94 𝑁𝑁 𝑁𝑁 PROPN american_scientific_journal-3424 58 95 = = SYM american_scientific_journal-3424 58 96 𝑆𝑆(𝑑𝑑 𝑆𝑆(𝑑𝑑 PROPN american_scientific_journal-3424 58 97 ) ) PUNCT american_scientific_journal-3424 59 1 + + CCONJ american_scientific_journal-3424 59 2 𝐼𝐼(𝑑𝑑 𝐼𝐼(𝑑𝑑 NOUN american_scientific_journal-3424 59 3 ) ) PUNCT american_scientific_journal-3424 59 4 + + NUM american_scientific_journal-3424 59 5 𝑅𝑅(𝑑𝑑 𝑅𝑅(𝑑𝑑 NOUN american_scientific_journal-3424 59 6 ) ) PUNCT american_scientific_journal-3424 59 7 is be AUX american_scientific_journal-3424 59 8 the the DET american_scientific_journal-3424 59 9 fixed fix VERB american_scientific_journal-3424 59 10 population population NOUN american_scientific_journal-3424 59 11 . . PUNCT american_scientific_journal-3424 60 1 according accord VERB american_scientific_journal-3424 60 2 to to ADP american_scientific_journal-3424 60 3 the the DET american_scientific_journal-3424 60 4 general general ADJ american_scientific_journal-3424 60 5 iterative iterative NOUN american_scientific_journal-3424 60 6 formula formula NOUN american_scientific_journal-3424 60 7 , , PUNCT american_scientific_journal-3424 60 8 the the DET american_scientific_journal-3424 60 9 iterative iterative NOUN american_scientific_journal-3424 60 10 formulas formula NOUN american_scientific_journal-3424 60 11 for for ADP american_scientific_journal-3424 60 12 𝑆𝑆(𝑑𝑑 𝑆𝑆(𝑑𝑑 NOUN american_scientific_journal-3424 60 13 ) ) PUNCT american_scientific_journal-3424 60 14 , , PUNCT american_scientific_journal-3424 60 15 𝐼𝐼(𝑑𝑑 𝐼𝐼(𝑑𝑑 NOUN american_scientific_journal-3424 60 16 ) ) PUNCT american_scientific_journal-3424 60 17 and and CCONJ american_scientific_journal-3424 60 18 𝑅𝑅(𝑑𝑑 𝑅𝑅(𝑑𝑑 NOUN american_scientific_journal-3424 60 19 ) ) PUNCT american_scientific_journal-3424 60 20 of of ADP american_scientific_journal-3424 60 21 sir sir PROPN american_scientific_journal-3424 60 22 model model NOUN american_scientific_journal-3424 60 23 can can AUX american_scientific_journal-3424 60 24 be be AUX american_scientific_journal-3424 60 25 written write VERB american_scientific_journal-3424 60 26 out out ADP american_scientific_journal-3424 60 27 𝑆𝑆𝑛𝑛+1 𝑆𝑆𝑛𝑛+1 NOUN american_scientific_journal-3424 60 28 = = SYM american_scientific_journal-3424 60 29 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 61 1 + + CCONJ american_scientific_journal-3424 61 2 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 61 3 6 6 NUM american_scientific_journal-3424 61 4 ( ( PUNCT american_scientific_journal-3424 61 5 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 61 6 ) ) PUNCT american_scientific_journal-3424 61 7 π‘˜π‘˜1𝑑𝑑 π‘˜π‘˜1𝑑𝑑 NOUN american_scientific_journal-3424 61 8 = = SYM american_scientific_journal-3424 61 9 𝑓𝑓(𝑑𝑑𝑛𝑛 𝑓𝑓(𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 61 10 , , PUNCT american_scientific_journal-3424 61 11 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 61 12 , , PUNCT american_scientific_journal-3424 61 13 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 ADV american_scientific_journal-3424 61 14 ) ) PUNCT american_scientific_journal-3424 62 1 = = PUNCT american_scientific_journal-3424 63 1 βˆ’π›½π›½π‘†π‘†π‘›π‘›πΌπΌπ‘›π‘› βˆ’π›½π›½π‘†π‘†π‘›π‘›πΌπΌπ‘›π‘› NOUN american_scientific_journal-3424 63 2 π‘˜π‘˜2𝑑𝑑 π‘˜π‘˜2𝑑𝑑 VERB american_scientific_journal-3424 63 3 = = NOUN american_scientific_journal-3424 63 4 𝑓𝑓 𝑓𝑓 ADP american_scientific_journal-3424 63 5 οΏ½ οΏ½ PROPN american_scientific_journal-3424 63 6 𝑑𝑑𝑛𝑛 𝑑𝑑𝑛𝑛 VERB american_scientific_journal-3424 63 7 + + CCONJ american_scientific_journal-3424 63 8 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 63 9 2 2 NUM american_scientific_journal-3424 63 10 , , PUNCT american_scientific_journal-3424 63 11 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 64 1 + + CCONJ american_scientific_journal-3424 65 1 π‘˜π‘˜1 π‘˜π‘˜1 CCONJ american_scientific_journal-3424 65 2 π‘†π‘†βˆ†π‘‘π‘‘ π‘†π‘†βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 65 3 2 2 NUM american_scientific_journal-3424 65 4 , , PUNCT american_scientific_journal-3424 65 5 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 65 6 + + CCONJ american_scientific_journal-3424 66 1 π‘˜π‘˜1 π‘˜π‘˜1 CCONJ american_scientific_journal-3424 66 2 πΌπΌβˆ†π‘‘π‘‘ πΌπΌβˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 66 3 2 2 NUM american_scientific_journal-3424 66 4 οΏ½ οΏ½ PROPN american_scientific_journal-3424 66 5 = = SYM american_scientific_journal-3424 66 6 βˆ’π›½π›½ βˆ’π›½π›½ PROPN american_scientific_journal-3424 66 7 οΏ½ οΏ½ NOUN american_scientific_journal-3424 66 8 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 67 1 + + CCONJ american_scientific_journal-3424 67 2 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 67 3 2 2 NUM american_scientific_journal-3424 67 4 οΏ½ οΏ½ PROPN american_scientific_journal-3424 67 5 ( ( PUNCT american_scientific_journal-3424 67 6 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 67 7 + + CCONJ american_scientific_journal-3424 67 8 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 67 9 2 2 X american_scientific_journal-3424 67 10 ) ) PUNCT american_scientific_journal-3424 67 11 π‘˜π‘˜3𝑑𝑑 π‘˜π‘˜3𝑑𝑑 NOUN american_scientific_journal-3424 67 12 = = PUNCT american_scientific_journal-3424 67 13 𝑓𝑓 𝑓𝑓 ADP american_scientific_journal-3424 67 14 οΏ½ οΏ½ PROPN american_scientific_journal-3424 67 15 𝑑𝑑𝑛𝑛 𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 67 16 + + CCONJ american_scientific_journal-3424 67 17 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 67 18 2 2 NUM american_scientific_journal-3424 67 19 , , PUNCT american_scientific_journal-3424 67 20 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 68 1 + + CCONJ american_scientific_journal-3424 69 1 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 69 2 2 2 NUM american_scientific_journal-3424 69 3 , , PUNCT american_scientific_journal-3424 69 4 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 69 5 + + CCONJ american_scientific_journal-3424 69 6 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 69 7 2 2 NUM american_scientific_journal-3424 69 8 οΏ½ οΏ½ PROPN american_scientific_journal-3424 69 9 = = SYM american_scientific_journal-3424 69 10 βˆ’π›½π›½ βˆ’π›½π›½ PROPN american_scientific_journal-3424 69 11 οΏ½ οΏ½ NOUN american_scientific_journal-3424 69 12 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 69 13 + + CCONJ american_scientific_journal-3424 69 14 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 69 15 2 2 NUM american_scientific_journal-3424 69 16 οΏ½ οΏ½ PROPN american_scientific_journal-3424 69 17 ( ( PUNCT american_scientific_journal-3424 69 18 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 69 19 + + CCONJ american_scientific_journal-3424 69 20 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 69 21 2 2 NUM american_scientific_journal-3424 69 22 ) ) PUNCT american_scientific_journal-3424 69 23 π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜4𝑑𝑑 NOUN american_scientific_journal-3424 69 24 = = SYM american_scientific_journal-3424 69 25 𝑓𝑓(𝑑𝑑𝑛𝑛 𝑓𝑓(𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 69 26 + + CCONJ american_scientific_journal-3424 69 27 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 69 28 , , PUNCT american_scientific_journal-3424 69 29 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 69 30 + + CCONJ american_scientific_journal-3424 69 31 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 69 32 , , PUNCT american_scientific_journal-3424 69 33 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 69 34 + + CCONJ american_scientific_journal-3424 69 35 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 69 36 ) ) PUNCT american_scientific_journal-3424 69 37 = = PUNCT american_scientific_journal-3424 70 1 βˆ’π›½π›½(𝑆𝑆𝑛𝑛 βˆ’π›½π›½(𝑆𝑆𝑛𝑛 NOUN american_scientific_journal-3424 71 1 + + CCONJ american_scientific_journal-3424 71 2 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼𝑛𝑛 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 71 3 + + CCONJ american_scientific_journal-3424 71 4 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ X american_scientific_journal-3424 71 5 ) ) PUNCT american_scientific_journal-3424 71 6 𝐼𝐼𝑛𝑛+1 𝐼𝐼𝑛𝑛+1 NOUN american_scientific_journal-3424 71 7 = = PUNCT american_scientific_journal-3424 72 1 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 72 2 + + CCONJ american_scientific_journal-3424 72 3 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 72 4 6 6 NUM american_scientific_journal-3424 72 5 ( ( PUNCT american_scientific_journal-3424 72 6 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 72 7 ) ) PUNCT american_scientific_journal-3424 72 8 π‘˜π‘˜1𝑑𝑑 π‘˜π‘˜1𝑑𝑑 PROPN american_scientific_journal-3424 72 9 = = SYM american_scientific_journal-3424 72 10 𝑓𝑓(𝑑𝑑𝑛𝑛 𝑓𝑓(𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 72 11 , , PUNCT american_scientific_journal-3424 72 12 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 72 13 , , PUNCT american_scientific_journal-3424 72 14 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 ADV american_scientific_journal-3424 72 15 ) ) PUNCT american_scientific_journal-3424 72 16 = = PUNCT american_scientific_journal-3424 73 1 𝛽𝛽𝑆𝑆𝑛𝑛𝐼𝐼𝑛𝑛 𝛽𝛽𝑆𝑆𝑛𝑛𝐼𝐼𝑛𝑛 ADV american_scientific_journal-3424 73 2 βˆ’ βˆ’ PUNCT american_scientific_journal-3424 73 3 𝛾𝛾𝐼𝐼𝑛𝑛 𝛾𝛾𝐼𝐼𝑛𝑛 NUM american_scientific_journal-3424 73 4 π‘˜π‘˜2𝑑𝑑 π‘˜π‘˜2𝑑𝑑 PROPN american_scientific_journal-3424 73 5 = = NOUN american_scientific_journal-3424 73 6 𝑓𝑓 𝑓𝑓 ADP american_scientific_journal-3424 73 7 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 8 𝑑𝑑𝑛𝑛 𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 73 9 + + CCONJ american_scientific_journal-3424 73 10 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 11 2 2 NUM american_scientific_journal-3424 73 12 , , PUNCT american_scientific_journal-3424 73 13 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 73 14 + + CCONJ american_scientific_journal-3424 73 15 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 73 16 2 2 NUM american_scientific_journal-3424 73 17 , , PUNCT american_scientific_journal-3424 73 18 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 73 19 + + CCONJ american_scientific_journal-3424 73 20 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 21 2 2 NUM american_scientific_journal-3424 73 22 οΏ½ οΏ½ NOUN american_scientific_journal-3424 73 23 = = PUNCT american_scientific_journal-3424 73 24 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 73 25 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 26 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 73 27 + + CCONJ american_scientific_journal-3424 73 28 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 29 2 2 NUM american_scientific_journal-3424 73 30 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 31 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 32 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 73 33 + + CCONJ american_scientific_journal-3424 73 34 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 35 2 2 NUM american_scientific_journal-3424 73 36 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 37 βˆ’ βˆ’ PROPN american_scientific_journal-3424 73 38 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 39 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 73 40 + + CCONJ american_scientific_journal-3424 73 41 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 42 2 2 NUM american_scientific_journal-3424 73 43 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 44 π‘˜π‘˜3𝑑𝑑 π‘˜π‘˜3𝑑𝑑 NOUN american_scientific_journal-3424 73 45 = = PUNCT american_scientific_journal-3424 73 46 𝑓𝑓 𝑓𝑓 ADP american_scientific_journal-3424 73 47 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 48 𝑑𝑑𝑛𝑛 𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 73 49 + + CCONJ american_scientific_journal-3424 73 50 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 51 2 2 NUM american_scientific_journal-3424 73 52 , , PUNCT american_scientific_journal-3424 73 53 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 73 54 + + CCONJ american_scientific_journal-3424 73 55 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 56 2 2 NUM american_scientific_journal-3424 73 57 , , PUNCT american_scientific_journal-3424 73 58 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 73 59 + + CCONJ american_scientific_journal-3424 73 60 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 61 2 2 NUM american_scientific_journal-3424 73 62 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 63 american american ADJ american_scientific_journal-3424 73 64 scientific scientific ADJ american_scientific_journal-3424 73 65 research research NOUN american_scientific_journal-3424 73 66 journal journal NOUN american_scientific_journal-3424 73 67 for for ADP american_scientific_journal-3424 73 68 engineering engineering NOUN american_scientific_journal-3424 73 69 , , PUNCT american_scientific_journal-3424 73 70 technology technology NOUN american_scientific_journal-3424 73 71 , , PUNCT american_scientific_journal-3424 73 72 and and CCONJ american_scientific_journal-3424 73 73 sciences science NOUN american_scientific_journal-3424 73 74 ( ( PUNCT american_scientific_journal-3424 73 75 asrjets asrjet NOUN american_scientific_journal-3424 73 76 ) ) PUNCT american_scientific_journal-3424 73 77 ( ( PUNCT american_scientific_journal-3424 73 78 2017 2017 NUM american_scientific_journal-3424 73 79 ) ) PUNCT american_scientific_journal-3424 73 80 volume volume NOUN american_scientific_journal-3424 73 81 37 37 NUM american_scientific_journal-3424 73 82 , , PUNCT american_scientific_journal-3424 73 83 no no DET american_scientific_journal-3424 73 84 1 1 NUM american_scientific_journal-3424 73 85 , , PUNCT american_scientific_journal-3424 73 86 pp pp ADV american_scientific_journal-3424 73 87 1 1 NUM american_scientific_journal-3424 73 88 - - SYM american_scientific_journal-3424 73 89 21 21 NUM american_scientific_journal-3424 73 90 6 6 NUM american_scientific_journal-3424 73 91 = = NOUN american_scientific_journal-3424 73 92 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 73 93 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 94 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 73 95 + + PROPN american_scientific_journal-3424 73 96 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 97 2 2 NUM american_scientific_journal-3424 73 98 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 99 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 100 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 73 101 + + CCONJ american_scientific_journal-3424 73 102 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 103 2 2 NUM american_scientific_journal-3424 73 104 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 105 βˆ’ βˆ’ PROPN american_scientific_journal-3424 73 106 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 107 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 73 108 + + CCONJ american_scientific_journal-3424 73 109 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 110 2 2 NUM american_scientific_journal-3424 73 111 οΏ½ οΏ½ PROPN american_scientific_journal-3424 73 112 π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜4𝑑𝑑 NOUN american_scientific_journal-3424 73 113 = = SYM american_scientific_journal-3424 73 114 𝑓𝑓(𝑑𝑑𝑛𝑛 𝑓𝑓(𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 73 115 + + CCONJ american_scientific_journal-3424 73 116 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 117 , , PUNCT american_scientific_journal-3424 73 118 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 73 119 + + CCONJ american_scientific_journal-3424 73 120 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 73 121 , , PUNCT american_scientific_journal-3424 73 122 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 73 123 + + CCONJ american_scientific_journal-3424 73 124 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 73 125 ) ) PUNCT american_scientific_journal-3424 74 1 = = PUNCT american_scientific_journal-3424 75 1 𝛽𝛽(𝑆𝑆𝑛𝑛 𝛽𝛽(𝑆𝑆𝑛𝑛 ADV american_scientific_journal-3424 75 2 + + NOUN american_scientific_journal-3424 75 3 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼𝑛𝑛 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 75 4 + + NUM american_scientific_journal-3424 75 5 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 75 6 ) ) PUNCT american_scientific_journal-3424 75 7 βˆ’ βˆ’ PROPN american_scientific_journal-3424 76 1 ( ( PUNCT american_scientific_journal-3424 76 2 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 76 3 + + NUM american_scientific_journal-3424 76 4 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 76 5 ) ) PUNCT american_scientific_journal-3424 76 6 𝑅𝑅𝑛𝑛+1 𝑅𝑅𝑛𝑛+1 NOUN american_scientific_journal-3424 76 7 = = PUNCT american_scientific_journal-3424 77 1 𝑅𝑅𝑛𝑛 𝑅𝑅𝑛𝑛 PROPN american_scientific_journal-3424 77 2 + + NUM american_scientific_journal-3424 77 3 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 77 4 6 6 NUM american_scientific_journal-3424 77 5 ( ( PUNCT american_scientific_journal-3424 77 6 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 77 7 ) ) PUNCT american_scientific_journal-3424 77 8 π‘˜π‘˜1𝑑𝑑 π‘˜π‘˜1𝑑𝑑 PROPN american_scientific_journal-3424 77 9 = = SYM american_scientific_journal-3424 77 10 𝑓𝑓(𝑑𝑑𝑛𝑛 𝑓𝑓(𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 77 11 , , PUNCT american_scientific_journal-3424 77 12 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 X american_scientific_journal-3424 77 13 ) ) PUNCT american_scientific_journal-3424 78 1 = = PUNCT american_scientific_journal-3424 79 1 𝛾𝛾𝐼𝐼𝑛𝑛 𝛾𝛾𝐼𝐼𝑛𝑛 NUM american_scientific_journal-3424 79 2 π‘˜π‘˜2𝑑𝑑 π‘˜π‘˜2𝑑𝑑 NOUN american_scientific_journal-3424 79 3 = = NOUN american_scientific_journal-3424 79 4 𝑓𝑓 𝑓𝑓 ADP american_scientific_journal-3424 79 5 οΏ½ οΏ½ PROPN american_scientific_journal-3424 79 6 𝑑𝑑𝑛𝑛 𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 79 7 + + CCONJ american_scientific_journal-3424 79 8 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 79 9 2 2 NUM american_scientific_journal-3424 79 10 , , PUNCT american_scientific_journal-3424 79 11 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 79 12 + + CCONJ american_scientific_journal-3424 79 13 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 79 14 2 2 NUM american_scientific_journal-3424 79 15 οΏ½ οΏ½ PROPN american_scientific_journal-3424 79 16 = = PUNCT american_scientific_journal-3424 79 17 𝛾𝛾 𝛾𝛾 PART american_scientific_journal-3424 79 18 οΏ½ οΏ½ PROPN american_scientific_journal-3424 79 19 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 79 20 + + CCONJ american_scientific_journal-3424 79 21 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 79 22 2 2 NUM american_scientific_journal-3424 79 23 οΏ½ οΏ½ PROPN american_scientific_journal-3424 79 24 π‘˜π‘˜3𝑑𝑑 π‘˜π‘˜3𝑑𝑑 NOUN american_scientific_journal-3424 79 25 = = PUNCT american_scientific_journal-3424 79 26 𝑓𝑓 𝑓𝑓 ADP american_scientific_journal-3424 79 27 οΏ½ οΏ½ PROPN american_scientific_journal-3424 79 28 𝑑𝑑𝑛𝑛 𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 79 29 + + CCONJ american_scientific_journal-3424 79 30 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 79 31 2 2 NUM american_scientific_journal-3424 79 32 , , PUNCT american_scientific_journal-3424 79 33 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 79 34 + + CCONJ american_scientific_journal-3424 79 35 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 79 36 2 2 NUM american_scientific_journal-3424 79 37 οΏ½ οΏ½ PROPN american_scientific_journal-3424 79 38 = = PUNCT american_scientific_journal-3424 79 39 𝛾𝛾 𝛾𝛾 PART american_scientific_journal-3424 79 40 οΏ½ οΏ½ PROPN american_scientific_journal-3424 79 41 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 79 42 + + CCONJ american_scientific_journal-3424 79 43 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 79 44 2 2 NUM american_scientific_journal-3424 79 45 οΏ½ οΏ½ PROPN american_scientific_journal-3424 79 46 π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜4𝑑𝑑 NOUN american_scientific_journal-3424 79 47 = = SYM american_scientific_journal-3424 79 48 𝑓𝑓(𝑑𝑑𝑛𝑛 𝑓𝑓(𝑑𝑑𝑛𝑛 PROPN american_scientific_journal-3424 79 49 + + CCONJ american_scientific_journal-3424 79 50 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 79 51 , , PUNCT american_scientific_journal-3424 79 52 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 79 53 + + X american_scientific_journal-3424 79 54 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 79 55 ) ) PUNCT american_scientific_journal-3424 80 1 = = PUNCT american_scientific_journal-3424 81 1 𝛾𝛾(𝐼𝐼𝑛𝑛 𝛾𝛾(𝐼𝐼𝑛𝑛 ADV american_scientific_journal-3424 81 2 + + CCONJ american_scientific_journal-3424 81 3 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 81 4 ) ) PUNCT american_scientific_journal-3424 81 5 2.3 2.3 NUM american_scientific_journal-3424 81 6 transformation transformation NOUN american_scientific_journal-3424 81 7 of of ADP american_scientific_journal-3424 81 8 euler euler NOUN american_scientific_journal-3424 81 9 equations equation NOUN american_scientific_journal-3424 81 10 for for ADP american_scientific_journal-3424 81 11 sir sir NOUN american_scientific_journal-3424 81 12 modeling modeling NOUN american_scientific_journal-3424 81 13 if if SCONJ american_scientific_journal-3424 81 14 we we PRON american_scientific_journal-3424 81 15 have have VERB american_scientific_journal-3424 81 16 a a DET american_scientific_journal-3424 81 17 " " PUNCT american_scientific_journal-3424 81 18 slope slope NOUN american_scientific_journal-3424 81 19 formula formula NOUN american_scientific_journal-3424 81 20 , , PUNCT american_scientific_journal-3424 81 21 " " PUNCT american_scientific_journal-3424 81 22 i.e. i.e. X american_scientific_journal-3424 81 23 , , PUNCT american_scientific_journal-3424 81 24 a a DET american_scientific_journal-3424 81 25 way way NOUN american_scientific_journal-3424 81 26 to to PART american_scientific_journal-3424 81 27 calculate calculate VERB american_scientific_journal-3424 81 28 𝑑𝑑𝑦𝑦/𝑑𝑑𝑑𝑑 𝑑𝑑𝑦𝑦/𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 81 29 at at ADP american_scientific_journal-3424 81 30 any any DET american_scientific_journal-3424 81 31 point point NOUN american_scientific_journal-3424 81 32 ( ( PUNCT american_scientific_journal-3424 81 33 𝑑𝑑,𝑦𝑦 𝑑𝑑,𝑦𝑦 NOUN american_scientific_journal-3424 81 34 ) ) PUNCT american_scientific_journal-3424 81 35 , , PUNCT american_scientific_journal-3424 81 36 then then ADV american_scientific_journal-3424 81 37 we we PRON american_scientific_journal-3424 81 38 can can AUX american_scientific_journal-3424 81 39 generate generate VERB american_scientific_journal-3424 81 40 a a DET american_scientific_journal-3424 81 41 sequence sequence NOUN american_scientific_journal-3424 81 42 of of ADP american_scientific_journal-3424 81 43 𝑦𝑦-values 𝑦𝑦-value NOUN american_scientific_journal-3424 81 44 , , PUNCT american_scientific_journal-3424 81 45 𝑦𝑦0 𝑦𝑦0 ADV american_scientific_journal-3424 81 46 , , PUNCT american_scientific_journal-3424 81 47 𝑦𝑦1,𝑦𝑦2,𝑦𝑦3 𝑦𝑦1,𝑦𝑦2,𝑦𝑦3 NOUN american_scientific_journal-3424 81 48 … … PUNCT american_scientific_journal-3424 81 49 … … PUNCT american_scientific_journal-3424 81 50 … … PUNCT american_scientific_journal-3424 81 51 … … PUNCT american_scientific_journal-3424 81 52 by by ADP american_scientific_journal-3424 81 53 starting start VERB american_scientific_journal-3424 81 54 from from ADP american_scientific_journal-3424 81 55 a a DET american_scientific_journal-3424 81 56 given give VERB american_scientific_journal-3424 81 57 𝑦𝑦0 𝑦𝑦0 NOUN american_scientific_journal-3424 81 58 and and CCONJ american_scientific_journal-3424 81 59 computing compute VERB american_scientific_journal-3424 81 60 each each DET american_scientific_journal-3424 81 61 rise rise NOUN american_scientific_journal-3424 81 62 as as ADP american_scientific_journal-3424 81 63 slope slope NOUN american_scientific_journal-3424 81 64 x x NOUN american_scientific_journal-3424 81 65 run run VERB american_scientific_journal-3424 81 66 . . PUNCT american_scientific_journal-3424 82 1 that that PRON american_scientific_journal-3424 82 2 is be AUX american_scientific_journal-3424 82 3 , , PUNCT american_scientific_journal-3424 82 4 𝑦𝑦𝑛𝑛+1 𝑦𝑦𝑛𝑛+1 PROPN american_scientific_journal-3424 82 5 = = SYM american_scientific_journal-3424 82 6 𝑦𝑦𝑛𝑛 𝑦𝑦𝑛𝑛 PROPN american_scientific_journal-3424 82 7 + + CCONJ american_scientific_journal-3424 82 8 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛 PROPN american_scientific_journal-3424 82 9 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 82 10 where where SCONJ american_scientific_journal-3424 82 11 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 82 12 is be AUX american_scientific_journal-3424 82 13 a a DET american_scientific_journal-3424 82 14 suitably suitably ADV american_scientific_journal-3424 82 15 small small ADJ american_scientific_journal-3424 82 16 step step NOUN american_scientific_journal-3424 82 17 size size NOUN american_scientific_journal-3424 82 18 in in ADP american_scientific_journal-3424 82 19 the the DET american_scientific_journal-3424 82 20 time time NOUN american_scientific_journal-3424 82 21 domain domain NOUN american_scientific_journal-3424 82 22 . . PUNCT american_scientific_journal-3424 83 1 it it PRON american_scientific_journal-3424 83 2 really really ADV american_scientific_journal-3424 83 3 does do AUX american_scientific_journal-3424 83 4 n't not PART american_scientific_journal-3424 83 5 matter matter VERB american_scientific_journal-3424 83 6 in in ADP american_scientific_journal-3424 83 7 this this DET american_scientific_journal-3424 83 8 calculation calculation NOUN american_scientific_journal-3424 83 9 if if SCONJ american_scientific_journal-3424 83 10 the the DET american_scientific_journal-3424 83 11 slope slope NOUN american_scientific_journal-3424 83 12 formula formula NOUN american_scientific_journal-3424 83 13 happens happen VERB american_scientific_journal-3424 83 14 to to PART american_scientific_journal-3424 83 15 depend depend VERB american_scientific_journal-3424 83 16 not not PART american_scientific_journal-3424 83 17 just just ADV american_scientific_journal-3424 83 18 on on ADP american_scientific_journal-3424 83 19 t t PROPN american_scientific_journal-3424 83 20 and and CCONJ american_scientific_journal-3424 83 21 y y PROPN american_scientific_journal-3424 83 22 but but CCONJ american_scientific_journal-3424 83 23 on on ADP american_scientific_journal-3424 83 24 other other ADJ american_scientific_journal-3424 83 25 variables variable NOUN american_scientific_journal-3424 83 26 , , PUNCT american_scientific_journal-3424 83 27 say say VERB american_scientific_journal-3424 83 28 x x PUNCT american_scientific_journal-3424 83 29 and and CCONJ american_scientific_journal-3424 83 30 z z NOUN american_scientific_journal-3424 83 31 -as -a NOUN american_scientific_journal-3424 83 32 long long ADV american_scientific_journal-3424 83 33 as as SCONJ american_scientific_journal-3424 83 34 we we PRON american_scientific_journal-3424 83 35 know know VERB american_scientific_journal-3424 83 36 how how SCONJ american_scientific_journal-3424 83 37 x x PUNCT american_scientific_journal-3424 83 38 and and CCONJ american_scientific_journal-3424 83 39 z z NOUN american_scientific_journal-3424 83 40 are be AUX american_scientific_journal-3424 83 41 related relate VERB american_scientific_journal-3424 83 42 to to ADP american_scientific_journal-3424 83 43 t t PROPN american_scientific_journal-3424 83 44 and and CCONJ american_scientific_journal-3424 83 45 y. y. NOUN american_scientific_journal-3424 83 46 if if SCONJ american_scientific_journal-3424 83 47 x x PROPN american_scientific_journal-3424 83 48 and and CCONJ american_scientific_journal-3424 83 49 z z AUX american_scientific_journal-3424 83 50 happen happen VERB american_scientific_journal-3424 83 51 to to PART american_scientific_journal-3424 83 52 be be AUX american_scientific_journal-3424 83 53 other other ADJ american_scientific_journal-3424 83 54 dependent dependent ADJ american_scientific_journal-3424 83 55 variables variable NOUN american_scientific_journal-3424 83 56 in in ADP american_scientific_journal-3424 83 57 a a DET american_scientific_journal-3424 83 58 system system NOUN american_scientific_journal-3424 83 59 of of ADP american_scientific_journal-3424 83 60 differential differential ADJ american_scientific_journal-3424 83 61 equations equation NOUN american_scientific_journal-3424 83 62 , , PUNCT american_scientific_journal-3424 83 63 i i PRON american_scientific_journal-3424 83 64 can can AUX american_scientific_journal-3424 83 65 generate generate VERB american_scientific_journal-3424 83 66 values value NOUN american_scientific_journal-3424 83 67 of of ADP american_scientific_journal-3424 83 68 x x X american_scientific_journal-3424 83 69 and and CCONJ american_scientific_journal-3424 83 70 z z PROPN american_scientific_journal-3424 83 71 in in ADP american_scientific_journal-3424 83 72 the the DET american_scientific_journal-3424 83 73 same same ADJ american_scientific_journal-3424 83 74 way way NOUN american_scientific_journal-3424 83 75 . . PUNCT american_scientific_journal-3424 84 1 of of ADP american_scientific_journal-3424 84 2 course course NOUN american_scientific_journal-3424 84 3 , , PUNCT american_scientific_journal-3424 84 4 for for ADP american_scientific_journal-3424 84 5 the the DET american_scientific_journal-3424 84 6 sir sir PROPN american_scientific_journal-3424 84 7 model model NOUN american_scientific_journal-3424 84 8 , , PUNCT american_scientific_journal-3424 84 9 we we PRON american_scientific_journal-3424 84 10 want want VERB american_scientific_journal-3424 84 11 the the DET american_scientific_journal-3424 84 12 dependent dependent ADJ american_scientific_journal-3424 84 13 variable variable ADJ american_scientific_journal-3424 84 14 names name NOUN american_scientific_journal-3424 84 15 to to PART american_scientific_journal-3424 84 16 be be AUX american_scientific_journal-3424 84 17 𝑆𝑆 𝑆𝑆 PROPN american_scientific_journal-3424 84 18 , , PUNCT american_scientific_journal-3424 84 19 𝐼𝐼 𝐼𝐼 PROPN american_scientific_journal-3424 84 20 π‘Žπ‘Žπ‘Žπ‘Žπ‘‘π‘‘ π‘Žπ‘Žπ‘Žπ‘Žπ‘‘π‘‘ NOUN american_scientific_journal-3424 84 21 𝑅𝑅. 𝑅𝑅. NOUN american_scientific_journal-3424 84 22 thus thus ADV american_scientific_journal-3424 84 23 we we PRON american_scientific_journal-3424 84 24 have have VERB american_scientific_journal-3424 84 25 three three NUM american_scientific_journal-3424 84 26 euler euler NOUN american_scientific_journal-3424 84 27 formulas formula NOUN american_scientific_journal-3424 84 28 of of ADP american_scientific_journal-3424 84 29 the the DET american_scientific_journal-3424 84 30 form form NOUN american_scientific_journal-3424 84 31 𝑆𝑆𝑛𝑛+1 𝑆𝑆𝑛𝑛+1 NOUN american_scientific_journal-3424 84 32 = = PUNCT american_scientific_journal-3424 84 33 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 85 1 + + NUM american_scientific_journal-3424 85 2 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛 PROPN american_scientific_journal-3424 85 3 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 85 4 american american PROPN american_scientific_journal-3424 85 5 scientific scientific ADJ american_scientific_journal-3424 85 6 research research PROPN american_scientific_journal-3424 85 7 journal journal NOUN american_scientific_journal-3424 85 8 for for ADP american_scientific_journal-3424 85 9 engineering engineering NOUN american_scientific_journal-3424 85 10 , , PUNCT american_scientific_journal-3424 85 11 technology technology NOUN american_scientific_journal-3424 85 12 , , PUNCT american_scientific_journal-3424 85 13 and and CCONJ american_scientific_journal-3424 85 14 sciences science NOUN american_scientific_journal-3424 85 15 ( ( PUNCT american_scientific_journal-3424 85 16 asrjets asrjet NOUN american_scientific_journal-3424 85 17 ) ) PUNCT american_scientific_journal-3424 85 18 ( ( PUNCT american_scientific_journal-3424 85 19 2017 2017 NUM american_scientific_journal-3424 85 20 ) ) PUNCT american_scientific_journal-3424 85 21 volume volume NOUN american_scientific_journal-3424 85 22 37 37 NUM american_scientific_journal-3424 85 23 , , PUNCT american_scientific_journal-3424 85 24 no no DET american_scientific_journal-3424 85 25 1 1 NUM american_scientific_journal-3424 85 26 , , PUNCT american_scientific_journal-3424 85 27 pp pp ADV american_scientific_journal-3424 85 28 1 1 NUM american_scientific_journal-3424 85 29 - - SYM american_scientific_journal-3424 85 30 21 21 NUM american_scientific_journal-3424 85 31 7 7 NUM american_scientific_journal-3424 85 32 𝐼𝐼𝑛𝑛+1 𝐼𝐼𝑛𝑛+1 NOUN american_scientific_journal-3424 85 33 = = SYM american_scientific_journal-3424 86 1 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 86 2 + + CCONJ american_scientific_journal-3424 86 3 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛 PROPN american_scientific_journal-3424 86 4 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 86 5 𝑅𝑅𝑛𝑛+1 𝑅𝑅𝑛𝑛+1 PROPN american_scientific_journal-3424 87 1 = = PUNCT american_scientific_journal-3424 88 1 𝑅𝑅𝑛𝑛 𝑅𝑅𝑛𝑛 PROPN american_scientific_journal-3424 88 2 + + NUM american_scientific_journal-3424 88 3 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛 NOUN american_scientific_journal-3424 88 4 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 88 5 more more ADV american_scientific_journal-3424 88 6 specifically specifically ADV american_scientific_journal-3424 88 7 , , PUNCT american_scientific_journal-3424 88 8 given give VERB american_scientific_journal-3424 88 9 the the DET american_scientific_journal-3424 88 10 sir sir PROPN american_scientific_journal-3424 88 11 equations equation NOUN american_scientific_journal-3424 88 12 , , PUNCT american_scientific_journal-3424 88 13 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 88 14 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 89 1 = = PUNCT american_scientific_journal-3424 90 1 βˆ’ βˆ’ PROPN american_scientific_journal-3424 90 2 𝛽𝛽𝐼𝐼𝑆𝑆 𝛽𝛽𝐼𝐼𝑆𝑆 NOUN american_scientific_journal-3424 90 3 ; ; PUNCT american_scientific_journal-3424 90 4 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 90 5 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 90 6 = = PUNCT american_scientific_journal-3424 90 7 𝛽𝛽𝐼𝐼𝑆𝑆 𝛽𝛽𝐼𝐼𝑆𝑆 PROPN american_scientific_journal-3424 90 8 βˆ’ βˆ’ NOUN american_scientific_journal-3424 90 9 𝛾𝛾𝐼𝐼 𝛾𝛾𝐼𝐼 NOUN american_scientific_journal-3424 90 10 ; ; PUNCT american_scientific_journal-3424 90 11 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 90 12 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-3424 90 13 = = PUNCT american_scientific_journal-3424 91 1 𝛾𝛾𝐼𝐼 𝛾𝛾𝐼𝐼 NOUN american_scientific_journal-3424 91 2 the the DET american_scientific_journal-3424 91 3 euler euler PROPN american_scientific_journal-3424 91 4 formulas formula NOUN american_scientific_journal-3424 91 5 become become VERB american_scientific_journal-3424 91 6 𝑆𝑆𝑛𝑛+1 𝑆𝑆𝑛𝑛+1 NOUN american_scientific_journal-3424 91 7 = = SYM american_scientific_journal-3424 91 8 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 92 1 βˆ’ βˆ’ PROPN american_scientific_journal-3424 92 2 π›½π›½πΌπΌπ‘›π‘›π‘†π‘†π‘›π‘›βˆ†π‘‘π‘‘ π›½π›½πΌπΌπ‘›π‘›π‘†π‘†π‘›π‘›βˆ†π‘‘π‘‘ PUNCT american_scientific_journal-3424 92 3 𝐼𝐼𝑛𝑛+1 𝐼𝐼𝑛𝑛+1 NOUN american_scientific_journal-3424 92 4 = = PUNCT american_scientific_journal-3424 92 5 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 92 6 + + CCONJ american_scientific_journal-3424 92 7 ( ( PUNCT american_scientific_journal-3424 92 8 𝛽𝛽𝐼𝐼𝑛𝑛𝑆𝑆𝑛𝑛 𝛽𝛽𝐼𝐼𝑛𝑛𝑆𝑆𝑛𝑛 ADP american_scientific_journal-3424 92 9 βˆ’ βˆ’ PROPN american_scientific_journal-3424 92 10 𝛾𝛾𝐼𝐼𝑛𝑛)βˆ†π‘‘π‘‘ 𝛾𝛾𝐼𝐼𝑛𝑛)βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 92 11 𝑅𝑅𝑛𝑛+1 𝑅𝑅𝑛𝑛+1 NOUN american_scientific_journal-3424 92 12 = = PUNCT american_scientific_journal-3424 93 1 𝑅𝑅𝑛𝑛 𝑅𝑅𝑛𝑛 PROPN american_scientific_journal-3424 93 2 + + CCONJ american_scientific_journal-3424 93 3 π›Ύπ›ΎπΌπΌπ‘›π‘›βˆ†π‘‘π‘‘ π›Ύπ›ΎπΌπΌπ‘›π‘›βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 93 4 to to PART american_scientific_journal-3424 93 5 calculate calculate VERB american_scientific_journal-3424 93 6 something something PRON american_scientific_journal-3424 93 7 from from ADP american_scientific_journal-3424 93 8 these these DET american_scientific_journal-3424 93 9 formulas formula NOUN american_scientific_journal-3424 93 10 , , PUNCT american_scientific_journal-3424 93 11 we we PRON american_scientific_journal-3424 93 12 must must AUX american_scientific_journal-3424 93 13 have have VERB american_scientific_journal-3424 93 14 explicit explicit ADJ american_scientific_journal-3424 93 15 values value NOUN american_scientific_journal-3424 93 16 for for ADP american_scientific_journal-3424 93 17 𝛽𝛽 𝛽𝛽 NOUN american_scientific_journal-3424 93 18 , , PUNCT american_scientific_journal-3424 93 19 𝛾𝛾 𝛾𝛾 PROPN american_scientific_journal-3424 93 20 , , PUNCT american_scientific_journal-3424 93 21 𝑆𝑆(0 𝑆𝑆(0 PROPN american_scientific_journal-3424 93 22 ) ) PUNCT american_scientific_journal-3424 93 23 , , PUNCT american_scientific_journal-3424 93 24 𝐼𝐼(0 𝐼𝐼(0 PROPN american_scientific_journal-3424 93 25 ) ) PUNCT american_scientific_journal-3424 93 26 , , PUNCT american_scientific_journal-3424 93 27 𝑅𝑅(0 𝑅𝑅(0 PROPN american_scientific_journal-3424 93 28 ) ) PUNCT american_scientific_journal-3424 93 29 π‘Žπ‘Žπ‘Žπ‘Žπ‘‘π‘‘ π‘Žπ‘Žπ‘Žπ‘Žπ‘‘π‘‘ PROPN american_scientific_journal-3424 93 30 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 93 31 . . PUNCT american_scientific_journal-3424 94 1 3 3 X american_scientific_journal-3424 94 2 . . X american_scientific_journal-3424 94 3 application application NOUN american_scientific_journal-3424 94 4 , , PUNCT american_scientific_journal-3424 94 5 comparison comparison NOUN american_scientific_journal-3424 94 6 and and CCONJ american_scientific_journal-3424 94 7 result result VERB american_scientific_journal-3424 94 8 discussion discussion NOUN american_scientific_journal-3424 94 9 if if SCONJ american_scientific_journal-3424 94 10 we we PRON american_scientific_journal-3424 94 11 now now ADV american_scientific_journal-3424 94 12 take take VERB american_scientific_journal-3424 94 13 the the DET american_scientific_journal-3424 94 14 example example NOUN american_scientific_journal-3424 94 15 of of ADP american_scientific_journal-3424 94 16 the the DET american_scientific_journal-3424 94 17 ebola ebola PROPN american_scientific_journal-3424 94 18 outbreak outbreak NOUN american_scientific_journal-3424 94 19 in in ADP american_scientific_journal-3424 94 20 liberia liberia PROPN american_scientific_journal-3424 94 21 2014 2014 NUM american_scientific_journal-3424 94 22 , , PUNCT american_scientific_journal-3424 94 23 we we PRON american_scientific_journal-3424 94 24 can can AUX american_scientific_journal-3424 94 25 assign assign VERB american_scientific_journal-3424 94 26 the the DET american_scientific_journal-3424 94 27 parameters parameter NOUN american_scientific_journal-3424 94 28 with with ADP american_scientific_journal-3424 94 29 the the DET american_scientific_journal-3424 94 30 following follow VERB american_scientific_journal-3424 94 31 values value NOUN american_scientific_journal-3424 94 32 . . PUNCT american_scientific_journal-3424 95 1 the the DET american_scientific_journal-3424 95 2 total total ADJ american_scientific_journal-3424 95 3 population population NOUN american_scientific_journal-3424 95 4 of of ADP american_scientific_journal-3424 95 5 liberia liberia PROPN american_scientific_journal-3424 95 6 , , PUNCT american_scientific_journal-3424 95 7 n n NOUN american_scientific_journal-3424 95 8 = = NOUN american_scientific_journal-3424 95 9 4294000 4294000 NUM american_scientific_journal-3424 96 1 [ [ X american_scientific_journal-3424 96 2 8 8 NUM american_scientific_journal-3424 96 3 ] ] PUNCT american_scientific_journal-3424 96 4 , , PUNCT american_scientific_journal-3424 96 5 and and CCONJ american_scientific_journal-3424 96 6 according accord VERB american_scientific_journal-3424 96 7 to to ADP american_scientific_journal-3424 96 8 data datum NOUN american_scientific_journal-3424 96 9 from from ADP american_scientific_journal-3424 96 10 who who PRON american_scientific_journal-3424 96 11 , , PUNCT american_scientific_journal-3424 96 12 the the DET american_scientific_journal-3424 96 13 number number NOUN american_scientific_journal-3424 96 14 of of ADP american_scientific_journal-3424 96 15 people people NOUN american_scientific_journal-3424 96 16 infected infect VERB american_scientific_journal-3424 96 17 , , PUNCT american_scientific_journal-3424 96 18 i i PRON american_scientific_journal-3424 96 19 = = NOUN american_scientific_journal-3424 96 20 391[9 391[9 NUM american_scientific_journal-3424 96 21 ] ] PUNCT american_scientific_journal-3424 96 22 and and CCONJ american_scientific_journal-3424 96 23 the the DET american_scientific_journal-3424 96 24 number number NOUN american_scientific_journal-3424 96 25 of of ADP american_scientific_journal-3424 96 26 people people NOUN american_scientific_journal-3424 96 27 dead dead ADJ american_scientific_journal-3424 96 28 is be AUX american_scientific_journal-3424 96 29 227 227 NUM american_scientific_journal-3424 97 1 [ [ X american_scientific_journal-3424 97 2 9 9 NUM american_scientific_journal-3424 97 3 ] ] PUNCT american_scientific_journal-3424 97 4 . . PUNCT american_scientific_journal-3424 98 1 seeing see VERB american_scientific_journal-3424 98 2 as as SCONJ american_scientific_journal-3424 98 3 r r NOUN american_scientific_journal-3424 98 4 includes include VERB american_scientific_journal-3424 98 5 the the DET american_scientific_journal-3424 98 6 number number NOUN american_scientific_journal-3424 98 7 of of ADP american_scientific_journal-3424 98 8 people people NOUN american_scientific_journal-3424 98 9 who who PRON american_scientific_journal-3424 98 10 have have AUX american_scientific_journal-3424 98 11 received receive VERB american_scientific_journal-3424 98 12 permanent permanent ADJ american_scientific_journal-3424 98 13 immunity immunity NOUN american_scientific_journal-3424 98 14 , , PUNCT american_scientific_journal-3424 98 15 this this PRON american_scientific_journal-3424 98 16 includes include VERB american_scientific_journal-3424 98 17 those those PRON american_scientific_journal-3424 98 18 who who PRON american_scientific_journal-3424 98 19 have have AUX american_scientific_journal-3424 98 20 died die VERB american_scientific_journal-3424 98 21 as as SCONJ american_scientific_journal-3424 98 22 they they PRON american_scientific_journal-3424 98 23 have have VERB american_scientific_journal-3424 98 24 permanent permanent ADJ american_scientific_journal-3424 98 25 immunity immunity NOUN american_scientific_journal-3424 98 26 , , PUNCT american_scientific_journal-3424 98 27 in in ADP american_scientific_journal-3424 98 28 addition addition NOUN american_scientific_journal-3424 98 29 to to ADP american_scientific_journal-3424 98 30 those those PRON american_scientific_journal-3424 98 31 who who PRON american_scientific_journal-3424 98 32 have have AUX american_scientific_journal-3424 98 33 recovered recover VERB american_scientific_journal-3424 98 34 with with ADP american_scientific_journal-3424 98 35 permanent permanent ADJ american_scientific_journal-3424 98 36 immunity immunity NOUN american_scientific_journal-3424 98 37 . . PUNCT american_scientific_journal-3424 99 1 therefore therefore ADV american_scientific_journal-3424 99 2 , , PUNCT american_scientific_journal-3424 99 3 number number NOUN american_scientific_journal-3424 99 4 of of ADP american_scientific_journal-3424 99 5 people people NOUN american_scientific_journal-3424 99 6 recovered recover VERB american_scientific_journal-3424 99 7 𝑅𝑅 𝑅𝑅 PROPN american_scientific_journal-3424 99 8 = = SYM american_scientific_journal-3424 99 9 227 227 NUM american_scientific_journal-3424 99 10 + + CCONJ american_scientific_journal-3424 99 11 ( ( PUNCT american_scientific_journal-3424 99 12 0.3 0.3 NUM american_scientific_journal-3424 99 13 Γ— Γ— NOUN american_scientific_journal-3424 99 14 391 391 NUM american_scientific_journal-3424 99 15 ) ) PUNCT american_scientific_journal-3424 99 16 = = SYM american_scientific_journal-3424 100 1 344 344 NUM american_scientific_journal-3424 100 2 we we PRON american_scientific_journal-3424 100 3 will will AUX american_scientific_journal-3424 100 4 now now ADV american_scientific_journal-3424 100 5 use use VERB american_scientific_journal-3424 100 6 this this DET american_scientific_journal-3424 100 7 data datum NOUN american_scientific_journal-3424 100 8 to to PART american_scientific_journal-3424 100 9 provide provide VERB american_scientific_journal-3424 100 10 the the DET american_scientific_journal-3424 100 11 parameters parameter NOUN american_scientific_journal-3424 100 12 with with ADP american_scientific_journal-3424 100 13 the the DET american_scientific_journal-3424 100 14 following follow VERB american_scientific_journal-3424 100 15 values value NOUN american_scientific_journal-3424 100 16 . . PUNCT american_scientific_journal-3424 101 1 𝑁𝑁 𝑁𝑁 PROPN american_scientific_journal-3424 101 2 = = SYM american_scientific_journal-3424 101 3 4294000 4294000 NUM american_scientific_journal-3424 101 4 ; ; PUNCT american_scientific_journal-3424 101 5 𝐼𝐼 𝐼𝐼 PROPN american_scientific_journal-3424 101 6 = = SYM american_scientific_journal-3424 101 7 391 391 NUM american_scientific_journal-3424 101 8 ; ; PUNCT american_scientific_journal-3424 102 1 𝑅𝑅 𝑅𝑅 PROPN american_scientific_journal-3424 102 2 = = SYM american_scientific_journal-3424 102 3 344 344 NUM american_scientific_journal-3424 102 4 therefore therefore ADV american_scientific_journal-3424 102 5 , , PUNCT american_scientific_journal-3424 102 6 𝑆𝑆 𝑆𝑆 PROPN american_scientific_journal-3424 102 7 = = SYM american_scientific_journal-3424 102 8 𝑁𝑁 𝑁𝑁 PROPN american_scientific_journal-3424 102 9 βˆ’ βˆ’ PROPN american_scientific_journal-3424 102 10 𝐼𝐼 𝐼𝐼 PROPN american_scientific_journal-3424 102 11 + + CCONJ american_scientific_journal-3424 102 12 𝑅𝑅 𝑅𝑅 PROPN american_scientific_journal-3424 102 13 = = SYM american_scientific_journal-3424 102 14 4294000 4294000 NUM american_scientific_journal-3424 102 15 βˆ’ βˆ’ NOUN american_scientific_journal-3424 102 16 ( ( PUNCT american_scientific_journal-3424 102 17 344 344 NUM american_scientific_journal-3424 102 18 + + NUM american_scientific_journal-3424 102 19 391 391 NUM american_scientific_journal-3424 102 20 ) ) PUNCT american_scientific_journal-3424 102 21 = = SYM american_scientific_journal-3424 102 22 4293265 4293265 NUM american_scientific_journal-3424 102 23 the the DET american_scientific_journal-3424 102 24 duration duration NOUN american_scientific_journal-3424 102 25 of of ADP american_scientific_journal-3424 102 26 the the DET american_scientific_journal-3424 102 27 disease disease NOUN american_scientific_journal-3424 102 28 ranges range VERB american_scientific_journal-3424 102 29 from from ADP american_scientific_journal-3424 102 30 2 2 NUM american_scientific_journal-3424 102 31 to to ADP american_scientific_journal-3424 102 32 21 21 NUM american_scientific_journal-3424 102 33 days day NOUN american_scientific_journal-3424 102 34 [ [ X american_scientific_journal-3424 102 35 10 10 NUM american_scientific_journal-3424 102 36 ] ] PUNCT american_scientific_journal-3424 102 37 , , PUNCT american_scientific_journal-3424 102 38 therefore therefore ADV american_scientific_journal-3424 102 39 we we PRON american_scientific_journal-3424 102 40 could could AUX american_scientific_journal-3424 102 41 roughly roughly ADV american_scientific_journal-3424 102 42 estimate estimate VERB american_scientific_journal-3424 102 43 the the DET american_scientific_journal-3424 102 44 duration duration NOUN american_scientific_journal-3424 102 45 of of ADP american_scientific_journal-3424 102 46 the the DET american_scientific_journal-3424 102 47 disease disease NOUN american_scientific_journal-3424 102 48 at at ADP american_scientific_journal-3424 102 49 the the DET american_scientific_journal-3424 102 50 midpoint midpoint NOUN american_scientific_journal-3424 102 51 , , PUNCT american_scientific_journal-3424 102 52 i.e.11 i.e.11 PROPN american_scientific_journal-3424 102 53 ( ( PUNCT american_scientific_journal-3424 102 54 approx approx PROPN american_scientific_journal-3424 102 55 . . PUNCT american_scientific_journal-3424 102 56 ) ) PUNCT american_scientific_journal-3424 103 1 days day NOUN american_scientific_journal-3424 103 2 . . PUNCT american_scientific_journal-3424 104 1 𝐷𝐷 𝐷𝐷 PROPN american_scientific_journal-3424 104 2 = = NOUN american_scientific_journal-3424 104 3 11 11 NUM american_scientific_journal-3424 104 4 ; ; PUNCT american_scientific_journal-3424 104 5 𝛾𝛾 𝛾𝛾 ADP american_scientific_journal-3424 104 6 = = SYM american_scientific_journal-3424 104 7 1 1 NUM american_scientific_journal-3424 104 8 11 11 NUM american_scientific_journal-3424 104 9 = = SYM american_scientific_journal-3424 104 10 0.09 0.09 NUM american_scientific_journal-3424 104 11 according accord VERB american_scientific_journal-3424 104 12 to to ADP american_scientific_journal-3424 104 13 who who PRON american_scientific_journal-3424 104 14 , , PUNCT american_scientific_journal-3424 104 15 the the DET american_scientific_journal-3424 104 16 mortality mortality NOUN american_scientific_journal-3424 104 17 rate rate NOUN american_scientific_journal-3424 104 18 of of ADP american_scientific_journal-3424 104 19 ebola ebola PROPN american_scientific_journal-3424 104 20 is be AUX american_scientific_journal-3424 104 21 0.7 0.7 NUM american_scientific_journal-3424 104 22 [ [ X american_scientific_journal-3424 104 23 3 3 NUM american_scientific_journal-3424 104 24 ] ] PUNCT american_scientific_journal-3424 104 25 and and CCONJ american_scientific_journal-3424 104 26 the the DET american_scientific_journal-3424 104 27 number number NOUN american_scientific_journal-3424 104 28 of of ADP american_scientific_journal-3424 104 29 people people NOUN american_scientific_journal-3424 104 30 susceptible susceptible ADJ american_scientific_journal-3424 104 31 is be AUX american_scientific_journal-3424 104 32 4293265 4293265 NUM american_scientific_journal-3424 104 33 . . PUNCT american_scientific_journal-3424 105 1 american american ADJ american_scientific_journal-3424 105 2 scientific scientific ADJ american_scientific_journal-3424 105 3 research research PROPN american_scientific_journal-3424 105 4 journal journal NOUN american_scientific_journal-3424 105 5 for for ADP american_scientific_journal-3424 105 6 engineering engineering NOUN american_scientific_journal-3424 105 7 , , PUNCT american_scientific_journal-3424 105 8 technology technology NOUN american_scientific_journal-3424 105 9 , , PUNCT american_scientific_journal-3424 105 10 and and CCONJ american_scientific_journal-3424 105 11 sciences science NOUN american_scientific_journal-3424 105 12 ( ( PUNCT american_scientific_journal-3424 105 13 asrjets asrjet NOUN american_scientific_journal-3424 105 14 ) ) PUNCT american_scientific_journal-3424 105 15 ( ( PUNCT american_scientific_journal-3424 105 16 2017 2017 NUM american_scientific_journal-3424 105 17 ) ) PUNCT american_scientific_journal-3424 105 18 volume volume NOUN american_scientific_journal-3424 105 19 37 37 NUM american_scientific_journal-3424 105 20 , , PUNCT american_scientific_journal-3424 105 21 no no DET american_scientific_journal-3424 105 22 1 1 NUM american_scientific_journal-3424 105 23 , , PUNCT american_scientific_journal-3424 105 24 pp pp ADV american_scientific_journal-3424 105 25 1 1 NUM american_scientific_journal-3424 105 26 - - SYM american_scientific_journal-3424 105 27 21 21 NUM american_scientific_journal-3424 105 28 8 8 NUM american_scientific_journal-3424 105 29 therefore therefore ADV american_scientific_journal-3424 105 30 , , PUNCT american_scientific_journal-3424 105 31 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 105 32 ( ( PUNCT american_scientific_journal-3424 105 33 the the DET american_scientific_journal-3424 105 34 rate rate NOUN american_scientific_journal-3424 105 35 of of ADP american_scientific_journal-3424 105 36 infection infection NOUN american_scientific_journal-3424 105 37 ) ) PUNCT american_scientific_journal-3424 106 1 = = NOUN american_scientific_journal-3424 106 2 0.7 0.7 NUM american_scientific_journal-3424 106 3 4293265 4293265 NUM american_scientific_journal-3424 106 4 = = SYM american_scientific_journal-3424 106 5 1.63 1.63 NUM american_scientific_journal-3424 106 6 Γ— Γ— NOUN american_scientific_journal-3424 106 7 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 106 8 in in ADP american_scientific_journal-3424 106 9 order order NOUN american_scientific_journal-3424 106 10 to to PART american_scientific_journal-3424 106 11 use use VERB american_scientific_journal-3424 106 12 the the DET american_scientific_journal-3424 106 13 sir sir NOUN american_scientific_journal-3424 106 14 model model NOUN american_scientific_journal-3424 106 15 to to PART american_scientific_journal-3424 106 16 predict predict VERB american_scientific_journal-3424 106 17 the the DET american_scientific_journal-3424 106 18 evolution evolution NOUN american_scientific_journal-3424 106 19 of of ADP american_scientific_journal-3424 106 20 the the DET american_scientific_journal-3424 106 21 disease disease NOUN american_scientific_journal-3424 106 22 , , PUNCT american_scientific_journal-3424 106 23 it it PRON american_scientific_journal-3424 106 24 would would AUX american_scientific_journal-3424 106 25 be be AUX american_scientific_journal-3424 106 26 helpful helpful ADJ american_scientific_journal-3424 106 27 if if SCONJ american_scientific_journal-3424 106 28 we we PRON american_scientific_journal-3424 106 29 could could AUX american_scientific_journal-3424 106 30 solve solve VERB american_scientific_journal-3424 106 31 the the DET american_scientific_journal-3424 106 32 system system NOUN american_scientific_journal-3424 106 33 of of ADP american_scientific_journal-3424 106 34 differential differential ADJ american_scientific_journal-3424 106 35 equations equation NOUN american_scientific_journal-3424 106 36 . . PUNCT american_scientific_journal-3424 107 1 unfortunately unfortunately ADV american_scientific_journal-3424 107 2 , , PUNCT american_scientific_journal-3424 107 3 we we PRON american_scientific_journal-3424 107 4 can can AUX american_scientific_journal-3424 107 5 not not PART american_scientific_journal-3424 107 6 completely completely ADV american_scientific_journal-3424 107 7 solve solve VERB american_scientific_journal-3424 107 8 these these DET american_scientific_journal-3424 107 9 equations equation NOUN american_scientific_journal-3424 107 10 with with ADP american_scientific_journal-3424 107 11 an an DET american_scientific_journal-3424 107 12 explicit explicit ADJ american_scientific_journal-3424 107 13 formula formula NOUN american_scientific_journal-3424 107 14 solution solution NOUN american_scientific_journal-3424 107 15 . . PUNCT american_scientific_journal-3424 108 1 therefore therefore ADV american_scientific_journal-3424 108 2 , , PUNCT american_scientific_journal-3424 108 3 we we PRON american_scientific_journal-3424 108 4 will will AUX american_scientific_journal-3424 108 5 use use VERB american_scientific_journal-3424 108 6 numerical numerical ADJ american_scientific_journal-3424 108 7 approaches approach NOUN american_scientific_journal-3424 108 8 . . PUNCT american_scientific_journal-3424 109 1 we we PRON american_scientific_journal-3424 109 2 will will AUX american_scientific_journal-3424 109 3 use use VERB american_scientific_journal-3424 109 4 euler euler NOUN american_scientific_journal-3424 109 5 method method NOUN american_scientific_journal-3424 109 6 and and CCONJ american_scientific_journal-3424 109 7 fourth fourth ADJ american_scientific_journal-3424 109 8 order order NOUN american_scientific_journal-3424 109 9 runge runge NOUN american_scientific_journal-3424 109 10 - - PUNCT american_scientific_journal-3424 109 11 kutta kutta NOUN american_scientific_journal-3424 109 12 method method NOUN american_scientific_journal-3424 109 13 to to PART american_scientific_journal-3424 109 14 extract extract VERB american_scientific_journal-3424 109 15 the the DET american_scientific_journal-3424 109 16 solution solution NOUN american_scientific_journal-3424 109 17 . . PUNCT american_scientific_journal-3424 110 1 3.1 3.1 NUM american_scientific_journal-3424 110 2 euler euler NOUN american_scientific_journal-3424 110 3 method method NOUN american_scientific_journal-3424 110 4 for for ADP american_scientific_journal-3424 110 5 each each DET american_scientific_journal-3424 110 6 day day NOUN american_scientific_journal-3424 110 7 , , PUNCT american_scientific_journal-3424 110 8 we we PRON american_scientific_journal-3424 110 9 will will AUX american_scientific_journal-3424 110 10 calculate calculate VERB american_scientific_journal-3424 110 11 the the DET american_scientific_journal-3424 110 12 values value NOUN american_scientific_journal-3424 110 13 of of ADP american_scientific_journal-3424 110 14 𝑆𝑆 𝑆𝑆 PROPN american_scientific_journal-3424 110 15 , , PUNCT american_scientific_journal-3424 110 16 𝐼𝐼 𝐼𝐼 PROPN american_scientific_journal-3424 110 17 and and CCONJ american_scientific_journal-3424 110 18 𝑅𝑅 𝑅𝑅 PROPN american_scientific_journal-3424 110 19 using use VERB american_scientific_journal-3424 110 20 1 1 NUM american_scientific_journal-3424 110 21 . . PUNCT american_scientific_journal-3424 111 1 𝑆𝑆𝑛𝑛+1 𝑆𝑆𝑛𝑛+1 NOUN american_scientific_journal-3424 111 2 = = SYM american_scientific_journal-3424 111 3 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 111 4 βˆ’ βˆ’ PROPN american_scientific_journal-3424 112 1 𝛽𝛽𝐼𝐼𝑛𝑛𝑆𝑆𝑛𝑛 𝛽𝛽𝐼𝐼𝑛𝑛𝑆𝑆𝑛𝑛 ADV american_scientific_journal-3424 112 2 2 2 NUM american_scientific_journal-3424 112 3 . . PUNCT american_scientific_journal-3424 112 4 𝐼𝐼𝑛𝑛+1 𝐼𝐼𝑛𝑛+1 NOUN american_scientific_journal-3424 112 5 = = PUNCT american_scientific_journal-3424 113 1 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 113 2 + + CCONJ american_scientific_journal-3424 113 3 ( ( PUNCT american_scientific_journal-3424 113 4 𝛽𝛽𝐼𝐼𝑛𝑛𝑆𝑆𝑛𝑛 𝛽𝛽𝐼𝐼𝑛𝑛𝑆𝑆𝑛𝑛 ADV american_scientific_journal-3424 113 5 βˆ’ βˆ’ PROPN american_scientific_journal-3424 113 6 𝛾𝛾𝐼𝐼𝑛𝑛 𝛾𝛾𝐼𝐼𝑛𝑛 NUM american_scientific_journal-3424 113 7 ) ) PUNCT american_scientific_journal-3424 113 8 3 3 NUM american_scientific_journal-3424 113 9 . . PUNCT american_scientific_journal-3424 113 10 𝑅𝑅𝑛𝑛+1 𝑅𝑅𝑛𝑛+1 PROPN american_scientific_journal-3424 113 11 = = PUNCT american_scientific_journal-3424 114 1 𝑅𝑅𝑛𝑛 𝑅𝑅𝑛𝑛 PROPN american_scientific_journal-3424 114 2 + + CCONJ american_scientific_journal-3424 114 3 𝛾𝛾𝐼𝐼𝑛𝑛 𝛾𝛾𝐼𝐼𝑛𝑛 ADV american_scientific_journal-3424 114 4 we we PRON american_scientific_journal-3424 114 5 take take VERB american_scientific_journal-3424 114 6 the the DET american_scientific_journal-3424 114 7 initial initial ADJ american_scientific_journal-3424 114 8 values value NOUN american_scientific_journal-3424 114 9 as as ADP american_scientific_journal-3424 114 10 𝑆𝑆0 𝑆𝑆0 ADV american_scientific_journal-3424 114 11 = = SYM american_scientific_journal-3424 114 12 4293265 4293265 NUM american_scientific_journal-3424 114 13 ; ; PUNCT american_scientific_journal-3424 114 14 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 114 15 = = PROPN american_scientific_journal-3424 114 16 391 391 NUM american_scientific_journal-3424 114 17 ; ; PUNCT american_scientific_journal-3424 114 18 𝑅𝑅0 𝑅𝑅0 PROPN american_scientific_journal-3424 114 19 = = PROPN american_scientific_journal-3424 114 20 344 344 NUM american_scientific_journal-3424 114 21 ; ; PUNCT american_scientific_journal-3424 114 22 𝛾𝛾 𝛾𝛾 ADP american_scientific_journal-3424 114 23 = = SYM american_scientific_journal-3424 114 24 0.09 0.09 NUM american_scientific_journal-3424 114 25 ; ; PUNCT american_scientific_journal-3424 114 26 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 114 27 = = SYM american_scientific_journal-3424 114 28 1.63 1.63 NUM american_scientific_journal-3424 114 29 Γ— Γ— NOUN american_scientific_journal-3424 114 30 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 114 31 ; ; PUNCT american_scientific_journal-3424 114 32 we we PRON american_scientific_journal-3424 114 33 will will AUX american_scientific_journal-3424 114 34 do do VERB american_scientific_journal-3424 114 35 this this PRON american_scientific_journal-3424 114 36 explicitly explicitly ADV american_scientific_journal-3424 114 37 for for ADP american_scientific_journal-3424 114 38 the the DET american_scientific_journal-3424 114 39 transition transition NOUN american_scientific_journal-3424 114 40 from from ADP american_scientific_journal-3424 114 41 t t PROPN american_scientific_journal-3424 114 42 = = SYM american_scientific_journal-3424 114 43 0 0 PROPN american_scientific_journal-3424 114 44 to to ADP american_scientific_journal-3424 114 45 t t NOUN american_scientific_journal-3424 114 46 = = SYM american_scientific_journal-3424 114 47 1 1 X american_scientific_journal-3424 114 48 . . X american_scientific_journal-3424 114 49 using use VERB american_scientific_journal-3424 114 50 equations equation NOUN american_scientific_journal-3424 114 51 1 1 NUM american_scientific_journal-3424 114 52 , , PUNCT american_scientific_journal-3424 114 53 2 2 NUM american_scientific_journal-3424 114 54 and and CCONJ american_scientific_journal-3424 114 55 3 3 NUM american_scientific_journal-3424 114 56 , , PUNCT american_scientific_journal-3424 114 57 the the DET american_scientific_journal-3424 114 58 following follow VERB american_scientific_journal-3424 114 59 values value NOUN american_scientific_journal-3424 114 60 for for ADP american_scientific_journal-3424 114 61 s s PROPN american_scientific_journal-3424 114 62 , , PUNCT american_scientific_journal-3424 114 63 i i PRON american_scientific_journal-3424 114 64 and and CCONJ american_scientific_journal-3424 114 65 r r NOUN american_scientific_journal-3424 114 66 can can AUX american_scientific_journal-3424 114 67 be be AUX american_scientific_journal-3424 114 68 calculated calculate VERB american_scientific_journal-3424 114 69 . . PUNCT american_scientific_journal-3424 115 1 𝑆𝑆1 𝑆𝑆1 NOUN american_scientific_journal-3424 115 2 = = PUNCT american_scientific_journal-3424 115 3 𝑆𝑆0 𝑆𝑆0 ADV american_scientific_journal-3424 115 4 βˆ’ βˆ’ PROPN american_scientific_journal-3424 115 5 𝛽𝛽𝐼𝐼0𝑆𝑆0 𝛽𝛽𝐼𝐼0𝑆𝑆0 ADV american_scientific_journal-3424 115 6 Γ— Γ— PROPN american_scientific_journal-3424 115 7 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 115 8 = = SYM american_scientific_journal-3424 115 9 4293265 4293265 NUM american_scientific_journal-3424 115 10 βˆ’ βˆ’ PROPN american_scientific_journal-3424 115 11 ( ( PUNCT american_scientific_journal-3424 115 12 1.63 1.63 NUM american_scientific_journal-3424 115 13 Γ— Γ— NOUN american_scientific_journal-3424 115 14 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 115 15 Γ— Γ— NOUN american_scientific_journal-3424 115 16 391 391 NUM american_scientific_journal-3424 115 17 Γ— Γ— NOUN american_scientific_journal-3424 115 18 4293265 4293265 NUM american_scientific_journal-3424 115 19 ) ) PUNCT american_scientific_journal-3424 115 20 Γ— Γ— NOUN american_scientific_journal-3424 115 21 1 1 NUM american_scientific_journal-3424 115 22 = = SYM american_scientific_journal-3424 116 1 4292991.377 4292991.377 PROPN american_scientific_journal-3424 116 2 β‰ˆ β‰ˆ NUM american_scientific_journal-3424 116 3 4292991 4292991 NUM american_scientific_journal-3424 117 1 𝐼𝐼1 𝐼𝐼1 PROPN american_scientific_journal-3424 117 2 = = SYM american_scientific_journal-3424 117 3 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 117 4 + + CCONJ american_scientific_journal-3424 117 5 ( ( PUNCT american_scientific_journal-3424 117 6 𝛽𝛽𝐼𝐼0𝑆𝑆0 𝛽𝛽𝐼𝐼0𝑆𝑆0 ADV american_scientific_journal-3424 117 7 βˆ’ βˆ’ PROPN american_scientific_journal-3424 117 8 𝛾𝛾𝐼𝐼0 𝛾𝛾𝐼𝐼0 NOUN american_scientific_journal-3424 117 9 ) ) PUNCT american_scientific_journal-3424 117 10 Γ— Γ— NOUN american_scientific_journal-3424 117 11 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 118 1 = = PUNCT american_scientific_journal-3424 119 1 391 391 NUM american_scientific_journal-3424 119 2 + + CCONJ american_scientific_journal-3424 119 3 ( ( PUNCT american_scientific_journal-3424 119 4 1.63 1.63 NUM american_scientific_journal-3424 119 5 Γ— Γ— NOUN american_scientific_journal-3424 119 6 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 119 7 Γ— Γ— NOUN american_scientific_journal-3424 119 8 391 391 NUM american_scientific_journal-3424 119 9 Γ— Γ— NOUN american_scientific_journal-3424 119 10 4293265 4293265 NUM american_scientific_journal-3424 119 11 βˆ’ βˆ’ NOUN american_scientific_journal-3424 119 12 0.09 0.09 NUM american_scientific_journal-3424 119 13 Γ— Γ— NOUN american_scientific_journal-3424 119 14 391 391 NUM american_scientific_journal-3424 119 15 ) ) PUNCT american_scientific_journal-3424 119 16 Γ— Γ— NOUN american_scientific_journal-3424 119 17 1 1 NUM american_scientific_journal-3424 119 18 = = SYM american_scientific_journal-3424 119 19 629.4326582 629.4326582 NUM american_scientific_journal-3424 119 20 β‰ˆ β‰ˆ PROPN american_scientific_journal-3424 119 21 630 630 NUM american_scientific_journal-3424 119 22 𝑅𝑅1 𝑅𝑅1 PROPN american_scientific_journal-3424 119 23 = = SYM american_scientific_journal-3424 119 24 𝑅𝑅0 𝑅𝑅0 PROPN american_scientific_journal-3424 119 25 + + CCONJ american_scientific_journal-3424 119 26 𝛾𝛾𝐼𝐼0 𝛾𝛾𝐼𝐼0 NOUN american_scientific_journal-3424 119 27 = = PUNCT american_scientific_journal-3424 119 28 344 344 NUM american_scientific_journal-3424 119 29 + + NUM american_scientific_journal-3424 119 30 0.09 0.09 NUM american_scientific_journal-3424 119 31 Γ— Γ— NOUN american_scientific_journal-3424 119 32 391 391 NUM american_scientific_journal-3424 119 33 = = SYM american_scientific_journal-3424 119 34 379.19 379.19 NUM american_scientific_journal-3424 119 35 β‰ˆ β‰ˆ PROPN american_scientific_journal-3424 119 36 379 379 NUM american_scientific_journal-3424 119 37 here here ADV american_scientific_journal-3424 119 38 we we PRON american_scientific_journal-3424 119 39 use use VERB american_scientific_journal-3424 119 40 matlab matlab PROPN american_scientific_journal-3424 119 41 to to PART american_scientific_journal-3424 119 42 evaluate evaluate VERB american_scientific_journal-3424 119 43 s s PROPN american_scientific_journal-3424 119 44 , , PUNCT american_scientific_journal-3424 119 45 i i PRON american_scientific_journal-3424 119 46 , , PUNCT american_scientific_journal-3424 119 47 r r VERB american_scientific_journal-3424 119 48 over over ADP american_scientific_journal-3424 119 49 a a DET american_scientific_journal-3424 119 50 two two NUM american_scientific_journal-3424 119 51 month month NOUN american_scientific_journal-3424 119 52 period period NOUN american_scientific_journal-3424 119 53 . . PUNCT american_scientific_journal-3424 120 1 table-3.1 table-3.1 NOUN american_scientific_journal-3424 120 2 shows show VERB american_scientific_journal-3424 120 3 the the DET american_scientific_journal-3424 120 4 result result NOUN american_scientific_journal-3424 120 5 . . PUNCT american_scientific_journal-3424 121 1 american american ADJ american_scientific_journal-3424 121 2 scientific scientific ADJ american_scientific_journal-3424 121 3 research research PROPN american_scientific_journal-3424 121 4 journal journal NOUN american_scientific_journal-3424 121 5 for for ADP american_scientific_journal-3424 121 6 engineering engineering NOUN american_scientific_journal-3424 121 7 , , PUNCT american_scientific_journal-3424 121 8 technology technology NOUN american_scientific_journal-3424 121 9 , , PUNCT american_scientific_journal-3424 121 10 and and CCONJ american_scientific_journal-3424 121 11 sciences science NOUN american_scientific_journal-3424 121 12 ( ( PUNCT american_scientific_journal-3424 121 13 asrjets asrjet NOUN american_scientific_journal-3424 121 14 ) ) PUNCT american_scientific_journal-3424 121 15 ( ( PUNCT american_scientific_journal-3424 121 16 2017 2017 NUM american_scientific_journal-3424 121 17 ) ) PUNCT american_scientific_journal-3424 121 18 volume volume NOUN american_scientific_journal-3424 121 19 37 37 NUM american_scientific_journal-3424 121 20 , , PUNCT american_scientific_journal-3424 121 21 no no DET american_scientific_journal-3424 121 22 1 1 NUM american_scientific_journal-3424 121 23 , , PUNCT american_scientific_journal-3424 121 24 pp pp ADV american_scientific_journal-3424 121 25 1 1 NUM american_scientific_journal-3424 121 26 - - SYM american_scientific_journal-3424 121 27 21 21 NUM american_scientific_journal-3424 121 28 9 9 NUM american_scientific_journal-3424 121 29 table table NOUN american_scientific_journal-3424 121 30 3.1 3.1 NUM american_scientific_journal-3424 121 31 : : PUNCT american_scientific_journal-3424 121 32 euler euler NOUN american_scientific_journal-3424 121 33 method method PROPN american_scientific_journal-3424 121 34 day day PROPN american_scientific_journal-3424 121 35 s s PART american_scientific_journal-3424 121 36 i i NOUN american_scientific_journal-3424 121 37 r r NOUN american_scientific_journal-3424 121 38 s+i+r s+i+r NOUN american_scientific_journal-3424 121 39 01 01 NUM american_scientific_journal-3424 121 40 4293265 4293265 NUM american_scientific_journal-3424 121 41 391 391 NUM american_scientific_journal-3424 121 42 344 344 NUM american_scientific_journal-3424 121 43 4294000 4294000 NUM american_scientific_journal-3424 121 44 02 02 NUM american_scientific_journal-3424 121 45 4292991 4292991 NUM american_scientific_journal-3424 121 46 630 630 NUM american_scientific_journal-3424 121 47 379 379 NUM american_scientific_journal-3424 121 48 4294000 4294000 NUM american_scientific_journal-3424 121 49 03 03 NUM american_scientific_journal-3424 121 50 4292550 4292550 NUM american_scientific_journal-3424 121 51 1014 1014 NUM american_scientific_journal-3424 121 52 436 436 NUM american_scientific_journal-3424 121 53 4294000 4294000 NUM american_scientific_journal-3424 121 54 04 04 NUM american_scientific_journal-3424 121 55 4291842 4291842 NUM american_scientific_journal-3424 121 56 1630 1630 NUM american_scientific_journal-3424 121 57 528 528 NUM american_scientific_journal-3424 121 58 4294000 4294000 NUM american_scientific_journal-3424 121 59 05 05 NUM american_scientific_journal-3424 121 60 4290700 4290700 NUM american_scientific_journal-3424 121 61 2625 2625 NUM american_scientific_journal-3424 121 62 675 675 NUM american_scientific_journal-3424 121 63 4294000 4294000 NUM american_scientific_journal-3424 121 64 06 06 NUM american_scientific_journal-3424 121 65 4288865 4288865 NUM american_scientific_journal-3424 121 66 4225 4225 NUM american_scientific_journal-3424 121 67 910 910 NUM american_scientific_journal-3424 121 68 4294000 4294000 NUM american_scientific_journal-3424 121 69 07 07 NUM american_scientific_journal-3424 121 70 4285912 4285912 NUM american_scientific_journal-3424 121 71 6798 6798 NUM american_scientific_journal-3424 121 72 1290 1290 NUM american_scientific_journal-3424 121 73 4294000 4294000 NUM american_scientific_journal-3424 121 74 08 08 NUM american_scientific_journal-3424 121 75 4281162 4281162 NUM american_scientific_journal-3424 121 76 10936 10936 NUM american_scientific_journal-3424 121 77 1902 1902 NUM american_scientific_journal-3424 121 78 4294000 4294000 NUM american_scientific_journal-3424 121 79 09 09 NUM american_scientific_journal-3424 121 80 4273530 4273530 NUM american_scientific_journal-3424 121 81 17584 17584 NUM american_scientific_journal-3424 121 82 2886 2886 NUM american_scientific_journal-3424 121 83 4294000 4294000 NUM american_scientific_journal-3424 121 84 10 10 NUM american_scientific_journal-3424 121 85 4261283 4261283 NUM american_scientific_journal-3424 121 86 28248 28248 NUM american_scientific_journal-3424 121 87 4469 4469 NUM american_scientific_journal-3424 121 88 4294000 4294000 NUM american_scientific_journal-3424 121 89 11 11 NUM american_scientific_journal-3424 121 90 4241662 4241662 NUM american_scientific_journal-3424 121 91 45327 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american_scientific_journal-3424 121 143 4294000 4294000 NUM american_scientific_journal-3424 121 144 22 22 NUM american_scientific_journal-3424 121 145 836453 836453 NUM american_scientific_journal-3424 121 146 2677585 2677585 NUM american_scientific_journal-3424 121 147 779962 779962 NUM american_scientific_journal-3424 121 148 4294000 4294000 NUM american_scientific_journal-3424 121 149 23 23 NUM american_scientific_journal-3424 121 150 471386 471386 NUM american_scientific_journal-3424 121 151 2801669 2801669 NUM american_scientific_journal-3424 121 152 1020945 1020945 NUM american_scientific_journal-3424 121 153 4294000 4294000 NUM american_scientific_journal-3424 121 154 24 24 NUM american_scientific_journal-3424 121 155 256117 256117 NUM american_scientific_journal-3424 121 156 2764788 2764788 NUM american_scientific_journal-3424 121 157 1273095 1273095 NUM american_scientific_journal-3424 121 158 4294000 4294000 NUM american_scientific_journal-3424 121 159 25 25 NUM american_scientific_journal-3424 121 160 140695 140695 NUM american_scientific_journal-3424 121 161 2631379 2631379 NUM american_scientific_journal-3424 121 162 1521926 1521926 NUM american_scientific_journal-3424 121 163 4294000 4294000 NUM american_scientific_journal-3424 121 164 26 26 NUM american_scientific_journal-3424 121 165 80349 80349 NUM american_scientific_journal-3424 121 166 2454901 2454901 NUM american_scientific_journal-3424 121 167 1758750 1758750 NUM american_scientific_journal-3424 121 168 4294000 4294000 NUM american_scientific_journal-3424 121 169 27 27 NUM american_scientific_journal-3424 121 170 48198 48198 NUM american_scientific_journal-3424 121 171 2266111 2266111 NUM american_scientific_journal-3424 121 172 1979691 1979691 NUM american_scientific_journal-3424 121 173 4294000 4294000 NUM american_scientific_journal-3424 121 174 28 28 NUM american_scientific_journal-3424 121 175 30394 30394 NUM american_scientific_journal-3424 121 176 2079964 2079964 NUM american_scientific_journal-3424 121 177 2183642 2183642 NUM american_scientific_journal-3424 121 178 4294000 4294000 NUM american_scientific_journal-3424 121 179 29 29 NUM american_scientific_journal-3424 121 180 20090 20090 NUM american_scientific_journal-3424 121 181 1903072 1903072 NUM american_scientific_journal-3424 121 182 2370838 2370838 NUM american_scientific_journal-3424 121 183 4294000 4294000 NUM american_scientific_journal-3424 121 184 30 30 NUM american_scientific_journal-3424 121 185 13858 13858 NUM american_scientific_journal-3424 121 186 1738028 1738028 NUM american_scientific_journal-3424 121 187 2542114 2542114 NUM american_scientific_journal-3424 121 188 4294000 4294000 NUM american_scientific_journal-3424 121 189 31 31 NUM american_scientific_journal-3424 121 190 9932 9932 NUM american_scientific_journal-3424 121 191 1585531 1585531 NUM american_scientific_journal-3424 121 192 2698537 2698537 NUM american_scientific_journal-3424 121 193 4294000 4294000 NUM american_scientific_journal-3424 121 194 32 32 NUM american_scientific_journal-3424 121 195 7365 7365 NUM american_scientific_journal-3424 121 196 1445400 1445400 NUM american_scientific_journal-3424 121 197 2841235 2841235 NUM american_scientific_journal-3424 121 198 4294000 4294000 NUM american_scientific_journal-3424 121 199 33 33 NUM american_scientific_journal-3424 121 200 5630 5630 NUM american_scientific_journal-3424 121 201 1317049 1317049 NUM american_scientific_journal-3424 121 202 2971321 2971321 NUM american_scientific_journal-3424 121 203 4294000 4294000 NUM american_scientific_journal-3424 121 204 34 34 NUM american_scientific_journal-3424 121 205 4422 4422 NUM american_scientific_journal-3424 121 206 1199723 1199723 NUM american_scientific_journal-3424 121 207 3089855 3089855 NUM american_scientific_journal-3424 121 208 4294000 4294000 NUM american_scientific_journal-3424 121 209 35 35 NUM american_scientific_journal-3424 121 210 3557 3557 NUM american_scientific_journal-3424 121 211 1092613 1092613 NUM american_scientific_journal-3424 121 212 3197830 3197830 NUM american_scientific_journal-3424 121 213 4294000 4294000 NUM american_scientific_journal-3424 121 214 american american ADJ american_scientific_journal-3424 121 215 scientific scientific ADJ american_scientific_journal-3424 121 216 research research NOUN american_scientific_journal-3424 121 217 journal journal NOUN american_scientific_journal-3424 121 218 for for ADP american_scientific_journal-3424 121 219 engineering engineering NOUN american_scientific_journal-3424 121 220 , , PUNCT american_scientific_journal-3424 121 221 technology technology NOUN american_scientific_journal-3424 121 222 , , PUNCT american_scientific_journal-3424 121 223 and and CCONJ american_scientific_journal-3424 121 224 sciences science NOUN american_scientific_journal-3424 121 225 ( ( PUNCT american_scientific_journal-3424 121 226 asrjets asrjet NOUN american_scientific_journal-3424 121 227 ) ) PUNCT american_scientific_journal-3424 121 228 ( ( PUNCT american_scientific_journal-3424 121 229 2017 2017 NUM american_scientific_journal-3424 121 230 ) ) PUNCT american_scientific_journal-3424 121 231 volume volume NOUN american_scientific_journal-3424 121 232 37 37 NUM american_scientific_journal-3424 121 233 , , PUNCT american_scientific_journal-3424 121 234 no no DET american_scientific_journal-3424 121 235 1 1 NUM american_scientific_journal-3424 121 236 , , PUNCT american_scientific_journal-3424 121 237 pp pp ADV american_scientific_journal-3424 121 238 1 1 NUM american_scientific_journal-3424 121 239 - - SYM american_scientific_journal-3424 121 240 21 21 NUM american_scientific_journal-3424 121 241 10 10 NUM american_scientific_journal-3424 121 242 36 36 NUM american_scientific_journal-3424 121 243 2923 2923 NUM american_scientific_journal-3424 121 244 994911 994911 NUM american_scientific_journal-3424 121 245 3296166 3296166 NUM american_scientific_journal-3424 121 246 4294000 4294000 NUM american_scientific_journal-3424 121 247 37 37 NUM american_scientific_journal-3424 121 248 2449 2449 NUM american_scientific_journal-3424 121 249 905843 905843 NUM american_scientific_journal-3424 121 250 3385708 3385708 NUM american_scientific_journal-3424 121 251 4294000 4294000 NUM american_scientific_journal-3424 121 252 38 38 NUM american_scientific_journal-3424 121 253 2088 2088 NUM american_scientific_journal-3424 121 254 824679 824679 NUM american_scientific_journal-3424 121 255 3467233 3467233 NUM american_scientific_journal-3424 121 256 4294000 4294000 NUM american_scientific_journal-3424 121 257 39 39 NUM american_scientific_journal-3424 121 258 1807 1807 NUM american_scientific_journal-3424 121 259 750738 750738 NUM american_scientific_journal-3424 121 260 3541455 3541455 NUM american_scientific_journal-3424 121 261 4294000 4294000 NUM american_scientific_journal-3424 121 262 40 40 NUM american_scientific_journal-3424 121 263 1586 1586 NUM american_scientific_journal-3424 121 264 683393 683393 NUM american_scientific_journal-3424 121 265 3609021 3609021 NUM american_scientific_journal-3424 121 266 4294000 4294000 NUM american_scientific_journal-3424 121 267 41 41 NUM american_scientific_journal-3424 121 268 1409 1409 NUM american_scientific_journal-3424 121 269 622065 622065 NUM american_scientific_journal-3424 121 270 3670526 3670526 NUM american_scientific_journal-3424 121 271 4294000 4294000 NUM american_scientific_journal-3424 121 272 42 42 NUM american_scientific_journal-3424 121 273 1266 1266 NUM american_scientific_journal-3424 121 274 566222 566222 NUM american_scientific_journal-3424 121 275 3726512 3726512 NUM american_scientific_journal-3424 121 276 4294000 4294000 NUM american_scientific_journal-3424 121 277 43 43 NUM american_scientific_journal-3424 121 278 1150 1150 NUM american_scientific_journal-3424 121 279 515378 515378 NUM american_scientific_journal-3424 121 280 3777472 3777472 NUM american_scientific_journal-3424 121 281 4294000 4294000 NUM american_scientific_journal-3424 121 282 44 44 NUM american_scientific_journal-3424 121 283 1053 1053 NUM american_scientific_journal-3424 121 284 469091 469091 NUM american_scientific_journal-3424 121 285 3823856 3823856 NUM american_scientific_journal-3424 121 286 4294000 4294000 NUM american_scientific_journal-3424 121 287 45 45 NUM american_scientific_journal-3424 121 288 972 972 NUM american_scientific_journal-3424 121 289 426953 426953 NUM american_scientific_journal-3424 121 290 3866075 3866075 NUM american_scientific_journal-3424 121 291 4294000 4294000 NUM american_scientific_journal-3424 121 292 46 46 NUM american_scientific_journal-3424 121 293 905 905 NUM american_scientific_journal-3424 121 294 388595 388595 NUM american_scientific_journal-3424 121 295 3904500 3904500 NUM american_scientific_journal-3424 121 296 4294000 4294000 NUM american_scientific_journal-3424 121 297 47 47 NUM american_scientific_journal-3424 121 298 847 847 NUM american_scientific_journal-3424 121 299 353679 353679 NUM american_scientific_journal-3424 121 300 3939474 3939474 NUM american_scientific_journal-3424 121 301 4294000 4294000 NUM american_scientific_journal-3424 121 302 48 48 NUM american_scientific_journal-3424 121 303 799 799 NUM american_scientific_journal-3424 121 304 321896 321896 NUM american_scientific_journal-3424 121 305 3971305 3971305 NUM american_scientific_journal-3424 121 306 4294000 4294000 NUM american_scientific_journal-3424 121 307 49 49 NUM american_scientific_journal-3424 121 308 757 757 NUM american_scientific_journal-3424 121 309 292968 292968 NUM american_scientific_journal-3424 121 310 4000275 4000275 NUM american_scientific_journal-3424 121 311 4294000 4294000 NUM american_scientific_journal-3424 121 312 50 50 NUM american_scientific_journal-3424 121 313 720 720 NUM american_scientific_journal-3424 121 314 266637 266637 NUM american_scientific_journal-3424 121 315 4026643 4026643 NUM american_scientific_journal-3424 121 316 4294000 4294000 NUM american_scientific_journal-3424 121 317 51 51 NUM american_scientific_journal-3424 121 318 689 689 NUM american_scientific_journal-3424 121 319 242671 242671 NUM american_scientific_journal-3424 121 320 4050640 4050640 NUM american_scientific_journal-3424 121 321 4294000 4294000 NUM american_scientific_journal-3424 121 322 52 52 NUM american_scientific_journal-3424 121 323 662 662 NUM american_scientific_journal-3424 121 324 220858 220858 NUM american_scientific_journal-3424 121 325 4072480 4072480 NUM american_scientific_journal-3424 121 326 4294000 4294000 NUM american_scientific_journal-3424 121 327 53 53 NUM american_scientific_journal-3424 121 328 638 638 NUM american_scientific_journal-3424 121 329 201004 201004 NUM american_scientific_journal-3424 121 330 4092358 4092358 NUM american_scientific_journal-3424 121 331 4294000 4294000 NUM american_scientific_journal-3424 121 332 54 54 NUM american_scientific_journal-3424 121 333 617 617 NUM american_scientific_journal-3424 121 334 182935 182935 NUM american_scientific_journal-3424 121 335 4110448 4110448 NUM american_scientific_journal-3424 121 336 4294000 4294000 NUM american_scientific_journal-3424 121 337 55 55 NUM american_scientific_journal-3424 121 338 599 599 NUM american_scientific_journal-3424 121 339 166489 166489 NUM american_scientific_journal-3424 121 340 4126912 4126912 NUM american_scientific_journal-3424 121 341 4294000 4294000 NUM american_scientific_journal-3424 121 342 56 56 NUM american_scientific_journal-3424 121 343 583 583 NUM american_scientific_journal-3424 121 344 151521 151521 NUM american_scientific_journal-3424 121 345 4141896 4141896 NUM american_scientific_journal-3424 121 346 4294000 4294000 NUM american_scientific_journal-3424 121 347 57 57 NUM american_scientific_journal-3424 121 348 568 568 NUM american_scientific_journal-3424 121 349 137899 137899 NUM american_scientific_journal-3424 121 350 4155533 4155533 NUM american_scientific_journal-3424 121 351 4294000 4294000 NUM american_scientific_journal-3424 121 352 58 58 NUM american_scientific_journal-3424 121 353 555 555 NUM american_scientific_journal-3424 121 354 125501 125501 NUM american_scientific_journal-3424 121 355 4167944 4167944 NUM american_scientific_journal-3424 121 356 4294000 4294000 NUM american_scientific_journal-3424 121 357 59 59 NUM american_scientific_journal-3424 121 358 544 544 NUM american_scientific_journal-3424 121 359 114217 114217 NUM american_scientific_journal-3424 121 360 4179239 4179239 NUM american_scientific_journal-3424 121 361 4294000 4294000 NUM american_scientific_journal-3424 121 362 60 60 NUM american_scientific_journal-3424 121 363 533 533 NUM american_scientific_journal-3424 121 364 103948 103948 NUM american_scientific_journal-3424 121 365 4189519 4189519 NUM american_scientific_journal-3424 121 366 4294000 4294000 NUM american_scientific_journal-3424 121 367 3.2 3.2 NUM american_scientific_journal-3424 121 368 runge runge NOUN american_scientific_journal-3424 121 369 - - PUNCT american_scientific_journal-3424 121 370 kutta kutta NOUN american_scientific_journal-3424 121 371 ( ( PUNCT american_scientific_journal-3424 121 372 rk4 rk4 NOUN american_scientific_journal-3424 121 373 ) ) PUNCT american_scientific_journal-3424 121 374 method method NOUN american_scientific_journal-3424 121 375 for for ADP american_scientific_journal-3424 121 376 each each DET american_scientific_journal-3424 121 377 day day NOUN american_scientific_journal-3424 121 378 , , PUNCT american_scientific_journal-3424 121 379 we we PRON american_scientific_journal-3424 121 380 will will AUX american_scientific_journal-3424 121 381 calculate calculate VERB american_scientific_journal-3424 121 382 the the DET american_scientific_journal-3424 121 383 values value NOUN american_scientific_journal-3424 121 384 of of ADP american_scientific_journal-3424 121 385 𝑆𝑆 𝑆𝑆 PROPN american_scientific_journal-3424 121 386 , , PUNCT american_scientific_journal-3424 121 387 𝐼𝐼 𝐼𝐼 PROPN american_scientific_journal-3424 121 388 and and CCONJ american_scientific_journal-3424 121 389 𝑅𝑅 𝑅𝑅 PROPN american_scientific_journal-3424 121 390 using use VERB american_scientific_journal-3424 121 391 π‘˜π‘˜1𝑑𝑑 π‘˜π‘˜1𝑑𝑑 PROPN american_scientific_journal-3424 121 392 = = SYM american_scientific_journal-3424 121 393 βˆ’π›½π›½π‘†π‘†π‘›π‘›πΌπΌπ‘›π‘› βˆ’π›½π›½π‘†π‘†π‘›π‘›πΌπΌπ‘›π‘› X american_scientific_journal-3424 121 394 π‘˜π‘˜1𝑑𝑑 π‘˜π‘˜1𝑑𝑑 NOUN american_scientific_journal-3424 121 395 = = PUNCT american_scientific_journal-3424 121 396 𝛽𝛽𝑆𝑆𝑛𝑛𝐼𝐼𝑛𝑛 𝛽𝛽𝑆𝑆𝑛𝑛𝐼𝐼𝑛𝑛 ADV american_scientific_journal-3424 121 397 βˆ’ βˆ’ X american_scientific_journal-3424 121 398 𝛾𝛾𝐼𝐼𝑛𝑛 𝛾𝛾𝐼𝐼𝑛𝑛 ADV american_scientific_journal-3424 121 399 π‘˜π‘˜1𝑑𝑑 π‘˜π‘˜1𝑑𝑑 PROPN american_scientific_journal-3424 121 400 = = PUNCT american_scientific_journal-3424 121 401 𝛾𝛾𝐼𝐼𝑛𝑛 𝛾𝛾𝐼𝐼𝑛𝑛 NUM american_scientific_journal-3424 121 402 π‘˜π‘˜2𝑑𝑑 π‘˜π‘˜2𝑑𝑑 NOUN american_scientific_journal-3424 122 1 = = SYM american_scientific_journal-3424 122 2 βˆ’π›½π›½ βˆ’π›½π›½ NOUN american_scientific_journal-3424 122 3 οΏ½ οΏ½ NOUN american_scientific_journal-3424 122 4 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 122 5 + + CCONJ american_scientific_journal-3424 122 6 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 7 2 2 NUM american_scientific_journal-3424 122 8 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 9 ( ( PUNCT american_scientific_journal-3424 122 10 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 122 11 + + CCONJ american_scientific_journal-3424 122 12 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 13 2 2 X american_scientific_journal-3424 122 14 ) ) PUNCT american_scientific_journal-3424 122 15 american american ADJ american_scientific_journal-3424 122 16 scientific scientific ADJ american_scientific_journal-3424 122 17 research research NOUN american_scientific_journal-3424 122 18 journal journal NOUN american_scientific_journal-3424 122 19 for for ADP american_scientific_journal-3424 122 20 engineering engineering NOUN american_scientific_journal-3424 122 21 , , PUNCT american_scientific_journal-3424 122 22 technology technology NOUN american_scientific_journal-3424 122 23 , , PUNCT american_scientific_journal-3424 122 24 and and CCONJ american_scientific_journal-3424 122 25 sciences science NOUN american_scientific_journal-3424 122 26 ( ( PUNCT american_scientific_journal-3424 122 27 asrjets asrjet NOUN american_scientific_journal-3424 122 28 ) ) PUNCT american_scientific_journal-3424 122 29 ( ( PUNCT american_scientific_journal-3424 122 30 2017 2017 NUM american_scientific_journal-3424 122 31 ) ) PUNCT american_scientific_journal-3424 122 32 volume volume NOUN american_scientific_journal-3424 122 33 37 37 NUM american_scientific_journal-3424 122 34 , , PUNCT american_scientific_journal-3424 122 35 no no DET american_scientific_journal-3424 122 36 1 1 NUM american_scientific_journal-3424 122 37 , , PUNCT american_scientific_journal-3424 122 38 pp pp ADV american_scientific_journal-3424 122 39 1 1 NUM american_scientific_journal-3424 122 40 - - SYM american_scientific_journal-3424 122 41 21 21 NUM american_scientific_journal-3424 122 42 11 11 NUM american_scientific_journal-3424 122 43 π‘˜π‘˜2𝑑𝑑 π‘˜π‘˜2𝑑𝑑 NOUN american_scientific_journal-3424 122 44 = = PUNCT american_scientific_journal-3424 122 45 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 122 46 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 47 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 122 48 + + CCONJ american_scientific_journal-3424 122 49 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 50 2 2 NUM american_scientific_journal-3424 122 51 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 52 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 53 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 122 54 + + CCONJ american_scientific_journal-3424 122 55 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 56 2 2 NUM american_scientific_journal-3424 122 57 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 58 βˆ’ βˆ’ PROPN american_scientific_journal-3424 122 59 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 60 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 122 61 + + CCONJ american_scientific_journal-3424 122 62 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 63 2 2 NUM american_scientific_journal-3424 122 64 οΏ½ οΏ½ NOUN american_scientific_journal-3424 122 65 π‘˜π‘˜2𝑑𝑑 π‘˜π‘˜2𝑑𝑑 NOUN american_scientific_journal-3424 122 66 = = PUNCT american_scientific_journal-3424 122 67 𝛾𝛾 𝛾𝛾 ADP american_scientific_journal-3424 122 68 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 69 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 122 70 + + CCONJ american_scientific_journal-3424 122 71 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 72 2 2 NUM american_scientific_journal-3424 122 73 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 74 π‘˜π‘˜3𝑑𝑑 π‘˜π‘˜3𝑑𝑑 NOUN american_scientific_journal-3424 122 75 = = SYM american_scientific_journal-3424 122 76 βˆ’π›½π›½ βˆ’π›½π›½ PROPN american_scientific_journal-3424 122 77 οΏ½ οΏ½ NOUN american_scientific_journal-3424 122 78 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 122 79 + + CCONJ american_scientific_journal-3424 122 80 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 81 2 2 NUM american_scientific_journal-3424 122 82 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 83 ( ( PUNCT american_scientific_journal-3424 122 84 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 122 85 + + CCONJ american_scientific_journal-3424 122 86 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 87 2 2 NUM american_scientific_journal-3424 122 88 ) ) PUNCT american_scientific_journal-3424 122 89 π‘˜π‘˜3𝑑𝑑 π‘˜π‘˜3𝑑𝑑 NOUN american_scientific_journal-3424 122 90 = = PUNCT american_scientific_journal-3424 122 91 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 122 92 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 93 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 122 94 + + PROPN american_scientific_journal-3424 122 95 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 96 2 2 NUM american_scientific_journal-3424 122 97 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 98 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 99 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 122 100 + + CCONJ american_scientific_journal-3424 122 101 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 102 2 2 NUM american_scientific_journal-3424 122 103 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 104 βˆ’ βˆ’ PROPN american_scientific_journal-3424 122 105 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 106 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 122 107 + + CCONJ american_scientific_journal-3424 122 108 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 109 2 2 NUM american_scientific_journal-3424 122 110 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 111 π‘˜π‘˜3𝑑𝑑 π‘˜π‘˜3𝑑𝑑 NOUN american_scientific_journal-3424 122 112 = = PUNCT american_scientific_journal-3424 122 113 𝛾𝛾 𝛾𝛾 ADP american_scientific_journal-3424 122 114 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 115 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 122 116 + + CCONJ american_scientific_journal-3424 122 117 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 122 118 2 2 NUM american_scientific_journal-3424 122 119 οΏ½ οΏ½ PROPN american_scientific_journal-3424 122 120 π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 122 121 = = PUNCT american_scientific_journal-3424 122 122 βˆ’π›½π›½(𝑆𝑆𝑛𝑛 βˆ’π›½π›½(𝑆𝑆𝑛𝑛 NOUN american_scientific_journal-3424 122 123 + + CCONJ american_scientific_journal-3424 122 124 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼𝑛𝑛 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 122 125 + + NUM american_scientific_journal-3424 122 126 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 122 127 ) ) PUNCT american_scientific_journal-3424 123 1 π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜4𝑑𝑑 NOUN american_scientific_journal-3424 123 2 = = PUNCT american_scientific_journal-3424 124 1 𝛽𝛽(𝑆𝑆𝑛𝑛 𝛽𝛽(𝑆𝑆𝑛𝑛 ADV american_scientific_journal-3424 124 2 + + NOUN american_scientific_journal-3424 124 3 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼𝑛𝑛 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 124 4 + + NUM american_scientific_journal-3424 124 5 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 124 6 ) ) PUNCT american_scientific_journal-3424 124 7 βˆ’ βˆ’ PROPN american_scientific_journal-3424 125 1 ( ( PUNCT american_scientific_journal-3424 125 2 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 125 3 + + CCONJ american_scientific_journal-3424 125 4 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 125 5 ) ) PUNCT american_scientific_journal-3424 125 6 π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜4𝑑𝑑 NOUN american_scientific_journal-3424 125 7 = = PUNCT american_scientific_journal-3424 126 1 𝛾𝛾(𝐼𝐼𝑛𝑛 𝛾𝛾(𝐼𝐼𝑛𝑛 ADV american_scientific_journal-3424 126 2 + + CCONJ american_scientific_journal-3424 126 3 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ X american_scientific_journal-3424 126 4 ) ) PUNCT american_scientific_journal-3424 126 5 𝑆𝑆𝑛𝑛+1 𝑆𝑆𝑛𝑛+1 NOUN american_scientific_journal-3424 126 6 = = SYM american_scientific_journal-3424 126 7 𝑆𝑆𝑛𝑛 𝑆𝑆𝑛𝑛 PROPN american_scientific_journal-3424 127 1 + + CCONJ american_scientific_journal-3424 127 2 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 127 3 6 6 NUM american_scientific_journal-3424 127 4 ( ( PUNCT american_scientific_journal-3424 127 5 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 NOUN american_scientific_journal-3424 127 6 ) ) PUNCT american_scientific_journal-3424 127 7 𝐼𝐼𝑛𝑛+1 𝐼𝐼𝑛𝑛+1 NOUN american_scientific_journal-3424 127 8 = = PUNCT american_scientific_journal-3424 128 1 𝐼𝐼𝑛𝑛 𝐼𝐼𝑛𝑛 PROPN american_scientific_journal-3424 128 2 + + CCONJ american_scientific_journal-3424 128 3 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 128 4 6 6 NUM american_scientific_journal-3424 128 5 ( ( PUNCT american_scientific_journal-3424 128 6 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 128 7 ) ) PUNCT american_scientific_journal-3424 128 8 𝑅𝑅𝑛𝑛+1 𝑅𝑅𝑛𝑛+1 NOUN american_scientific_journal-3424 129 1 = = PUNCT american_scientific_journal-3424 130 1 𝑅𝑅𝑛𝑛 𝑅𝑅𝑛𝑛 PROPN american_scientific_journal-3424 130 2 + + NUM american_scientific_journal-3424 130 3 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 130 4 6 6 NUM american_scientific_journal-3424 130 5 ( ( PUNCT american_scientific_journal-3424 130 6 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 130 7 ) ) PUNCT american_scientific_journal-3424 130 8 we we PRON american_scientific_journal-3424 130 9 take take VERB american_scientific_journal-3424 130 10 the the DET american_scientific_journal-3424 130 11 initial initial ADJ american_scientific_journal-3424 130 12 values value NOUN american_scientific_journal-3424 130 13 as as ADP american_scientific_journal-3424 130 14 𝑆𝑆0 𝑆𝑆0 ADV american_scientific_journal-3424 130 15 = = SYM american_scientific_journal-3424 130 16 4293265 4293265 NUM american_scientific_journal-3424 130 17 ; ; PUNCT american_scientific_journal-3424 130 18 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 130 19 = = PROPN american_scientific_journal-3424 130 20 391 391 NUM american_scientific_journal-3424 130 21 ; ; PUNCT american_scientific_journal-3424 130 22 𝑅𝑅0 𝑅𝑅0 PROPN american_scientific_journal-3424 130 23 = = PROPN american_scientific_journal-3424 130 24 344 344 NUM american_scientific_journal-3424 130 25 ; ; PUNCT american_scientific_journal-3424 130 26 𝛾𝛾 𝛾𝛾 ADP american_scientific_journal-3424 130 27 = = NOUN american_scientific_journal-3424 130 28 0.09 0.09 NUM american_scientific_journal-3424 130 29 ; ; PUNCT american_scientific_journal-3424 130 30 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 130 31 = = SYM american_scientific_journal-3424 130 32 1.63 1.63 NUM american_scientific_journal-3424 130 33 Γ— Γ— NOUN american_scientific_journal-3424 130 34 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 130 35 we we PRON american_scientific_journal-3424 130 36 will will AUX american_scientific_journal-3424 130 37 do do VERB american_scientific_journal-3424 130 38 this this PRON american_scientific_journal-3424 130 39 explicitly explicitly ADV american_scientific_journal-3424 130 40 for for ADP american_scientific_journal-3424 130 41 the the DET american_scientific_journal-3424 130 42 transition transition NOUN american_scientific_journal-3424 130 43 from from ADP american_scientific_journal-3424 130 44 t t PROPN american_scientific_journal-3424 130 45 = = SYM american_scientific_journal-3424 130 46 0 0 PROPN american_scientific_journal-3424 130 47 to to ADP american_scientific_journal-3424 130 48 t t NOUN american_scientific_journal-3424 130 49 = = SYM american_scientific_journal-3424 130 50 1 1 X american_scientific_journal-3424 130 51 . . PUNCT american_scientific_journal-3424 130 52 using use VERB american_scientific_journal-3424 130 53 those those DET american_scientific_journal-3424 130 54 equations equation NOUN american_scientific_journal-3424 130 55 the the DET american_scientific_journal-3424 130 56 following follow VERB american_scientific_journal-3424 130 57 values value NOUN american_scientific_journal-3424 130 58 for for ADP american_scientific_journal-3424 130 59 s s PROPN american_scientific_journal-3424 130 60 , , PUNCT american_scientific_journal-3424 130 61 i i PRON american_scientific_journal-3424 130 62 and and CCONJ american_scientific_journal-3424 130 63 r r NOUN american_scientific_journal-3424 130 64 can can AUX american_scientific_journal-3424 130 65 be be AUX american_scientific_journal-3424 130 66 calculated calculate VERB american_scientific_journal-3424 130 67 . . PUNCT american_scientific_journal-3424 131 1 π‘˜π‘˜1𝑑𝑑 π‘˜π‘˜1𝑑𝑑 NUM american_scientific_journal-3424 131 2 = = SYM american_scientific_journal-3424 131 3 βˆ’π›½π›½π‘†π‘†0𝐼𝐼0 βˆ’π›½π›½π‘†π‘†0𝐼𝐼0 PROPN american_scientific_journal-3424 131 4 = = X american_scientific_journal-3424 132 1 βˆ’1.63 βˆ’1.63 INTJ american_scientific_journal-3424 132 2 Γ— Γ— NOUN american_scientific_journal-3424 132 3 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 132 4 Γ— Γ— NOUN american_scientific_journal-3424 132 5 4293265 4293265 NUM american_scientific_journal-3424 132 6 Γ— Γ— NOUN american_scientific_journal-3424 132 7 391 391 NUM american_scientific_journal-3424 132 8 = = NUM american_scientific_journal-3424 132 9 βˆ’273.622658245000 βˆ’273.622658245000 X american_scientific_journal-3424 132 10 π‘˜π‘˜1𝑑𝑑 π‘˜π‘˜1𝑑𝑑 NOUN american_scientific_journal-3424 132 11 = = PUNCT american_scientific_journal-3424 132 12 𝛽𝛽𝑆𝑆0𝐼𝐼0 𝛽𝛽𝑆𝑆0𝐼𝐼0 CCONJ american_scientific_journal-3424 132 13 βˆ’ βˆ’ NOUN american_scientific_journal-3424 132 14 𝛾𝛾𝐼𝐼0 𝛾𝛾𝐼𝐼0 NOUN american_scientific_journal-3424 132 15 = = NOUN american_scientific_journal-3424 132 16 1.63 1.63 NUM american_scientific_journal-3424 132 17 Γ— Γ— NOUN american_scientific_journal-3424 132 18 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 132 19 Γ— Γ— NOUN american_scientific_journal-3424 132 20 4293265 4293265 NUM american_scientific_journal-3424 132 21 Γ— Γ— NOUN american_scientific_journal-3424 132 22 391 391 NUM american_scientific_journal-3424 132 23 βˆ’ βˆ’ NOUN american_scientific_journal-3424 132 24 0.09 0.09 NUM american_scientific_journal-3424 132 25 Γ— Γ— NOUN american_scientific_journal-3424 132 26 391 391 NUM american_scientific_journal-3424 132 27 = = SYM american_scientific_journal-3424 132 28 238.432658245000 238.432658245000 NUM american_scientific_journal-3424 132 29 american american ADJ american_scientific_journal-3424 132 30 scientific scientific ADJ american_scientific_journal-3424 132 31 research research NOUN american_scientific_journal-3424 132 32 journal journal NOUN american_scientific_journal-3424 132 33 for for ADP american_scientific_journal-3424 132 34 engineering engineering NOUN american_scientific_journal-3424 132 35 , , PUNCT american_scientific_journal-3424 132 36 technology technology NOUN american_scientific_journal-3424 132 37 , , PUNCT american_scientific_journal-3424 132 38 and and CCONJ american_scientific_journal-3424 132 39 sciences science NOUN american_scientific_journal-3424 132 40 ( ( PUNCT american_scientific_journal-3424 132 41 asrjets asrjet NOUN american_scientific_journal-3424 132 42 ) ) PUNCT american_scientific_journal-3424 132 43 ( ( PUNCT american_scientific_journal-3424 132 44 2017 2017 NUM american_scientific_journal-3424 132 45 ) ) PUNCT american_scientific_journal-3424 132 46 volume volume NOUN american_scientific_journal-3424 132 47 37 37 NUM american_scientific_journal-3424 132 48 , , PUNCT american_scientific_journal-3424 132 49 no no DET american_scientific_journal-3424 132 50 1 1 NUM american_scientific_journal-3424 132 51 , , PUNCT american_scientific_journal-3424 132 52 pp pp ADV american_scientific_journal-3424 132 53 1 1 NUM american_scientific_journal-3424 132 54 - - SYM american_scientific_journal-3424 132 55 21 21 NUM american_scientific_journal-3424 132 56 12 12 NUM american_scientific_journal-3424 132 57 π‘˜π‘˜1𝑑𝑑 π‘˜π‘˜1𝑑𝑑 NOUN american_scientific_journal-3424 132 58 = = NOUN american_scientific_journal-3424 132 59 𝛾𝛾𝐼𝐼0 𝛾𝛾𝐼𝐼0 NOUN american_scientific_journal-3424 132 60 = = NUM american_scientific_journal-3424 132 61 0.09 0.09 NUM american_scientific_journal-3424 132 62 Γ— Γ— NOUN american_scientific_journal-3424 132 63 391 391 NUM american_scientific_journal-3424 132 64 = = SYM american_scientific_journal-3424 132 65 35.1900000000000 35.1900000000000 NUM american_scientific_journal-3424 132 66 π‘˜π‘˜2𝑑𝑑 π‘˜π‘˜2𝑑𝑑 NOUN american_scientific_journal-3424 132 67 = = SYM american_scientific_journal-3424 132 68 βˆ’π›½π›½ βˆ’π›½π›½ NOUN american_scientific_journal-3424 132 69 οΏ½ οΏ½ NOUN american_scientific_journal-3424 132 70 𝑆𝑆0 𝑆𝑆0 PROPN american_scientific_journal-3424 132 71 + + PRON american_scientific_journal-3424 132 72 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 132 73 2 2 NUM american_scientific_journal-3424 132 74 οΏ½ οΏ½ PROPN american_scientific_journal-3424 132 75 ( ( PUNCT american_scientific_journal-3424 132 76 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 132 77 + + PROPN american_scientific_journal-3424 132 78 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 132 79 2 2 NUM american_scientific_journal-3424 132 80 ) ) PUNCT american_scientific_journal-3424 132 81 = = PUNCT american_scientific_journal-3424 133 1 βˆ’1.63 βˆ’1.63 INTJ american_scientific_journal-3424 133 2 Γ— Γ— NOUN american_scientific_journal-3424 133 3 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 133 4 Γ— Γ— PROPN american_scientific_journal-3424 133 5 οΏ½ οΏ½ PROPN american_scientific_journal-3424 133 6 4293265 4293265 NUM american_scientific_journal-3424 133 7 βˆ’ βˆ’ NOUN american_scientific_journal-3424 133 8 273.622658245000 273.622658245000 NUM american_scientific_journal-3424 133 9 2 2 NUM american_scientific_journal-3424 133 10 οΏ½ οΏ½ PROPN american_scientific_journal-3424 133 11 Γ— Γ— PROPN american_scientific_journal-3424 133 12 οΏ½ οΏ½ PROPN american_scientific_journal-3424 133 13 391 391 NUM american_scientific_journal-3424 133 14 + + CCONJ american_scientific_journal-3424 133 15 238.432658245000 238.432658245000 NUM american_scientific_journal-3424 133 16 2 2 NUM american_scientific_journal-3424 133 17 οΏ½ οΏ½ NOUN american_scientific_journal-3424 133 18 = = PUNCT american_scientific_journal-3424 133 19 βˆ’357.039129094785 βˆ’357.039129094785 X american_scientific_journal-3424 133 20 π‘˜π‘˜2𝑑𝑑 π‘˜π‘˜2𝑑𝑑 NOUN american_scientific_journal-3424 133 21 = = PUNCT american_scientific_journal-3424 133 22 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 133 23 οΏ½ οΏ½ PROPN american_scientific_journal-3424 133 24 𝑆𝑆0 𝑆𝑆0 PROPN american_scientific_journal-3424 133 25 + + PRON american_scientific_journal-3424 133 26 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 133 27 2 2 NUM american_scientific_journal-3424 133 28 οΏ½ οΏ½ PROPN american_scientific_journal-3424 133 29 οΏ½ οΏ½ PROPN american_scientific_journal-3424 133 30 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 133 31 + + PROPN american_scientific_journal-3424 133 32 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 133 33 2 2 NUM american_scientific_journal-3424 133 34 οΏ½ οΏ½ PROPN american_scientific_journal-3424 133 35 βˆ’ βˆ’ PROPN american_scientific_journal-3424 133 36 οΏ½ οΏ½ PROPN american_scientific_journal-3424 133 37 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 133 38 + + CCONJ american_scientific_journal-3424 133 39 π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜1π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 133 40 2 2 NUM american_scientific_journal-3424 133 41 οΏ½ οΏ½ NOUN american_scientific_journal-3424 133 42 = = PUNCT american_scientific_journal-3424 134 1 βˆ’1.63 βˆ’1.63 INTJ american_scientific_journal-3424 134 2 Γ— Γ— NOUN american_scientific_journal-3424 134 3 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 134 4 Γ— Γ— PROPN american_scientific_journal-3424 134 5 οΏ½ οΏ½ PROPN american_scientific_journal-3424 134 6 4293265 4293265 NUM american_scientific_journal-3424 134 7 + + CCONJ american_scientific_journal-3424 134 8 βˆ’273.622658245000 βˆ’273.622658245000 X american_scientific_journal-3424 134 9 2 2 NUM american_scientific_journal-3424 134 10 οΏ½ οΏ½ PROPN american_scientific_journal-3424 134 11 Γ— Γ— PROPN american_scientific_journal-3424 134 12 οΏ½ οΏ½ PROPN american_scientific_journal-3424 134 13 391 391 NUM american_scientific_journal-3424 134 14 + + CCONJ american_scientific_journal-3424 134 15 238.432658245000 238.432658245000 NUM american_scientific_journal-3424 134 16 2 2 NUM american_scientific_journal-3424 134 17 οΏ½ οΏ½ PROPN american_scientific_journal-3424 134 18 βˆ’ βˆ’ PROPN american_scientific_journal-3424 134 19 οΏ½ οΏ½ NOUN american_scientific_journal-3424 134 20 391 391 NUM american_scientific_journal-3424 134 21 + + CCONJ american_scientific_journal-3424 134 22 238.432658245000 238.432658245000 NUM american_scientific_journal-3424 134 23 2 2 NUM american_scientific_journal-3424 134 24 οΏ½ οΏ½ NOUN american_scientific_journal-3424 134 25 = = SYM american_scientific_journal-3424 135 1 311.119659473760 311.119659473760 NUM american_scientific_journal-3424 135 2 π‘˜π‘˜2𝑑𝑑 π‘˜π‘˜2𝑑𝑑 NOUN american_scientific_journal-3424 135 3 = = PUNCT american_scientific_journal-3424 135 4 𝛾𝛾 𝛾𝛾 PART american_scientific_journal-3424 135 5 οΏ½ οΏ½ PROPN american_scientific_journal-3424 135 6 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 135 7 + + CCONJ american_scientific_journal-3424 135 8 π‘˜π‘˜1 π‘˜π‘˜1 NOUN american_scientific_journal-3424 135 9 πΌπΌβˆ†π‘‘π‘‘ πΌπΌβˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 135 10 2 2 NUM american_scientific_journal-3424 135 11 οΏ½ οΏ½ PROPN american_scientific_journal-3424 135 12 = = SYM american_scientific_journal-3424 135 13 0.09 0.09 NUM american_scientific_journal-3424 135 14 Γ— Γ— PROPN american_scientific_journal-3424 135 15 οΏ½ οΏ½ NOUN american_scientific_journal-3424 135 16 391 391 NUM american_scientific_journal-3424 135 17 + + CCONJ american_scientific_journal-3424 135 18 238.432658245000 238.432658245000 NUM american_scientific_journal-3424 135 19 2 2 NUM american_scientific_journal-3424 135 20 οΏ½ οΏ½ NOUN american_scientific_journal-3424 135 21 = = NOUN american_scientific_journal-3424 135 22 45.9194696210250 45.9194696210250 NUM american_scientific_journal-3424 135 23 π‘˜π‘˜3𝑑𝑑 π‘˜π‘˜3𝑑𝑑 NOUN american_scientific_journal-3424 135 24 = = SYM american_scientific_journal-3424 135 25 βˆ’π›½π›½ βˆ’π›½π›½ NUM american_scientific_journal-3424 135 26 οΏ½ οΏ½ NOUN american_scientific_journal-3424 135 27 𝑆𝑆0 𝑆𝑆0 PROPN american_scientific_journal-3424 135 28 + + CCONJ american_scientific_journal-3424 135 29 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 135 30 2 2 NUM american_scientific_journal-3424 135 31 οΏ½ οΏ½ PROPN american_scientific_journal-3424 135 32 ( ( PUNCT american_scientific_journal-3424 135 33 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 135 34 + + PROPN american_scientific_journal-3424 135 35 π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜2π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 135 36 2 2 NUM american_scientific_journal-3424 135 37 ) ) PUNCT american_scientific_journal-3424 136 1 = = PUNCT american_scientific_journal-3424 137 1 βˆ’1.63 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american_scientific_journal-3424 137 19 π‘˜π‘˜3𝑑𝑑 π‘˜π‘˜3𝑑𝑑 NOUN american_scientific_journal-3424 137 20 = = PUNCT american_scientific_journal-3424 137 21 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-3424 137 22 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 23 𝑆𝑆0 𝑆𝑆0 PROPN american_scientific_journal-3424 137 24 + + ADJ american_scientific_journal-3424 137 25 π‘˜π‘˜2 π‘˜π‘˜2 PROPN american_scientific_journal-3424 137 26 π‘†π‘†βˆ†π‘‘π‘‘ π‘†π‘†βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 137 27 2 2 NUM american_scientific_journal-3424 137 28 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 29 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 30 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 137 31 + + CCONJ american_scientific_journal-3424 137 32 π‘˜π‘˜2 π‘˜π‘˜2 PROPN american_scientific_journal-3424 137 33 πΌπΌβˆ†π‘‘π‘‘ πΌπΌβˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 137 34 2 2 NUM american_scientific_journal-3424 137 35 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 36 βˆ’ βˆ’ PROPN american_scientific_journal-3424 137 37 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 38 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 137 39 + + CCONJ american_scientific_journal-3424 137 40 π‘˜π‘˜2 π‘˜π‘˜2 PROPN american_scientific_journal-3424 137 41 πΌπΌβˆ†π‘‘π‘‘ πΌπΌβˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 137 42 2 2 NUM american_scientific_journal-3424 137 43 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 44 = = SYM american_scientific_journal-3424 137 45 1.63 1.63 NUM american_scientific_journal-3424 137 46 Γ— Γ— NOUN american_scientific_journal-3424 137 47 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 137 48 Γ— Γ— PROPN american_scientific_journal-3424 137 49 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 50 4293265 4293265 NUM american_scientific_journal-3424 137 51 + + CCONJ american_scientific_journal-3424 137 52 βˆ’357.039129094785 βˆ’357.039129094785 X american_scientific_journal-3424 137 53 2 2 NUM american_scientific_journal-3424 137 54 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 55 Γ— Γ— PROPN american_scientific_journal-3424 137 56 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 57 391 391 NUM american_scientific_journal-3424 137 58 + + CCONJ american_scientific_journal-3424 137 59 311.119659473760 311.119659473760 NUM american_scientific_journal-3424 137 60 2 2 NUM american_scientific_journal-3424 137 61 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 62 βˆ’ βˆ’ NOUN american_scientific_journal-3424 137 63 οΏ½ οΏ½ NOUN american_scientific_journal-3424 137 64 391 391 NUM american_scientific_journal-3424 137 65 + + CCONJ american_scientific_journal-3424 137 66 311.119659473760 311.119659473760 NUM american_scientific_journal-3424 137 67 2 2 NUM american_scientific_journal-3424 137 68 οΏ½ οΏ½ NOUN american_scientific_journal-3424 137 69 = = NOUN american_scientific_journal-3424 137 70 333.277479697859 333.277479697859 NUM american_scientific_journal-3424 137 71 π‘˜π‘˜3𝑑𝑑 π‘˜π‘˜3𝑑𝑑 NOUN american_scientific_journal-3424 137 72 = = PUNCT american_scientific_journal-3424 137 73 𝛾𝛾 𝛾𝛾 PART american_scientific_journal-3424 137 74 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 75 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 137 76 + + CCONJ american_scientific_journal-3424 137 77 π‘˜π‘˜2 π‘˜π‘˜2 PROPN american_scientific_journal-3424 137 78 πΌπΌβˆ†π‘‘π‘‘ πΌπΌβˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 137 79 2 2 NUM american_scientific_journal-3424 137 80 οΏ½ οΏ½ PROPN american_scientific_journal-3424 137 81 = = SYM american_scientific_journal-3424 137 82 0.09 0.09 NUM american_scientific_journal-3424 137 83 Γ— Γ— PROPN american_scientific_journal-3424 137 84 οΏ½ οΏ½ NOUN american_scientific_journal-3424 137 85 391 391 NUM american_scientific_journal-3424 137 86 + + CCONJ american_scientific_journal-3424 137 87 311.119659473760 311.119659473760 NUM american_scientific_journal-3424 137 88 2 2 NUM american_scientific_journal-3424 137 89 οΏ½ οΏ½ NOUN american_scientific_journal-3424 137 90 = = NOUN american_scientific_journal-3424 137 91 49.1903846763192 49.1903846763192 NUM american_scientific_journal-3424 137 92 π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 137 93 = = SYM american_scientific_journal-3424 137 94 βˆ’π›½π›½(𝑆𝑆0 βˆ’π›½π›½(𝑆𝑆0 PUNCT american_scientific_journal-3424 137 95 + + CCONJ american_scientific_journal-3424 137 96 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼0 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼0 PROPN american_scientific_journal-3424 137 97 + + CCONJ american_scientific_journal-3424 137 98 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ X american_scientific_journal-3424 137 99 ) ) PUNCT american_scientific_journal-3424 137 100 american american ADJ american_scientific_journal-3424 137 101 scientific scientific ADJ american_scientific_journal-3424 137 102 research research NOUN 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no DET american_scientific_journal-3424 137 121 1 1 NUM american_scientific_journal-3424 137 122 , , PUNCT american_scientific_journal-3424 137 123 pp pp ADV american_scientific_journal-3424 137 124 1 1 NUM american_scientific_journal-3424 137 125 - - SYM american_scientific_journal-3424 137 126 21 21 NUM american_scientific_journal-3424 137 127 13 13 NUM american_scientific_journal-3424 137 128 = = NOUN american_scientific_journal-3424 138 1 βˆ’1.63 βˆ’1.63 INTJ american_scientific_journal-3424 138 2 Γ— Γ— NOUN american_scientific_journal-3424 138 3 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 138 4 Γ— Γ— NOUN american_scientific_journal-3424 138 5 ( ( PUNCT american_scientific_journal-3424 138 6 4293265 4293265 NUM american_scientific_journal-3424 138 7 βˆ’ βˆ’ NOUN american_scientific_journal-3424 138 8 382.467864374178 382.467864374178 NUM american_scientific_journal-3424 138 9 ) ) PUNCT american_scientific_journal-3424 138 10 Γ— Γ— NOUN american_scientific_journal-3424 138 11 ( ( PUNCT american_scientific_journal-3424 138 12 391 391 NUM american_scientific_journal-3424 138 13 + + NUM american_scientific_journal-3424 138 14 333.277479697859 333.277479697859 NUM american_scientific_journal-3424 138 15 ) ) PUNCT american_scientific_journal-3424 138 16 = = NOUN american_scientific_journal-3424 139 1 βˆ’506.805816985307 βˆ’506.805816985307 PUNCT american_scientific_journal-3424 139 2 π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 139 3 = = SYM american_scientific_journal-3424 139 4 𝛽𝛽(𝑆𝑆0 𝛽𝛽(𝑆𝑆0 PROPN american_scientific_journal-3424 139 5 + + CCONJ american_scientific_journal-3424 139 6 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼0 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘)(𝐼𝐼0 PROPN american_scientific_journal-3424 139 7 + + X american_scientific_journal-3424 139 8 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ NOUN american_scientific_journal-3424 139 9 ) ) PUNCT american_scientific_journal-3424 139 10 βˆ’ βˆ’ PROPN american_scientific_journal-3424 140 1 ( ( PUNCT american_scientific_journal-3424 140 2 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 140 3 + + X american_scientific_journal-3424 140 4 π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ π‘˜π‘˜3π‘‘π‘‘βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 140 5 ) ) PUNCT american_scientific_journal-3424 141 1 = = SYM american_scientific_journal-3424 141 2 1.63 1.63 NUM american_scientific_journal-3424 141 3 Γ— Γ— NOUN american_scientific_journal-3424 141 4 10βˆ’7 10βˆ’7 NUM american_scientific_journal-3424 141 5 Γ— Γ— NOUN american_scientific_journal-3424 141 6 ( ( PUNCT american_scientific_journal-3424 141 7 4293265 4293265 NUM american_scientific_journal-3424 141 8 βˆ’ βˆ’ NOUN american_scientific_journal-3424 141 9 382.467864374178 382.467864374178 NUM american_scientific_journal-3424 141 10 ) ) PUNCT american_scientific_journal-3424 141 11 Γ— Γ— NOUN american_scientific_journal-3424 141 12 ( ( PUNCT american_scientific_journal-3424 141 13 391 391 NUM american_scientific_journal-3424 141 14 + + 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π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 144 7 ) ) PUNCT american_scientific_journal-3424 144 8 = = SYM american_scientific_journal-3424 144 9 4293265 4293265 NUM american_scientific_journal-3424 144 10 + + CCONJ american_scientific_journal-3424 144 11 1 1 NUM american_scientific_journal-3424 144 12 6 6 NUM american_scientific_journal-3424 144 13 ( ( PUNCT american_scientific_journal-3424 144 14 βˆ’273.622658245000 βˆ’273.622658245000 X american_scientific_journal-3424 144 15 βˆ’ βˆ’ PROPN american_scientific_journal-3424 144 16 2 2 NUM american_scientific_journal-3424 144 17 Γ— Γ— NOUN american_scientific_journal-3424 144 18 357.039129094785 357.039129094785 NUM american_scientific_journal-3424 144 19 βˆ’ βˆ’ NOUN american_scientific_journal-3424 144 20 2 2 NUM american_scientific_journal-3424 144 21 Γ— Γ— NOUN american_scientific_journal-3424 144 22 382.467864374178 382.467864374178 NUM american_scientific_journal-3424 144 23 βˆ’ βˆ’ NOUN american_scientific_journal-3424 144 24 506.805816985307 506.805816985307 NUM american_scientific_journal-3424 144 25 ) ) PUNCT american_scientific_journal-3424 144 26 = = SYM american_scientific_journal-3424 145 1 4292888.42625631 4292888.42625631 NUM american_scientific_journal-3424 146 1 β‰ˆ β‰ˆ PROPN american_scientific_journal-3424 146 2 4292888 4292888 NUM american_scientific_journal-3424 146 3 ∴ ∴ PROPN american_scientific_journal-3424 146 4 𝐼𝐼1 𝐼𝐼1 PROPN american_scientific_journal-3424 146 5 = = SYM american_scientific_journal-3424 146 6 𝐼𝐼0 𝐼𝐼0 PROPN american_scientific_journal-3424 146 7 + + CCONJ american_scientific_journal-3424 146 8 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 146 9 6 6 NUM american_scientific_journal-3424 146 10 ( ( PUNCT american_scientific_journal-3424 146 11 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 146 12 ) ) PUNCT american_scientific_journal-3424 146 13 = = SYM american_scientific_journal-3424 147 1 391 391 NUM american_scientific_journal-3424 147 2 + + NUM american_scientific_journal-3424 147 3 1 1 NUM american_scientific_journal-3424 147 4 6 6 NUM american_scientific_journal-3424 147 5 ( ( PUNCT american_scientific_journal-3424 147 6 238.432658245000 238.432658245000 NUM american_scientific_journal-3424 147 7 + + NOUN american_scientific_journal-3424 147 8 311.119659473760 311.119659473760 NUM american_scientific_journal-3424 147 9 + + CCONJ american_scientific_journal-3424 147 10 333.277479697859 333.277479697859 NUM american_scientific_journal-3424 147 11 + + NUM american_scientific_journal-3424 147 12 441.62084381250 441.62084381250 NUM american_scientific_journal-3424 147 13 ) ) PUNCT american_scientific_journal-3424 147 14 = = PUNCT american_scientific_journal-3424 148 1 719.141296733456 719.141296733456 NUM american_scientific_journal-3424 148 2 β‰ˆ β‰ˆ PROPN american_scientific_journal-3424 148 3 719 719 NUM american_scientific_journal-3424 148 4 ∴ ∴ PROPN american_scientific_journal-3424 148 5 𝑅𝑅1 𝑅𝑅1 PROPN american_scientific_journal-3424 148 6 = = SYM american_scientific_journal-3424 148 7 𝑅𝑅0 𝑅𝑅0 PROPN american_scientific_journal-3424 148 8 + + CCONJ american_scientific_journal-3424 148 9 βˆ†π‘‘π‘‘ βˆ†π‘‘π‘‘ PROPN american_scientific_journal-3424 148 10 6 6 NUM american_scientific_journal-3424 148 11 ( ( PUNCT american_scientific_journal-3424 148 12 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 π‘˜π‘˜1𝑑𝑑+2π‘˜π‘˜2𝑑𝑑+2π‘˜π‘˜3𝑑𝑑+π‘˜π‘˜4𝑑𝑑 NUM american_scientific_journal-3424 148 13 ) ) PUNCT american_scientific_journal-3424 149 1 = = SYM american_scientific_journal-3424 149 2 344 344 NUM american_scientific_journal-3424 150 1 + + NUM american_scientific_journal-3424 150 2 1 1 NUM american_scientific_journal-3424 150 3 6 6 NUM american_scientific_journal-3424 150 4 ( ( 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153 208 535640 535640 NUM american_scientific_journal-3424 153 209 3753562 3753562 NUM american_scientific_journal-3424 153 210 4294000 4294000 NUM american_scientific_journal-3424 153 211 41 41 NUM american_scientific_journal-3424 153 212 4414 4414 NUM american_scientific_journal-3424 153 213 489905 489905 NUM american_scientific_journal-3424 153 214 3799681 3799681 NUM american_scientific_journal-3424 153 215 4294000 4294000 NUM american_scientific_journal-3424 153 216 42 42 NUM american_scientific_journal-3424 153 217 4089 4089 NUM american_scientific_journal-3424 153 218 448050 448050 NUM american_scientific_journal-3424 153 219 3841861 3841861 NUM american_scientific_journal-3424 153 220 4294000 4294000 NUM american_scientific_journal-3424 153 221 43 43 NUM american_scientific_journal-3424 153 222 3813 3813 NUM american_scientific_journal-3424 153 223 409750 409750 NUM american_scientific_journal-3424 153 224 3880437 3880437 NUM american_scientific_journal-3424 153 225 4294000 4294000 NUM american_scientific_journal-3424 153 226 44 44 NUM american_scientific_journal-3424 153 227 3577 3577 NUM american_scientific_journal-3424 153 228 374709 374709 NUM american_scientific_journal-3424 153 229 3915714 3915714 NUM american_scientific_journal-3424 153 230 4294000 4294000 NUM american_scientific_journal-3424 153 231 45 45 NUM american_scientific_journal-3424 153 232 3374 3374 NUM american_scientific_journal-3424 153 233 342652 342652 NUM american_scientific_journal-3424 153 234 3947974 3947974 NUM american_scientific_journal-3424 153 235 4294000 4294000 NUM american_scientific_journal-3424 153 236 46 46 NUM american_scientific_journal-3424 153 237 3199 3199 NUM american_scientific_journal-3424 153 238 313328 313328 NUM american_scientific_journal-3424 153 239 3977473 3977473 NUM american_scientific_journal-3424 153 240 4294000 4294000 NUM american_scientific_journal-3424 153 241 47 47 NUM american_scientific_journal-3424 153 242 3046 3046 NUM american_scientific_journal-3424 153 243 286506 286506 NUM american_scientific_journal-3424 153 244 4004448 4004448 NUM american_scientific_journal-3424 153 245 4294000 4294000 NUM american_scientific_journal-3424 153 246 48 48 NUM american_scientific_journal-3424 153 247 2913 2913 NUM american_scientific_journal-3424 153 248 261974 261974 NUM american_scientific_journal-3424 153 249 4029113 4029113 NUM american_scientific_journal-3424 153 250 4294000 4294000 NUM american_scientific_journal-3424 153 251 49 49 NUM american_scientific_journal-3424 153 252 2796 2796 NUM american_scientific_journal-3424 153 253 239538 239538 NUM american_scientific_journal-3424 153 254 4051666 4051666 NUM american_scientific_journal-3424 153 255 4294000 4294000 NUM american_scientific_journal-3424 153 256 50 50 NUM american_scientific_journal-3424 153 257 2694 2694 NUM american_scientific_journal-3424 153 258 219019 219019 NUM american_scientific_journal-3424 153 259 4072287 4072287 NUM american_scientific_journal-3424 153 260 4294000 4294000 NUM american_scientific_journal-3424 153 261 51 51 NUM american_scientific_journal-3424 153 262 2603 2603 NUM american_scientific_journal-3424 153 263 200255 200255 NUM american_scientific_journal-3424 153 264 4091142 4091142 NUM american_scientific_journal-3424 153 265 4294000 4294000 NUM american_scientific_journal-3424 153 266 52 52 NUM american_scientific_journal-3424 153 267 2523 2523 NUM american_scientific_journal-3424 153 268 183095 183095 NUM american_scientific_journal-3424 153 269 4108382 4108382 NUM american_scientific_journal-3424 153 270 4294000 4294000 NUM american_scientific_journal-3424 153 271 53 53 NUM american_scientific_journal-3424 153 272 2452 2452 NUM american_scientific_journal-3424 153 273 167404 167404 NUM american_scientific_journal-3424 153 274 4124144 4124144 NUM american_scientific_journal-3424 153 275 4294000 4294000 NUM american_scientific_journal-3424 153 276 54 54 NUM american_scientific_journal-3424 153 277 2389 2389 NUM american_scientific_journal-3424 153 278 153057 153057 NUM american_scientific_journal-3424 153 279 4138554 4138554 NUM american_scientific_journal-3424 153 280 4294000 4294000 NUM american_scientific_journal-3424 153 281 55 55 NUM american_scientific_journal-3424 153 282 2333 2333 NUM american_scientific_journal-3424 153 283 139937 139937 NUM american_scientific_journal-3424 153 284 4151730 4151730 NUM american_scientific_journal-3424 153 285 4294000 4294000 NUM american_scientific_journal-3424 153 286 56 56 NUM american_scientific_journal-3424 153 287 2283 2283 NUM american_scientific_journal-3424 153 288 127941 127941 NUM american_scientific_journal-3424 153 289 4163776 4163776 NUM american_scientific_journal-3424 153 290 4294000 4294000 NUM american_scientific_journal-3424 153 291 57 57 NUM american_scientific_journal-3424 153 292 2238 2238 NUM american_scientific_journal-3424 153 293 116972 116972 NUM american_scientific_journal-3424 153 294 4174790 4174790 NUM american_scientific_journal-3424 153 295 4294000 4294000 NUM american_scientific_journal-3424 153 296 58 58 NUM american_scientific_journal-3424 153 297 2197 2197 NUM american_scientific_journal-3424 153 298 106943 106943 NUM american_scientific_journal-3424 153 299 4184860 4184860 NUM american_scientific_journal-3424 153 300 4294000 4294000 NUM american_scientific_journal-3424 153 301 59 59 NUM american_scientific_journal-3424 153 302 2161 2161 NUM american_scientific_journal-3424 153 303 97773 97773 NUM american_scientific_journal-3424 153 304 4194066 4194066 NUM american_scientific_journal-3424 153 305 4294000 4294000 NUM american_scientific_journal-3424 153 306 60 60 NUM american_scientific_journal-3424 153 307 2128 2128 NUM american_scientific_journal-3424 153 308 89389 89389 NUM american_scientific_journal-3424 153 309 4202483 4202483 NUM american_scientific_journal-3424 153 310 4294000 4294000 NUM american_scientific_journal-3424 153 311 figure figure NOUN american_scientific_journal-3424 153 312 3.1 3.1 NUM american_scientific_journal-3424 153 313 - - SYM american_scientific_journal-3424 153 314 3.3 3.3 NUM american_scientific_journal-3424 153 315 shows show VERB american_scientific_journal-3424 153 316 the the DET american_scientific_journal-3424 153 317 comparison comparison NOUN american_scientific_journal-3424 153 318 between between ADP american_scientific_journal-3424 153 319 euler euler NOUN american_scientific_journal-3424 153 320 and and CCONJ american_scientific_journal-3424 153 321 rk-4 rk-4 NOUN american_scientific_journal-3424 153 322 method method NOUN american_scientific_journal-3424 153 323 in in ADP american_scientific_journal-3424 153 324 the the DET american_scientific_journal-3424 153 325 cases case NOUN american_scientific_journal-3424 153 326 of of ADP american_scientific_journal-3424 153 327 infectives infective NOUN american_scientific_journal-3424 153 328 , , PUNCT american_scientific_journal-3424 153 329 recovered recover VERB american_scientific_journal-3424 153 330 and and CCONJ american_scientific_journal-3424 153 331 susceptives susceptive NOUN american_scientific_journal-3424 153 332 respectively respectively ADV american_scientific_journal-3424 153 333 . . PUNCT american_scientific_journal-3424 154 1 figure figure VERB american_scientific_journal-3424 154 2 3.1 3.1 NUM american_scientific_journal-3424 154 3 american american PROPN american_scientific_journal-3424 154 4 scientific scientific ADJ american_scientific_journal-3424 154 5 research research NOUN american_scientific_journal-3424 154 6 journal journal NOUN american_scientific_journal-3424 154 7 for for ADP american_scientific_journal-3424 154 8 engineering engineering NOUN american_scientific_journal-3424 154 9 , , PUNCT american_scientific_journal-3424 154 10 technology technology NOUN american_scientific_journal-3424 154 11 , , PUNCT american_scientific_journal-3424 154 12 and and CCONJ american_scientific_journal-3424 154 13 sciences science NOUN american_scientific_journal-3424 154 14 ( ( PUNCT american_scientific_journal-3424 154 15 asrjets asrjet NOUN american_scientific_journal-3424 154 16 ) ) PUNCT american_scientific_journal-3424 154 17 ( ( PUNCT american_scientific_journal-3424 154 18 2017 2017 NUM american_scientific_journal-3424 154 19 ) ) PUNCT american_scientific_journal-3424 154 20 volume volume NOUN american_scientific_journal-3424 154 21 37 37 NUM american_scientific_journal-3424 154 22 , , PUNCT american_scientific_journal-3424 154 23 no no DET american_scientific_journal-3424 154 24 1 1 NUM american_scientific_journal-3424 154 25 , , PUNCT american_scientific_journal-3424 154 26 pp pp ADV american_scientific_journal-3424 154 27 1 1 NUM american_scientific_journal-3424 154 28 - - SYM american_scientific_journal-3424 154 29 21 21 NUM american_scientific_journal-3424 154 30 16 16 NUM american_scientific_journal-3424 154 31 figure figure NOUN american_scientific_journal-3424 154 32 3.2 3.2 NUM american_scientific_journal-3424 154 33 figure figure NOUN american_scientific_journal-3424 154 34 3.3 3.3 NUM american_scientific_journal-3424 154 35 for for AUX american_scientific_journal-3424 154 36 predict predict VERB american_scientific_journal-3424 154 37 the the DET american_scientific_journal-3424 154 38 evolution evolution NOUN american_scientific_journal-3424 154 39 , , PUNCT american_scientific_journal-3424 154 40 we we PRON american_scientific_journal-3424 154 41 only only ADV american_scientific_journal-3424 154 42 discuss discuss VERB american_scientific_journal-3424 154 43 about about ADP american_scientific_journal-3424 154 44 the the DET american_scientific_journal-3424 154 45 infectives infective NOUN american_scientific_journal-3424 154 46 . . PUNCT american_scientific_journal-3424 155 1 each each DET american_scientific_journal-3424 155 2 strategies strategy NOUN american_scientific_journal-3424 155 3 show show VERB american_scientific_journal-3424 155 4 that that SCONJ american_scientific_journal-3424 155 5 initially initially ADV american_scientific_journal-3424 155 6 , , PUNCT american_scientific_journal-3424 155 7 the the DET american_scientific_journal-3424 155 8 number number NOUN american_scientific_journal-3424 155 9 of of ADP american_scientific_journal-3424 155 10 individuals individual NOUN american_scientific_journal-3424 155 11 infected infect VERB american_scientific_journal-3424 155 12 will will AUX american_scientific_journal-3424 155 13 increase increase VERB american_scientific_journal-3424 155 14 steeply steeply ADV american_scientific_journal-3424 155 15 , , PUNCT american_scientific_journal-3424 155 16 however however ADV american_scientific_journal-3424 155 17 , , PUNCT american_scientific_journal-3424 155 18 over over ADP american_scientific_journal-3424 155 19 an an DET american_scientific_journal-3424 155 20 extended extended ADJ american_scientific_journal-3424 155 21 period period NOUN american_scientific_journal-3424 155 22 of of ADP american_scientific_journal-3424 155 23 time time NOUN american_scientific_journal-3424 155 24 , , PUNCT american_scientific_journal-3424 155 25 the the DET american_scientific_journal-3424 155 26 numbers number NOUN american_scientific_journal-3424 155 27 eventually eventually ADV american_scientific_journal-3424 155 28 decrease decrease VERB american_scientific_journal-3424 155 29 . . PUNCT american_scientific_journal-3424 156 1 this this PRON american_scientific_journal-3424 156 2 happens happen VERB american_scientific_journal-3424 156 3 simultaneously simultaneously ADV american_scientific_journal-3424 156 4 because because SCONJ american_scientific_journal-3424 156 5 the the DET american_scientific_journal-3424 156 6 range range NOUN american_scientific_journal-3424 156 7 of of ADP american_scientific_journal-3424 156 8 individuals individual NOUN american_scientific_journal-3424 156 9 recovered recover VERB american_scientific_journal-3424 156 10 will will AUX american_scientific_journal-3424 156 11 increase increase VERB american_scientific_journal-3424 156 12 because because SCONJ american_scientific_journal-3424 156 13 as as SCONJ american_scientific_journal-3424 156 14 those those DET american_scientific_journal-3424 156 15 infected infected ADJ american_scientific_journal-3424 156 16 decreases decrease NOUN american_scientific_journal-3424 156 17 , , PUNCT american_scientific_journal-3424 156 18 they they PRON american_scientific_journal-3424 156 19 're be AUX american_scientific_journal-3424 156 20 being be AUX american_scientific_journal-3424 156 21 transferred transfer VERB american_scientific_journal-3424 156 22 into into ADP american_scientific_journal-3424 156 23 the the DET american_scientific_journal-3424 156 24 recovered recovered ADJ american_scientific_journal-3424 156 25 class class NOUN american_scientific_journal-3424 156 26 . . PUNCT american_scientific_journal-3424 157 1 the the DET american_scientific_journal-3424 157 2 main main ADJ american_scientific_journal-3424 157 3 reason reason NOUN american_scientific_journal-3424 157 4 is be AUX american_scientific_journal-3424 157 5 owing owe VERB american_scientific_journal-3424 157 6 to to ADP american_scientific_journal-3424 157 7 the the DET american_scientific_journal-3424 157 8 raised raise VERB american_scientific_journal-3424 157 9 awareness awareness NOUN american_scientific_journal-3424 157 10 of of ADP american_scientific_journal-3424 157 11 the the DET american_scientific_journal-3424 157 12 disease disease NOUN american_scientific_journal-3424 157 13 leasing lease VERB american_scientific_journal-3424 157 14 to to ADP american_scientific_journal-3424 157 15 additional additional ADJ american_scientific_journal-3424 157 16 medical medical ADJ american_scientific_journal-3424 157 17 support support NOUN american_scientific_journal-3424 157 18 being be AUX american_scientific_journal-3424 157 19 given give VERB american_scientific_journal-3424 157 20 in in ADP american_scientific_journal-3424 157 21 order order NOUN american_scientific_journal-3424 157 22 to to PART american_scientific_journal-3424 157 23 assist assist VERB american_scientific_journal-3424 157 24 combat combat VERB american_scientific_journal-3424 157 25 the the DET american_scientific_journal-3424 157 26 transmission transmission NOUN american_scientific_journal-3424 157 27 of of ADP american_scientific_journal-3424 157 28 the the DET american_scientific_journal-3424 157 29 disease disease NOUN american_scientific_journal-3424 157 30 . . PUNCT american_scientific_journal-3424 158 1 furthermore furthermore ADV american_scientific_journal-3424 158 2 , , PUNCT american_scientific_journal-3424 158 3 an an DET american_scientific_journal-3424 158 4 increased increase VERB american_scientific_journal-3424 158 5 awareness awareness NOUN american_scientific_journal-3424 158 6 ends end VERB american_scientific_journal-3424 158 7 up up ADP american_scientific_journal-3424 158 8 in in ADP american_scientific_journal-3424 158 9 additional additional ADJ american_scientific_journal-3424 158 10 folks folk NOUN american_scientific_journal-3424 158 11 being be AUX american_scientific_journal-3424 158 12 conscious conscious ADJ american_scientific_journal-3424 158 13 of of ADP american_scientific_journal-3424 158 14 strategies strategy NOUN american_scientific_journal-3424 158 15 of of ADP american_scientific_journal-3424 158 16 protection protection NOUN american_scientific_journal-3424 158 17 . . PUNCT american_scientific_journal-3424 159 1 the the DET american_scientific_journal-3424 159 2 steep steep ADJ american_scientific_journal-3424 159 3 increase increase NOUN american_scientific_journal-3424 159 4 within within ADP american_scientific_journal-3424 159 5 the the DET american_scientific_journal-3424 159 6 beginning beginning NOUN american_scientific_journal-3424 159 7 of of ADP american_scientific_journal-3424 159 8 the the DET american_scientific_journal-3424 159 9 primary primary ADJ american_scientific_journal-3424 159 10 fifteen fifteen NUM american_scientific_journal-3424 159 11 days day NOUN american_scientific_journal-3424 159 12 is be AUX american_scientific_journal-3424 159 13 possibly possibly ADV american_scientific_journal-3424 159 14 to to PART american_scientific_journal-3424 159 15 flow flow VERB american_scientific_journal-3424 159 16 from from ADP american_scientific_journal-3424 159 17 to to ADP american_scientific_journal-3424 159 18 the the DET american_scientific_journal-3424 159 19 good good ADJ american_scientific_journal-3424 159 20 uncertainty uncertainty NOUN american_scientific_journal-3424 159 21 that that PRON american_scientific_journal-3424 159 22 lied lie VERB american_scientific_journal-3424 159 23 with with ADP american_scientific_journal-3424 159 24 ebola ebola NOUN american_scientific_journal-3424 159 25 allowing allow VERB american_scientific_journal-3424 159 26 a a DET american_scientific_journal-3424 159 27 greater great ADJ american_scientific_journal-3424 159 28 rate rate NOUN american_scientific_journal-3424 159 29 of of ADP american_scientific_journal-3424 159 30 transmission transmission NOUN american_scientific_journal-3424 159 31 . . PUNCT american_scientific_journal-3424 160 1 the the DET american_scientific_journal-3424 160 2 peak peak NOUN american_scientific_journal-3424 160 3 of of ADP american_scientific_journal-3424 160 4 every every DET american_scientific_journal-3424 160 5 graph graph NOUN american_scientific_journal-3424 160 6 illustrates illustrate VERB american_scientific_journal-3424 160 7 the the DET american_scientific_journal-3424 160 8 utmost utmost ADJ american_scientific_journal-3424 160 9 number number NOUN american_scientific_journal-3424 160 10 of of ADP american_scientific_journal-3424 160 11 individuals individual NOUN american_scientific_journal-3424 160 12 ever ever ADV american_scientific_journal-3424 160 13 to to PART american_scientific_journal-3424 160 14 be be AUX american_scientific_journal-3424 160 15 infected infect VERB american_scientific_journal-3424 160 16 and and CCONJ american_scientific_journal-3424 160 17 once once ADV american_scientific_journal-3424 160 18 this this DET american_scientific_journal-3424 160 19 point point NOUN american_scientific_journal-3424 160 20 ; ; PUNCT american_scientific_journal-3424 160 21 there there PRON american_scientific_journal-3424 160 22 's be VERB american_scientific_journal-3424 160 23 a a DET american_scientific_journal-3424 160 24 transition transition NOUN american_scientific_journal-3424 160 25 whereby whereby SCONJ american_scientific_journal-3424 160 26 the the DET american_scientific_journal-3424 160 27 numbers number NOUN american_scientific_journal-3424 160 28 decrease decrease VERB american_scientific_journal-3424 160 29 . . PUNCT american_scientific_journal-3424 161 1 3.3 3.3 NUM american_scientific_journal-3424 161 2 comparing compare VERB american_scientific_journal-3424 161 3 the the DET american_scientific_journal-3424 161 4 model model NOUN american_scientific_journal-3424 161 5 to to ADP american_scientific_journal-3424 161 6 actual actual ADJ american_scientific_journal-3424 161 7 data datum NOUN american_scientific_journal-3424 161 8 american american PROPN american_scientific_journal-3424 161 9 scientific scientific ADJ american_scientific_journal-3424 161 10 research research NOUN american_scientific_journal-3424 161 11 journal journal NOUN american_scientific_journal-3424 161 12 for for ADP american_scientific_journal-3424 161 13 engineering engineering NOUN american_scientific_journal-3424 161 14 , , PUNCT american_scientific_journal-3424 161 15 technology technology NOUN american_scientific_journal-3424 161 16 , , PUNCT american_scientific_journal-3424 161 17 and and CCONJ american_scientific_journal-3424 161 18 sciences science NOUN american_scientific_journal-3424 161 19 ( ( PUNCT american_scientific_journal-3424 161 20 asrjets asrjet NOUN american_scientific_journal-3424 161 21 ) ) PUNCT american_scientific_journal-3424 161 22 ( ( PUNCT american_scientific_journal-3424 161 23 2017 2017 NUM american_scientific_journal-3424 161 24 ) ) PUNCT american_scientific_journal-3424 161 25 volume volume NOUN american_scientific_journal-3424 161 26 37 37 NUM american_scientific_journal-3424 161 27 , , PUNCT american_scientific_journal-3424 161 28 no no DET american_scientific_journal-3424 161 29 1 1 NUM american_scientific_journal-3424 161 30 , , PUNCT american_scientific_journal-3424 161 31 pp pp ADV american_scientific_journal-3424 161 32 1 1 NUM american_scientific_journal-3424 161 33 - - SYM american_scientific_journal-3424 161 34 21 21 NUM american_scientific_journal-3424 161 35 17 17 NUM american_scientific_journal-3424 161 36 however however ADV american_scientific_journal-3424 161 37 , , PUNCT american_scientific_journal-3424 161 38 in in ADP american_scientific_journal-3424 161 39 order order NOUN american_scientific_journal-3424 161 40 for for SCONJ american_scientific_journal-3424 161 41 the the DET american_scientific_journal-3424 161 42 model model NOUN american_scientific_journal-3424 161 43 to to PART american_scientific_journal-3424 161 44 be be AUX american_scientific_journal-3424 161 45 valid valid ADJ american_scientific_journal-3424 161 46 and and CCONJ american_scientific_journal-3424 161 47 allow allow VERB american_scientific_journal-3424 161 48 informing inform VERB american_scientific_journal-3424 161 49 government government NOUN american_scientific_journal-3424 161 50 policy policy NOUN american_scientific_journal-3424 161 51 , , PUNCT american_scientific_journal-3424 161 52 it it PRON american_scientific_journal-3424 161 53 obviously obviously ADV american_scientific_journal-3424 161 54 needs need VERB american_scientific_journal-3424 161 55 to to PART american_scientific_journal-3424 161 56 correspond correspond VERB american_scientific_journal-3424 161 57 fairly fairly ADV american_scientific_journal-3424 161 58 close close ADJ american_scientific_journal-3424 161 59 to to ADP american_scientific_journal-3424 161 60 reality reality NOUN american_scientific_journal-3424 161 61 . . PUNCT american_scientific_journal-3424 162 1 the the DET american_scientific_journal-3424 162 2 table-3.3.1 table-3.3.1 NOUN american_scientific_journal-3424 162 3 below below ADV american_scientific_journal-3424 162 4 compares compare VERB american_scientific_journal-3424 162 5 the the DET american_scientific_journal-3424 162 6 data datum NOUN american_scientific_journal-3424 162 7 collected collect VERB american_scientific_journal-3424 162 8 from from ADP american_scientific_journal-3424 162 9 the the DET american_scientific_journal-3424 162 10 sir sir NOUN american_scientific_journal-3424 162 11 model model NOUN american_scientific_journal-3424 162 12 ( ( PUNCT american_scientific_journal-3424 162 13 using use VERB american_scientific_journal-3424 162 14 euler euler NOUN american_scientific_journal-3424 162 15 and and CCONJ american_scientific_journal-3424 162 16 rk4 rk4 NOUN american_scientific_journal-3424 162 17 ) ) PUNCT american_scientific_journal-3424 162 18 for for ADP american_scientific_journal-3424 162 19 the the DET american_scientific_journal-3424 162 20 number number NOUN american_scientific_journal-3424 162 21 of of ADP american_scientific_journal-3424 162 22 people people NOUN american_scientific_journal-3424 162 23 infected infect VERB american_scientific_journal-3424 162 24 and and CCONJ american_scientific_journal-3424 162 25 the the DET american_scientific_journal-3424 162 26 real real ADJ american_scientific_journal-3424 162 27 life life NOUN american_scientific_journal-3424 162 28 data datum NOUN american_scientific_journal-3424 162 29 of of ADP american_scientific_journal-3424 162 30 the the DET american_scientific_journal-3424 162 31 number number NOUN american_scientific_journal-3424 162 32 of of ADP american_scientific_journal-3424 162 33 people people NOUN american_scientific_journal-3424 162 34 infected infect VERB american_scientific_journal-3424 162 35 . . PUNCT american_scientific_journal-3424 163 1 table table NOUN american_scientific_journal-3424 163 2 3.3.1 3.3.1 NUM american_scientific_journal-3424 163 3 time(days time(day NOUN american_scientific_journal-3424 163 4 ) ) PUNCT american_scientific_journal-3424 164 1 i i PRON american_scientific_journal-3424 164 2 -actual -actual ADJ american_scientific_journal-3424 164 3 ieuler ieuler NOUN american_scientific_journal-3424 164 4 i i PROPN american_scientific_journal-3424 164 5 -rk4 -rk4 PROPN american_scientific_journal-3424 164 6 time(days time(days PROPN american_scientific_journal-3424 164 7 ) ) PUNCT american_scientific_journal-3424 165 1 i i PRON american_scientific_journal-3424 165 2 -actual -actual ADJ american_scientific_journal-3424 165 3 ieuler ieuler NOUN american_scientific_journal-3424 165 4 i i PRON american_scientific_journal-3424 165 5 -rk4 -rk4 VERB american_scientific_journal-3424 165 6 1 1 NUM american_scientific_journal-3424 165 7 391 391 NUM american_scientific_journal-3424 165 8 391 391 NUM american_scientific_journal-3424 165 9 391 391 NUM american_scientific_journal-3424 165 10 35 35 NUM american_scientific_journal-3424 165 11 1871 1871 NUM american_scientific_journal-3424 165 12 1092613 1092613 NUM american_scientific_journal-3424 165 13 835770 835770 NUM american_scientific_journal-3424 165 14 2 2 NUM american_scientific_journal-3424 165 15 486 486 NUM american_scientific_journal-3424 165 16 630 630 NUM american_scientific_journal-3424 165 17 719 719 NUM american_scientific_journal-3424 165 18 37 37 NUM american_scientific_journal-3424 165 19 2046 2046 NUM american_scientific_journal-3424 165 20 905843 905843 NUM american_scientific_journal-3424 165 21 699764 699764 NUM american_scientific_journal-3424 165 22 6 6 NUM american_scientific_journal-3424 165 23 554 554 NUM american_scientific_journal-3424 165 24 4225 4225 NUM american_scientific_journal-3424 165 25 8214 8214 NUM american_scientific_journal-3424 165 26 41 41 NUM american_scientific_journal-3424 165 27 2081 2081 NUM american_scientific_journal-3424 165 28 622065 622065 NUM american_scientific_journal-3424 165 29 489905 489905 NUM american_scientific_journal-3424 165 30 10 10 NUM american_scientific_journal-3424 165 31 599 599 NUM american_scientific_journal-3424 165 32 28248 28248 NUM american_scientific_journal-3424 165 33 91623 91623 NUM american_scientific_journal-3424 165 34 45 45 NUM american_scientific_journal-3424 165 35 2407 2407 NUM american_scientific_journal-3424 165 36 426953 426953 NUM american_scientific_journal-3424 165 37 342652 342652 NUM american_scientific_journal-3424 165 38 11 11 NUM american_scientific_journal-3424 165 39 670 670 NUM american_scientific_journal-3424 165 40 45327 45327 NUM american_scientific_journal-3424 165 41 164649 164649 NUM american_scientific_journal-3424 165 42 47 47 NUM american_scientific_journal-3424 165 43 2710 2710 NUM american_scientific_journal-3424 165 44 353679 353679 NUM american_scientific_journal-3424 165 45 286506 286506 NUM american_scientific_journal-3424 165 46 13 13 NUM american_scientific_journal-3424 165 47 786 786 NUM american_scientific_journal-3424 165 48 115868 115868 NUM american_scientific_journal-3424 165 49 496967 496967 NUM american_scientific_journal-3424 165 50 51 51 NUM american_scientific_journal-3424 165 51 3022 3022 NUM american_scientific_journal-3424 165 52 242671 242671 NUM american_scientific_journal-3424 165 53 200255 200255 NUM american_scientific_journal-3424 165 54 17 17 NUM american_scientific_journal-3424 165 55 834 834 NUM american_scientific_journal-3424 165 56 687575 687575 NUM american_scientific_journal-3424 165 57 2124419 2124419 NUM american_scientific_journal-3424 165 58 53 53 NUM american_scientific_journal-3424 165 59 3280 3280 NUM american_scientific_journal-3424 165 60 201004 201004 NUM american_scientific_journal-3424 165 61 167404 167404 NUM american_scientific_journal-3424 165 62 19 19 NUM american_scientific_journal-3424 165 63 972 972 NUM american_scientific_journal-3424 165 64 1440508 1440508 NUM american_scientific_journal-3424 165 65 2580728 2580728 NUM american_scientific_journal-3424 165 66 55 55 NUM american_scientific_journal-3424 165 67 3458 3458 NUM american_scientific_journal-3424 165 68 166489 166489 NUM american_scientific_journal-3424 165 69 139937 139937 NUM american_scientific_journal-3424 165 70 20 20 NUM american_scientific_journal-3424 165 71 1082 1082 NUM american_scientific_journal-3424 165 72 1918710 1918710 NUM american_scientific_journal-3424 165 73 2605010 2605010 NUM american_scientific_journal-3424 165 74 60 60 NUM american_scientific_journal-3424 165 75 3696 3696 NUM american_scientific_journal-3424 165 76 103948 103948 NUM american_scientific_journal-3424 165 77 89389 89389 NUM american_scientific_journal-3424 165 78 26 26 NUM american_scientific_journal-3424 165 79 1378 1378 NUM american_scientific_journal-3424 165 80 2454901 2454901 NUM american_scientific_journal-3424 165 81 1819893 1819893 NUM american_scientific_journal-3424 165 82 using use VERB american_scientific_journal-3424 165 83 the the DET american_scientific_journal-3424 165 84 value value NOUN american_scientific_journal-3424 165 85 of of ADP american_scientific_journal-3424 165 86 table-3.3.1 table-3.3.1 NUM american_scientific_journal-3424 165 87 we we PRON american_scientific_journal-3424 165 88 can can AUX american_scientific_journal-3424 165 89 plot plot VERB american_scientific_journal-3424 165 90 a a DET american_scientific_journal-3424 165 91 graph graph NOUN american_scientific_journal-3424 165 92 using use VERB american_scientific_journal-3424 165 93 matlab matlab PROPN american_scientific_journal-3424 165 94 which which PRON american_scientific_journal-3424 165 95 compares compare VERB american_scientific_journal-3424 165 96 the the DET american_scientific_journal-3424 165 97 model model NOUN american_scientific_journal-3424 165 98 data datum NOUN american_scientific_journal-3424 165 99 to to ADP american_scientific_journal-3424 165 100 the the DET american_scientific_journal-3424 165 101 actual actual ADJ american_scientific_journal-3424 165 102 data datum NOUN american_scientific_journal-3424 165 103 for for ADP american_scientific_journal-3424 165 104 the the DET american_scientific_journal-3424 165 105 number number NOUN american_scientific_journal-3424 165 106 of of ADP american_scientific_journal-3424 165 107 people people NOUN american_scientific_journal-3424 165 108 infected infect VERB american_scientific_journal-3424 165 109 ( ( PUNCT american_scientific_journal-3424 165 110 figure-3.4 figure-3.4 NOUN american_scientific_journal-3424 165 111 ) ) PUNCT american_scientific_journal-3424 165 112 . . PUNCT american_scientific_journal-3424 166 1 figure figure VERB american_scientific_journal-3424 166 2 3.4 3.4 NUM american_scientific_journal-3424 166 3 as as SCONJ american_scientific_journal-3424 166 4 the the DET american_scientific_journal-3424 166 5 graph graph NOUN american_scientific_journal-3424 166 6 demonstrates demonstrate VERB american_scientific_journal-3424 166 7 , , PUNCT american_scientific_journal-3424 166 8 the the DET american_scientific_journal-3424 166 9 real real ADJ american_scientific_journal-3424 166 10 data datum NOUN american_scientific_journal-3424 166 11 does do AUX american_scientific_journal-3424 166 12 not not PART american_scientific_journal-3424 166 13 correspond correspond VERB american_scientific_journal-3424 166 14 very very ADV american_scientific_journal-3424 166 15 well well ADV american_scientific_journal-3424 166 16 to to ADP american_scientific_journal-3424 166 17 the the DET american_scientific_journal-3424 166 18 data datum NOUN american_scientific_journal-3424 166 19 received receive VERB american_scientific_journal-3424 166 20 from from ADP american_scientific_journal-3424 166 21 the the DET american_scientific_journal-3424 166 22 model model NOUN american_scientific_journal-3424 166 23 . . PUNCT american_scientific_journal-3424 167 1 although although SCONJ american_scientific_journal-3424 167 2 the the DET american_scientific_journal-3424 167 3 actual actual ADJ american_scientific_journal-3424 167 4 data datum NOUN american_scientific_journal-3424 167 5 may may AUX american_scientific_journal-3424 167 6 seem seem VERB american_scientific_journal-3424 167 7 to to PART american_scientific_journal-3424 167 8 follow follow VERB american_scientific_journal-3424 167 9 a a DET american_scientific_journal-3424 167 10 straight straight ADJ american_scientific_journal-3424 167 11 like like ADP american_scientific_journal-3424 167 12 graph graph NOUN american_scientific_journal-3424 167 13 , , PUNCT american_scientific_journal-3424 167 14 this this PRON american_scientific_journal-3424 167 15 is be AUX american_scientific_journal-3424 167 16 untrue untrue ADJ american_scientific_journal-3424 167 17 as as SCONJ american_scientific_journal-3424 167 18 it it PRON american_scientific_journal-3424 167 19 is be AUX american_scientific_journal-3424 167 20 only only ADV american_scientific_journal-3424 167 21 depicted depict VERB american_scientific_journal-3424 167 22 in in ADP american_scientific_journal-3424 167 23 this this DET american_scientific_journal-3424 167 24 american american ADJ american_scientific_journal-3424 167 25 scientific scientific ADJ american_scientific_journal-3424 167 26 research research NOUN american_scientific_journal-3424 167 27 journal journal NOUN american_scientific_journal-3424 167 28 for for ADP american_scientific_journal-3424 167 29 engineering engineering NOUN american_scientific_journal-3424 167 30 , , PUNCT american_scientific_journal-3424 167 31 technology technology NOUN american_scientific_journal-3424 167 32 , , PUNCT american_scientific_journal-3424 167 33 and and CCONJ american_scientific_journal-3424 167 34 sciences science NOUN american_scientific_journal-3424 167 35 ( ( PUNCT american_scientific_journal-3424 167 36 asrjets asrjet NOUN american_scientific_journal-3424 167 37 ) ) PUNCT american_scientific_journal-3424 167 38 ( ( PUNCT american_scientific_journal-3424 167 39 2017 2017 NUM american_scientific_journal-3424 167 40 ) ) PUNCT american_scientific_journal-3424 167 41 volume volume NOUN american_scientific_journal-3424 167 42 37 37 NUM american_scientific_journal-3424 167 43 , , PUNCT american_scientific_journal-3424 167 44 no no DET american_scientific_journal-3424 167 45 1 1 NUM american_scientific_journal-3424 167 46 , , PUNCT american_scientific_journal-3424 167 47 pp pp ADV american_scientific_journal-3424 167 48 1 1 NUM american_scientific_journal-3424 167 49 - - SYM american_scientific_journal-3424 167 50 21 21 NUM american_scientific_journal-3424 167 51 18 18 NUM american_scientific_journal-3424 167 52 manner manner NOUN american_scientific_journal-3424 167 53 due due ADP american_scientific_journal-3424 167 54 to to ADP american_scientific_journal-3424 167 55 the the DET american_scientific_journal-3424 167 56 limitations limitation NOUN american_scientific_journal-3424 167 57 on on ADP american_scientific_journal-3424 167 58 the the DET american_scientific_journal-3424 167 59 axis axis NOUN american_scientific_journal-3424 167 60 of of ADP american_scientific_journal-3424 167 61 the the DET american_scientific_journal-3424 167 62 graph graph NOUN american_scientific_journal-3424 167 63 . . PUNCT american_scientific_journal-3424 168 1 the the DET american_scientific_journal-3424 168 2 difference difference NOUN american_scientific_journal-3424 168 3 between between ADP american_scientific_journal-3424 168 4 the the DET american_scientific_journal-3424 168 5 real real ADJ american_scientific_journal-3424 168 6 life life NOUN american_scientific_journal-3424 168 7 data datum NOUN american_scientific_journal-3424 168 8 and and CCONJ american_scientific_journal-3424 168 9 the the DET american_scientific_journal-3424 168 10 data datum NOUN american_scientific_journal-3424 168 11 from from ADP american_scientific_journal-3424 168 12 the the DET american_scientific_journal-3424 168 13 model model NOUN american_scientific_journal-3424 168 14 is be AUX american_scientific_journal-3424 168 15 so so ADV american_scientific_journal-3424 168 16 vast vast ADJ american_scientific_journal-3424 168 17 that that SCONJ american_scientific_journal-3424 168 18 the the DET american_scientific_journal-3424 168 19 straight straight ADJ american_scientific_journal-3424 168 20 line line NOUN american_scientific_journal-3424 168 21 looks look VERB american_scientific_journal-3424 168 22 like like ADP american_scientific_journal-3424 168 23 a a DET american_scientific_journal-3424 168 24 graph graph NOUN american_scientific_journal-3424 168 25 of of ADP american_scientific_journal-3424 168 26 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-3424 168 27 = = PROPN american_scientific_journal-3424 168 28 0 0 PROPN american_scientific_journal-3424 168 29 . . PUNCT american_scientific_journal-3424 169 1 therefore therefore ADV american_scientific_journal-3424 169 2 , , PUNCT american_scientific_journal-3424 169 3 we we PRON american_scientific_journal-3424 169 4 decided decide VERB american_scientific_journal-3424 169 5 to to PART american_scientific_journal-3424 169 6 plot plot VERB american_scientific_journal-3424 169 7 it it PRON american_scientific_journal-3424 169 8 separately separately ADV american_scientific_journal-3424 169 9 ( ( PUNCT american_scientific_journal-3424 169 10 figure-3.5 figure-3.5 PROPN american_scientific_journal-3424 169 11 ) ) PUNCT american_scientific_journal-3424 169 12 . . PUNCT american_scientific_journal-3424 170 1 figure figure VERB american_scientific_journal-3424 170 2 3.5 3.5 NUM american_scientific_journal-3424 170 3 3.4 3.4 NUM american_scientific_journal-3424 170 4 curve curve NOUN american_scientific_journal-3424 170 5 fitting fit VERB american_scientific_journal-3424 170 6 with with ADP american_scientific_journal-3424 170 7 actual actual ADJ american_scientific_journal-3424 170 8 data datum NOUN american_scientific_journal-3424 170 9 the the DET american_scientific_journal-3424 170 10 model model NOUN american_scientific_journal-3424 170 11 has have AUX american_scientific_journal-3424 170 12 significantly significantly ADV american_scientific_journal-3424 170 13 overestimated overestimate VERB american_scientific_journal-3424 170 14 the the DET american_scientific_journal-3424 170 15 number number NOUN american_scientific_journal-3424 170 16 of of ADP american_scientific_journal-3424 170 17 individuals individual NOUN american_scientific_journal-3424 170 18 who who PRON american_scientific_journal-3424 170 19 can can AUX american_scientific_journal-3424 170 20 become become VERB american_scientific_journal-3424 170 21 infected infected ADJ american_scientific_journal-3424 170 22 with with ADP american_scientific_journal-3424 170 23 ebola ebola PROPN american_scientific_journal-3424 170 24 fever fever NOUN american_scientific_journal-3424 170 25 . . PUNCT american_scientific_journal-3424 171 1 this this PRON american_scientific_journal-3424 171 2 is be AUX american_scientific_journal-3424 171 3 often often ADV american_scientific_journal-3424 171 4 because because SCONJ american_scientific_journal-3424 171 5 of of ADP american_scientific_journal-3424 171 6 the the DET american_scientific_journal-3424 171 7 many many ADJ american_scientific_journal-3424 171 8 limitations limitation NOUN american_scientific_journal-3424 171 9 that that SCONJ american_scientific_journal-3424 171 10 the the DET american_scientific_journal-3424 171 11 model model NOUN american_scientific_journal-3424 171 12 presents present VERB american_scientific_journal-3424 171 13 . . PUNCT american_scientific_journal-3424 172 1 one one NUM american_scientific_journal-3424 172 2 of of ADP american_scientific_journal-3424 172 3 the the DET american_scientific_journal-3424 172 4 main main ADJ american_scientific_journal-3424 172 5 limitations limitation NOUN american_scientific_journal-3424 172 6 includes include VERB american_scientific_journal-3424 172 7 the the DET american_scientific_journal-3424 172 8 incorrect incorrect ADJ american_scientific_journal-3424 172 9 beta beta NOUN american_scientific_journal-3424 172 10 and and CCONJ american_scientific_journal-3424 172 11 gamma gamma NOUN american_scientific_journal-3424 172 12 values value NOUN american_scientific_journal-3424 172 13 that that PRON american_scientific_journal-3424 172 14 were be AUX american_scientific_journal-3424 172 15 calculated calculate VERB american_scientific_journal-3424 172 16 . . PUNCT american_scientific_journal-3424 173 1 once once ADV american_scientific_journal-3424 173 2 fixing fix VERB american_scientific_journal-3424 173 3 the the DET american_scientific_journal-3424 173 4 beta beta NOUN american_scientific_journal-3424 173 5 and and CCONJ american_scientific_journal-3424 173 6 gamma gamma NOUN american_scientific_journal-3424 173 7 values value NOUN american_scientific_journal-3424 173 8 , , PUNCT american_scientific_journal-3424 173 9 we we PRON american_scientific_journal-3424 173 10 were be AUX american_scientific_journal-3424 173 11 able able ADJ american_scientific_journal-3424 173 12 to to PART american_scientific_journal-3424 173 13 find find VERB american_scientific_journal-3424 173 14 another another DET american_scientific_journal-3424 173 15 gamma gamma NOUN american_scientific_journal-3424 173 16 value value NOUN american_scientific_journal-3424 173 17 that that PRON american_scientific_journal-3424 173 18 resulted result VERB american_scientific_journal-3424 173 19 in in ADP american_scientific_journal-3424 173 20 similar similar ADJ american_scientific_journal-3424 173 21 values value NOUN american_scientific_journal-3424 173 22 to to ADP american_scientific_journal-3424 173 23 the the DET american_scientific_journal-3424 173 24 real real ADJ american_scientific_journal-3424 173 25 data datum NOUN american_scientific_journal-3424 173 26 . . PUNCT american_scientific_journal-3424 174 1 here here ADV american_scientific_journal-3424 174 2 is be AUX american_scientific_journal-3424 174 3 that that SCONJ american_scientific_journal-3424 174 4 the the DET american_scientific_journal-3424 174 5 graph graph NOUN american_scientific_journal-3424 174 6 to to PART american_scientific_journal-3424 174 7 indicate indicate VERB american_scientific_journal-3424 174 8 this this PRON american_scientific_journal-3424 174 9 , , PUNCT american_scientific_journal-3424 174 10 with with ADP american_scientific_journal-3424 174 11 the the DET american_scientific_journal-3424 174 12 suitable suitable ADJ american_scientific_journal-3424 174 13 gamma gamma NOUN american_scientific_journal-3424 174 14 value value NOUN american_scientific_journal-3424 174 15 of of ADP american_scientific_journal-3424 174 16 0.66 0.66 NUM american_scientific_journal-3424 174 17 . . PUNCT american_scientific_journal-3424 175 1 the the DET american_scientific_journal-3424 175 2 table-3.4.1 table-3.4.1 NOUN american_scientific_journal-3424 175 3 below below ADV american_scientific_journal-3424 175 4 compares compare VERB american_scientific_journal-3424 175 5 the the DET american_scientific_journal-3424 175 6 data datum NOUN american_scientific_journal-3424 175 7 collected collect VERB american_scientific_journal-3424 175 8 from from ADP american_scientific_journal-3424 175 9 the the DET american_scientific_journal-3424 175 10 fitted fit VERB american_scientific_journal-3424 175 11 model model NOUN american_scientific_journal-3424 175 12 for for ADP american_scientific_journal-3424 175 13 the the DET american_scientific_journal-3424 175 14 number number NOUN american_scientific_journal-3424 175 15 of of ADP american_scientific_journal-3424 175 16 people people NOUN american_scientific_journal-3424 175 17 infected infect VERB american_scientific_journal-3424 175 18 and and CCONJ american_scientific_journal-3424 175 19 the the DET american_scientific_journal-3424 175 20 real real ADJ american_scientific_journal-3424 175 21 life life NOUN american_scientific_journal-3424 175 22 data datum NOUN american_scientific_journal-3424 175 23 of of ADP american_scientific_journal-3424 175 24 the the DET american_scientific_journal-3424 175 25 number number NOUN american_scientific_journal-3424 175 26 of of ADP american_scientific_journal-3424 175 27 people people NOUN american_scientific_journal-3424 175 28 infected infect VERB american_scientific_journal-3424 175 29 . . PUNCT american_scientific_journal-3424 176 1 table-3.4.1 table-3.4.1 X american_scientific_journal-3424 176 2 time(days time(day NOUN american_scientific_journal-3424 176 3 ) ) PUNCT american_scientific_journal-3424 177 1 i i PRON american_scientific_journal-3424 177 2 -actual -actual ADJ american_scientific_journal-3424 177 3 ieuler ieuler NOUN american_scientific_journal-3424 177 4 i i PROPN american_scientific_journal-3424 177 5 -rk4 -rk4 PROPN american_scientific_journal-3424 177 6 time(days time(days PROPN american_scientific_journal-3424 177 7 ) ) PUNCT american_scientific_journal-3424 178 1 i i PRON american_scientific_journal-3424 178 2 -actual -actual ADJ american_scientific_journal-3424 178 3 ieuler ieuler NOUN american_scientific_journal-3424 178 4 i i PRON american_scientific_journal-3424 178 5 -rk4 -rk4 VERB american_scientific_journal-3424 178 6 1 1 NUM american_scientific_journal-3424 178 7 391 391 NUM american_scientific_journal-3424 178 8 391 391 NUM american_scientific_journal-3424 178 9 391 391 NUM american_scientific_journal-3424 178 10 35 35 NUM american_scientific_journal-3424 178 11 1871 1871 NUM american_scientific_journal-3424 178 12 1555 1555 NUM american_scientific_journal-3424 178 13 1419 1419 NUM american_scientific_journal-3424 178 14 2 2 NUM american_scientific_journal-3424 178 15 486 486 NUM american_scientific_journal-3424 178 16 408 408 NUM american_scientific_journal-3424 178 17 407 407 NUM american_scientific_journal-3424 178 18 37 37 NUM american_scientific_journal-3424 178 19 2046 2046 NUM american_scientific_journal-3424 178 20 1679 1679 NUM american_scientific_journal-3424 178 21 1525 1525 NUM american_scientific_journal-3424 178 22 6 6 NUM american_scientific_journal-3424 178 23 554 554 NUM american_scientific_journal-3424 178 24 482 482 NUM american_scientific_journal-3424 178 25 475 475 NUM american_scientific_journal-3424 178 26 41 41 NUM american_scientific_journal-3424 178 27 2081 2081 NUM american_scientific_journal-3424 178 28 1952 1952 NUM american_scientific_journal-3424 178 29 1758 1758 NUM american_scientific_journal-3424 178 30 10 10 NUM american_scientific_journal-3424 178 31 599 599 NUM american_scientific_journal-3424 178 32 569 569 NUM american_scientific_journal-3424 178 33 555 555 NUM american_scientific_journal-3424 178 34 45 45 NUM american_scientific_journal-3424 178 35 2407 2407 NUM american_scientific_journal-3424 178 36 2261 2261 NUM american_scientific_journal-3424 178 37 2020 2020 NUM american_scientific_journal-3424 178 38 11 11 NUM american_scientific_journal-3424 178 39 670 670 NUM american_scientific_journal-3424 178 40 593 593 NUM american_scientific_journal-3424 178 41 576 576 NUM american_scientific_journal-3424 178 42 47 47 NUM american_scientific_journal-3424 178 43 2710 2710 NUM american_scientific_journal-3424 178 44 2430 2430 NUM american_scientific_journal-3424 178 45 2163 2163 NUM american_scientific_journal-3424 178 46 13 13 NUM american_scientific_journal-3424 178 47 786 786 NUM american_scientific_journal-3424 178 48 644 644 NUM american_scientific_journal-3424 178 49 623 623 NUM american_scientific_journal-3424 178 50 51 51 NUM american_scientific_journal-3424 178 51 3022 3022 NUM american_scientific_journal-3424 178 52 2796 2796 NUM american_scientific_journal-3424 178 53 2472 2472 NUM american_scientific_journal-3424 178 54 17 17 NUM american_scientific_journal-3424 178 55 834 834 NUM american_scientific_journal-3424 178 56 759 759 NUM american_scientific_journal-3424 178 57 726 726 NUM american_scientific_journal-3424 178 58 53 53 NUM american_scientific_journal-3424 178 59 3280 3280 NUM american_scientific_journal-3424 178 60 2994 2994 NUM american_scientific_journal-3424 178 61 2639 2639 NUM american_scientific_journal-3424 178 62 19 19 NUM american_scientific_journal-3424 178 63 972 972 NUM american_scientific_journal-3424 178 64 824 824 NUM american_scientific_journal-3424 178 65 783 783 NUM american_scientific_journal-3424 178 66 55 55 NUM american_scientific_journal-3424 178 67 3458 3458 NUM american_scientific_journal-3424 178 68 3201 3201 NUM american_scientific_journal-3424 178 69 2814 2814 NUM american_scientific_journal-3424 178 70 20 20 NUM american_scientific_journal-3424 178 71 1082 1082 NUM american_scientific_journal-3424 178 72 858 858 NUM american_scientific_journal-3424 178 73 813 813 NUM american_scientific_journal-3424 178 74 60 60 NUM american_scientific_journal-3424 178 75 3696 3696 NUM american_scientific_journal-3424 178 76 3757 3757 NUM american_scientific_journal-3424 178 77 3287 3287 NUM american_scientific_journal-3424 178 78 26 26 NUM american_scientific_journal-3424 178 79 1378 1378 NUM american_scientific_journal-3424 178 80 1092 1092 NUM american_scientific_journal-3424 178 81 1019 1019 NUM american_scientific_journal-3424 178 82 american american PROPN american_scientific_journal-3424 178 83 scientific scientific ADJ american_scientific_journal-3424 178 84 research research NOUN american_scientific_journal-3424 178 85 journal journal NOUN american_scientific_journal-3424 178 86 for for ADP american_scientific_journal-3424 178 87 engineering engineering NOUN american_scientific_journal-3424 178 88 , , PUNCT american_scientific_journal-3424 178 89 technology technology NOUN american_scientific_journal-3424 178 90 , , PUNCT american_scientific_journal-3424 178 91 and and CCONJ american_scientific_journal-3424 178 92 sciences science NOUN american_scientific_journal-3424 178 93 ( ( PUNCT american_scientific_journal-3424 178 94 asrjets asrjet NOUN american_scientific_journal-3424 178 95 ) ) PUNCT american_scientific_journal-3424 178 96 ( ( PUNCT american_scientific_journal-3424 178 97 2017 2017 NUM american_scientific_journal-3424 178 98 ) ) PUNCT american_scientific_journal-3424 178 99 volume volume NOUN american_scientific_journal-3424 178 100 37 37 NUM american_scientific_journal-3424 178 101 , , PUNCT american_scientific_journal-3424 178 102 no no DET american_scientific_journal-3424 178 103 1 1 NUM american_scientific_journal-3424 178 104 , , PUNCT american_scientific_journal-3424 178 105 pp pp ADV american_scientific_journal-3424 178 106 1 1 NUM american_scientific_journal-3424 178 107 - - SYM american_scientific_journal-3424 178 108 21 21 NUM american_scientific_journal-3424 178 109 19 19 NUM american_scientific_journal-3424 178 110 using use VERB american_scientific_journal-3424 178 111 the the DET american_scientific_journal-3424 178 112 value value NOUN american_scientific_journal-3424 178 113 of of ADP american_scientific_journal-3424 178 114 table-3.4.1 table-3.4.1 NUM american_scientific_journal-3424 178 115 we we PRON american_scientific_journal-3424 178 116 can can AUX american_scientific_journal-3424 178 117 plot plot VERB american_scientific_journal-3424 178 118 a a DET american_scientific_journal-3424 178 119 graph graph NOUN american_scientific_journal-3424 178 120 using use VERB american_scientific_journal-3424 178 121 matlab matlab PROPN american_scientific_journal-3424 178 122 which which PRON american_scientific_journal-3424 178 123 compares compare VERB american_scientific_journal-3424 178 124 curve curve NOUN american_scientific_journal-3424 178 125 fitted fit VERB american_scientific_journal-3424 178 126 data datum NOUN american_scientific_journal-3424 178 127 with with ADP american_scientific_journal-3424 178 128 real real ADJ american_scientific_journal-3424 178 129 data datum NOUN american_scientific_journal-3424 178 130 for for ADP american_scientific_journal-3424 178 131 the the DET american_scientific_journal-3424 178 132 number number NOUN american_scientific_journal-3424 178 133 of of ADP american_scientific_journal-3424 178 134 people people NOUN american_scientific_journal-3424 178 135 infected infect VERB american_scientific_journal-3424 178 136 ( ( PUNCT american_scientific_journal-3424 178 137 figure-3.6 figure-3.6 PROPN american_scientific_journal-3424 178 138 ) ) PUNCT american_scientific_journal-3424 178 139 . . PUNCT american_scientific_journal-3424 179 1 figure figure VERB american_scientific_journal-3424 179 2 3.6 3.6 NUM american_scientific_journal-3424 179 3 3.5 3.5 NUM american_scientific_journal-3424 179 4 result result NOUN american_scientific_journal-3424 179 5 discussion discussion NOUN american_scientific_journal-3424 179 6 although although SCONJ american_scientific_journal-3424 179 7 , , PUNCT american_scientific_journal-3424 179 8 this this PRON american_scientific_journal-3424 179 9 does do AUX american_scientific_journal-3424 179 10 n't not PART american_scientific_journal-3424 179 11 match match VERB american_scientific_journal-3424 179 12 the the DET american_scientific_journal-3424 179 13 graph graph NOUN american_scientific_journal-3424 179 14 exactly exactly ADV american_scientific_journal-3424 179 15 , , PUNCT american_scientific_journal-3424 179 16 it it PRON american_scientific_journal-3424 179 17 shows show VERB american_scientific_journal-3424 179 18 a a DET american_scientific_journal-3424 179 19 much much ADV american_scientific_journal-3424 179 20 better well ADJ american_scientific_journal-3424 179 21 correlation correlation NOUN american_scientific_journal-3424 179 22 of of ADP american_scientific_journal-3424 179 23 the the DET american_scientific_journal-3424 179 24 number number NOUN american_scientific_journal-3424 179 25 of of ADP american_scientific_journal-3424 179 26 individuals individual NOUN american_scientific_journal-3424 179 27 infected infect VERB american_scientific_journal-3424 179 28 . . PUNCT american_scientific_journal-3424 180 1 between between ADP american_scientific_journal-3424 180 2 euler euler PROPN american_scientific_journal-3424 180 3 and and CCONJ american_scientific_journal-3424 180 4 rk4 rk4 PROPN american_scientific_journal-3424 180 5 technique technique NOUN american_scientific_journal-3424 180 6 , , PUNCT american_scientific_journal-3424 180 7 rk4 rk4 NOUN american_scientific_journal-3424 180 8 provides provide VERB american_scientific_journal-3424 180 9 better well ADJ american_scientific_journal-3424 180 10 correlation correlation NOUN american_scientific_journal-3424 180 11 as as SCONJ american_scientific_journal-3424 180 12 because because SCONJ american_scientific_journal-3424 180 13 rk4 rk4 NOUN american_scientific_journal-3424 180 14 methods method NOUN american_scientific_journal-3424 180 15 divide divide VERB american_scientific_journal-3424 180 16 its its PRON american_scientific_journal-3424 180 17 step step NOUN american_scientific_journal-3424 180 18 size size NOUN american_scientific_journal-3424 180 19 more more ADJ american_scientific_journal-3424 180 20 than than ADP american_scientific_journal-3424 180 21 euler euler NOUN american_scientific_journal-3424 180 22 methods method NOUN american_scientific_journal-3424 180 23 and and CCONJ american_scientific_journal-3424 180 24 the the DET american_scientific_journal-3424 180 25 local local ADJ american_scientific_journal-3424 180 26 truncation truncation NOUN american_scientific_journal-3424 180 27 error error NOUN american_scientific_journal-3424 180 28 is be AUX american_scientific_journal-3424 180 29 less less ADJ american_scientific_journal-3424 180 30 than than ADP american_scientific_journal-3424 180 31 euler euler NOUN american_scientific_journal-3424 180 32 methods method NOUN american_scientific_journal-3424 180 33 . . PUNCT american_scientific_journal-3424 181 1 therefore therefore ADV american_scientific_journal-3424 181 2 , , PUNCT american_scientific_journal-3424 181 3 in in ADP american_scientific_journal-3424 181 4 order order NOUN american_scientific_journal-3424 181 5 to to PART american_scientific_journal-3424 181 6 improve improve VERB american_scientific_journal-3424 181 7 the the DET american_scientific_journal-3424 181 8 model model NOUN american_scientific_journal-3424 181 9 , , PUNCT american_scientific_journal-3424 181 10 many many ADJ american_scientific_journal-3424 181 11 changes change NOUN american_scientific_journal-3424 181 12 should should AUX american_scientific_journal-3424 181 13 be be AUX american_scientific_journal-3424 181 14 done do VERB american_scientific_journal-3424 181 15 , , PUNCT american_scientific_journal-3424 181 16 together together ADV american_scientific_journal-3424 181 17 with with ADP american_scientific_journal-3424 181 18 altering alter VERB american_scientific_journal-3424 181 19 the the DET american_scientific_journal-3424 181 20 gamma gamma NOUN american_scientific_journal-3424 181 21 value value NOUN american_scientific_journal-3424 181 22 . . PUNCT american_scientific_journal-3424 182 1 the the DET american_scientific_journal-3424 182 2 value value NOUN american_scientific_journal-3424 182 3 that that PRON american_scientific_journal-3424 182 4 we we PRON american_scientific_journal-3424 182 5 eventually eventually ADV american_scientific_journal-3424 182 6 used use VERB american_scientific_journal-3424 182 7 to to PART american_scientific_journal-3424 182 8 alter alter VERB american_scientific_journal-3424 182 9 the the DET american_scientific_journal-3424 182 10 model model NOUN american_scientific_journal-3424 182 11 , , PUNCT american_scientific_journal-3424 182 12 led lead VERB american_scientific_journal-3424 182 13 to to ADP american_scientific_journal-3424 182 14 being be AUX american_scientific_journal-3424 182 15 in in ADP american_scientific_journal-3424 182 16 2 2 NUM american_scientific_journal-3424 182 17 decimal decimal ADJ american_scientific_journal-3424 182 18 places place NOUN american_scientific_journal-3424 182 19 . . PUNCT american_scientific_journal-3424 183 1 this this PRON american_scientific_journal-3424 183 2 goes go VERB american_scientific_journal-3424 183 3 to to PART american_scientific_journal-3424 183 4 illustrate illustrate VERB american_scientific_journal-3424 183 5 the the DET american_scientific_journal-3424 183 6 necessary necessary ADJ american_scientific_journal-3424 183 7 precision precision NOUN american_scientific_journal-3424 183 8 required require VERB american_scientific_journal-3424 183 9 as as ADP american_scientific_journal-3424 183 10 very very ADV american_scientific_journal-3424 183 11 little little ADJ american_scientific_journal-3424 183 12 deviance deviance NOUN american_scientific_journal-3424 183 13 will will AUX american_scientific_journal-3424 183 14 cause cause VERB american_scientific_journal-3424 183 15 massive massive ADJ american_scientific_journal-3424 183 16 changes change NOUN american_scientific_journal-3424 183 17 . . PUNCT american_scientific_journal-3424 184 1 this this PRON american_scientific_journal-3424 184 2 can can AUX american_scientific_journal-3424 184 3 be be AUX american_scientific_journal-3424 184 4 because because SCONJ american_scientific_journal-3424 184 5 ; ; PUNCT american_scientific_journal-3424 184 6 the the DET american_scientific_journal-3424 184 7 gamma gamma NOUN american_scientific_journal-3424 184 8 is be AUX american_scientific_journal-3424 184 9 calculated calculate VERB american_scientific_journal-3424 184 10 through through ADP american_scientific_journal-3424 184 11 extreme extreme ADJ american_scientific_journal-3424 184 12 simplification simplification NOUN american_scientific_journal-3424 184 13 , , PUNCT american_scientific_journal-3424 184 14 leaving leave VERB american_scientific_journal-3424 184 15 great great ADJ american_scientific_journal-3424 184 16 possibilities possibility NOUN american_scientific_journal-3424 184 17 for for ADP american_scientific_journal-3424 184 18 more more ADJ american_scientific_journal-3424 184 19 room room NOUN american_scientific_journal-3424 184 20 for for ADP american_scientific_journal-3424 184 21 errors error NOUN american_scientific_journal-3424 184 22 . . PUNCT american_scientific_journal-3424 185 1 furthermore furthermore ADV american_scientific_journal-3424 185 2 , , PUNCT american_scientific_journal-3424 185 3 it it PRON american_scientific_journal-3424 185 4 is be AUX american_scientific_journal-3424 185 5 tough tough ADJ american_scientific_journal-3424 185 6 to to PART american_scientific_journal-3424 185 7 differentiate differentiate VERB american_scientific_journal-3424 185 8 between between ADP american_scientific_journal-3424 185 9 the the DET american_scientific_journal-3424 185 10 numbers number NOUN american_scientific_journal-3424 185 11 of of ADP american_scientific_journal-3424 185 12 people people NOUN american_scientific_journal-3424 185 13 who who PRON american_scientific_journal-3424 185 14 have have AUX american_scientific_journal-3424 185 15 died die VERB american_scientific_journal-3424 185 16 and and CCONJ american_scientific_journal-3424 185 17 also also ADV american_scientific_journal-3424 185 18 the the DET american_scientific_journal-3424 185 19 numbers number NOUN american_scientific_journal-3424 185 20 of of ADP american_scientific_journal-3424 185 21 people people NOUN american_scientific_journal-3424 185 22 who who PRON american_scientific_journal-3424 185 23 have have AUX american_scientific_journal-3424 185 24 survived survive VERB american_scientific_journal-3424 185 25 with with ADP american_scientific_journal-3424 185 26 permanent permanent ADJ american_scientific_journal-3424 185 27 immunity immunity NOUN american_scientific_journal-3424 185 28 as as SCONJ american_scientific_journal-3424 185 29 they they PRON american_scientific_journal-3424 185 30 both both PRON american_scientific_journal-3424 185 31 fall fall VERB american_scientific_journal-3424 185 32 under under ADP american_scientific_journal-3424 185 33 the the DET american_scientific_journal-3424 185 34 same same ADJ american_scientific_journal-3424 185 35 class class NOUN american_scientific_journal-3424 185 36 of of ADP american_scientific_journal-3424 185 37 being be AUX american_scientific_journal-3424 185 38 β€˜ ' PUNCT american_scientific_journal-3424 185 39 recovered recover VERB american_scientific_journal-3424 185 40 ’ ' PUNCT american_scientific_journal-3424 185 41 . . PUNCT american_scientific_journal-3424 186 1 it it PRON american_scientific_journal-3424 186 2 is be AUX american_scientific_journal-3424 186 3 also also ADV american_scientific_journal-3424 186 4 a a DET american_scientific_journal-3424 186 5 fact fact NOUN american_scientific_journal-3424 186 6 that that SCONJ american_scientific_journal-3424 186 7 rate rate NOUN american_scientific_journal-3424 186 8 of of ADP american_scientific_journal-3424 186 9 recovery recovery NOUN american_scientific_journal-3424 186 10 is be AUX american_scientific_journal-3424 186 11 faster fast ADJ american_scientific_journal-3424 186 12 that that SCONJ american_scientific_journal-3424 186 13 the the DET american_scientific_journal-3424 186 14 time time NOUN american_scientific_journal-3424 186 15 scale scale NOUN american_scientific_journal-3424 186 16 of of ADP american_scientific_journal-3424 186 17 birth birth NOUN american_scientific_journal-3424 186 18 and and CCONJ american_scientific_journal-3424 186 19 death death NOUN american_scientific_journal-3424 186 20 . . PUNCT american_scientific_journal-3424 187 1 the the DET american_scientific_journal-3424 187 2 infection infection NOUN american_scientific_journal-3424 187 3 rate rate NOUN american_scientific_journal-3424 187 4 and and CCONJ american_scientific_journal-3424 187 5 recovery recovery NOUN american_scientific_journal-3424 187 6 rate rate NOUN american_scientific_journal-3424 187 7 plays play VERB american_scientific_journal-3424 187 8 a a DET american_scientific_journal-3424 187 9 vital vital ADJ american_scientific_journal-3424 187 10 role role NOUN american_scientific_journal-3424 187 11 in in ADP american_scientific_journal-3424 187 12 the the DET american_scientific_journal-3424 187 13 model model NOUN american_scientific_journal-3424 187 14 and and CCONJ american_scientific_journal-3424 187 15 in in ADP american_scientific_journal-3424 187 16 this this DET american_scientific_journal-3424 187 17 method method NOUN american_scientific_journal-3424 187 18 we we PRON american_scientific_journal-3424 187 19 find find VERB american_scientific_journal-3424 187 20 more more ADV american_scientific_journal-3424 187 21 accurate accurate ADJ american_scientific_journal-3424 187 22 value value NOUN american_scientific_journal-3424 187 23 of of ADP american_scientific_journal-3424 187 24 infection infection NOUN american_scientific_journal-3424 187 25 rate rate NOUN american_scientific_journal-3424 187 26 and and CCONJ american_scientific_journal-3424 187 27 recovery recovery NOUN american_scientific_journal-3424 187 28 rate rate NOUN american_scientific_journal-3424 187 29 to to PART american_scientific_journal-3424 187 30 fit fit VERB american_scientific_journal-3424 187 31 the the DET american_scientific_journal-3424 187 32 model model NOUN american_scientific_journal-3424 187 33 with with ADP american_scientific_journal-3424 187 34 the the DET american_scientific_journal-3424 187 35 actual actual ADJ american_scientific_journal-3424 187 36 data datum NOUN american_scientific_journal-3424 187 37 collected collect VERB american_scientific_journal-3424 187 38 from from ADP american_scientific_journal-3424 187 39 cdc cdc PROPN american_scientific_journal-3424 187 40 . . PROPN american_scientific_journal-3424 188 1 4 4 X american_scientific_journal-3424 188 2 . . X american_scientific_journal-3424 188 3 conclusion conclusion NOUN american_scientific_journal-3424 188 4 the the DET american_scientific_journal-3424 188 5 results result NOUN american_scientific_journal-3424 188 6 obtained obtain VERB american_scientific_journal-3424 188 7 from from ADP american_scientific_journal-3424 188 8 modeling model VERB american_scientific_journal-3424 188 9 data datum NOUN american_scientific_journal-3424 188 10 will will AUX american_scientific_journal-3424 188 11 lead lead VERB american_scientific_journal-3424 188 12 to to ADP american_scientific_journal-3424 188 13 completely completely ADV american_scientific_journal-3424 188 14 different different ADJ american_scientific_journal-3424 188 15 views view NOUN american_scientific_journal-3424 188 16 and and CCONJ american_scientific_journal-3424 188 17 interpretations interpretation NOUN american_scientific_journal-3424 188 18 . . PUNCT american_scientific_journal-3424 189 1 this this PRON american_scientific_journal-3424 189 2 is be AUX american_scientific_journal-3424 189 3 due due ADJ american_scientific_journal-3424 189 4 to to ADP american_scientific_journal-3424 189 5 the the DET american_scientific_journal-3424 189 6 unequal unequal ADJ american_scientific_journal-3424 189 7 distribution distribution NOUN american_scientific_journal-3424 189 8 of of ADP american_scientific_journal-3424 189 9 knowledge knowledge NOUN american_scientific_journal-3424 189 10 across across ADP american_scientific_journal-3424 189 11 the the DET american_scientific_journal-3424 189 12 globe globe NOUN american_scientific_journal-3424 189 13 whereby whereby SCONJ american_scientific_journal-3424 189 14 in in ADP american_scientific_journal-3424 189 15 countries country NOUN american_scientific_journal-3424 189 16 like like ADP american_scientific_journal-3424 189 17 liberia liberia PROPN american_scientific_journal-3424 189 18 , , PUNCT american_scientific_journal-3424 189 19 there there PRON american_scientific_journal-3424 189 20 is be VERB american_scientific_journal-3424 189 21 little little ADJ american_scientific_journal-3424 189 22 access access NOUN american_scientific_journal-3424 189 23 to to ADP american_scientific_journal-3424 189 24 the the DET american_scientific_journal-3424 189 25 statistics statistic NOUN american_scientific_journal-3424 189 26 which which PRON american_scientific_journal-3424 189 27 makes make VERB american_scientific_journal-3424 189 28 it it PRON american_scientific_journal-3424 189 29 troublesome troublesome ADJ american_scientific_journal-3424 189 30 to to PART american_scientific_journal-3424 189 31 form form VERB american_scientific_journal-3424 189 32 constructive constructive ADJ american_scientific_journal-3424 189 33 predictions prediction NOUN american_scientific_journal-3424 189 34 regarding regard VERB american_scientific_journal-3424 189 35 the the DET american_scientific_journal-3424 189 36 outbreak outbreak NOUN american_scientific_journal-3424 189 37 . . PUNCT american_scientific_journal-3424 190 1 through through ADP american_scientific_journal-3424 190 2 our our PRON american_scientific_journal-3424 190 3 research research NOUN american_scientific_journal-3424 190 4 , , PUNCT american_scientific_journal-3424 190 5 we we PRON american_scientific_journal-3424 190 6 have have AUX american_scientific_journal-3424 190 7 gained gain VERB american_scientific_journal-3424 190 8 further further ADJ american_scientific_journal-3424 190 9 insight insight NOUN american_scientific_journal-3424 190 10 into into ADP american_scientific_journal-3424 190 11 the the DET american_scientific_journal-3424 190 12 uses use NOUN american_scientific_journal-3424 190 13 of of ADP american_scientific_journal-3424 190 14 mathematical mathematical ADJ american_scientific_journal-3424 190 15 modeling modeling NOUN american_scientific_journal-3424 190 16 so so SCONJ american_scientific_journal-3424 190 17 as as SCONJ american_scientific_journal-3424 190 18 to to PART american_scientific_journal-3424 190 19 work work VERB american_scientific_journal-3424 190 20 out out ADP american_scientific_journal-3424 190 21 the the DET american_scientific_journal-3424 190 22 outbreak outbreak NOUN american_scientific_journal-3424 190 23 of of ADP american_scientific_journal-3424 190 24 diseases disease NOUN american_scientific_journal-3424 190 25 similarly similarly ADV american_scientific_journal-3424 190 26 as as ADP american_scientific_journal-3424 190 27 evaluating evaluate VERB american_scientific_journal-3424 190 28 its its PRON american_scientific_journal-3424 190 29 flaws flaw NOUN american_scientific_journal-3424 190 30 . . PUNCT american_scientific_journal-3424 191 1 having having AUX american_scientific_journal-3424 191 2 chosen choose VERB american_scientific_journal-3424 191 3 ebola ebola PROPN american_scientific_journal-3424 191 4 as as ADP american_scientific_journal-3424 191 5 the the DET american_scientific_journal-3424 191 6 diseases disease NOUN american_scientific_journal-3424 191 7 of of ADP american_scientific_journal-3424 191 8 concentration concentration NOUN american_scientific_journal-3424 191 9 , , PUNCT american_scientific_journal-3424 191 10 as as SCONJ american_scientific_journal-3424 191 11 it it PRON american_scientific_journal-3424 191 12 is be AUX american_scientific_journal-3424 191 13 incredibly incredibly ADV american_scientific_journal-3424 191 14 relevant relevant ADJ american_scientific_journal-3424 191 15 to to ADP american_scientific_journal-3424 191 16 this this DET american_scientific_journal-3424 191 17 situation situation NOUN american_scientific_journal-3424 191 18 in in ADP american_scientific_journal-3424 191 19 continent continent NOUN american_scientific_journal-3424 191 20 , , PUNCT american_scientific_journal-3424 191 21 it it PRON american_scientific_journal-3424 191 22 has have AUX american_scientific_journal-3424 191 23 enabled enable VERB american_scientific_journal-3424 191 24 a a DET american_scientific_journal-3424 191 25 practical practical ADJ american_scientific_journal-3424 191 26 understanding understanding NOUN american_scientific_journal-3424 191 27 of of ADP american_scientific_journal-3424 191 28 its its PRON american_scientific_journal-3424 191 29 rate rate NOUN american_scientific_journal-3424 191 30 of of ADP american_scientific_journal-3424 191 31 american american ADJ american_scientific_journal-3424 191 32 scientific scientific ADJ american_scientific_journal-3424 191 33 research research NOUN american_scientific_journal-3424 191 34 journal journal NOUN american_scientific_journal-3424 191 35 for for ADP american_scientific_journal-3424 191 36 engineering engineering NOUN american_scientific_journal-3424 191 37 , , PUNCT american_scientific_journal-3424 191 38 technology technology NOUN american_scientific_journal-3424 191 39 , , PUNCT american_scientific_journal-3424 191 40 and and CCONJ american_scientific_journal-3424 191 41 sciences science NOUN american_scientific_journal-3424 191 42 ( ( PUNCT american_scientific_journal-3424 191 43 asrjets asrjet NOUN american_scientific_journal-3424 191 44 ) ) PUNCT american_scientific_journal-3424 191 45 ( ( PUNCT american_scientific_journal-3424 191 46 2017 2017 NUM american_scientific_journal-3424 191 47 ) ) PUNCT american_scientific_journal-3424 191 48 volume volume NOUN american_scientific_journal-3424 191 49 37 37 NUM american_scientific_journal-3424 191 50 , , PUNCT american_scientific_journal-3424 191 51 no no DET american_scientific_journal-3424 191 52 1 1 NUM american_scientific_journal-3424 191 53 , , PUNCT american_scientific_journal-3424 191 54 pp pp ADV american_scientific_journal-3424 191 55 1 1 NUM american_scientific_journal-3424 191 56 - - SYM american_scientific_journal-3424 191 57 21 21 NUM american_scientific_journal-3424 191 58 20 20 NUM american_scientific_journal-3424 191 59 transmission transmission NOUN american_scientific_journal-3424 191 60 . . PUNCT american_scientific_journal-3424 192 1 5 5 X american_scientific_journal-3424 192 2 . . X american_scientific_journal-3424 192 3 recommendations recommendation NOUN american_scientific_journal-3424 192 4 the the DET american_scientific_journal-3424 192 5 numerical numerical ADJ american_scientific_journal-3424 192 6 methods method NOUN american_scientific_journal-3424 192 7 give give VERB american_scientific_journal-3424 192 8 a a DET american_scientific_journal-3424 192 9 better well ADJ american_scientific_journal-3424 192 10 prediction prediction NOUN american_scientific_journal-3424 192 11 if if SCONJ american_scientific_journal-3424 192 12 the the DET american_scientific_journal-3424 192 13 data datum NOUN american_scientific_journal-3424 192 14 collected collect VERB american_scientific_journal-3424 192 15 from from ADP american_scientific_journal-3424 192 16 an an DET american_scientific_journal-3424 192 17 authentic authentic ADJ american_scientific_journal-3424 192 18 source source NOUN american_scientific_journal-3424 192 19 . . PUNCT american_scientific_journal-3424 193 1 this this DET american_scientific_journal-3424 193 2 result result NOUN american_scientific_journal-3424 193 3 can can AUX american_scientific_journal-3424 193 4 help help VERB american_scientific_journal-3424 193 5 to to PART american_scientific_journal-3424 193 6 estimate estimate VERB american_scientific_journal-3424 193 7 future future ADJ american_scientific_journal-3424 193 8 predictions prediction NOUN american_scientific_journal-3424 193 9 of of ADP american_scientific_journal-3424 193 10 the the DET american_scientific_journal-3424 193 11 disease disease NOUN american_scientific_journal-3424 193 12 and and CCONJ american_scientific_journal-3424 193 13 consequently consequently ADV american_scientific_journal-3424 193 14 , , PUNCT american_scientific_journal-3424 193 15 it it PRON american_scientific_journal-3424 193 16 will will AUX american_scientific_journal-3424 193 17 facilitate facilitate VERB american_scientific_journal-3424 193 18 to to PART american_scientific_journal-3424 193 19 determine determine VERB american_scientific_journal-3424 193 20 practical practical ADJ american_scientific_journal-3424 193 21 components component NOUN american_scientific_journal-3424 193 22 like like ADP american_scientific_journal-3424 193 23 the the DET american_scientific_journal-3424 193 24 quantity quantity NOUN american_scientific_journal-3424 193 25 of of ADP american_scientific_journal-3424 193 26 beds bed NOUN american_scientific_journal-3424 193 27 required require VERB american_scientific_journal-3424 193 28 in in ADP american_scientific_journal-3424 193 29 the the DET american_scientific_journal-3424 193 30 hospitable hospitable ADJ american_scientific_journal-3424 193 31 , , PUNCT american_scientific_journal-3424 193 32 number number NOUN american_scientific_journal-3424 193 33 of of ADP american_scientific_journal-3424 193 34 vaccination vaccination NOUN american_scientific_journal-3424 193 35 and and CCONJ american_scientific_journal-3424 193 36 reallocation reallocation NOUN american_scientific_journal-3424 193 37 costs cost NOUN american_scientific_journal-3424 193 38 etc etc X american_scientific_journal-3424 193 39 . . X american_scientific_journal-3424 194 1 references reference NOUN american_scientific_journal-3424 194 2 [ [ X american_scientific_journal-3424 194 3 1 1 NUM american_scientific_journal-3424 194 4 ] ] PUNCT american_scientific_journal-3424 194 5 " " PUNCT american_scientific_journal-3424 194 6 ebola ebola PROPN american_scientific_journal-3424 194 7 virus virus NOUN american_scientific_journal-3424 194 8 disease disease NOUN american_scientific_journal-3424 194 9 " " PUNCT american_scientific_journal-3424 194 10 . . PUNCT american_scientific_journal-3424 195 1 world world PROPN american_scientific_journal-3424 195 2 health health PROPN american_scientific_journal-3424 195 3 organization organization PROPN american_scientific_journal-3424 195 4 . . PUNCT american_scientific_journal-3424 196 1 n.p n.p PROPN american_scientific_journal-3424 196 2 . . PROPN american_scientific_journal-3424 196 3 , , PUNCT american_scientific_journal-3424 196 4 2017 2017 NUM american_scientific_journal-3424 196 5 . . PUNCT american_scientific_journal-3424 197 1 web web NOUN american_scientific_journal-3424 197 2 . . PROPN american_scientific_journal-3424 197 3 29 29 NUM american_scientific_journal-3424 197 4 mar mar PROPN american_scientific_journal-3424 197 5 . . PROPN american_scientific_journal-3424 197 6 2017 2017 NUM american_scientific_journal-3424 197 7 . . PUNCT american_scientific_journal-3424 198 1 < < X american_scientific_journal-3424 198 2 http://www.who.int/mediacentre/factsheets/fs103/en/ http://www.who.int/mediacentre/factsheets/fs103/en/ X american_scientific_journal-3424 198 3 > > X american_scientific_journal-3424 198 4 [ [ X american_scientific_journal-3424 198 5 2 2 NUM american_scientific_journal-3424 198 6 ] ] PUNCT american_scientific_journal-3424 198 7 " " PUNCT american_scientific_journal-3424 198 8 2014 2014 NUM american_scientific_journal-3424 198 9 - - SYM american_scientific_journal-3424 198 10 2016 2016 NUM american_scientific_journal-3424 198 11 ebola ebola NOUN american_scientific_journal-3424 198 12 outbreak outbreak NOUN american_scientific_journal-3424 198 13 in in ADP american_scientific_journal-3424 198 14 west west PROPN american_scientific_journal-3424 198 15 africa| africa| PROPN american_scientific_journal-3424 198 16 ebola ebola PROPN american_scientific_journal-3424 198 17 hemorrhagic hemorrhagic PROPN american_scientific_journal-3424 198 18 fever fever NOUN american_scientific_journal-3424 198 19 | | ADV american_scientific_journal-3424 198 20 cdc cdc PROPN american_scientific_journal-3424 198 21 " " PUNCT american_scientific_journal-3424 198 22 . . PUNCT american_scientific_journal-3424 199 1 cdc.gov cdc.gov NOUN american_scientific_journal-3424 199 2 . . PUNCT american_scientific_journal-3424 200 1 n.p n.p PROPN american_scientific_journal-3424 200 2 . . PROPN american_scientific_journal-3424 200 3 , , PUNCT american_scientific_journal-3424 200 4 2017 2017 NUM american_scientific_journal-3424 200 5 . . PUNCT american_scientific_journal-3424 201 1 web web NOUN american_scientific_journal-3424 201 2 . . PROPN american_scientific_journal-3424 201 3 29 29 NUM american_scientific_journal-3424 201 4 mar mar PROPN american_scientific_journal-3424 201 5 . . PROPN american_scientific_journal-3424 201 6 2017 2017 NUM american_scientific_journal-3424 201 7 . . PUNCT american_scientific_journal-3424 202 1 < < AUX american_scientific_journal-3424 202 2 https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/ https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/ X american_scientific_journal-3424 202 3 > > X american_scientific_journal-3424 203 1 [ [ X american_scientific_journal-3424 203 2 3 3 X american_scientific_journal-3424 203 3 ] ] PUNCT american_scientific_journal-3424 203 4 " " PUNCT american_scientific_journal-3424 203 5 who who PRON american_scientific_journal-3424 203 6 finds find VERB american_scientific_journal-3424 203 7 70 70 NUM american_scientific_journal-3424 203 8 percent percent NOUN american_scientific_journal-3424 203 9 ebola ebola NOUN american_scientific_journal-3424 203 10 mortality mortality NOUN american_scientific_journal-3424 203 11 rate rate NOUN american_scientific_journal-3424 203 12 " " PUNCT american_scientific_journal-3424 203 13 . . PUNCT american_scientific_journal-3424 204 1 aljazeera.com aljazeera.com X american_scientific_journal-3424 204 2 . . PUNCT american_scientific_journal-3424 205 1 n.p n.p PROPN american_scientific_journal-3424 205 2 . . PROPN american_scientific_journal-3424 205 3 , , PUNCT american_scientific_journal-3424 205 4 2017 2017 NUM american_scientific_journal-3424 205 5 . . PUNCT american_scientific_journal-3424 206 1 web web NOUN american_scientific_journal-3424 206 2 . . PROPN american_scientific_journal-3424 206 3 29 29 NUM american_scientific_journal-3424 206 4 mar mar PROPN american_scientific_journal-3424 206 5 . . PROPN american_scientific_journal-3424 206 6 2017 2017 NUM american_scientific_journal-3424 206 7 . . PUNCT american_scientific_journal-3424 207 1 < < X american_scientific_journal-3424 207 2 http://www.aljazeera.com/news/africa/2014/10/ebola-outbreak-killing-70-percent-victims20141014132345720164.html http://www.aljazeera.com/news/africa/2014/10/ebola-outbreak-killing-70-percent-victims20141014132345720164.html X american_scientific_journal-3424 207 3 > > X american_scientific_journal-3424 208 1 [ [ X american_scientific_journal-3424 208 2 4 4 X american_scientific_journal-3424 208 3 ] ] PUNCT american_scientific_journal-3424 208 4 " " PUNCT american_scientific_journal-3424 208 5 previous previous ADJ american_scientific_journal-3424 208 6 case case NOUN american_scientific_journal-3424 208 7 counts| counts| NOUN american_scientific_journal-3424 208 8 ebola ebola PROPN american_scientific_journal-3424 208 9 hemorrhagic hemorrhagic PROPN american_scientific_journal-3424 208 10 fever fever NOUN american_scientific_journal-3424 208 11 | | ADV american_scientific_journal-3424 208 12 cdc cdc PROPN american_scientific_journal-3424 208 13 " " PUNCT american_scientific_journal-3424 208 14 . . PUNCT american_scientific_journal-3424 209 1 cdc.gov cdc.gov NOUN american_scientific_journal-3424 209 2 . . PUNCT american_scientific_journal-3424 210 1 n.p n.p PROPN american_scientific_journal-3424 210 2 . . PROPN american_scientific_journal-3424 210 3 , , PUNCT american_scientific_journal-3424 210 4 2017 2017 NUM american_scientific_journal-3424 210 5 . . PUNCT american_scientific_journal-3424 211 1 web web NOUN american_scientific_journal-3424 211 2 . . PROPN american_scientific_journal-3424 211 3 29 29 NUM american_scientific_journal-3424 211 4 mar mar PROPN american_scientific_journal-3424 211 5 . . PROPN american_scientific_journal-3424 211 6 2017 2017 NUM american_scientific_journal-3424 211 7 . . PUNCT american_scientific_journal-3424 212 1 < < X american_scientific_journal-3424 212 2 https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/previous-case-counts.html https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/previous-case-counts.html X american_scientific_journal-3424 212 3 > > X american_scientific_journal-3424 213 1 [ [ X american_scientific_journal-3424 213 2 5 5 NUM american_scientific_journal-3424 213 3 ] ] X american_scientific_journal-3424 213 4 dolgoarshinnykh dolgoarshinnykh PROPN american_scientific_journal-3424 213 5 , , PUNCT american_scientific_journal-3424 213 6 r. r. PROPN american_scientific_journal-3424 213 7 g. g. PROPN american_scientific_journal-3424 213 8 , , PUNCT american_scientific_journal-3424 213 9 & & CCONJ american_scientific_journal-3424 213 10 lalley lalley PROPN american_scientific_journal-3424 213 11 , , PUNCT american_scientific_journal-3424 213 12 s. s. PROPN american_scientific_journal-3424 213 13 p. p. PROPN american_scientific_journal-3424 213 14 ( ( PUNCT american_scientific_journal-3424 213 15 2003 2003 NUM american_scientific_journal-3424 213 16 ) ) PUNCT american_scientific_journal-3424 213 17 . . PUNCT american_scientific_journal-3424 214 1 epidemic epidemic NOUN american_scientific_journal-3424 214 2 modelling modelling NOUN american_scientific_journal-3424 214 3 : : PUNCT american_scientific_journal-3424 214 4 sirs sir NOUN american_scientific_journal-3424 214 5 models model NOUN american_scientific_journal-3424 214 6 ( ( PUNCT american_scientific_journal-3424 214 7 doctoral doctoral ADJ american_scientific_journal-3424 214 8 dissertation dissertation NOUN american_scientific_journal-3424 214 9 , , PUNCT american_scientific_journal-3424 214 10 university university NOUN american_scientific_journal-3424 214 11 of of ADP american_scientific_journal-3424 214 12 chicago chicago PROPN american_scientific_journal-3424 214 13 , , PUNCT american_scientific_journal-3424 214 14 department department NOUN american_scientific_journal-3424 214 15 of of ADP american_scientific_journal-3424 214 16 statistics statistic NOUN american_scientific_journal-3424 214 17 ) ) PUNCT american_scientific_journal-3424 214 18 . . PUNCT american_scientific_journal-3424 215 1 [ [ X american_scientific_journal-3424 215 2 6 6 NUM american_scientific_journal-3424 215 3 ] ] PUNCT american_scientific_journal-3424 215 4 " " PUNCT american_scientific_journal-3424 215 5 modelling model VERB american_scientific_journal-3424 215 6 infectious infectious ADJ american_scientific_journal-3424 215 7 diseases disease NOUN american_scientific_journal-3424 215 8 . . PUNCT american_scientific_journal-3424 215 9 " " PUNCT american_scientific_journal-3424 216 1 ib ib PROPN american_scientific_journal-3424 216 2 maths math NOUN american_scientific_journal-3424 216 3 resources resource NOUN american_scientific_journal-3424 216 4 from from ADP american_scientific_journal-3424 216 5 british british PROPN american_scientific_journal-3424 216 6 international international PROPN american_scientific_journal-3424 216 7 school school NOUN american_scientific_journal-3424 216 8 phuket phuket NOUN american_scientific_journal-3424 216 9 " " PUNCT american_scientific_journal-3424 216 10 . . PUNCT american_scientific_journal-3424 217 1 ibmathsresources.com ibmathsresources.com X american_scientific_journal-3424 217 2 . . PUNCT american_scientific_journal-3424 218 1 n.p n.p PROPN american_scientific_journal-3424 218 2 . . PROPN american_scientific_journal-3424 218 3 , , PUNCT american_scientific_journal-3424 218 4 2017 2017 NUM american_scientific_journal-3424 218 5 . . PUNCT american_scientific_journal-3424 219 1 web web NOUN american_scientific_journal-3424 219 2 . . PROPN american_scientific_journal-3424 219 3 29 29 NUM american_scientific_journal-3424 219 4 mar mar PROPN american_scientific_journal-3424 219 5 . . PROPN american_scientific_journal-3424 219 6 2017 2017 NUM american_scientific_journal-3424 219 7 . . PUNCT american_scientific_journal-3424 220 1 [ [ X american_scientific_journal-3424 220 2 7 7 X american_scientific_journal-3424 220 3 ] ] PUNCT american_scientific_journal-3424 220 4 " " PUNCT american_scientific_journal-3424 220 5 the the DET american_scientific_journal-3424 220 6 spread spread NOUN american_scientific_journal-3424 220 7 of of ADP american_scientific_journal-3424 220 8 infectious infectious ADJ american_scientific_journal-3424 220 9 diseases disease NOUN american_scientific_journal-3424 220 10 . . PUNCT american_scientific_journal-3424 220 11 " " PUNCT american_scientific_journal-3424 221 1 the the DET american_scientific_journal-3424 221 2 british british PROPN american_scientific_journal-3424 221 3 medical medical PROPN american_scientific_journal-3424 221 4 journal journal PROPN american_scientific_journal-3424 221 5 2.1281 2.1281 NUM american_scientific_journal-3424 221 6 ( ( PUNCT american_scientific_journal-3424 221 7 1885 1885 NUM american_scientific_journal-3424 221 8 ): ): PUNCT american_scientific_journal-3424 221 9 108 108 NUM american_scientific_journal-3424 221 10 . . PUNCT american_scientific_journal-3424 221 11 web web NOUN american_scientific_journal-3424 221 12 . . PUNCT american_scientific_journal-3424 222 1 [ [ X american_scientific_journal-3424 222 2 8 8 NUM american_scientific_journal-3424 222 3 ] ] PUNCT american_scientific_journal-3424 222 4 leone leone NOUN american_scientific_journal-3424 222 5 , , PUNCT american_scientific_journal-3424 222 6 s. s. PROPN american_scientific_journal-3424 222 7 appendix appendix PROPN american_scientific_journal-3424 222 8 : : PUNCT american_scientific_journal-3424 222 9 additional additional ADJ american_scientific_journal-3424 222 10 results result NOUN american_scientific_journal-3424 222 11 and and CCONJ american_scientific_journal-3424 222 12 technical technical ADJ american_scientific_journal-3424 222 13 notes note NOUN american_scientific_journal-3424 222 14 for for ADP american_scientific_journal-3424 222 15 the the DET american_scientific_journal-3424 222 16 ebolaresponse ebolaresponse NOUN american_scientific_journal-3424 222 17 modeling model VERB american_scientific_journal-3424 222 18 tool tool NOUN american_scientific_journal-3424 222 19 additional additional ADJ american_scientific_journal-3424 222 20 results result NOUN american_scientific_journal-3424 222 21 . . PUNCT american_scientific_journal-3424 223 1 population population NOUN american_scientific_journal-3424 223 2 , , PUNCT american_scientific_journal-3424 223 3 4 4 NUM american_scientific_journal-3424 223 4 , , PUNCT american_scientific_journal-3424 223 5 3 3 NUM american_scientific_journal-3424 223 6 . . PUNCT american_scientific_journal-3424 224 1 [ [ X american_scientific_journal-3424 224 2 9 9 NUM american_scientific_journal-3424 224 3 ] ] PUNCT american_scientific_journal-3424 224 4 " " PUNCT american_scientific_journal-3424 224 5 previous previous ADJ american_scientific_journal-3424 224 6 case case NOUN american_scientific_journal-3424 224 7 counts| counts| NOUN american_scientific_journal-3424 224 8 ebola ebola PROPN american_scientific_journal-3424 224 9 hemorrhagic hemorrhagic PROPN american_scientific_journal-3424 224 10 fever fever NOUN american_scientific_journal-3424 224 11 | | ADV american_scientific_journal-3424 224 12 cdc cdc PROPN american_scientific_journal-3424 224 13 " " PUNCT american_scientific_journal-3424 224 14 . . PUNCT american_scientific_journal-3424 225 1 cdc.gov cdc.gov NOUN american_scientific_journal-3424 225 2 . . PUNCT american_scientific_journal-3424 226 1 n.p n.p PROPN american_scientific_journal-3424 226 2 . . PROPN american_scientific_journal-3424 226 3 , , PUNCT american_scientific_journal-3424 226 4 2017 2017 NUM american_scientific_journal-3424 226 5 . . PUNCT american_scientific_journal-3424 227 1 web web NOUN american_scientific_journal-3424 227 2 . . PROPN american_scientific_journal-3424 227 3 29 29 NUM american_scientific_journal-3424 227 4 mar mar PROPN american_scientific_journal-3424 227 5 . . PROPN american_scientific_journal-3424 227 6 2017 2017 NUM american_scientific_journal-3424 227 7 . . PUNCT american_scientific_journal-3424 228 1 retrieve retrieve NOUN american_scientific_journal-3424 228 2 date date NOUN american_scientific_journal-3424 228 3 : : PUNCT american_scientific_journal-3424 228 4 03 03 NUM american_scientific_journal-3424 228 5 august august PROPN american_scientific_journal-3424 228 6 2014 2014 NUM american_scientific_journal-3424 228 7 american american PROPN american_scientific_journal-3424 228 8 scientific scientific ADJ american_scientific_journal-3424 228 9 research research NOUN american_scientific_journal-3424 228 10 journal journal NOUN american_scientific_journal-3424 228 11 for for ADP american_scientific_journal-3424 228 12 engineering engineering NOUN american_scientific_journal-3424 228 13 , , PUNCT american_scientific_journal-3424 228 14 technology technology NOUN american_scientific_journal-3424 228 15 , , PUNCT american_scientific_journal-3424 228 16 and and CCONJ american_scientific_journal-3424 228 17 sciences science NOUN american_scientific_journal-3424 228 18 ( ( PUNCT american_scientific_journal-3424 228 19 asrjets asrjet NOUN american_scientific_journal-3424 228 20 ) ) PUNCT american_scientific_journal-3424 228 21 ( ( PUNCT american_scientific_journal-3424 228 22 2017 2017 NUM american_scientific_journal-3424 228 23 ) ) PUNCT american_scientific_journal-3424 228 24 volume volume NOUN american_scientific_journal-3424 228 25 37 37 NUM american_scientific_journal-3424 228 26 , , PUNCT american_scientific_journal-3424 228 27 no no DET american_scientific_journal-3424 228 28 1 1 NUM american_scientific_journal-3424 228 29 , , PUNCT american_scientific_journal-3424 228 30 pp pp ADV american_scientific_journal-3424 228 31 1 1 NUM american_scientific_journal-3424 228 32 - - SYM american_scientific_journal-3424 228 33 21 21 NUM american_scientific_journal-3424 228 34 21 21 NUM american_scientific_journal-3424 228 35 < < NOUN american_scientific_journal-3424 228 36 https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/previous-case-counts.html https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/previous-case-counts.html X american_scientific_journal-3424 228 37 > > X american_scientific_journal-3424 229 1 [ [ X american_scientific_journal-3424 229 2 10 10 NUM american_scientific_journal-3424 229 3 ] ] X american_scientific_journal-3424 229 4 clinaero clinaero NOUN american_scientific_journal-3424 229 5 , , PUNCT american_scientific_journal-3424 229 6 inc inc PROPN american_scientific_journal-3424 229 7 . . PUNCT american_scientific_journal-3424 229 8 " " PUNCT american_scientific_journal-3424 229 9 ebola ebola NOUN american_scientific_journal-3424 229 10 incubation incubation NOUN american_scientific_journal-3424 229 11 period period NOUN american_scientific_journal-3424 229 12 " " PUNCT american_scientific_journal-3424 229 13 . . PUNCT american_scientific_journal-3424 230 1 emedtv emedtv ADJ american_scientific_journal-3424 230 2 : : PUNCT american_scientific_journal-3424 230 3 health health NOUN american_scientific_journal-3424 230 4 information information NOUN american_scientific_journal-3424 230 5 brought bring VERB american_scientific_journal-3424 230 6 to to ADP american_scientific_journal-3424 230 7 life life NOUN american_scientific_journal-3424 230 8 . . PUNCT american_scientific_journal-3424 231 1 n.p n.p PROPN american_scientific_journal-3424 231 2 . . PROPN american_scientific_journal-3424 231 3 , , PUNCT american_scientific_journal-3424 231 4 2017 2017 NUM american_scientific_journal-3424 231 5 . . PUNCT american_scientific_journal-3424 232 1 web web NOUN american_scientific_journal-3424 232 2 . . PROPN american_scientific_journal-3424 232 3 29 29 NUM american_scientific_journal-3424 232 4 mar mar PROPN american_scientific_journal-3424 232 5 . . PROPN american_scientific_journal-3424 232 6 2017 2017 NUM american_scientific_journal-3424 232 7 . . PUNCT american_scientific_journal-3424 233 1 [ [ X american_scientific_journal-3424 233 2 11 11 NUM american_scientific_journal-3424 233 3 ] ] X american_scientific_journal-3424 233 4 " " PUNCT american_scientific_journal-3424 233 5 kermack kermack NOUN american_scientific_journal-3424 233 6 - - PUNCT american_scientific_journal-3424 233 7 mckendrick mckendrick NOUN american_scientific_journal-3424 233 8 model model NOUN american_scientific_journal-3424 233 9 – – PUNCT american_scientific_journal-3424 233 10 from from ADP american_scientific_journal-3424 233 11 wolfram wolfram PROPN american_scientific_journal-3424 233 12 mathworld mathworld PROPN american_scientific_journal-3424 233 13 " " PUNCT american_scientific_journal-3424 233 14 . . PUNCT american_scientific_journal-3424 234 1 mathworld.wolfram.com mathworld.wolfram.com PROPN american_scientific_journal-3424 234 2 . . PUNCT american_scientific_journal-3424 235 1 n.p n.p PROPN american_scientific_journal-3424 235 2 . . PROPN american_scientific_journal-3424 235 3 , , PUNCT american_scientific_journal-3424 235 4 2017 2017 NUM american_scientific_journal-3424 235 5 . . PUNCT american_scientific_journal-3424 236 1 web web NOUN american_scientific_journal-3424 236 2 . . PROPN american_scientific_journal-3424 236 3 29 29 NUM american_scientific_journal-3424 236 4 mar mar PROPN american_scientific_journal-3424 236 5 . . PROPN american_scientific_journal-3424 236 6 2017 2017 NUM american_scientific_journal-3424 236 7 . . PUNCT american_scientific_journal-3424 237 1 [ [ X american_scientific_journal-3424 237 2 12 12 NUM american_scientific_journal-3424 237 3 ] ] PUNCT american_scientific_journal-3424 237 4 " " PUNCT american_scientific_journal-3424 237 5 the the DET american_scientific_journal-3424 237 6 sir sir NOUN american_scientific_journal-3424 237 7 model model NOUN american_scientific_journal-3424 237 8 for for ADP american_scientific_journal-3424 237 9 spread spread NOUN american_scientific_journal-3424 237 10 of of ADP american_scientific_journal-3424 237 11 disease disease NOUN american_scientific_journal-3424 237 12 euler euler NOUN american_scientific_journal-3424 237 13 's 's PART american_scientific_journal-3424 237 14 method method NOUN american_scientific_journal-3424 237 15 for for ADP american_scientific_journal-3424 237 16 systems system NOUN american_scientific_journal-3424 237 17 " " PUNCT american_scientific_journal-3424 237 18 . . PUNCT american_scientific_journal-3424 238 1 mathematical mathematical ADJ american_scientific_journal-3424 238 2 association association PROPN american_scientific_journal-3424 238 3 of of ADP american_scientific_journal-3424 238 4 america america PROPN american_scientific_journal-3424 238 5 . . PUNCT american_scientific_journal-3424 239 1 n.p n.p PROPN american_scientific_journal-3424 239 2 . . PROPN american_scientific_journal-3424 239 3 , , PUNCT american_scientific_journal-3424 239 4 2017 2017 NUM american_scientific_journal-3424 239 5 . . PUNCT american_scientific_journal-3424 240 1 web web NOUN american_scientific_journal-3424 240 2 . . PROPN american_scientific_journal-3424 240 3 29 29 NUM american_scientific_journal-3424 240 4 mar mar PROPN american_scientific_journal-3424 240 5 . . PROPN american_scientific_journal-3424 240 6 2017 2017 NUM american_scientific_journal-3424 240 7 . . PUNCT american_scientific_journal-3424 241 1 [ [ X american_scientific_journal-3424 241 2 13 13 NUM american_scientific_journal-3424 241 3 ] ] X american_scientific_journal-3424 241 4 rahman rahman PROPN american_scientific_journal-3424 241 5 , , PUNCT american_scientific_journal-3424 241 6 prof prof PROPN american_scientific_journal-3424 241 7 . . PUNCT american_scientific_journal-3424 241 8 dr dr PROPN american_scientific_journal-3424 241 9 . . PROPN american_scientific_journal-3424 241 10 md md PROPN american_scientific_journal-3424 241 11 . . PROPN american_scientific_journal-3424 241 12 fazlur fazlur PROPN american_scientific_journal-3424 241 13 . . PUNCT american_scientific_journal-3424 242 1 mathematical mathematical ADJ american_scientific_journal-3424 242 2 modelling modelling NOUN american_scientific_journal-3424 242 3 in in ADP american_scientific_journal-3424 242 4 biology biology NOUN american_scientific_journal-3424 242 5 . . PUNCT american_scientific_journal-3424 243 1 7th 7th ADJ american_scientific_journal-3424 243 2 ed ed NOUN american_scientific_journal-3424 243 3 . . PUNCT american_scientific_journal-3424 244 1 isbn-984 isbn-984 PROPN american_scientific_journal-3424 244 2 - - PUNCT american_scientific_journal-3424 244 3 8759 8759 NUM american_scientific_journal-3424 244 4 - - SYM american_scientific_journal-3424 244 5 19 19 NUM american_scientific_journal-3424 244 6 - - PUNCT american_scientific_journal-3424 244 7 0 0 NUM american_scientific_journal-3424 244 8 , , PUNCT american_scientific_journal-3424 244 9 2015 2015 NUM american_scientific_journal-3424 244 10 . . PUNCT american_scientific_journal-3424 245 1 print print NOUN american_scientific_journal-3424 245 2 . . PUNCT american_scientific_journal-3424 246 1 [ [ X american_scientific_journal-3424 246 2 14 14 NUM american_scientific_journal-3424 246 3 ] ] X american_scientific_journal-3424 246 4 tsai tsai PROPN american_scientific_journal-3424 246 5 , , PUNCT american_scientific_journal-3424 246 6 tony tony PROPN american_scientific_journal-3424 246 7 . . PUNCT american_scientific_journal-3424 247 1 β€œ " PUNCT american_scientific_journal-3424 247 2 tony tony PROPN american_scientific_journal-3424 247 3 tsai tsai PROPN american_scientific_journal-3424 247 4 . . PUNCT american_scientific_journal-3424 247 5 ” " PUNCT american_scientific_journal-3424 248 1 rk4 rk4 PROPN american_scientific_journal-3424 248 2 method method NOUN american_scientific_journal-3424 248 3 for for ADP american_scientific_journal-3424 248 4 solving solve VERB american_scientific_journal-3424 248 5 sir sir PROPN american_scientific_journal-3424 248 6 model.n.p model.n.p PROPN american_scientific_journal-3424 248 7 . . PROPN american_scientific_journal-3424 248 8 , , PUNCT american_scientific_journal-3424 248 9 n.d n.d PROPN american_scientific_journal-3424 248 10 . . PROPN american_scientific_journal-3424 248 11 web web PROPN american_scientific_journal-3424 248 12 . . PROPN american_scientific_journal-3424 248 13 16 16 NUM american_scientific_journal-3424 248 14 apr apr NOUN american_scientific_journal-3424 248 15 . . PUNCT american_scientific_journal-3424 249 1 2017 2017 NUM american_scientific_journal-3424 249 2 < < X american_scientific_journal-3424 249 3 http://blog.tonytsai.name/blog/2014-11-24-rk4-method-for-solving-sir-model/ http://blog.tonytsai.name/blog/2014-11-24-rk4-method-for-solving-sir-model/ X american_scientific_journal-3424 249 4 > > X