id sid tid token lemma pos iajs-2818 1 1 97 97 NUM iajs-2818 1 2 this this DET iajs-2818 1 3 work work NOUN iajs-2818 1 4 is be AUX iajs-2818 1 5 licensed license VERB iajs-2818 1 6 under under ADP iajs-2818 1 7 a a DET iajs-2818 1 8 creative creative ADJ iajs-2818 1 9 commons common NOUN iajs-2818 1 10 attribution attribution NOUN iajs-2818 1 11 4.0 4.0 NUM iajs-2818 1 12 international international ADJ iajs-2818 1 13 license license NOUN iajs-2818 1 14 . . PUNCT iajs-2818 2 1 solving solve VERB iajs-2818 2 2 nonlinear nonlinear ADJ iajs-2818 2 3 covid-19 covid-19 PROPN iajs-2818 2 4 mathematical mathematical ADJ iajs-2818 2 5 model model NOUN iajs-2818 2 6 using use VERB iajs-2818 2 7 a a DET iajs-2818 2 8 reliable reliable ADJ iajs-2818 2 9 numerical numerical ADJ iajs-2818 2 10 method method NOUN iajs-2818 2 11 abstract abstract ADV iajs-2818 2 12 this this DET iajs-2818 2 13 research research NOUN iajs-2818 2 14 aims aim VERB iajs-2818 2 15 to to PART iajs-2818 2 16 numerically numerically ADV iajs-2818 2 17 solve solve VERB iajs-2818 2 18 a a DET iajs-2818 2 19 nonlinear nonlinear ADJ iajs-2818 2 20 initial initial ADJ iajs-2818 2 21 value value NOUN iajs-2818 2 22 problem problem NOUN iajs-2818 2 23 presented present VERB iajs-2818 2 24 as as ADP iajs-2818 2 25 a a DET iajs-2818 2 26 system system NOUN iajs-2818 2 27 of of ADP iajs-2818 2 28 ordinary ordinary ADJ iajs-2818 2 29 differential differential ADJ iajs-2818 2 30 equations equation NOUN iajs-2818 2 31 . . PUNCT iajs-2818 3 1 our our PRON iajs-2818 3 2 focus focus NOUN iajs-2818 3 3 is be AUX iajs-2818 3 4 on on ADP iajs-2818 3 5 epidemiological epidemiological ADJ iajs-2818 3 6 systems system NOUN iajs-2818 3 7 in in ADP iajs-2818 3 8 particular particular ADJ iajs-2818 3 9 . . PUNCT iajs-2818 4 1 the the DET iajs-2818 4 2 accurate accurate ADJ iajs-2818 4 3 numerical numerical ADJ iajs-2818 4 4 method method NOUN iajs-2818 4 5 that that PRON iajs-2818 4 6 is be AUX iajs-2818 4 7 the the DET iajs-2818 4 8 runge runge NOUN iajs-2818 4 9 - - PUNCT iajs-2818 4 10 kutta kutta NOUN iajs-2818 4 11 method method NOUN iajs-2818 4 12 of of ADP iajs-2818 4 13 order order NOUN iajs-2818 4 14 four four NUM iajs-2818 4 15 has have AUX iajs-2818 4 16 been be AUX iajs-2818 4 17 used use VERB iajs-2818 4 18 to to PART iajs-2818 4 19 solve solve VERB iajs-2818 4 20 this this DET iajs-2818 4 21 problem problem NOUN iajs-2818 4 22 that that PRON iajs-2818 4 23 is be AUX iajs-2818 4 24 represented represent VERB iajs-2818 4 25 in in ADP iajs-2818 4 26 the the DET iajs-2818 4 27 epidemic epidemic NOUN iajs-2818 4 28 model model NOUN iajs-2818 4 29 . . PUNCT iajs-2818 5 1 the the DET iajs-2818 5 2 covid-19 covid-19 PROPN iajs-2818 5 3 mathematical mathematical ADJ iajs-2818 5 4 epidemic epidemic NOUN iajs-2818 5 5 model model NOUN iajs-2818 5 6 in in ADP iajs-2818 5 7 iraq iraq PROPN iajs-2818 5 8 from from ADP iajs-2818 5 9 2020 2020 NUM iajs-2818 5 10 to to ADP iajs-2818 5 11 the the DET iajs-2818 5 12 next next ADJ iajs-2818 5 13 years year NOUN iajs-2818 5 14 is be AUX iajs-2818 5 15 the the DET iajs-2818 5 16 application application NOUN iajs-2818 5 17 under under ADP iajs-2818 5 18 study study NOUN iajs-2818 5 19 . . PUNCT iajs-2818 6 1 finally finally ADV iajs-2818 6 2 , , PUNCT iajs-2818 6 3 the the DET iajs-2818 6 4 results result NOUN iajs-2818 6 5 obtained obtain VERB iajs-2818 6 6 for for ADP iajs-2818 6 7 the the DET iajs-2818 6 8 covid-19 covid-19 PROPN iajs-2818 6 9 model model NOUN iajs-2818 6 10 have have AUX iajs-2818 6 11 been be AUX iajs-2818 6 12 discussed discuss VERB iajs-2818 6 13 tabular tabular NOUN iajs-2818 6 14 and and CCONJ iajs-2818 6 15 graphically graphically ADV iajs-2818 6 16 . . PUNCT iajs-2818 7 1 the the DET iajs-2818 7 2 spread spread NOUN iajs-2818 7 3 of of ADP iajs-2818 7 4 the the DET iajs-2818 7 5 covid-19 covid-19 PROPN iajs-2818 7 6 pandemic pandemic NOUN iajs-2818 7 7 can can AUX iajs-2818 7 8 be be AUX iajs-2818 7 9 observed observe VERB iajs-2818 7 10 via via ADP iajs-2818 7 11 the the DET iajs-2818 7 12 behavior behavior NOUN iajs-2818 7 13 of of ADP iajs-2818 7 14 the the DET iajs-2818 7 15 different different ADJ iajs-2818 7 16 stages stage NOUN iajs-2818 7 17 of of ADP iajs-2818 7 18 the the DET iajs-2818 7 19 model model NOUN iajs-2818 7 20 that that PRON iajs-2818 7 21 approximates approximate VERB iajs-2818 7 22 the the DET iajs-2818 7 23 behavior behavior NOUN iajs-2818 7 24 of of ADP iajs-2818 7 25 actual actual ADJ iajs-2818 7 26 the the DET iajs-2818 7 27 covid-19 covid-19 PROPN iajs-2818 7 28 epidemic epidemic NOUN iajs-2818 7 29 in in ADP iajs-2818 7 30 iraq iraq PROPN iajs-2818 7 31 . . PUNCT iajs-2818 8 1 in in ADP iajs-2818 8 2 our our PRON iajs-2818 8 3 study study NOUN iajs-2818 8 4 , , PUNCT iajs-2818 8 5 the the DET iajs-2818 8 6 covid-19 covid-19 PROPN iajs-2818 8 7 pandemic pandemic NOUN iajs-2818 8 8 will will AUX iajs-2818 8 9 disappear disappear VERB iajs-2818 8 10 during during ADP iajs-2818 8 11 the the DET iajs-2818 8 12 next next ADJ iajs-2818 8 13 few few ADJ iajs-2818 8 14 years year NOUN iajs-2818 8 15 within within ADP iajs-2818 8 16 about about ADV iajs-2818 8 17 five five NUM iajs-2818 8 18 years year NOUN iajs-2818 8 19 , , PUNCT iajs-2818 8 20 through through ADP iajs-2818 8 21 the the DET iajs-2818 8 22 behavior behavior NOUN iajs-2818 8 23 of of ADP iajs-2818 8 24 all all DET iajs-2818 8 25 stages stage NOUN iajs-2818 8 26 of of ADP iajs-2818 8 27 the the DET iajs-2818 8 28 epidemic epidemic NOUN iajs-2818 8 29 presented present VERB iajs-2818 8 30 in in ADP iajs-2818 8 31 our our PRON iajs-2818 8 32 research research NOUN iajs-2818 8 33 . . PUNCT iajs-2818 9 1 keywords keyword NOUN iajs-2818 9 2 : : PUNCT iajs-2818 9 3 system system NOUN iajs-2818 9 4 of of ADP iajs-2818 9 5 ordinary ordinary ADJ iajs-2818 9 6 differential differential ADJ iajs-2818 9 7 equations equation NOUN iajs-2818 9 8 , , PUNCT iajs-2818 9 9 infectious infectious ADJ iajs-2818 9 10 diseases disease NOUN iajs-2818 9 11 , , PUNCT iajs-2818 9 12 epidemic epidemic NOUN iajs-2818 9 13 model model NOUN iajs-2818 9 14 , , PUNCT iajs-2818 9 15 covid-19 covid-19 PROPN iajs-2818 9 16 mathematical mathematical ADJ iajs-2818 9 17 model model NOUN iajs-2818 9 18 , , PUNCT iajs-2818 9 19 runge runge NOUN iajs-2818 9 20 - - PUNCT iajs-2818 9 21 kutta kutta NOUN iajs-2818 9 22 methods method NOUN iajs-2818 9 23 . . PUNCT iajs-2818 10 1 1 1 X iajs-2818 10 2 . . X iajs-2818 10 3 introduction introduction NOUN iajs-2818 10 4 the the DET iajs-2818 10 5 covid-19 covid-19 PROPN iajs-2818 10 6 virus virus NOUN iajs-2818 10 7 was be AUX iajs-2818 10 8 discovered discover VERB iajs-2818 10 9 in in ADP iajs-2818 10 10 wuhan wuhan PROPN iajs-2818 10 11 , , PUNCT iajs-2818 10 12 hubei hubei PROPN iajs-2818 10 13 in in ADP iajs-2818 10 14 china china PROPN iajs-2818 10 15 . . PUNCT iajs-2818 11 1 in in ADP iajs-2818 11 2 december december PROPN iajs-2818 11 3 2019 2019 NUM iajs-2818 11 4 , , PUNCT iajs-2818 11 5 the the DET iajs-2818 11 6 world world PROPN iajs-2818 11 7 health health NOUN iajs-2818 11 8 organization organization NOUN iajs-2818 11 9 ( ( PUNCT iajs-2818 11 10 who who PRON iajs-2818 11 11 ) ) PUNCT iajs-2818 11 12 declared declare VERB iajs-2818 11 13 coronavirus coronavirus NOUN iajs-2818 11 14 a a DET iajs-2818 11 15 pandemic pandemic NOUN iajs-2818 11 16 on on ADP iajs-2818 11 17 march march PROPN iajs-2818 11 18 11 11 NUM iajs-2818 11 19 since since SCONJ iajs-2818 11 20 it it PRON iajs-2818 11 21 was be AUX iajs-2818 11 22 quickly quickly ADV iajs-2818 11 23 outbreaking outbreake VERB iajs-2818 11 24 in in ADP iajs-2818 11 25 all all PRON iajs-2818 11 26 of of ADP iajs-2818 11 27 china china PROPN iajs-2818 11 28 , , PUNCT iajs-2818 11 29 [ [ X iajs-2818 11 30 1 1 NUM iajs-2818 11 31 ] ] PUNCT iajs-2818 11 32 . . PUNCT iajs-2818 12 1 covid-19 covid-19 PROPN iajs-2818 12 2 varies vary VERB iajs-2818 12 3 from from ADP iajs-2818 12 4 infectious infectious ADJ iajs-2818 12 5 diseases disease NOUN iajs-2818 12 6 since since SCONJ iajs-2818 12 7 it it PRON iajs-2818 12 8 includes include VERB iajs-2818 12 9 strongly strongly ADV iajs-2818 12 10 infectivity infectivity NOUN iajs-2818 12 11 during during ADP iajs-2818 12 12 the the DET iajs-2818 12 13 disease disease NOUN iajs-2818 12 14 incubation incubation NOUN iajs-2818 12 15 period period NOUN iajs-2818 12 16 of of ADP iajs-2818 12 17 3 3 NUM iajs-2818 12 18 - - SYM iajs-2818 12 19 7 7 NUM iajs-2818 12 20 days day NOUN iajs-2818 12 21 or or CCONJ iajs-2818 12 22 a a DET iajs-2818 12 23 maximum maximum NOUN iajs-2818 12 24 of of ADP iajs-2818 12 25 14 14 NUM iajs-2818 12 26 days day NOUN iajs-2818 12 27 which which PRON iajs-2818 12 28 differs differ VERB iajs-2818 12 29 basically basically ADV iajs-2818 12 30 across across ADP iajs-2818 12 31 patients patient NOUN iajs-2818 12 32 , , PUNCT iajs-2818 12 33 in in ADP iajs-2818 12 34 addition addition NOUN iajs-2818 12 35 , , PUNCT iajs-2818 12 36 the the DET iajs-2818 12 37 time time NOUN iajs-2818 12 38 delay delay NOUN iajs-2818 12 39 between between ADP iajs-2818 12 40 for for ADP iajs-2818 12 41 getting get VERB iajs-2818 12 42 the the DET iajs-2818 12 43 number number NOUN iajs-2818 12 44 of of ADP iajs-2818 12 45 confirmed confirm VERB iajs-2818 12 46 cases case NOUN iajs-2818 12 47 each each DET iajs-2818 12 48 day day NOUN iajs-2818 12 49 and and CCONJ iajs-2818 12 50 true true ADJ iajs-2818 12 51 dynamics,[1 dynamics,[1 NUM iajs-2818 12 52 ] ] PUNCT iajs-2818 12 53 . . PUNCT iajs-2818 13 1 covid-19 covid-19 PROPN iajs-2818 13 2 , , PUNCT iajs-2818 13 3 unlike unlike ADP iajs-2818 13 4 its its PRON iajs-2818 13 5 close close ADJ iajs-2818 13 6 sibling sible VERB iajs-2818 13 7 sars sar NOUN iajs-2818 13 8 , , PUNCT iajs-2818 13 9 does do AUX iajs-2818 13 10 not not PART iajs-2818 13 11 appear appear VERB iajs-2818 13 12 any any DET iajs-2818 13 13 symptoms symptom NOUN iajs-2818 13 14 for for ADP iajs-2818 13 15 covid-19 covid-19 PROPN iajs-2818 13 16 on on ADP iajs-2818 13 17 the the DET iajs-2818 13 18 patients patient NOUN iajs-2818 13 19 during during ADP iajs-2818 13 20 the the DET iajs-2818 13 21 incubation incubation NOUN iajs-2818 13 22 phase phase NOUN iajs-2818 13 23 [ [ X iajs-2818 13 24 2 2 NUM iajs-2818 13 25 ] ] PUNCT iajs-2818 13 26 . . PUNCT iajs-2818 14 1 one one NUM iajs-2818 14 2 of of ADP iajs-2818 14 3 the the DET iajs-2818 14 4 most most ADV iajs-2818 14 5 difficult difficult ADJ iajs-2818 14 6 problems problem NOUN iajs-2818 14 7 in in ADP iajs-2818 14 8 the the DET iajs-2818 14 9 study study NOUN iajs-2818 14 10 of of ADP iajs-2818 14 11 epidemics epidemic NOUN iajs-2818 14 12 is be AUX iajs-2818 14 13 predicting predict VERB iajs-2818 14 14 future future ADJ iajs-2818 14 15 trends trend NOUN iajs-2818 14 16 , , PUNCT iajs-2818 14 17 such such ADJ iajs-2818 14 18 as as ADP iajs-2818 14 19 how how SCONJ iajs-2818 14 20 article article NOUN iajs-2818 14 21 history history NOUN iajs-2818 14 22 : : PUNCT iajs-2818 14 23 received receive VERB iajs-2818 14 24 , , PUNCT iajs-2818 14 25 28 28 NUM iajs-2818 14 26 , , PUNCT iajs-2818 14 27 february,2022 february,2022 NOUN iajs-2818 14 28 , , PUNCT iajs-2818 14 29 accepted,7 accepted,7 NOUN iajs-2818 14 30 , , PUNCT iajs-2818 14 31 march march NOUN iajs-2818 14 32 , , PUNCT iajs-2818 14 33 2022 2022 NUM iajs-2818 14 34 , , PUNCT iajs-2818 14 35 published publish VERB iajs-2818 14 36 in in ADP iajs-2818 14 37 april april PROPN iajs-2818 14 38 2022 2022 NUM iajs-2818 14 39 . . PUNCT iajs-2818 15 1 doi doi NOUN iajs-2818 15 2 : : PUNCT iajs-2818 15 3 10.30526/35.2.2818 10.30526/35.2.2818 PROPN iajs-2818 15 4 ibn ibn PROPN iajs-2818 15 5 al al PROPN iajs-2818 15 6 haitham haitham PROPN iajs-2818 15 7 journal journal PROPN iajs-2818 15 8 for for ADP iajs-2818 15 9 pure pure ADJ iajs-2818 15 10 and and CCONJ iajs-2818 15 11 applied applied ADJ iajs-2818 15 12 sciences sciences PROPN iajs-2818 15 13 journal journal PROPN iajs-2818 15 14 homepage homepage NOUN iajs-2818 15 15 : : PUNCT iajs-2818 15 16 http://jih.uobaghdad.edu.iq/index.php/j/index http://jih.uobaghdad.edu.iq/index.php/j/index PROPN iajs-2818 15 17 emad emad PROPN iajs-2818 15 18 talal talal PROPN iajs-2818 15 19 ghadeer ghadeer PROPN iajs-2818 15 20 for for ADP iajs-2818 15 21 education education NOUN iajs-2818 15 22 of of ADP iajs-2818 15 23 collegedepartment collegedepartment NOUN iajs-2818 15 24 of of ADP iajs-2818 15 25 mathematics mathematic NOUN iajs-2818 15 26 , , PUNCT iajs-2818 15 27 haytham haytham PROPN iajs-2818 15 28 - - PUNCT iajs-2818 15 29 al al PROPN iajs-2818 15 30 ibn ibn PROPN iajs-2818 15 31 / / SYM iajs-2818 15 32 science science PROPN iajs-2818 15 33 pure pure ADJ iajs-2818 15 34 university university PROPN iajs-2818 15 35 of of ADP iajs-2818 15 36 baghdad baghdad PROPN iajs-2818 15 37 , , PUNCT iajs-2818 15 38 baghdad baghdad PROPN iajs-2818 15 39 , , PUNCT iajs-2818 15 40 iraq iraq PROPN iajs-2818 15 41 . . PUNCT iajs-2818 16 1 emad.talal1203a@ihcoedu.uobaghdad.edu.iq emad.talal1203a@ihcoedu.uobaghdad.edu.iq PROPN iajs-2818 16 2 maha maha PROPN iajs-2818 16 3 abduljabbar abduljabbar PROPN iajs-2818 16 4 mohammed mohammed PROPN iajs-2818 16 5 of of ADP iajs-2818 16 6 collegedepartment collegedepartment NOUN iajs-2818 16 7 of of ADP iajs-2818 16 8 mathematics mathematic NOUN iajs-2818 16 9 , , PUNCT iajs-2818 16 10 -al -al CCONJ iajs-2818 16 11 ibn ibn NOUN iajs-2818 16 12 / / SYM iajs-2818 16 13 science science NOUN iajs-2818 16 14 pure pure ADJ iajs-2818 16 15 for for ADP iajs-2818 16 16 education education NOUN iajs-2818 16 17 university university PROPN iajs-2818 16 18 of of ADP iajs-2818 16 19 baghdad baghdad PROPN iajs-2818 16 20 , , PUNCT iajs-2818 16 21 baghdad baghdad PROPN iajs-2818 16 22 , , PUNCT iajs-2818 16 23 haytham haytham PROPN iajs-2818 16 24 iraq iraq PROPN iajs-2818 16 25 . . PUNCT iajs-2818 17 1 maha.aj.m@ihcoedu.uobaghdad.edu.iq maha.aj.m@ihcoedu.uobaghdad.edu.iq PROPN iajs-2818 17 2 https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ PROPN iajs-2818 17 3 http://en.uobaghdad.edu.iq/?page_id=15060 http://en.uobaghdad.edu.iq/?page_id=15060 NOUN iajs-2818 17 4 http://en.uobaghdad.edu.iq/?page_id=15060 http://en.uobaghdad.edu.iq/?page_id=15060 NOUN iajs-2818 17 5 mailto:emad.talal1203a@ihcoedu.uobaghdad.edu.iq mailto:emad.talal1203a@ihcoedu.uobaghdad.edu.iq NOUN iajs-2818 17 6 http://en.uobaghdad.edu.iq/?page_id=15060 http://en.uobaghdad.edu.iq/?page_id=15060 NOUN iajs-2818 17 7 http://en.uobaghdad.edu.iq/?page_id=15060 http://en.uobaghdad.edu.iq/?page_id=15060 NOUN iajs-2818 17 8 http://en.uobaghdad.edu.iq/?page_id=15060 http://en.uobaghdad.edu.iq/?page_id=15060 NOUN iajs-2818 17 9 mailto:maha.aj.m@ihcoedu.uobaghdad.edu.iq mailto:maha.aj.m@ihcoedu.uobaghdad.edu.iq PROPN iajs-2818 17 10 ibn ibn PROPN iajs-2818 17 11 al al PROPN iajs-2818 17 12 - - PUNCT iajs-2818 17 13 haitham haitham PROPN iajs-2818 17 14 jour jour X iajs-2818 17 15 . . PROPN iajs-2818 18 1 for for ADP iajs-2818 18 2 pure pure ADJ iajs-2818 18 3 & & CCONJ iajs-2818 18 4 appl appl PROPN iajs-2818 18 5 . . PUNCT iajs-2818 19 1 sci sci PROPN iajs-2818 19 2 . . PROPN iajs-2818 20 1 53 53 NUM iajs-2818 20 2 ( ( PUNCT iajs-2818 20 3 2)2022 2)2022 VERB iajs-2818 20 4 98 98 NUM iajs-2818 20 5 many many ADJ iajs-2818 20 6 people people NOUN iajs-2818 20 7 will will AUX iajs-2818 20 8 be be AUX iajs-2818 20 9 infected infect VERB iajs-2818 20 10 daily daily ADV iajs-2818 20 11 , , PUNCT iajs-2818 20 12 [ [ X iajs-2818 20 13 3,4,5 3,4,5 NOUN iajs-2818 20 14 ] ] X iajs-2818 20 15 , , PUNCT iajs-2818 20 16 what what DET iajs-2818 20 17 policies policy NOUN iajs-2818 20 18 will will AUX iajs-2818 20 19 be be AUX iajs-2818 20 20 needed need VERB iajs-2818 20 21 to to PART iajs-2818 20 22 control control VERB iajs-2818 20 23 this this DET iajs-2818 20 24 epidemic epidemic NOUN iajs-2818 20 25 and and CCONJ iajs-2818 20 26 how how SCONJ iajs-2818 20 27 the the DET iajs-2818 20 28 policies policy NOUN iajs-2818 20 29 will will AUX iajs-2818 20 30 affect affect VERB iajs-2818 20 31 the the DET iajs-2818 20 32 epidemics epidemic NOUN iajs-2818 20 33 , , PUNCT iajs-2818 20 34 and and CCONJ iajs-2818 20 35 so so ADV iajs-2818 20 36 on on ADP iajs-2818 20 37 [ [ PUNCT iajs-2818 20 38 6 6 NUM iajs-2818 20 39 - - SYM iajs-2818 20 40 8 8 NUM iajs-2818 20 41 ] ] PUNCT iajs-2818 20 42 . . PUNCT iajs-2818 21 1 following follow VERB iajs-2818 21 2 the the DET iajs-2818 21 3 epidemic epidemic NOUN iajs-2818 21 4 outbreak outbreak NOUN iajs-2818 21 5 , , PUNCT iajs-2818 21 6 all all DET iajs-2818 21 7 necessary necessary ADJ iajs-2818 21 8 measures measure NOUN iajs-2818 21 9 have have AUX iajs-2818 21 10 been be AUX iajs-2818 21 11 adopted adopt VERB iajs-2818 21 12 to to PART iajs-2818 21 13 understand understand VERB iajs-2818 21 14 and and CCONJ iajs-2818 21 15 control control VERB iajs-2818 21 16 the the DET iajs-2818 21 17 behavior behavior NOUN iajs-2818 21 18 of of ADP iajs-2818 21 19 this this DET iajs-2818 21 20 epidemic epidemic NOUN iajs-2818 21 21 by by ADP iajs-2818 21 22 the the DET iajs-2818 21 23 government government NOUN iajs-2818 21 24 and and CCONJ iajs-2818 21 25 individuals individual NOUN iajs-2818 21 26 together together ADV iajs-2818 21 27 . . PUNCT iajs-2818 22 1 several several ADJ iajs-2818 22 2 well well ADV iajs-2818 22 3 - - PUNCT iajs-2818 22 4 known know VERB iajs-2818 22 5 cases case NOUN iajs-2818 22 6 in in ADP iajs-2818 22 7 2003 2003 NUM iajs-2818 22 8 were be AUX iajs-2818 22 9 sars sar NOUN iajs-2818 22 10 [ [ X iajs-2818 22 11 9 9 NUM iajs-2818 22 12 ] ] PUNCT iajs-2818 22 13 , , PUNCT iajs-2818 22 14 2009 2009 NUM iajs-2818 22 15 h1n1 h1n1 NOUN iajs-2818 22 16 flu flu NOUN iajs-2818 22 17 [ [ X iajs-2818 22 18 10 10 NUM iajs-2818 22 19 ] ] PUNCT iajs-2818 22 20 , , PUNCT iajs-2818 22 21 and and CCONJ iajs-2818 22 22 the the DET iajs-2818 22 23 current current ADJ iajs-2818 22 24 covid-19 covid-19 PROPN iajs-2818 22 25 . . PUNCT iajs-2818 22 26 epidemic epidemic NOUN iajs-2818 22 27 modeling modeling NOUN iajs-2818 22 28 was be AUX iajs-2818 22 29 constructed construct VERB iajs-2818 22 30 in in ADP iajs-2818 22 31 1927 1927 NUM iajs-2818 22 32 by by ADP iajs-2818 22 33 kermack kermack NOUN iajs-2818 22 34 and and CCONJ iajs-2818 22 35 mckendrick mckendrick NOUN iajs-2818 22 36 's 's PART iajs-2818 22 37 work work NOUN iajs-2818 22 38 , , PUNCT iajs-2818 22 39 their their PRON iajs-2818 22 40 models model NOUN iajs-2818 22 41 were be AUX iajs-2818 22 42 used use VERB iajs-2818 22 43 during during ADP iajs-2818 22 44 cholera cholera NOUN iajs-2818 22 45 and and CCONJ iajs-2818 22 46 plague plague NOUN iajs-2818 22 47 outbreaks outbreak NOUN iajs-2818 22 48 [ [ X iajs-2818 22 49 11,12 11,12 NOUN iajs-2818 22 50 ] ] PUNCT iajs-2818 22 51 . . PUNCT iajs-2818 23 1 the the DET iajs-2818 23 2 most most ADV iajs-2818 23 3 important important ADJ iajs-2818 23 4 contributions contribution NOUN iajs-2818 23 5 to to ADP iajs-2818 23 6 epidemiology epidemiology NOUN iajs-2818 23 7 modeling modeling NOUN iajs-2818 23 8 are be AUX iajs-2818 23 9 to to PART iajs-2818 23 10 understand understand VERB iajs-2818 23 11 virus virus NOUN iajs-2818 23 12 dynamics dynamic NOUN iajs-2818 23 13 best well ADV iajs-2818 23 14 , , PUNCT iajs-2818 23 15 give give VERB iajs-2818 23 16 good good ADJ iajs-2818 23 17 predictions prediction NOUN iajs-2818 23 18 for for ADP iajs-2818 23 19 transmission transmission NOUN iajs-2818 23 20 of of ADP iajs-2818 23 21 the the DET iajs-2818 23 22 virus virus NOUN iajs-2818 23 23 , , PUNCT iajs-2818 23 24 and and CCONJ iajs-2818 23 25 provide provide VERB iajs-2818 23 26 the the DET iajs-2818 23 27 public public ADJ iajs-2818 23 28 health health NOUN iajs-2818 23 29 policymakers policymaker NOUN iajs-2818 23 30 with with ADP iajs-2818 23 31 beneficial beneficial ADJ iajs-2818 23 32 information information NOUN iajs-2818 23 33 to to PART iajs-2818 23 34 control control VERB iajs-2818 23 35 the the DET iajs-2818 23 36 virus virus NOUN iajs-2818 23 37 [ [ X iajs-2818 23 38 13 13 NUM iajs-2818 23 39 - - SYM iajs-2818 23 40 15 15 NUM iajs-2818 23 41 ] ] PUNCT iajs-2818 23 42 . . PUNCT iajs-2818 24 1 coronaviruses coronaviruse NOUN iajs-2818 24 2 are be AUX iajs-2818 24 3 three three NUM iajs-2818 24 4 subgroups subgroup NOUN iajs-2818 24 5 : : PUNCT iajs-2818 24 6 alpha alpha NOUN iajs-2818 24 7 , , PUNCT iajs-2818 24 8 beta beta NOUN iajs-2818 24 9 , , PUNCT iajs-2818 24 10 and and CCONJ iajs-2818 24 11 gamma gamma NOUN iajs-2818 24 12 ; ; PUNCT iajs-2818 24 13 the the DET iajs-2818 24 14 new new ADJ iajs-2818 24 15 group group NOUN iajs-2818 24 16 is be AUX iajs-2818 24 17 called call VERB iajs-2818 24 18 delta delta NOUN iajs-2818 24 19 coronaviruses coronaviruse NOUN iajs-2818 24 20 ( ( PUNCT iajs-2818 24 21 sars sars NOUN iajs-2818 24 22 - - PUNCT iajs-2818 24 23 cov cov NOUN iajs-2818 24 24 ) ) PUNCT iajs-2818 24 25 . . PUNCT iajs-2818 25 1 the the DET iajs-2818 25 2 first first ADJ iajs-2818 25 3 appearance appearance NOUN iajs-2818 25 4 of of ADP iajs-2818 25 5 the the DET iajs-2818 25 6 coronavirus coronavirus NOUN iajs-2818 25 7 was be AUX iajs-2818 25 8 in in ADP iajs-2818 25 9 the the DET iajs-2818 25 10 mid-1960s mid-1960 NOUN iajs-2818 25 11 , , PUNCT iajs-2818 25 12 and and CCONJ iajs-2818 25 13 this this DET iajs-2818 25 14 virus virus NOUN iajs-2818 25 15 was be AUX iajs-2818 25 16 among among ADP iajs-2818 25 17 humans human NOUN iajs-2818 25 18 . . PUNCT iajs-2818 26 1 in in ADP iajs-2818 26 2 2020 2020 NUM iajs-2818 26 3 , , PUNCT iajs-2818 26 4 this this DET iajs-2818 26 5 virus virus NOUN iajs-2818 26 6 reappeared reappear VERB iajs-2818 26 7 and and CCONJ iajs-2818 26 8 was be AUX iajs-2818 26 9 spread spread VERB iajs-2818 26 10 all all ADV iajs-2818 26 11 over over ADP iajs-2818 26 12 the the DET iajs-2818 26 13 world world NOUN iajs-2818 26 14 quickly,[11,12 quickly,[11,12 PROPN iajs-2818 26 15 ] ] PUNCT iajs-2818 26 16 . . PUNCT iajs-2818 27 1 many many ADJ iajs-2818 27 2 researchers researcher NOUN iajs-2818 27 3 analyzed analyze VERB iajs-2818 27 4 different different ADJ iajs-2818 27 5 types type NOUN iajs-2818 27 6 of of ADP iajs-2818 27 7 epidemics epidemic NOUN iajs-2818 27 8 , , PUNCT iajs-2818 27 9 some some PRON iajs-2818 27 10 of of ADP iajs-2818 27 11 the the DET iajs-2818 27 12 social social ADJ iajs-2818 27 13 epidemics epidemic NOUN iajs-2818 27 14 like like ADP iajs-2818 27 15 the the DET iajs-2818 27 16 obesity obesity NOUN iajs-2818 27 17 mathematical mathematical ADJ iajs-2818 27 18 model model NOUN iajs-2818 27 19 that that PRON iajs-2818 27 20 was be AUX iajs-2818 27 21 solved solve VERB iajs-2818 27 22 numerically numerically ADV iajs-2818 27 23 using use VERB iajs-2818 27 24 rk4 rk4 NOUN iajs-2818 27 25 , , PUNCT iajs-2818 27 26 rk4 rk4 NOUN iajs-2818 27 27 , , PUNCT iajs-2818 27 28 rk45 rk45 PROPN iajs-2818 27 29 and and CCONJ iajs-2818 27 30 rk78 rk78 PROPN iajs-2818 27 31 methods,[16 methods,[16 PROPN iajs-2818 27 32 ] ] PUNCT iajs-2818 27 33 . . PUNCT iajs-2818 28 1 the the DET iajs-2818 28 2 alcohol alcohol NOUN iajs-2818 28 3 consumption consumption NOUN iajs-2818 28 4 model model NOUN iajs-2818 28 5 and and CCONJ iajs-2818 28 6 smoking smoking NOUN iajs-2818 28 7 habit habit NOUN iajs-2818 28 8 model model NOUN iajs-2818 28 9 analyzed analyze VERB iajs-2818 28 10 the the DET iajs-2818 28 11 epidemic epidemic NOUN iajs-2818 28 12 's 's PART iajs-2818 28 13 behavior behavior NOUN iajs-2818 28 14 analytically analytically ADV iajs-2818 28 15 and and CCONJ iajs-2818 28 16 numerically,[17,18 numerically,[17,18 PROPN iajs-2818 28 17 ] ] PUNCT iajs-2818 28 18 . . PUNCT iajs-2818 29 1 on on ADP iajs-2818 29 2 the the DET iajs-2818 29 3 other other ADJ iajs-2818 29 4 hand hand NOUN iajs-2818 29 5 , , PUNCT iajs-2818 29 6 some some DET iajs-2818 29 7 disease disease NOUN iajs-2818 29 8 epidemics epidemic NOUN iajs-2818 29 9 analyzed analyze VERB iajs-2818 29 10 the the DET iajs-2818 29 11 epidemic epidemic NOUN iajs-2818 29 12 's 's PART iajs-2818 29 13 behavior behavior NOUN iajs-2818 29 14 numerically numerically ADV iajs-2818 29 15 , , PUNCT iajs-2818 29 16 like like ADP iajs-2818 29 17 the the DET iajs-2818 29 18 influenza influenza NOUN iajs-2818 29 19 epidemic epidemic NOUN iajs-2818 29 20 model model NOUN iajs-2818 29 21 discussed discuss VERB iajs-2818 29 22 and and CCONJ iajs-2818 29 23 solved solve VERB iajs-2818 29 24 using use VERB iajs-2818 29 25 the the DET iajs-2818 29 26 runge runge NOUN iajs-2818 29 27 - - PUNCT iajs-2818 29 28 kutta kutta NOUN iajs-2818 29 29 numerical numerical PROPN iajs-2818 29 30 method method NOUN iajs-2818 29 31 of of ADP iajs-2818 29 32 orders order NOUN iajs-2818 29 33 4 4 NUM iajs-2818 29 34 and and CCONJ iajs-2818 29 35 45,[19 45,[19 NUM iajs-2818 29 36 ] ] PUNCT iajs-2818 29 37 . . PUNCT iajs-2818 30 1 furthermore furthermore ADV iajs-2818 30 2 , , PUNCT iajs-2818 30 3 the the DET iajs-2818 30 4 other other ADJ iajs-2818 30 5 analyzed analyze VERB iajs-2818 30 6 the the DET iajs-2818 30 7 behavior behavior NOUN iajs-2818 30 8 analytically analytically ADV iajs-2818 30 9 solved solve VERB iajs-2818 30 10 sir sir NOUN iajs-2818 30 11 epidemic epidemic NOUN iajs-2818 30 12 model model NOUN iajs-2818 30 13 using use VERB iajs-2818 30 14 the the DET iajs-2818 30 15 tamimi tamimi NOUN iajs-2818 30 16 and and CCONJ iajs-2818 30 17 ansari ansari ADJ iajs-2818 30 18 iterative iterative NOUN iajs-2818 30 19 method method NOUN iajs-2818 30 20 with with ADP iajs-2818 30 21 laplace laplace NOUN iajs-2818 30 22 transform,[20 transform,[20 NOUN iajs-2818 30 23 ] ] PUNCT iajs-2818 30 24 . . PUNCT iajs-2818 31 1 the the DET iajs-2818 31 2 interest interest NOUN iajs-2818 31 3 in in ADP iajs-2818 31 4 studying study VERB iajs-2818 31 5 epidemiological epidemiological ADJ iajs-2818 31 6 mathematical mathematical ADJ iajs-2818 31 7 models model NOUN iajs-2818 31 8 increases increase VERB iajs-2818 31 9 to to PART iajs-2818 31 10 know know VERB iajs-2818 31 11 whether whether SCONJ iajs-2818 31 12 the the DET iajs-2818 31 13 epidemic epidemic NOUN iajs-2818 31 14 will will AUX iajs-2818 31 15 increase increase VERB iajs-2818 31 16 or or CCONJ iajs-2818 31 17 decrease decrease VERB iajs-2818 31 18 in in ADP iajs-2818 31 19 the the DET iajs-2818 31 20 future future NOUN iajs-2818 31 21 , , PUNCT iajs-2818 31 22 especially especially ADV iajs-2818 31 23 when when SCONJ iajs-2818 31 24 coronavirus coronavirus NOUN iajs-2818 31 25 appears appear VERB iajs-2818 31 26 in in ADP iajs-2818 31 27 2020 2020 NUM iajs-2818 31 28 . . PUNCT iajs-2818 32 1 the the DET iajs-2818 32 2 global global ADJ iajs-2818 32 3 stability stability NOUN iajs-2818 32 4 of of ADP iajs-2818 32 5 covid-19 covid-19 PROPN iajs-2818 32 6 model model NOUN iajs-2818 32 7 was be AUX iajs-2818 32 8 discussed discuss VERB iajs-2818 32 9 by by ADP iajs-2818 32 10 [ [ X iajs-2818 32 11 21 21 NUM iajs-2818 32 12 ] ] PUNCT iajs-2818 32 13 . . PUNCT iajs-2818 33 1 the the DET iajs-2818 33 2 covid-19 covid-19 PROPN iajs-2818 33 3 model model NOUN iajs-2818 33 4 was be AUX iajs-2818 33 5 analyzed analyze VERB iajs-2818 33 6 using use VERB iajs-2818 33 7 euler euler NOUN iajs-2818 33 8 ’s ’s NOUN iajs-2818 33 9 and and CCONJ iajs-2818 33 10 runge runge NOUN iajs-2818 33 11 - - PUNCT iajs-2818 33 12 kutta kutta NOUN iajs-2818 33 13 methods method NOUN iajs-2818 33 14 of of ADP iajs-2818 33 15 orders order NOUN iajs-2818 33 16 2 2 NUM iajs-2818 33 17 and and CCONJ iajs-2818 33 18 4 4 NUM iajs-2818 33 19 , , PUNCT iajs-2818 33 20 applying apply VERB iajs-2818 33 21 to to ADP iajs-2818 33 22 turkey turkey NOUN iajs-2818 33 23 and and CCONJ iajs-2818 33 24 iraq iraq PROPN iajs-2818 34 1 [ [ X iajs-2818 34 2 22 22 NUM iajs-2818 34 3 ] ] PUNCT iajs-2818 34 4 . . PUNCT iajs-2818 35 1 the the DET iajs-2818 35 2 sir sir PROPN iajs-2818 35 3 covid-19 covid-19 PROPN iajs-2818 35 4 mathematical mathematical ADJ iajs-2818 35 5 model model NOUN iajs-2818 35 6 in in ADP iajs-2818 35 7 kurdistan kurdistan PROPN iajs-2818 35 8 region region NOUN iajs-2818 35 9 in in ADP iajs-2818 35 10 iraq iraq PROPN iajs-2818 35 11 , , PUNCT iajs-2818 35 12 estimates estimate VERB iajs-2818 35 13 the the DET iajs-2818 35 14 reproductive reproductive ADJ iajs-2818 35 15 number number NOUN iajs-2818 35 16 and and CCONJ iajs-2818 35 17 solve solve VERB iajs-2818 35 18 the the DET iajs-2818 35 19 model model NOUN iajs-2818 35 20 numerically numerically ADV iajs-2818 35 21 by by ADP iajs-2818 35 22 rk4 rk4 NOUN iajs-2818 35 23 was be AUX iajs-2818 35 24 analyzed analyze VERB iajs-2818 35 25 by by ADP iajs-2818 35 26 [ [ X iajs-2818 35 27 23 23 NUM iajs-2818 35 28 ] ] PUNCT iajs-2818 35 29 . . PUNCT iajs-2818 36 1 a a DET iajs-2818 36 2 new new ADJ iajs-2818 36 3 seivr seivr NOUN iajs-2818 36 4 covid-19 covid-19 PROPN iajs-2818 36 5 model model NOUN iajs-2818 36 6 with with ADP iajs-2818 36 7 vaccination vaccination NOUN iajs-2818 36 8 campaign campaign NOUN iajs-2818 36 9 was be AUX iajs-2818 36 10 created create VERB iajs-2818 36 11 by by ADP iajs-2818 36 12 [ [ X iajs-2818 36 13 24 24 NUM iajs-2818 36 14 ] ] PUNCT iajs-2818 36 15 , , PUNCT iajs-2818 36 16 and and CCONJ iajs-2818 36 17 solve solve AUX iajs-2818 36 18 numerically numerically ADV iajs-2818 36 19 using use VERB iajs-2818 36 20 runge runge NOUN iajs-2818 36 21 - - PUNCT iajs-2818 36 22 kutta kutta NOUN iajs-2818 36 23 method method NOUN iajs-2818 36 24 of of ADP iajs-2818 36 25 order order NOUN iajs-2818 36 26 4 4 NUM iajs-2818 36 27 . . PUNCT iajs-2818 36 28 multi multi ADJ iajs-2818 36 29 parameters parameter NOUN iajs-2818 36 30 and and CCONJ iajs-2818 36 31 multivariate multivariate NOUN iajs-2818 36 32 in in ADP iajs-2818 36 33 one one NUM iajs-2818 36 34 system system NOUN iajs-2818 36 35 are be AUX iajs-2818 36 36 difficult difficult ADJ iajs-2818 36 37 to to PART iajs-2818 36 38 get get VERB iajs-2818 36 39 the the DET iajs-2818 36 40 exact exact ADJ iajs-2818 36 41 or or CCONJ iajs-2818 36 42 analytic analytic ADJ iajs-2818 36 43 solutions solution NOUN iajs-2818 36 44 for for ADP iajs-2818 36 45 some some DET iajs-2818 36 46 real real ADJ iajs-2818 36 47 complex complex ADJ iajs-2818 36 48 modeling modeling NOUN iajs-2818 36 49 . . PUNCT iajs-2818 37 1 these these DET iajs-2818 37 2 models model NOUN iajs-2818 37 3 are be AUX iajs-2818 37 4 our our PRON iajs-2818 37 5 systems system NOUN iajs-2818 37 6 under under ADP iajs-2818 37 7 study study NOUN iajs-2818 37 8 . . PUNCT iajs-2818 38 1 this this DET iajs-2818 38 2 research research NOUN iajs-2818 38 3 is be AUX iajs-2818 38 4 concerned concern VERB iajs-2818 38 5 with with ADP iajs-2818 38 6 solving solve VERB iajs-2818 38 7 these these DET iajs-2818 38 8 models model NOUN iajs-2818 38 9 efficiently efficiently ADV iajs-2818 38 10 , , PUNCT iajs-2818 38 11 fast fast ADJ iajs-2818 38 12 , , PUNCT iajs-2818 38 13 accuracy accuracy NOUN iajs-2818 38 14 , , PUNCT iajs-2818 38 15 with with ADP iajs-2818 38 16 a a DET iajs-2818 38 17 common common ADJ iajs-2818 38 18 numerical numerical ADJ iajs-2818 38 19 method method NOUN iajs-2818 38 20 which which PRON iajs-2818 38 21 is be AUX iajs-2818 38 22 the the DET iajs-2818 38 23 runge runge NOUN iajs-2818 38 24 - - PUNCT iajs-2818 38 25 kutta kutta NOUN iajs-2818 38 26 method method NOUN iajs-2818 38 27 . . PUNCT iajs-2818 39 1 computer computer NOUN iajs-2818 39 2 programming programming NOUN iajs-2818 39 3 for for ADP iajs-2818 39 4 these these DET iajs-2818 39 5 numerical numerical ADJ iajs-2818 39 6 methods method NOUN iajs-2818 39 7 is be AUX iajs-2818 39 8 established establish VERB iajs-2818 39 9 to to PART iajs-2818 39 10 quickly quickly ADV iajs-2818 39 11 and and CCONJ iajs-2818 39 12 easily easily ADV iajs-2818 39 13 get get VERB iajs-2818 39 14 results result NOUN iajs-2818 39 15 , , PUNCT iajs-2818 39 16 [ [ X iajs-2818 39 17 25 25 NUM iajs-2818 39 18 ] ] PUNCT iajs-2818 39 19 . . PUNCT iajs-2818 40 1 the the DET iajs-2818 40 2 present present ADJ iajs-2818 40 3 study study NOUN iajs-2818 40 4 is be AUX iajs-2818 40 5 arranged arrange VERB iajs-2818 40 6 as as SCONJ iajs-2818 40 7 follows follow VERB iajs-2818 40 8 : : PUNCT iajs-2818 40 9 in in ADP iajs-2818 40 10 section section NOUN iajs-2818 40 11 2 2 NUM iajs-2818 40 12 , , PUNCT iajs-2818 40 13 the the DET iajs-2818 40 14 mathematical mathematical ADJ iajs-2818 40 15 model model NOUN iajs-2818 40 16 of of ADP iajs-2818 40 17 seivr seivr PROPN iajs-2818 40 18 covid-19 covid-19 PROPN iajs-2818 40 19 model model NOUN iajs-2818 40 20 with with ADP iajs-2818 40 21 vaccination vaccination NOUN iajs-2818 40 22 campaign campaign NOUN iajs-2818 40 23 , , PUNCT iajs-2818 40 24 section section NOUN iajs-2818 40 25 3 3 NUM iajs-2818 40 26 is be AUX iajs-2818 40 27 establishing establish VERB iajs-2818 40 28 the the DET iajs-2818 40 29 covid-19 covid-19 PROPN iajs-2818 40 30 model model NOUN iajs-2818 40 31 numerically numerically ADV iajs-2818 40 32 using use VERB iajs-2818 40 33 runge runge NOUN iajs-2818 40 34 - - PUNCT iajs-2818 40 35 kutta kutta NOUN iajs-2818 40 36 of of ADP iajs-2818 40 37 4 4 NUM iajs-2818 40 38 order order NOUN iajs-2818 40 39 ( ( PUNCT iajs-2818 40 40 rk4 rk4 NOUN iajs-2818 40 41 ) ) PUNCT iajs-2818 40 42 method method NOUN iajs-2818 40 43 . . PUNCT iajs-2818 41 1 section section NOUN iajs-2818 41 2 4 4 NUM iajs-2818 41 3 , , PUNCT iajs-2818 41 4 provides provide VERB iajs-2818 41 5 some some DET iajs-2818 41 6 results result NOUN iajs-2818 41 7 that that PRON iajs-2818 41 8 are be AUX iajs-2818 41 9 presented present VERB iajs-2818 41 10 tabular tabular NOUN iajs-2818 41 11 and and CCONJ iajs-2818 41 12 graphically graphically ADV iajs-2818 41 13 with with ADP iajs-2818 41 14 their their PRON iajs-2818 41 15 discussion discussion NOUN iajs-2818 41 16 . . PUNCT iajs-2818 42 1 the the DET iajs-2818 42 2 end end NOUN iajs-2818 42 3 of of ADP iajs-2818 42 4 our our PRON iajs-2818 42 5 research research NOUN iajs-2818 42 6 in in ADP iajs-2818 42 7 section section NOUN iajs-2818 42 8 5 5 NUM iajs-2818 42 9 supplies supply VERB iajs-2818 42 10 the the DET iajs-2818 42 11 conclusion conclusion NOUN iajs-2818 42 12 of of ADP iajs-2818 42 13 this this DET iajs-2818 42 14 study study NOUN iajs-2818 42 15 . . PUNCT iajs-2818 43 1 2 2 X iajs-2818 43 2 . . X iajs-2818 43 3 covid-19 covid-19 PROPN iajs-2818 43 4 mathematical mathematical ADJ iajs-2818 43 5 model model NOUN iajs-2818 43 6 mathematical mathematical PROPN iajs-2818 43 7 modeling modeling NOUN iajs-2818 43 8 depends depend VERB iajs-2818 43 9 on on ADP iajs-2818 43 10 the the DET iajs-2818 43 11 mathematical mathematical ADJ iajs-2818 43 12 language language NOUN iajs-2818 43 13 that that PRON iajs-2818 43 14 describes describe VERB iajs-2818 43 15 the the DET iajs-2818 43 16 behavior behavior NOUN iajs-2818 43 17 of of ADP iajs-2818 43 18 a a DET iajs-2818 43 19 natural natural ADJ iajs-2818 43 20 phenomenon phenomenon NOUN iajs-2818 43 21 . . PUNCT iajs-2818 44 1 the the DET iajs-2818 44 2 covid-19 covid-19 PROPN iajs-2818 44 3 pandemic pandemic ADJ iajs-2818 44 4 model model NOUN iajs-2818 44 5 including include VERB iajs-2818 44 6 the the DET iajs-2818 44 7 vaccination vaccination NOUN iajs-2818 44 8 campaign campaign NOUN iajs-2818 44 9 is be AUX iajs-2818 44 10 of of ADP iajs-2818 44 11 natural natural ADJ iajs-2818 44 12 phenomenon phenomenon NOUN iajs-2818 44 13 which which PRON iajs-2818 44 14 can can AUX iajs-2818 44 15 be be AUX iajs-2818 44 16 represented represent VERB iajs-2818 44 17 as as ADP iajs-2818 44 18 a a DET iajs-2818 44 19 system system NOUN iajs-2818 44 20 of of ADP iajs-2818 44 21 differential differential ADJ iajs-2818 44 22 equations equation NOUN iajs-2818 44 23 for for ADP iajs-2818 44 24 the the DET iajs-2818 44 25 first first ADJ iajs-2818 44 26 order order NOUN iajs-2818 44 27 , , PUNCT iajs-2818 44 28 the the DET iajs-2818 44 29 model model NOUN iajs-2818 44 30 is be AUX iajs-2818 44 31 formed form VERB iajs-2818 44 32 ( ( PUNCT iajs-2818 44 33 1),[24 1),[24 NUM iajs-2818 44 34 ] ] PUNCT iajs-2818 44 35 . . PUNCT iajs-2818 45 1 the the DET iajs-2818 45 2 population population NOUN iajs-2818 45 3 of of ADP iajs-2818 45 4 covid-19 covid-19 PROPN iajs-2818 45 5 pandemic pandemic ADJ iajs-2818 45 6 model model NOUN iajs-2818 45 7 is be AUX iajs-2818 45 8 divided divide VERB iajs-2818 45 9 into into ADP iajs-2818 45 10 five five NUM iajs-2818 45 11 individuals individual NOUN iajs-2818 45 12 named name VERB iajs-2818 45 13 compartments compartment NOUN iajs-2818 45 14 , , PUNCT iajs-2818 45 15 𝑆(𝑑 𝑆(𝑑 NOUN iajs-2818 45 16 ) ) PUNCT iajs-2818 45 17 , , PUNCT iajs-2818 45 18 𝐸(𝑑 𝐸(𝑑 VERB iajs-2818 45 19 ) ) PUNCT iajs-2818 45 20 , , PUNCT iajs-2818 45 21 𝐼(𝑑 𝐼(𝑑 NUM iajs-2818 45 22 ) ) PUNCT iajs-2818 45 23 , , PUNCT iajs-2818 45 24 𝑉(𝑑 𝑉(𝑑 ADP iajs-2818 45 25 ) ) PUNCT iajs-2818 45 26 and and CCONJ iajs-2818 45 27 𝑅(𝑑 𝑅(𝑑 NOUN iajs-2818 45 28 ) ) PUNCT iajs-2818 45 29 , , PUNCT iajs-2818 45 30 so so CCONJ iajs-2818 45 31 this this DET iajs-2818 45 32 model model NOUN iajs-2818 45 33 is be AUX iajs-2818 45 34 made make VERB iajs-2818 45 35 ( ( PUNCT iajs-2818 45 36 𝑆𝐸𝐼𝑉𝑅),[24 𝑆𝐸𝐼𝑉𝑅),[24 NOUN iajs-2818 45 37 ] ] PUNCT iajs-2818 45 38 . . PUNCT iajs-2818 46 1 the the DET iajs-2818 46 2 first first ADJ iajs-2818 46 3 stage;susceptible stage;susceptible ADJ iajs-2818 46 4 population population NOUN iajs-2818 46 5 is be AUX iajs-2818 46 6 the the DET iajs-2818 46 7 healthy healthy ADJ iajs-2818 46 8 individuals individual NOUN iajs-2818 46 9 with with ADP iajs-2818 46 10 the the DET iajs-2818 46 11 symbol symbol NOUN iajs-2818 46 12 ( ( PUNCT iajs-2818 46 13 𝑆 𝑆 PROPN iajs-2818 46 14 ) ) PUNCT iajs-2818 46 15 , , PUNCT iajs-2818 46 16 the the DET iajs-2818 46 17 second second ADJ iajs-2818 46 18 stage stage NOUN iajs-2818 46 19 ; ; PUNCT iajs-2818 46 20 ibn ibn PROPN iajs-2818 46 21 al al PROPN iajs-2818 46 22 - - PUNCT iajs-2818 46 23 haitham haitham PROPN iajs-2818 46 24 jour jour X iajs-2818 46 25 . . PROPN iajs-2818 47 1 for for ADP iajs-2818 47 2 pure pure ADJ iajs-2818 47 3 & & CCONJ iajs-2818 47 4 appl appl PROPN iajs-2818 47 5 . . PUNCT iajs-2818 48 1 sci sci PROPN iajs-2818 48 2 . . PROPN iajs-2818 49 1 53 53 NUM iajs-2818 49 2 ( ( PUNCT iajs-2818 49 3 2)2022 2)2022 NUM iajs-2818 49 4 99 99 NUM iajs-2818 49 5 exposed expose VERB iajs-2818 49 6 population population NOUN iajs-2818 49 7 ; ; PUNCT iajs-2818 49 8 the the DET iajs-2818 49 9 infected infect VERB iajs-2818 49 10 individuals individual NOUN iajs-2818 49 11 in in ADP iajs-2818 49 12 the the DET iajs-2818 49 13 incubation incubation NOUN iajs-2818 49 14 period period NOUN iajs-2818 49 15 who who PRON iajs-2818 49 16 do do AUX iajs-2818 49 17 not not PART iajs-2818 49 18 show show VERB iajs-2818 49 19 symptoms symptom NOUN iajs-2818 49 20 of of ADP iajs-2818 49 21 disease disease NOUN iajs-2818 49 22 and and CCONJ iajs-2818 49 23 are be AUX iajs-2818 49 24 denoted denote VERB iajs-2818 49 25 by by ADP iajs-2818 49 26 ( ( PUNCT iajs-2818 49 27 𝐸 𝐸 PROPN iajs-2818 49 28 ) ) PUNCT iajs-2818 49 29 . . PUNCT iajs-2818 50 1 the the DET iajs-2818 50 2 third third ADJ iajs-2818 50 3 stage stage NOUN iajs-2818 50 4 ; ; PUNCT iajs-2818 50 5 the the DET iajs-2818 50 6 infected infected ADJ iajs-2818 50 7 population population NOUN iajs-2818 50 8 is be AUX iajs-2818 50 9 the the DET iajs-2818 50 10 infected infect VERB iajs-2818 50 11 individuals individual NOUN iajs-2818 50 12 and and CCONJ iajs-2818 50 13 the the DET iajs-2818 50 14 given give VERB iajs-2818 50 15 rise rise NOUN iajs-2818 50 16 to to ADP iajs-2818 50 17 infection infection NOUN iajs-2818 50 18 after after ADP iajs-2818 50 19 incubation incubation NOUN iajs-2818 50 20 interval interval NOUN iajs-2818 50 21 and and CCONJ iajs-2818 50 22 symbolized symbolize VERB iajs-2818 50 23 by by ADP iajs-2818 50 24 ( ( PUNCT iajs-2818 50 25 𝐼 𝐼 PROPN iajs-2818 50 26 ) ) PUNCT iajs-2818 50 27 , , PUNCT iajs-2818 50 28 the the DET iajs-2818 50 29 fourth fourth ADJ iajs-2818 50 30 stage stage NOUN iajs-2818 50 31 ; ; PUNCT iajs-2818 50 32 the the DET iajs-2818 50 33 vaccinated vaccinated ADJ iajs-2818 50 34 population population NOUN iajs-2818 50 35 is be AUX iajs-2818 50 36 the the DET iajs-2818 50 37 individuals individual NOUN iajs-2818 50 38 who who PRON iajs-2818 50 39 take take VERB iajs-2818 50 40 the the DET iajs-2818 50 41 vaccination vaccination NOUN iajs-2818 50 42 and and CCONJ iajs-2818 50 43 symbolized symbolize VERB iajs-2818 50 44 by by ADP iajs-2818 50 45 ( ( PUNCT iajs-2818 50 46 𝑉 𝑉 PROPN iajs-2818 50 47 ) ) PUNCT iajs-2818 50 48 , , PUNCT iajs-2818 50 49 the the DET iajs-2818 50 50 fifth fifth ADJ iajs-2818 50 51 stage stage NOUN iajs-2818 50 52 ; ; PUNCT iajs-2818 50 53 recovered recover VERB iajs-2818 50 54 population population NOUN iajs-2818 50 55 are be AUX iajs-2818 50 56 the the DET iajs-2818 50 57 individuals individual NOUN iajs-2818 50 58 who who PRON iajs-2818 50 59 die die VERB iajs-2818 50 60 or or CCONJ iajs-2818 50 61 recover recover VERB iajs-2818 50 62 which which PRON iajs-2818 50 63 are be AUX iajs-2818 50 64 coded code VERB iajs-2818 50 65 by by ADP iajs-2818 50 66 ( ( PUNCT iajs-2818 50 67 𝑅 𝑅 PROPN iajs-2818 50 68 ) ) PUNCT iajs-2818 50 69 . . PUNCT iajs-2818 51 1 the the DET iajs-2818 51 2 derivatives derivative NOUN iajs-2818 51 3 of of ADP iajs-2818 51 4 all all DET iajs-2818 51 5 compartments compartment NOUN iajs-2818 51 6 of of ADP iajs-2818 51 7 the the DET iajs-2818 51 8 coronavirus coronavirus NOUN iajs-2818 51 9 model model NOUN iajs-2818 51 10 are be AUX iajs-2818 51 11 continuous continuous ADJ iajs-2818 51 12 at at ADP iajs-2818 51 13 t t PROPN iajs-2818 51 14 β‰₯ β‰₯ NOUN iajs-2818 51 15 0 0 NUM iajs-2818 51 16 . . PUNCT iajs-2818 52 1 the the DET iajs-2818 52 2 solutions solution NOUN iajs-2818 52 3 of of ADP iajs-2818 52 4 the the DET iajs-2818 52 5 model model NOUN iajs-2818 52 6 are be AUX iajs-2818 52 7 non non ADJ iajs-2818 52 8 - - ADJ iajs-2818 52 9 negativity negativity ADJ iajs-2818 52 10 , , PUNCT iajs-2818 52 11 the the DET iajs-2818 52 12 existence existence NOUN iajs-2818 52 13 and and CCONJ iajs-2818 52 14 uniqueness uniqueness NOUN iajs-2818 52 15 can can AUX iajs-2818 52 16 be be AUX iajs-2818 52 17 viewed view VERB iajs-2818 52 18 in in ADP iajs-2818 52 19 [ [ X iajs-2818 52 20 21 21 NUM iajs-2818 52 21 ] ] PUNCT iajs-2818 52 22 . . PUNCT iajs-2818 53 1 the the DET iajs-2818 53 2 system system NOUN iajs-2818 53 3 of of ADP iajs-2818 53 4 covid-19 covid-19 PROPN iajs-2818 53 5 understudy understudy NOUN iajs-2818 53 6 is be AUX iajs-2818 53 7 offered offer VERB iajs-2818 53 8 in in ADP iajs-2818 53 9 ( ( PUNCT iajs-2818 53 10 1 1 NUM iajs-2818 53 11 ) ) PUNCT iajs-2818 53 12 , , PUNCT iajs-2818 54 1 [ [ X iajs-2818 54 2 24 24 NUM iajs-2818 54 3 ] ] X iajs-2818 54 4 : : PUNCT iajs-2818 54 5 𝑑𝑆 𝑑𝑆 ADJ iajs-2818 54 6 𝑑𝑑 𝑑𝑑 ADP iajs-2818 54 7 = = SYM iajs-2818 54 8 Ξ» Ξ» PROPN iajs-2818 54 9 βˆ’ βˆ’ PROPN iajs-2818 54 10 ( ( PUNCT iajs-2818 54 11 𝛼𝐸 𝛼𝐸 NOUN iajs-2818 54 12 + + CCONJ iajs-2818 54 13 π‘š π‘š X iajs-2818 54 14 + + X iajs-2818 54 15 πœ‡)𝑆 πœ‡)𝑆 ADJ iajs-2818 54 16 , , PUNCT iajs-2818 54 17 𝑑𝐸 𝑑𝐸 ADJ iajs-2818 54 18 𝑑𝑑 𝑑𝑑 ADP iajs-2818 54 19 = = PROPN iajs-2818 54 20 𝛼𝑆𝐸 𝛼𝑆𝐸 PROPN iajs-2818 54 21 + + CCONJ iajs-2818 54 22 𝑝𝑉𝐸 𝑝𝑉𝐸 ADJ iajs-2818 54 23 βˆ’ βˆ’ PROPN iajs-2818 54 24 ( ( PUNCT iajs-2818 54 25 𝑓𝐼 𝑓𝐼 PROPN iajs-2818 54 26 + + CCONJ iajs-2818 54 27 𝑐 𝑐 NOUN iajs-2818 54 28 + + NUM iajs-2818 54 29 πœ‡)𝐸 πœ‡)𝐸 NOUN iajs-2818 54 30 , , PUNCT iajs-2818 54 31 𝑑𝐼 𝑑𝐼 ADJ iajs-2818 54 32 𝑑𝑑 𝑑𝑑 ADP iajs-2818 54 33 = = PUNCT iajs-2818 54 34 𝑓𝐸𝐼 𝑓𝐸𝐼 NOUN iajs-2818 54 35 βˆ’ βˆ’ PROPN iajs-2818 54 36 ( ( PUNCT iajs-2818 54 37 𝑧 𝑧 PROPN iajs-2818 54 38 + + X iajs-2818 54 39 πœ‡ πœ‡ X iajs-2818 54 40 + + NOUN iajs-2818 54 41 𝜎)𝐼 𝜎)𝐼 NOUN iajs-2818 54 42 , , PUNCT iajs-2818 54 43 𝑑𝑉 𝑑𝑉 ADP iajs-2818 54 44 𝑑𝑑 𝑑𝑑 ADP iajs-2818 54 45 = = PUNCT iajs-2818 54 46 π‘šπ‘† π‘šπ‘† NOUN iajs-2818 54 47 βˆ’ βˆ’ PROPN iajs-2818 54 48 ( ( PUNCT iajs-2818 54 49 𝑝𝐸 𝑝𝐸 PROPN iajs-2818 54 50 + + CCONJ iajs-2818 54 51 πœ‡)𝑉 πœ‡)𝑉 ADJ iajs-2818 54 52 , , PUNCT iajs-2818 54 53 𝑑𝑅 𝑑𝑅 VERB iajs-2818 54 54 𝑑𝑑 𝑑𝑑 ADP iajs-2818 54 55 = = SYM iajs-2818 54 56 𝑧𝐼 𝑧𝐼 PROPN iajs-2818 54 57 + + CCONJ iajs-2818 54 58 𝑐𝐸 𝑐𝐸 NOUN iajs-2818 54 59 βˆ’ βˆ’ NOUN iajs-2818 54 60 πœ‡π‘… πœ‡π‘… NOUN iajs-2818 54 61 , , PUNCT iajs-2818 54 62 ( ( PUNCT iajs-2818 54 63 1 1 X iajs-2818 54 64 ) ) PUNCT iajs-2818 54 65 where where SCONJ iajs-2818 54 66 table table NOUN iajs-2818 54 67 1 1 NUM iajs-2818 54 68 . . PUNCT iajs-2818 54 69 has have VERB iajs-2818 54 70 a a DET iajs-2818 54 71 description description NOUN iajs-2818 54 72 of of ADP iajs-2818 54 73 the the DET iajs-2818 54 74 parameters parameter NOUN iajs-2818 54 75 of of ADP iajs-2818 54 76 the the DET iajs-2818 54 77 covid-19 covid-19 PROPN iajs-2818 54 78 model model NOUN iajs-2818 54 79 . . PUNCT iajs-2818 55 1 table table NOUN iajs-2818 55 2 1 1 NUM iajs-2818 55 3 . . PUNCT iajs-2818 56 1 description description NOUN iajs-2818 56 2 parameters parameter NOUN iajs-2818 56 3 of of ADP iajs-2818 56 4 the the DET iajs-2818 56 5 covid-19 covid-19 PROPN iajs-2818 56 6 model model NOUN iajs-2818 56 7 with with ADP iajs-2818 56 8 their their PRON iajs-2818 56 9 values value NOUN iajs-2818 56 10 [ [ X iajs-2818 56 11 24 24 NUM iajs-2818 56 12 ] ] PUNCT iajs-2818 56 13 parameters parameter NOUN iajs-2818 56 14 description description NOUN iajs-2818 56 15 value value NOUN iajs-2818 56 16 of of ADP iajs-2818 56 17 parameters parameter NOUN iajs-2818 56 18 source source NOUN iajs-2818 56 19 𝛬 𝛬 NOUN iajs-2818 56 20 mobilization mobilization NOUN iajs-2818 56 21 rate rate NOUN iajs-2818 56 22 of of ADP iajs-2818 56 23 coronavirus coronavirus NOUN iajs-2818 56 24 50 50 NUM iajs-2818 57 1 [ [ SYM iajs-2818 57 2 26 26 NUM iajs-2818 57 3 ] ] SYM iajs-2818 57 4 𝛼 𝛼 PRON iajs-2818 57 5 rate rate NOUN iajs-2818 57 6 of of ADP iajs-2818 57 7 transition transition NOUN iajs-2818 57 8 from from ADP iajs-2818 57 9 susceptible susceptible ADJ iajs-2818 57 10 persons person NOUN iajs-2818 57 11 to to ADP iajs-2818 57 12 exposed expose VERB iajs-2818 57 13 persons person NOUN iajs-2818 57 14 0.002 0.002 NUM iajs-2818 57 15 estimated estimate VERB iajs-2818 57 16 π‘š π‘š ADP iajs-2818 57 17 the the DET iajs-2818 57 18 proportion proportion NOUN iajs-2818 57 19 of of ADP iajs-2818 57 20 vaccinated vaccinated ADJ iajs-2818 57 21 susceptible susceptible ADJ iajs-2818 57 22 persons person NOUN iajs-2818 57 23 0.5 0.5 NUM iajs-2818 57 24 estimated estimate VERB iajs-2818 57 25 𝑓 𝑓 DET iajs-2818 57 26 the the DET iajs-2818 57 27 rate rate NOUN iajs-2818 57 28 at at ADP iajs-2818 57 29 which which PRON iajs-2818 57 30 exposed expose VERB iajs-2818 57 31 people people NOUN iajs-2818 57 32 become become VERB iajs-2818 57 33 infected infected ADJ iajs-2818 57 34 0.008 0.008 NUM iajs-2818 57 35 estimated estimate VERB iajs-2818 57 36 𝑝 𝑝 ADP iajs-2818 57 37 the the DET iajs-2818 57 38 rate rate NOUN iajs-2818 57 39 for for ADP iajs-2818 57 40 vaccinated vaccinated ADJ iajs-2818 57 41 persons person NOUN iajs-2818 57 42 who who PRON iajs-2818 57 43 are be AUX iajs-2818 57 44 exposed expose VERB iajs-2818 57 45 to to ADP iajs-2818 57 46 disease disease NOUN iajs-2818 57 47 0.08 0.08 NUM iajs-2818 57 48 estimated estimate VERB iajs-2818 57 49 𝑧 𝑧 ADP iajs-2818 57 50 the the DET iajs-2818 57 51 recovery recovery NOUN iajs-2818 57 52 rate rate NOUN iajs-2818 57 53 of of ADP iajs-2818 57 54 infected infected ADJ iajs-2818 57 55 persons person NOUN iajs-2818 57 56 0.012 0.012 NUM iajs-2818 57 57 estimated estimate VERB iajs-2818 57 58 πœ‡ πœ‡ ADP iajs-2818 57 59 rate rate NOUN iajs-2818 57 60 of of ADP iajs-2818 57 61 natural natural ADJ iajs-2818 57 62 death death NOUN iajs-2818 57 63 0.009 0.009 NUM iajs-2818 57 64 estimated estimate VERB iajs-2818 57 65 𝑐 𝑐 PROPN iajs-2818 57 66 the the DET iajs-2818 57 67 recovery recovery NOUN iajs-2818 57 68 rate rate NOUN iajs-2818 57 69 of of ADP iajs-2818 57 70 exposed expose VERB iajs-2818 57 71 persons person NOUN iajs-2818 57 72 0.05 0.05 NUM iajs-2818 57 73 estimated estimate VERB iajs-2818 57 74 𝜎 𝜎 NUM iajs-2818 57 75 mortality mortality NOUN iajs-2818 57 76 related relate VERB iajs-2818 57 77 to to ADP iajs-2818 57 78 the the DET iajs-2818 57 79 disease disease NOUN iajs-2818 57 80 0.25 0.25 NUM iajs-2818 57 81 estimated estimate VERB iajs-2818 57 82 3 3 NUM iajs-2818 57 83 . . PUNCT iajs-2818 57 84 solving solve VERB iajs-2818 57 85 covid-19 covid-19 PROPN iajs-2818 57 86 model model NOUN iajs-2818 57 87 by by ADP iajs-2818 57 88 numerical numerical PROPN iajs-2818 57 89 method method PROPN iajs-2818 57 90 a a DET iajs-2818 57 91 numerical numerical ADJ iajs-2818 57 92 method method NOUN iajs-2818 57 93 is be AUX iajs-2818 57 94 a a DET iajs-2818 57 95 process process NOUN iajs-2818 57 96 to to PART iajs-2818 57 97 find find VERB iajs-2818 57 98 the the DET iajs-2818 57 99 solutions solution NOUN iajs-2818 57 100 approximately approximately ADV iajs-2818 57 101 at at ADP iajs-2818 57 102 specified specified ADJ iajs-2818 57 103 points point NOUN iajs-2818 57 104 , , PUNCT iajs-2818 57 105 most most ADJ iajs-2818 57 106 initial initial ADJ iajs-2818 57 107 value value NOUN iajs-2818 57 108 problems problem NOUN iajs-2818 57 109 can can AUX iajs-2818 57 110 be be AUX iajs-2818 57 111 solved solve VERB iajs-2818 57 112 numerically numerically ADV iajs-2818 57 113 like like ADP iajs-2818 57 114 the the DET iajs-2818 57 115 covid-19 covid-19 PROPN iajs-2818 57 116 epidemic epidemic NOUN iajs-2818 57 117 system system NOUN iajs-2818 57 118 in in ADP iajs-2818 57 119 the the DET iajs-2818 57 120 present present ADJ iajs-2818 57 121 work work NOUN iajs-2818 57 122 . . PUNCT iajs-2818 58 1 in in ADP iajs-2818 58 2 this this DET iajs-2818 58 3 section section NOUN iajs-2818 58 4 , , PUNCT iajs-2818 58 5 a a DET iajs-2818 58 6 numerical numerical ADJ iajs-2818 58 7 method method NOUN iajs-2818 58 8 rk rk NOUN iajs-2818 58 9 of of ADP iajs-2818 58 10 order order NOUN iajs-2818 58 11 4 4 NUM iajs-2818 58 12 can can AUX iajs-2818 58 13 be be AUX iajs-2818 58 14 utilized utilize VERB iajs-2818 58 15 to to PART iajs-2818 58 16 solve solve VERB iajs-2818 58 17 the the DET iajs-2818 58 18 covid-19 covid-19 PROPN iajs-2818 58 19 epidemic epidemic NOUN iajs-2818 58 20 problem problem NOUN iajs-2818 58 21 in in ADP iajs-2818 58 22 iraq iraq PROPN iajs-2818 58 23 in in ADP iajs-2818 58 24 2020 2020 NUM iajs-2818 58 25 . . PUNCT iajs-2818 59 1 ibn ibn PROPN iajs-2818 59 2 al al PROPN iajs-2818 59 3 - - PUNCT iajs-2818 59 4 haitham haitham PROPN iajs-2818 59 5 jour jour X iajs-2818 59 6 . . PROPN iajs-2818 59 7 for for ADP iajs-2818 59 8 pure pure ADJ iajs-2818 59 9 & & CCONJ iajs-2818 59 10 appl appl PROPN iajs-2818 59 11 . . PUNCT iajs-2818 60 1 sci sci PROPN iajs-2818 60 2 . . PROPN iajs-2818 61 1 53 53 NUM iajs-2818 61 2 ( ( PUNCT iajs-2818 61 3 2)2022 2)2022 NUM iajs-2818 61 4 100 100 NUM iajs-2818 61 5 different different ADJ iajs-2818 61 6 forms form NOUN iajs-2818 61 7 of of ADP iajs-2818 61 8 the the DET iajs-2818 61 9 rk rk NOUN iajs-2818 61 10 method method NOUN iajs-2818 61 11 concerning concern VERB iajs-2818 61 12 the the DET iajs-2818 61 13 order order NOUN iajs-2818 61 14 of of ADP iajs-2818 61 15 the the DET iajs-2818 61 16 method method NOUN iajs-2818 61 17 , , PUNCT iajs-2818 61 18 in in ADP iajs-2818 61 19 the the DET iajs-2818 61 20 current current ADJ iajs-2818 61 21 work work NOUN iajs-2818 61 22 , , PUNCT iajs-2818 61 23 rk rk NOUN iajs-2818 61 24 has have VERB iajs-2818 61 25 the the DET iajs-2818 61 26 form form NOUN iajs-2818 61 27 of of ADP iajs-2818 61 28 order order NOUN iajs-2818 61 29 4 4 NUM iajs-2818 61 30 , , PUNCT iajs-2818 61 31 so so ADV iajs-2818 61 32 , , PUNCT iajs-2818 61 33 this this DET iajs-2818 61 34 work work NOUN iajs-2818 61 35 needs need VERB iajs-2818 61 36 four four NUM iajs-2818 61 37 stages stage NOUN iajs-2818 61 38 to to PART iajs-2818 61 39 get get VERB iajs-2818 61 40 the the DET iajs-2818 61 41 final final ADJ iajs-2818 61 42 formula formula NOUN iajs-2818 61 43 [ [ X iajs-2818 61 44 27 27 NUM iajs-2818 61 45 ] ] PUNCT iajs-2818 61 46 . . PUNCT iajs-2818 62 1 rk4 rk4 VERB iajs-2818 62 2 the the DET iajs-2818 62 3 method method NOUN iajs-2818 62 4 in in ADP iajs-2818 62 5 a a DET iajs-2818 62 6 general general ADJ iajs-2818 62 7 form form NOUN iajs-2818 62 8 can can AUX iajs-2818 62 9 be be AUX iajs-2818 62 10 shown show VERB iajs-2818 62 11 in in ADP iajs-2818 62 12 [ [ X iajs-2818 62 13 27 27 NUM iajs-2818 62 14 ] ] PUNCT iajs-2818 62 15 . . PUNCT iajs-2818 63 1 first first ADV iajs-2818 63 2 , , PUNCT iajs-2818 63 3 the the DET iajs-2818 63 4 form form NOUN iajs-2818 63 5 of of ADP iajs-2818 63 6 rk4 rk4 NOUN iajs-2818 63 7 is be AUX iajs-2818 63 8 presented present VERB iajs-2818 63 9 below below ADV iajs-2818 63 10 , , PUNCT iajs-2818 63 11 the the DET iajs-2818 63 12 general general ADJ iajs-2818 63 13 formula formula NOUN iajs-2818 63 14 of of ADP iajs-2818 63 15 𝑆𝑖+1 𝑆𝑖+1 NOUN iajs-2818 63 16 , , PUNCT iajs-2818 63 17 𝐸𝑖+1 𝐸𝑖+1 NOUN iajs-2818 63 18 , , PUNCT iajs-2818 63 19 𝐼𝑖+1 𝐼𝑖+1 PROPN iajs-2818 63 20 , , PUNCT iajs-2818 63 21 𝑉𝑖+1 𝑉𝑖+1 NOUN iajs-2818 63 22 and and CCONJ iajs-2818 63 23 𝑅𝑖+1 𝑅𝑖+1 NOUN iajs-2818 63 24 for for ADP iajs-2818 63 25 the the DET iajs-2818 63 26 rk4 rk4 NOUN iajs-2818 63 27 method method NOUN iajs-2818 63 28 is be AUX iajs-2818 63 29 : : PUNCT iajs-2818 63 30 𝑆𝑖+1 𝑆𝑖+1 X iajs-2818 64 1 = = PUNCT iajs-2818 64 2 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 64 3 + + NUM iajs-2818 64 4 1 1 NUM iajs-2818 64 5 6 6 NUM iajs-2818 64 6 ( ( PUNCT iajs-2818 64 7 𝑔𝑆1 𝑔𝑆1 NOUN iajs-2818 64 8 + + NUM iajs-2818 64 9 2𝑔𝑆2 2𝑔𝑆2 NUM iajs-2818 64 10 + + CCONJ iajs-2818 64 11 2𝑔𝑆3 2𝑔𝑆3 PROPN iajs-2818 64 12 + + NUM iajs-2818 64 13 𝑔𝑆4 𝑔𝑆4 NOUN iajs-2818 64 14 ) ) PUNCT iajs-2818 64 15 , , PUNCT iajs-2818 64 16 𝐸𝑖+1 𝐸𝑖+1 X iajs-2818 64 17 = = SYM iajs-2818 65 1 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 65 2 + + NOUN iajs-2818 65 3 1 1 NUM iajs-2818 65 4 6 6 NUM iajs-2818 65 5 ( ( PUNCT iajs-2818 65 6 𝑔𝐸1 𝑔𝐸1 PROPN iajs-2818 65 7 + + CCONJ iajs-2818 65 8 2𝑔𝐸2 2𝑔𝐸2 NUM iajs-2818 65 9 + + SYM iajs-2818 65 10 2𝑔𝐸3 2𝑔𝐸3 NUM iajs-2818 65 11 + + CCONJ iajs-2818 65 12 𝑔𝐸4 𝑔𝐸4 PROPN iajs-2818 65 13 ) ) PUNCT iajs-2818 65 14 , , PUNCT iajs-2818 65 15 𝐼𝑖+1 𝐼𝑖+1 X iajs-2818 66 1 = = PUNCT iajs-2818 66 2 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 66 3 + + CCONJ iajs-2818 66 4 1 1 NUM iajs-2818 66 5 6 6 NUM iajs-2818 66 6 ( ( PUNCT iajs-2818 66 7 𝑔𝐼1 𝑔𝐼1 PROPN iajs-2818 66 8 + + PROPN iajs-2818 66 9 2𝑔𝐼2 2𝑔𝐼2 NUM iajs-2818 66 10 + + CCONJ iajs-2818 66 11 2𝑔𝐼3 2𝑔𝐼3 NUM iajs-2818 66 12 + + CCONJ iajs-2818 66 13 𝑔𝐼4 𝑔𝐼4 PROPN iajs-2818 66 14 ) ) PUNCT iajs-2818 66 15 , , PUNCT iajs-2818 66 16 𝑉𝑖+1 𝑉𝑖+1 NOUN iajs-2818 66 17 = = SYM iajs-2818 66 18 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 66 19 + + NOUN iajs-2818 66 20 1 1 NUM iajs-2818 66 21 6 6 NUM iajs-2818 66 22 ( ( PUNCT iajs-2818 66 23 𝑔𝑉1 𝑔𝑉1 VERB iajs-2818 66 24 + + CCONJ iajs-2818 66 25 2𝑔𝑉2 2𝑔𝑉2 NUM iajs-2818 66 26 + + CCONJ iajs-2818 66 27 2𝑔𝑉3 2𝑔𝑉3 NUM iajs-2818 66 28 + + CCONJ iajs-2818 66 29 𝑔𝑉4 𝑔𝑉4 PROPN iajs-2818 66 30 ) ) PUNCT iajs-2818 66 31 , , PUNCT iajs-2818 66 32 𝑅𝑖+1 𝑅𝑖+1 X iajs-2818 67 1 = = PUNCT iajs-2818 67 2 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 67 3 + + CCONJ iajs-2818 67 4 1 1 NUM iajs-2818 67 5 6 6 NUM iajs-2818 67 6 ( ( PUNCT iajs-2818 67 7 𝑔𝑅1 𝑔𝑅1 PROPN iajs-2818 67 8 + + PROPN iajs-2818 67 9 2𝑔𝑅2 2𝑔𝑅2 PROPN iajs-2818 67 10 + + CCONJ iajs-2818 67 11 2𝑔𝑅3 2𝑔𝑅3 NUM iajs-2818 67 12 + + NUM iajs-2818 67 13 𝑔𝑅4 𝑔𝑅4 NOUN iajs-2818 67 14 ) ) PUNCT iajs-2818 67 15 . . PUNCT iajs-2818 68 1 where where SCONJ iajs-2818 68 2 𝑖 𝑖 NOUN iajs-2818 68 3 = = SYM iajs-2818 68 4 0,1 0,1 NUM iajs-2818 68 5 , , PUNCT iajs-2818 68 6 … … PUNCT iajs-2818 68 7 , , PUNCT iajs-2818 68 8 π‘š π‘š ADP iajs-2818 68 9 βˆ’ βˆ’ PROPN iajs-2818 68 10 1 1 NUM iajs-2818 68 11 . . PUNCT iajs-2818 68 12 ( ( PUNCT iajs-2818 68 13 2 2 X iajs-2818 68 14 ) ) PUNCT iajs-2818 68 15 now now ADV iajs-2818 68 16 , , PUNCT iajs-2818 68 17 to to PART iajs-2818 68 18 find find VERB iajs-2818 68 19 𝑔𝑆1 𝑔𝑆1 PROPN iajs-2818 68 20 , , PUNCT iajs-2818 68 21 𝑔𝐸1 𝑔𝐸1 PROPN iajs-2818 68 22 , , PUNCT iajs-2818 68 23 𝑔𝐼1 𝑔𝐼1 PROPN iajs-2818 68 24 , , PUNCT iajs-2818 68 25 𝑔𝑉1 𝑔𝑉1 VERB iajs-2818 68 26 and and CCONJ iajs-2818 68 27 𝑔𝑅1 𝑔𝑅1 PROPN iajs-2818 68 28 , , PUNCT iajs-2818 68 29 the the DET iajs-2818 68 30 next next ADJ iajs-2818 68 31 steps step NOUN iajs-2818 68 32 are be AUX iajs-2818 68 33 done do VERB iajs-2818 68 34 by by ADP iajs-2818 68 35 substituting substitute VERB iajs-2818 68 36 the the DET iajs-2818 68 37 form form NOUN iajs-2818 68 38 of of ADP iajs-2818 68 39 𝑔𝑆1 𝑔𝑆1 PROPN iajs-2818 68 40 , , PUNCT iajs-2818 68 41 𝑔𝐸1 𝑔𝐸1 PROPN iajs-2818 68 42 , , PUNCT iajs-2818 68 43 𝑔𝐼1 𝑔𝐼1 PROPN iajs-2818 68 44 , , PUNCT iajs-2818 68 45 𝑔𝑉1 𝑔𝑉1 VERB iajs-2818 68 46 and and CCONJ iajs-2818 68 47 𝑔𝑅1 𝑔𝑅1 NOUN iajs-2818 68 48 in in ADP iajs-2818 68 49 ( ( PUNCT iajs-2818 68 50 1 1 NUM iajs-2818 68 51 ) ) PUNCT iajs-2818 68 52 as as ADP iajs-2818 68 53 below below ADV iajs-2818 68 54 ; ; PUNCT iajs-2818 68 55 where where SCONJ iajs-2818 68 56 πΈπ‘ž1 πΈπ‘ž1 NOUN iajs-2818 68 57 , , PUNCT iajs-2818 68 58 πΈπ‘ž2 πΈπ‘ž2 NOUN iajs-2818 68 59 , , PUNCT iajs-2818 68 60 πΈπ‘ž3 πΈπ‘ž3 NOUN iajs-2818 68 61 , , PUNCT iajs-2818 68 62 πΈπ‘ž4 πΈπ‘ž4 NOUN iajs-2818 68 63 , , PUNCT iajs-2818 68 64 πΈπ‘ž5 πΈπ‘ž5 ADJ iajs-2818 68 65 are be AUX iajs-2818 68 66 the the DET iajs-2818 68 67 equations equation NOUN iajs-2818 68 68 of of ADP iajs-2818 68 69 ( ( PUNCT iajs-2818 68 70 1 1 NUM iajs-2818 68 71 ) ) PUNCT iajs-2818 68 72 , , PUNCT iajs-2818 68 73 β„Ž β„Ž PROPN iajs-2818 68 74 is be AUX iajs-2818 68 75 a a DET iajs-2818 68 76 step step NOUN iajs-2818 68 77 size size NOUN iajs-2818 68 78 and and CCONJ iajs-2818 68 79 𝑑 𝑑 PROPN iajs-2818 68 80 is be AUX iajs-2818 68 81 a a DET iajs-2818 68 82 time time NOUN iajs-2818 68 83 : : PUNCT iajs-2818 68 84 𝑔𝑆1 𝑔𝑆1 PROPN iajs-2818 68 85 = = SYM iajs-2818 68 86 β„ŽπΈπ‘ž1(𝑑𝑖 β„ŽπΈπ‘ž1(𝑑𝑖 PROPN iajs-2818 68 87 , , PUNCT iajs-2818 68 88 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 68 89 , , PUNCT iajs-2818 68 90 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 68 91 , , PUNCT iajs-2818 68 92 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 68 93 , , PUNCT iajs-2818 68 94 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 68 95 , , PUNCT iajs-2818 68 96 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 68 97 ) ) PUNCT iajs-2818 68 98 = = SYM iajs-2818 68 99 β„Ž(𝛬 β„Ž(𝛬 NOUN iajs-2818 68 100 βˆ’ βˆ’ NOUN iajs-2818 68 101 ( ( PUNCT iajs-2818 68 102 𝛼𝐸𝑖 𝛼𝐸𝑖 X iajs-2818 68 103 + + NOUN iajs-2818 68 104 π‘š π‘š X iajs-2818 68 105 + + CCONJ iajs-2818 68 106 πœ‡)𝑆𝑖 πœ‡)𝑆𝑖 NOUN iajs-2818 68 107 ) ) PUNCT iajs-2818 68 108 , , PUNCT iajs-2818 68 109 𝑔𝐸1 𝑔𝐸1 PROPN iajs-2818 68 110 = = SYM iajs-2818 68 111 β„ŽπΈπ‘ž2(𝑑𝑖 β„ŽπΈπ‘ž2(𝑑𝑖 PROPN iajs-2818 68 112 , , PUNCT iajs-2818 68 113 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 68 114 , , PUNCT iajs-2818 68 115 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 68 116 , , PUNCT iajs-2818 68 117 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 68 118 , , PUNCT iajs-2818 68 119 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 68 120 , , PUNCT iajs-2818 68 121 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 68 122 ) ) PUNCT iajs-2818 68 123 = = PUNCT iajs-2818 69 1 β„Ž(𝛼𝑆𝑖𝐸𝑖 β„Ž(𝛼𝑆𝑖𝐸𝑖 PROPN iajs-2818 69 2 + + CCONJ iajs-2818 69 3 𝑝𝑉𝑖𝐸𝑖 𝑝𝑉𝑖𝐸𝑖 PROPN iajs-2818 69 4 βˆ’ βˆ’ PROPN iajs-2818 69 5 ( ( PUNCT iajs-2818 69 6 𝑓𝐼𝑖 𝑓𝐼𝑖 NOUN iajs-2818 69 7 + + NOUN iajs-2818 69 8 𝑐 𝑐 PROPN iajs-2818 69 9 + + PUNCT iajs-2818 69 10 πœ‡)𝐸𝑖 πœ‡)𝐸𝑖 PROPN iajs-2818 69 11 ) ) PUNCT iajs-2818 69 12 , , PUNCT iajs-2818 69 13 𝑔𝐼1 𝑔𝐼1 PROPN iajs-2818 69 14 = = SYM iajs-2818 69 15 β„ŽπΈπ‘ž3(𝑑𝑖 β„ŽπΈπ‘ž3(𝑑𝑖 PROPN iajs-2818 69 16 , , PUNCT iajs-2818 69 17 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 69 18 , , PUNCT iajs-2818 69 19 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 69 20 , , PUNCT iajs-2818 69 21 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 69 22 , , PUNCT iajs-2818 69 23 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 69 24 , , PUNCT iajs-2818 69 25 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 69 26 ) ) PUNCT iajs-2818 69 27 = = SYM iajs-2818 69 28 β„Ž β„Ž PROPN iajs-2818 69 29 ( ( PUNCT iajs-2818 69 30 𝑓𝐸𝑖𝐼𝑖 𝑓𝐸𝑖𝐼𝑖 PROPN iajs-2818 69 31 βˆ’ βˆ’ PROPN iajs-2818 69 32 ( ( PUNCT iajs-2818 69 33 𝑧 𝑧 PROPN iajs-2818 69 34 + + X iajs-2818 69 35 πœ‡ πœ‡ X iajs-2818 69 36 + + NOUN iajs-2818 69 37 𝜎)𝐼𝑖 𝜎)𝐼𝑖 ADJ iajs-2818 69 38 ) ) PUNCT iajs-2818 69 39 , , PUNCT iajs-2818 69 40 𝑔𝑉1 𝑔𝑉1 VERB iajs-2818 69 41 = = PUNCT iajs-2818 69 42 β„ŽπΈπ‘ž4(𝑑𝑖 β„ŽπΈπ‘ž4(𝑑𝑖 PROPN iajs-2818 69 43 , , PUNCT iajs-2818 69 44 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 69 45 , , PUNCT iajs-2818 69 46 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 69 47 , , PUNCT iajs-2818 69 48 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 69 49 , , PUNCT iajs-2818 69 50 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 69 51 , , PUNCT iajs-2818 69 52 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 69 53 ) ) PUNCT iajs-2818 69 54 = = SYM iajs-2818 69 55 β„Ž β„Ž NOUN iajs-2818 69 56 ( ( PUNCT iajs-2818 69 57 π‘šπ‘†π‘– π‘šπ‘†π‘– NOUN iajs-2818 69 58 βˆ’ βˆ’ PROPN iajs-2818 69 59 ( ( PUNCT iajs-2818 69 60 𝑝𝐸𝑖 𝑝𝐸𝑖 X iajs-2818 69 61 + + CCONJ iajs-2818 69 62 πœ‡)𝑉𝑖 πœ‡)𝑉𝑖 PROPN iajs-2818 69 63 ) ) PUNCT iajs-2818 69 64 , , PUNCT iajs-2818 69 65 𝑔𝑅1 𝑔𝑅1 PROPN iajs-2818 69 66 = = SYM iajs-2818 69 67 β„ŽπΈπ‘ž5(𝑑𝑖 β„ŽπΈπ‘ž5(𝑑𝑖 PROPN iajs-2818 69 68 , , PUNCT iajs-2818 69 69 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 69 70 , , PUNCT iajs-2818 69 71 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 69 72 , , PUNCT iajs-2818 69 73 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 69 74 , , PUNCT iajs-2818 69 75 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 69 76 , , PUNCT iajs-2818 69 77 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 69 78 ) ) PUNCT iajs-2818 69 79 = = SYM iajs-2818 69 80 β„Ž β„Ž NOUN iajs-2818 69 81 ( ( PUNCT iajs-2818 69 82 𝑧𝐼𝑖 𝑧𝐼𝑖 NOUN iajs-2818 69 83 + + NOUN iajs-2818 69 84 𝑐𝐸𝑖 𝑐𝐸𝑖 NOUN iajs-2818 69 85 βˆ’ βˆ’ NOUN iajs-2818 69 86 πœ‡π‘…π‘– πœ‡π‘…π‘– NOUN iajs-2818 69 87 ) ) PUNCT iajs-2818 69 88 . . PUNCT iajs-2818 70 1 in in ADP iajs-2818 70 2 the the DET iajs-2818 70 3 same same ADJ iajs-2818 70 4 process process NOUN iajs-2818 70 5 , , PUNCT iajs-2818 70 6 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 70 7 , , PUNCT iajs-2818 70 8 𝑔𝐸2 𝑔𝐸2 PROPN iajs-2818 70 9 , , PUNCT iajs-2818 70 10 𝑔𝐼2 𝑔𝐼2 ADP iajs-2818 70 11 , , PUNCT iajs-2818 70 12 𝑔𝑉2 𝑔𝑉2 PROPN iajs-2818 70 13 and and CCONJ iajs-2818 70 14 𝑔𝑅2 𝑔𝑅2 PROPN iajs-2818 70 15 can can AUX iajs-2818 70 16 be be AUX iajs-2818 70 17 found find VERB iajs-2818 70 18 by by ADP iajs-2818 70 19 substituting substitute VERB iajs-2818 70 20 the the DET iajs-2818 70 21 form form NOUN iajs-2818 70 22 of of ADP iajs-2818 70 23 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 70 24 , , PUNCT iajs-2818 70 25 𝑔𝐸2 𝑔𝐸2 PROPN iajs-2818 70 26 , , PUNCT iajs-2818 70 27 𝑔𝐼2 𝑔𝐼2 ADP iajs-2818 70 28 , , PUNCT iajs-2818 70 29 𝑔𝑉2 𝑔𝑉2 PROPN iajs-2818 70 30 and and CCONJ iajs-2818 70 31 𝑔𝑅2 𝑔𝑅2 PROPN iajs-2818 70 32 in in ADP iajs-2818 70 33 ( ( PUNCT iajs-2818 70 34 1 1 NUM iajs-2818 70 35 ): ): PUNCT iajs-2818 70 36 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 70 37 = = SYM iajs-2818 70 38 β„ŽπΈπ‘ž1(𝑑𝑖 β„ŽπΈπ‘ž1(𝑑𝑖 PROPN iajs-2818 70 39 + + NUM iajs-2818 70 40 β„Ž β„Ž X iajs-2818 70 41 2 2 NUM iajs-2818 70 42 , , PUNCT iajs-2818 70 43 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 70 44 + + NUM iajs-2818 70 45 1 1 NUM iajs-2818 70 46 2 2 NUM iajs-2818 70 47 𝑔𝑆1 𝑔𝑆1 NOUN iajs-2818 70 48 , , PUNCT iajs-2818 70 49 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 70 50 + + NOUN iajs-2818 70 51 1 1 NUM iajs-2818 70 52 2 2 NUM iajs-2818 70 53 𝑔𝐸1 𝑔𝐸1 VERB iajs-2818 70 54 , , PUNCT iajs-2818 70 55 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 70 56 + + CCONJ iajs-2818 70 57 1 1 NUM iajs-2818 70 58 2 2 NUM iajs-2818 70 59 𝑔𝐼1 𝑔𝐼1 NOUN iajs-2818 70 60 , , PUNCT iajs-2818 71 1 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 71 2 + + NOUN iajs-2818 71 3 1 1 NUM iajs-2818 71 4 2 2 NUM iajs-2818 71 5 𝑔𝑉1 𝑔𝑉1 NOUN iajs-2818 71 6 , , PUNCT iajs-2818 71 7 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 71 8 + + CCONJ iajs-2818 71 9 1 1 NUM iajs-2818 71 10 2 2 NUM iajs-2818 71 11 𝑔𝑅1 𝑔𝑅1 NOUN iajs-2818 71 12 ) ) PUNCT iajs-2818 72 1 = = SYM iajs-2818 72 2 β„Ž β„Ž NOUN iajs-2818 72 3 ( ( PUNCT iajs-2818 72 4 𝛬 𝛬 PROPN iajs-2818 72 5 βˆ’ βˆ’ PROPN iajs-2818 72 6 ( ( PUNCT iajs-2818 72 7 𝛼(𝐸𝑖 𝛼(𝐸𝑖 NOUN iajs-2818 72 8 + + CCONJ iajs-2818 72 9 1 1 NUM iajs-2818 72 10 2 2 NUM iajs-2818 72 11 𝑔𝐸1 𝑔𝐸1 NUM iajs-2818 72 12 ) ) PUNCT iajs-2818 73 1 + + CCONJ iajs-2818 73 2 π‘š π‘š X iajs-2818 73 3 + + X iajs-2818 73 4 πœ‡)(𝑆𝑖 πœ‡)(𝑆𝑖 X iajs-2818 73 5 + + CCONJ iajs-2818 73 6 1 1 NUM iajs-2818 73 7 2 2 NUM iajs-2818 73 8 𝑔𝑆1 𝑔𝑆1 PROPN iajs-2818 73 9 ) ) PUNCT iajs-2818 73 10 ) ) PUNCT iajs-2818 73 11 , , PUNCT iajs-2818 73 12 𝑔𝐸2 𝑔𝐸2 PROPN iajs-2818 73 13 = = SYM iajs-2818 73 14 β„ŽπΈπ‘ž2 β„ŽπΈπ‘ž2 PROPN iajs-2818 73 15 ( ( PUNCT iajs-2818 73 16 𝑑𝑖 𝑑𝑖 X iajs-2818 73 17 + + CCONJ iajs-2818 73 18 β„Ž β„Ž X iajs-2818 73 19 2 2 NUM iajs-2818 73 20 , , PUNCT iajs-2818 73 21 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 73 22 + + NUM iajs-2818 73 23 1 1 NUM iajs-2818 73 24 2 2 NUM iajs-2818 73 25 𝑔𝑆1 𝑔𝑆1 NOUN iajs-2818 73 26 , , PUNCT iajs-2818 73 27 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 73 28 + + NOUN iajs-2818 73 29 1 1 NUM iajs-2818 73 30 2 2 NUM iajs-2818 73 31 𝑔𝐸1 𝑔𝐸1 VERB iajs-2818 73 32 , , PUNCT iajs-2818 73 33 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 73 34 + + CCONJ iajs-2818 73 35 1 1 NUM iajs-2818 73 36 2 2 NUM iajs-2818 73 37 𝑔𝐼1 𝑔𝐼1 NOUN iajs-2818 73 38 , , PUNCT iajs-2818 73 39 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 73 40 + + NOUN iajs-2818 73 41 1 1 NUM iajs-2818 73 42 2 2 NUM iajs-2818 73 43 𝑔𝑉1 𝑔𝑉1 NOUN iajs-2818 73 44 , , PUNCT iajs-2818 73 45 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 73 46 + + CCONJ iajs-2818 73 47 1 1 NUM iajs-2818 73 48 2 2 NUM iajs-2818 73 49 𝑔𝑅1 𝑔𝑅1 NOUN iajs-2818 73 50 ) ) PUNCT iajs-2818 73 51 ibn ibn PROPN iajs-2818 73 52 al al PROPN iajs-2818 73 53 - - PUNCT iajs-2818 73 54 haitham haitham PROPN iajs-2818 73 55 jour jour X iajs-2818 73 56 . . PROPN iajs-2818 74 1 for for ADP iajs-2818 74 2 pure pure ADJ iajs-2818 74 3 & & CCONJ iajs-2818 74 4 appl appl PROPN iajs-2818 74 5 . . PUNCT iajs-2818 75 1 sci sci PROPN iajs-2818 75 2 . . PROPN iajs-2818 76 1 53 53 NUM iajs-2818 76 2 ( ( PUNCT iajs-2818 76 3 2)2022 2)2022 VERB iajs-2818 76 4 101 101 NUM iajs-2818 76 5 = = SYM iajs-2818 76 6 β„Ž β„Ž PROPN iajs-2818 76 7 ( ( PUNCT iajs-2818 76 8 𝛼 𝛼 PROPN iajs-2818 76 9 ( ( PUNCT iajs-2818 76 10 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 76 11 + + NUM iajs-2818 76 12 1 1 NUM iajs-2818 76 13 2 2 NUM iajs-2818 76 14 𝑔𝑆1 𝑔𝑆1 PROPN iajs-2818 76 15 ) ) PUNCT iajs-2818 76 16 ( ( PUNCT iajs-2818 76 17 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 76 18 + + CCONJ iajs-2818 76 19 1 1 NUM iajs-2818 76 20 2 2 NUM iajs-2818 76 21 𝑔𝐸1 𝑔𝐸1 NUM iajs-2818 76 22 ) ) PUNCT iajs-2818 76 23 + + NUM iajs-2818 76 24 𝑝(𝑉𝑖 𝑝(𝑉𝑖 NOUN iajs-2818 76 25 + + CCONJ iajs-2818 76 26 1 1 NUM iajs-2818 76 27 2 2 NUM iajs-2818 76 28 𝑔𝑉1)(𝐸𝑖 𝑔𝑉1)(𝐸𝑖 NOUN iajs-2818 76 29 + + CCONJ iajs-2818 76 30 1 1 NUM iajs-2818 76 31 2 2 NUM iajs-2818 76 32 𝑔𝐸1 𝑔𝐸1 NUM iajs-2818 76 33 ) ) PUNCT iajs-2818 76 34 βˆ’ βˆ’ PROPN iajs-2818 76 35 ( ( PUNCT iajs-2818 76 36 𝑓(𝐼𝑖 𝑓(𝐼𝑖 NOUN iajs-2818 76 37 + + X iajs-2818 76 38 1 1 NUM iajs-2818 76 39 2 2 NUM iajs-2818 76 40 𝑔𝐼1 𝑔𝐼1 NOUN iajs-2818 76 41 ) ) PUNCT iajs-2818 77 1 + + CCONJ iajs-2818 77 2 𝑐 𝑐 PROPN iajs-2818 77 3 + + CCONJ iajs-2818 77 4 πœ‡)(𝐸𝑖 πœ‡)(𝐸𝑖 NUM iajs-2818 77 5 + + CCONJ iajs-2818 77 6 1 1 NUM iajs-2818 77 7 2 2 NUM iajs-2818 77 8 𝑔𝐸1 𝑔𝐸1 NUM iajs-2818 77 9 ) ) PUNCT iajs-2818 77 10 ) ) PUNCT iajs-2818 77 11 , , PUNCT iajs-2818 77 12 𝑔𝐼2 𝑔𝐼2 PUNCT iajs-2818 77 13 = = PUNCT iajs-2818 77 14 β„ŽπΈπ‘ž3 β„ŽπΈπ‘ž3 PROPN iajs-2818 77 15 ( ( PUNCT iajs-2818 77 16 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 77 17 + + CCONJ iajs-2818 77 18 β„Ž β„Ž X iajs-2818 77 19 2 2 NUM iajs-2818 77 20 , , PUNCT iajs-2818 77 21 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 77 22 + + NUM iajs-2818 77 23 1 1 NUM iajs-2818 77 24 2 2 NUM iajs-2818 77 25 𝑔𝑆1 𝑔𝑆1 NOUN iajs-2818 77 26 , , PUNCT iajs-2818 77 27 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 77 28 + + NOUN iajs-2818 77 29 1 1 NUM iajs-2818 77 30 2 2 NUM iajs-2818 77 31 𝑔𝐸1 𝑔𝐸1 VERB iajs-2818 77 32 , , PUNCT iajs-2818 77 33 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 77 34 + + CCONJ iajs-2818 77 35 1 1 NUM iajs-2818 77 36 2 2 NUM iajs-2818 77 37 𝑔𝐼1 𝑔𝐼1 NOUN iajs-2818 77 38 , , PUNCT iajs-2818 77 39 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 77 40 + + NOUN iajs-2818 77 41 1 1 NUM iajs-2818 77 42 2 2 NUM iajs-2818 77 43 𝑔𝑉1 𝑔𝑉1 NOUN iajs-2818 77 44 , , PUNCT iajs-2818 77 45 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 77 46 + + CCONJ iajs-2818 77 47 1 1 NUM iajs-2818 77 48 2 2 NUM iajs-2818 77 49 𝑔𝑅1 𝑔𝑅1 NOUN iajs-2818 77 50 ) ) PUNCT iajs-2818 78 1 = = SYM iajs-2818 78 2 β„Ž β„Ž NOUN iajs-2818 78 3 ( ( PUNCT iajs-2818 78 4 𝑓(𝐸𝑖 𝑓(𝐸𝑖 X iajs-2818 78 5 + + X iajs-2818 78 6 1 1 NUM iajs-2818 78 7 2 2 NUM iajs-2818 78 8 𝑔𝐸1)(𝐼𝑖 𝑔𝐸1)(𝐼𝑖 NOUN iajs-2818 78 9 + + CCONJ iajs-2818 78 10 1 1 NUM iajs-2818 78 11 2 2 NUM iajs-2818 78 12 𝑔𝐼1 𝑔𝐼1 NOUN iajs-2818 78 13 ) ) PUNCT iajs-2818 78 14 βˆ’ βˆ’ PROPN iajs-2818 78 15 ( ( PUNCT iajs-2818 78 16 𝑧 𝑧 PROPN iajs-2818 78 17 + + X iajs-2818 78 18 πœ‡ πœ‡ X iajs-2818 78 19 + + X iajs-2818 78 20 𝜎)(𝐼𝑖 𝜎)(𝐼𝑖 NOUN iajs-2818 78 21 + + CCONJ iajs-2818 78 22 1 1 NUM iajs-2818 78 23 2 2 NUM iajs-2818 78 24 𝑔𝐼1 𝑔𝐼1 NOUN iajs-2818 78 25 ) ) PUNCT iajs-2818 78 26 ) ) PUNCT iajs-2818 78 27 , , PUNCT iajs-2818 78 28 𝑔𝑉2 𝑔𝑉2 PROPN iajs-2818 78 29 = = SYM iajs-2818 78 30 β„ŽπΈπ‘ž4 β„ŽπΈπ‘ž4 PROPN iajs-2818 78 31 ( ( PUNCT iajs-2818 78 32 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 78 33 + + CCONJ iajs-2818 78 34 β„Ž β„Ž X iajs-2818 78 35 2 2 NUM iajs-2818 78 36 , , PUNCT iajs-2818 78 37 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 78 38 + + NUM iajs-2818 78 39 1 1 NUM iajs-2818 78 40 2 2 NUM iajs-2818 78 41 𝑔𝑆1 𝑔𝑆1 NOUN iajs-2818 78 42 , , PUNCT iajs-2818 78 43 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 78 44 + + NOUN iajs-2818 78 45 1 1 NUM iajs-2818 78 46 2 2 NUM iajs-2818 78 47 𝑔𝐸1 𝑔𝐸1 VERB iajs-2818 78 48 , , PUNCT iajs-2818 78 49 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 78 50 + + CCONJ iajs-2818 78 51 1 1 NUM iajs-2818 78 52 2 2 NUM iajs-2818 78 53 𝑔𝐼1 𝑔𝐼1 NOUN iajs-2818 78 54 , , PUNCT iajs-2818 78 55 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 78 56 + + NOUN iajs-2818 78 57 1 1 NUM iajs-2818 78 58 2 2 NUM iajs-2818 78 59 𝑔𝑉1 𝑔𝑉1 NOUN iajs-2818 78 60 , , PUNCT iajs-2818 78 61 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 78 62 + + CCONJ iajs-2818 78 63 1 1 NUM iajs-2818 78 64 2 2 NUM iajs-2818 78 65 𝑔𝑅1 𝑔𝑅1 NOUN iajs-2818 78 66 ) ) PUNCT iajs-2818 78 67 = = SYM iajs-2818 78 68 β„Ž β„Ž NOUN iajs-2818 78 69 ( ( PUNCT iajs-2818 78 70 π‘š(𝑆𝑖 π‘š(𝑆𝑖 VERB iajs-2818 78 71 + + CCONJ iajs-2818 78 72 1 1 NUM iajs-2818 78 73 2 2 NUM iajs-2818 78 74 𝑔𝑆1 𝑔𝑆1 PROPN iajs-2818 78 75 ) ) PUNCT iajs-2818 78 76 βˆ’ βˆ’ PROPN iajs-2818 78 77 ( ( PUNCT iajs-2818 78 78 𝑝(𝐸𝑖 𝑝(𝐸𝑖 VERB iajs-2818 78 79 + + CCONJ iajs-2818 78 80 1 1 NUM iajs-2818 78 81 2 2 NUM iajs-2818 78 82 𝑔𝐸1 𝑔𝐸1 NUM iajs-2818 78 83 ) ) PUNCT iajs-2818 78 84 + + CCONJ iajs-2818 78 85 πœ‡ πœ‡ X iajs-2818 78 86 ) ) PUNCT iajs-2818 78 87 ( ( PUNCT iajs-2818 78 88 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 78 89 + + NOUN iajs-2818 78 90 1 1 NUM iajs-2818 78 91 2 2 NUM iajs-2818 78 92 𝑔𝑉1 𝑔𝑉1 NOUN iajs-2818 78 93 ) ) PUNCT iajs-2818 78 94 ) ) PUNCT iajs-2818 78 95 , , PUNCT iajs-2818 78 96 𝑔𝑅2 𝑔𝑅2 PROPN iajs-2818 78 97 = = PUNCT iajs-2818 78 98 β„Žπ‘“5 β„Žπ‘“5 PROPN iajs-2818 78 99 ( ( PUNCT iajs-2818 78 100 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 78 101 + + CCONJ iajs-2818 78 102 β„Ž β„Ž X iajs-2818 78 103 2 2 NUM iajs-2818 78 104 , , PUNCT iajs-2818 78 105 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 78 106 + + NUM iajs-2818 78 107 1 1 NUM iajs-2818 78 108 2 2 NUM iajs-2818 78 109 𝑔𝑆1 𝑔𝑆1 NOUN iajs-2818 78 110 , , PUNCT iajs-2818 78 111 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 78 112 + + NOUN iajs-2818 78 113 1 1 NUM iajs-2818 78 114 2 2 NUM iajs-2818 78 115 𝑔𝐸1 𝑔𝐸1 VERB iajs-2818 78 116 , , PUNCT iajs-2818 78 117 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 78 118 + + CCONJ iajs-2818 78 119 1 1 NUM iajs-2818 78 120 2 2 NUM iajs-2818 78 121 𝑔𝐼1 𝑔𝐼1 NOUN iajs-2818 78 122 , , PUNCT iajs-2818 78 123 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 78 124 + + NOUN iajs-2818 78 125 1 1 NUM iajs-2818 78 126 2 2 NUM iajs-2818 78 127 𝑔𝑉1 𝑔𝑉1 NOUN iajs-2818 78 128 , , PUNCT iajs-2818 78 129 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 78 130 + + CCONJ iajs-2818 78 131 1 1 NUM iajs-2818 78 132 2 2 NUM iajs-2818 78 133 𝑔𝑅1 𝑔𝑅1 NOUN iajs-2818 78 134 ) ) PUNCT iajs-2818 78 135 = = SYM iajs-2818 78 136 β„Ž β„Ž NOUN iajs-2818 78 137 ( ( PUNCT iajs-2818 78 138 𝑧(𝐼𝑖 𝑧(𝐼𝑖 VERB iajs-2818 78 139 + + CCONJ iajs-2818 78 140 1 1 NUM iajs-2818 78 141 2 2 NUM iajs-2818 78 142 𝑔𝐼1 𝑔𝐼1 NOUN iajs-2818 78 143 ) ) PUNCT iajs-2818 79 1 + + CCONJ iajs-2818 79 2 𝑐(𝐸𝑖 𝑐(𝐸𝑖 X iajs-2818 79 3 + + CCONJ iajs-2818 79 4 1 1 NUM iajs-2818 79 5 2 2 NUM iajs-2818 79 6 𝑔𝐸1 𝑔𝐸1 NUM iajs-2818 79 7 ) ) PUNCT iajs-2818 79 8 βˆ’ βˆ’ NOUN iajs-2818 79 9 πœ‡ πœ‡ ADP iajs-2818 79 10 ( ( PUNCT iajs-2818 79 11 𝑅𝑖 𝑅𝑖 NOUN iajs-2818 79 12 + + CCONJ iajs-2818 79 13 1 1 NUM iajs-2818 79 14 2 2 NUM iajs-2818 79 15 𝑔𝑅1 𝑔𝑅1 NOUN iajs-2818 79 16 ) ) PUNCT iajs-2818 79 17 ) ) PUNCT iajs-2818 79 18 . . PUNCT iajs-2818 80 1 in in ADP iajs-2818 80 2 the the DET iajs-2818 80 3 third third ADJ iajs-2818 80 4 stage stage NOUN iajs-2818 80 5 , , PUNCT iajs-2818 80 6 try try VERB iajs-2818 80 7 to to PART iajs-2818 80 8 find find VERB iajs-2818 80 9 𝑔𝑆3 𝑔𝑆3 PRON iajs-2818 80 10 , , PUNCT iajs-2818 80 11 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 80 12 , , PUNCT iajs-2818 80 13 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 80 14 , , PUNCT iajs-2818 80 15 𝑔𝑉3 𝑔𝑉3 PROPN iajs-2818 80 16 and and CCONJ iajs-2818 80 17 𝑔𝑅3 𝑔𝑅3 PROPN iajs-2818 80 18 , , PUNCT iajs-2818 80 19 by by ADP iajs-2818 80 20 substituting substitute VERB iajs-2818 80 21 the the DET iajs-2818 80 22 form form NOUN iajs-2818 80 23 of of ADP iajs-2818 80 24 𝑔𝑆3 𝑔𝑆3 PROPN iajs-2818 80 25 , , PUNCT iajs-2818 80 26 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 80 27 , , PUNCT iajs-2818 80 28 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 80 29 , , PUNCT iajs-2818 80 30 𝑔𝑉3 𝑔𝑉3 PROPN iajs-2818 80 31 and and CCONJ iajs-2818 80 32 𝑔𝑅3 𝑔𝑅3 PROPN iajs-2818 80 33 in in ADP iajs-2818 80 34 ( ( PUNCT iajs-2818 80 35 1 1 NUM iajs-2818 80 36 ) ) PUNCT iajs-2818 80 37 as as ADP iajs-2818 80 38 below below ADV iajs-2818 80 39 : : PUNCT iajs-2818 80 40 𝑔𝑆3 𝑔𝑆3 PROPN iajs-2818 80 41 = = PUNCT iajs-2818 80 42 β„ŽπΈπ‘ž1 β„ŽπΈπ‘ž1 PROPN iajs-2818 80 43 ( ( PUNCT iajs-2818 80 44 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 80 45 + + CCONJ iajs-2818 80 46 β„Ž β„Ž X iajs-2818 80 47 2 2 NUM iajs-2818 80 48 , , PUNCT iajs-2818 80 49 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 80 50 + + NUM iajs-2818 80 51 1 1 NUM iajs-2818 80 52 2 2 NUM iajs-2818 80 53 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 80 54 , , PUNCT iajs-2818 80 55 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 80 56 + + NOUN iajs-2818 80 57 1 1 NUM iajs-2818 80 58 2 2 NUM iajs-2818 80 59 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 80 60 , , PUNCT iajs-2818 80 61 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 80 62 + + CCONJ iajs-2818 80 63 1 1 NUM iajs-2818 80 64 2 2 NUM iajs-2818 80 65 𝑔𝐼2 𝑔𝐼2 NOUN iajs-2818 80 66 , , PUNCT iajs-2818 80 67 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 80 68 + + NOUN iajs-2818 80 69 1 1 NUM iajs-2818 80 70 2 2 NUM iajs-2818 80 71 𝑔𝑉2 𝑔𝑉2 NOUN iajs-2818 80 72 , , PUNCT iajs-2818 80 73 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 80 74 + + CCONJ iajs-2818 80 75 1 1 NUM iajs-2818 80 76 2 2 NUM iajs-2818 80 77 𝑔𝑅2 𝑔𝑅2 NUM iajs-2818 80 78 ) ) PUNCT iajs-2818 80 79 = = SYM iajs-2818 81 1 β„Ž β„Ž NOUN iajs-2818 81 2 ( ( PUNCT iajs-2818 81 3 𝛬 𝛬 PROPN iajs-2818 81 4 βˆ’ βˆ’ PROPN iajs-2818 81 5 ( ( PUNCT iajs-2818 81 6 𝛼(𝐸𝑖 𝛼(𝐸𝑖 NOUN iajs-2818 81 7 + + CCONJ iajs-2818 81 8 1 1 NUM iajs-2818 81 9 2 2 NUM iajs-2818 81 10 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 81 11 ) ) PUNCT iajs-2818 82 1 + + CCONJ iajs-2818 82 2 π‘š π‘š X iajs-2818 82 3 + + X iajs-2818 82 4 πœ‡)(𝑆𝑖 πœ‡)(𝑆𝑖 X iajs-2818 82 5 + + CCONJ iajs-2818 82 6 1 1 NUM iajs-2818 82 7 2 2 NUM iajs-2818 82 8 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 82 9 ) ) PUNCT iajs-2818 82 10 ) ) PUNCT iajs-2818 82 11 , , PUNCT iajs-2818 82 12 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 82 13 = = SYM iajs-2818 82 14 β„ŽπΈπ‘ž2 β„ŽπΈπ‘ž2 PROPN iajs-2818 82 15 ( ( PUNCT iajs-2818 82 16 𝑑𝑖 𝑑𝑖 X iajs-2818 82 17 + + CCONJ iajs-2818 82 18 β„Ž β„Ž X iajs-2818 82 19 2 2 NUM iajs-2818 82 20 , , PUNCT iajs-2818 82 21 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 82 22 + + NUM iajs-2818 82 23 1 1 NUM iajs-2818 82 24 2 2 NUM iajs-2818 82 25 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 82 26 , , PUNCT iajs-2818 82 27 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 82 28 + + NOUN iajs-2818 82 29 1 1 NUM iajs-2818 82 30 2 2 NUM iajs-2818 82 31 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 82 32 , , PUNCT iajs-2818 82 33 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 82 34 + + CCONJ iajs-2818 82 35 1 1 NUM iajs-2818 82 36 2 2 NUM iajs-2818 82 37 𝑔𝐼2 𝑔𝐼2 NOUN iajs-2818 82 38 , , PUNCT iajs-2818 82 39 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 82 40 + + CCONJ iajs-2818 82 41 1 1 NUM iajs-2818 82 42 2 2 NUM iajs-2818 82 43 𝑔𝑅2 𝑔𝑅2 NUM iajs-2818 82 44 ) ) PUNCT iajs-2818 82 45 = = SYM iajs-2818 82 46 β„Ž β„Ž PROPN iajs-2818 82 47 ( ( PUNCT iajs-2818 82 48 𝛼(𝑆𝑖 𝛼(𝑆𝑖 NOUN iajs-2818 82 49 + + NOUN iajs-2818 82 50 1 1 NUM iajs-2818 82 51 2 2 NUM iajs-2818 82 52 𝑔𝑆2)(𝐸𝑖 𝑔𝑆2)(𝐸𝑖 PROPN iajs-2818 83 1 + + CCONJ iajs-2818 83 2 1 1 NUM iajs-2818 83 3 2 2 NUM iajs-2818 83 4 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 83 5 ) ) PUNCT iajs-2818 84 1 + + NUM iajs-2818 84 2 𝑝(𝑉𝑖 𝑝(𝑉𝑖 NOUN iajs-2818 85 1 + + CCONJ iajs-2818 85 2 1 1 NUM iajs-2818 85 3 2 2 NUM iajs-2818 85 4 𝑔𝑉2)(𝐸𝑖 𝑔𝑉2)(𝐸𝑖 NOUN iajs-2818 85 5 + + CCONJ iajs-2818 85 6 1 1 NUM iajs-2818 85 7 2 2 NUM iajs-2818 85 8 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 85 9 ) ) PUNCT iajs-2818 85 10 βˆ’ βˆ’ PROPN iajs-2818 85 11 ( ( PUNCT iajs-2818 85 12 𝑓(𝐼𝑖 𝑓(𝐼𝑖 NOUN iajs-2818 85 13 + + X iajs-2818 85 14 1 1 NUM iajs-2818 85 15 2 2 NUM iajs-2818 85 16 𝑔𝐼2 𝑔𝐼2 NUM iajs-2818 85 17 ) ) PUNCT iajs-2818 86 1 + + CCONJ iajs-2818 86 2 𝑐 𝑐 PROPN iajs-2818 86 3 + + CCONJ iajs-2818 86 4 πœ‡)(𝐸𝑖 πœ‡)(𝐸𝑖 NUM iajs-2818 86 5 + + CCONJ iajs-2818 86 6 1 1 NUM iajs-2818 86 7 2 2 NUM iajs-2818 86 8 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 86 9 ) ) PUNCT iajs-2818 86 10 ) ) PUNCT iajs-2818 86 11 , , PUNCT iajs-2818 86 12 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 86 13 = = SYM iajs-2818 86 14 β„ŽπΈπ‘ž3 β„ŽπΈπ‘ž3 PROPN iajs-2818 86 15 ( ( PUNCT iajs-2818 86 16 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 86 17 + + CCONJ iajs-2818 86 18 β„Ž β„Ž X iajs-2818 86 19 2 2 NUM iajs-2818 86 20 , , PUNCT iajs-2818 86 21 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 86 22 + + NUM iajs-2818 86 23 1 1 NUM iajs-2818 86 24 2 2 NUM iajs-2818 86 25 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 86 26 , , PUNCT iajs-2818 86 27 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 86 28 + + NOUN iajs-2818 86 29 1 1 NUM iajs-2818 86 30 2 2 NUM iajs-2818 86 31 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 86 32 , , PUNCT iajs-2818 86 33 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 86 34 + + CCONJ iajs-2818 86 35 1 1 NUM iajs-2818 86 36 2 2 NUM iajs-2818 86 37 𝑔𝐼2 𝑔𝐼2 NOUN iajs-2818 86 38 , , PUNCT iajs-2818 86 39 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 86 40 + + NOUN iajs-2818 86 41 1 1 NUM iajs-2818 86 42 2 2 NUM iajs-2818 86 43 𝑔𝑉2 𝑔𝑉2 NOUN iajs-2818 86 44 , , PUNCT iajs-2818 86 45 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 86 46 + + CCONJ iajs-2818 86 47 1 1 NUM iajs-2818 86 48 2 2 NUM iajs-2818 86 49 𝑔𝑅2 𝑔𝑅2 NUM iajs-2818 86 50 ) ) PUNCT iajs-2818 86 51 = = SYM iajs-2818 87 1 β„Ž β„Ž NOUN iajs-2818 87 2 ( ( PUNCT iajs-2818 87 3 𝑓(𝐸𝑖 𝑓(𝐸𝑖 X iajs-2818 87 4 + + X iajs-2818 87 5 1 1 NUM iajs-2818 87 6 2 2 NUM iajs-2818 87 7 𝑔𝐸2)(𝐼𝑖 𝑔𝐸2)(𝐼𝑖 NOUN iajs-2818 87 8 + + CCONJ iajs-2818 87 9 1 1 NUM iajs-2818 87 10 2 2 NUM iajs-2818 87 11 𝑔𝐼2 𝑔𝐼2 NUM iajs-2818 87 12 ) ) PUNCT iajs-2818 87 13 βˆ’ βˆ’ PROPN iajs-2818 87 14 ( ( PUNCT iajs-2818 87 15 𝑧 𝑧 PROPN iajs-2818 87 16 + + X iajs-2818 87 17 πœ‡ πœ‡ X iajs-2818 87 18 + + X iajs-2818 87 19 𝜎)(𝐼𝑖 𝜎)(𝐼𝑖 NOUN iajs-2818 87 20 + + CCONJ iajs-2818 87 21 1 1 NUM iajs-2818 87 22 2 2 NUM iajs-2818 87 23 𝑔𝐼2 𝑔𝐼2 NOUN iajs-2818 87 24 ) ) PUNCT iajs-2818 87 25 ) ) PUNCT iajs-2818 87 26 , , PUNCT iajs-2818 87 27 𝑔𝑉3 𝑔𝑉3 NOUN iajs-2818 87 28 = = SYM iajs-2818 87 29 β„ŽπΈπ‘ž4 β„ŽπΈπ‘ž4 PROPN iajs-2818 87 30 ( ( PUNCT iajs-2818 87 31 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 87 32 + + CCONJ iajs-2818 87 33 β„Ž β„Ž X iajs-2818 87 34 2 2 NUM iajs-2818 87 35 , , PUNCT iajs-2818 87 36 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 87 37 + + NUM iajs-2818 87 38 1 1 NUM iajs-2818 87 39 2 2 NUM iajs-2818 87 40 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 87 41 , , PUNCT iajs-2818 87 42 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 87 43 + + NOUN iajs-2818 87 44 1 1 NUM iajs-2818 87 45 2 2 NUM iajs-2818 87 46 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 87 47 , , PUNCT iajs-2818 87 48 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 87 49 + + CCONJ iajs-2818 87 50 1 1 NUM iajs-2818 87 51 2 2 NUM iajs-2818 87 52 𝑔𝐼2 𝑔𝐼2 NOUN iajs-2818 87 53 , , PUNCT iajs-2818 87 54 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 87 55 + + NOUN iajs-2818 87 56 1 1 NUM iajs-2818 87 57 2 2 NUM iajs-2818 87 58 𝑔𝑉2 𝑔𝑉2 NOUN iajs-2818 87 59 , , PUNCT iajs-2818 87 60 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 87 61 + + CCONJ iajs-2818 87 62 1 1 NUM iajs-2818 87 63 2 2 NUM iajs-2818 87 64 𝑔𝑅2 𝑔𝑅2 NUM iajs-2818 87 65 ) ) PUNCT iajs-2818 87 66 = = SYM iajs-2818 87 67 β„Ž β„Ž NOUN iajs-2818 87 68 ( ( PUNCT iajs-2818 87 69 π‘š(𝑆𝑖 π‘š(𝑆𝑖 VERB iajs-2818 87 70 + + CCONJ iajs-2818 87 71 1 1 NUM iajs-2818 87 72 2 2 NUM iajs-2818 87 73 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 87 74 ) ) PUNCT iajs-2818 87 75 βˆ’ βˆ’ PROPN iajs-2818 87 76 ( ( PUNCT iajs-2818 87 77 𝑝(𝐸𝑖 𝑝(𝐸𝑖 VERB iajs-2818 87 78 + + CCONJ iajs-2818 87 79 1 1 NUM iajs-2818 87 80 2 2 NUM iajs-2818 87 81 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 87 82 ) ) PUNCT iajs-2818 87 83 + + CCONJ iajs-2818 87 84 πœ‡ πœ‡ X iajs-2818 87 85 ) ) PUNCT iajs-2818 87 86 ( ( PUNCT iajs-2818 87 87 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 87 88 + + NOUN iajs-2818 87 89 1 1 NUM iajs-2818 87 90 2 2 NUM iajs-2818 87 91 𝑔𝑉2 𝑔𝑉2 PROPN iajs-2818 87 92 ) ) PUNCT iajs-2818 87 93 ) ) PUNCT iajs-2818 87 94 , , PUNCT iajs-2818 87 95 𝑔𝑅3 𝑔𝑅3 PROPN iajs-2818 87 96 = = PUNCT iajs-2818 87 97 β„ŽπΈπ‘ž5 β„ŽπΈπ‘ž5 PROPN iajs-2818 87 98 ( ( PUNCT iajs-2818 87 99 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 87 100 + + CCONJ iajs-2818 87 101 β„Ž β„Ž X iajs-2818 87 102 2 2 NUM iajs-2818 87 103 , , PUNCT iajs-2818 87 104 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 87 105 + + NUM iajs-2818 87 106 1 1 NUM iajs-2818 87 107 2 2 NUM iajs-2818 87 108 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 87 109 , , PUNCT iajs-2818 87 110 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 87 111 + + NOUN iajs-2818 87 112 1 1 NUM iajs-2818 87 113 2 2 NUM iajs-2818 87 114 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 87 115 , , PUNCT iajs-2818 87 116 𝐼𝑖 𝐼𝑖 NOUN iajs-2818 87 117 + + CCONJ iajs-2818 87 118 1 1 NUM iajs-2818 87 119 2 2 NUM iajs-2818 87 120 𝑔𝐼2 𝑔𝐼2 NOUN iajs-2818 87 121 , , PUNCT iajs-2818 87 122 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 87 123 + + NOUN iajs-2818 87 124 1 1 NUM iajs-2818 87 125 2 2 NUM iajs-2818 87 126 𝑔𝑉2 𝑔𝑉2 NOUN iajs-2818 87 127 , , PUNCT iajs-2818 87 128 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 87 129 + + CCONJ iajs-2818 87 130 1 1 NUM iajs-2818 87 131 2 2 NUM iajs-2818 87 132 𝑔𝑅2 𝑔𝑅2 NUM iajs-2818 87 133 ) ) PUNCT iajs-2818 87 134 = = SYM iajs-2818 87 135 β„Ž β„Ž NOUN iajs-2818 87 136 ( ( PUNCT iajs-2818 87 137 𝑧(𝐼𝑖 𝑧(𝐼𝑖 VERB iajs-2818 87 138 + + CCONJ iajs-2818 87 139 1 1 NUM iajs-2818 87 140 2 2 NUM iajs-2818 87 141 𝑔𝐼2 𝑔𝐼2 NUM iajs-2818 87 142 ) ) PUNCT iajs-2818 88 1 + + CCONJ iajs-2818 88 2 𝑐(𝐸𝑖 𝑐(𝐸𝑖 X iajs-2818 88 3 + + CCONJ iajs-2818 88 4 1 1 NUM iajs-2818 88 5 2 2 NUM iajs-2818 88 6 𝑔𝐸2 𝑔𝐸2 NOUN iajs-2818 88 7 ) ) PUNCT iajs-2818 88 8 βˆ’ βˆ’ NOUN iajs-2818 88 9 πœ‡ πœ‡ ADP iajs-2818 88 10 ( ( PUNCT iajs-2818 88 11 𝑅𝑖 𝑅𝑖 NOUN iajs-2818 88 12 + + CCONJ iajs-2818 88 13 1 1 NUM iajs-2818 88 14 2 2 NUM iajs-2818 88 15 𝑔𝑅2 𝑔𝑅2 NUM iajs-2818 88 16 ) ) PUNCT iajs-2818 88 17 ) ) PUNCT iajs-2818 88 18 . . PUNCT iajs-2818 89 1 the the DET iajs-2818 89 2 fourth fourth ADJ iajs-2818 89 3 stage stage NOUN iajs-2818 89 4 needs need VERB iajs-2818 89 5 to to PART iajs-2818 89 6 find find VERB iajs-2818 89 7 𝑔𝑆4 𝑔𝑆4 NOUN iajs-2818 89 8 , , PUNCT iajs-2818 89 9 𝑔𝐸4 𝑔𝐸4 PROPN iajs-2818 89 10 , , PUNCT iajs-2818 89 11 𝑔𝐼4 𝑔𝐼4 PROPN iajs-2818 89 12 , , PUNCT iajs-2818 89 13 𝑔𝑉4 𝑔𝑉4 PROPN iajs-2818 89 14 and and CCONJ iajs-2818 89 15 𝑔𝑅4 𝑔𝑅4 PROPN iajs-2818 89 16 , , PUNCT iajs-2818 89 17 substituting substitute VERB iajs-2818 89 18 the the DET iajs-2818 89 19 form form NOUN iajs-2818 89 20 of of ADP iajs-2818 89 21 𝑔𝑆4 𝑔𝑆4 PROPN iajs-2818 89 22 , , PUNCT iajs-2818 89 23 𝑔𝐸4 𝑔𝐸4 PROPN iajs-2818 89 24 , , PUNCT iajs-2818 89 25 𝑔𝐼4 𝑔𝐼4 PROPN iajs-2818 89 26 , , PUNCT iajs-2818 89 27 𝑔𝑉4 𝑔𝑉4 PROPN iajs-2818 89 28 and and CCONJ iajs-2818 89 29 𝑔𝑅4 𝑔𝑅4 PROPN iajs-2818 89 30 in in ADP iajs-2818 89 31 ( ( PUNCT iajs-2818 89 32 1 1 NUM iajs-2818 89 33 ) ) PUNCT iajs-2818 89 34 as as ADP iajs-2818 89 35 below below ADV iajs-2818 89 36 : : PUNCT iajs-2818 89 37 as as ADP iajs-2818 89 38 below below ADV iajs-2818 89 39 : : PUNCT iajs-2818 89 40 𝑔𝑆4 𝑔𝑆4 PROPN iajs-2818 89 41 = = SYM iajs-2818 89 42 β„ŽπΈπ‘ž1 β„ŽπΈπ‘ž1 NOUN iajs-2818 89 43 ( ( PUNCT iajs-2818 89 44 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 89 45 + + CCONJ iajs-2818 89 46 β„Ž β„Ž PROPN iajs-2818 89 47 , , PUNCT iajs-2818 89 48 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 89 49 + + NUM iajs-2818 89 50 𝑔𝑆3 𝑔𝑆3 ADJ iajs-2818 89 51 , , PUNCT iajs-2818 89 52 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 89 53 + + CCONJ iajs-2818 89 54 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 89 55 , , PUNCT iajs-2818 89 56 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 89 57 + + CCONJ iajs-2818 89 58 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 89 59 , , PUNCT iajs-2818 89 60 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 89 61 + + PROPN iajs-2818 89 62 𝑔𝑉3 𝑔𝑉3 NOUN iajs-2818 89 63 , , PUNCT iajs-2818 89 64 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 89 65 + + CCONJ iajs-2818 89 66 𝑔𝑅3 𝑔𝑅3 PROPN iajs-2818 89 67 ) ) PUNCT iajs-2818 89 68 = = SYM iajs-2818 90 1 β„Ž β„Ž PROPN iajs-2818 90 2 ( ( PUNCT iajs-2818 90 3 𝛬 𝛬 PROPN iajs-2818 90 4 βˆ’ βˆ’ PROPN iajs-2818 90 5 ( ( PUNCT iajs-2818 90 6 𝛼(𝐸𝑖 𝛼(𝐸𝑖 NOUN iajs-2818 90 7 + + CCONJ iajs-2818 91 1 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 91 2 ) ) PUNCT iajs-2818 92 1 + + CCONJ iajs-2818 92 2 π‘š π‘š X iajs-2818 92 3 + + X iajs-2818 92 4 πœ‡)(𝑆𝑖 πœ‡)(𝑆𝑖 X iajs-2818 92 5 + + CCONJ iajs-2818 92 6 𝑔𝑆3 𝑔𝑆3 PROPN iajs-2818 92 7 ) ) PUNCT iajs-2818 92 8 ) ) PUNCT iajs-2818 92 9 , , PUNCT iajs-2818 92 10 𝑔𝐸4 𝑔𝐸4 PROPN iajs-2818 92 11 = = SYM iajs-2818 92 12 β„ŽπΈπ‘ž2 β„ŽπΈπ‘ž2 PROPN iajs-2818 92 13 ( ( PUNCT iajs-2818 92 14 𝑑𝑖 𝑑𝑖 X iajs-2818 92 15 + + CCONJ iajs-2818 92 16 β„Ž β„Ž PROPN iajs-2818 92 17 , , PUNCT iajs-2818 92 18 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 92 19 + + NUM iajs-2818 92 20 𝑔𝑆3 𝑔𝑆3 ADJ iajs-2818 92 21 , , PUNCT iajs-2818 92 22 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 92 23 + + CCONJ iajs-2818 92 24 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 92 25 , , PUNCT iajs-2818 92 26 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 92 27 + + CCONJ iajs-2818 92 28 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 92 29 , , PUNCT iajs-2818 93 1 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 93 2 + + PROPN iajs-2818 93 3 𝑔𝑉3 𝑔𝑉3 NOUN iajs-2818 93 4 , , PUNCT iajs-2818 93 5 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 93 6 + + CCONJ iajs-2818 93 7 𝑔𝑅3 𝑔𝑅3 PROPN iajs-2818 93 8 ) ) PUNCT iajs-2818 94 1 = = SYM iajs-2818 94 2 β„Ž β„Ž PROPN iajs-2818 94 3 ( ( PUNCT iajs-2818 94 4 𝛼(𝑆𝑖 𝛼(𝑆𝑖 PROPN iajs-2818 94 5 + + CCONJ iajs-2818 94 6 𝑔𝑆3)(𝐸𝑖 𝑔𝑆3)(𝐸𝑖 PROPN iajs-2818 94 7 + + CCONJ iajs-2818 94 8 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 94 9 ) ) PUNCT iajs-2818 94 10 + + NUM iajs-2818 94 11 𝑝(𝑉𝑖 𝑝(𝑉𝑖 NOUN iajs-2818 94 12 + + CCONJ iajs-2818 94 13 𝑔𝑉3)(𝐸𝑖 𝑔𝑉3)(𝐸𝑖 X iajs-2818 94 14 + + PUNCT iajs-2818 94 15 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 94 16 ) ) PUNCT iajs-2818 94 17 βˆ’ βˆ’ PROPN iajs-2818 95 1 ( ( PUNCT iajs-2818 95 2 𝑓(𝐼𝑖 𝑓(𝐼𝑖 NOUN iajs-2818 95 3 + + CCONJ iajs-2818 95 4 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 95 5 ) ) PUNCT iajs-2818 96 1 + + CCONJ iajs-2818 96 2 𝑐 𝑐 PROPN iajs-2818 96 3 + + CCONJ iajs-2818 96 4 πœ‡)(𝐸𝑖 πœ‡)(𝐸𝑖 NUM iajs-2818 96 5 + + CCONJ iajs-2818 96 6 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 96 7 ) ) PUNCT iajs-2818 96 8 ) ) PUNCT iajs-2818 96 9 , , PUNCT iajs-2818 96 10 ibn ibn PROPN iajs-2818 96 11 al al PROPN iajs-2818 96 12 - - PUNCT iajs-2818 96 13 haitham haitham PROPN iajs-2818 96 14 jour jour X iajs-2818 96 15 . . PROPN iajs-2818 96 16 for for ADP iajs-2818 96 17 pure pure ADJ iajs-2818 96 18 & & CCONJ iajs-2818 96 19 appl appl PROPN iajs-2818 96 20 . . PUNCT iajs-2818 97 1 sci sci PROPN iajs-2818 97 2 . . PROPN iajs-2818 98 1 53 53 NUM iajs-2818 98 2 ( ( PUNCT iajs-2818 98 3 2)2022 2)2022 VERB iajs-2818 98 4 102 102 NUM iajs-2818 98 5 𝑔𝐼4 𝑔𝐼4 PROPN iajs-2818 98 6 = = PUNCT iajs-2818 98 7 β„ŽπΈπ‘ž3 β„ŽπΈπ‘ž3 PROPN iajs-2818 98 8 ( ( PUNCT iajs-2818 98 9 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 98 10 + + CCONJ iajs-2818 98 11 β„Ž β„Ž PROPN iajs-2818 98 12 , , PUNCT iajs-2818 98 13 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 98 14 + + NUM iajs-2818 98 15 𝑔𝑆3 𝑔𝑆3 ADJ iajs-2818 98 16 , , PUNCT iajs-2818 98 17 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 98 18 + + CCONJ iajs-2818 98 19 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 98 20 , , PUNCT iajs-2818 98 21 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 98 22 + + CCONJ iajs-2818 98 23 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 98 24 , , PUNCT iajs-2818 98 25 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 98 26 + + PROPN iajs-2818 98 27 𝑔𝑉3 𝑔𝑉3 NOUN iajs-2818 98 28 , , PUNCT iajs-2818 98 29 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 98 30 + + CCONJ iajs-2818 98 31 𝑔𝑅3 𝑔𝑅3 PROPN iajs-2818 98 32 ) ) PUNCT iajs-2818 98 33 = = SYM iajs-2818 98 34 β„Ž β„Ž NOUN iajs-2818 98 35 ( ( PUNCT iajs-2818 98 36 𝑓(𝐸𝑖 𝑓(𝐸𝑖 X iajs-2818 98 37 + + CCONJ iajs-2818 98 38 𝑔𝐸3)(𝐼𝑖 𝑔𝐸3)(𝐼𝑖 NOUN iajs-2818 98 39 + + CCONJ iajs-2818 98 40 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 98 41 ) ) PUNCT iajs-2818 98 42 βˆ’ βˆ’ PROPN iajs-2818 99 1 ( ( PUNCT iajs-2818 99 2 𝑧 𝑧 PROPN iajs-2818 99 3 + + X iajs-2818 99 4 πœ‡ πœ‡ X iajs-2818 99 5 + + X iajs-2818 99 6 𝜎)(𝐼𝑖 𝜎)(𝐼𝑖 X iajs-2818 99 7 + + CCONJ iajs-2818 99 8 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 99 9 ) ) PUNCT iajs-2818 99 10 ) ) PUNCT iajs-2818 99 11 , , PUNCT iajs-2818 100 1 𝑔𝑉4 𝑔𝑉4 PROPN iajs-2818 100 2 = = SYM iajs-2818 100 3 β„ŽπΈπ‘ž4 β„ŽπΈπ‘ž4 PROPN iajs-2818 100 4 ( ( PUNCT iajs-2818 100 5 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 100 6 + + CCONJ iajs-2818 100 7 β„Ž β„Ž PROPN iajs-2818 100 8 , , PUNCT iajs-2818 100 9 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 100 10 + + NUM iajs-2818 100 11 𝑔𝑆3 𝑔𝑆3 ADJ iajs-2818 100 12 , , PUNCT iajs-2818 100 13 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 100 14 + + CCONJ iajs-2818 100 15 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 100 16 , , PUNCT iajs-2818 100 17 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 100 18 + + CCONJ iajs-2818 100 19 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 100 20 , , PUNCT iajs-2818 100 21 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 100 22 + + PROPN iajs-2818 100 23 𝑔𝑉3 𝑔𝑉3 NOUN iajs-2818 100 24 , , PUNCT iajs-2818 100 25 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 100 26 + + CCONJ iajs-2818 100 27 𝑔𝑅3 𝑔𝑅3 PROPN iajs-2818 100 28 ) ) PUNCT iajs-2818 100 29 = = SYM iajs-2818 100 30 β„Ž β„Ž NOUN iajs-2818 100 31 ( ( PUNCT iajs-2818 100 32 π‘š(𝑆𝑖 π‘š(𝑆𝑖 X iajs-2818 100 33 + + X iajs-2818 100 34 𝑔𝑆3 𝑔𝑆3 NOUN iajs-2818 100 35 ) ) PUNCT iajs-2818 100 36 βˆ’ βˆ’ PROPN iajs-2818 100 37 ( ( PUNCT iajs-2818 100 38 𝑝(𝐸𝑖 𝑝(𝐸𝑖 PROPN iajs-2818 100 39 + + X iajs-2818 100 40 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 100 41 ) ) PUNCT iajs-2818 100 42 + + CCONJ iajs-2818 100 43 πœ‡)(𝑉𝑖 πœ‡)(𝑉𝑖 NUM iajs-2818 100 44 + + NUM iajs-2818 100 45 𝑔𝑉3 𝑔𝑉3 NOUN iajs-2818 100 46 ) ) PUNCT iajs-2818 100 47 ) ) PUNCT iajs-2818 100 48 , , PUNCT iajs-2818 100 49 𝑔𝑅4 𝑔𝑅4 NOUN iajs-2818 100 50 = = PUNCT iajs-2818 100 51 β„ŽπΈπ‘ž5 β„ŽπΈπ‘ž5 PROPN iajs-2818 100 52 ( ( PUNCT iajs-2818 100 53 𝑑𝑖 𝑑𝑖 NOUN iajs-2818 100 54 + + NUM iajs-2818 100 55 β„Ž β„Ž PROPN iajs-2818 100 56 , , PUNCT iajs-2818 100 57 𝑆𝑖 𝑆𝑖 PROPN iajs-2818 100 58 + + NUM iajs-2818 100 59 𝑔𝑆3 𝑔𝑆3 ADJ iajs-2818 100 60 , , PUNCT iajs-2818 100 61 𝐸𝑖 𝐸𝑖 PROPN iajs-2818 100 62 + + CCONJ iajs-2818 100 63 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 100 64 , , PUNCT iajs-2818 100 65 𝐼𝑖 𝐼𝑖 PROPN iajs-2818 100 66 + + CCONJ iajs-2818 100 67 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 100 68 , , PUNCT iajs-2818 100 69 𝑉𝑖 𝑉𝑖 PROPN iajs-2818 100 70 + + PROPN iajs-2818 100 71 𝑔𝑉3 𝑔𝑉3 NOUN iajs-2818 100 72 , , PUNCT iajs-2818 100 73 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 100 74 + + CCONJ iajs-2818 100 75 𝑔𝑅3 𝑔𝑅3 PROPN iajs-2818 100 76 ) ) PUNCT iajs-2818 100 77 = = SYM iajs-2818 100 78 β„Ž β„Ž NOUN iajs-2818 100 79 ( ( PUNCT iajs-2818 100 80 𝑧(𝐼𝑖 𝑧(𝐼𝑖 NOUN iajs-2818 100 81 + + CCONJ iajs-2818 100 82 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 100 83 ) ) PUNCT iajs-2818 101 1 + + PUNCT iajs-2818 101 2 𝑐(𝐸𝑖 𝑐(𝐸𝑖 X iajs-2818 101 3 + + CCONJ iajs-2818 101 4 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 101 5 ) ) PUNCT iajs-2818 101 6 βˆ’ βˆ’ PROPN iajs-2818 102 1 πœ‡ πœ‡ ADP iajs-2818 102 2 ( ( PUNCT iajs-2818 102 3 𝑅𝑖 𝑅𝑖 PROPN iajs-2818 102 4 + + CCONJ iajs-2818 102 5 𝑔𝑅3 𝑔𝑅3 PROPN iajs-2818 102 6 ) ) PUNCT iajs-2818 102 7 ) ) PUNCT iajs-2818 102 8 . . PUNCT iajs-2818 103 1 finally finally ADV iajs-2818 103 2 , , PUNCT iajs-2818 103 3 by by ADP iajs-2818 103 4 substituting substitute VERB iajs-2818 103 5 in in ADP iajs-2818 103 6 ( ( PUNCT iajs-2818 103 7 2 2 NUM iajs-2818 103 8 ) ) PUNCT iajs-2818 103 9 , , PUNCT iajs-2818 103 10 all all PRON iajs-2818 103 11 of of ADP iajs-2818 103 12 𝑔𝑆1 𝑔𝑆1 PROPN iajs-2818 103 13 , , PUNCT iajs-2818 103 14 𝑔𝐸1 𝑔𝐸1 PROPN iajs-2818 103 15 , , PUNCT iajs-2818 103 16 𝑔𝐼1 𝑔𝐼1 PROPN iajs-2818 103 17 , , PUNCT iajs-2818 103 18 𝑔𝑉1,𝑔𝑅1 𝑔𝑉1,𝑔𝑅1 PROPN iajs-2818 103 19 , , PUNCT iajs-2818 103 20 𝑔𝑆2 𝑔𝑆2 NOUN iajs-2818 103 21 , , PUNCT iajs-2818 103 22 𝑔𝐸2 𝑔𝐸2 PROPN iajs-2818 103 23 , , PUNCT iajs-2818 103 24 𝑔𝐼2 𝑔𝐼2 ADP iajs-2818 103 25 , , PUNCT iajs-2818 103 26 𝑔𝑉2,𝑔𝑅2 𝑔𝑉2,𝑔𝑅2 PROPN iajs-2818 103 27 , , PUNCT iajs-2818 103 28 𝑔𝑆3 𝑔𝑆3 PROPN iajs-2818 103 29 , , PUNCT iajs-2818 103 30 𝑔𝐸3 𝑔𝐸3 PROPN iajs-2818 103 31 , , PUNCT iajs-2818 103 32 𝑔𝐼3 𝑔𝐼3 PROPN iajs-2818 103 33 , , PUNCT iajs-2818 103 34 𝑔𝑉3,𝑔𝑅3 𝑔𝑉3,𝑔𝑅3 PROPN iajs-2818 103 35 , , PUNCT iajs-2818 103 36 𝑔𝑆4 𝑔𝑆4 NOUN iajs-2818 103 37 , , PUNCT iajs-2818 103 38 𝑔𝐸4 𝑔𝐸4 PROPN iajs-2818 103 39 , , PUNCT iajs-2818 103 40 𝑔𝐼4 𝑔𝐼4 NOUN iajs-2818 103 41 , , PUNCT iajs-2818 103 42 𝑔𝑉4,𝑔𝑅4 𝑔𝑉4,𝑔𝑅4 NOUN iajs-2818 103 43 for for ADP iajs-2818 103 44 four four NUM iajs-2818 103 45 steps step NOUN iajs-2818 103 46 , , PUNCT iajs-2818 103 47 the the DET iajs-2818 103 48 numerical numerical ADJ iajs-2818 103 49 results result NOUN iajs-2818 103 50 for for ADP iajs-2818 103 51 each each PRON iajs-2818 103 52 of of ADP iajs-2818 103 53 𝑆(𝑑 𝑆(𝑑 NUM iajs-2818 103 54 ) ) PUNCT iajs-2818 103 55 , , PUNCT iajs-2818 103 56 𝐸(𝑑 𝐸(𝑑 VERB iajs-2818 103 57 ) ) PUNCT iajs-2818 103 58 , , PUNCT iajs-2818 103 59 𝐼(𝑑 𝐼(𝑑 NUM iajs-2818 103 60 ) ) PUNCT iajs-2818 103 61 , , PUNCT iajs-2818 103 62 𝑉(𝑑 𝑉(𝑑 ADP iajs-2818 103 63 ) ) PUNCT iajs-2818 103 64 and and CCONJ iajs-2818 103 65 𝑅(𝑑 𝑅(𝑑 NOUN iajs-2818 103 66 ) ) PUNCT iajs-2818 103 67 can can AUX iajs-2818 103 68 be be AUX iajs-2818 103 69 computed compute VERB iajs-2818 103 70 . . PUNCT iajs-2818 104 1 4 4 X iajs-2818 104 2 . . NOUN iajs-2818 104 3 results result NOUN iajs-2818 104 4 and and CCONJ iajs-2818 104 5 discussion discussion VERB iajs-2818 104 6 the the DET iajs-2818 104 7 initial initial ADJ iajs-2818 104 8 conditions condition NOUN iajs-2818 104 9 of of ADP iajs-2818 104 10 ( ( PUNCT iajs-2818 104 11 1 1 X iajs-2818 104 12 ) ) PUNCT iajs-2818 104 13 are be AUX iajs-2818 104 14 taken take VERB iajs-2818 104 15 from from ADP iajs-2818 104 16 the the DET iajs-2818 104 17 iraq iraq PROPN iajs-2818 104 18 data datum NOUN iajs-2818 104 19 from from ADP iajs-2818 104 20 the the DET iajs-2818 104 21 world world PROPN iajs-2818 104 22 health health PROPN iajs-2818 104 23 organization organization NOUN iajs-2818 104 24 website website NOUN iajs-2818 104 25 [ [ X iajs-2818 104 26 28,29 28,29 NUM iajs-2818 104 27 ] ] PUNCT iajs-2818 104 28 , , PUNCT iajs-2818 104 29 and and CCONJ iajs-2818 104 30 it it PRON iajs-2818 104 31 is be AUX iajs-2818 104 32 as as SCONJ iajs-2818 104 33 follows follow VERB iajs-2818 104 34 : : PUNCT iajs-2818 104 35 𝑆0 𝑆0 X iajs-2818 104 36 = = SYM iajs-2818 104 37 500 500 NUM iajs-2818 104 38 , , PUNCT iajs-2818 104 39 𝐸0 𝐸0 X iajs-2818 104 40 = = SYM iajs-2818 104 41 46 46 NUM iajs-2818 104 42 , , PUNCT iajs-2818 104 43 𝐼0 𝐼0 ADJ iajs-2818 104 44 = = SYM iajs-2818 104 45 23 23 NUM iajs-2818 104 46 , , PUNCT iajs-2818 104 47 𝑉0 𝑉0 NOUN iajs-2818 104 48 = = SYM iajs-2818 104 49 0 0 NUM iajs-2818 104 50 , , PUNCT iajs-2818 104 51 and and CCONJ iajs-2818 104 52 𝑅0 𝑅0 PROPN iajs-2818 104 53 = = SYM iajs-2818 104 54 12 12 NUM iajs-2818 104 55 . . PUNCT iajs-2818 105 1 numerical numerical ADJ iajs-2818 105 2 results result NOUN iajs-2818 105 3 for for ADP iajs-2818 105 4 the the DET iajs-2818 105 5 covid-19 covid-19 PROPN iajs-2818 105 6 epidemic epidemic NOUN iajs-2818 105 7 problem problem NOUN iajs-2818 105 8 in in ADP iajs-2818 105 9 iraq iraq PROPN iajs-2818 105 10 in in ADP iajs-2818 105 11 2020 2020 NUM iajs-2818 105 12 are be AUX iajs-2818 105 13 discussed discuss VERB iajs-2818 105 14 and and CCONJ iajs-2818 105 15 analyzed analyze VERB iajs-2818 105 16 in in ADP iajs-2818 105 17 this this DET iajs-2818 105 18 section section NOUN iajs-2818 105 19 . . PUNCT iajs-2818 106 1 table table NOUN iajs-2818 106 2 2 2 NUM iajs-2818 106 3 gives give VERB iajs-2818 106 4 the the DET iajs-2818 106 5 results result NOUN iajs-2818 106 6 of of ADP iajs-2818 106 7 each each PRON iajs-2818 106 8 of of ADP iajs-2818 106 9 the the DET iajs-2818 106 10 epidemic epidemic NOUN iajs-2818 106 11 stages stage NOUN iajs-2818 106 12 𝑆(𝑑 𝑆(𝑑 VERB iajs-2818 106 13 ) ) PUNCT iajs-2818 106 14 , , PUNCT iajs-2818 106 15 𝐸(𝑑 𝐸(𝑑 VERB iajs-2818 106 16 ) ) PUNCT iajs-2818 106 17 , , PUNCT iajs-2818 106 18 𝐼(𝑑 𝐼(𝑑 NUM iajs-2818 106 19 ) ) PUNCT iajs-2818 106 20 , , PUNCT iajs-2818 106 21 𝑉(𝑑 𝑉(𝑑 ADP iajs-2818 106 22 ) ) PUNCT iajs-2818 106 23 and and CCONJ iajs-2818 106 24 𝑅(𝑑 𝑅(𝑑 NOUN iajs-2818 106 25 ) ) PUNCT iajs-2818 106 26 for for ADP iajs-2818 106 27 rk4 rk4 NOUN iajs-2818 106 28 method method NOUN iajs-2818 106 29 , , PUNCT iajs-2818 106 30 that that SCONJ iajs-2818 106 31 rk4 rk4 NOUN iajs-2818 106 32 results result NOUN iajs-2818 106 33 converge converge VERB iajs-2818 106 34 with with ADP iajs-2818 106 35 step step NOUN iajs-2818 106 36 sizes size NOUN iajs-2818 106 37 0.02 0.02 NUM iajs-2818 106 38 in in ADP iajs-2818 106 39 a a DET iajs-2818 106 40 weak weak ADJ iajs-2818 106 41 and and CCONJ iajs-2818 106 42 0.003 0.003 NUM iajs-2818 106 43 in in ADP iajs-2818 106 44 a a DET iajs-2818 106 45 day day NOUN iajs-2818 106 46 . . PUNCT iajs-2818 107 1 but but CCONJ iajs-2818 107 2 the the DET iajs-2818 107 3 results result NOUN iajs-2818 107 4 of of ADP iajs-2818 107 5 step step NOUN iajs-2818 107 6 size size NOUN iajs-2818 107 7 β„Ž β„Ž PROPN iajs-2818 107 8 = = NOUN iajs-2818 107 9 0.003 0.003 NUM iajs-2818 107 10 are be AUX iajs-2818 107 11 more more ADV iajs-2818 107 12 accurate accurate ADJ iajs-2818 107 13 than than ADP iajs-2818 107 14 the the DET iajs-2818 107 15 results result NOUN iajs-2818 107 16 of of ADP iajs-2818 107 17 step step NOUN iajs-2818 107 18 size size NOUN iajs-2818 107 19 β„Ž β„Ž PROPN iajs-2818 107 20 = = NOUN iajs-2818 107 21 0.02 0.02 NUM iajs-2818 107 22 , , PUNCT iajs-2818 107 23 this this PRON iajs-2818 107 24 is be AUX iajs-2818 107 25 the the DET iajs-2818 107 26 principle principle NOUN iajs-2818 107 27 of of ADP iajs-2818 107 28 numerical numerical ADJ iajs-2818 107 29 methods method NOUN iajs-2818 107 30 . . PUNCT iajs-2818 108 1 figures figure NOUN iajs-2818 108 2 1 1 NUM iajs-2818 108 3 , , PUNCT iajs-2818 108 4 2 2 NUM iajs-2818 108 5 , , PUNCT iajs-2818 108 6 3 3 NUM iajs-2818 108 7 , , PUNCT iajs-2818 108 8 and and CCONJ iajs-2818 108 9 4 4 NUM iajs-2818 108 10 are be AUX iajs-2818 108 11 to to PART iajs-2818 108 12 show show VERB iajs-2818 108 13 the the DET iajs-2818 108 14 behavior behavior NOUN iajs-2818 108 15 of of ADP iajs-2818 108 16 all all DET iajs-2818 108 17 epidemic epidemic NOUN iajs-2818 108 18 stages stage NOUN iajs-2818 108 19 𝑆(𝑑 𝑆(𝑑 VERB iajs-2818 108 20 ) ) PUNCT iajs-2818 108 21 , , PUNCT iajs-2818 108 22 𝐸(𝑑 𝐸(𝑑 VERB iajs-2818 108 23 ) ) PUNCT iajs-2818 108 24 , , PUNCT iajs-2818 108 25 𝐼(𝑑 𝐼(𝑑 NUM iajs-2818 108 26 ) ) PUNCT iajs-2818 108 27 , , PUNCT iajs-2818 108 28 𝑉(𝑑 𝑉(𝑑 ADP iajs-2818 108 29 ) ) PUNCT iajs-2818 108 30 and and CCONJ iajs-2818 108 31 𝑅(𝑑 𝑅(𝑑 NOUN iajs-2818 108 32 ) ) PUNCT iajs-2818 108 33 for for ADP iajs-2818 108 34 rk4 rk4 NOUN iajs-2818 108 35 the the DET iajs-2818 108 36 method method NOUN iajs-2818 108 37 in in ADP iajs-2818 108 38 two two NUM iajs-2818 108 39 cases case NOUN iajs-2818 108 40 : : PUNCT iajs-2818 108 41 case1 case1 NOUN iajs-2818 108 42 : : PUNCT iajs-2818 108 43 when when SCONJ iajs-2818 108 44 the the DET iajs-2818 108 45 step step NOUN iajs-2818 108 46 size size NOUN iajs-2818 108 47 β„Ž β„Ž PROPN iajs-2818 108 48 is be AUX iajs-2818 108 49 0.02 0.02 NUM iajs-2818 108 50 in in ADP iajs-2818 108 51 a a DET iajs-2818 108 52 weak weak ADJ iajs-2818 108 53 during during ADP iajs-2818 108 54 10 10 NUM iajs-2818 108 55 and and CCONJ iajs-2818 108 56 15 15 NUM iajs-2818 108 57 years year NOUN iajs-2818 108 58 ; ; PUNCT iajs-2818 108 59 the the DET iajs-2818 108 60 results result NOUN iajs-2818 108 61 are be AUX iajs-2818 108 62 presented present VERB iajs-2818 108 63 in in ADP iajs-2818 108 64 figures figure NOUN iajs-2818 108 65 1 1 NUM iajs-2818 108 66 and and CCONJ iajs-2818 108 67 2 2 NUM iajs-2818 108 68 , , PUNCT iajs-2818 108 69 from from ADP iajs-2818 108 70 2020 2020 NUM iajs-2818 108 71 the the DET iajs-2818 108 72 beginning beginning NOUN iajs-2818 108 73 of of ADP iajs-2818 108 74 the the DET iajs-2818 108 75 breakout breakout NOUN iajs-2818 108 76 of of ADP iajs-2818 108 77 the the DET iajs-2818 108 78 virus virus NOUN iajs-2818 108 79 until until ADP iajs-2818 108 80 2030 2030 NUM iajs-2818 108 81 and and CCONJ iajs-2818 108 82 2035 2035 NUM iajs-2818 108 83 respectively respectively ADV iajs-2818 108 84 . . PUNCT iajs-2818 109 1 case2 case2 PROPN iajs-2818 109 2 : : PUNCT iajs-2818 109 3 when when SCONJ iajs-2818 109 4 the the DET iajs-2818 109 5 step step NOUN iajs-2818 109 6 size size NOUN iajs-2818 109 7 β„Ž β„Ž PROPN iajs-2818 109 8 is be AUX iajs-2818 109 9 0.003 0.003 NUM iajs-2818 109 10 in in ADP iajs-2818 109 11 a a DET iajs-2818 109 12 day day NOUN iajs-2818 109 13 for for ADP iajs-2818 109 14 10 10 NUM iajs-2818 109 15 and and CCONJ iajs-2818 109 16 15 15 NUM iajs-2818 109 17 years year NOUN iajs-2818 109 18 ; ; PUNCT iajs-2818 109 19 the the DET iajs-2818 109 20 results result NOUN iajs-2818 109 21 are be AUX iajs-2818 109 22 presented present VERB iajs-2818 109 23 in in ADP iajs-2818 109 24 figures figure NOUN iajs-2818 109 25 3 3 NUM iajs-2818 109 26 and and CCONJ iajs-2818 109 27 4 4 NUM iajs-2818 109 28 , , PUNCT iajs-2818 109 29 from from ADP iajs-2818 109 30 2020 2020 NUM iajs-2818 109 31 the the DET iajs-2818 109 32 beginning beginning NOUN iajs-2818 109 33 of of ADP iajs-2818 109 34 the the DET iajs-2818 109 35 breakout breakout NOUN iajs-2818 109 36 of of ADP iajs-2818 109 37 the the DET iajs-2818 109 38 virus virus NOUN iajs-2818 109 39 until until ADP iajs-2818 109 40 2030 2030 NUM iajs-2818 109 41 and and CCONJ iajs-2818 109 42 2035 2035 NUM iajs-2818 109 43 respectively respectively ADV iajs-2818 109 44 . . PUNCT iajs-2818 110 1 figures figure NOUN iajs-2818 110 2 1 1 NUM iajs-2818 110 3 , , PUNCT iajs-2818 110 4 2 2 NUM iajs-2818 110 5 , , PUNCT iajs-2818 110 6 3 3 NUM iajs-2818 110 7 , , PUNCT iajs-2818 110 8 and and CCONJ iajs-2818 110 9 4 4 NUM iajs-2818 110 10 describe describe VERB iajs-2818 110 11 the the DET iajs-2818 110 12 behavior behavior NOUN iajs-2818 110 13 of of ADP iajs-2818 110 14 each each DET iajs-2818 110 15 phase phase NOUN iajs-2818 110 16 of of ADP iajs-2818 110 17 the the DET iajs-2818 110 18 covid-19 covid-19 PROPN iajs-2818 110 19 epidemic epidemic NOUN iajs-2818 110 20 . . PUNCT iajs-2818 111 1 the the DET iajs-2818 111 2 behavior behavior NOUN iajs-2818 111 3 of of ADP iajs-2818 111 4 𝑆(𝑑 𝑆(𝑑 ADJ iajs-2818 111 5 ) ) PUNCT iajs-2818 111 6 , , PUNCT iajs-2818 111 7 the the DET iajs-2818 111 8 population population NOUN iajs-2818 111 9 has have AUX iajs-2818 111 10 decreased decrease VERB iajs-2818 111 11 gradually gradually ADV iajs-2818 111 12 since since SCONJ iajs-2818 111 13 the the DET iajs-2818 111 14 virus virus NOUN iajs-2818 111 15 began begin VERB iajs-2818 111 16 , , PUNCT iajs-2818 111 17 then then ADV iajs-2818 111 18 will will AUX iajs-2818 111 19 be be AUX iajs-2818 111 20 stable stable ADJ iajs-2818 111 21 at at ADP iajs-2818 111 22 the the DET iajs-2818 111 23 end end NOUN iajs-2818 111 24 of of ADP iajs-2818 111 25 2022 2022 NUM iajs-2818 111 26 to to ADP iajs-2818 111 27 the the DET iajs-2818 111 28 following following ADJ iajs-2818 111 29 years year NOUN iajs-2818 111 30 . . PUNCT iajs-2818 112 1 on on ADP iajs-2818 112 2 the the DET iajs-2818 112 3 other other ADJ iajs-2818 112 4 hand hand NOUN iajs-2818 112 5 , , PUNCT iajs-2818 112 6 it it PRON iajs-2818 112 7 is be AUX iajs-2818 112 8 noticeable noticeable ADJ iajs-2818 112 9 that that SCONJ iajs-2818 112 10 the the DET iajs-2818 112 11 𝐸(𝑑 𝐸(𝑑 NOUN iajs-2818 112 12 ) ) PUNCT iajs-2818 112 13 has have AUX iajs-2818 112 14 increased increase VERB iajs-2818 112 15 since since SCONJ iajs-2818 112 16 the the DET iajs-2818 112 17 beginning beginning NOUN iajs-2818 112 18 of of ADP iajs-2818 112 19 the the DET iajs-2818 112 20 spread spread NOUN iajs-2818 112 21 of of ADP iajs-2818 112 22 the the DET iajs-2818 112 23 virus virus NOUN iajs-2818 112 24 , , PUNCT iajs-2818 112 25 reaching reach VERB iajs-2818 112 26 its its PRON iajs-2818 112 27 highest high ADJ iajs-2818 112 28 possible possible ADJ iajs-2818 112 29 in in ADP iajs-2818 112 30 2021 2021 NUM iajs-2818 112 31 . . PUNCT iajs-2818 113 1 then then ADV iajs-2818 113 2 it it PRON iajs-2818 113 3 starts start VERB iajs-2818 113 4 declining decline VERB iajs-2818 113 5 from from ADP iajs-2818 113 6 2021 2021 NUM iajs-2818 113 7 to to ADP iajs-2818 113 8 the the DET iajs-2818 113 9 end end NOUN iajs-2818 113 10 of of ADP iajs-2818 113 11 2022 2022 NUM iajs-2818 113 12 . . PUNCT iajs-2818 114 1 after after ADP iajs-2818 114 2 that that PRON iajs-2818 114 3 , , PUNCT iajs-2818 114 4 it it PRON iajs-2818 114 5 settles settle VERB iajs-2818 114 6 to to ADP iajs-2818 114 7 the the DET iajs-2818 114 8 same same ADJ iajs-2818 114 9 level level NOUN iajs-2818 114 10 . . PUNCT iajs-2818 115 1 it it PRON iajs-2818 115 2 is be AUX iajs-2818 115 3 clear clear ADJ iajs-2818 115 4 that that SCONJ iajs-2818 115 5 the the DET iajs-2818 115 6 behavior behavior NOUN iajs-2818 115 7 of of ADP iajs-2818 115 8 𝐼(𝑑 𝐼(𝑑 PROPN iajs-2818 115 9 ) ) PUNCT iajs-2818 115 10 the the DET iajs-2818 115 11 population population NOUN iajs-2818 115 12 has have AUX iajs-2818 115 13 been be AUX iajs-2818 115 14 increasing increase VERB iajs-2818 115 15 since since SCONJ iajs-2818 115 16 the the DET iajs-2818 115 17 beginning beginning NOUN iajs-2818 115 18 of of ADP iajs-2818 115 19 the the DET iajs-2818 115 20 epidemic epidemic NOUN iajs-2818 115 21 and and CCONJ iajs-2818 115 22 begins begin VERB iajs-2818 115 23 to to PART iajs-2818 115 24 decrease decrease VERB iajs-2818 115 25 gradually gradually ADV iajs-2818 115 26 after after ADP iajs-2818 115 27 2023 2023 NUM iajs-2818 115 28 , , PUNCT iajs-2818 115 29 it it PRON iajs-2818 115 30 will will AUX iajs-2818 115 31 maintain maintain VERB iajs-2818 115 32 the the DET iajs-2818 115 33 same same ADJ iajs-2818 115 34 level level NOUN iajs-2818 115 35 after after ADP iajs-2818 115 36 2025 2025 NUM iajs-2818 115 37 . . PUNCT iajs-2818 116 1 at at ADP iajs-2818 116 2 the the DET iajs-2818 116 3 beginning beginning NOUN iajs-2818 116 4 of of ADP iajs-2818 116 5 the the DET iajs-2818 116 6 spread spread NOUN iajs-2818 116 7 of of ADP iajs-2818 116 8 the the DET iajs-2818 116 9 virus virus NOUN iajs-2818 116 10 , , PUNCT iajs-2818 116 11 the the DET iajs-2818 116 12 vaccine vaccine NOUN iajs-2818 116 13 was be AUX iajs-2818 116 14 not not PART iajs-2818 116 15 available available ADJ iajs-2818 116 16 until until ADP iajs-2818 116 17 the the DET iajs-2818 116 18 end end NOUN iajs-2818 116 19 of of ADP iajs-2818 116 20 2021 2021 NUM iajs-2818 116 21 , , PUNCT iajs-2818 116 22 therefore therefore ADV iajs-2818 116 23 , , PUNCT iajs-2818 116 24 the the DET iajs-2818 116 25 behavior behavior NOUN iajs-2818 116 26 of of ADP iajs-2818 116 27 the the DET iajs-2818 116 28 vaccine vaccine NOUN iajs-2818 116 29 curve curve VERB iajs-2818 116 30 before before SCONJ iajs-2818 116 31 the the DET iajs-2818 116 32 middle middle NOUN iajs-2818 116 33 of of ADP iajs-2818 116 34 2021 2021 NUM iajs-2818 116 35 should should AUX iajs-2818 116 36 be be AUX iajs-2818 116 37 ignored ignore VERB iajs-2818 116 38 . . PUNCT iajs-2818 117 1 with with SCONJ iajs-2818 117 2 the the DET iajs-2818 117 3 vaccination vaccination NOUN iajs-2818 117 4 campaign campaign NOUN iajs-2818 117 5 began begin VERB iajs-2818 117 6 , , PUNCT iajs-2818 117 7 we we PRON iajs-2818 117 8 note note VERB iajs-2818 117 9 that that SCONJ iajs-2818 117 10 the the DET iajs-2818 117 11 curve curve NOUN iajs-2818 117 12 of of ADP iajs-2818 117 13 𝑉(𝑑 𝑉(𝑑 ADP iajs-2818 117 14 ) ) PUNCT iajs-2818 117 15 gradually gradually ADV iajs-2818 117 16 raised raise VERB iajs-2818 117 17 to to ADP iajs-2818 117 18 2023 2023 NUM iajs-2818 117 19 and and CCONJ iajs-2818 117 20 remained remain VERB iajs-2818 117 21 in in ADP iajs-2818 117 22 a a DET iajs-2818 117 23 noticeable noticeable ADJ iajs-2818 117 24 rise rise NOUN iajs-2818 117 25 until until ADP iajs-2818 117 26 2025 2025 NUM iajs-2818 117 27 , , PUNCT iajs-2818 117 28 then then ADV iajs-2818 117 29 began begin VERB iajs-2818 117 30 to to PART iajs-2818 117 31 decline decline VERB iajs-2818 117 32 and and CCONJ iajs-2818 117 33 stabilize stabilize VERB iajs-2818 117 34 at at ADP iajs-2818 117 35 a a DET iajs-2818 117 36 certain certain ADJ iajs-2818 117 37 level level NOUN iajs-2818 117 38 in in ADP iajs-2818 117 39 2025 2025 NUM iajs-2818 117 40 for for ADP iajs-2818 117 41 the the DET iajs-2818 117 42 coming come VERB iajs-2818 117 43 years year NOUN iajs-2818 117 44 . . PUNCT iajs-2818 118 1 finally finally ADV iajs-2818 118 2 , , PUNCT iajs-2818 118 3 the the DET iajs-2818 118 4 curve curve NOUN iajs-2818 118 5 𝑅(𝑑 𝑅(𝑑 NOUN iajs-2818 118 6 ) ) PUNCT iajs-2818 118 7 began begin VERB iajs-2818 118 8 to to PART iajs-2818 118 9 increase increase VERB iajs-2818 118 10 and and CCONJ iajs-2818 118 11 rise rise VERB iajs-2818 118 12 gradually gradually ADV iajs-2818 118 13 until until ADP iajs-2818 118 14 2026 2026 NUM iajs-2818 118 15 . . PUNCT iajs-2818 119 1 the the DET iajs-2818 119 2 increase increase NOUN iajs-2818 119 3 would would AUX iajs-2818 119 4 be be AUX iajs-2818 119 5 very very ADV iajs-2818 119 6 little little ADJ iajs-2818 119 7 in in ADP iajs-2818 119 8 the the DET iajs-2818 119 9 coming come VERB iajs-2818 119 10 years year NOUN iajs-2818 119 11 for for ADP iajs-2818 119 12 the the DET iajs-2818 119 13 curve curve NOUN iajs-2818 119 14 𝑅(𝑑 𝑅(𝑑 NOUN iajs-2818 119 15 ) ) PUNCT iajs-2818 119 16 . . PUNCT iajs-2818 120 1 ibn ibn PROPN iajs-2818 120 2 al al PROPN iajs-2818 120 3 - - PUNCT iajs-2818 120 4 haitham haitham PROPN iajs-2818 120 5 jour jour X iajs-2818 120 6 . . PROPN iajs-2818 120 7 for for ADP iajs-2818 120 8 pure pure ADJ iajs-2818 120 9 & & CCONJ iajs-2818 120 10 appl appl PROPN iajs-2818 120 11 . . PUNCT iajs-2818 121 1 sci sci PROPN iajs-2818 121 2 . . PROPN iajs-2818 122 1 53 53 NUM iajs-2818 122 2 ( ( PUNCT iajs-2818 122 3 2)2022 2)2022 VERB iajs-2818 122 4 103 103 NUM iajs-2818 122 5 all all DET iajs-2818 122 6 the the DET iajs-2818 122 7 present present ADJ iajs-2818 122 8 study study NOUN iajs-2818 122 9 results result NOUN iajs-2818 122 10 agree agree VERB iajs-2818 122 11 with with ADP iajs-2818 122 12 the the DET iajs-2818 122 13 previous previous ADJ iajs-2818 122 14 studies study NOUN iajs-2818 122 15 , , PUNCT iajs-2818 122 16 [ [ X iajs-2818 122 17 24 24 NUM iajs-2818 122 18 ] ] PUNCT iajs-2818 122 19 for for ADP iajs-2818 122 20 all all DET iajs-2818 122 21 stages stage NOUN iajs-2818 122 22 of of ADP iajs-2818 122 23 the the DET iajs-2818 122 24 coronavirus coronavirus NOUN iajs-2818 122 25 epidemic epidemic NOUN iajs-2818 122 26 in in ADP iajs-2818 122 27 the the DET iajs-2818 122 28 results result NOUN iajs-2818 122 29 . . PUNCT iajs-2818 123 1 the the DET iajs-2818 123 2 matlab matlab PROPN iajs-2818 123 3 program program NOUN iajs-2818 123 4 of of ADP iajs-2818 123 5 version version NOUN iajs-2818 123 6 r2017a r2017a PROPN iajs-2818 123 7 has have AUX iajs-2818 123 8 helped help VERB iajs-2818 123 9 to to PART iajs-2818 123 10 supply supply VERB iajs-2818 123 11 numerically numerically ADV iajs-2818 123 12 solving solve VERB iajs-2818 123 13 the the DET iajs-2818 123 14 pandemic pandemic ADJ iajs-2818 123 15 model model NOUN iajs-2818 123 16 at at ADP iajs-2818 123 17 the the DET iajs-2818 123 18 present present ADJ iajs-2818 123 19 work work NOUN iajs-2818 123 20 . . PUNCT iajs-2818 124 1 table table NOUN iajs-2818 124 2 2 2 NUM iajs-2818 124 3 . . PUNCT iajs-2818 124 4 numerical numerical ADJ iajs-2818 124 5 solutions solution NOUN iajs-2818 124 6 for for ADP iajs-2818 124 7 the the DET iajs-2818 124 8 covid-19 covid-19 PROPN iajs-2818 124 9 model model NOUN iajs-2818 124 10 15 15 NUM iajs-2818 124 11 years year NOUN iajs-2818 124 12 10 10 NUM iajs-2818 124 13 years year NOUN iajs-2818 124 14 step step NOUN iajs-2818 124 15 size size NOUN iajs-2818 124 16 ( ( PUNCT iajs-2818 124 17 h h NOUN iajs-2818 124 18 ) ) PUNCT iajs-2818 124 19 population population NOUN iajs-2818 124 20 87.5900398275115 87.5900398275115 NUM iajs-2818 124 21 89.3593198158165 89.3593198158165 NUM iajs-2818 124 22 0.02 0.02 NUM iajs-2818 124 23 s s NOUN iajs-2818 124 24 87.5900398209401 87.5900398209401 NUM iajs-2818 124 25 89.3598850965887 89.3598850965887 NUM iajs-2818 124 26 0.003 0.003 NUM iajs-2818 124 27 32.09564036298 32.09564036298 NUM iajs-2818 124 28 28.4319382456529 28.4319382456529 NUM iajs-2818 124 29 0.02 0.02 NUM iajs-2818 124 30 e e NOUN iajs-2818 124 31 32.0956403779949 32.0956403779949 NUM iajs-2818 124 32 28.4309679558064 28.4309679558064 NUM iajs-2818 124 33 0.003 0.003 NUM iajs-2818 124 34 183.971491059345 183.971491059345 NUM iajs-2818 124 35 210.285219546379 210.285219546379 NUM iajs-2818 124 36 0.02 0.02 NUM iajs-2818 124 37 i i NOUN iajs-2818 124 38 183.971490970528 183.971490970528 NUM iajs-2818 124 39 210.294376974796 210.294376974796 NUM iajs-2818 124 40 0.003 0.003 NUM iajs-2818 124 41 17.1116618577972 17.1116618577972 NUM iajs-2818 124 42 19.9586546831238 19.9586546831238 NUM iajs-2818 124 43 0.02 0.02 NUM iajs-2818 124 44 v v NUM iajs-2818 124 45 17.1116618474704 17.1116618474704 NUM iajs-2818 124 46 19.9595517884747 19.9595517884747 NUM iajs-2818 124 47 0.003 0.003 NUM iajs-2818 124 48 84.1216912610883 84.1216912610883 NUM iajs-2818 124 49 68.2557582669928 68.2557582669928 NUM iajs-2818 124 50 0.02 0.02 NUM iajs-2818 124 51 r r NOUN iajs-2818 124 52 84.1216910919618 84.1216910919618 NUM iajs-2818 124 53 68.2524273304788 68.2524273304788 NUM iajs-2818 124 54 0.003 0.003 NUM iajs-2818 124 55 figure figure NOUN iajs-2818 124 56 1 1 NUM iajs-2818 124 57 . . PUNCT iajs-2818 125 1 rk4 rk4 PROPN iajs-2818 125 2 numerical numerical ADJ iajs-2818 125 3 results result NOUN iajs-2818 125 4 of of ADP iajs-2818 125 5 covid-19 covid-19 PROPN iajs-2818 125 6 model model NOUN iajs-2818 125 7 of of ADP iajs-2818 125 8 𝑆 𝑆 PROPN iajs-2818 125 9 , , PUNCT iajs-2818 125 10 𝐸 𝐸 PROPN iajs-2818 125 11 , , PUNCT iajs-2818 125 12 𝐼 𝐼 PROPN iajs-2818 125 13 , , PUNCT iajs-2818 125 14 𝑉 𝑉 PROPN iajs-2818 125 15 , , PUNCT iajs-2818 125 16 𝑅 𝑅 PROPN iajs-2818 125 17 from from ADP iajs-2818 125 18 2020 2020 NUM iajs-2818 125 19 with with ADP iajs-2818 125 20 step step NOUN iajs-2818 125 21 size size NOUN iajs-2818 125 22 β„Ž β„Ž PROPN iajs-2818 125 23 = = NOUN iajs-2818 125 24 0.02 0.02 NUM iajs-2818 125 25 during during ADP iajs-2818 125 26 10 10 NUM iajs-2818 125 27 years year NOUN iajs-2818 125 28 . . PUNCT iajs-2818 126 1 ibn ibn PROPN iajs-2818 126 2 al al PROPN iajs-2818 126 3 - - PUNCT iajs-2818 126 4 haitham haitham PROPN iajs-2818 126 5 jour jour X iajs-2818 126 6 . . PROPN iajs-2818 126 7 for for ADP iajs-2818 126 8 pure pure ADJ iajs-2818 126 9 & & CCONJ iajs-2818 126 10 appl appl PROPN iajs-2818 126 11 . . PUNCT iajs-2818 127 1 sci sci PROPN iajs-2818 127 2 . . PROPN iajs-2818 128 1 53 53 NUM iajs-2818 128 2 ( ( PUNCT iajs-2818 128 3 2)2022 2)2022 VERB iajs-2818 128 4 104 104 NUM iajs-2818 128 5 figure figure NOUN iajs-2818 128 6 2 2 NUM iajs-2818 128 7 . . PUNCT iajs-2818 128 8 rk4 rk4 PROPN iajs-2818 128 9 numerical numerical ADJ iajs-2818 128 10 results result NOUN iajs-2818 128 11 of of ADP iajs-2818 128 12 covid-19 covid-19 PROPN iajs-2818 128 13 model model NOUN iajs-2818 128 14 of of ADP iajs-2818 128 15 𝑆 𝑆 PROPN iajs-2818 128 16 , , PUNCT iajs-2818 128 17 𝐸 𝐸 PROPN iajs-2818 128 18 , , PUNCT iajs-2818 128 19 𝐼 𝐼 PROPN iajs-2818 128 20 , , PUNCT iajs-2818 128 21 𝑉 𝑉 PROPN iajs-2818 128 22 , , PUNCT iajs-2818 128 23 𝑅 𝑅 PROPN iajs-2818 128 24 from from ADP iajs-2818 128 25 2020 2020 NUM iajs-2818 128 26 with with ADP iajs-2818 128 27 step step NOUN iajs-2818 128 28 size size NOUN iajs-2818 128 29 β„Ž β„Ž PROPN iajs-2818 128 30 = = NOUN iajs-2818 128 31 0.02 0.02 NUM iajs-2818 128 32 during during ADP iajs-2818 128 33 15 15 NUM iajs-2818 128 34 years year NOUN iajs-2818 128 35 . . PUNCT iajs-2818 129 1 figure figure VERB iajs-2818 129 2 3 3 NUM iajs-2818 129 3 . . PUNCT iajs-2818 129 4 rk4 rk4 PROPN iajs-2818 129 5 numerical numerical ADJ iajs-2818 129 6 results result NOUN iajs-2818 129 7 of of ADP iajs-2818 129 8 covid-19 covid-19 PROPN iajs-2818 129 9 model model NOUN iajs-2818 129 10 of of ADP iajs-2818 129 11 𝑆 𝑆 PROPN iajs-2818 129 12 , , PUNCT iajs-2818 129 13 𝐸 𝐸 PROPN iajs-2818 129 14 , , PUNCT iajs-2818 129 15 𝐼 𝐼 PROPN iajs-2818 129 16 , , PUNCT iajs-2818 129 17 𝑉 𝑉 PROPN iajs-2818 129 18 , , PUNCT iajs-2818 129 19 𝑅 𝑅 PROPN iajs-2818 129 20 from from ADP iajs-2818 129 21 2020 2020 NUM iajs-2818 129 22 with with ADP iajs-2818 129 23 step step NOUN iajs-2818 129 24 size size NOUN iajs-2818 129 25 β„Ž β„Ž PROPN iajs-2818 129 26 = = NOUN iajs-2818 129 27 0.003 0.003 NUM iajs-2818 129 28 during during ADP iajs-2818 129 29 10 10 NUM iajs-2818 129 30 years year NOUN iajs-2818 129 31 . . PUNCT iajs-2818 130 1 ibn ibn PROPN iajs-2818 130 2 al al PROPN iajs-2818 130 3 - - PUNCT iajs-2818 130 4 haitham haitham PROPN iajs-2818 130 5 jour jour X iajs-2818 130 6 . . PROPN iajs-2818 130 7 for for ADP iajs-2818 130 8 pure pure ADJ iajs-2818 130 9 & & CCONJ iajs-2818 130 10 appl appl PROPN iajs-2818 130 11 . . PUNCT iajs-2818 131 1 sci sci PROPN iajs-2818 131 2 . . PROPN iajs-2818 132 1 53 53 NUM iajs-2818 132 2 ( ( PUNCT iajs-2818 132 3 2)2022 2)2022 NUM iajs-2818 132 4 105 105 NUM iajs-2818 132 5 figure figure NOUN iajs-2818 132 6 4 4 NUM iajs-2818 132 7 . . PUNCT iajs-2818 133 1 rk4 rk4 PROPN iajs-2818 133 2 numerical numerical ADJ iajs-2818 133 3 results result NOUN iajs-2818 133 4 of of ADP iajs-2818 133 5 covid-19 covid-19 PROPN iajs-2818 133 6 model model NOUN iajs-2818 133 7 of of ADP iajs-2818 133 8 𝑆 𝑆 PROPN iajs-2818 133 9 , , PUNCT iajs-2818 133 10 𝐸 𝐸 PROPN iajs-2818 133 11 , , PUNCT iajs-2818 133 12 𝐼 𝐼 PROPN iajs-2818 133 13 , , PUNCT iajs-2818 133 14 𝑉 𝑉 PROPN iajs-2818 133 15 , , PUNCT iajs-2818 133 16 𝑅 𝑅 PROPN iajs-2818 133 17 from from ADP iajs-2818 133 18 2020 2020 NUM iajs-2818 133 19 with with ADP iajs-2818 133 20 step step NOUN iajs-2818 133 21 size size NOUN iajs-2818 133 22 β„Ž β„Ž PROPN iajs-2818 133 23 = = NOUN iajs-2818 133 24 0.003 0.003 NUM iajs-2818 133 25 during during ADP iajs-2818 133 26 15 15 NUM iajs-2818 133 27 years year NOUN iajs-2818 133 28 . . PUNCT iajs-2818 134 1 5 5 X iajs-2818 134 2 . . X iajs-2818 134 3 conclusion conclusion NOUN iajs-2818 134 4 this this DET iajs-2818 134 5 model model NOUN iajs-2818 134 6 is be AUX iajs-2818 134 7 compatible compatible ADJ iajs-2818 134 8 with with ADP iajs-2818 134 9 the the DET iajs-2818 134 10 corona corona PROPN iajs-2818 134 11 virus virus NOUN iajs-2818 134 12 epidemic epidemic NOUN iajs-2818 134 13 in in ADP iajs-2818 134 14 iraq iraq PROPN iajs-2818 134 15 in in ADP iajs-2818 134 16 all all DET iajs-2818 134 17 its its PRON iajs-2818 134 18 stages stage NOUN iajs-2818 134 19 , , PUNCT iajs-2818 134 20 and and CCONJ iajs-2818 134 21 the the DET iajs-2818 134 22 observation observation NOUN iajs-2818 134 23 data datum NOUN iajs-2818 134 24 for for ADP iajs-2818 134 25 iraq iraq PROPN iajs-2818 134 26 is be AUX iajs-2818 134 27 used use VERB iajs-2818 134 28 as as ADP iajs-2818 134 29 initial initial ADJ iajs-2818 134 30 values value NOUN iajs-2818 134 31 , , PUNCT iajs-2818 134 32 so so ADV iajs-2818 134 33 the the DET iajs-2818 134 34 obtained obtain VERB iajs-2818 134 35 results result NOUN iajs-2818 134 36 match match VERB iajs-2818 134 37 the the DET iajs-2818 134 38 spread spread NOUN iajs-2818 134 39 of of ADP iajs-2818 134 40 the the DET iajs-2818 134 41 virus virus NOUN iajs-2818 134 42 in in ADP iajs-2818 134 43 iraq iraq PROPN iajs-2818 134 44 . . PUNCT iajs-2818 135 1 using use VERB iajs-2818 135 2 rk4 rk4 NOUN iajs-2818 135 3 the the DET iajs-2818 135 4 method method NOUN iajs-2818 135 5 gives give VERB iajs-2818 135 6 accurate accurate ADJ iajs-2818 135 7 results result NOUN iajs-2818 135 8 . . PUNCT iajs-2818 136 1 as as ADV iajs-2818 136 2 well well ADV iajs-2818 136 3 , , PUNCT iajs-2818 136 4 it it PRON iajs-2818 136 5 is be AUX iajs-2818 136 6 an an DET iajs-2818 136 7 effective effective ADJ iajs-2818 136 8 iterative iterative NOUN iajs-2818 136 9 numerical numerical ADJ iajs-2818 136 10 method method NOUN iajs-2818 136 11 that that PRON iajs-2818 136 12 is be AUX iajs-2818 136 13 applied apply VERB iajs-2818 136 14 for for ADP iajs-2818 136 15 solving solve VERB iajs-2818 136 16 the the DET iajs-2818 136 17 nonlinear nonlinear ADJ iajs-2818 136 18 system system NOUN iajs-2818 136 19 of of ADP iajs-2818 136 20 differential differential ADJ iajs-2818 136 21 equations equation NOUN iajs-2818 136 22 for for ADP iajs-2818 136 23 initial initial ADJ iajs-2818 136 24 value value NOUN iajs-2818 136 25 problems problem NOUN iajs-2818 136 26 , , PUNCT iajs-2818 136 27 it it PRON iajs-2818 136 28 has have AUX iajs-2818 136 29 given give VERB iajs-2818 136 30 accurate accurate ADJ iajs-2818 136 31 and and CCONJ iajs-2818 136 32 reliable reliable ADJ iajs-2818 136 33 results result NOUN iajs-2818 136 34 at at ADP iajs-2818 136 35 present present ADJ iajs-2818 136 36 work work NOUN iajs-2818 136 37 , , PUNCT iajs-2818 136 38 for for ADP iajs-2818 136 39 the the DET iajs-2818 136 40 corona corona PROPN iajs-2818 136 41 virus virus PROPN iajs-2818 136 42 epidemic epidemic NOUN iajs-2818 136 43 model model NOUN iajs-2818 136 44 . . PUNCT iajs-2818 137 1 in in ADP iajs-2818 137 2 the the DET iajs-2818 137 3 current current ADJ iajs-2818 137 4 research research NOUN iajs-2818 137 5 , , PUNCT iajs-2818 137 6 the the DET iajs-2818 137 7 used use VERB iajs-2818 137 8 numerical numerical ADJ iajs-2818 137 9 method method NOUN iajs-2818 137 10 helped help VERB iajs-2818 137 11 us we PRON iajs-2818 137 12 analyze analyze VERB iajs-2818 137 13 the the DET iajs-2818 137 14 outbreak outbreak NOUN iajs-2818 137 15 of of ADP iajs-2818 137 16 the the DET iajs-2818 137 17 epidemic epidemic NOUN iajs-2818 137 18 in in ADP iajs-2818 137 19 the the DET iajs-2818 137 20 covid-19 covid-19 PROPN iajs-2818 137 21 model model NOUN iajs-2818 137 22 in in ADP iajs-2818 137 23 iraq iraq PROPN iajs-2818 137 24 . . PUNCT iajs-2818 138 1 the the DET iajs-2818 138 2 results result NOUN iajs-2818 138 3 obtained obtain VERB iajs-2818 138 4 displayed display VERB iajs-2818 138 5 that that SCONJ iajs-2818 138 6 the the DET iajs-2818 138 7 number number NOUN iajs-2818 138 8 of of ADP iajs-2818 138 9 susceptible susceptible ADJ iajs-2818 138 10 populations population NOUN iajs-2818 138 11 gradually gradually ADV iajs-2818 138 12 decreased decrease VERB iajs-2818 138 13 in in ADP iajs-2818 138 14 some some DET iajs-2818 138 15 years year NOUN iajs-2818 138 16 , , PUNCT iajs-2818 138 17 then then ADV iajs-2818 138 18 maintained maintain VERB iajs-2818 138 19 its its PRON iajs-2818 138 20 level level NOUN iajs-2818 138 21 after after ADP iajs-2818 138 22 3 3 NUM iajs-2818 138 23 years year NOUN iajs-2818 138 24 of of ADP iajs-2818 138 25 disease disease NOUN iajs-2818 138 26 beginning begin VERB iajs-2818 138 27 . . PUNCT iajs-2818 139 1 while while SCONJ iajs-2818 139 2 the the DET iajs-2818 139 3 number number NOUN iajs-2818 139 4 of of ADP iajs-2818 139 5 exposed expose VERB iajs-2818 139 6 and and CCONJ iajs-2818 139 7 infective infective ADJ iajs-2818 139 8 populations population NOUN iajs-2818 139 9 increased increase VERB iajs-2818 139 10 in in ADP iajs-2818 139 11 the the DET iajs-2818 139 12 same same ADJ iajs-2818 139 13 years year NOUN iajs-2818 139 14 , , PUNCT iajs-2818 139 15 then then ADV iajs-2818 139 16 it it PRON iajs-2818 139 17 has have VERB iajs-2818 139 18 some some DET iajs-2818 139 19 stability stability NOUN iajs-2818 139 20 after after ADP iajs-2818 139 21 ( ( PUNCT iajs-2818 139 22 2 2 NUM iajs-2818 139 23 - - SYM iajs-2818 139 24 5 5 NUM iajs-2818 139 25 ) ) PUNCT iajs-2818 139 26 years year NOUN iajs-2818 139 27 from from ADP iajs-2818 139 28 the the DET iajs-2818 139 29 starting starting NOUN iajs-2818 139 30 of of ADP iajs-2818 139 31 the the DET iajs-2818 139 32 disease disease NOUN iajs-2818 139 33 . . PUNCT iajs-2818 140 1 when when SCONJ iajs-2818 140 2 the the DET iajs-2818 140 3 vaccination vaccination NOUN iajs-2818 140 4 campaign campaign NOUN iajs-2818 140 5 began begin VERB iajs-2818 140 6 , , PUNCT iajs-2818 140 7 the the DET iajs-2818 140 8 number number NOUN iajs-2818 140 9 of of ADP iajs-2818 140 10 vaccinated vaccinate VERB iajs-2818 140 11 gradually gradually ADV iajs-2818 140 12 rises rise VERB iajs-2818 140 13 for for ADP iajs-2818 140 14 3 3 NUM iajs-2818 140 15 years year NOUN iajs-2818 140 16 , , PUNCT iajs-2818 140 17 then then ADV iajs-2818 140 18 begins begin VERB iajs-2818 140 19 to to PART iajs-2818 140 20 decline decline VERB iajs-2818 140 21 and and CCONJ iajs-2818 140 22 stabilize stabilize VERB iajs-2818 140 23 at at ADP iajs-2818 140 24 a a DET iajs-2818 140 25 certain certain ADJ iajs-2818 140 26 level level NOUN iajs-2818 140 27 in in ADP iajs-2818 140 28 2025 2025 NUM iajs-2818 140 29 for for ADP iajs-2818 140 30 the the DET iajs-2818 140 31 coming come VERB iajs-2818 140 32 years year NOUN iajs-2818 140 33 . . PUNCT iajs-2818 141 1 on on ADP iajs-2818 141 2 the the DET iajs-2818 141 3 other other ADJ iajs-2818 141 4 hand hand NOUN iajs-2818 141 5 , , PUNCT iajs-2818 141 6 note note VERB iajs-2818 141 7 a a DET iajs-2818 141 8 slight slight ADJ iajs-2818 141 9 rise rise NOUN iajs-2818 141 10 from from ADP iajs-2818 141 11 the the DET iajs-2818 141 12 beginning beginning NOUN iajs-2818 141 13 of of ADP iajs-2818 141 14 the the DET iajs-2818 141 15 disease disease NOUN iajs-2818 141 16 to to ADP iajs-2818 141 17 the the DET iajs-2818 141 18 coming coming ADJ iajs-2818 141 19 years year NOUN iajs-2818 141 20 , , PUNCT iajs-2818 141 21 and and CCONJ iajs-2818 141 22 then then ADV iajs-2818 141 23 it it PRON iajs-2818 141 24 stabilizes stabilize VERB iajs-2818 141 25 for for ADP iajs-2818 141 26 the the DET iajs-2818 141 27 recovered recovered ADJ iajs-2818 141 28 population population NOUN iajs-2818 141 29 . . PUNCT iajs-2818 142 1 we we PRON iajs-2818 142 2 conclude conclude VERB iajs-2818 142 3 our our PRON iajs-2818 142 4 research research NOUN iajs-2818 142 5 , , PUNCT iajs-2818 142 6 through through ADP iajs-2818 142 7 the the DET iajs-2818 142 8 behavior behavior NOUN iajs-2818 142 9 of of ADP iajs-2818 142 10 all all DET iajs-2818 142 11 epidemic epidemic NOUN iajs-2818 142 12 stages stage NOUN iajs-2818 142 13 , , PUNCT iajs-2818 142 14 with with ADP iajs-2818 142 15 the the DET iajs-2818 142 16 expectation expectation NOUN iajs-2818 142 17 that that SCONJ iajs-2818 142 18 the the DET iajs-2818 142 19 epidemic epidemic NOUN iajs-2818 142 20 will will AUX iajs-2818 142 21 disappear disappear VERB iajs-2818 142 22 during during ADP iajs-2818 142 23 the the DET iajs-2818 142 24 next next ADJ iajs-2818 142 25 few few ADJ iajs-2818 142 26 years year NOUN iajs-2818 142 27 within within ADP iajs-2818 142 28 about about ADV iajs-2818 142 29 five five NUM iajs-2818 142 30 years year NOUN iajs-2818 142 31 . . PUNCT iajs-2818 143 1 references reference NOUN iajs-2818 143 2 1.wang 1.wang NUM iajs-2818 143 3 , , PUNCT iajs-2818 143 4 c. c. PROPN iajs-2818 143 5 ; ; PUNCT iajs-2818 143 6 horby horby PROPN iajs-2818 143 7 , , PUNCT iajs-2818 143 8 p. p. PROPN iajs-2818 143 9 w. w. PROPN iajs-2818 143 10 ; ; PUNCT iajs-2818 144 1 hayden hayden PROPN iajs-2818 144 2 , , PUNCT iajs-2818 144 3 f. f. PROPN iajs-2818 144 4 g. g. PROPN iajs-2818 144 5 ; ; PUNCT iajs-2818 144 6 gao gao PROPN iajs-2818 144 7 . . PUNCT iajs-2818 145 1 g. g. PROPN iajs-2818 145 2 f. f. PROPN iajs-2818 145 3 a a DET iajs-2818 145 4 novel novel ADJ iajs-2818 145 5 coronavirus coronavirus NOUN iajs-2818 145 6 outbreak outbreak NOUN iajs-2818 145 7 of of ADP iajs-2818 145 8 global global ADJ iajs-2818 145 9 health health NOUN iajs-2818 145 10 concern concern NOUN iajs-2818 145 11 . . PUNCT iajs-2818 146 1 the the DET iajs-2818 146 2 lancet lancet PROPN iajs-2818 146 3 . . PUNCT iajs-2818 147 1 2020 2020 NUM iajs-2818 147 2 , , PUNCT iajs-2818 147 3 395(10223 395(10223 NUM iajs-2818 147 4 ) ) PUNCT iajs-2818 147 5 , , PUNCT iajs-2818 147 6 470 470 NUM iajs-2818 147 7 - - SYM iajs-2818 147 8 473 473 NUM iajs-2818 147 9 . . PUNCT iajs-2818 148 1 2.zhao 2.zhao NUM iajs-2818 148 2 , , PUNCT iajs-2818 148 3 s. s. PROPN iajs-2818 148 4 ; ; PUNCT iajs-2818 148 5 chen chen PROPN iajs-2818 148 6 , , PUNCT iajs-2818 148 7 h. h. PROPN iajs-2818 148 8 modeling model VERB iajs-2818 148 9 the the DET iajs-2818 148 10 epidemic epidemic NOUN iajs-2818 148 11 dynamics dynamic NOUN iajs-2818 148 12 and and CCONJ iajs-2818 148 13 control control NOUN iajs-2818 148 14 of of ADP iajs-2818 148 15 covid-19 covid-19 PROPN iajs-2818 148 16 outbreak outbreak NOUN iajs-2818 148 17 in in ADP iajs-2818 148 18 china china PROPN iajs-2818 148 19 . . PUNCT iajs-2818 149 1 quantitative quantitative ADJ iajs-2818 149 2 biology biology NOUN iajs-2818 149 3 . . PUNCT iajs-2818 150 1 2020 2020 NUM iajs-2818 150 2 , , PUNCT iajs-2818 150 3 8(1 8(1 NOUN iajs-2818 150 4 ) ) PUNCT iajs-2818 150 5 , , PUNCT iajs-2818 150 6 11 11 NUM iajs-2818 150 7 - - SYM iajs-2818 150 8 19 19 NUM iajs-2818 150 9 . . PUNCT iajs-2818 151 1 ibn ibn PROPN iajs-2818 151 2 al al PROPN iajs-2818 151 3 - - PUNCT iajs-2818 151 4 haitham haitham PROPN iajs-2818 151 5 jour jour X iajs-2818 151 6 . . PROPN iajs-2818 151 7 for for ADP iajs-2818 151 8 pure pure ADJ iajs-2818 151 9 & & CCONJ iajs-2818 151 10 appl appl PROPN iajs-2818 151 11 . . PUNCT iajs-2818 152 1 sci sci PROPN iajs-2818 152 2 . . PROPN iajs-2818 153 1 53 53 NUM iajs-2818 153 2 ( ( PUNCT iajs-2818 153 3 2)2022 2)2022 NUM iajs-2818 153 4 106 106 NUM iajs-2818 153 5 3 3 NUM iajs-2818 153 6 . . PUNCT iajs-2818 153 7 huang huang PROPN iajs-2818 153 8 , , PUNCT iajs-2818 153 9 y. y. PROPN iajs-2818 153 10 ; ; PUNCT iajs-2818 153 11 yang yang PROPN iajs-2818 153 12 , , PUNCT iajs-2818 153 13 l. l. PROPN iajs-2818 153 14 ; ; PUNCT iajs-2818 153 15 dai dai PROPN iajs-2818 153 16 , , PUNCT iajs-2818 153 17 h. h. PROPN iajs-2818 153 18 ; ; PUNCT iajs-2818 153 19 tian tian PROPN iajs-2818 153 20 , , PUNCT iajs-2818 153 21 f. f. PROPN iajs-2818 153 22 ; ; PUNCT iajs-2818 153 23 chen chen PROPN iajs-2818 153 24 , , PUNCT iajs-2818 153 25 k. k. PROPN iajs-2818 153 26 epidemic epidemic PROPN iajs-2818 153 27 situation situation NOUN iajs-2818 153 28 and and CCONJ iajs-2818 153 29 forecasting forecasting NOUN iajs-2818 153 30 of of ADP iajs-2818 153 31 covid-19 covid-19 PROPN iajs-2818 153 32 in in ADP iajs-2818 153 33 and and CCONJ iajs-2818 153 34 outside outside ADP iajs-2818 153 35 china china PROPN iajs-2818 153 36 . . PUNCT iajs-2818 154 1 bull bull PROPN iajs-2818 154 2 world world PROPN iajs-2818 154 3 health health NOUN iajs-2818 154 4 organ organ NOUN iajs-2818 154 5 . . PUNCT iajs-2818 155 1 2020 2020 NUM iajs-2818 155 2 , , PUNCT iajs-2818 155 3 10 10 NUM iajs-2818 155 4 . . PUNCT iajs-2818 155 5 doi:10.2471 doi:10.2471 PROPN iajs-2818 155 6 / / SYM iajs-2818 155 7 blt.20.255158 blt.20.255158 PROPN iajs-2818 155 8 4 4 NUM iajs-2818 155 9 . . PUNCT iajs-2818 156 1 jd jd PROPN iajs-2818 156 2 , , PUNCT iajs-2818 156 3 v. v. PROPN iajs-2818 156 4 w. w. PROPN iajs-2818 156 5 ; ; PUNCT iajs-2818 156 6 osinga osinga PROPN iajs-2818 156 7 . . PUNCT iajs-2818 157 1 s. s. PROPN iajs-2818 157 2 ; ; PUNCT iajs-2818 157 3 kuip kuip PROPN iajs-2818 157 4 . . PUNCT iajs-2818 158 1 v. v. ADP iajs-2818 158 2 m. m. NOUN iajs-2818 158 3 ; ; PUNCT iajs-2818 158 4 tanck tanck ADJ iajs-2818 158 5 . . PUNCT iajs-2818 158 6 m. m. NOUN iajs-2818 158 7 ; ; PUNCT iajs-2818 158 8 hanegraaf hanegraaf PROPN iajs-2818 158 9 . . PUNCT iajs-2818 158 10 m. m. NOUN iajs-2818 158 11 ; ; PUNCT iajs-2818 159 1 pluymaekers pluymaekers PROPN iajs-2818 159 2 . . PUNCT iajs-2818 159 3 m. m. NOUN iajs-2818 159 4 ; ; PUNCT iajs-2818 159 5 et et PROPN iajs-2818 159 6 al al PROPN iajs-2818 159 7 . . PUNCT iajs-2818 159 8 forecasting forecasting NOUN iajs-2818 159 9 hospitalization hospitalization NOUN iajs-2818 159 10 and and CCONJ iajs-2818 159 11 icu icu PROPN iajs-2818 159 12 rates rate NOUN iajs-2818 159 13 of of ADP iajs-2818 159 14 the the DET iajs-2818 159 15 covid-19 covid-19 PROPN iajs-2818 159 16 outbreak outbreak NOUN iajs-2818 159 17 : : PUNCT iajs-2818 159 18 an an DET iajs-2818 159 19 efficient efficient ADJ iajs-2818 159 20 seir seir NOUN iajs-2818 159 21 model.[submitted model.[submitte VERB iajs-2818 159 22 ] ] PUNCT iajs-2818 159 23 . . PUNCT iajs-2818 160 1 bull bull PROPN iajs-2818 160 2 world world PROPN iajs-2818 160 3 health health NOUN iajs-2818 160 4 organ organ NOUN iajs-2818 160 5 . . PUNCT iajs-2818 161 1 2020 2020 NUM iajs-2818 161 2 . . PUNCT iajs-2818 162 1 5.yang 5.yang NUM iajs-2818 162 2 , , PUNCT iajs-2818 162 3 w. w. PROPN iajs-2818 162 4 ; ; PUNCT iajs-2818 162 5 zhang zhang PROPN iajs-2818 162 6 , , PUNCT iajs-2818 162 7 d. d. PROPN iajs-2818 162 8 ; ; PUNCT iajs-2818 162 9 peng peng PROPN iajs-2818 162 10 , , PUNCT iajs-2818 162 11 l. l. PROPN iajs-2818 162 12 ; ; PUNCT iajs-2818 162 13 zhuge zhuge PROPN iajs-2818 162 14 , , PUNCT iajs-2818 162 15 c. c. PROPN iajs-2818 162 16 ; ; PUNCT iajs-2818 162 17 hong hong PROPN iajs-2818 162 18 , , PUNCT iajs-2818 162 19 l. l. PROPN iajs-2818 162 20 rational rational ADJ iajs-2818 162 21 evaluation evaluation NOUN iajs-2818 162 22 of of ADP iajs-2818 162 23 various various ADJ iajs-2818 162 24 epidemic epidemic NOUN iajs-2818 162 25 models model NOUN iajs-2818 162 26 based base VERB iajs-2818 162 27 on on ADP iajs-2818 162 28 the the DET iajs-2818 162 29 covid-19 covid-19 PROPN iajs-2818 162 30 data datum NOUN iajs-2818 162 31 of of ADP iajs-2818 162 32 china china PROPN iajs-2818 162 33 . . PUNCT iajs-2818 163 1 epidemics epidemic NOUN iajs-2818 163 2 . . PUNCT iajs-2818 164 1 2021 2021 NUM iajs-2818 164 2 , , PUNCT iajs-2818 164 3 37 37 NUM iajs-2818 164 4 , , PUNCT iajs-2818 164 5 100 100 NUM iajs-2818 164 6 - - SYM iajs-2818 164 7 501 501 NUM iajs-2818 164 8 . . PUNCT iajs-2818 165 1 6 6 NUM iajs-2818 165 2 . . X iajs-2818 166 1 li li PROPN iajs-2818 166 2 , , PUNCT iajs-2818 166 3 m. m. NOUN iajs-2818 166 4 y. y. PROPN iajs-2818 166 5 an an DET iajs-2818 166 6 introduction introduction NOUN iajs-2818 166 7 to to ADP iajs-2818 166 8 mathematical mathematical ADJ iajs-2818 166 9 modeling modeling NOUN iajs-2818 166 10 of of ADP iajs-2818 166 11 infectious infectious ADJ iajs-2818 166 12 diseases disease NOUN iajs-2818 166 13 ( ( PUNCT iajs-2818 166 14 vol vol NOUN iajs-2818 166 15 . . NOUN iajs-2818 166 16 2 2 NUM iajs-2818 166 17 ): ): PUNCT iajs-2818 166 18 springer springer NOUN iajs-2818 166 19 , , PUNCT iajs-2818 166 20 2018 2018 NUM iajs-2818 166 21 , , PUNCT iajs-2818 166 22 isbn isbn ADJ iajs-2818 166 23 978 978 NUM iajs-2818 166 24 - - SYM iajs-2818 166 25 3 3 NUM iajs-2818 166 26 - - NUM iajs-2818 166 27 319 319 NUM iajs-2818 166 28 - - PUNCT iajs-2818 166 29 722121 722121 NUM iajs-2818 166 30 - - SYM iajs-2818 166 31 7 7 NUM iajs-2818 166 32 . . NUM iajs-2818 166 33 7.lutz 7.lutz NUM iajs-2818 166 34 , , PUNCT iajs-2818 166 35 c. c. PROPN iajs-2818 166 36 s. s. PROPN iajs-2818 166 37 ; ; PUNCT iajs-2818 166 38 huynh huynh PROPN iajs-2818 166 39 , , PUNCT iajs-2818 166 40 m. m. NOUN iajs-2818 166 41 p. p. NOUN iajs-2818 166 42 ; ; PUNCT iajs-2818 166 43 schroeder schroeder PROPN iajs-2818 166 44 , , PUNCT iajs-2818 166 45 m. m. NOUN iajs-2818 166 46 ; ; PUNCT iajs-2818 166 47 anyatonwu anyatonwu PROPN iajs-2818 166 48 , , PUNCT iajs-2818 166 49 s. s. PROPN iajs-2818 166 50 ; ; PUNCT iajs-2818 166 51 dahlgren dahlgren PROPN iajs-2818 166 52 . . PUNCT iajs-2818 167 1 f. f. PROPN iajs-2818 167 2 s. s. PROPN iajs-2818 167 3 ; ; PUNCT iajs-2818 167 4 lutz lutz PROPN iajs-2818 167 5 . . PUNCT iajs-2818 168 1 c. c. PROPN iajs-2818 168 2 s. s. PROPN iajs-2818 168 3 ; ; PUNCT iajs-2818 168 4 huynh.m huynh.m PROPN iajs-2818 168 5 . . PUNCT iajs-2818 169 1 p. p. NOUN iajs-2818 169 2 ; ; PUNCT iajs-2818 170 1 schroeder schroeder PROPN iajs-2818 170 2 , , PUNCT iajs-2818 170 3 m. m. NOUN iajs-2818 170 4 ; ; PUNCT iajs-2818 170 5 anyatonwu anyatonwu PROPN iajs-2818 170 6 , , PUNCT iajs-2818 170 7 s. s. PROPN iajs-2818 170 8 ; ; PUNCT iajs-2818 170 9 dahlgren dahlgren PROPN iajs-2818 170 10 , , PUNCT iajs-2818 170 11 f. f. PROPN iajs-2818 170 12 s. s. PROPN iajs-2818 170 13 g. g. PROPN iajs-2818 170 14 ; ; PUNCT iajs-2818 170 15 danyluk danyluk PROPN iajs-2818 170 16 , , PUNCT iajs-2818 170 17 d. d. PROPN iajs-2818 170 18 ; ; PUNCT iajs-2818 170 19 fernandez fernandez PROPN iajs-2818 170 20 , , PUNCT iajs-2818 170 21 s.k s.k PROPN iajs-2818 170 22 . . PROPN iajs-2818 170 23 ; ; PUNCT iajs-2818 170 24 greene greene PROPN iajs-2818 170 25 , , PUNCT iajs-2818 170 26 n. n. NOUN iajs-2818 170 27 ; ; PUNCT iajs-2818 170 28 kipshidze kipshidze PROPN iajs-2818 170 29 . . PUNCT iajs-2818 171 1 l. l. PROPN iajs-2818 171 2 l. l. PROPN iajs-2818 171 3 , , PUNCT iajs-2818 171 4 et et PROPN iajs-2818 171 5 al al PROPN iajs-2818 171 6 . . PUNCT iajs-2818 171 7 applying apply VERB iajs-2818 171 8 infectious infectious ADJ iajs-2818 171 9 disease disease NOUN iajs-2818 171 10 forecasting forecasting NOUN iajs-2818 171 11 to to ADP iajs-2818 171 12 public public ADJ iajs-2818 171 13 health health NOUN iajs-2818 171 14 : : PUNCT iajs-2818 171 15 a a DET iajs-2818 171 16 path path NOUN iajs-2818 171 17 forward forward ADV iajs-2818 171 18 using use VERB iajs-2818 171 19 influenza influenza NOUN iajs-2818 171 20 forecasting forecasting NOUN iajs-2818 171 21 examples example NOUN iajs-2818 171 22 . . PUNCT iajs-2818 172 1 bmc bmc ADJ iajs-2818 172 2 public public ADJ iajs-2818 172 3 health health NOUN iajs-2818 172 4 . . PUNCT iajs-2818 173 1 2019 2019 NUM iajs-2818 173 2 , , PUNCT iajs-2818 173 3 19(1 19(1 NUM iajs-2818 173 4 ) ) PUNCT iajs-2818 173 5 , , PUNCT iajs-2818 173 6 1 1 NUM iajs-2818 173 7 - - SYM iajs-2818 173 8 12 12 NUM iajs-2818 173 9 . . NOUN iajs-2818 174 1 8 8 NUM iajs-2818 174 2 . . X iajs-2818 175 1 basu basu PROPN iajs-2818 175 2 , , PUNCT iajs-2818 175 3 s. s. PROPN iajs-2818 175 4 ; ; PUNCT iajs-2818 175 5 andrews andrews PROPN iajs-2818 175 6 , , PUNCT iajs-2818 175 7 j. j. PROPN iajs-2818 175 8 complexity complexity PROPN iajs-2818 175 9 in in ADP iajs-2818 175 10 mathematical mathematical ADJ iajs-2818 175 11 models model NOUN iajs-2818 175 12 of of ADP iajs-2818 175 13 public public ADJ iajs-2818 175 14 health health NOUN iajs-2818 175 15 policies policy NOUN iajs-2818 175 16 : : PUNCT iajs-2818 175 17 a a DET iajs-2818 175 18 guide guide NOUN iajs-2818 175 19 for for ADP iajs-2818 175 20 consumers consumer NOUN iajs-2818 175 21 of of ADP iajs-2818 175 22 models model NOUN iajs-2818 175 23 . . PUNCT iajs-2818 176 1 plos plos PROPN iajs-2818 176 2 medicine medicine PROPN iajs-2818 176 3 . . PUNCT iajs-2818 177 1 2013 2013 NUM iajs-2818 177 2 , , PUNCT iajs-2818 177 3 10(10 10(10 NUM iajs-2818 177 4 ) ) PUNCT iajs-2818 177 5 , , PUNCT iajs-2818 177 6 e1001540 e1001540 PROPN iajs-2818 177 7 . . PUNCT iajs-2818 178 1 [ [ X iajs-2818 178 2 9 9 NUM iajs-2818 178 3 ] ] SYM iajs-2818 178 4 han han PROPN iajs-2818 178 5 , , PUNCT iajs-2818 178 6 x. x. NOUN iajs-2818 178 7 n. n. PROPN iajs-2818 178 8 ; ; PUNCT iajs-2818 178 9 de de X iajs-2818 178 10 vlas vlas PROPN iajs-2818 178 11 , , PUNCT iajs-2818 178 12 s. s. PROPN iajs-2818 178 13 j. j. PROPN iajs-2818 178 14 ; ; PUNCT iajs-2818 178 15 fang fang PROPN iajs-2818 178 16 , , PUNCT iajs-2818 178 17 l. l. PROPN iajs-2818 178 18 q. q. PROPN iajs-2818 178 19 ; ; PUNCT iajs-2818 178 20 feng feng PROPN iajs-2818 178 21 , , PUNCT iajs-2818 178 22 d. d. PROPN iajs-2818 178 23 ; ; PUNCT iajs-2818 178 24 cao cao PROPN iajs-2818 178 25 , , PUNCT iajs-2818 178 26 w. w. PROPN iajs-2818 178 27 c. c. PROPN iajs-2818 178 28 ; ; PUNCT iajs-2818 178 29 habbema habbema PROPN iajs-2818 178 30 , , PUNCT iajs-2818 178 31 j. j. PROPN iajs-2818 178 32 d. d. PROPN iajs-2818 178 33 f. f. PROPN iajs-2818 178 34 mathematical mathematical PROPN iajs-2818 178 35 modelling modelling NOUN iajs-2818 178 36 of of ADP iajs-2818 178 37 sars sar NOUN iajs-2818 178 38 and and CCONJ iajs-2818 178 39 other other ADJ iajs-2818 178 40 infectious infectious ADJ iajs-2818 178 41 diseases disease NOUN iajs-2818 178 42 in in ADP iajs-2818 178 43 china china PROPN iajs-2818 178 44 : : PUNCT iajs-2818 178 45 a a DET iajs-2818 178 46 review review NOUN iajs-2818 178 47 . . PUNCT iajs-2818 179 1 tropical tropical ADJ iajs-2818 179 2 medicine medicine PROPN iajs-2818 179 3 & & CCONJ iajs-2818 179 4 international international ADJ iajs-2818 179 5 health health NOUN iajs-2818 179 6 . . PUNCT iajs-2818 180 1 2009 2009 NUM iajs-2818 180 2 , , PUNCT iajs-2818 180 3 14 14 NUM iajs-2818 180 4 , , PUNCT iajs-2818 180 5 92 92 NUM iajs-2818 180 6 - - SYM iajs-2818 180 7 100 100 NUM iajs-2818 180 8 . . PUNCT iajs-2818 181 1 10 10 NUM iajs-2818 181 2 . . X iajs-2818 182 1 beauchemin beauchemin NOUN iajs-2818 182 2 , , PUNCT iajs-2818 182 3 c. c. PROPN iajs-2818 182 4 a. a. PROPN iajs-2818 182 5 ; ; PUNCT iajs-2818 182 6 handel handel PROPN iajs-2818 182 7 , , PUNCT iajs-2818 182 8 a. a. NOUN iajs-2818 182 9 a a DET iajs-2818 182 10 review review NOUN iajs-2818 182 11 of of ADP iajs-2818 182 12 mathematical mathematical ADJ iajs-2818 182 13 models model NOUN iajs-2818 182 14 of of ADP iajs-2818 182 15 influenza influenza NOUN iajs-2818 182 16 a a DET iajs-2818 182 17 infections infection NOUN iajs-2818 182 18 within within ADP iajs-2818 182 19 a a DET iajs-2818 182 20 host host NOUN iajs-2818 182 21 or or CCONJ iajs-2818 182 22 cell cell NOUN iajs-2818 182 23 culture culture NOUN iajs-2818 182 24 : : PUNCT iajs-2818 183 1 lessons lesson NOUN iajs-2818 183 2 learned learn VERB iajs-2818 183 3 and and CCONJ iajs-2818 183 4 challenges challenge VERB iajs-2818 183 5 ahead ahead ADV iajs-2818 183 6 . . PUNCT iajs-2818 184 1 bmc bmc VERB iajs-2818 184 2 public public ADJ iajs-2818 184 3 health health NOUN iajs-2818 184 4 . . PUNCT iajs-2818 185 1 2011 2011 NUM iajs-2818 185 2 , , PUNCT iajs-2818 185 3 11(1 11(1 NUM iajs-2818 185 4 ) ) PUNCT iajs-2818 185 5 , , PUNCT iajs-2818 185 6 1 1 NUM iajs-2818 185 7 - - SYM iajs-2818 185 8 15 15 NUM iajs-2818 185 9 . . PUNCT iajs-2818 186 1 11.kermack 11.kermack NUM iajs-2818 186 2 , , PUNCT iajs-2818 186 3 w. w. PROPN iajs-2818 186 4 o. o. PROPN iajs-2818 186 5 ; ; PUNCT iajs-2818 186 6 mckendrick mckendrick PROPN iajs-2818 186 7 , , PUNCT iajs-2818 186 8 a. a. NOUN iajs-2818 186 9 g. g. PROPN iajs-2818 186 10 contributions contribution NOUN iajs-2818 186 11 to to ADP iajs-2818 186 12 the the DET iajs-2818 186 13 mathematical mathematical ADJ iajs-2818 186 14 theory theory NOUN iajs-2818 186 15 of of ADP iajs-2818 186 16 epidemics epidemic NOUN iajs-2818 186 17 -- -- PUNCT iajs-2818 186 18 i. i. NOUN iajs-2818 186 19 1927 1927 NUM iajs-2818 186 20 . . PUNCT iajs-2818 187 1 bulletin bulletin NOUN iajs-2818 187 2 of of ADP iajs-2818 187 3 mathematical mathematical ADJ iajs-2818 187 4 biology biology NOUN iajs-2818 187 5 . . PUNCT iajs-2818 188 1 1991 1991 NUM iajs-2818 188 2 , , PUNCT iajs-2818 188 3 53(1 53(1 PROPN iajs-2818 188 4 - - SYM iajs-2818 188 5 2 2 NUM iajs-2818 188 6 ) ) PUNCT iajs-2818 188 7 , , PUNCT iajs-2818 188 8 33 33 NUM iajs-2818 188 9 - - SYM iajs-2818 188 10 55 55 NUM iajs-2818 188 11 . . PUNCT iajs-2818 189 1 12 12 NUM iajs-2818 189 2 . . PUNCT iajs-2818 190 1 kermack kermack PROPN iajs-2818 190 2 , , PUNCT iajs-2818 190 3 w. w. PROPN iajs-2818 190 4 o. o. PROPN iajs-2818 190 5 ; ; PUNCT iajs-2818 190 6 mckendrick mckendrick PROPN iajs-2818 190 7 , , PUNCT iajs-2818 190 8 a. a. NOUN iajs-2818 190 9 g. g. PROPN iajs-2818 190 10 contributions contribution NOUN iajs-2818 190 11 to to ADP iajs-2818 190 12 the the DET iajs-2818 190 13 mathematical mathematical ADJ iajs-2818 190 14 theory theory NOUN iajs-2818 190 15 of of ADP iajs-2818 190 16 epidemics epidemic NOUN iajs-2818 190 17 . . PUNCT iajs-2818 191 1 ii.β€”the ii.β€”the PRON iajs-2818 191 2 problem problem NOUN iajs-2818 191 3 of of ADP iajs-2818 191 4 endemicity endemicity NOUN iajs-2818 191 5 . . PUNCT iajs-2818 192 1 proceedings proceeding NOUN iajs-2818 192 2 of of ADP iajs-2818 192 3 the the DET iajs-2818 192 4 royal royal ADJ iajs-2818 192 5 society society NOUN iajs-2818 192 6 of of ADP iajs-2818 192 7 london london PROPN iajs-2818 192 8 . . PUNCT iajs-2818 193 1 series series PROPN iajs-2818 193 2 a a PROPN iajs-2818 193 3 , , PUNCT iajs-2818 193 4 containing contain VERB iajs-2818 193 5 papers paper NOUN iajs-2818 193 6 of of ADP iajs-2818 193 7 a a DET iajs-2818 193 8 mathematical mathematical ADJ iajs-2818 193 9 and and CCONJ iajs-2818 193 10 physical physical ADJ iajs-2818 193 11 character character NOUN iajs-2818 193 12 . . PUNCT iajs-2818 194 1 1932 1932 NUM iajs-2818 194 2 , , PUNCT iajs-2818 194 3 138(834 138(834 NUM iajs-2818 194 4 ) ) PUNCT iajs-2818 194 5 , , PUNCT iajs-2818 194 6 55 55 NUM iajs-2818 194 7 - - SYM iajs-2818 194 8 83 83 NUM iajs-2818 194 9 . . PUNCT iajs-2818 195 1 13.diekmann 13.diekmann NUM iajs-2818 195 2 , , PUNCT iajs-2818 195 3 o. o. INTJ iajs-2818 195 4 ; ; PUNCT iajs-2818 195 5 heesterbeek heesterbeek NOUN iajs-2818 195 6 , , PUNCT iajs-2818 195 7 h h NOUN iajs-2818 195 8 .. .. PUNCT iajs-2818 195 9 ; ; PUNCT iajs-2818 195 10 britton britton PROPN iajs-2818 195 11 , , PUNCT iajs-2818 195 12 t. t. PROPN iajs-2818 195 13 mathematical mathematical ADJ iajs-2818 195 14 tools tool NOUN iajs-2818 195 15 for for ADP iajs-2818 195 16 understanding understand VERB iajs-2818 195 17 infectious infectious ADJ iajs-2818 195 18 disease disease NOUN iajs-2818 195 19 dynamics dynamic NOUN iajs-2818 195 20 : : PUNCT iajs-2818 195 21 princeton princeton PROPN iajs-2818 195 22 university university PROPN iajs-2818 195 23 press press NOUN iajs-2818 195 24 , , PUNCT iajs-2818 195 25 2012 2012 NUM iajs-2818 195 26 ; ; PUNCT iajs-2818 195 27 isbn isbn ADJ iajs-2818 195 28 : : PUNCT iajs-2818 195 29 9781400845620 9781400845620 NUM iajs-2818 195 30 14 14 NUM iajs-2818 195 31 . . PUNCT iajs-2818 196 1 kretzschmar kretzschmar PROPN iajs-2818 196 2 , , PUNCT iajs-2818 196 3 m. m. NOUN iajs-2818 196 4 ; ; PUNCT iajs-2818 196 5 van van PROPN iajs-2818 196 6 h. h. PROPN iajs-2818 196 7 s. s. PROPN iajs-2818 196 8 ; ; PUNCT iajs-2818 196 9 wallinga wallinga PROPN iajs-2818 196 10 , , PUNCT iajs-2818 196 11 j. j. PROPN iajs-2818 196 12 ; ; PUNCT iajs-2818 196 13 van van PROPN iajs-2818 196 14 w. w. PROPN iajs-2818 196 15 j. j. PROPN iajs-2818 196 16 ring ring PROPN iajs-2818 196 17 vaccination vaccination NOUN iajs-2818 196 18 and and CCONJ iajs-2818 196 19 smallpox smallpox NOUN iajs-2818 196 20 control control NOUN iajs-2818 196 21 . . PUNCT iajs-2818 197 1 emerging emerge VERB iajs-2818 197 2 infectious infectious ADJ iajs-2818 197 3 diseases disease NOUN iajs-2818 197 4 . . PUNCT iajs-2818 198 1 2004 2004 NUM iajs-2818 198 2 , , PUNCT iajs-2818 198 3 10(5 10(5 NUM iajs-2818 198 4 ) ) PUNCT iajs-2818 198 5 , , PUNCT iajs-2818 198 6 832 832 NUM iajs-2818 198 7 . . NOUN iajs-2818 198 8 15 15 NUM iajs-2818 198 9 . . X iajs-2818 198 10 rodrigues rodrigues PROPN iajs-2818 198 11 , , PUNCT iajs-2818 198 12 h. h. PROPN iajs-2818 198 13 s. s. PROPN iajs-2818 198 14 ; ; PUNCT iajs-2818 198 15 monteiro monteiro PROPN iajs-2818 198 16 , , PUNCT iajs-2818 198 17 m. m. NOUN iajs-2818 198 18 t. t. PROPN iajs-2818 198 19 t. t. PROPN iajs-2818 198 20 ; ; PUNCT iajs-2818 198 21 torres torre NOUN iajs-2818 198 22 , , PUNCT iajs-2818 198 23 d. d. PROPN iajs-2818 198 24 f. f. PROPN iajs-2818 198 25 vaccination vaccination NOUN iajs-2818 198 26 models model NOUN iajs-2818 198 27 and and CCONJ iajs-2818 198 28 optimal optimal ADJ iajs-2818 198 29 control control NOUN iajs-2818 198 30 strategies strategy NOUN iajs-2818 198 31 to to ADP iajs-2818 198 32 dengue dengue NOUN iajs-2818 198 33 . . PUNCT iajs-2818 199 1 mathematical mathematical ADJ iajs-2818 199 2 biosciences bioscience NOUN iajs-2818 199 3 . . PUNCT iajs-2818 199 4 2014 2014 NUM iajs-2818 199 5 , , PUNCT iajs-2818 199 6 247 247 NUM iajs-2818 199 7 , , PUNCT iajs-2818 199 8 1 1 NUM iajs-2818 199 9 - - SYM iajs-2818 199 10 12 12 NUM iajs-2818 199 11 . . PUNCT iajs-2818 200 1 16 16 NUM iajs-2818 200 2 . . PUNCT iajs-2818 201 1 mohammed mohammed PROPN iajs-2818 201 2 , , PUNCT iajs-2818 201 3 m. m. NOUN iajs-2818 201 4 a. a. PROPN iajs-2818 201 5 , , PUNCT iajs-2818 201 6 noor noor PROPN iajs-2818 201 7 , , PUNCT iajs-2818 201 8 n. n. PROPN iajs-2818 201 9 f. f. PROPN iajs-2818 201 10 m. m. PROPN iajs-2818 201 11 , , PUNCT iajs-2818 201 12 siri siri NOUN iajs-2818 201 13 , , PUNCT iajs-2818 201 14 z. z. PROPN iajs-2818 201 15 , , PUNCT iajs-2818 201 16 ; ; PUNCT iajs-2818 201 17 ibrahim ibrahim PROPN iajs-2818 201 18 , , PUNCT iajs-2818 201 19 a. a. PROPN iajs-2818 201 20 i. i. PROPN iajs-2818 201 21 n. n. PROPN iajs-2818 201 22 ( ( PUNCT iajs-2818 201 23 2015 2015 NUM iajs-2818 201 24 ) ) PUNCT iajs-2818 201 25 . . PUNCT iajs-2818 202 1 numerical numerical ADJ iajs-2818 202 2 solution solution NOUN iajs-2818 202 3 for for ADP iajs-2818 202 4 weight weight NOUN iajs-2818 202 5 reduction reduction NOUN iajs-2818 202 6 model model NOUN iajs-2818 202 7 due due ADP iajs-2818 202 8 to to ADP iajs-2818 202 9 health health NOUN iajs-2818 202 10 campaigns campaign NOUN iajs-2818 202 11 in in ADP iajs-2818 202 12 spain spain PROPN iajs-2818 202 13 . . PUNCT iajs-2818 203 1 paper paper PROPN iajs-2818 203 2 presented present VERB iajs-2818 203 3 at at ADP iajs-2818 203 4 the the DET iajs-2818 203 5 aip aip PROPN iajs-2818 203 6 conference conference NOUN iajs-2818 203 7 proceedings proceeding NOUN iajs-2818 203 8 . . PUNCT iajs-2818 204 1 17.sabaa 17.sabaa X iajs-2818 204 2 , , PUNCT iajs-2818 204 3 m. m. NOUN iajs-2818 204 4 a. a. PROPN iajs-2818 204 5 ; ; PUNCT iajs-2818 204 6 mohammed mohammed PROPN iajs-2818 204 7 , , PUNCT iajs-2818 204 8 m. m. NOUN iajs-2818 204 9 a. a. PROPN iajs-2818 204 10 , , PUNCT iajs-2818 204 11 abd abd PROPN iajs-2818 204 12 almjeed almjeed NOUN iajs-2818 204 13 , , PUNCT iajs-2818 204 14 s. s. PROPN iajs-2818 204 15 h. h. PROPN iajs-2818 204 16 approximate approximate PROPN iajs-2818 204 17 solutions solution NOUN iajs-2818 204 18 for for ADP iajs-2818 204 19 alcohol alcohol NOUN iajs-2818 204 20 consumption consumption NOUN iajs-2818 204 21 model model NOUN iajs-2818 204 22 in in ADP iajs-2818 204 23 spain spain PROPN iajs-2818 204 24 . . PUNCT iajs-2818 205 1 ibn ibn PROPN iajs-2818 205 2 al al PROPN iajs-2818 205 3 - - PUNCT iajs-2818 205 4 haitham haitham PROPN iajs-2818 205 5 journal journal PROPN iajs-2818 205 6 for for ADP iajs-2818 205 7 pure pure ADJ iajs-2818 205 8 and and CCONJ iajs-2818 205 9 applied applied ADJ iajs-2818 205 10 sciences science NOUN iajs-2818 205 11 . . PUNCT iajs-2818 205 12 2019 2019 NUM iajs-2818 205 13 , , PUNCT iajs-2818 205 14 32(3 32(3 NUM iajs-2818 205 15 ) ) PUNCT iajs-2818 205 16 , , PUNCT iajs-2818 205 17 153 153 NUM iajs-2818 205 18 - - SYM iajs-2818 205 19 164 164 NUM iajs-2818 205 20 . . PUNCT iajs-2818 206 1 18 18 NUM iajs-2818 206 2 . . X iajs-2818 206 3 sabaa sabaa PROPN iajs-2818 206 4 , , PUNCT iajs-2818 206 5 m. m. NOUN iajs-2818 206 6 a. a. PROPN iajs-2818 206 7 ; ; PUNCT iajs-2818 206 8 mohammed mohammed PROPN iajs-2818 206 9 , , PUNCT iajs-2818 206 10 m. m. NOUN iajs-2818 206 11 a. a. PROPN iajs-2818 206 12 approximate approximate PROPN iajs-2818 206 13 solutions solution NOUN iajs-2818 206 14 of of ADP iajs-2818 206 15 nonlinear nonlinear ADJ iajs-2818 206 16 smoking smoking NOUN iajs-2818 206 17 habit habit NOUN iajs-2818 206 18 model model NOUN iajs-2818 206 19 . . PUNCT iajs-2818 207 1 iraqi iraqi ADJ iajs-2818 207 2 journal journal PROPN iajs-2818 207 3 of of ADP iajs-2818 207 4 science science NOUN iajs-2818 207 5 . . PUNCT iajs-2818 208 1 2020 2020 NUM iajs-2818 208 2 , , PUNCT iajs-2818 208 3 435 435 NUM iajs-2818 208 4 - - SYM iajs-2818 208 5 443 443 NUM iajs-2818 208 6 . . NOUN iajs-2818 208 7 19 19 NUM iajs-2818 208 8 . . PUNCT iajs-2818 209 1 mohammed mohammed PROPN iajs-2818 209 2 , , PUNCT iajs-2818 209 3 s. s. PROPN iajs-2818 209 4 j. j. PROPN iajs-2818 209 5 ; ; PUNCT iajs-2818 209 6 mohammed mohammed PROPN iajs-2818 209 7 , , PUNCT iajs-2818 209 8 m. m. NOUN iajs-2818 209 9 a. a. NOUN iajs-2818 209 10 ( ( PUNCT iajs-2818 209 11 2021 2021 NUM iajs-2818 209 12 ) ) PUNCT iajs-2818 209 13 . . PUNCT iajs-2818 210 1 runge runge NOUN iajs-2818 210 2 - - PUNCT iajs-2818 210 3 kutta kutta PROPN iajs-2818 210 4 numerical numerical PROPN iajs-2818 210 5 method method NOUN iajs-2818 210 6 for for ADP iajs-2818 210 7 solving solve VERB iajs-2818 210 8 nonlinear nonlinear ADJ iajs-2818 210 9 influenza influenza NOUN iajs-2818 210 10 model model NOUN iajs-2818 210 11 . . PUNCT iajs-2818 211 1 paper paper NOUN iajs-2818 211 2 presented present VERB iajs-2818 211 3 at at ADP iajs-2818 211 4 the the DET iajs-2818 211 5 journal journal NOUN iajs-2818 211 6 of of ADP iajs-2818 211 7 physics physics PROPN iajs-2818 211 8 : : PUNCT iajs-2818 211 9 conference conference NOUN iajs-2818 211 10 series series NOUN iajs-2818 211 11 . . PUNCT iajs-2818 212 1 20 20 NUM iajs-2818 212 2 . . X iajs-2818 212 3 huisen huisen PROPN iajs-2818 212 4 , , PUNCT iajs-2818 212 5 r. r. PROPN iajs-2818 212 6 w. w. PROPN iajs-2818 212 7 ; ; PUNCT iajs-2818 212 8 abd abd PROPN iajs-2818 212 9 almjeed almjeed NOUN iajs-2818 212 10 , , PUNCT iajs-2818 212 11 s. s. PROPN iajs-2818 212 12 h. h. PROPN iajs-2818 212 13 ; ; PUNCT iajs-2818 212 14 mohammed mohammed PROPN iajs-2818 212 15 , , PUNCT iajs-2818 212 16 a. a. PROPN iajs-2818 212 17 s. s. PROPN iajs-2818 213 1 a a DET iajs-2818 213 2 reliable reliable ADJ iajs-2818 213 3 iterative iterative NOUN iajs-2818 213 4 transform transform NOUN iajs-2818 213 5 method method NOUN iajs-2818 213 6 for for ADP iajs-2818 213 7 solving solve VERB iajs-2818 213 8 an an DET iajs-2818 213 9 epidemic epidemic NOUN iajs-2818 213 10 model model NOUN iajs-2818 213 11 . . PUNCT iajs-2818 214 1 iraqi iraqi ADJ iajs-2818 214 2 journal journal PROPN iajs-2818 214 3 of of ADP iajs-2818 214 4 science science NOUN iajs-2818 214 5 . . PUNCT iajs-2818 215 1 2021 2021 NUM iajs-2818 215 2 , , PUNCT iajs-2818 215 3 4839 4839 NUM iajs-2818 215 4 - - SYM iajs-2818 215 5 4846 4846 NUM iajs-2818 215 6 . . PUNCT iajs-2818 216 1 21.mohsen 21.mohsen NUM iajs-2818 216 2 , , PUNCT iajs-2818 216 3 a. a. NOUN iajs-2818 216 4 a. a. PROPN iajs-2818 216 5 ; ; PUNCT iajs-2818 216 6 al al PROPN iajs-2818 216 7 - - PUNCT iajs-2818 216 8 husseiny husseiny PROPN iajs-2818 216 9 , , PUNCT iajs-2818 216 10 h. h. PROPN iajs-2818 216 11 f. f. PROPN iajs-2818 216 12 ; ; PUNCT iajs-2818 216 13 zhou zhou PROPN iajs-2818 216 14 , , PUNCT iajs-2818 216 15 x. x. PROPN iajs-2818 216 16 ; ; PUNCT iajs-2818 216 17 hattaf hattaf NOUN iajs-2818 216 18 , , PUNCT iajs-2818 216 19 k. k. PROPN iajs-2818 216 20 global global ADJ iajs-2818 216 21 stability stability NOUN iajs-2818 216 22 of of ADP iajs-2818 216 23 covid-19 covid-19 PROPN iajs-2818 216 24 model model NOUN iajs-2818 216 25 involving involve VERB iajs-2818 216 26 the the DET iajs-2818 216 27 quarantine quarantine NOUN iajs-2818 216 28 strategy strategy NOUN iajs-2818 216 29 and and CCONJ iajs-2818 216 30 media medium NOUN iajs-2818 216 31 coverage coverage NOUN iajs-2818 216 32 effects effect NOUN iajs-2818 216 33 . . PUNCT iajs-2818 216 34 aims aim VERB iajs-2818 216 35 public public ADJ iajs-2818 216 36 health health NOUN iajs-2818 216 37 . . PUNCT iajs-2818 217 1 2020 2020 NUM iajs-2818 217 2 , , PUNCT iajs-2818 217 3 7(3 7(3 NUM iajs-2818 217 4 ) ) PUNCT iajs-2818 217 5 , , PUNCT iajs-2818 217 6 587 587 NUM iajs-2818 217 7 . . PUNCT iajs-2818 218 1 22 22 NUM iajs-2818 218 2 . . PUNCT iajs-2818 219 1 ahmed ahmed PROPN iajs-2818 219 2 , , PUNCT iajs-2818 219 3 a. a. PROPN iajs-2818 219 4 ; ; PUNCT iajs-2818 219 5 salam salam PROPN iajs-2818 219 6 , , PUNCT iajs-2818 219 7 b. b. PROPN iajs-2818 219 8 ; ; PUNCT iajs-2818 219 9 mohammad mohammad PROPN iajs-2818 219 10 , , PUNCT iajs-2818 219 11 m. m. NOUN iajs-2818 219 12 ; ; PUNCT iajs-2818 219 13 akgul akgul NOUN iajs-2818 219 14 , , PUNCT iajs-2818 219 15 a. a. NOUN iajs-2818 219 16 ; ; PUNCT iajs-2818 219 17 khoshnaw khoshnaw NOUN iajs-2818 219 18 , , PUNCT iajs-2818 219 19 s. s. PROPN iajs-2818 219 20 h. h. PROPN iajs-2818 219 21 analysis analysis PROPN iajs-2818 219 22 coronavirus coronavirus NOUN iajs-2818 219 23 disease disease NOUN iajs-2818 219 24 ( ( PUNCT iajs-2818 219 25 covid-19 covid-19 PROPN iajs-2818 219 26 ) ) PUNCT iajs-2818 219 27 model model NOUN iajs-2818 219 28 using use VERB iajs-2818 219 29 numerical numerical ADJ iajs-2818 219 30 approaches approach NOUN iajs-2818 219 31 and and CCONJ iajs-2818 219 32 logistic logistic ADJ iajs-2818 219 33 model model NOUN iajs-2818 219 34 . . PUNCT iajs-2818 219 35 aims aim VERB iajs-2818 219 36 bioeng bioeng PROPN iajs-2818 219 37 . . PUNCT iajs-2818 220 1 2020 2020 NUM iajs-2818 220 2 , , PUNCT iajs-2818 220 3 7(3 7(3 NUM iajs-2818 220 4 ) ) PUNCT iajs-2818 220 5 , , PUNCT iajs-2818 220 6 130 130 NUM iajs-2818 220 7 - - SYM iajs-2818 220 8 146 146 NUM iajs-2818 220 9 . . PUNCT iajs-2818 220 10 23 23 NUM iajs-2818 220 11 . . PUNCT iajs-2818 221 1 mohammed mohammed PROPN iajs-2818 221 2 , , PUNCT iajs-2818 221 3 d. d. PROPN iajs-2818 221 4 a. a. PROPN iajs-2818 221 5 ; ; PUNCT iajs-2818 221 6 tawfeeq tawfeeq PROPN iajs-2818 221 7 , , PUNCT iajs-2818 221 8 h. h. PROPN iajs-2818 221 9 m. m. PROPN iajs-2818 221 10 ; ; PUNCT iajs-2818 221 11 ali ali PROPN iajs-2818 221 12 , , PUNCT iajs-2818 221 13 k. k. PROPN iajs-2818 221 14 m. m. PROPN iajs-2818 221 15 ; ; PUNCT iajs-2818 221 16 rostam rostam NOUN iajs-2818 221 17 , , PUNCT iajs-2818 221 18 h. h. PROPN iajs-2818 221 19 m. m. NOUN iajs-2818 221 20 analysis analysis NOUN iajs-2818 221 21 and and CCONJ iajs-2818 221 22 prediction prediction NOUN iajs-2818 221 23 of of ADP iajs-2818 221 24 covid-19 covid-19 PROPN iajs-2818 221 25 outbreak outbreak NOUN iajs-2818 221 26 by by ADP iajs-2818 221 27 the the DET iajs-2818 221 28 numerical numerical PROPN iajs-2818 221 29 modelling modelling PROPN iajs-2818 221 30 . . PUNCT iajs-2818 222 1 iraqi iraqi ADJ iajs-2818 222 2 journal journal PROPN iajs-2818 222 3 of of ADP iajs-2818 222 4 science science NOUN iajs-2818 222 5 . . PUNCT iajs-2818 223 1 2021 2021 NUM iajs-2818 223 2 , , PUNCT iajs-2818 223 3 62 62 NUM iajs-2818 223 4 ( ( PUNCT iajs-2818 223 5 5 5 NUM iajs-2818 223 6 ) ) PUNCT iajs-2818 223 7 , , PUNCT iajs-2818 223 8 1452 1452 NUM iajs-2818 223 9 - - SYM iajs-2818 223 10 1459 1459 NUM iajs-2818 223 11 . . PUNCT iajs-2818 224 1 http://dx.doi.org/10.2471/blt.20.255158 http://dx.doi.org/10.2471/blt.20.255158 PROPN iajs-2818 224 2 ibn ibn PROPN iajs-2818 224 3 al al PROPN iajs-2818 224 4 - - PUNCT iajs-2818 224 5 haitham haitham PROPN iajs-2818 224 6 jour jour X iajs-2818 224 7 . . PROPN iajs-2818 224 8 for for ADP iajs-2818 224 9 pure pure ADJ iajs-2818 224 10 & & CCONJ iajs-2818 224 11 appl appl PROPN iajs-2818 224 12 . . PUNCT iajs-2818 225 1 sci sci PROPN iajs-2818 225 2 . . PROPN iajs-2818 226 1 53 53 NUM iajs-2818 226 2 ( ( PUNCT iajs-2818 226 3 2)2022 2)2022 VERB iajs-2818 226 4 107 107 NUM iajs-2818 226 5 24 24 NUM iajs-2818 226 6 . . PUNCT iajs-2818 227 1 yavuz yavuz PROPN iajs-2818 227 2 , , PUNCT iajs-2818 227 3 m. m. NOUN iajs-2818 227 4 ; ; PUNCT iajs-2818 227 5 coşar coşar PROPN iajs-2818 227 6 , , PUNCT iajs-2818 227 7 f. f. PROPN iajs-2818 227 8 ΓΆ. ΓΆ. PROPN iajs-2818 227 9 ; ; PUNCT iajs-2818 227 10 gΓΌnay gΓΌnay PROPN iajs-2818 227 11 , , PUNCT iajs-2818 227 12 f. f. PROPN iajs-2818 227 13 ; ; PUNCT iajs-2818 227 14 ΓΆzdemir ΓΆzdemir PROPN iajs-2818 227 15 , , PUNCT iajs-2818 227 16 f. f. PROPN iajs-2818 227 17 n. n. PROPN iajs-2818 227 18 a a DET iajs-2818 227 19 new new ADJ iajs-2818 227 20 mathematical mathematical ADJ iajs-2818 227 21 modeling modeling NOUN iajs-2818 227 22 of of ADP iajs-2818 227 23 the the DET iajs-2818 227 24 covid-19 covid-19 PROPN iajs-2818 227 25 pandemic pandemic NOUN iajs-2818 227 26 including include VERB iajs-2818 227 27 the the DET iajs-2818 227 28 vaccination vaccination NOUN iajs-2818 227 29 campaign campaign NOUN iajs-2818 227 30 . . PUNCT iajs-2818 228 1 open open ADJ iajs-2818 228 2 journal journal NOUN iajs-2818 228 3 of of ADP iajs-2818 228 4 modelling modelling NOUN iajs-2818 228 5 and and CCONJ iajs-2818 228 6 simulation simulation NOUN iajs-2818 228 7 . . PUNCT iajs-2818 229 1 2021 2021 NUM iajs-2818 229 2 , , PUNCT iajs-2818 229 3 9(3 9(3 NUM iajs-2818 229 4 ) ) PUNCT iajs-2818 229 5 , , PUNCT iajs-2818 229 6 299321 299321 NUM iajs-2818 229 7 . . PUNCT iajs-2818 230 1 25 25 NUM iajs-2818 230 2 . . X iajs-2818 230 3 yousif yousif PROPN iajs-2818 230 4 , , PUNCT iajs-2818 230 5 m.s m.s PROPN iajs-2818 230 6 . . PROPN iajs-2818 230 7 and and CCONJ iajs-2818 230 8 kashiem kashiem PROPN iajs-2818 230 9 , , PUNCT iajs-2818 230 10 b.e b.e PROPN iajs-2818 230 11 . . PROPN iajs-2818 230 12 , , PUNCT iajs-2818 230 13 solving solve VERB iajs-2818 230 14 linear linear ADJ iajs-2818 230 15 boundary boundary ADJ iajs-2818 230 16 value value NOUN iajs-2818 230 17 problem problem NOUN iajs-2818 230 18 using use VERB iajs-2818 230 19 shooting shoot VERB iajs-2818 230 20 continuous continuous ADJ iajs-2818 230 21 explicit explicit ADJ iajs-2818 230 22 runge runge NOUN iajs-2818 230 23 - - PUNCT iajs-2818 230 24 kutta kutta NOUN iajs-2818 230 25 method method NOUN iajs-2818 230 26 . . PUNCT iajs-2818 231 1 ibn ibn PROPN iajs-2818 231 2 al al PROPN iajs-2818 231 3 - - PUNCT iajs-2818 231 4 haitham haitham PROPN iajs-2818 231 5 journal journal PROPN iajs-2818 231 6 for for ADP iajs-2818 231 7 pure pure ADJ iajs-2818 231 8 and and CCONJ iajs-2818 231 9 applied applied ADJ iajs-2818 231 10 science science NOUN iajs-2818 231 11 , , PUNCT iajs-2818 231 12 2017 2017 NUM iajs-2818 231 13 , , PUNCT iajs-2818 231 14 26(3 26(3 NUM iajs-2818 231 15 ) ) PUNCT iajs-2818 231 16 , , PUNCT iajs-2818 231 17 324 324 NUM iajs-2818 231 18 - - SYM iajs-2818 231 19 330 330 NUM iajs-2818 231 20 . . NUM iajs-2818 231 21 26 26 NUM iajs-2818 231 22 . . PUNCT iajs-2818 232 1 mandal mandal PROPN iajs-2818 232 2 , , PUNCT iajs-2818 232 3 m. m. NOUN iajs-2818 232 4 ; ; PUNCT iajs-2818 232 5 jana jana PROPN iajs-2818 232 6 , , PUNCT iajs-2818 232 7 s. s. PROPN iajs-2818 232 8 ; ; PUNCT iajs-2818 232 9 nandi nandi PROPN iajs-2818 232 10 , , PUNCT iajs-2818 232 11 s. s. PROPN iajs-2818 232 12 k. k. PROPN iajs-2818 232 13 ; ; PUNCT iajs-2818 232 14 khatua khatua NOUN iajs-2818 232 15 , , PUNCT iajs-2818 232 16 a. a. NOUN iajs-2818 232 17 ; ; PUNCT iajs-2818 232 18 adak adak PROPN iajs-2818 232 19 , , PUNCT iajs-2818 232 20 s. s. PROPN iajs-2818 232 21 ; ; PUNCT iajs-2818 232 22 kar kar PROPN iajs-2818 232 23 , , PUNCT iajs-2818 232 24 t. t. PROPN iajs-2818 232 25 a a DET iajs-2818 232 26 model model NOUN iajs-2818 232 27 based base VERB iajs-2818 232 28 study study NOUN iajs-2818 232 29 on on ADP iajs-2818 232 30 the the DET iajs-2818 232 31 dynamics dynamic NOUN iajs-2818 232 32 of of ADP iajs-2818 232 33 covid-19 covid-19 PROPN iajs-2818 232 34 : : PUNCT iajs-2818 232 35 prediction prediction NOUN iajs-2818 232 36 and and CCONJ iajs-2818 232 37 control control NOUN iajs-2818 232 38 . . PUNCT iajs-2818 233 1 chaos chaos NOUN iajs-2818 233 2 , , PUNCT iajs-2818 233 3 solitons soliton NOUN iajs-2818 233 4 & & CCONJ iajs-2818 233 5 fractals fractal NOUN iajs-2818 233 6 . . PUNCT iajs-2818 234 1 2020 2020 NUM iajs-2818 234 2 , , PUNCT iajs-2818 234 3 136 136 NUM iajs-2818 234 4 , , PUNCT iajs-2818 234 5 109889 109889 NUM iajs-2818 234 6 . . PUNCT iajs-2818 235 1 27 27 NUM iajs-2818 235 2 . . X iajs-2818 235 3 tay tay PROPN iajs-2818 235 4 , , PUNCT iajs-2818 235 5 k. k. PROPN iajs-2818 235 6 g. g. PROPN iajs-2818 235 7 ; ; PUNCT iajs-2818 235 8 kek kek PROPN iajs-2818 235 9 , , PUNCT iajs-2818 235 10 s. s. PROPN iajs-2818 235 11 l. l. PROPN iajs-2818 235 12 ; ; PUNCT iajs-2818 235 13 cheong cheong PROPN iajs-2818 235 14 , , PUNCT iajs-2818 235 15 t. t. PROPN iajs-2818 235 16 h. h. PROPN iajs-2818 235 17 ; ; PUNCT iajs-2818 235 18 abdul abdul PROPN iajs-2818 235 19 - - PUNCT iajs-2818 235 20 kahar kahar PROPN iajs-2818 235 21 , , PUNCT iajs-2818 235 22 r. r. PROPN iajs-2818 235 23 ; ; PUNCT iajs-2818 235 24 lee lee PROPN iajs-2818 235 25 , , PUNCT iajs-2818 235 26 m. m. PROPN iajs-2818 235 27 f. f. PROPN iajs-2818 236 1 the the DET iajs-2818 236 2 fourth fourth ADJ iajs-2818 236 3 order order NOUN iajs-2818 236 4 runge runge NOUN iajs-2818 236 5 - - PUNCT iajs-2818 236 6 kutta kutta NOUN iajs-2818 236 7 spreadsheet spreadsheet NOUN iajs-2818 236 8 calculator calculator NOUN iajs-2818 236 9 using use VERB iajs-2818 236 10 vba vba PROPN iajs-2818 236 11 programing programing NOUN iajs-2818 236 12 for for ADP iajs-2818 236 13 ordinary ordinary ADJ iajs-2818 236 14 differential differential ADJ iajs-2818 236 15 equations equation NOUN iajs-2818 236 16 . . PUNCT iajs-2818 237 1 procedia procedia NOUN iajs-2818 237 2 - - PUNCT iajs-2818 237 3 social social ADJ iajs-2818 237 4 and and CCONJ iajs-2818 237 5 behavioral behavioral ADJ iajs-2818 237 6 sciences science NOUN iajs-2818 237 7 . . PUNCT iajs-2818 238 1 2015 2015 NUM iajs-2818 238 2 , , PUNCT iajs-2818 238 3 204 204 NUM iajs-2818 238 4 , , PUNCT iajs-2818 238 5 231 231 NUM iajs-2818 238 6 - - SYM iajs-2818 238 7 239 239 NUM iajs-2818 238 8 . . PUNCT iajs-2818 239 1 28 28 NUM iajs-2818 239 2 . . PUNCT iajs-2818 240 1 world world PROPN iajs-2818 240 2 health health PROPN iajs-2818 240 3 organization organization PROPN iajs-2818 240 4 . . PUNCT iajs-2818 241 1 weekly weekly ADJ iajs-2818 241 2 report report NOUN iajs-2818 241 3 . . PUNCT iajs-2818 242 1 2022 2022 NUM iajs-2818 242 2 , , PUNCT iajs-2818 242 3 january january PROPN iajs-2818 242 4 5 5 NUM iajs-2818 242 5 β€œ " PUNCT iajs-2818 242 6 weekly weekly ADJ iajs-2818 242 7 epidemiological epidemiological ADJ iajs-2818 242 8 update update NOUN iajs-2818 242 9 ” " PUNCT iajs-2818 242 10 . . PUNCT iajs-2818 243 1 who who PRON iajs-2818 243 2 team team VERB iajs-2818 243 3 . . PUNCT iajs-2818 244 1 retrieved retrieve VERB iajs-2818 244 2 january january PROPN iajs-2818 244 3 28 28 NUM iajs-2818 244 4 , , PUNCT iajs-2818 244 5 2022 2022 NUM iajs-2818 244 6 , , PUNCT iajs-2818 244 7 from from ADP iajs-2818 244 8 https://www.who.int/publications/m/item/weeklyepidemiological-update---5-january-2021 https://www.who.int/publications/m/item/weeklyepidemiological-update---5-january-2021 NOUN iajs-2818 244 9 29 29 NUM iajs-2818 244 10 . . PUNCT iajs-2818 245 1 world world PROPN iajs-2818 245 2 health health PROPN iajs-2818 245 3 organization organization PROPN iajs-2818 245 4 weekly weekly ADJ iajs-2818 245 5 report report NOUN iajs-2818 245 6 . . PUNCT iajs-2818 246 1 2022 2022 NUM iajs-2818 246 2 , , PUNCT iajs-2818 246 3 january january PROPN iajs-2818 246 4 5 5 NUM iajs-2818 246 5 β€œ " PUNCT iajs-2818 246 6 weekly weekly ADJ iajs-2818 246 7 epidemiological epidemiological ADJ iajs-2818 246 8 update update NOUN iajs-2818 246 9 ” " PUNCT iajs-2818 246 10 . . PUNCT iajs-2818 247 1 who who PRON iajs-2818 247 2 team team VERB iajs-2818 247 3 . . PUNCT iajs-2818 248 1 retrieved retrieve VERB iajs-2818 248 2 january january PROPN iajs-2818 248 3 28 28 NUM iajs-2818 248 4 , , PUNCT iajs-2818 248 5 2022 2022 NUM iajs-2818 248 6 , , PUNCT iajs-2818 248 7 from from ADP iajs-2818 248 8 https://covid19.who.int/region/emro/country/iq https://covid19.who.int/region/emro/country/iq PROPN iajs-2818 248 9 . . PUNCT iajs-2818 249 1 https://www.who.int/publications/m/item/weekly-epidemiological-update---5-january-2021 https://www.who.int/publications/m/item/weekly-epidemiological-update---5-january-2021 PROPN iajs-2818 249 2 https://www.who.int/publications/m/item/weekly-epidemiological-update---5-january-2021 https://www.who.int/publications/m/item/weekly-epidemiological-update---5-january-2021 PROPN iajs-2818 249 3 https://covid19.who.int/region/emro/country/iq https://covid19.who.int/region/emro/country/iq PRON