id sid tid token lemma pos iajs-2945 1 1 ihjpas ihjpas PROPN iajs-2945 1 2 . . PUNCT iajs-2945 2 1 36 36 NUM iajs-2945 2 2 ( ( PUNCT iajs-2945 2 3 3 3 NUM iajs-2945 2 4 ) ) PUNCT iajs-2945 2 5 2023 2023 NUM iajs-2945 2 6 289 289 NUM iajs-2945 2 7 this this DET iajs-2945 2 8 work work NOUN iajs-2945 2 9 is be AUX iajs-2945 2 10 licensed license VERB iajs-2945 2 11 under under ADP iajs-2945 2 12 a a DET iajs-2945 2 13 creative creative ADJ iajs-2945 2 14 commons common NOUN iajs-2945 2 15 attribution attribution NOUN iajs-2945 2 16 4.0 4.0 NUM iajs-2945 2 17 international international ADJ iajs-2945 2 18 license license NOUN iajs-2945 2 19 * * PUNCT iajs-2945 2 20 corresponding correspond VERB iajs-2945 2 21 author author NOUN iajs-2945 2 22 : : PUNCT iajs-2945 2 23 mahasssa@yahoo.com mahasssa@yahoo.com X iajs-2945 2 24 abstract abstract ADJ iajs-2945 2 25 the the DET iajs-2945 2 26 aim aim NOUN iajs-2945 2 27 of of ADP iajs-2945 2 28 our our PRON iajs-2945 2 29 study study NOUN iajs-2945 2 30 is be AUX iajs-2945 2 31 to to PART iajs-2945 2 32 solve solve VERB iajs-2945 2 33 a a DET iajs-2945 2 34 nonlinear nonlinear ADJ iajs-2945 2 35 epidemic epidemic NOUN iajs-2945 2 36 model model NOUN iajs-2945 2 37 , , PUNCT iajs-2945 2 38 which which PRON iajs-2945 2 39 is be AUX iajs-2945 2 40 the the DET iajs-2945 2 41 covid-19 covid-19 PROPN iajs-2945 2 42 epidemic epidemic NOUN iajs-2945 2 43 model model NOUN iajs-2945 2 44 in in ADP iajs-2945 2 45 iraq iraq PROPN iajs-2945 2 46 , , PUNCT iajs-2945 2 47 through through ADP iajs-2945 2 48 the the DET iajs-2945 2 49 application application NOUN iajs-2945 2 50 of of ADP iajs-2945 2 51 initial initial ADJ iajs-2945 2 52 value value NOUN iajs-2945 2 53 problems problem NOUN iajs-2945 2 54 in in ADP iajs-2945 2 55 the the DET iajs-2945 2 56 current current ADJ iajs-2945 2 57 study study NOUN iajs-2945 2 58 . . PUNCT iajs-2945 3 1 the the DET iajs-2945 3 2 model model NOUN iajs-2945 3 3 has have AUX iajs-2945 3 4 been be AUX iajs-2945 3 5 presented present VERB iajs-2945 3 6 as as ADP iajs-2945 3 7 a a DET iajs-2945 3 8 system system NOUN iajs-2945 3 9 of of ADP iajs-2945 3 10 ordinary ordinary ADJ iajs-2945 3 11 differential differential ADJ iajs-2945 3 12 equations equation NOUN iajs-2945 3 13 that that PRON iajs-2945 3 14 has have VERB iajs-2945 3 15 parameters parameter NOUN iajs-2945 3 16 that that PRON iajs-2945 3 17 change change VERB iajs-2945 3 18 with with ADP iajs-2945 3 19 time time NOUN iajs-2945 3 20 . . PUNCT iajs-2945 4 1 two two NUM iajs-2945 4 2 numerical numerical PROPN iajs-2945 4 3 simulation simulation NOUN iajs-2945 4 4 methods method NOUN iajs-2945 4 5 are be AUX iajs-2945 4 6 proposed propose VERB iajs-2945 4 7 to to PART iajs-2945 4 8 solve solve VERB iajs-2945 4 9 this this DET iajs-2945 4 10 model model NOUN iajs-2945 4 11 as as ADP iajs-2945 4 12 suitable suitable ADJ iajs-2945 4 13 methods method NOUN iajs-2945 4 14 for for ADP iajs-2945 4 15 solving solve VERB iajs-2945 4 16 systems system NOUN iajs-2945 4 17 whose whose DET iajs-2945 4 18 coefficients coefficient NOUN iajs-2945 4 19 change change VERB iajs-2945 4 20 over over ADP iajs-2945 4 21 time time NOUN iajs-2945 4 22 . . PUNCT iajs-2945 5 1 these these DET iajs-2945 5 2 methods method NOUN iajs-2945 5 3 are be AUX iajs-2945 5 4 the the DET iajs-2945 5 5 mean mean ADJ iajs-2945 5 6 monte monte PROPN iajs-2945 5 7 carlo carlo PROPN iajs-2945 5 8 runge runge PROPN iajs-2945 5 9 - - PUNCT iajs-2945 5 10 kutta kutta NOUN iajs-2945 5 11 method method NOUN iajs-2945 5 12 ( ( PUNCT iajs-2945 5 13 mmc_rk mmc_rk PROPN iajs-2945 5 14 ) ) PUNCT iajs-2945 5 15 and and CCONJ iajs-2945 5 16 the the DET iajs-2945 5 17 mean mean ADJ iajs-2945 5 18 latin latin ADJ iajs-2945 5 19 hypercube hypercube NOUN iajs-2945 5 20 runge runge NOUN iajs-2945 5 21 - - PUNCT iajs-2945 5 22 kutta kutta NOUN iajs-2945 5 23 method method NOUN iajs-2945 5 24 ( ( PUNCT iajs-2945 5 25 mlh_rk mlh_rk NUM iajs-2945 5 26 ) ) PUNCT iajs-2945 5 27 . . PUNCT iajs-2945 6 1 the the DET iajs-2945 6 2 results result NOUN iajs-2945 6 3 of of ADP iajs-2945 6 4 numerical numerical ADJ iajs-2945 6 5 simulation simulation PROPN iajs-2945 6 6 methods method NOUN iajs-2945 6 7 are be AUX iajs-2945 6 8 compared compare VERB iajs-2945 6 9 with with ADP iajs-2945 6 10 the the DET iajs-2945 6 11 results result NOUN iajs-2945 6 12 of of ADP iajs-2945 6 13 the the DET iajs-2945 6 14 numerical numerical PROPN iajs-2945 6 15 runge runge NOUN iajs-2945 6 16 - - PUNCT iajs-2945 6 17 kutta kutta NOUN iajs-2945 6 18 4th 4th ADJ iajs-2945 6 19 order order NOUN iajs-2945 6 20 method method NOUN iajs-2945 6 21 ( ( PUNCT iajs-2945 6 22 rk4 rk4 NOUN iajs-2945 6 23 ) ) PUNCT iajs-2945 6 24 from from ADP iajs-2945 6 25 2021 2021 NUM iajs-2945 6 26 to to ADP iajs-2945 6 27 2025 2025 NUM iajs-2945 6 28 using use VERB iajs-2945 6 29 the the DET iajs-2945 6 30 absolute absolute ADJ iajs-2945 6 31 error error NOUN iajs-2945 6 32 , , PUNCT iajs-2945 6 33 which which PRON iajs-2945 6 34 proves prove VERB iajs-2945 6 35 that that SCONJ iajs-2945 6 36 the the DET iajs-2945 6 37 mlh_rk mlh_rk PROPN iajs-2945 6 38 method method NOUN iajs-2945 6 39 is be AUX iajs-2945 6 40 the the DET iajs-2945 6 41 best good ADJ iajs-2945 6 42 and and CCONJ iajs-2945 6 43 closest close ADJ iajs-2945 6 44 to to ADP iajs-2945 6 45 the the DET iajs-2945 6 46 expected expect VERB iajs-2945 6 47 values value NOUN iajs-2945 6 48 . . PUNCT iajs-2945 7 1 the the DET iajs-2945 7 2 results result NOUN iajs-2945 7 3 have have AUX iajs-2945 7 4 been be AUX iajs-2945 7 5 discussed discuss VERB iajs-2945 7 6 after after ADP iajs-2945 7 7 being be AUX iajs-2945 7 8 tabulated tabulate VERB iajs-2945 7 9 and and CCONJ iajs-2945 7 10 represented represent VERB iajs-2945 7 11 graphically graphically ADV iajs-2945 7 12 . . PUNCT iajs-2945 8 1 epidemic epidemic NOUN iajs-2945 8 2 behavior behavior NOUN iajs-2945 8 3 for for ADP iajs-2945 8 4 the the DET iajs-2945 8 5 next next ADJ iajs-2945 8 6 two two NUM iajs-2945 8 7 years year NOUN iajs-2945 8 8 until until SCONJ iajs-2945 8 9 2025 2025 NUM iajs-2945 8 10 has have AUX iajs-2945 8 11 been be AUX iajs-2945 8 12 projected project VERB iajs-2945 8 13 using use VERB iajs-2945 8 14 the the DET iajs-2945 8 15 proposed propose VERB iajs-2945 8 16 methods method NOUN iajs-2945 8 17 . . PUNCT iajs-2945 9 1 keywords keyword NOUN iajs-2945 9 2 : : PUNCT iajs-2945 9 3 epidemic epidemic NOUN iajs-2945 9 4 models model NOUN iajs-2945 9 5 , , PUNCT iajs-2945 9 6 coronavirus coronavirus NOUN iajs-2945 9 7 ( ( PUNCT iajs-2945 9 8 covid-19 covid-19 PROPN iajs-2945 9 9 ) ) PUNCT iajs-2945 9 10 model model NOUN iajs-2945 9 11 , , PUNCT iajs-2945 9 12 runge runge NOUN iajs-2945 9 13 - - PUNCT iajs-2945 9 14 kutta kutta NOUN iajs-2945 9 15 method method NOUN iajs-2945 9 16 , , PUNCT iajs-2945 9 17 simulation simulation NOUN iajs-2945 9 18 process process NOUN iajs-2945 9 19 , , PUNCT iajs-2945 9 20 numerical numerical PROPN iajs-2945 9 21 simulation simulation PROPN iajs-2945 9 22 techniques technique NOUN iajs-2945 9 23 . . PUNCT iajs-2945 10 1 1 1 X iajs-2945 10 2 . . X iajs-2945 10 3 introduction introduction NOUN iajs-2945 10 4 coronavirus coronavirus NOUN iajs-2945 10 5 disease disease NOUN iajs-2945 10 6 ( ( PUNCT iajs-2945 10 7 covid-19 covid-19 PROPN iajs-2945 10 8 ) ) PUNCT iajs-2945 10 9 is be AUX iajs-2945 10 10 a a DET iajs-2945 10 11 new new ADJ iajs-2945 10 12 pandemic pandemic ADJ iajs-2945 10 13 disease disease NOUN iajs-2945 10 14 that that PRON iajs-2945 10 15 began begin VERB iajs-2945 10 16 to to PART iajs-2945 10 17 appear appear VERB iajs-2945 10 18 in in ADP iajs-2945 10 19 china china PROPN iajs-2945 10 20 , , PUNCT iajs-2945 10 21 specifically specifically ADV iajs-2945 10 22 in in ADP iajs-2945 10 23 the the DET iajs-2945 10 24 city city NOUN iajs-2945 10 25 of of ADP iajs-2945 10 26 wuhan wuhan PROPN iajs-2945 10 27 , , PUNCT iajs-2945 10 28 and and CCONJ iajs-2945 10 29 then then ADV iajs-2945 10 30 spread spread VERB iajs-2945 10 31 rapidly rapidly ADV iajs-2945 10 32 around around ADP iajs-2945 10 33 the the DET iajs-2945 10 34 world world NOUN iajs-2945 10 35 . . PUNCT iajs-2945 11 1 this this DET iajs-2945 11 2 epidemic epidemic NOUN iajs-2945 11 3 represented represent VERB iajs-2945 11 4 a a DET iajs-2945 11 5 global global ADJ iajs-2945 11 6 health health NOUN iajs-2945 11 7 problem problem NOUN iajs-2945 11 8 , , PUNCT iajs-2945 11 9 so so SCONJ iajs-2945 11 10 some some DET iajs-2945 11 11 solutions solution NOUN iajs-2945 11 12 and and CCONJ iajs-2945 11 13 suggestions suggestion NOUN iajs-2945 11 14 are be AUX iajs-2945 11 15 discussed discuss VERB iajs-2945 11 16 and and CCONJ iajs-2945 11 17 studied study VERB iajs-2945 11 18 to to PART iajs-2945 11 19 limit limit VERB iajs-2945 11 20 its its PRON iajs-2945 11 21 spread spread NOUN iajs-2945 11 22 as as ADV iajs-2945 11 23 well well ADV iajs-2945 11 24 as as ADP iajs-2945 11 25 control control VERB iajs-2945 11 26 it it PRON iajs-2945 11 27 . . PUNCT iajs-2945 12 1 although although SCONJ iajs-2945 12 2 , , PUNCT iajs-2945 12 3 there there PRON iajs-2945 12 4 are be VERB iajs-2945 12 5 many many ADJ iajs-2945 12 6 researchers researcher NOUN iajs-2945 12 7 that that PRON iajs-2945 12 8 have have AUX iajs-2945 12 9 talked talk VERB iajs-2945 12 10 about about ADP iajs-2945 12 11 this this DET iajs-2945 12 12 epidemiological epidemiological ADJ iajs-2945 12 13 model model NOUN iajs-2945 12 14 , , PUNCT iajs-2945 12 15 studying study VERB iajs-2945 12 16 its its PRON iajs-2945 12 17 effects effect NOUN iajs-2945 12 18 and and CCONJ iajs-2945 12 19 the the DET iajs-2945 12 20 speed speed NOUN iajs-2945 12 21 of of ADP iajs-2945 12 22 its its PRON iajs-2945 12 23 spread spread NOUN iajs-2945 12 24 , , PUNCT iajs-2945 12 25 as as ADV iajs-2945 12 26 well well ADV iajs-2945 12 27 as as ADP iajs-2945 12 28 the the DET iajs-2945 12 29 number number NOUN iajs-2945 12 30 of of ADP iajs-2945 12 31 people people NOUN iajs-2945 12 32 infected infect VERB iajs-2945 12 33 due due ADP iajs-2945 12 34 to to ADP iajs-2945 12 35 this this DET iajs-2945 12 36 epidemic epidemic NOUN iajs-2945 12 37 and and CCONJ iajs-2945 12 38 the the DET iajs-2945 12 39 extent extent NOUN iajs-2945 12 40 of of ADP iajs-2945 12 41 its its PRON iajs-2945 12 42 impact impact NOUN iajs-2945 12 43 in in ADP iajs-2945 12 44 the the DET iajs-2945 12 45 future future NOUN iajs-2945 12 46 [ [ X iajs-2945 12 47 1 1 NUM iajs-2945 12 48 ] ] PUNCT iajs-2945 12 49 , , PUNCT iajs-2945 12 50 the the DET iajs-2945 12 51 spread spread NOUN iajs-2945 12 52 of of ADP iajs-2945 12 53 doi.org/10.30526/36.3.2945 doi.org/10.30526/36.3.2945 ADJ iajs-2945 12 54 article article NOUN iajs-2945 12 55 history history NOUN iajs-2945 12 56 : : PUNCT iajs-2945 12 57 received receive VERB iajs-2945 12 58 20 20 NUM iajs-2945 12 59 july july PROPN iajs-2945 12 60 2022 2022 NUM iajs-2945 12 61 , , PUNCT iajs-2945 12 62 accepted accept VERB iajs-2945 12 63 24 24 NUM iajs-2945 12 64 october october PROPN iajs-2945 12 65 2022 2022 NUM iajs-2945 12 66 , , PUNCT iajs-2945 12 67 published publish VERB iajs-2945 12 68 in in ADP iajs-2945 12 69 july july PROPN iajs-2945 12 70 2023 2023 NUM iajs-2945 12 71 . . PUNCT iajs-2945 13 1 ibn ibn PROPN iajs-2945 13 2 al al PROPN iajs-2945 13 3 - - PUNCT iajs-2945 13 4 haitham haitham PROPN iajs-2945 13 5 journal journal PROPN iajs-2945 13 6 for for ADP iajs-2945 13 7 pure pure ADJ iajs-2945 13 8 and and CCONJ iajs-2945 13 9 applied applied ADJ iajs-2945 13 10 sciences sciences PROPN iajs-2945 13 11 journal journal PROPN iajs-2945 13 12 homepage homepage NOUN iajs-2945 13 13 : : PUNCT iajs-2945 13 14 jih.uobaghdad.edu.iq jih.uobaghdad.edu.iq VERB iajs-2945 13 15 comparison comparison NOUN iajs-2945 13 16 of of ADP iajs-2945 13 17 some some DET iajs-2945 13 18 numerical numerical PROPN iajs-2945 13 19 simulation simulation NOUN iajs-2945 13 20 techniques technique NOUN iajs-2945 13 21 for for ADP iajs-2945 13 22 covid-19 covid-19 PROPN iajs-2945 13 23 model model NOUN iajs-2945 13 24 in in ADP iajs-2945 13 25 iraq iraq PROPN iajs-2945 13 26 mahdi mahdi PROPN iajs-2945 13 27 a. a. PROPN iajs-2945 13 28 sabea sabea PROPN iajs-2945 13 29 department department PROPN iajs-2945 13 30 of of ADP iajs-2945 13 31 mathematics mathematics PROPN iajs-2945 13 32 , , PUNCT iajs-2945 13 33 college college NOUN iajs-2945 13 34 of of ADP iajs-2945 13 35 education education NOUN iajs-2945 13 36 for for ADP iajs-2945 13 37 pure pure ADJ iajs-2945 13 38 sciences science NOUN iajs-2945 13 39 ibn ibn PROPN iajs-2945 13 40 al al PROPN iajs-2945 13 41 - - PUNCT iajs-2945 13 42 haytham haytham PROPN iajs-2945 13 43 , , PUNCT iajs-2945 13 44 university university NOUN iajs-2945 13 45 of of ADP iajs-2945 13 46 baghdad baghdad PROPN iajs-2945 13 47 , , PUNCT iajs-2945 13 48 baghdad baghdad PROPN iajs-2945 13 49 , , PUNCT iajs-2945 13 50 iraq iraq PROPN iajs-2945 13 51 . . PUNCT iajs-2945 14 1 mahdiabd281@gmail.com mahdiabd281@gmail.com X iajs-2945 15 1 maha maha PROPN iajs-2945 15 2 a. a. PROPN iajs-2945 15 3 mohammed mohammed PROPN iajs-2945 15 4 * * PROPN iajs-2945 15 5 department department PROPN iajs-2945 15 6 of of ADP iajs-2945 15 7 mathematics mathematics PROPN iajs-2945 15 8 , , PUNCT iajs-2945 15 9 college college NOUN iajs-2945 15 10 of of ADP iajs-2945 15 11 education education NOUN iajs-2945 15 12 for for ADP iajs-2945 15 13 pure pure ADJ iajs-2945 15 14 sciences science NOUN iajs-2945 15 15 ibn ibn PROPN iajs-2945 15 16 al al PROPN iajs-2945 15 17 - - PUNCT iajs-2945 15 18 haytham haytham PROPN iajs-2945 15 19 , , PUNCT iajs-2945 15 20 university university NOUN iajs-2945 15 21 of of ADP iajs-2945 15 22 baghdad baghdad PROPN iajs-2945 15 23 , , PUNCT iajs-2945 15 24 baghdad baghdad PROPN iajs-2945 15 25 , , PUNCT iajs-2945 15 26 iraq iraq PROPN iajs-2945 15 27 . . PUNCT iajs-2945 16 1 mahasssa@yahoo.com mahasssa@yahoo.com X iajs-2945 17 1 noor noor PROPN iajs-2945 17 2 fadiya fadiya PROPN iajs-2945 17 3 mohd mohd PROPN iajs-2945 17 4 noor noor PROPN iajs-2945 17 5 institute institute PROPN iajs-2945 17 6 of of ADP iajs-2945 17 7 mathematical mathematical ADJ iajs-2945 17 8 sciences sciences PROPN iajs-2945 17 9 faculty faculty NOUN iajs-2945 17 10 of of ADP iajs-2945 17 11 science science PROPN iajs-2945 17 12 universiti universiti PROPN iajs-2945 17 13 malaya malaya PROPN iajs-2945 17 14 , , PUNCT iajs-2945 17 15 malaysia malaysia PROPN iajs-2945 17 16 https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ PROPN iajs-2945 17 17 mailto:mahasssa@yahoo.com mailto:mahasssa@yahoo.com PROPN iajs-2945 17 18 http://en.uobaghdad.edu.iq/?page_id=15060 http://en.uobaghdad.edu.iq/?page_id=15060 NOUN iajs-2945 17 19 http://en.uobaghdad.edu.iq/?page_id=15060 http://en.uobaghdad.edu.iq/?page_id=15060 NOUN iajs-2945 17 20 mailto:mahdiabd281@gmail.com mailto:mahdiabd281@gmail.com PROPN iajs-2945 17 21 mailto:mahdiabd281@gmail.com mailto:mahdiabd281@gmail.com PROPN iajs-2945 18 1 http://en.uobaghdad.edu.iq/?page_id=15060 http://en.uobaghdad.edu.iq/?page_id=15060 PROPN iajs-2945 18 2 http://en.uobaghdad.edu.iq/?page_id=15060 http://en.uobaghdad.edu.iq/?page_id=15060 NOUN iajs-2945 18 3 mailto:mahasssa@yahoo.com mailto:mahasssa@yahoo.com PROPN iajs-2945 18 4 mailto:mahasssa@yahoo.com mailto:mahasssa@yahoo.com PROPN iajs-2945 19 1 mailto:drfadiya@um.edu.my mailto:drfadiya@um.edu.my PROPN iajs-2945 19 2 ihjpas ihjpa VERB iajs-2945 19 3 . . PUNCT iajs-2945 20 1 36(3)2023 36(3)2023 NUM iajs-2945 20 2 290 290 NUM iajs-2945 20 3 the the DET iajs-2945 20 4 coronavirus coronavirus NOUN iajs-2945 20 5 began begin VERB iajs-2945 20 6 in in ADP iajs-2945 20 7 2019 2019 NUM iajs-2945 20 8 - - SYM iajs-2945 20 9 2020 2020 NUM iajs-2945 20 10 , , PUNCT iajs-2945 20 11 and and CCONJ iajs-2945 20 12 this this DET iajs-2945 20 13 new new ADJ iajs-2945 20 14 disease disease NOUN iajs-2945 20 15 is be AUX iajs-2945 20 16 considered consider VERB iajs-2945 20 17 as as ADP iajs-2945 20 18 a a DET iajs-2945 20 19 type type NOUN iajs-2945 20 20 of of ADP iajs-2945 20 21 ( ( PUNCT iajs-2945 20 22 sars sars PROPN iajs-2945 20 23 - - PUNCT iajs-2945 20 24 cov cov NOUN iajs-2945 20 25 ) ) PUNCT iajs-2945 20 26 and and CCONJ iajs-2945 20 27 has have VERB iajs-2945 20 28 the the DET iajs-2945 20 29 fastest fast ADJ iajs-2945 20 30 spread spread NOUN iajs-2945 20 31 compared compare VERB iajs-2945 20 32 to to ADP iajs-2945 20 33 other other ADJ iajs-2945 20 34 viruses virus NOUN iajs-2945 20 35 [ [ X iajs-2945 20 36 2 2 NUM iajs-2945 20 37 ] ] PUNCT iajs-2945 20 38 . . PUNCT iajs-2945 21 1 specifically specifically ADV iajs-2945 21 2 , , PUNCT iajs-2945 21 3 it it PRON iajs-2945 21 4 quickly quickly ADV iajs-2945 21 5 and and CCONJ iajs-2945 21 6 suddenly suddenly ADV iajs-2945 21 7 spread spread VERB iajs-2945 21 8 around around ADP iajs-2945 21 9 the the DET iajs-2945 21 10 world world NOUN iajs-2945 21 11 on on ADP iajs-2945 21 12 29th 29th ADJ iajs-2945 21 13 march march NOUN iajs-2945 21 14 2020 2020 NUM iajs-2945 22 1 [ [ X iajs-2945 22 2 3 3 NUM iajs-2945 22 3 , , PUNCT iajs-2945 22 4 4 4 NUM iajs-2945 22 5 ] ] PUNCT iajs-2945 22 6 . . PUNCT iajs-2945 23 1 the the DET iajs-2945 23 2 world world PROPN iajs-2945 23 3 health health PROPN iajs-2945 23 4 organization organization NOUN iajs-2945 23 5 declared declare VERB iajs-2945 23 6 that that SCONJ iajs-2945 23 7 this this DET iajs-2945 23 8 disease disease NOUN iajs-2945 23 9 is be AUX iajs-2945 23 10 a a DET iajs-2945 23 11 pandemic pandemic NOUN iajs-2945 23 12 after after ADP iajs-2945 23 13 spreading spread VERB iajs-2945 23 14 to to ADP iajs-2945 23 15 199 199 NUM iajs-2945 23 16 countries country NOUN iajs-2945 23 17 , , PUNCT iajs-2945 23 18 as as SCONJ iajs-2945 23 19 it it PRON iajs-2945 23 20 first first ADV iajs-2945 23 21 appeared appear VERB iajs-2945 23 22 in in ADP iajs-2945 23 23 china china PROPN iajs-2945 23 24 in in ADP iajs-2945 23 25 the the DET iajs-2945 23 26 city city NOUN iajs-2945 23 27 of of ADP iajs-2945 23 28 wuhan wuhan PROPN iajs-2945 23 29 , , PUNCT iajs-2945 23 30 and and CCONJ iajs-2945 23 31 in in ADP iajs-2945 23 32 early early ADJ iajs-2945 23 33 2020 2020 NUM iajs-2945 23 34 , , PUNCT iajs-2945 23 35 thousands thousand NOUN iajs-2945 23 36 of of ADP iajs-2945 23 37 people people NOUN iajs-2945 23 38 died die VERB iajs-2945 23 39 around around ADP iajs-2945 23 40 the the DET iajs-2945 23 41 world world NOUN iajs-2945 24 1 [ [ X iajs-2945 24 2 5 5 NUM iajs-2945 24 3 ] ] PUNCT iajs-2945 24 4 . . PUNCT iajs-2945 25 1 the the DET iajs-2945 25 2 infection infection NOUN iajs-2945 25 3 of of ADP iajs-2945 25 4 this this DET iajs-2945 25 5 virus virus NOUN iajs-2945 25 6 occurred occur VERB iajs-2945 25 7 unevenly unevenly ADV iajs-2945 25 8 in in ADP iajs-2945 25 9 terms term NOUN iajs-2945 25 10 of of ADP iajs-2945 25 11 damage damage NOUN iajs-2945 25 12 , , PUNCT iajs-2945 25 13 according accord VERB iajs-2945 25 14 to to ADP iajs-2945 25 15 immunity immunity NOUN iajs-2945 25 16 and and CCONJ iajs-2945 25 17 adherence adherence NOUN iajs-2945 25 18 to to ADP iajs-2945 25 19 health health NOUN iajs-2945 25 20 prevention prevention NOUN iajs-2945 25 21 methods method NOUN iajs-2945 25 22 [ [ X iajs-2945 25 23 5 5 NUM iajs-2945 25 24 ] ] PUNCT iajs-2945 25 25 . . PUNCT iajs-2945 26 1 the the DET iajs-2945 26 2 spread spread NOUN iajs-2945 26 3 of of ADP iajs-2945 26 4 this this DET iajs-2945 26 5 virus virus NOUN iajs-2945 26 6 has have AUX iajs-2945 26 7 continuously continuously ADV iajs-2945 26 8 led lead VERB iajs-2945 26 9 to to ADP iajs-2945 26 10 great great ADJ iajs-2945 26 11 damage damage NOUN iajs-2945 26 12 in in ADP iajs-2945 26 13 most most ADJ iajs-2945 26 14 of of ADP iajs-2945 26 15 the the DET iajs-2945 26 16 countries country NOUN iajs-2945 26 17 that that PRON iajs-2945 26 18 have have AUX iajs-2945 26 19 been be AUX iajs-2945 26 20 affected affect VERB iajs-2945 26 21 . . PUNCT iajs-2945 27 1 this this PRON iajs-2945 27 2 has have VERB iajs-2945 27 3 a a DET iajs-2945 27 4 significant significant ADJ iajs-2945 27 5 impact impact NOUN iajs-2945 27 6 on on ADP iajs-2945 27 7 both both CCONJ iajs-2945 27 8 global global ADJ iajs-2945 27 9 health health NOUN iajs-2945 27 10 and and CCONJ iajs-2945 27 11 economic economic ADJ iajs-2945 27 12 movement movement NOUN iajs-2945 27 13 [ [ X iajs-2945 27 14 6 6 NUM iajs-2945 27 15 ] ] PUNCT iajs-2945 27 16 . . PUNCT iajs-2945 28 1 a a DET iajs-2945 28 2 large large ADJ iajs-2945 28 3 number number NOUN iajs-2945 28 4 of of ADP iajs-2945 28 5 people people NOUN iajs-2945 28 6 have have AUX iajs-2945 28 7 been be AUX iajs-2945 28 8 infected infect VERB iajs-2945 28 9 with with ADP iajs-2945 28 10 this this DET iajs-2945 28 11 epidemic epidemic NOUN iajs-2945 28 12 as as ADP iajs-2945 28 13 a a DET iajs-2945 28 14 result result NOUN iajs-2945 28 15 of of ADP iajs-2945 28 16 mixing mixing NOUN iajs-2945 28 17 , , PUNCT iajs-2945 28 18 interaction interaction NOUN iajs-2945 28 19 , , PUNCT iajs-2945 28 20 and and CCONJ iajs-2945 28 21 constant constant ADJ iajs-2945 28 22 movement movement NOUN iajs-2945 28 23 , , PUNCT iajs-2945 28 24 just just ADV iajs-2945 28 25 as as SCONJ iajs-2945 28 26 some some DET iajs-2945 28 27 countries country NOUN iajs-2945 28 28 suffer suffer VERB iajs-2945 28 29 from from ADP iajs-2945 28 30 a a DET iajs-2945 28 31 lack lack NOUN iajs-2945 28 32 of of ADP iajs-2945 28 33 adherence adherence NOUN iajs-2945 28 34 to to ADP iajs-2945 28 35 health health NOUN iajs-2945 28 36 prevention prevention NOUN iajs-2945 28 37 methods method NOUN iajs-2945 28 38 and and CCONJ iajs-2945 28 39 a a DET iajs-2945 28 40 large large ADJ iajs-2945 28 41 number number NOUN iajs-2945 28 42 of of ADP iajs-2945 28 43 them they PRON iajs-2945 28 44 die die VERB iajs-2945 28 45 . . PUNCT iajs-2945 29 1 some some DET iajs-2945 29 2 countries country NOUN iajs-2945 29 3 have have AUX iajs-2945 29 4 adhered adhere VERB iajs-2945 29 5 to to ADP iajs-2945 29 6 the the DET iajs-2945 29 7 system system NOUN iajs-2945 29 8 of of ADP iajs-2945 29 9 spacing spacing NOUN iajs-2945 29 10 , , PUNCT iajs-2945 29 11 and and CCONJ iajs-2945 29 12 a a DET iajs-2945 29 13 curfew curfew NOUN iajs-2945 29 14 was be AUX iajs-2945 29 15 imposed impose VERB iajs-2945 29 16 for for ADP iajs-2945 29 17 a a DET iajs-2945 29 18 specified specified ADJ iajs-2945 29 19 period period NOUN iajs-2945 29 20 of of ADP iajs-2945 29 21 time time NOUN iajs-2945 29 22 to to PART iajs-2945 29 23 limit limit VERB iajs-2945 29 24 the the DET iajs-2945 29 25 spread spread NOUN iajs-2945 29 26 of of ADP iajs-2945 29 27 the the DET iajs-2945 29 28 disease disease NOUN iajs-2945 29 29 [ [ X iajs-2945 29 30 7 7 NUM iajs-2945 29 31 ] ] PUNCT iajs-2945 29 32 . . PUNCT iajs-2945 30 1 the the DET iajs-2945 30 2 epidemic epidemic NOUN iajs-2945 30 3 model model NOUN iajs-2945 30 4 is be AUX iajs-2945 30 5 the the DET iajs-2945 30 6 one one NUM iajs-2945 30 7 that that PRON iajs-2945 30 8 deals deal VERB iajs-2945 30 9 with with ADP iajs-2945 30 10 a a DET iajs-2945 30 11 disease disease NOUN iajs-2945 30 12 that that PRON iajs-2945 30 13 spreads spread VERB iajs-2945 30 14 suddenly suddenly ADV iajs-2945 30 15 and and CCONJ iajs-2945 30 16 rapidly rapidly ADV iajs-2945 30 17 and and CCONJ iajs-2945 30 18 occupies occupy VERB iajs-2945 30 19 large large ADJ iajs-2945 30 20 areas area NOUN iajs-2945 30 21 of of ADP iajs-2945 30 22 society society NOUN iajs-2945 30 23 . . PUNCT iajs-2945 31 1 these these DET iajs-2945 31 2 epidemiological epidemiological ADJ iajs-2945 31 3 models model NOUN iajs-2945 31 4 can can AUX iajs-2945 31 5 be be AUX iajs-2945 31 6 formulated formulate VERB iajs-2945 31 7 as as ADP iajs-2945 31 8 a a DET iajs-2945 31 9 system system NOUN iajs-2945 31 10 of of ADP iajs-2945 31 11 nonlinear nonlinear ADJ iajs-2945 31 12 differential differential ADJ iajs-2945 31 13 equations equation NOUN iajs-2945 31 14 , , PUNCT iajs-2945 31 15 and and CCONJ iajs-2945 31 16 this this DET iajs-2945 31 17 epidemic epidemic NOUN iajs-2945 31 18 model model NOUN iajs-2945 31 19 is be AUX iajs-2945 31 20 considered consider VERB iajs-2945 31 21 a a DET iajs-2945 31 22 stochastic stochastic ADJ iajs-2945 31 23 - - PUNCT iajs-2945 31 24 deterministic deterministic ADJ iajs-2945 31 25 model model NOUN iajs-2945 31 26 [ [ X iajs-2945 31 27 8 8 NUM iajs-2945 31 28 , , PUNCT iajs-2945 31 29 9 9 NUM iajs-2945 31 30 ] ] PUNCT iajs-2945 31 31 . . PUNCT iajs-2945 32 1 many many ADJ iajs-2945 32 2 researchers researcher NOUN iajs-2945 32 3 have have AUX iajs-2945 32 4 studied study VERB iajs-2945 32 5 analyzing analyze VERB iajs-2945 32 6 the the DET iajs-2945 32 7 behavior behavior NOUN iajs-2945 32 8 of of ADP iajs-2945 32 9 the the DET iajs-2945 32 10 epidemic epidemic NOUN iajs-2945 32 11 and and CCONJ iajs-2945 32 12 observing observe VERB iajs-2945 32 13 it it PRON iajs-2945 32 14 over over ADP iajs-2945 32 15 time time NOUN iajs-2945 32 16 to to PART iajs-2945 32 17 see see VERB iajs-2945 32 18 whether whether SCONJ iajs-2945 32 19 it it PRON iajs-2945 32 20 grows grow VERB iajs-2945 32 21 or or CCONJ iajs-2945 32 22 settles settle VERB iajs-2945 32 23 in in ADP iajs-2945 32 24 the the DET iajs-2945 32 25 population population NOUN iajs-2945 32 26 exposed expose VERB iajs-2945 32 27 to to ADP iajs-2945 32 28 it it PRON iajs-2945 32 29 . . PUNCT iajs-2945 33 1 the the DET iajs-2945 33 2 sir sir PROPN iajs-2945 33 3 epidemic epidemic NOUN iajs-2945 33 4 model model NOUN iajs-2945 33 5 was be AUX iajs-2945 33 6 considered consider VERB iajs-2945 33 7 by by ADP iajs-2945 33 8 the the DET iajs-2945 33 9 banach banach NOUN iajs-2945 33 10 contraction contraction NOUN iajs-2945 33 11 method method NOUN iajs-2945 33 12 , , PUNCT iajs-2945 33 13 the the DET iajs-2945 33 14 daftardar daftardar ADV iajs-2945 33 15 - - PUNCT iajs-2945 33 16 jafari jafari ADJ iajs-2945 33 17 method method NOUN iajs-2945 33 18 , , PUNCT iajs-2945 33 19 and and CCONJ iajs-2945 33 20 the the DET iajs-2945 33 21 temimi temimi NOUN iajs-2945 33 22 - - PUNCT iajs-2945 33 23 ansari ansari ADJ iajs-2945 33 24 method method NOUN iajs-2945 33 25 [ [ X iajs-2945 33 26 10 10 NUM iajs-2945 33 27 ] ] PUNCT iajs-2945 33 28 . . PUNCT iajs-2945 34 1 ltam ltam PROPN iajs-2945 34 2 was be AUX iajs-2945 34 3 discussed discuss VERB iajs-2945 34 4 for for ADP iajs-2945 34 5 the the DET iajs-2945 34 6 first first ADJ iajs-2945 34 7 time time NOUN iajs-2945 34 8 to to PART iajs-2945 34 9 apply apply VERB iajs-2945 34 10 to to ADP iajs-2945 34 11 the the DET iajs-2945 34 12 epidemic epidemic PROPN iajs-2945 34 13 nonlinear nonlinear PROPN iajs-2945 34 14 model model NOUN iajs-2945 34 15 ; ; PUNCT iajs-2945 34 16 this this DET iajs-2945 34 17 method method NOUN iajs-2945 34 18 is be AUX iajs-2945 34 19 a a DET iajs-2945 34 20 merge merge NOUN iajs-2945 34 21 of of ADP iajs-2945 34 22 the the DET iajs-2945 34 23 laplace laplace NOUN iajs-2945 34 24 transform transform NOUN iajs-2945 34 25 with with ADP iajs-2945 34 26 tamimi tamimi NOUN iajs-2945 34 27 and and CCONJ iajs-2945 34 28 the the DET iajs-2945 34 29 ansari ansari ADJ iajs-2945 34 30 iterative iterative NOUN iajs-2945 34 31 method method NOUN iajs-2945 34 32 [ [ X iajs-2945 34 33 11 11 NUM iajs-2945 34 34 ] ] PUNCT iajs-2945 34 35 . . PUNCT iajs-2945 35 1 the the DET iajs-2945 35 2 study study NOUN iajs-2945 35 3 's 's PART iajs-2945 35 4 findings finding NOUN iajs-2945 35 5 for for ADP iajs-2945 35 6 the the DET iajs-2945 35 7 covid-19 covid-19 PROPN iajs-2945 35 8 sir sir NOUN iajs-2945 35 9 epidemic epidemic NOUN iajs-2945 35 10 model model NOUN iajs-2945 35 11 were be AUX iajs-2945 35 12 designed design VERB iajs-2945 35 13 with with ADP iajs-2945 35 14 stochasticity stochasticity NOUN iajs-2945 35 15 in in ADP iajs-2945 35 16 mind mind NOUN iajs-2945 35 17 in in ADP iajs-2945 35 18 order order NOUN iajs-2945 35 19 to to PART iajs-2945 35 20 eradicate eradicate VERB iajs-2945 35 21 the the DET iajs-2945 35 22 epidemic epidemic NOUN iajs-2945 35 23 in in ADP iajs-2945 35 24 iraq iraq PROPN iajs-2945 35 25 [ [ X iajs-2945 35 26 12 12 NUM iajs-2945 35 27 ] ] PUNCT iajs-2945 35 28 . . PUNCT iajs-2945 36 1 to to PART iajs-2945 36 2 analyze analyze VERB iajs-2945 36 3 the the DET iajs-2945 36 4 behavior behavior NOUN iajs-2945 36 5 of of ADP iajs-2945 36 6 smoking smoking NOUN iajs-2945 36 7 habits habit NOUN iajs-2945 36 8 , , PUNCT iajs-2945 36 9 the the DET iajs-2945 36 10 adomian adomian NOUN iajs-2945 36 11 decomposition decomposition NOUN iajs-2945 36 12 method method NOUN iajs-2945 36 13 , , PUNCT iajs-2945 36 14 variational variational ADJ iajs-2945 36 15 iteration iteration NOUN iajs-2945 36 16 method method NOUN iajs-2945 36 17 , , PUNCT iajs-2945 36 18 finite finite ADJ iajs-2945 36 19 difference difference NOUN iajs-2945 36 20 method method NOUN iajs-2945 36 21 , , PUNCT iajs-2945 36 22 and and CCONJ iajs-2945 36 23 runge runge NOUN iajs-2945 36 24 - - PUNCT iajs-2945 36 25 kutta kutta NOUN iajs-2945 36 26 method method NOUN iajs-2945 36 27 were be AUX iajs-2945 36 28 used use VERB iajs-2945 36 29 [ [ PUNCT iajs-2945 36 30 13 13 NUM iajs-2945 36 31 ] ] PUNCT iajs-2945 36 32 . . PUNCT iajs-2945 37 1 in in ADP iajs-2945 37 2 addition addition NOUN iajs-2945 37 3 , , PUNCT iajs-2945 37 4 the the DET iajs-2945 37 5 adomian adomian NOUN iajs-2945 37 6 decomposition decomposition NOUN iajs-2945 37 7 method method NOUN iajs-2945 37 8 and and CCONJ iajs-2945 37 9 variation variation NOUN iajs-2945 37 10 iteration iteration NOUN iajs-2945 37 11 method method NOUN iajs-2945 37 12 were be AUX iajs-2945 37 13 used use VERB iajs-2945 37 14 for for ADP iajs-2945 37 15 alcohol alcohol NOUN iajs-2945 37 16 consumption consumption NOUN iajs-2945 37 17 [ [ X iajs-2945 37 18 14 14 NUM iajs-2945 37 19 ] ] PUNCT iajs-2945 37 20 . . PUNCT iajs-2945 38 1 some some DET iajs-2945 38 2 researchers researcher NOUN iajs-2945 38 3 use use VERB iajs-2945 38 4 the the DET iajs-2945 38 5 numerical numerical ADJ iajs-2945 38 6 runge runge NOUN iajs-2945 38 7 - - PUNCT iajs-2945 38 8 kutta kutta NOUN iajs-2945 38 9 method method NOUN iajs-2945 38 10 to to PART iajs-2945 38 11 analyze analyze VERB iajs-2945 38 12 the the DET iajs-2945 38 13 behavior behavior NOUN iajs-2945 38 14 of of ADP iajs-2945 38 15 obesity obesity NOUN iajs-2945 38 16 [ [ X iajs-2945 38 17 15 15 NUM iajs-2945 38 18 ] ] PUNCT iajs-2945 38 19 , , PUNCT iajs-2945 38 20 smoking smoking NOUN iajs-2945 38 21 habits habit NOUN iajs-2945 39 1 [ [ X iajs-2945 39 2 13 13 NUM iajs-2945 39 3 ] ] PUNCT iajs-2945 39 4 , , PUNCT iajs-2945 39 5 influenza influenza NOUN iajs-2945 39 6 [ [ X iajs-2945 39 7 16 16 NUM iajs-2945 39 8 ] ] PUNCT iajs-2945 39 9 , , PUNCT iajs-2945 39 10 and and CCONJ iajs-2945 39 11 covid-19 covid-19 PROPN iajs-2945 40 1 [ [ X iajs-2945 40 2 17 17 NUM iajs-2945 40 3 ] ] PUNCT iajs-2945 40 4 . . PUNCT iajs-2945 41 1 on on ADP iajs-2945 41 2 the the DET iajs-2945 41 3 other other ADJ iajs-2945 41 4 hand hand NOUN iajs-2945 41 5 , , PUNCT iajs-2945 41 6 there there PRON iajs-2945 41 7 are be VERB iajs-2945 41 8 those those PRON iajs-2945 41 9 who who PRON iajs-2945 41 10 are be AUX iajs-2945 41 11 interested interested ADJ iajs-2945 41 12 in in ADP iajs-2945 41 13 studying study VERB iajs-2945 41 14 epidemiological epidemiological ADJ iajs-2945 41 15 models model NOUN iajs-2945 41 16 that that PRON iajs-2945 41 17 have have VERB iajs-2945 41 18 random random ADJ iajs-2945 41 19 coefficients coefficient NOUN iajs-2945 41 20 and and CCONJ iajs-2945 41 21 using use VERB iajs-2945 41 22 suitable suitable ADJ iajs-2945 41 23 numerical numerical PROPN iajs-2945 41 24 simulation simulation NOUN iajs-2945 41 25 methods method NOUN iajs-2945 41 26 to to PART iajs-2945 41 27 solve solve VERB iajs-2945 41 28 them they PRON iajs-2945 41 29 , , PUNCT iajs-2945 41 30 such such ADJ iajs-2945 41 31 as as ADP iajs-2945 41 32 [ [ X iajs-2945 41 33 18 18 NUM iajs-2945 41 34 - - SYM iajs-2945 41 35 21 21 NUM iajs-2945 41 36 ] ] PUNCT iajs-2945 41 37 . . PUNCT iajs-2945 42 1 the the DET iajs-2945 42 2 numerical numerical ADJ iajs-2945 42 3 method method NOUN iajs-2945 42 4 in in ADP iajs-2945 42 5 this this DET iajs-2945 42 6 study study NOUN iajs-2945 42 7 is be AUX iajs-2945 42 8 the the DET iajs-2945 42 9 runge runge NOUN iajs-2945 42 10 - - PUNCT iajs-2945 42 11 kutta kutta NOUN iajs-2945 42 12 method method NOUN iajs-2945 42 13 for for ADP iajs-2945 42 14 the the DET iajs-2945 42 15 4th 4th ADJ iajs-2945 42 16 order order NOUN iajs-2945 42 17 . . PUNCT iajs-2945 43 1 it it PRON iajs-2945 43 2 is be AUX iajs-2945 43 3 considered consider VERB iajs-2945 43 4 one one NUM iajs-2945 43 5 of of ADP iajs-2945 43 6 the the DET iajs-2945 43 7 most most ADV iajs-2945 43 8 efficient efficient ADJ iajs-2945 43 9 numerical numerical ADJ iajs-2945 43 10 methods method NOUN iajs-2945 43 11 for for ADP iajs-2945 43 12 solving solve VERB iajs-2945 43 13 ordinary ordinary ADJ iajs-2945 43 14 differential differential ADJ iajs-2945 43 15 equations equation NOUN iajs-2945 43 16 of of ADP iajs-2945 43 17 different different ADJ iajs-2945 43 18 orders order NOUN iajs-2945 43 19 . . PUNCT iajs-2945 44 1 high high ADJ iajs-2945 44 2 accuracy accuracy NOUN iajs-2945 44 3 using use VERB iajs-2945 44 4 this this DET iajs-2945 44 5 method method NOUN iajs-2945 44 6 can can AUX iajs-2945 44 7 be be AUX iajs-2945 44 8 achieved achieve VERB iajs-2945 44 9 with with ADP iajs-2945 44 10 order order NOUN iajs-2945 44 11 four four NUM iajs-2945 44 12 to to PART iajs-2945 44 13 decrease decrease VERB iajs-2945 44 14 the the DET iajs-2945 44 15 errors error NOUN iajs-2945 44 16 [ [ X iajs-2945 44 17 22 22 NUM iajs-2945 44 18 ] ] PUNCT iajs-2945 44 19 and and CCONJ iajs-2945 44 20 [ [ X iajs-2945 44 21 9 9 NUM iajs-2945 44 22 ] ] PUNCT iajs-2945 44 23 . . PUNCT iajs-2945 45 1 four four NUM iajs-2945 45 2 stages stage NOUN iajs-2945 45 3 are be AUX iajs-2945 45 4 considered consider VERB iajs-2945 45 5 in in ADP iajs-2945 45 6 this this DET iajs-2945 45 7 method method NOUN iajs-2945 45 8 of of ADP iajs-2945 45 9 order order NOUN iajs-2945 45 10 four four NUM iajs-2945 46 1 [ [ X iajs-2945 46 2 23 23 NUM iajs-2945 46 3 ] ] PUNCT iajs-2945 46 4 . . PUNCT iajs-2945 47 1 two two NUM iajs-2945 47 2 numerical numerical PROPN iajs-2945 47 3 simulation simulation NOUN iajs-2945 47 4 methods method NOUN iajs-2945 47 5 are be AUX iajs-2945 47 6 used use VERB iajs-2945 47 7 , , PUNCT iajs-2945 47 8 the the DET iajs-2945 47 9 first first ADJ iajs-2945 47 10 being be AUX iajs-2945 47 11 the the DET iajs-2945 47 12 mean mean ADJ iajs-2945 47 13 monte monte PROPN iajs-2945 47 14 carlo carlo PROPN iajs-2945 47 15 runge runge PROPN iajs-2945 47 16 - - PUNCT iajs-2945 47 17 kutta kutta NOUN iajs-2945 47 18 method method NOUN iajs-2945 47 19 ( ( PUNCT iajs-2945 47 20 mmcrk mmcrk PROPN iajs-2945 47 21 ) ) PUNCT iajs-2945 47 22 , , PUNCT iajs-2945 47 23 which which PRON iajs-2945 47 24 is be AUX iajs-2945 47 25 a a DET iajs-2945 47 26 reliable reliable ADJ iajs-2945 47 27 numerical numerical PROPN iajs-2945 47 28 simulation simulation NOUN iajs-2945 47 29 technique technique NOUN iajs-2945 47 30 that that PRON iajs-2945 47 31 merges merge VERB iajs-2945 47 32 two two NUM iajs-2945 47 33 methods method NOUN iajs-2945 47 34 of of ADP iajs-2945 47 35 different different ADJ iajs-2945 47 36 natures nature NOUN iajs-2945 47 37 together together ADV iajs-2945 47 38 in in ADP iajs-2945 47 39 this this DET iajs-2945 47 40 study study NOUN iajs-2945 47 41 : : PUNCT iajs-2945 47 42 the the DET iajs-2945 47 43 monte monte PROPN iajs-2945 47 44 carlo carlo PROPN iajs-2945 47 45 simulation simulation PROPN iajs-2945 47 46 process process NOUN iajs-2945 47 47 ( ( PUNCT iajs-2945 47 48 mc mc PROPN iajs-2945 47 49 ) ) PUNCT iajs-2945 47 50 and and CCONJ iajs-2945 47 51 the the DET iajs-2945 47 52 runge runge NOUN iajs-2945 47 53 - - PUNCT iajs-2945 47 54 kutta kutta NOUN iajs-2945 47 55 method method NOUN iajs-2945 47 56 ( ( PUNCT iajs-2945 47 57 rk rk NOUN iajs-2945 47 58 ) ) PUNCT iajs-2945 47 59 that that PRON iajs-2945 47 60 are be AUX iajs-2945 47 61 used use VERB iajs-2945 47 62 to to PART iajs-2945 47 63 solve solve VERB iajs-2945 47 64 ordinary ordinary ADJ iajs-2945 47 65 differential differential ADJ iajs-2945 47 66 equations equation NOUN iajs-2945 47 67 . . PUNCT iajs-2945 48 1 mahdi mahdi PROPN iajs-2945 48 2 a. a. PROPN iajs-2945 48 3 s. s. PROPN iajs-2945 48 4 and and CCONJ iajs-2945 48 5 maha maha PROPN iajs-2945 48 6 a. a. NOUN iajs-2945 48 7 m. m. NOUN iajs-2945 48 8 in in ADP iajs-2945 48 9 2019 2019 NUM iajs-2945 48 10 discussed discuss VERB iajs-2945 48 11 a a DET iajs-2945 48 12 modified modify VERB iajs-2945 48 13 numerical numerical PROPN iajs-2945 48 14 simulation simulation NOUN iajs-2945 48 15 technique technique NOUN iajs-2945 48 16 for for ADP iajs-2945 48 17 solving solve VERB iajs-2945 48 18 nonlinear nonlinear ADJ iajs-2945 48 19 epidemic epidemic NOUN iajs-2945 48 20 models model NOUN iajs-2945 48 21 [ [ X iajs-2945 48 22 19 19 NUM iajs-2945 48 23 ] ] PUNCT iajs-2945 48 24 . . PUNCT iajs-2945 49 1 the the DET iajs-2945 49 2 second second PROPN iajs-2945 49 3 numerical numerical PROPN iajs-2945 49 4 simulation simulation NOUN iajs-2945 49 5 method method NOUN iajs-2945 49 6 is be AUX iajs-2945 49 7 mean mean ADJ iajs-2945 49 8 latin latin ADJ iajs-2945 49 9 hypercube hypercube NOUN iajs-2945 49 10 runge runge NOUN iajs-2945 49 11 - - PUNCT iajs-2945 49 12 kutta kutta NOUN iajs-2945 49 13 ( ( PUNCT iajs-2945 49 14 mlhrk mlhrk PROPN iajs-2945 49 15 ) ) PUNCT iajs-2945 49 16 . . PUNCT iajs-2945 50 1 mlhrk mlhrk PROPN iajs-2945 50 2 is be AUX iajs-2945 50 3 a a DET iajs-2945 50 4 numerical numerical ADJ iajs-2945 50 5 simulation simulation NOUN iajs-2945 50 6 method method NOUN iajs-2945 50 7 that that PRON iajs-2945 50 8 is be AUX iajs-2945 50 9 a a DET iajs-2945 50 10 mixture mixture NOUN iajs-2945 50 11 of of ADP iajs-2945 50 12 the the DET iajs-2945 50 13 simulation simulation NOUN iajs-2945 50 14 method method PROPN iajs-2945 50 15 latin latin ADJ iajs-2945 50 16 hypercube hypercube NOUN iajs-2945 50 17 ( ( PUNCT iajs-2945 50 18 lh lh PROPN iajs-2945 50 19 ) ) PUNCT iajs-2945 50 20 and and CCONJ iajs-2945 50 21 the the DET iajs-2945 50 22 numerical numerical PROPN iajs-2945 50 23 method method PROPN iajs-2945 50 24 runge runge NOUN iajs-2945 50 25 - - PUNCT iajs-2945 50 26 kutta kutta NOUN iajs-2945 50 27 ( ( PUNCT iajs-2945 50 28 rk rk NOUN iajs-2945 50 29 ) ) PUNCT iajs-2945 50 30 . . PUNCT iajs-2945 51 1 it it PRON iajs-2945 51 2 is be AUX iajs-2945 51 3 one one NUM iajs-2945 51 4 of of ADP iajs-2945 51 5 the the DET iajs-2945 51 6 reliable reliable ADJ iajs-2945 51 7 methods method NOUN iajs-2945 51 8 to to PART iajs-2945 51 9 solve solve VERB iajs-2945 51 10 such such ADJ iajs-2945 51 11 systems system NOUN iajs-2945 51 12 . . PUNCT iajs-2945 52 1 shatha shatha PROPN iajs-2945 52 2 j. j. PROPN iajs-2945 52 3 m. m. PROPN iajs-2945 52 4 and and CCONJ iajs-2945 52 5 maha maha PROPN iajs-2945 52 6 a. a. NOUN iajs-2945 52 7 m. m. NOUN iajs-2945 52 8 ( ( PUNCT iajs-2945 52 9 2021 2021 NUM iajs-2945 52 10 ) ) PUNCT iajs-2945 52 11 studied study VERB iajs-2945 52 12 the the DET iajs-2945 52 13 mean mean ADJ iajs-2945 52 14 latin latin ADJ iajs-2945 52 15 hypercube hypercube NOUN iajs-2945 52 16 runge runge PROPN iajs-2945 52 17 kutta kutta NOUN iajs-2945 52 18 method method NOUN iajs-2945 52 19 to to PART iajs-2945 52 20 solve solve VERB iajs-2945 52 21 the the DET iajs-2945 52 22 influenza influenza NOUN iajs-2945 52 23 model model NOUN iajs-2945 52 24 . . PUNCT iajs-2945 53 1 emad emad PROPN iajs-2945 53 2 t. t. PROPN iajs-2945 53 3 g. g. PROPN iajs-2945 53 4 and and CCONJ iajs-2945 53 5 maha maha PROPN iajs-2945 53 6 a. a. PROPN iajs-2945 53 7 m. m. PROPN iajs-2945 53 8 discussed discuss VERB iajs-2945 53 9 applying apply VERB iajs-2945 53 10 a a DET iajs-2945 53 11 suitable suitable ADJ iajs-2945 53 12 approximateihjpas approximateihjpas NOUN iajs-2945 53 13 . . PUNCT iajs-2945 54 1 36(3)2023 36(3)2023 NUM iajs-2945 54 2 291 291 NUM iajs-2945 54 3 simulation simulation NOUN iajs-2945 54 4 technique technique NOUN iajs-2945 54 5 to to ADP iajs-2945 54 6 the the DET iajs-2945 54 7 covid-19 covid-19 PROPN iajs-2945 54 8 epidemic epidemic NOUN iajs-2945 54 9 model model NOUN iajs-2945 54 10 with with ADP iajs-2945 54 11 random random ADJ iajs-2945 54 12 parameters parameter NOUN iajs-2945 54 13 in in ADP iajs-2945 54 14 2022 2022 NUM iajs-2945 54 15 ; ; PUNCT iajs-2945 54 16 see see VERB iajs-2945 54 17 [ [ X iajs-2945 54 18 20 20 NUM iajs-2945 54 19 ] ] PUNCT iajs-2945 54 20 and and CCONJ iajs-2945 55 1 [ [ X iajs-2945 55 2 21 21 NUM iajs-2945 55 3 ] ] PUNCT iajs-2945 55 4 . . PUNCT iajs-2945 56 1 2 2 X iajs-2945 56 2 . . X iajs-2945 56 3 mathematical mathematical ADJ iajs-2945 56 4 model model NOUN iajs-2945 56 5 of of ADP iajs-2945 56 6 covid-19 covid-19 PROPN iajs-2945 56 7 the the DET iajs-2945 56 8 mentioned mention VERB iajs-2945 56 9 model model NOUN iajs-2945 56 10 has have AUX iajs-2945 56 11 been be AUX iajs-2945 56 12 successfully successfully ADV iajs-2945 56 13 used use VERB iajs-2945 56 14 to to PART iajs-2945 56 15 study study VERB iajs-2945 56 16 the the DET iajs-2945 56 17 people people NOUN iajs-2945 56 18 vaccinated vaccinate VERB iajs-2945 56 19 against against ADP iajs-2945 56 20 the the DET iajs-2945 56 21 covid-19 covid-19 PROPN iajs-2945 56 22 epidemic epidemic NOUN iajs-2945 56 23 in in ADP iajs-2945 56 24 iraq iraq PROPN iajs-2945 57 1 [ [ X iajs-2945 57 2 24 24 NUM iajs-2945 57 3 ] ] PUNCT iajs-2945 57 4 . . PUNCT iajs-2945 58 1 the the DET iajs-2945 58 2 population population NOUN iajs-2945 58 3 consists consist VERB iajs-2945 58 4 of of ADP iajs-2945 58 5 five five NUM iajs-2945 58 6 types type NOUN iajs-2945 58 7 of of ADP iajs-2945 58 8 individuals individual NOUN iajs-2945 58 9 s s NOUN iajs-2945 58 10 , , PUNCT iajs-2945 58 11 v v NOUN iajs-2945 58 12 , , PUNCT iajs-2945 58 13 a a PRON iajs-2945 58 14 , , PUNCT iajs-2945 58 15 i i PRON iajs-2945 58 16 and and CCONJ iajs-2945 58 17 r r NOUN iajs-2945 58 18 represent represent VERB iajs-2945 58 19 susceptible susceptible ADJ iajs-2945 58 20 , , PUNCT iajs-2945 58 21 vaccinated vaccinated ADJ iajs-2945 58 22 , , PUNCT iajs-2945 58 23 asymptomatic asymptomatic ADJ iajs-2945 58 24 , , PUNCT iajs-2945 58 25 symptomatic symptomatic ADJ iajs-2945 58 26 , , PUNCT iajs-2945 58 27 and and CCONJ iajs-2945 58 28 the the DET iajs-2945 58 29 recovery recovery NOUN iajs-2945 58 30 respectively respectively ADV iajs-2945 58 31 . . PUNCT iajs-2945 59 1 these these DET iajs-2945 59 2 individuals individual NOUN iajs-2945 59 3 are be AUX iajs-2945 59 4 functions function NOUN iajs-2945 59 5 according accord VERB iajs-2945 59 6 to to ADP iajs-2945 59 7 time time NOUN iajs-2945 59 8 in in ADP iajs-2945 59 9 the the DET iajs-2945 59 10 system system NOUN iajs-2945 59 11 . . PUNCT iajs-2945 60 1 the the DET iajs-2945 60 2 governing govern VERB iajs-2945 60 3 equations equation NOUN iajs-2945 60 4 for for ADP iajs-2945 60 5 the the DET iajs-2945 60 6 epidemic epidemic NOUN iajs-2945 60 7 under under ADP iajs-2945 60 8 study study NOUN iajs-2945 60 9 are be AUX iajs-2945 60 10 the the DET iajs-2945 60 11 nonlinear nonlinear ADJ iajs-2945 60 12 first first ADJ iajs-2945 60 13 - - PUNCT iajs-2945 60 14 order order NOUN iajs-2945 60 15 ordinary ordinary ADJ iajs-2945 60 16 differential differential ADJ iajs-2945 60 17 equations equation NOUN iajs-2945 60 18 [ [ X iajs-2945 60 19 25 25 NUM iajs-2945 60 20 ] ] PUNCT iajs-2945 60 21 . . PUNCT iajs-2945 61 1 𝑆′(𝑑 𝑆′(𝑑 X iajs-2945 61 2 ) ) PUNCT iajs-2945 62 1 = = SYM iajs-2945 62 2 𝑀 𝑀 PROPN iajs-2945 62 3 βˆ’ βˆ’ PROPN iajs-2945 62 4 πœπ‘† πœπ‘† ADJ iajs-2945 62 5 βˆ’ βˆ’ ADP iajs-2945 62 6 𝛼(1+𝛽𝐴)𝑆 𝛼(1+𝛽𝐴)𝑆 ADV iajs-2945 62 7 𝑁 𝑁 PROPN iajs-2945 62 8 βˆ’ βˆ’ PROPN iajs-2945 62 9 πœ‡π‘† πœ‡π‘† PROPN iajs-2945 62 10 + + CCONJ iajs-2945 62 11 𝛾𝑅 𝛾𝑅 PROPN iajs-2945 62 12 , , PUNCT iajs-2945 62 13 𝑉′(𝑑 𝑉′(𝑑 X iajs-2945 62 14 ) ) PUNCT iajs-2945 62 15 = = SYM iajs-2945 63 1 πœπ‘† πœπ‘† ADJ iajs-2945 63 2 βˆ’ βˆ’ NOUN iajs-2945 63 3 πœŒπ›Ό(1+𝛽𝐴)𝑉 πœŒπ›Ό(1+𝛽𝐴)𝑉 ADJ iajs-2945 63 4 𝑁 𝑁 NOUN iajs-2945 63 5 βˆ’ βˆ’ NOUN iajs-2945 63 6 πœ‡π‘‰ πœ‡π‘‰ NOUN iajs-2945 63 7 , , PUNCT iajs-2945 63 8 𝐴′(𝑑 𝐴′(𝑑 X iajs-2945 63 9 ) ) PUNCT iajs-2945 63 10 = = SYM iajs-2945 63 11 𝛼(1+𝛽𝐴)𝑆 𝛼(1+𝛽𝐴)𝑆 VERB iajs-2945 63 12 𝑁 𝑁 PROPN iajs-2945 63 13 + + CCONJ iajs-2945 63 14 πœŒπ›Ό(1+𝛽𝐴)𝑉 πœŒπ›Ό(1+𝛽𝐴)𝑉 ADJ iajs-2945 63 15 𝑁 𝑁 PROPN iajs-2945 63 16 βˆ’ βˆ’ NOUN iajs-2945 63 17 𝛿𝐴 𝛿𝐴 NOUN iajs-2945 63 18 βˆ’ βˆ’ NOUN iajs-2945 63 19 πœ‡π΄ πœ‡π΄ ADP iajs-2945 63 20 , , PUNCT iajs-2945 63 21 ( ( PUNCT iajs-2945 63 22 1 1 X iajs-2945 63 23 ) ) PUNCT iajs-2945 63 24 𝐼′(𝑑 𝐼′(𝑑 PROPN iajs-2945 63 25 ) ) PUNCT iajs-2945 64 1 = = SYM iajs-2945 64 2 πœƒπ›Ώπ΄ πœƒπ›Ώπ΄ PROPN iajs-2945 65 1 βˆ’ βˆ’ PROPN iajs-2945 65 2 𝜎𝐼 𝜎𝐼 ADJ iajs-2945 65 3 βˆ’ βˆ’ PROPN iajs-2945 65 4 πœ‡πΌ πœ‡πΌ NOUN iajs-2945 65 5 𝑅′(𝑑 𝑅′(𝑑 NOUN iajs-2945 65 6 ) ) PUNCT iajs-2945 65 7 = = PUNCT iajs-2945 66 1 ( ( PUNCT iajs-2945 66 2 1 1 NUM iajs-2945 66 3 βˆ’ βˆ’ PRON iajs-2945 66 4 πœƒ)𝛿𝐴 πœƒ)𝛿𝐴 PROPN iajs-2945 66 5 + + SYM iajs-2945 66 6 𝜎𝐼 𝜎𝐼 ADJ iajs-2945 66 7 βˆ’ βˆ’ PROPN iajs-2945 66 8 𝛾𝑅 𝛾𝑅 PROPN iajs-2945 66 9 βˆ’ βˆ’ PROPN iajs-2945 66 10 πœ‡π‘… πœ‡π‘… NOUN iajs-2945 66 11 , , PUNCT iajs-2945 66 12 where where SCONJ iajs-2945 66 13 tables table NOUN iajs-2945 66 14 1 1 NUM iajs-2945 66 15 and and CCONJ iajs-2945 66 16 2 2 NUM iajs-2945 66 17 represent represent VERB iajs-2945 66 18 subpopulation subpopulation NOUN iajs-2945 66 19 𝑆 𝑆 PROPN iajs-2945 66 20 , , PUNCT iajs-2945 66 21 𝑉 𝑉 PROPN iajs-2945 66 22 , , PUNCT iajs-2945 66 23 𝐴 𝐴 PROPN iajs-2945 66 24 , , PUNCT iajs-2945 66 25 𝐼 𝐼 PROPN iajs-2945 66 26 , , PUNCT iajs-2945 66 27 𝑅 𝑅 PROPN iajs-2945 66 28 as as ADP iajs-2945 66 29 the the DET iajs-2945 66 30 variables variable NOUN iajs-2945 66 31 of of ADP iajs-2945 66 32 model model NOUN iajs-2945 66 33 ( ( PUNCT iajs-2945 66 34 1 1 NUM iajs-2945 66 35 ) ) PUNCT iajs-2945 66 36 , , PUNCT iajs-2945 66 37 and and CCONJ iajs-2945 66 38 parameters parameter NOUN iajs-2945 66 39 𝑀 𝑀 PROPN iajs-2945 66 40 , , PUNCT iajs-2945 66 41 𝜏 𝜏 NOUN iajs-2945 66 42 , , PUNCT iajs-2945 66 43 𝛼 𝛼 X iajs-2945 66 44 , , PUNCT iajs-2945 66 45 𝛽 𝛽 NOUN iajs-2945 66 46 , , PUNCT iajs-2945 66 47 πœ‡ πœ‡ X iajs-2945 66 48 , , PUNCT iajs-2945 66 49 𝛾 𝛾 NOUN iajs-2945 66 50 , , PUNCT iajs-2945 66 51 𝜌 𝜌 X iajs-2945 66 52 , , PUNCT iajs-2945 66 53 𝛿 𝛿 ADJ iajs-2945 66 54 , , PUNCT iajs-2945 66 55 πœƒ πœƒ NOUN iajs-2945 66 56 and and CCONJ iajs-2945 66 57 𝜎. 𝜎. NOUN iajs-2945 66 58 system system NOUN iajs-2945 66 59 ( ( PUNCT iajs-2945 66 60 1 1 X iajs-2945 66 61 ) ) PUNCT iajs-2945 66 62 have have VERB iajs-2945 66 63 the the DET iajs-2945 66 64 initial initial ADJ iajs-2945 66 65 conditions condition NOUN iajs-2945 66 66 for for ADP iajs-2945 66 67 the the DET iajs-2945 66 68 system system NOUN iajs-2945 66 69 obtained obtain VERB iajs-2945 66 70 from from ADP iajs-2945 66 71 the the DET iajs-2945 66 72 world world PROPN iajs-2945 66 73 health health PROPN iajs-2945 66 74 organization organization NOUN iajs-2945 66 75 website website NOUN iajs-2945 66 76 for for ADP iajs-2945 66 77 iraq iraq PROPN iajs-2945 66 78 data datum NOUN iajs-2945 67 1 [ [ X iajs-2945 67 2 4 4 NUM iajs-2945 67 3 ] ] PUNCT iajs-2945 67 4 as as ADP iajs-2945 67 5 the the DET iajs-2945 67 6 folwing folwing NOUN iajs-2945 67 7 : : PUNCT iajs-2945 67 8 𝑆(0 𝑆(0 NUM iajs-2945 67 9 ) ) PUNCT iajs-2945 67 10 = = SYM iajs-2945 67 11 500 500 NUM iajs-2945 67 12 , , PUNCT iajs-2945 67 13 𝑉(0 𝑉(0 NUM iajs-2945 67 14 ) ) PUNCT iajs-2945 67 15 = = SYM iajs-2945 67 16 30 30 NUM iajs-2945 67 17 , , PUNCT iajs-2945 67 18 𝐴(0 𝐴(0 NUM iajs-2945 67 19 ) ) PUNCT iajs-2945 67 20 = = SYM iajs-2945 67 21 36 36 NUM iajs-2945 67 22 , , PUNCT iajs-2945 67 23 𝐼(0 𝐼(0 X iajs-2945 67 24 ) ) PUNCT iajs-2945 68 1 = = SYM iajs-2945 68 2 24 24 NUM iajs-2945 68 3 and and CCONJ iajs-2945 68 4 𝑅(0 𝑅(0 NUM iajs-2945 68 5 ) ) PUNCT iajs-2945 68 6 = = SYM iajs-2945 69 1 10 10 NUM iajs-2945 69 2 , , PUNCT iajs-2945 69 3 with with ADP iajs-2945 69 4 the the DET iajs-2945 69 5 predicted predict VERB iajs-2945 69 6 parameters parameter NOUN iajs-2945 69 7 that that PRON iajs-2945 69 8 are be AUX iajs-2945 69 9 given give VERB iajs-2945 69 10 in in ADP iajs-2945 69 11 table table NOUN iajs-2945 69 12 2 2 NUM iajs-2945 69 13 . . PUNCT iajs-2945 69 14 table table NOUN iajs-2945 69 15 1 1 NUM iajs-2945 69 16 variables variable NOUN iajs-2945 69 17 of of ADP iajs-2945 69 18 covid-19 covid-19 PROPN iajs-2945 69 19 model model NOUN iajs-2945 69 20 [ [ X iajs-2945 69 21 25 25 NUM iajs-2945 69 22 ] ] PUNCT iajs-2945 69 23 . . PUNCT iajs-2945 70 1 variable variable ADJ iajs-2945 70 2 definition definition NOUN iajs-2945 70 3 𝑺(𝒕 𝑺(𝒕 NOUN iajs-2945 70 4 ) ) PUNCT iajs-2945 70 5 people people NOUN iajs-2945 70 6 who who PRON iajs-2945 70 7 are be AUX iajs-2945 70 8 not not PART iajs-2945 70 9 infected infect VERB iajs-2945 70 10 but but CCONJ iajs-2945 70 11 are be AUX iajs-2945 70 12 vulnerable vulnerable ADJ iajs-2945 70 13 not not PART iajs-2945 70 14 to to PART iajs-2945 70 15 have have VERB iajs-2945 70 16 immunity immunity NOUN iajs-2945 70 17 𝑽(𝒕 𝑽(𝒕 NOUN iajs-2945 70 18 ) ) PUNCT iajs-2945 70 19 people people NOUN iajs-2945 70 20 vaccinated vaccinate VERB iajs-2945 70 21 against against ADP iajs-2945 70 22 coronavirus coronavirus NOUN iajs-2945 70 23 𝑨(𝒕 𝑨(𝒕 NUM iajs-2945 70 24 ) ) PUNCT iajs-2945 70 25 people people NOUN iajs-2945 70 26 infected infect VERB iajs-2945 70 27 with with ADP iajs-2945 70 28 the the DET iajs-2945 70 29 virus virus NOUN iajs-2945 70 30 without without ADP iajs-2945 70 31 showing show VERB iajs-2945 70 32 any any DET iajs-2945 70 33 symptoms symptom NOUN iajs-2945 70 34 𝑰(𝒕 𝑰(𝒕 VERB iajs-2945 70 35 ) ) PUNCT iajs-2945 70 36 infected infected ADJ iajs-2945 70 37 people people NOUN iajs-2945 70 38 have have VERB iajs-2945 70 39 clear clear ADJ iajs-2945 70 40 symptoms symptom NOUN iajs-2945 70 41 of of ADP iajs-2945 70 42 infection infection NOUN iajs-2945 70 43 in in ADP iajs-2945 70 44 their their PRON iajs-2945 70 45 bodies body NOUN iajs-2945 70 46 𝑹(𝒕 𝑹(𝒕 NOUN iajs-2945 70 47 ) ) PUNCT iajs-2945 70 48 people people NOUN iajs-2945 70 49 who who PRON iajs-2945 70 50 have have AUX iajs-2945 70 51 recovered recover VERB iajs-2945 70 52 from from ADP iajs-2945 70 53 the the DET iajs-2945 70 54 coronavirus coronavirus NOUN iajs-2945 70 55 or or CCONJ iajs-2945 70 56 who who PRON iajs-2945 70 57 died die VERB iajs-2945 70 58 because because SCONJ iajs-2945 70 59 of of ADP iajs-2945 70 60 coronavirus coronavirus NOUN iajs-2945 70 61 infection infection NOUN iajs-2945 70 62 ihjpas ihjpa VERB iajs-2945 70 63 . . PUNCT iajs-2945 71 1 36(3)2023 36(3)2023 NUM iajs-2945 71 2 292 292 NUM iajs-2945 71 3 table table NOUN iajs-2945 71 4 2 2 NUM iajs-2945 71 5 parameters parameter NOUN iajs-2945 71 6 of of ADP iajs-2945 71 7 covid-19 covid-19 PROPN iajs-2945 71 8 model model NOUN iajs-2945 71 9 [ [ X iajs-2945 71 10 25 25 NUM iajs-2945 71 11 ] ] PUNCT iajs-2945 71 12 . . PUNCT iajs-2945 72 1 parameter parameter NOUN iajs-2945 72 2 definition definition NOUN iajs-2945 72 3 value value NOUN iajs-2945 72 4 source source NOUN iajs-2945 72 5 𝜢 𝜢 ADP iajs-2945 72 6 the the DET iajs-2945 72 7 rate rate NOUN iajs-2945 72 8 of of ADP iajs-2945 72 9 transmission transmission NOUN iajs-2945 72 10 people people NOUN iajs-2945 72 11 who who PRON iajs-2945 72 12 are be AUX iajs-2945 72 13 infected infect VERB iajs-2945 72 14 with with ADP iajs-2945 72 15 this this DET iajs-2945 72 16 virus virus NOUN iajs-2945 73 1 0.8883 0.8883 NUM iajs-2945 73 2 [ [ X iajs-2945 73 3 26 26 NUM iajs-2945 73 4 ] ] SYM iajs-2945 73 5 𝜷 𝜷 NOUN iajs-2945 73 6 correction correction NOUN iajs-2945 73 7 factor factor NOUN iajs-2945 73 8 for for ADP iajs-2945 73 9 the the DET iajs-2945 73 10 rate rate NOUN iajs-2945 73 11 of of ADP iajs-2945 73 12 transmission transmission NOUN iajs-2945 73 13 of of ADP iajs-2945 73 14 people people NOUN iajs-2945 73 15 without without ADP iajs-2945 73 16 infection infection NOUN iajs-2945 73 17 0.45 0.45 NUM iajs-2945 73 18 [ [ X iajs-2945 73 19 26 26 NUM iajs-2945 73 20 ] ] PUNCT iajs-2945 73 21 𝝁 𝝁 NOUN iajs-2945 73 22 the the DET iajs-2945 73 23 rate rate NOUN iajs-2945 73 24 of of ADP iajs-2945 73 25 natural natural ADJ iajs-2945 73 26 death death NOUN iajs-2945 73 27 0.00003349 0.00003349 NUM iajs-2945 73 28 day day NOUN iajs-2945 74 1 [ [ X iajs-2945 74 2 26 26 NUM iajs-2945 74 3 ] ] PUNCT iajs-2945 74 4 𝜸 𝜸 X iajs-2945 74 5 the the DET iajs-2945 74 6 rate rate NOUN iajs-2945 74 7 of of ADP iajs-2945 74 8 immunity immunity NOUN iajs-2945 74 9 0.005 0.005 NUM iajs-2945 74 10 assume assume VERB iajs-2945 74 11 𝟏 𝟏 NUM iajs-2945 74 12 βˆ’ βˆ’ NOUN iajs-2945 75 1 𝝆 𝝆 ADP iajs-2945 75 2 the the DET iajs-2945 75 3 vaccine vaccine NOUN iajs-2945 75 4 efficacy efficacy NOUN iajs-2945 75 5 and and CCONJ iajs-2945 75 6 potency potency NOUN iajs-2945 75 7 0.8 0.8 NUM iajs-2945 75 8 assume assume VERB iajs-2945 75 9 𝟏/𝜹 𝟏/𝜹 X iajs-2945 76 1 the the DET iajs-2945 76 2 average average ADJ iajs-2945 76 3 period period NOUN iajs-2945 76 4 without without ADP iajs-2945 76 5 symptoms symptom NOUN iajs-2945 76 6 of of ADP iajs-2945 76 7 infection infection NOUN iajs-2945 76 8 7 7 NUM iajs-2945 76 9 days day NOUN iajs-2945 76 10 [ [ X iajs-2945 76 11 27 27 NUM iajs-2945 76 12 ] ] X iajs-2945 76 13 𝜽 𝜽 ADP iajs-2945 76 14 the the DET iajs-2945 76 15 proportion proportion NOUN iajs-2945 76 16 of of ADP iajs-2945 76 17 people people NOUN iajs-2945 76 18 does do AUX iajs-2945 76 19 not not PART iajs-2945 76 20 show show VERB iajs-2945 76 21 the the DET iajs-2945 76 22 effects effect NOUN iajs-2945 76 23 of of ADP iajs-2945 76 24 the the DET iajs-2945 76 25 symptoms symptom NOUN iajs-2945 76 26 of of ADP iajs-2945 76 27 the the DET iajs-2945 76 28 virus virus NOUN iajs-2945 76 29 , , PUNCT iajs-2945 76 30 but but CCONJ iajs-2945 76 31 it it PRON iajs-2945 76 32 develops develop VERB iajs-2945 76 33 into into ADP iajs-2945 76 34 a a DET iajs-2945 76 35 state state NOUN iajs-2945 76 36 of of ADP iajs-2945 76 37 infection infection NOUN iajs-2945 76 38 0.2 0.2 NUM iajs-2945 77 1 [ [ X iajs-2945 77 2 27 27 NUM iajs-2945 77 3 ] ] SYM iajs-2945 77 4 𝟏 𝟏 NUM iajs-2945 78 1 βˆ’ βˆ’ NOUN iajs-2945 78 2 𝜽 𝜽 INTJ iajs-2945 78 3 the the DET iajs-2945 78 4 proportion proportion NOUN iajs-2945 78 5 of of ADP iajs-2945 78 6 individuals individual NOUN iajs-2945 78 7 who who PRON iajs-2945 78 8 recover recover VERB iajs-2945 78 9 but but CCONJ iajs-2945 78 10 are be AUX iajs-2945 78 11 asymptomatic asymptomatic ADJ iajs-2945 78 12 0.8 0.8 NUM iajs-2945 78 13 [ [ SYM iajs-2945 78 14 27 27 NUM iajs-2945 78 15 ] ] X iajs-2945 78 16 𝑴 𝑴 NOUN iajs-2945 78 17 the the DET iajs-2945 78 18 birth birth NOUN iajs-2945 78 19 rate rate NOUN iajs-2945 78 20 in in ADP iajs-2945 78 21 the the DET iajs-2945 78 22 community community NOUN iajs-2945 78 23 1500 1500 NUM iajs-2945 78 24 / / SYM iajs-2945 78 25 day day NOUN iajs-2945 78 26 assume assume VERB iajs-2945 78 27 𝝉 𝝉 ADP iajs-2945 78 28 the the DET iajs-2945 78 29 vaccination vaccination NOUN iajs-2945 78 30 rate rate NOUN iajs-2945 78 31 against against ADP iajs-2945 78 32 the the DET iajs-2945 78 33 virus virus NOUN iajs-2945 78 34 0.01 0.01 NUM iajs-2945 78 35 day day NOUN iajs-2945 78 36 assume assume VERB iajs-2945 78 37 𝟏/𝝈 𝟏/𝝈 NOUN iajs-2945 78 38 the the DET iajs-2945 78 39 average average ADJ iajs-2945 78 40 rate rate NOUN iajs-2945 78 41 of of ADP iajs-2945 78 42 people people NOUN iajs-2945 78 43 recovering recover VERB iajs-2945 78 44 from from ADP iajs-2945 78 45 infection infection NOUN iajs-2945 78 46 with with ADP iajs-2945 78 47 the the DET iajs-2945 78 48 virus virus NOUN iajs-2945 78 49 10 10 NUM iajs-2945 78 50 days day NOUN iajs-2945 78 51 assume assume VERB iajs-2945 78 52 3 3 NUM iajs-2945 78 53 . . NOUN iajs-2945 78 54 numerical numerical ADJ iajs-2945 78 55 method method NOUN iajs-2945 78 56 for for ADP iajs-2945 78 57 solving solve VERB iajs-2945 78 58 covid-19 covid-19 PROPN iajs-2945 78 59 model model NOUN iajs-2945 78 60 rk4 rk4 NOUN iajs-2945 78 61 is be AUX iajs-2945 78 62 one one NUM iajs-2945 78 63 of of ADP iajs-2945 78 64 the the DET iajs-2945 78 65 numerical numerical ADJ iajs-2945 78 66 iterative iterative NOUN iajs-2945 78 67 methods method NOUN iajs-2945 78 68 with with ADP iajs-2945 78 69 high high ADJ iajs-2945 78 70 accuracy accuracy NOUN iajs-2945 78 71 . . PUNCT iajs-2945 79 1 the the DET iajs-2945 79 2 nonlinear nonlinear ADJ iajs-2945 79 3 system system NOUN iajs-2945 79 4 ( ( PUNCT iajs-2945 79 5 1 1 NUM iajs-2945 79 6 ) ) PUNCT iajs-2945 79 7 for for ADP iajs-2945 79 8 the the DET iajs-2945 79 9 covid-19 covid-19 PROPN iajs-2945 79 10 model model NOUN iajs-2945 79 11 can can AUX iajs-2945 79 12 be be AUX iajs-2945 79 13 solved solve VERB iajs-2945 79 14 by by ADP iajs-2945 79 15 rk4 rk4 NOUN iajs-2945 79 16 with with ADP iajs-2945 79 17 the the DET iajs-2945 79 18 mentioned mention VERB iajs-2945 79 19 initial initial NOUN iajs-2945 79 20 conditions.the conditions.the DET iajs-2945 79 21 general general ADJ iajs-2945 79 22 form form NOUN iajs-2945 79 23 of of ADP iajs-2945 79 24 rk4 rk4 NOUN iajs-2945 79 25 is be AUX iajs-2945 79 26 : : PUNCT iajs-2945 79 27 𝑦𝑖+1 𝑦𝑖+1 PROPN iajs-2945 79 28 = = SYM iajs-2945 79 29 𝑦𝑖 𝑦𝑖 PROPN iajs-2945 79 30 + + NUM iajs-2945 79 31 β„Ž β„Ž PROPN iajs-2945 79 32 6 6 NUM iajs-2945 79 33 ( ( PUNCT iajs-2945 79 34 𝑙1 𝑙1 PROPN iajs-2945 79 35 + + CCONJ iajs-2945 79 36 2𝑙2 2𝑙2 NUM iajs-2945 79 37 + + CCONJ iajs-2945 79 38 2𝑙3 2𝑙3 NUM iajs-2945 79 39 + + CCONJ iajs-2945 79 40 𝑙4 𝑙4 PROPN iajs-2945 79 41 ) ) PUNCT iajs-2945 79 42 , , PUNCT iajs-2945 79 43 ( ( PUNCT iajs-2945 79 44 2 2 X iajs-2945 79 45 ) ) PUNCT iajs-2945 79 46 where where SCONJ iajs-2945 79 47 𝑆𝑖+1 𝑆𝑖+1 X iajs-2945 79 48 = = SYM iajs-2945 79 49 𝑓(𝑑𝑖 𝑓(𝑑𝑖 NUM iajs-2945 79 50 , , PUNCT iajs-2945 79 51 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 79 52 , , PUNCT iajs-2945 79 53 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 79 54 , , PUNCT iajs-2945 79 55 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 79 56 , , PUNCT iajs-2945 79 57 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 79 58 , , PUNCT iajs-2945 79 59 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 79 60 ) ) PUNCT iajs-2945 79 61 , , PUNCT iajs-2945 79 62 = = SYM iajs-2945 80 1 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 80 2 + + NUM iajs-2945 80 3 1 1 NUM iajs-2945 80 4 6 6 NUM iajs-2945 80 5 ( ( PUNCT iajs-2945 80 6 𝑙𝑆1 𝑙𝑆1 PROPN iajs-2945 81 1 + + CCONJ iajs-2945 81 2 2𝑙𝑆2 2𝑙𝑆2 NUM iajs-2945 82 1 + + CCONJ iajs-2945 82 2 2𝑙𝑆3 2𝑙𝑆3 PROPN iajs-2945 82 3 + + CCONJ iajs-2945 82 4 𝑙𝑆4 𝑙𝑆4 PROPN iajs-2945 82 5 ) ) PUNCT iajs-2945 82 6 βˆ— βˆ— NOUN iajs-2945 82 7 β„Ž β„Ž PROPN iajs-2945 82 8 , , PUNCT iajs-2945 82 9 ( ( PUNCT iajs-2945 82 10 3 3 NUM iajs-2945 82 11 ) ) PUNCT iajs-2945 82 12 𝑉𝑖+1 𝑉𝑖+1 NOUN iajs-2945 82 13 = = SYM iajs-2945 82 14 𝑓(𝑑𝑖 𝑓(𝑑𝑖 NUM iajs-2945 82 15 , , PUNCT iajs-2945 82 16 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 82 17 , , PUNCT iajs-2945 82 18 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 82 19 , , PUNCT iajs-2945 82 20 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 82 21 , , PUNCT iajs-2945 82 22 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 82 23 , , PUNCT iajs-2945 82 24 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 82 25 ) ) PUNCT iajs-2945 82 26 , , PUNCT iajs-2945 83 1 = = PUNCT iajs-2945 83 2 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 83 3 + + NOUN iajs-2945 83 4 1 1 NUM iajs-2945 83 5 6 6 NUM iajs-2945 83 6 ( ( PUNCT iajs-2945 83 7 𝑙𝑉1 𝑙𝑉1 PROPN iajs-2945 83 8 + + CCONJ iajs-2945 83 9 2𝑙𝑉2 2𝑙𝑉2 NUM iajs-2945 83 10 + + SYM iajs-2945 83 11 2𝑙𝑉3 2𝑙𝑉3 NUM iajs-2945 83 12 + + NUM iajs-2945 83 13 𝑙𝑉4 𝑙𝑉4 NOUN iajs-2945 83 14 ) ) PUNCT iajs-2945 83 15 βˆ— βˆ— NOUN iajs-2945 83 16 β„Ž β„Ž PROPN iajs-2945 83 17 , , PUNCT iajs-2945 83 18 ( ( PUNCT iajs-2945 83 19 4 4 X iajs-2945 83 20 ) ) PUNCT iajs-2945 83 21 𝐴𝑖+1 𝐴𝑖+1 NOUN iajs-2945 83 22 = = SYM iajs-2945 83 23 𝑓(𝑑𝑖 𝑓(𝑑𝑖 NUM iajs-2945 83 24 , , PUNCT iajs-2945 83 25 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 83 26 , , PUNCT iajs-2945 83 27 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 83 28 , , PUNCT iajs-2945 83 29 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 83 30 , , PUNCT iajs-2945 83 31 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 83 32 , , PUNCT iajs-2945 83 33 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 83 34 ) ) PUNCT iajs-2945 83 35 , , PUNCT iajs-2945 83 36 = = PUNCT iajs-2945 84 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 84 2 + + NOUN iajs-2945 84 3 1 1 NUM iajs-2945 84 4 6 6 NUM iajs-2945 84 5 ( ( PUNCT iajs-2945 84 6 𝑙𝐴1 𝑙𝐴1 PROPN iajs-2945 84 7 + + NUM iajs-2945 84 8 2𝑙𝐴2 2𝑙𝐴2 NUM iajs-2945 84 9 + + SYM iajs-2945 84 10 2𝑙𝐴3 2𝑙𝐴3 NUM iajs-2945 84 11 + + CCONJ iajs-2945 84 12 𝑙𝐴4 𝑙𝐴4 NOUN iajs-2945 84 13 ) ) PUNCT iajs-2945 84 14 βˆ— βˆ— NOUN iajs-2945 84 15 β„Ž β„Ž PROPN iajs-2945 84 16 , , PUNCT iajs-2945 84 17 ( ( PUNCT iajs-2945 84 18 5 5 NUM iajs-2945 84 19 ) ) PUNCT iajs-2945 84 20 𝐼𝑖+1 𝐼𝑖+1 NOUN iajs-2945 84 21 = = SYM iajs-2945 84 22 𝑓(𝑑𝑖 𝑓(𝑑𝑖 NUM iajs-2945 84 23 , , PUNCT iajs-2945 84 24 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 84 25 , , PUNCT iajs-2945 84 26 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 84 27 , , PUNCT iajs-2945 84 28 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 84 29 , , PUNCT iajs-2945 84 30 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 84 31 , , PUNCT iajs-2945 84 32 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 84 33 ) ) PUNCT iajs-2945 84 34 , , PUNCT iajs-2945 84 35 = = PUNCT iajs-2945 84 36 𝐼𝑖 𝐼𝑖 NOUN iajs-2945 84 37 + + CCONJ iajs-2945 84 38 1 1 NUM iajs-2945 84 39 6 6 NUM iajs-2945 84 40 ( ( PUNCT iajs-2945 84 41 𝑙𝐼1 𝑙𝐼1 NOUN iajs-2945 84 42 + + NOUN iajs-2945 84 43 2𝑙𝐼2 2𝑙𝐼2 PROPN iajs-2945 84 44 + + CCONJ iajs-2945 84 45 2𝑙𝐼3 2𝑙𝐼3 NUM iajs-2945 84 46 + + NUM iajs-2945 84 47 𝑙𝐼4 𝑙𝐼4 NOUN iajs-2945 84 48 ) ) PUNCT iajs-2945 84 49 βˆ— βˆ— NOUN iajs-2945 84 50 β„Ž β„Ž PROPN iajs-2945 84 51 , , PUNCT iajs-2945 84 52 ( ( PUNCT iajs-2945 84 53 6 6 NUM iajs-2945 84 54 ) ) PUNCT iajs-2945 84 55 𝑅𝑖+1 𝑅𝑖+1 NOUN iajs-2945 85 1 = = SYM iajs-2945 85 2 𝑓(𝑑𝑖 𝑓(𝑑𝑖 NUM iajs-2945 85 3 , , PUNCT iajs-2945 85 4 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 85 5 , , PUNCT iajs-2945 85 6 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 85 7 , , PUNCT iajs-2945 85 8 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 85 9 , , PUNCT iajs-2945 85 10 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 85 11 , , PUNCT iajs-2945 85 12 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 85 13 ) ) PUNCT iajs-2945 85 14 , , PUNCT iajs-2945 85 15 = = PUNCT iajs-2945 86 1 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 86 2 + + CCONJ iajs-2945 86 3 1 1 NUM iajs-2945 86 4 6 6 NUM iajs-2945 86 5 ( ( PUNCT iajs-2945 86 6 𝑙𝑅1 𝑙𝑅1 NOUN iajs-2945 86 7 + + X iajs-2945 86 8 2𝑙𝑅2 2𝑙𝑅2 NUM iajs-2945 86 9 + + CCONJ iajs-2945 86 10 2𝑙𝑅3 2𝑙𝑅3 NUM iajs-2945 86 11 + + CCONJ iajs-2945 86 12 𝑙𝑅4 𝑙𝑅4 PROPN iajs-2945 86 13 ) ) PUNCT iajs-2945 86 14 βˆ— βˆ— NOUN iajs-2945 86 15 β„Ž β„Ž PROPN iajs-2945 86 16 , , PUNCT iajs-2945 86 17 for for ADP iajs-2945 86 18 all all PRON iajs-2945 86 19 𝑖 𝑖 NOUN iajs-2945 86 20 = = SYM iajs-2945 86 21 1,2 1,2 NUM iajs-2945 86 22 , , PUNCT iajs-2945 86 23 … … PUNCT iajs-2945 86 24 , , PUNCT iajs-2945 86 25 π‘š. π‘š. ADJ iajs-2945 86 26 ( ( PUNCT iajs-2945 86 27 7 7 X iajs-2945 86 28 ) ) PUNCT iajs-2945 86 29 ihjpas ihjpa NOUN iajs-2945 86 30 . . PUNCT iajs-2945 87 1 36(3)2023 36(3)2023 NUM iajs-2945 87 2 293 293 NUM iajs-2945 87 3 now now ADV iajs-2945 87 4 , , PUNCT iajs-2945 87 5 the the DET iajs-2945 87 6 first first ADJ iajs-2945 87 7 iteration iteration NOUN iajs-2945 87 8 𝑙𝑆1 𝑙𝑆1 PROPN iajs-2945 87 9 , , PUNCT iajs-2945 87 10 𝑙𝑉1 𝑙𝑉1 PROPN iajs-2945 87 11 , , PUNCT iajs-2945 87 12 𝑙𝐴1 𝑙𝐴1 PROPN iajs-2945 87 13 , , PUNCT iajs-2945 87 14 𝑙𝐼1 𝑙𝐼1 PROPN iajs-2945 87 15 and and CCONJ iajs-2945 87 16 𝑙𝑅1 𝑙𝑅1 PROPN iajs-2945 87 17 can can AUX iajs-2945 87 18 be be AUX iajs-2945 87 19 found find VERB iajs-2945 87 20 as as SCONJ iajs-2945 87 21 follows follow VERB iajs-2945 87 22 : : PUNCT iajs-2945 87 23 𝑙𝑆1 𝑙𝑆1 PROPN iajs-2945 87 24 = = SYM iajs-2945 87 25 𝑓1(𝑑𝑖 𝑓1(𝑑𝑖 PROPN iajs-2945 87 26 , , PUNCT iajs-2945 87 27 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 87 28 , , PUNCT iajs-2945 87 29 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 87 30 , , PUNCT iajs-2945 87 31 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 87 32 , , PUNCT iajs-2945 87 33 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 87 34 , , PUNCT iajs-2945 87 35 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 87 36 ) ) PUNCT iajs-2945 87 37 , , PUNCT iajs-2945 87 38 ( ( PUNCT iajs-2945 87 39 8) 8) NUM iajs-2945 87 40 𝑙𝑉1 𝑙𝑉1 NOUN iajs-2945 87 41 = = SYM iajs-2945 88 1 𝑓1(𝑑𝑖 𝑓1(𝑑𝑖 PROPN iajs-2945 88 2 , , PUNCT iajs-2945 88 3 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 88 4 , , PUNCT iajs-2945 88 5 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 88 6 , , PUNCT iajs-2945 88 7 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 88 8 , , PUNCT iajs-2945 88 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 88 10 , , PUNCT iajs-2945 88 11 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 88 12 ) ) PUNCT iajs-2945 88 13 , , PUNCT iajs-2945 88 14 ( ( PUNCT iajs-2945 88 15 9 9 X iajs-2945 88 16 ) ) PUNCT iajs-2945 88 17 𝑙𝐴1 𝑙𝐴1 PROPN iajs-2945 88 18 = = PUNCT iajs-2945 88 19 𝑓1(𝑑𝑖 𝑓1(𝑑𝑖 PROPN iajs-2945 88 20 , , PUNCT iajs-2945 88 21 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 88 22 , , PUNCT iajs-2945 88 23 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 88 24 , , PUNCT iajs-2945 88 25 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 88 26 , , PUNCT iajs-2945 88 27 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 88 28 , , PUNCT iajs-2945 88 29 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 88 30 ) ) PUNCT iajs-2945 88 31 , , PUNCT iajs-2945 88 32 ( ( PUNCT iajs-2945 88 33 10 10 NUM iajs-2945 88 34 ) ) PUNCT iajs-2945 88 35 𝑙𝐼1 𝑙𝐼1 NOUN iajs-2945 88 36 = = SYM iajs-2945 88 37 𝑓1(𝑑𝑖 𝑓1(𝑑𝑖 PROPN iajs-2945 88 38 , , PUNCT iajs-2945 88 39 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 88 40 , , PUNCT iajs-2945 88 41 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 88 42 , , PUNCT iajs-2945 88 43 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 88 44 , , PUNCT iajs-2945 88 45 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 88 46 , , PUNCT iajs-2945 88 47 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 88 48 ) ) PUNCT iajs-2945 88 49 , , PUNCT iajs-2945 88 50 ( ( PUNCT iajs-2945 88 51 11 11 NUM iajs-2945 88 52 ) ) PUNCT iajs-2945 88 53 𝑙𝑅1 𝑙𝑅1 NOUN iajs-2945 88 54 = = PUNCT iajs-2945 88 55 𝑓1(𝑑𝑖 𝑓1(𝑑𝑖 PROPN iajs-2945 88 56 , , PUNCT iajs-2945 88 57 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 88 58 , , PUNCT iajs-2945 88 59 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 88 60 , , PUNCT iajs-2945 88 61 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 88 62 , , PUNCT iajs-2945 88 63 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 88 64 , , PUNCT iajs-2945 88 65 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 88 66 ) ) PUNCT iajs-2945 88 67 . . PUNCT iajs-2945 89 1 for for ADP iajs-2945 89 2 all all DET iajs-2945 89 3 𝑖 𝑖 NOUN iajs-2945 89 4 = = SYM iajs-2945 89 5 0,1 0,1 NUM iajs-2945 89 6 , , PUNCT iajs-2945 89 7 … … PUNCT iajs-2945 89 8 , , PUNCT iajs-2945 89 9 π‘š. π‘š. ADJ iajs-2945 89 10 ( ( PUNCT iajs-2945 89 11 12 12 NUM iajs-2945 89 12 ) ) PUNCT iajs-2945 89 13 also also ADV iajs-2945 89 14 , , PUNCT iajs-2945 89 15 the the DET iajs-2945 89 16 second second ADJ iajs-2945 89 17 iteration iteration NOUN iajs-2945 89 18 𝑙𝑆2 𝑙𝑆2 PROPN iajs-2945 89 19 , , PUNCT iajs-2945 89 20 𝑙𝑉2 𝑙𝑉2 PROPN iajs-2945 89 21 , , PUNCT iajs-2945 89 22 𝑙𝐼2 𝑙𝐼2 PROPN iajs-2945 89 23 , , PUNCT iajs-2945 89 24 𝑙𝑄2 𝑙𝑄2 PROPN iajs-2945 89 25 and and CCONJ iajs-2945 89 26 𝑙𝑅2 𝑙𝑅2 NOUN iajs-2945 89 27 , , PUNCT iajs-2945 89 28 in in ADP iajs-2945 89 29 the the DET iajs-2945 89 30 same same ADJ iajs-2945 89 31 way way NOUN iajs-2945 89 32 , , PUNCT iajs-2945 89 33 is be AUX iajs-2945 89 34 given give VERB iajs-2945 89 35 as as SCONJ iajs-2945 89 36 follows follow VERB iajs-2945 89 37 : : PUNCT iajs-2945 89 38 𝑙𝑆2 𝑙𝑆2 PROPN iajs-2945 89 39 = = SYM iajs-2945 89 40 𝑓2 𝑓2 NOUN iajs-2945 89 41 ( ( PUNCT iajs-2945 89 42 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 89 43 1 1 NUM iajs-2945 89 44 2 2 NUM iajs-2945 89 45 β„Ž β„Ž NOUN iajs-2945 89 46 , , PUNCT iajs-2945 89 47 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 89 48 + + NUM iajs-2945 89 49 1 1 NUM iajs-2945 89 50 2 2 NUM iajs-2945 89 51 β„Ž β„Ž PROPN iajs-2945 89 52 βˆ— βˆ— NOUN iajs-2945 89 53 𝑙𝑆1 𝑙𝑆1 PROPN iajs-2945 89 54 , , PUNCT iajs-2945 90 1 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 90 2 + + NOUN iajs-2945 90 3 1 1 NUM iajs-2945 90 4 2 2 NUM iajs-2945 90 5 β„Ž β„Ž PROPN iajs-2945 90 6 βˆ— βˆ— NOUN iajs-2945 90 7 𝑙𝑉1 𝑙𝑉1 PROPN iajs-2945 90 8 , , PUNCT iajs-2945 91 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 91 2 + + NOUN iajs-2945 91 3 1 1 NUM iajs-2945 91 4 2 2 NUM iajs-2945 91 5 β„Ž β„Ž PROPN iajs-2945 91 6 βˆ— βˆ— NOUN iajs-2945 91 7 𝑙𝐴1 𝑙𝐴1 PROPN iajs-2945 91 8 , , PUNCT iajs-2945 91 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 91 10 + + CCONJ iajs-2945 91 11 1 1 NUM iajs-2945 91 12 2 2 NUM iajs-2945 91 13 β„Ž β„Ž PROPN iajs-2945 91 14 βˆ— βˆ— NOUN iajs-2945 91 15 𝑙𝐼1 𝑙𝐼1 PROPN iajs-2945 91 16 , , PUNCT iajs-2945 91 17 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 91 18 + + CCONJ iajs-2945 91 19 1 1 NUM iajs-2945 91 20 2 2 NUM iajs-2945 91 21 β„Ž β„Ž PROPN iajs-2945 91 22 βˆ— βˆ— PROPN iajs-2945 91 23 𝑙𝑅1 𝑙𝑅1 PROPN iajs-2945 91 24 ) ) PUNCT iajs-2945 91 25 , , PUNCT iajs-2945 91 26 ( ( PUNCT iajs-2945 91 27 13 13 NUM iajs-2945 91 28 ) ) PUNCT iajs-2945 91 29 𝑙𝑉2 𝑙𝑉2 PROPN iajs-2945 92 1 = = SYM iajs-2945 92 2 𝑓2 𝑓2 NOUN iajs-2945 92 3 ( ( PUNCT iajs-2945 92 4 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 92 5 1 1 NUM iajs-2945 92 6 2 2 NUM iajs-2945 92 7 β„Ž β„Ž NOUN iajs-2945 92 8 , , PUNCT iajs-2945 92 9 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 92 10 + + NUM iajs-2945 92 11 1 1 NUM iajs-2945 92 12 2 2 NUM iajs-2945 92 13 β„Ž β„Ž PROPN iajs-2945 92 14 βˆ— βˆ— NOUN iajs-2945 92 15 𝑙𝑆1 𝑙𝑆1 PROPN iajs-2945 92 16 , , PUNCT iajs-2945 93 1 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 93 2 + + NOUN iajs-2945 93 3 1 1 NUM iajs-2945 93 4 2 2 NUM iajs-2945 93 5 β„Ž β„Ž PROPN iajs-2945 93 6 βˆ— βˆ— NOUN iajs-2945 93 7 𝑙𝑉1 𝑙𝑉1 PROPN iajs-2945 93 8 , , PUNCT iajs-2945 94 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 94 2 + + NOUN iajs-2945 94 3 1 1 NUM iajs-2945 94 4 2 2 NUM iajs-2945 94 5 β„Ž β„Ž PROPN iajs-2945 94 6 βˆ— βˆ— NOUN iajs-2945 94 7 𝑙𝐴1 𝑙𝐴1 PROPN iajs-2945 94 8 , , PUNCT iajs-2945 94 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 94 10 + + CCONJ iajs-2945 94 11 1 1 NUM iajs-2945 94 12 2 2 NUM iajs-2945 94 13 β„Ž β„Ž PROPN iajs-2945 94 14 βˆ— βˆ— NOUN iajs-2945 94 15 𝑙𝐼1 𝑙𝐼1 PROPN iajs-2945 94 16 , , PUNCT iajs-2945 94 17 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 94 18 + + CCONJ iajs-2945 94 19 1 1 NUM iajs-2945 94 20 2 2 NUM iajs-2945 94 21 β„Ž β„Ž PROPN iajs-2945 94 22 βˆ— βˆ— PROPN iajs-2945 94 23 𝑙𝑅1 𝑙𝑅1 PROPN iajs-2945 94 24 ) ) PUNCT iajs-2945 94 25 , , PUNCT iajs-2945 94 26 ( ( PUNCT iajs-2945 94 27 14 14 NUM iajs-2945 94 28 ) ) PUNCT iajs-2945 94 29 𝑙𝐴2 𝑙𝐴2 NOUN iajs-2945 94 30 = = SYM iajs-2945 94 31 𝑓2 𝑓2 NOUN iajs-2945 94 32 ( ( PUNCT iajs-2945 94 33 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 94 34 1 1 NUM iajs-2945 94 35 2 2 NUM iajs-2945 94 36 β„Ž β„Ž NOUN iajs-2945 94 37 , , PUNCT iajs-2945 94 38 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 94 39 + + NUM iajs-2945 94 40 1 1 NUM iajs-2945 94 41 2 2 NUM iajs-2945 94 42 β„Ž β„Ž PROPN iajs-2945 94 43 βˆ— βˆ— NOUN iajs-2945 94 44 𝑙𝑆1 𝑙𝑆1 PROPN iajs-2945 94 45 , , PUNCT iajs-2945 95 1 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 95 2 + + NOUN iajs-2945 95 3 1 1 NUM iajs-2945 95 4 2 2 NUM iajs-2945 95 5 β„Ž β„Ž PROPN iajs-2945 95 6 βˆ— βˆ— NOUN iajs-2945 95 7 𝑙𝑉1 𝑙𝑉1 PROPN iajs-2945 95 8 , , PUNCT iajs-2945 96 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 96 2 + + NOUN iajs-2945 96 3 1 1 NUM iajs-2945 96 4 2 2 NUM iajs-2945 96 5 β„Ž β„Ž PROPN iajs-2945 96 6 βˆ— βˆ— NOUN iajs-2945 96 7 𝑙𝐴1 𝑙𝐴1 PROPN iajs-2945 96 8 , , PUNCT iajs-2945 96 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 96 10 + + CCONJ iajs-2945 96 11 1 1 NUM iajs-2945 96 12 2 2 NUM iajs-2945 96 13 β„Ž β„Ž PROPN iajs-2945 96 14 βˆ— βˆ— NOUN iajs-2945 96 15 𝑙𝐼1 𝑙𝐼1 PROPN iajs-2945 96 16 , , PUNCT iajs-2945 96 17 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 96 18 + + CCONJ iajs-2945 96 19 1 1 NUM iajs-2945 96 20 2 2 NUM iajs-2945 96 21 β„Ž β„Ž PROPN iajs-2945 96 22 βˆ— βˆ— PROPN iajs-2945 96 23 𝑙𝑅1 𝑙𝑅1 PROPN iajs-2945 96 24 ) ) PUNCT iajs-2945 96 25 , , PUNCT iajs-2945 96 26 ( ( PUNCT iajs-2945 96 27 15 15 NUM iajs-2945 96 28 ) ) PUNCT iajs-2945 96 29 𝑙𝐼2 𝑙𝐼2 PROPN iajs-2945 97 1 = = SYM iajs-2945 97 2 𝑓2 𝑓2 PROPN iajs-2945 97 3 ( ( PUNCT iajs-2945 97 4 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 97 5 1 1 NUM iajs-2945 97 6 2 2 NUM iajs-2945 97 7 β„Ž β„Ž NOUN iajs-2945 97 8 , , PUNCT iajs-2945 97 9 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 97 10 + + NUM iajs-2945 97 11 1 1 NUM iajs-2945 97 12 2 2 NUM iajs-2945 97 13 β„Ž β„Ž PROPN iajs-2945 97 14 βˆ— βˆ— NOUN iajs-2945 97 15 𝑙𝑆1 𝑙𝑆1 PROPN iajs-2945 97 16 , , PUNCT iajs-2945 98 1 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 98 2 + + NOUN iajs-2945 98 3 1 1 NUM iajs-2945 98 4 2 2 NUM iajs-2945 98 5 β„Ž β„Ž PROPN iajs-2945 98 6 βˆ— βˆ— NOUN iajs-2945 98 7 𝑙𝑉1 𝑙𝑉1 PROPN iajs-2945 98 8 , , PUNCT iajs-2945 99 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 99 2 + + NOUN iajs-2945 99 3 1 1 NUM iajs-2945 99 4 2 2 NUM iajs-2945 99 5 β„Ž β„Ž PROPN iajs-2945 99 6 βˆ— βˆ— NOUN iajs-2945 99 7 𝑙𝐴1 𝑙𝐴1 PROPN iajs-2945 99 8 , , PUNCT iajs-2945 99 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 99 10 + + CCONJ iajs-2945 99 11 1 1 NUM iajs-2945 99 12 2 2 NUM iajs-2945 99 13 β„Ž β„Ž PROPN iajs-2945 99 14 βˆ— βˆ— NOUN iajs-2945 99 15 𝑙𝐼1 𝑙𝐼1 PROPN iajs-2945 99 16 , , PUNCT iajs-2945 99 17 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 99 18 + + CCONJ iajs-2945 99 19 1 1 NUM iajs-2945 99 20 2 2 NUM iajs-2945 99 21 β„Ž β„Ž PROPN iajs-2945 99 22 βˆ— βˆ— PROPN iajs-2945 99 23 𝑙𝑅1 𝑙𝑅1 PROPN iajs-2945 99 24 ) ) PUNCT iajs-2945 99 25 , , PUNCT iajs-2945 99 26 ( ( PUNCT iajs-2945 99 27 16 16 NUM iajs-2945 99 28 ) ) PUNCT iajs-2945 99 29 𝑙𝑅2 𝑙𝑅2 NOUN iajs-2945 99 30 = = SYM iajs-2945 99 31 𝑓2 𝑓2 NOUN iajs-2945 99 32 ( ( PUNCT iajs-2945 99 33 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 99 34 1 1 NUM iajs-2945 99 35 2 2 NUM iajs-2945 99 36 β„Ž β„Ž NOUN iajs-2945 99 37 , , PUNCT iajs-2945 99 38 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 99 39 + + NUM iajs-2945 99 40 1 1 NUM iajs-2945 99 41 2 2 NUM iajs-2945 99 42 β„Ž β„Ž PROPN iajs-2945 99 43 βˆ— βˆ— NOUN iajs-2945 99 44 𝑙𝑆1 𝑙𝑆1 PROPN iajs-2945 99 45 , , PUNCT iajs-2945 100 1 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 100 2 + + NOUN iajs-2945 100 3 1 1 NUM iajs-2945 100 4 2 2 NUM iajs-2945 100 5 β„Ž β„Ž PROPN iajs-2945 100 6 βˆ— βˆ— NOUN iajs-2945 100 7 𝑙𝑉1 𝑙𝑉1 PROPN iajs-2945 100 8 , , PUNCT iajs-2945 101 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 101 2 + + NOUN iajs-2945 101 3 1 1 NUM iajs-2945 101 4 2 2 NUM iajs-2945 101 5 β„Ž β„Ž PROPN iajs-2945 101 6 βˆ— βˆ— NOUN iajs-2945 101 7 𝑙𝐴1 𝑙𝐴1 PROPN iajs-2945 101 8 , , PUNCT iajs-2945 101 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 101 10 + + CCONJ iajs-2945 101 11 1 1 NUM iajs-2945 101 12 2 2 NUM iajs-2945 101 13 β„Ž β„Ž PROPN iajs-2945 101 14 βˆ— βˆ— NOUN iajs-2945 101 15 𝑙𝐼1 𝑙𝐼1 PROPN iajs-2945 101 16 , , PUNCT iajs-2945 101 17 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 101 18 + + CCONJ iajs-2945 101 19 1 1 NUM iajs-2945 101 20 2 2 NUM iajs-2945 101 21 β„Ž β„Ž PROPN iajs-2945 101 22 βˆ— βˆ— NOUN iajs-2945 101 23 𝑙𝑅1 𝑙𝑅1 PROPN iajs-2945 101 24 ) ) PUNCT iajs-2945 101 25 . . PUNCT iajs-2945 102 1 for for ADP iajs-2945 102 2 all all DET iajs-2945 102 3 𝑖 𝑖 NOUN iajs-2945 102 4 = = SYM iajs-2945 102 5 0,1 0,1 NUM iajs-2945 102 6 , , PUNCT iajs-2945 102 7 … … PUNCT iajs-2945 102 8 , , PUNCT iajs-2945 102 9 π‘š. π‘š. ADJ iajs-2945 102 10 ( ( PUNCT iajs-2945 102 11 17 17 NUM iajs-2945 102 12 ) ) PUNCT iajs-2945 102 13 to to PART iajs-2945 102 14 get get VERB iajs-2945 102 15 the the DET iajs-2945 102 16 third third ADJ iajs-2945 102 17 iteration iteration NOUN iajs-2945 102 18 , , PUNCT iajs-2945 102 19 𝑙𝑆3 𝑙𝑆3 PROPN iajs-2945 102 20 , , PUNCT iajs-2945 102 21 𝑙𝑉3 𝑙𝑉3 VERB iajs-2945 102 22 , , PUNCT iajs-2945 102 23 𝑙𝐴3 𝑙𝐴3 PROPN iajs-2945 102 24 , , PUNCT iajs-2945 102 25 𝑙𝐼3 𝑙𝐼3 PROPN iajs-2945 102 26 and and CCONJ iajs-2945 102 27 𝑙𝑅3 𝑙𝑅3 PROPN iajs-2945 102 28 , , PUNCT iajs-2945 102 29 follow follow VERB iajs-2945 102 30 the the DET iajs-2945 102 31 same same ADJ iajs-2945 102 32 way way NOUN iajs-2945 102 33 : : PUNCT iajs-2945 102 34 𝑙𝑆3 𝑙𝑆3 NOUN iajs-2945 102 35 = = SYM iajs-2945 102 36 𝑓3 𝑓3 PROPN iajs-2945 102 37 ( ( PUNCT iajs-2945 102 38 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 102 39 1 1 NUM iajs-2945 102 40 2 2 NUM iajs-2945 102 41 β„Ž β„Ž NOUN iajs-2945 102 42 , , PUNCT iajs-2945 102 43 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 102 44 + + NUM iajs-2945 102 45 1 1 NUM iajs-2945 102 46 2 2 NUM iajs-2945 102 47 β„Ž β„Ž ADP iajs-2945 102 48 βˆ— βˆ— NOUN iajs-2945 102 49 𝑙𝑆2 𝑙𝑆2 PROPN iajs-2945 102 50 , , PUNCT iajs-2945 102 51 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 102 52 + + NOUN iajs-2945 102 53 1 1 NUM iajs-2945 102 54 2 2 NUM iajs-2945 102 55 β„Ž β„Ž ADP iajs-2945 102 56 βˆ— βˆ— NOUN iajs-2945 102 57 𝑙𝑉2 𝑙𝑉2 PROPN iajs-2945 102 58 , , PUNCT iajs-2945 102 59 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 102 60 + + NOUN iajs-2945 102 61 1 1 NUM iajs-2945 102 62 2 2 NUM iajs-2945 102 63 β„Ž β„Ž PROPN iajs-2945 102 64 βˆ— βˆ— NOUN iajs-2945 102 65 𝑙𝐴2 𝑙𝐴2 NOUN iajs-2945 102 66 , , PUNCT iajs-2945 103 1 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 103 2 + + CCONJ iajs-2945 103 3 1 1 NUM iajs-2945 103 4 2 2 NUM iajs-2945 103 5 β„Ž β„Ž PROPN iajs-2945 103 6 βˆ— βˆ— NOUN iajs-2945 103 7 𝑙𝐼2 𝑙𝐼2 PROPN iajs-2945 103 8 , , PUNCT iajs-2945 104 1 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 104 2 + + CCONJ iajs-2945 104 3 1 1 NUM iajs-2945 104 4 2 2 NUM iajs-2945 104 5 β„Ž β„Ž PROPN iajs-2945 104 6 βˆ— βˆ— NOUN iajs-2945 104 7 𝑙𝑅2 𝑙𝑅2 PROPN iajs-2945 104 8 ) ) PUNCT iajs-2945 104 9 , , PUNCT iajs-2945 104 10 ( ( PUNCT iajs-2945 104 11 18 18 NUM iajs-2945 104 12 ) ) PUNCT iajs-2945 104 13 𝑙𝑉3 𝑙𝑉3 PROPN iajs-2945 104 14 = = SYM iajs-2945 104 15 𝑓3 𝑓3 PROPN iajs-2945 104 16 ( ( PUNCT iajs-2945 104 17 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 104 18 1 1 NUM iajs-2945 104 19 2 2 NUM iajs-2945 104 20 β„Ž β„Ž NOUN iajs-2945 104 21 , , PUNCT iajs-2945 104 22 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 104 23 + + NUM iajs-2945 104 24 1 1 NUM iajs-2945 104 25 2 2 NUM iajs-2945 104 26 β„Ž β„Ž ADP iajs-2945 104 27 βˆ— βˆ— NOUN iajs-2945 104 28 𝑙𝑆2 𝑙𝑆2 PROPN iajs-2945 104 29 , , PUNCT iajs-2945 104 30 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 104 31 + + NOUN iajs-2945 104 32 1 1 NUM iajs-2945 104 33 2 2 NUM iajs-2945 104 34 β„Ž β„Ž ADP iajs-2945 104 35 βˆ— βˆ— NOUN iajs-2945 104 36 𝑙𝑉2 𝑙𝑉2 PROPN iajs-2945 104 37 , , PUNCT iajs-2945 105 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 105 2 + + NOUN iajs-2945 105 3 1 1 NUM iajs-2945 105 4 2 2 NUM iajs-2945 105 5 β„Ž β„Ž PROPN iajs-2945 105 6 βˆ— βˆ— NOUN iajs-2945 105 7 𝑙𝐴2 𝑙𝐴2 NOUN iajs-2945 105 8 , , PUNCT iajs-2945 105 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 105 10 + + CCONJ iajs-2945 106 1 1 1 NUM iajs-2945 106 2 2 2 NUM iajs-2945 106 3 β„Ž β„Ž PROPN iajs-2945 106 4 βˆ— βˆ— NOUN iajs-2945 106 5 𝑙𝐼2 𝑙𝐼2 PROPN iajs-2945 106 6 , , PUNCT iajs-2945 106 7 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 106 8 + + CCONJ iajs-2945 106 9 1 1 NUM iajs-2945 106 10 2 2 NUM iajs-2945 106 11 β„Ž β„Ž PROPN iajs-2945 106 12 βˆ— βˆ— NOUN iajs-2945 106 13 𝑙𝑅2 𝑙𝑅2 PROPN iajs-2945 106 14 ) ) PUNCT iajs-2945 106 15 , , PUNCT iajs-2945 106 16 ( ( PUNCT iajs-2945 106 17 19 19 NUM iajs-2945 106 18 ) ) PUNCT iajs-2945 106 19 𝑙𝐴3 𝑙𝐴3 PROPN iajs-2945 106 20 = = SYM iajs-2945 106 21 𝑓3 𝑓3 PROPN iajs-2945 106 22 ( ( PUNCT iajs-2945 106 23 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 106 24 1 1 NUM iajs-2945 106 25 2 2 NUM iajs-2945 106 26 β„Ž β„Ž NOUN iajs-2945 106 27 , , PUNCT iajs-2945 106 28 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 106 29 + + NUM iajs-2945 106 30 1 1 NUM iajs-2945 106 31 2 2 NUM iajs-2945 106 32 β„Ž β„Ž ADP iajs-2945 106 33 βˆ— βˆ— NOUN iajs-2945 106 34 𝑙𝑆2 𝑙𝑆2 PROPN iajs-2945 106 35 , , PUNCT iajs-2945 106 36 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 106 37 + + NOUN iajs-2945 106 38 1 1 NUM iajs-2945 106 39 2 2 NUM iajs-2945 106 40 β„Ž β„Ž ADP iajs-2945 106 41 βˆ— βˆ— NOUN iajs-2945 106 42 𝑙𝑉2 𝑙𝑉2 PROPN iajs-2945 106 43 , , PUNCT iajs-2945 107 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 107 2 + + NOUN iajs-2945 107 3 1 1 NUM iajs-2945 107 4 2 2 NUM iajs-2945 107 5 β„Ž β„Ž PROPN iajs-2945 107 6 βˆ— βˆ— NOUN iajs-2945 107 7 𝑙𝐴2 𝑙𝐴2 NOUN iajs-2945 107 8 , , PUNCT iajs-2945 107 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 107 10 + + CCONJ iajs-2945 108 1 1 1 NUM iajs-2945 108 2 2 2 NUM iajs-2945 108 3 β„Ž β„Ž PROPN iajs-2945 108 4 βˆ— βˆ— NOUN iajs-2945 108 5 𝑙𝐼2 𝑙𝐼2 PROPN iajs-2945 108 6 , , PUNCT iajs-2945 108 7 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 108 8 + + CCONJ iajs-2945 108 9 1 1 NUM iajs-2945 108 10 2 2 NUM iajs-2945 108 11 β„Ž β„Ž PROPN iajs-2945 108 12 βˆ— βˆ— NOUN iajs-2945 108 13 𝑙𝑅2 𝑙𝑅2 PROPN iajs-2945 108 14 ) ) PUNCT iajs-2945 108 15 , , PUNCT iajs-2945 108 16 ( ( PUNCT iajs-2945 108 17 20 20 NUM iajs-2945 108 18 ) ) PUNCT iajs-2945 108 19 𝑙𝐼3 𝑙𝐼3 PROPN iajs-2945 108 20 = = SYM iajs-2945 108 21 𝑓3 𝑓3 PROPN iajs-2945 108 22 ( ( PUNCT iajs-2945 108 23 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 108 24 1 1 NUM iajs-2945 108 25 2 2 NUM iajs-2945 108 26 β„Ž β„Ž NOUN iajs-2945 108 27 , , PUNCT iajs-2945 108 28 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 108 29 + + NUM iajs-2945 108 30 1 1 NUM iajs-2945 108 31 2 2 NUM iajs-2945 108 32 β„Ž β„Ž ADP iajs-2945 108 33 βˆ— βˆ— NOUN iajs-2945 108 34 𝑙𝑆2 𝑙𝑆2 PROPN iajs-2945 108 35 , , PUNCT iajs-2945 108 36 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 108 37 + + NOUN iajs-2945 108 38 1 1 NUM iajs-2945 108 39 2 2 NUM iajs-2945 108 40 β„Ž β„Ž ADP iajs-2945 108 41 βˆ— βˆ— NOUN iajs-2945 108 42 𝑙𝑉2 𝑙𝑉2 PROPN iajs-2945 108 43 , , PUNCT iajs-2945 109 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 109 2 + + NOUN iajs-2945 109 3 1 1 NUM iajs-2945 109 4 2 2 NUM iajs-2945 109 5 β„Ž β„Ž PROPN iajs-2945 109 6 βˆ— βˆ— NOUN iajs-2945 109 7 𝑙𝐴2 𝑙𝐴2 NOUN iajs-2945 109 8 , , PUNCT iajs-2945 109 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 109 10 + + CCONJ iajs-2945 110 1 1 1 NUM iajs-2945 110 2 2 2 NUM iajs-2945 110 3 β„Ž β„Ž PROPN iajs-2945 110 4 βˆ— βˆ— NOUN iajs-2945 110 5 𝑙𝐼2 𝑙𝐼2 PROPN iajs-2945 110 6 , , PUNCT iajs-2945 110 7 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 110 8 + + CCONJ iajs-2945 110 9 1 1 NUM iajs-2945 110 10 2 2 NUM iajs-2945 110 11 β„Ž β„Ž PROPN iajs-2945 110 12 βˆ— βˆ— NOUN iajs-2945 110 13 𝑙𝑅2 𝑙𝑅2 PROPN iajs-2945 110 14 ) ) PUNCT iajs-2945 110 15 , , PUNCT iajs-2945 110 16 ( ( PUNCT iajs-2945 110 17 21 21 NUM iajs-2945 110 18 ) ) PUNCT iajs-2945 110 19 𝑙𝑅3 𝑙𝑅3 PROPN iajs-2945 110 20 = = SYM iajs-2945 110 21 𝑓3 𝑓3 PROPN iajs-2945 110 22 ( ( PUNCT iajs-2945 110 23 𝑑𝑖 𝑑𝑖 NOUN iajs-2945 110 24 1 1 NUM iajs-2945 110 25 2 2 NUM iajs-2945 110 26 β„Ž β„Ž NOUN iajs-2945 110 27 , , PUNCT iajs-2945 110 28 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 110 29 + + NUM iajs-2945 110 30 1 1 NUM iajs-2945 110 31 2 2 NUM iajs-2945 110 32 β„Ž β„Ž ADP iajs-2945 110 33 βˆ— βˆ— NOUN iajs-2945 110 34 𝑙𝑆2 𝑙𝑆2 PROPN iajs-2945 110 35 , , PUNCT iajs-2945 110 36 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 110 37 + + NOUN iajs-2945 110 38 1 1 NUM iajs-2945 110 39 2 2 NUM iajs-2945 110 40 β„Ž β„Ž ADP iajs-2945 110 41 βˆ— βˆ— NOUN iajs-2945 110 42 𝑙𝑉2 𝑙𝑉2 PROPN iajs-2945 110 43 , , PUNCT iajs-2945 111 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 111 2 + + NOUN iajs-2945 111 3 1 1 NUM iajs-2945 111 4 2 2 NUM iajs-2945 111 5 β„Ž β„Ž PROPN iajs-2945 111 6 βˆ— βˆ— NOUN iajs-2945 111 7 𝑙𝐴2 𝑙𝐴2 NOUN iajs-2945 111 8 , , PUNCT iajs-2945 111 9 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 111 10 + + CCONJ iajs-2945 112 1 1 1 NUM iajs-2945 112 2 2 2 NUM iajs-2945 112 3 β„Ž β„Ž PROPN iajs-2945 112 4 βˆ— βˆ— NOUN iajs-2945 112 5 𝑙𝐼2 𝑙𝐼2 PROPN iajs-2945 112 6 , , PUNCT iajs-2945 112 7 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 112 8 + + CCONJ iajs-2945 112 9 1 1 NUM iajs-2945 112 10 2 2 NUM iajs-2945 112 11 β„Ž β„Ž PROPN iajs-2945 112 12 βˆ— βˆ— NOUN iajs-2945 112 13 𝑙𝑅2 𝑙𝑅2 NOUN iajs-2945 112 14 ) ) PUNCT iajs-2945 112 15 . . PUNCT iajs-2945 113 1 for for ADP iajs-2945 113 2 all all DET iajs-2945 113 3 𝑖 𝑖 NOUN iajs-2945 113 4 = = SYM iajs-2945 113 5 0,1 0,1 NUM iajs-2945 113 6 , , PUNCT iajs-2945 113 7 … … PUNCT iajs-2945 113 8 , , PUNCT iajs-2945 113 9 π‘š. π‘š. ADJ iajs-2945 113 10 ( ( PUNCT iajs-2945 113 11 22 22 NUM iajs-2945 113 12 ) ) PUNCT iajs-2945 113 13 to to PART iajs-2945 113 14 obtain obtain VERB iajs-2945 113 15 the the DET iajs-2945 113 16 fourth fourth ADJ iajs-2945 113 17 iteration iteration NOUN iajs-2945 113 18 , , PUNCT iajs-2945 113 19 𝑙𝑆4 𝑙𝑆4 PROPN iajs-2945 113 20 , , PUNCT iajs-2945 113 21 𝑙𝑉4 𝑙𝑉4 PROPN iajs-2945 113 22 , , PUNCT iajs-2945 113 23 𝑙𝐴4 𝑙𝐴4 PROPN iajs-2945 113 24 , , PUNCT iajs-2945 113 25 𝑙𝐼4 𝑙𝐼4 PROPN iajs-2945 113 26 and and CCONJ iajs-2945 113 27 𝑙𝑅4 𝑙𝑅4 PROPN iajs-2945 113 28 , , PUNCT iajs-2945 113 29 follow follow VERB iajs-2945 113 30 this this PRON iajs-2945 113 31 : : PUNCT iajs-2945 113 32 𝑙𝑆4 𝑙𝑆4 PROPN iajs-2945 113 33 = = SYM iajs-2945 113 34 𝑓4(𝑑𝑖 𝑓4(𝑑𝑖 PROPN iajs-2945 113 35 + + NUM iajs-2945 113 36 β„Ž β„Ž PROPN iajs-2945 113 37 , , PUNCT iajs-2945 113 38 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 113 39 + + NUM iajs-2945 113 40 β„Ž β„Ž PROPN iajs-2945 113 41 βˆ— βˆ— NOUN iajs-2945 113 42 𝑙𝑆3 𝑙𝑆3 NOUN iajs-2945 113 43 , , PUNCT iajs-2945 113 44 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 113 45 + + NUM iajs-2945 113 46 β„Ž β„Ž PROPN iajs-2945 113 47 βˆ— βˆ— NOUN iajs-2945 113 48 𝑙𝑉3 𝑙𝑉3 PROPN iajs-2945 113 49 , , PUNCT iajs-2945 114 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 114 2 + + NOUN iajs-2945 114 3 β„Ž β„Ž NOUN iajs-2945 114 4 βˆ— βˆ— NOUN iajs-2945 114 5 𝑙𝐴3 𝑙𝐴3 PROPN iajs-2945 114 6 , , PUNCT iajs-2945 115 1 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 115 2 + + CCONJ iajs-2945 115 3 β„Ž β„Ž PROPN iajs-2945 115 4 βˆ— βˆ— NOUN iajs-2945 115 5 𝑙𝐼3 𝑙𝐼3 PROPN iajs-2945 115 6 , , PUNCT iajs-2945 115 7 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 115 8 + + CCONJ iajs-2945 115 9 β„Ž β„Ž NOUN iajs-2945 115 10 βˆ— βˆ— NOUN iajs-2945 115 11 𝑙𝑅3 𝑙𝑅3 NUM iajs-2945 115 12 ) ) PUNCT iajs-2945 115 13 , , PUNCT iajs-2945 115 14 ( ( PUNCT iajs-2945 115 15 23 23 NUM iajs-2945 115 16 ) ) PUNCT iajs-2945 115 17 𝑙𝑉4 𝑙𝑉4 NOUN iajs-2945 115 18 = = PUNCT iajs-2945 115 19 𝑓4(𝑑𝑖 𝑓4(𝑑𝑖 PROPN iajs-2945 115 20 + + NUM iajs-2945 115 21 β„Ž β„Ž PROPN iajs-2945 115 22 , , PUNCT iajs-2945 115 23 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 115 24 + + NUM iajs-2945 115 25 β„Ž β„Ž PROPN iajs-2945 115 26 βˆ— βˆ— NOUN iajs-2945 115 27 𝑙𝑆3 𝑙𝑆3 NOUN iajs-2945 115 28 , , PUNCT iajs-2945 116 1 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 116 2 + + NUM iajs-2945 116 3 β„Ž β„Ž PROPN iajs-2945 116 4 βˆ— βˆ— NOUN iajs-2945 116 5 𝑙𝑉3 𝑙𝑉3 PROPN iajs-2945 116 6 , , PUNCT iajs-2945 116 7 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 116 8 + + NOUN iajs-2945 116 9 β„Ž β„Ž NOUN iajs-2945 116 10 βˆ— βˆ— NOUN iajs-2945 116 11 𝑙𝐴3 𝑙𝐴3 PROPN iajs-2945 116 12 , , PUNCT iajs-2945 116 13 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 116 14 + + CCONJ iajs-2945 116 15 β„Ž β„Ž PROPN iajs-2945 116 16 βˆ— βˆ— NOUN iajs-2945 116 17 𝑙𝐼3 𝑙𝐼3 PROPN iajs-2945 116 18 , , PUNCT iajs-2945 116 19 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 116 20 + + CCONJ iajs-2945 116 21 β„Ž β„Ž NOUN iajs-2945 116 22 βˆ— βˆ— NOUN iajs-2945 116 23 𝑙𝑅3 𝑙𝑅3 NUM iajs-2945 116 24 ) ) PUNCT iajs-2945 116 25 , , PUNCT iajs-2945 116 26 ( ( PUNCT iajs-2945 116 27 24 24 NUM iajs-2945 116 28 ) ) PUNCT iajs-2945 116 29 𝑙𝐴4 𝑙𝐴4 PROPN iajs-2945 116 30 = = SYM iajs-2945 116 31 𝑓4(𝑑𝑖 𝑓4(𝑑𝑖 PROPN iajs-2945 116 32 + + NUM iajs-2945 116 33 β„Ž β„Ž PROPN iajs-2945 116 34 , , PUNCT iajs-2945 116 35 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 116 36 + + NUM iajs-2945 116 37 β„Ž β„Ž PROPN iajs-2945 116 38 βˆ— βˆ— NOUN iajs-2945 116 39 𝑙𝑆3 𝑙𝑆3 NOUN iajs-2945 116 40 , , PUNCT iajs-2945 116 41 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 116 42 + + NUM iajs-2945 116 43 β„Ž β„Ž PROPN iajs-2945 116 44 βˆ— βˆ— NOUN iajs-2945 116 45 𝑙𝑉3 𝑙𝑉3 PROPN iajs-2945 116 46 , , PUNCT iajs-2945 117 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 117 2 + + NOUN iajs-2945 117 3 β„Ž β„Ž NOUN iajs-2945 117 4 βˆ— βˆ— NOUN iajs-2945 117 5 𝑙𝐴3 𝑙𝐴3 PROPN iajs-2945 117 6 , , PUNCT iajs-2945 118 1 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 118 2 + + CCONJ iajs-2945 118 3 β„Ž β„Ž PROPN iajs-2945 118 4 βˆ— βˆ— NOUN iajs-2945 118 5 𝑙𝐼3 𝑙𝐼3 PROPN iajs-2945 118 6 , , PUNCT iajs-2945 118 7 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 118 8 + + CCONJ iajs-2945 118 9 β„Ž β„Ž NOUN iajs-2945 118 10 βˆ— βˆ— NOUN iajs-2945 118 11 𝑙𝑅3 𝑙𝑅3 NUM iajs-2945 118 12 ) ) PUNCT iajs-2945 118 13 , , PUNCT iajs-2945 118 14 ( ( PUNCT iajs-2945 118 15 25 25 NUM iajs-2945 118 16 ) ) PUNCT iajs-2945 118 17 𝑙𝐼4 𝑙𝐼4 NOUN iajs-2945 118 18 = = SYM iajs-2945 118 19 𝑓4(𝑑𝑖 𝑓4(𝑑𝑖 PROPN iajs-2945 118 20 + + NUM iajs-2945 118 21 β„Ž β„Ž PROPN iajs-2945 118 22 , , PUNCT iajs-2945 118 23 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 118 24 + + NUM iajs-2945 118 25 β„Ž β„Ž PROPN iajs-2945 118 26 βˆ— βˆ— NOUN iajs-2945 118 27 𝑙𝑆3 𝑙𝑆3 NOUN iajs-2945 118 28 , , PUNCT iajs-2945 119 1 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 119 2 + + NUM iajs-2945 119 3 β„Ž β„Ž PROPN iajs-2945 119 4 βˆ— βˆ— NOUN iajs-2945 119 5 𝑙𝑉3 𝑙𝑉3 PROPN iajs-2945 119 6 , , PUNCT iajs-2945 119 7 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 119 8 + + NOUN iajs-2945 119 9 β„Ž β„Ž NOUN iajs-2945 119 10 βˆ— βˆ— NOUN iajs-2945 119 11 𝑙𝐴3 𝑙𝐴3 PROPN iajs-2945 119 12 , , PUNCT iajs-2945 119 13 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 119 14 + + CCONJ iajs-2945 119 15 β„Ž β„Ž PROPN iajs-2945 119 16 βˆ— βˆ— NOUN iajs-2945 119 17 𝑙𝐼3 𝑙𝐼3 PROPN iajs-2945 119 18 , , PUNCT iajs-2945 119 19 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 119 20 + + CCONJ iajs-2945 119 21 β„Ž β„Ž NOUN iajs-2945 119 22 βˆ— βˆ— NOUN iajs-2945 119 23 𝑙𝑅3 𝑙𝑅3 NUM iajs-2945 119 24 ) ) PUNCT iajs-2945 119 25 , , PUNCT iajs-2945 119 26 ( ( PUNCT iajs-2945 119 27 26 26 NUM iajs-2945 119 28 ) ) PUNCT iajs-2945 119 29 𝑙𝑅4 𝑙𝑅4 PROPN iajs-2945 119 30 = = SYM iajs-2945 119 31 𝑓4(𝑑𝑖 𝑓4(𝑑𝑖 PROPN iajs-2945 119 32 + + NUM iajs-2945 119 33 β„Ž β„Ž PROPN iajs-2945 119 34 , , PUNCT iajs-2945 119 35 𝑆𝑖 𝑆𝑖 PROPN iajs-2945 119 36 + + NUM iajs-2945 119 37 β„Ž β„Ž PROPN iajs-2945 119 38 βˆ— βˆ— NOUN iajs-2945 119 39 𝑙𝑆3 𝑙𝑆3 NOUN iajs-2945 119 40 , , PUNCT iajs-2945 119 41 𝑉𝑖 𝑉𝑖 PROPN iajs-2945 119 42 + + NUM iajs-2945 119 43 β„Ž β„Ž PROPN iajs-2945 119 44 βˆ— βˆ— NOUN iajs-2945 119 45 𝑙𝑉3 𝑙𝑉3 PROPN iajs-2945 119 46 , , PUNCT iajs-2945 120 1 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 120 2 + + NOUN iajs-2945 120 3 β„Ž β„Ž NOUN iajs-2945 120 4 βˆ— βˆ— NOUN iajs-2945 120 5 𝑙𝐴3 𝑙𝐴3 PROPN iajs-2945 120 6 , , PUNCT iajs-2945 121 1 𝐼𝑖 𝐼𝑖 PROPN iajs-2945 121 2 + + CCONJ iajs-2945 121 3 β„Ž β„Ž PROPN iajs-2945 121 4 βˆ— βˆ— NOUN iajs-2945 121 5 𝑙𝐼3 𝑙𝐼3 PROPN iajs-2945 121 6 , , PUNCT iajs-2945 121 7 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 121 8 + + CCONJ iajs-2945 121 9 β„Ž β„Ž NOUN iajs-2945 121 10 βˆ— βˆ— NOUN iajs-2945 121 11 𝑙𝑅3 𝑙𝑅3 NUM iajs-2945 121 12 ) ) PUNCT iajs-2945 121 13 . . PUNCT iajs-2945 122 1 ( ( PUNCT iajs-2945 122 2 27 27 NUM iajs-2945 122 3 ) ) PUNCT iajs-2945 122 4 for for ADP iajs-2945 122 5 all all DET iajs-2945 122 6 𝑖 𝑖 NOUN iajs-2945 122 7 = = SYM iajs-2945 122 8 0,1 0,1 NUM iajs-2945 122 9 , , PUNCT iajs-2945 122 10 … … PUNCT iajs-2945 122 11 , , PUNCT iajs-2945 122 12 π‘š. π‘š. ADV iajs-2945 122 13 we we PRON iajs-2945 122 14 substitute substitute VERB iajs-2945 122 15 eqs eqs PROPN iajs-2945 122 16 . . PUNCT iajs-2945 123 1 ( ( PUNCT iajs-2945 123 2 8) 8) NUM iajs-2945 123 3 , , PUNCT iajs-2945 123 4 ( ( PUNCT iajs-2945 123 5 13 13 NUM iajs-2945 123 6 ) ) PUNCT iajs-2945 123 7 , , PUNCT iajs-2945 123 8 ( ( PUNCT iajs-2945 123 9 18 18 NUM iajs-2945 123 10 ) ) PUNCT iajs-2945 123 11 and and CCONJ iajs-2945 123 12 ( ( PUNCT iajs-2945 123 13 23 23 NUM iajs-2945 123 14 ) ) PUNCT iajs-2945 123 15 into into ADP iajs-2945 123 16 eq eq NOUN iajs-2945 123 17 . . PUNCT iajs-2945 124 1 ( ( PUNCT iajs-2945 124 2 3 3 X iajs-2945 124 3 ) ) PUNCT iajs-2945 124 4 to to PART iajs-2945 124 5 find find VERB iajs-2945 124 6 the the DET iajs-2945 124 7 numerical numerical ADJ iajs-2945 124 8 solutions solution NOUN iajs-2945 124 9 of of ADP iajs-2945 124 10 𝑆𝑖. 𝑆𝑖. PROPN iajs-2945 124 11 also also ADV iajs-2945 124 12 , , PUNCT iajs-2945 124 13 we we PRON iajs-2945 124 14 put put VERB iajs-2945 124 15 eqs eqs PROPN iajs-2945 124 16 . . PUNCT iajs-2945 125 1 ( ( PUNCT iajs-2945 125 2 9 9 NUM iajs-2945 125 3 ) ) PUNCT iajs-2945 125 4 , , PUNCT iajs-2945 125 5 ( ( PUNCT iajs-2945 125 6 14 14 NUM iajs-2945 125 7 ) ) PUNCT iajs-2945 125 8 , , PUNCT iajs-2945 125 9 ( ( PUNCT iajs-2945 125 10 19 19 NUM iajs-2945 125 11 ) ) PUNCT iajs-2945 125 12 and and CCONJ iajs-2945 125 13 ( ( PUNCT iajs-2945 125 14 24 24 NUM iajs-2945 125 15 ) ) PUNCT iajs-2945 125 16 into into ADP iajs-2945 125 17 eq eq NOUN iajs-2945 125 18 . . PUNCT iajs-2945 126 1 ( ( PUNCT iajs-2945 126 2 4 4 NUM iajs-2945 126 3 ) ) PUNCT iajs-2945 126 4 to to PART iajs-2945 126 5 achieve achieve VERB iajs-2945 126 6 the the DET iajs-2945 126 7 numerical numerical ADJ iajs-2945 126 8 solutions solution NOUN iajs-2945 126 9 of of ADP iajs-2945 126 10 𝑉𝑖. 𝑉𝑖. PROPN iajs-2945 126 11 in in ADP iajs-2945 126 12 the the DET iajs-2945 126 13 same same ADJ iajs-2945 126 14 manner manner NOUN iajs-2945 126 15 , , PUNCT iajs-2945 126 16 we we PRON iajs-2945 126 17 substitute substitute PROPN iajs-2945 126 18 eqs eqs PROPN iajs-2945 126 19 . . PUNCT iajs-2945 127 1 ( ( PUNCT iajs-2945 127 2 10 10 NUM iajs-2945 127 3 ) ) PUNCT iajs-2945 127 4 , , PUNCT iajs-2945 127 5 ( ( PUNCT iajs-2945 127 6 15 15 NUM iajs-2945 127 7 ) ) PUNCT iajs-2945 127 8 , , PUNCT iajs-2945 127 9 ( ( PUNCT iajs-2945 127 10 20 20 NUM iajs-2945 127 11 ) ) PUNCT iajs-2945 127 12 and and CCONJ iajs-2945 127 13 ( ( PUNCT iajs-2945 127 14 25 25 NUM iajs-2945 127 15 ) ) PUNCT iajs-2945 127 16 into into ADP iajs-2945 127 17 eq eq NOUN iajs-2945 127 18 . . PUNCT iajs-2945 128 1 ( ( PUNCT iajs-2945 128 2 5 5 NUM iajs-2945 128 3 ) ) PUNCT iajs-2945 128 4 to to PART iajs-2945 128 5 obtain obtain VERB iajs-2945 128 6 the the DET iajs-2945 128 7 numerical numerical ADJ iajs-2945 128 8 solutions solution NOUN iajs-2945 128 9 of of ADP iajs-2945 128 10 𝐴𝑖 𝐴𝑖 PROPN iajs-2945 128 11 and and CCONJ iajs-2945 128 12 substite substite PROPN iajs-2945 128 13 eqs eqs PROPN iajs-2945 128 14 . . PUNCT iajs-2945 129 1 ( ( PUNCT iajs-2945 129 2 11 11 NUM iajs-2945 129 3 ) ) PUNCT iajs-2945 129 4 , , PUNCT iajs-2945 129 5 ( ( PUNCT iajs-2945 129 6 16 16 NUM iajs-2945 129 7 ) ) PUNCT iajs-2945 129 8 , , PUNCT iajs-2945 129 9 ( ( PUNCT iajs-2945 129 10 21 21 NUM iajs-2945 129 11 ) ) PUNCT iajs-2945 129 12 and and CCONJ iajs-2945 129 13 ( ( PUNCT iajs-2945 129 14 26 26 NUM iajs-2945 129 15 ) ) PUNCT iajs-2945 129 16 into into ADP iajs-2945 129 17 eq eq NOUN iajs-2945 129 18 . . PUNCT iajs-2945 130 1 ( ( PUNCT iajs-2945 130 2 6 6 NUM iajs-2945 130 3 ) ) PUNCT iajs-2945 130 4 to to PART iajs-2945 130 5 find find VERB iajs-2945 130 6 the the DET iajs-2945 130 7 numerical numerical ADJ iajs-2945 130 8 solutions solution NOUN iajs-2945 130 9 of of ADP iajs-2945 130 10 𝐼𝑖. 𝐼𝑖. PROPN iajs-2945 130 11 finally finally ADV iajs-2945 130 12 , , PUNCT iajs-2945 130 13 we we PRON iajs-2945 130 14 substitute substitute PROPN iajs-2945 130 15 eqs eqs PROPN iajs-2945 130 16 . . PUNCT iajs-2945 131 1 ( ( PUNCT iajs-2945 131 2 12 12 NUM iajs-2945 131 3 ) ) PUNCT iajs-2945 131 4 , , PUNCT iajs-2945 131 5 ( ( PUNCT iajs-2945 131 6 17 17 NUM iajs-2945 131 7 ) ) PUNCT iajs-2945 131 8 , , PUNCT iajs-2945 131 9 ( ( PUNCT iajs-2945 131 10 22 22 NUM iajs-2945 131 11 ) ) PUNCT iajs-2945 131 12 and and CCONJ iajs-2945 131 13 ( ( PUNCT iajs-2945 131 14 27 27 NUM iajs-2945 131 15 ) ) PUNCT iajs-2945 131 16 into into ADP iajs-2945 131 17 eq eq NOUN iajs-2945 131 18 . . PUNCT iajs-2945 132 1 ( ( PUNCT iajs-2945 132 2 7 7 NUM iajs-2945 132 3 ) ) PUNCT iajs-2945 132 4 to to PART iajs-2945 132 5 get get VERB iajs-2945 132 6 the the DET iajs-2945 132 7 numerical numerical ADJ iajs-2945 132 8 solutions solution NOUN iajs-2945 132 9 of of ADP iajs-2945 132 10 𝑅𝑖 𝑅𝑖 PROPN iajs-2945 132 11 , , PUNCT iajs-2945 132 12 for for ADP iajs-2945 132 13 all all PRON iajs-2945 132 14 𝑖 𝑖 NOUN iajs-2945 132 15 = = SYM iajs-2945 132 16 0,1 0,1 NUM iajs-2945 132 17 , , PUNCT iajs-2945 132 18 … … PUNCT iajs-2945 132 19 , , PUNCT iajs-2945 132 20 π‘š. π‘š. PROPN iajs-2945 132 21 ihjpas ihjpas PROPN iajs-2945 132 22 . . PUNCT iajs-2945 133 1 36(3)2023 36(3)2023 NUM iajs-2945 133 2 294 294 NUM iajs-2945 133 3 4 4 NUM iajs-2945 133 4 . . PUNCT iajs-2945 133 5 numerical numerical PROPN iajs-2945 133 6 simulation simulation PROPN iajs-2945 133 7 methods method NOUN iajs-2945 133 8 for for ADP iajs-2945 133 9 solving solve VERB iajs-2945 133 10 covid-19 covid-19 PROPN iajs-2945 133 11 model model NOUN iajs-2945 133 12 4.1 4.1 NUM iajs-2945 133 13 mean mean NOUN iajs-2945 133 14 monte monte PROPN iajs-2945 133 15 carlo carlo PROPN iajs-2945 133 16 range range PROPN iajs-2945 133 17 - - PUNCT iajs-2945 133 18 kutta kutta NOUN iajs-2945 133 19 ( ( PUNCT iajs-2945 133 20 mmc_rk mmc_rk PROPN iajs-2945 133 21 ) ) PUNCT iajs-2945 133 22 mean mean PROPN iajs-2945 133 23 monte monte PROPN iajs-2945 133 24 carlo carlo PROPN iajs-2945 133 25 runge runge PROPN iajs-2945 133 26 - - PUNCT iajs-2945 133 27 kutta kutta NOUN iajs-2945 133 28 ( ( PUNCT iajs-2945 133 29 mmc_rk mmc_rk PROPN iajs-2945 133 30 ) ) PUNCT iajs-2945 133 31 is be AUX iajs-2945 133 32 an an DET iajs-2945 133 33 efficient efficient ADJ iajs-2945 133 34 numerical numerical PROPN iajs-2945 133 35 simulation simulation PROPN iajs-2945 133 36 method method NOUN iajs-2945 133 37 for for ADP iajs-2945 133 38 solving solve VERB iajs-2945 133 39 such such ADJ iajs-2945 133 40 mathematical mathematical ADJ iajs-2945 133 41 models model NOUN iajs-2945 133 42 under under ADP iajs-2945 133 43 study study NOUN iajs-2945 133 44 . . PUNCT iajs-2945 134 1 this this DET iajs-2945 134 2 method method NOUN iajs-2945 134 3 consists consist VERB iajs-2945 134 4 of of ADP iajs-2945 134 5 mixing mix VERB iajs-2945 134 6 two two NUM iajs-2945 134 7 different different ADJ iajs-2945 134 8 methods method NOUN iajs-2945 134 9 , , PUNCT iajs-2945 134 10 one one NUM iajs-2945 134 11 numerical numerical ADJ iajs-2945 134 12 , , PUNCT iajs-2945 134 13 the the DET iajs-2945 134 14 runge runge NOUN iajs-2945 134 15 - - PUNCT iajs-2945 134 16 kutta kutta NOUN iajs-2945 134 17 method method NOUN iajs-2945 134 18 ( ( PUNCT iajs-2945 134 19 rk rk NOUN iajs-2945 134 20 ) ) PUNCT iajs-2945 134 21 , , PUNCT iajs-2945 134 22 with with ADP iajs-2945 134 23 the the DET iajs-2945 134 24 monte monte PROPN iajs-2945 134 25 carlo carlo PROPN iajs-2945 134 26 simulation simulation PROPN iajs-2945 134 27 process process NOUN iajs-2945 134 28 ( ( PUNCT iajs-2945 134 29 mc mc PROPN iajs-2945 134 30 ) ) PUNCT iajs-2945 134 31 . . PUNCT iajs-2945 135 1 mc mc PROPN iajs-2945 135 2 estimates estimate VERB iajs-2945 135 3 the the DET iajs-2945 135 4 model model NOUN iajs-2945 135 5 coefficients coefficient NOUN iajs-2945 135 6 that that PRON iajs-2945 135 7 are be AUX iajs-2945 135 8 random random ADJ iajs-2945 135 9 variables variable NOUN iajs-2945 135 10 , , PUNCT iajs-2945 135 11 while while SCONJ iajs-2945 135 12 rk rk NOUN iajs-2945 135 13 is be AUX iajs-2945 135 14 used use VERB iajs-2945 135 15 to to PART iajs-2945 135 16 solve solve VERB iajs-2945 135 17 the the DET iajs-2945 135 18 model model NOUN iajs-2945 135 19 numerically numerically ADV iajs-2945 135 20 . . PUNCT iajs-2945 136 1 the the DET iajs-2945 136 2 average average NOUN iajs-2945 136 3 of of ADP iajs-2945 136 4 the the DET iajs-2945 136 5 last last ADJ iajs-2945 136 6 rk rk NOUN iajs-2945 136 7 iteration iteration NOUN iajs-2945 136 8 resulting result VERB iajs-2945 136 9 from from ADP iajs-2945 136 10 each each DET iajs-2945 136 11 mc mc PROPN iajs-2945 136 12 repetition repetition NOUN iajs-2945 136 13 is be AUX iajs-2945 136 14 considered consider VERB iajs-2945 136 15 the the DET iajs-2945 136 16 estimated estimate VERB iajs-2945 136 17 approximate approximate ADJ iajs-2945 136 18 solution solution NOUN iajs-2945 136 19 for for ADP iajs-2945 136 20 the the DET iajs-2945 136 21 model model NOUN iajs-2945 136 22 under under ADP iajs-2945 136 23 study study NOUN iajs-2945 136 24 . . PUNCT iajs-2945 137 1 because because SCONJ iajs-2945 137 2 the the DET iajs-2945 137 3 natural natural ADJ iajs-2945 137 4 epidemic epidemic NOUN iajs-2945 137 5 models model NOUN iajs-2945 137 6 have have VERB iajs-2945 137 7 randomness randomness NOUN iajs-2945 137 8 in in ADP iajs-2945 137 9 their their PRON iajs-2945 137 10 coefficients coefficient NOUN iajs-2945 137 11 , , PUNCT iajs-2945 137 12 the the DET iajs-2945 137 13 mmc_rk mmc_rk PROPN iajs-2945 137 14 numerical numerical PROPN iajs-2945 137 15 simulation simulation PROPN iajs-2945 137 16 process process NOUN iajs-2945 137 17 is be AUX iajs-2945 137 18 considered consider VERB iajs-2945 137 19 as as ADP iajs-2945 137 20 more more ADV iajs-2945 137 21 suitable suitable ADJ iajs-2945 137 22 method method NOUN iajs-2945 137 23 than than ADP iajs-2945 137 24 the the DET iajs-2945 137 25 classical classical ADJ iajs-2945 137 26 methods method NOUN iajs-2945 137 27 like like ADP iajs-2945 137 28 rk4 rk4 NOUN iajs-2945 137 29 that that PRON iajs-2945 137 30 solve solve VERB iajs-2945 137 31 models model NOUN iajs-2945 137 32 depending depend VERB iajs-2945 137 33 on on ADP iajs-2945 137 34 fixed fix VERB iajs-2945 137 35 parameters parameter NOUN iajs-2945 137 36 . . PUNCT iajs-2945 138 1 the the DET iajs-2945 138 2 mmc_rk mmc_rk PROPN iajs-2945 138 3 method method NOUN iajs-2945 138 4 is be AUX iajs-2945 138 5 explained explain VERB iajs-2945 138 6 in in ADP iajs-2945 138 7 fig fig NOUN iajs-2945 138 8 1 1 NUM iajs-2945 138 9 and and CCONJ iajs-2945 138 10 implemented implement VERB iajs-2945 138 11 by by ADP iajs-2945 138 12 using use VERB iajs-2945 138 13 matlab matlab PROPN iajs-2945 138 14 software software NOUN iajs-2945 138 15 . . PUNCT iajs-2945 139 1 more more ADJ iajs-2945 139 2 details detail NOUN iajs-2945 139 3 are be AUX iajs-2945 139 4 shown show VERB iajs-2945 139 5 in in ADP iajs-2945 139 6 [ [ X iajs-2945 139 7 19 19 NUM iajs-2945 139 8 ] ] PUNCT iajs-2945 139 9 . . PUNCT iajs-2945 140 1 mmc_rk mmc_rk PROPN iajs-2945 140 2 procedure procedure NOUN iajs-2945 140 3 figure figure NOUN iajs-2945 140 4 1 1 NUM iajs-2945 140 5 : : PUNCT iajs-2945 140 6 steps step NOUN iajs-2945 140 7 of of ADP iajs-2945 140 8 mmc_rk mmc_rk NOUN iajs-2945 140 9 process process NOUN iajs-2945 140 10 , , PUNCT iajs-2945 140 11 [ [ X iajs-2945 140 12 19 19 NUM iajs-2945 140 13 ] ] PUNCT iajs-2945 140 14 . . PUNCT iajs-2945 141 1 step step NOUN iajs-2945 141 2 5 5 NUM iajs-2945 141 3 compute compute NOUN iajs-2945 141 4 the the DET iajs-2945 141 5 mean mean NOUN iajs-2945 141 6 of of ADP iajs-2945 141 7 the the DET iajs-2945 141 8 n n PROPN iajs-2945 141 9 solutions solution NOUN iajs-2945 141 10 in in ADP iajs-2945 141 11 step step NOUN iajs-2945 141 12 4 4 NUM iajs-2945 141 13 ( ( PUNCT iajs-2945 141 14 mmc_rk mmc_rk NOUN iajs-2945 141 15 solutions solution NOUN iajs-2945 141 16 ) ) PUNCT iajs-2945 141 17 step step NOUN iajs-2945 141 18 4 4 NUM iajs-2945 141 19 repeat repeat NOUN iajs-2945 141 20 step step NOUN iajs-2945 141 21 2 2 NUM iajs-2945 141 22 & & CCONJ iajs-2945 141 23 3 3 NUM iajs-2945 141 24 for for ADP iajs-2945 141 25 n n NUM iajs-2945 141 26 times time NOUN iajs-2945 141 27 step step NOUN iajs-2945 141 28 3 3 NUM iajs-2945 141 29 solve solve VERB iajs-2945 141 30 the the DET iajs-2945 141 31 system system NOUN iajs-2945 141 32 using use VERB iajs-2945 141 33 rk4 rk4 NOUN iajs-2945 141 34 method method NOUN iajs-2945 141 35 with with ADP iajs-2945 141 36 m m PROPN iajs-2945 141 37 iterations iteration NOUN iajs-2945 141 38 and and CCONJ iajs-2945 141 39 the the DET iajs-2945 141 40 last last ADJ iajs-2945 141 41 iteration iteration NOUN iajs-2945 141 42 becomes become VERB iajs-2945 141 43 the the DET iajs-2945 141 44 final final ADJ iajs-2945 141 45 rk4 rk4 NOUN iajs-2945 141 46 solution solution NOUN iajs-2945 141 47 step step NOUN iajs-2945 141 48 2 2 NUM iajs-2945 141 49 select select VERB iajs-2945 141 50 randomly randomly ADV iajs-2945 141 51 one one NUM iajs-2945 141 52 value value NOUN iajs-2945 141 53 of of ADP iajs-2945 141 54 each each DET iajs-2945 141 55 parameter parameter NOUN iajs-2945 141 56 and and CCONJ iajs-2945 141 57 substitute substitute VERB iajs-2945 141 58 it it PRON iajs-2945 141 59 into into ADP iajs-2945 141 60 the the DET iajs-2945 141 61 system system NOUN iajs-2945 141 62 step step NOUN iajs-2945 141 63 1 1 NUM iajs-2945 141 64 simulate simulate VERB iajs-2945 141 65 the the DET iajs-2945 141 66 parameters parameter NOUN iajs-2945 141 67 by by ADP iajs-2945 141 68 mc mc PROPN iajs-2945 141 69 sample sample PROPN iajs-2945 141 70 for for ADP iajs-2945 141 71 n n NUM iajs-2945 141 72 times time NOUN iajs-2945 141 73 at at ADP iajs-2945 141 74 once once ADV iajs-2945 141 75 ihjpas ihjpa NOUN iajs-2945 141 76 . . PUNCT iajs-2945 142 1 36(3)2023 36(3)2023 NUM iajs-2945 142 2 295 295 NUM iajs-2945 142 3 4.2 4.2 NUM iajs-2945 142 4 mean mean NOUN iajs-2945 142 5 latin latin ADJ iajs-2945 142 6 hypercube hypercube NOUN iajs-2945 142 7 runge runge NOUN iajs-2945 142 8 - - PUNCT iajs-2945 142 9 kutta kutta NOUN iajs-2945 142 10 ( ( PUNCT iajs-2945 142 11 mlh_rk mlh_rk NUM iajs-2945 142 12 ) ) PUNCT iajs-2945 142 13 mean mean VERB iajs-2945 142 14 latin latin ADJ iajs-2945 142 15 hypercube hypercube NOUN iajs-2945 142 16 runge runge NOUN iajs-2945 142 17 - - PUNCT iajs-2945 142 18 kutta kutta NOUN iajs-2945 142 19 ( ( PUNCT iajs-2945 142 20 mlh_rk mlh_rk NUM iajs-2945 142 21 ) ) PUNCT iajs-2945 142 22 is be AUX iajs-2945 142 23 a a DET iajs-2945 142 24 numerical numerical ADJ iajs-2945 142 25 simulation simulation NOUN iajs-2945 142 26 method method NOUN iajs-2945 142 27 that that PRON iajs-2945 142 28 is be AUX iajs-2945 142 29 a a DET iajs-2945 142 30 mixture mixture NOUN iajs-2945 142 31 of of ADP iajs-2945 142 32 a a DET iajs-2945 142 33 numerical numerical ADJ iajs-2945 142 34 method method NOUN iajs-2945 142 35 called call VERB iajs-2945 142 36 latin latin ADJ iajs-2945 142 37 hypercube hypercube NOUN iajs-2945 142 38 ( ( PUNCT iajs-2945 142 39 lh lh PROPN iajs-2945 142 40 ) ) PUNCT iajs-2945 142 41 and and CCONJ iajs-2945 142 42 a a DET iajs-2945 142 43 numerical numerical ADJ iajs-2945 142 44 method method NOUN iajs-2945 142 45 called call VERB iajs-2945 142 46 rungekutta rungekutta NOUN iajs-2945 142 47 ( ( PUNCT iajs-2945 142 48 rk rk NOUN iajs-2945 142 49 ) ) PUNCT iajs-2945 142 50 . . PUNCT iajs-2945 143 1 this this DET iajs-2945 143 2 method method NOUN iajs-2945 143 3 is be AUX iajs-2945 143 4 implemented implement VERB iajs-2945 143 5 via via ADP iajs-2945 143 6 the the DET iajs-2945 143 7 matlab matlab PROPN iajs-2945 143 8 program program NOUN iajs-2945 143 9 , , PUNCT iajs-2945 143 10 and and CCONJ iajs-2945 143 11 more more ADJ iajs-2945 143 12 details detail NOUN iajs-2945 143 13 are be AUX iajs-2945 143 14 shown show VERB iajs-2945 143 15 in in ADP iajs-2945 143 16 [ [ X iajs-2945 143 17 20 20 NUM iajs-2945 143 18 ] ] PUNCT iajs-2945 143 19 . . PUNCT iajs-2945 144 1 lh lh PROPN iajs-2945 144 2 estimates estimate VERB iajs-2945 144 3 the the DET iajs-2945 144 4 coefficients coefficient NOUN iajs-2945 144 5 of of ADP iajs-2945 144 6 the the DET iajs-2945 144 7 model model NOUN iajs-2945 144 8 , , PUNCT iajs-2945 144 9 which which PRON iajs-2945 144 10 are be AUX iajs-2945 144 11 considered consider VERB iajs-2945 144 12 random random ADJ iajs-2945 144 13 variables variable NOUN iajs-2945 144 14 ; ; PUNCT iajs-2945 144 15 mc mc PROPN iajs-2945 144 16 estimates estimate VERB iajs-2945 144 17 the the DET iajs-2945 144 18 model model NOUN iajs-2945 144 19 coefficients coefficient NOUN iajs-2945 144 20 ; ; PUNCT iajs-2945 144 21 and and CCONJ iajs-2945 144 22 rk rk NOUN iajs-2945 144 23 is be AUX iajs-2945 144 24 used use VERB iajs-2945 144 25 to to PART iajs-2945 144 26 solve solve VERB iajs-2945 144 27 the the DET iajs-2945 144 28 model model NOUN iajs-2945 144 29 numerically numerically ADV iajs-2945 144 30 . . PUNCT iajs-2945 145 1 the the DET iajs-2945 145 2 average average NOUN iajs-2945 145 3 of of ADP iajs-2945 145 4 the the DET iajs-2945 145 5 last last ADJ iajs-2945 145 6 rk rk NOUN iajs-2945 145 7 iteration iteration NOUN iajs-2945 145 8 results result NOUN iajs-2945 145 9 with with ADP iajs-2945 145 10 each each DET iajs-2945 145 11 lh lh PROPN iajs-2945 145 12 repetition repetition NOUN iajs-2945 145 13 is be AUX iajs-2945 145 14 considered consider VERB iajs-2945 145 15 the the DET iajs-2945 145 16 estimated estimate VERB iajs-2945 145 17 approximate approximate ADJ iajs-2945 145 18 solution solution NOUN iajs-2945 145 19 for for ADP iajs-2945 145 20 the the DET iajs-2945 145 21 model model NOUN iajs-2945 145 22 under under ADP iajs-2945 145 23 study study NOUN iajs-2945 145 24 . . PUNCT iajs-2945 146 1 everything everything PRON iajs-2945 146 2 we we PRON iajs-2945 146 3 talked talk VERB iajs-2945 146 4 about about ADP iajs-2945 146 5 before before ADP iajs-2945 146 6 the the DET iajs-2945 146 7 method method NOUN iajs-2945 146 8 mmc_rk mmc_rk PROPN iajs-2945 146 9 applies apply VERB iajs-2945 146 10 to to ADP iajs-2945 146 11 the the DET iajs-2945 146 12 method method NOUN iajs-2945 146 13 mlh_rk mlh_rk PROPN iajs-2945 146 14 . . PUNCT iajs-2945 147 1 in in ADP iajs-2945 147 2 addition addition NOUN iajs-2945 147 3 to to ADP iajs-2945 147 4 that that PRON iajs-2945 147 5 , , PUNCT iajs-2945 147 6 the the DET iajs-2945 147 7 mlh_rk mlh_rk PROPN iajs-2945 147 8 method method NOUN iajs-2945 147 9 is be AUX iajs-2945 147 10 more more ADV iajs-2945 147 11 accurate accurate ADJ iajs-2945 147 12 and and CCONJ iajs-2945 147 13 faster fast ADJ iajs-2945 147 14 than than ADP iajs-2945 147 15 the the DET iajs-2945 147 16 mmc_rk mmc_rk PROPN iajs-2945 147 17 method method NOUN iajs-2945 147 18 because because SCONJ iajs-2945 147 19 it it PRON iajs-2945 147 20 simulates simulate VERB iajs-2945 147 21 all all DET iajs-2945 147 22 model model NOUN iajs-2945 147 23 parameters parameter NOUN iajs-2945 147 24 at at ADP iajs-2945 147 25 once once ADV iajs-2945 147 26 . . PUNCT iajs-2945 148 1 it it PRON iajs-2945 148 2 also also ADV iajs-2945 148 3 saves save VERB iajs-2945 148 4 time time NOUN iajs-2945 148 5 and and CCONJ iajs-2945 148 6 effort effort NOUN iajs-2945 148 7 . . PUNCT iajs-2945 149 1 fig fig NOUN iajs-2945 149 2 2 2 NUM iajs-2945 149 3 explains explain VERB iajs-2945 149 4 the the DET iajs-2945 149 5 mlhrk mlhrk NOUN iajs-2945 149 6 in in ADP iajs-2945 149 7 greater great ADJ iajs-2945 149 8 detail detail NOUN iajs-2945 149 9 . . PUNCT iajs-2945 149 10 . . PUNCT iajs-2945 150 1 mlh_rk mlh_rk PROPN iajs-2945 150 2 procedure procedure NOUN iajs-2945 150 3 figure figure NOUN iajs-2945 150 4 2 2 NUM iajs-2945 150 5 : : PUNCT iajs-2945 150 6 steps step NOUN iajs-2945 150 7 of of ADP iajs-2945 150 8 mlh_rk mlh_rk NOUN iajs-2945 150 9 process process NOUN iajs-2945 150 10 , , PUNCT iajs-2945 150 11 [ [ X iajs-2945 150 12 20 20 NUM iajs-2945 150 13 ] ] PUNCT iajs-2945 150 14 . . PUNCT iajs-2945 151 1 step step NOUN iajs-2945 151 2 5 5 NUM iajs-2945 151 3 step step NOUN iajs-2945 151 4 5 5 NUM iajs-2945 151 5 : : PUNCT iajs-2945 151 6 calculate calculate VERB iajs-2945 151 7 the the DET iajs-2945 151 8 mean mean NOUN iajs-2945 151 9 of of ADP iajs-2945 151 10 final final ADJ iajs-2945 151 11 solutions solution NOUN iajs-2945 151 12 from from ADP iajs-2945 151 13 step step NOUN iajs-2945 151 14 4 4 NUM iajs-2945 151 15 , , PUNCT iajs-2945 151 16 as as ADP iajs-2945 151 17 a a DET iajs-2945 151 18 solution solution NOUN iajs-2945 151 19 system system NOUN iajs-2945 151 20 , , PUNCT iajs-2945 151 21 called call VERB iajs-2945 151 22 mlh_rk mlh_rk PROPN iajs-2945 151 23 step step NOUN iajs-2945 151 24 4 4 NUM iajs-2945 151 25 step step NOUN iajs-2945 151 26 4 4 NUM iajs-2945 151 27 : : PUNCT iajs-2945 151 28 repeat repeat VERB iajs-2945 151 29 steps step NOUN iajs-2945 151 30 1 1 NUM iajs-2945 151 31 and and CCONJ iajs-2945 151 32 2 2 NUM iajs-2945 151 33 for for ADP iajs-2945 151 34 ntimesl ntimesl NOUN iajs-2945 151 35 step step NOUN iajs-2945 151 36 3 3 NUM iajs-2945 151 37 step step NOUN iajs-2945 151 38 3 3 NUM iajs-2945 151 39 : : PUNCT iajs-2945 151 40 solve solve VERB iajs-2945 151 41 the the DET iajs-2945 151 42 system system NOUN iajs-2945 151 43 m m NOUN iajs-2945 151 44 - - PUNCT iajs-2945 151 45 times time NOUN iajs-2945 151 46 iterations iteration NOUN iajs-2945 151 47 numerically numerically ADV iajs-2945 151 48 by by ADP iajs-2945 151 49 rk rk PROPN iajs-2945 151 50 . . PUNCT iajs-2945 152 1 the the DET iajs-2945 152 2 last last ADJ iajs-2945 152 3 iterative iterative NOUN iajs-2945 152 4 result result NOUN iajs-2945 152 5 is be AUX iajs-2945 152 6 the the DET iajs-2945 152 7 final final ADJ iajs-2945 152 8 solution solution NOUN iajs-2945 152 9 step step NOUN iajs-2945 152 10 2 2 NUM iajs-2945 152 11 step step NOUN iajs-2945 152 12 2 2 NUM iajs-2945 152 13 : : PUNCT iajs-2945 152 14 for for ADP iajs-2945 152 15 each each DET iajs-2945 152 16 random random ADJ iajs-2945 152 17 parameter parameter NOUN iajs-2945 152 18 , , PUNCT iajs-2945 152 19 one one NUM iajs-2945 152 20 value value NOUN iajs-2945 152 21 is be AUX iajs-2945 152 22 specified specify VERB iajs-2945 152 23 and and CCONJ iajs-2945 152 24 replaced replace VERB iajs-2945 152 25 in in ADP iajs-2945 152 26 the the DET iajs-2945 152 27 system system NOUN iajs-2945 152 28 step step NOUN iajs-2945 152 29 1 1 NUM iajs-2945 152 30 step1 step1 NOUN iajs-2945 152 31 : : PUNCT iajs-2945 152 32 all all DET iajs-2945 152 33 model model NOUN iajs-2945 152 34 parameters parameter NOUN iajs-2945 152 35 have have AUX iajs-2945 152 36 been be AUX iajs-2945 152 37 simulated simulate VERB iajs-2945 152 38 by by ADP iajs-2945 152 39 lhs lhs PROPN iajs-2945 152 40 times times PROPN iajs-2945 152 41 for for ADP iajs-2945 152 42 n n PROPN iajs-2945 152 43 times time NOUN iajs-2945 152 44 at at ADP iajs-2945 152 45 ones one NOUN iajs-2945 152 46 ihjpas ihjpas PROPN iajs-2945 152 47 . . PUNCT iajs-2945 153 1 36(3)2023 36(3)2023 NUM iajs-2945 153 2 296 296 NUM iajs-2945 153 3 5 5 NUM iajs-2945 153 4 . . PUNCT iajs-2945 153 5 results result NOUN iajs-2945 153 6 and and CCONJ iajs-2945 153 7 discussion discussion NOUN iajs-2945 153 8 numerical numerical ADJ iajs-2945 153 9 and and CCONJ iajs-2945 153 10 numerical numerical PROPN iajs-2945 153 11 simulation simulation PROPN iajs-2945 153 12 solutions solution NOUN iajs-2945 153 13 of of ADP iajs-2945 153 14 the the DET iajs-2945 153 15 nonlinear nonlinear NOUN iajs-2945 153 16 of of ADP iajs-2945 153 17 covid-19 covid-19 PROPN iajs-2945 153 18 epidemic epidemic NOUN iajs-2945 153 19 model model NOUN iajs-2945 153 20 in in ADP iajs-2945 153 21 iraq iraq PROPN iajs-2945 153 22 have have AUX iajs-2945 153 23 been be AUX iajs-2945 153 24 discussed discuss VERB iajs-2945 153 25 and and CCONJ iajs-2945 153 26 analyzed analyze VERB iajs-2945 153 27 in in ADP iajs-2945 153 28 this this DET iajs-2945 153 29 section section NOUN iajs-2945 153 30 . . PUNCT iajs-2945 154 1 in in ADP iajs-2945 154 2 this this DET iajs-2945 154 3 study study NOUN iajs-2945 154 4 , , PUNCT iajs-2945 154 5 the the DET iajs-2945 154 6 real real ADJ iajs-2945 154 7 step step NOUN iajs-2945 154 8 size size NOUN iajs-2945 154 9 has have AUX iajs-2945 154 10 been be AUX iajs-2945 154 11 used use VERB iajs-2945 154 12 such such ADJ iajs-2945 154 13 that that DET iajs-2945 154 14 β„Ž=0.02 β„Ž=0.02 NOUN iajs-2945 154 15 in in ADP iajs-2945 154 16 a a DET iajs-2945 154 17 week week NOUN iajs-2945 154 18 , , PUNCT iajs-2945 154 19 ( ( PUNCT iajs-2945 154 20 52 52 NUM iajs-2945 154 21 weeks week NOUN iajs-2945 154 22 in in ADP iajs-2945 154 23 a a DET iajs-2945 154 24 year year NOUN iajs-2945 154 25 , , PUNCT iajs-2945 154 26 the the DET iajs-2945 154 27 data datum NOUN iajs-2945 154 28 of of ADP iajs-2945 154 29 the the DET iajs-2945 154 30 covid-19 covid-19 PROPN iajs-2945 154 31 epidemic epidemic NOUN iajs-2945 154 32 is be AUX iajs-2945 154 33 taken take VERB iajs-2945 154 34 from from ADP iajs-2945 154 35 each each DET iajs-2945 154 36 week week NOUN iajs-2945 154 37 ; ; PUNCT iajs-2945 154 38 therefore therefore ADV iajs-2945 154 39 , , PUNCT iajs-2945 154 40 in in ADP iajs-2945 154 41 order order NOUN iajs-2945 154 42 to to PART iajs-2945 154 43 change change VERB iajs-2945 154 44 the the DET iajs-2945 154 45 weeks week NOUN iajs-2945 154 46 to to ADP iajs-2945 154 47 a a DET iajs-2945 154 48 months month NOUN iajs-2945 154 49 , , PUNCT iajs-2945 154 50 the the DET iajs-2945 154 51 real real ADJ iajs-2945 154 52 step step NOUN iajs-2945 154 53 size size NOUN iajs-2945 154 54 is be AUX iajs-2945 154 55 calculated calculate VERB iajs-2945 154 56 as as ADP iajs-2945 154 57 β„Ž β„Ž PROPN iajs-2945 154 58 = = SYM iajs-2945 154 59 1 1 NUM iajs-2945 154 60 52 52 NUM iajs-2945 154 61 β‰ˆ β‰ˆ NUM iajs-2945 154 62 0.02 0.02 NUM iajs-2945 154 63 ) ) PUNCT iajs-2945 154 64 and and CCONJ iajs-2945 154 65 β„Ž=0.08 β„Ž=0.08 NOUN iajs-2945 154 66 in in ADP iajs-2945 154 67 a a DET iajs-2945 154 68 month month NOUN iajs-2945 154 69 , , PUNCT iajs-2945 154 70 ( ( PUNCT iajs-2945 154 71 12 12 NUM iajs-2945 154 72 month month NOUN iajs-2945 154 73 in in ADP iajs-2945 154 74 a a DET iajs-2945 154 75 year year NOUN iajs-2945 154 76 , , PUNCT iajs-2945 154 77 the the DET iajs-2945 154 78 data datum NOUN iajs-2945 154 79 of of ADP iajs-2945 154 80 the the DET iajs-2945 154 81 covid-19 covid-19 PROPN iajs-2945 154 82 epidemic epidemic NOUN iajs-2945 154 83 is be AUX iajs-2945 154 84 taken take VERB iajs-2945 154 85 from from ADP iajs-2945 154 86 each each DET iajs-2945 154 87 month month NOUN iajs-2945 154 88 ; ; PUNCT iajs-2945 154 89 therefore therefore ADV iajs-2945 154 90 , , PUNCT iajs-2945 154 91 in in ADP iajs-2945 154 92 order order NOUN iajs-2945 154 93 to to PART iajs-2945 154 94 change change VERB iajs-2945 154 95 the the DET iajs-2945 154 96 months month NOUN iajs-2945 154 97 to to ADP iajs-2945 154 98 a a DET iajs-2945 154 99 year year NOUN iajs-2945 154 100 , , PUNCT iajs-2945 154 101 the the DET iajs-2945 154 102 real real ADJ iajs-2945 154 103 step step NOUN iajs-2945 154 104 size size NOUN iajs-2945 154 105 is be AUX iajs-2945 154 106 calculated calculate VERB iajs-2945 154 107 as as ADP iajs-2945 154 108 β„Ž β„Ž PROPN iajs-2945 154 109 = = SYM iajs-2945 154 110 1 1 NUM iajs-2945 154 111 12 12 NUM iajs-2945 154 112 β‰ˆ β‰ˆ NUM iajs-2945 154 113 0.08 0.08 NUM iajs-2945 154 114 ) ) PUNCT iajs-2945 154 115 . . PUNCT iajs-2945 155 1 table table NOUN iajs-2945 155 2 3 3 NUM iajs-2945 155 3 . . NOUN iajs-2945 155 4 numerical numerical PROPN iajs-2945 155 5 and and CCONJ iajs-2945 155 6 numerical numerical PROPN iajs-2945 155 7 simulation simulation PROPN iajs-2945 155 8 results result NOUN iajs-2945 155 9 of of ADP iajs-2945 155 10 covid-19 covid-19 PROPN iajs-2945 155 11 model model NOUN iajs-2945 155 12 from from ADP iajs-2945 155 13 2021 2021 NUM iajs-2945 155 14 to to ADP iajs-2945 155 15 2022 2022 NUM iajs-2945 155 16 model model NOUN iajs-2945 155 17 variables variable NOUN iajs-2945 155 18 step step NOUN iajs-2945 155 19 size size NOUN iajs-2945 155 20 , , PUNCT iajs-2945 155 21 h h NOUN iajs-2945 155 22 ( ( PUNCT iajs-2945 155 23 weekly weekly ADJ iajs-2945 155 24 & & CCONJ iajs-2945 155 25 monthly monthly ADJ iajs-2945 155 26 ) ) PUNCT iajs-2945 155 27 number number NOUN iajs-2945 155 28 of of ADP iajs-2945 155 29 iteration iteration NOUN iajs-2945 155 30 , , PUNCT iajs-2945 155 31 π’Ž π’Ž PROPN iajs-2945 155 32 ( ( PUNCT iajs-2945 155 33 weekly weekly PROPN iajs-2945 155 34 & & CCONJ iajs-2945 155 35 monthly monthly ADJ iajs-2945 155 36 ) ) PUNCT iajs-2945 155 37 rk4 rk4 NOUN iajs-2945 155 38 ( ( PUNCT iajs-2945 155 39 1 1 NUM iajs-2945 155 40 years year NOUN iajs-2945 155 41 ) ) PUNCT iajs-2945 155 42 mmc_rk mmc_rk PROPN iajs-2945 156 1 100 100 NUM iajs-2945 156 2 rep rep PROPN iajs-2945 156 3 . . PROPN iajs-2945 156 4 ( ( PUNCT iajs-2945 156 5 1 1 NUM iajs-2945 156 6 years year NOUN iajs-2945 156 7 ) ) PUNCT iajs-2945 156 8 mlh_rk mlh_rk PROPN iajs-2945 156 9 100 100 NUM iajs-2945 156 10 rep rep PROPN iajs-2945 156 11 . . PROPN iajs-2945 157 1 ( ( PUNCT iajs-2945 157 2 1 1 NUM iajs-2945 157 3 years year NOUN iajs-2945 157 4 ) ) PUNCT iajs-2945 157 5 𝑺(𝒕 𝑺(𝒕 PART iajs-2945 157 6 ) ) PUNCT iajs-2945 157 7 0.08 0.08 NUM iajs-2945 157 8 ( ( PUNCT iajs-2945 157 9 monthly monthly NOUN iajs-2945 157 10 ) ) PUNCT iajs-2945 157 11 150 150 NUM iajs-2945 157 12 111.2080 111.2080 NUM iajs-2945 157 13 112.0276 112.0276 NUM iajs-2945 157 14 112.02304 112.02304 NUM iajs-2945 157 15 0.02 0.02 NUM iajs-2945 157 16 ( ( PUNCT iajs-2945 157 17 weekly weekly ADJ iajs-2945 157 18 ) ) PUNCT iajs-2945 157 19 600 600 NUM iajs-2945 157 20 111.6410 111.6410 NUM iajs-2945 157 21 111.9771 111.9771 NUM iajs-2945 157 22 111.9769 111.9769 NUM iajs-2945 157 23 𝑽(𝒕 𝑽(𝒕 SYM iajs-2945 157 24 ) ) PUNCT iajs-2945 157 25 0.08 0.08 NUM iajs-2945 157 26 ( ( PUNCT iajs-2945 157 27 monthly monthly ADJ iajs-2945 157 28 ) ) PUNCT iajs-2945 157 29 150 150 NUM iajs-2945 157 30 46.2424 46.2424 NUM iajs-2945 157 31 45.3405 45.3405 NUM iajs-2945 157 32 47.1184 47.1184 NUM iajs-2945 157 33 0.02 0.02 NUM iajs-2945 157 34 ( ( PUNCT iajs-2945 157 35 weekly weekly ADJ iajs-2945 157 36 ) ) PUNCT iajs-2945 157 37 600 600 NUM iajs-2945 157 38 46.2938 46.2938 NUM iajs-2945 157 39 45.3136 45.3136 NUM iajs-2945 157 40 47.0938 47.0938 NUM iajs-2945 157 41 𝑨(𝒕 𝑨(𝒕 NUM iajs-2945 157 42 ) ) PUNCT iajs-2945 157 43 0.08 0.08 NUM iajs-2945 157 44 ( ( PUNCT iajs-2945 157 45 monthly monthly NOUN iajs-2945 157 46 ) ) PUNCT iajs-2945 157 47 150 150 NUM iajs-2945 157 48 198.0505 198.0505 NUM iajs-2945 157 49 198.4761 198.4761 NUM iajs-2945 157 50 198.4017 198.4017 NUM iajs-2945 157 51 0.02 0.02 NUM iajs-2945 157 52 ( ( PUNCT iajs-2945 157 53 weekly weekly ADJ iajs-2945 157 54 ) ) PUNCT iajs-2945 157 55 600 600 NUM iajs-2945 157 56 197.6970 197.6970 NUM iajs-2945 157 57 198.0655 198.0655 NUM iajs-2945 157 58 197.9236 197.9236 NUM iajs-2945 157 59 𝑰(𝒕 𝑰(𝒕 NOUN iajs-2945 157 60 ) ) PUNCT iajs-2945 157 61 0.08 0.08 NUM iajs-2945 157 62 ( ( PUNCT iajs-2945 157 63 monthly monthly ADV iajs-2945 157 64 ) ) PUNCT iajs-2945 157 65 150 150 NUM iajs-2945 157 66 38.2352 38.2352 NUM iajs-2945 157 67 37.9597 37.9597 NUM iajs-2945 157 68 38.6755 38.6755 NUM iajs-2945 157 69 0.02 0.02 NUM iajs-2945 157 70 ( ( PUNCT iajs-2945 157 71 weekly weekly ADJ iajs-2945 157 72 ) ) PUNCT iajs-2945 157 73 600 600 NUM iajs-2945 157 74 36.0473 36.0473 NUM iajs-2945 157 75 35.8729 35.8729 NUM iajs-2945 157 76 36.1012 36.1012 NUM iajs-2945 157 77 𝑹(𝒕 𝑹(𝒕 NOUN iajs-2945 157 78 ) ) PUNCT iajs-2945 157 79 0.08 0.08 NUM iajs-2945 157 80 ( ( PUNCT iajs-2945 157 81 monthly monthly NOUN iajs-2945 157 82 ) ) PUNCT iajs-2945 157 83 150 150 NUM iajs-2945 157 84 205.2406 205.2406 NUM iajs-2945 157 85 205.7047 205.7047 NUM iajs-2945 157 86 205.4156 205.4156 NUM iajs-2945 157 87 0.02 0.02 NUM iajs-2945 157 88 ( ( PUNCT iajs-2945 157 89 weekly weekly ADJ iajs-2945 157 90 ) ) PUNCT iajs-2945 157 91 600 600 NUM iajs-2945 157 92 205.6102 205.6102 NUM iajs-2945 157 93 206.3006 206.3006 NUM iajs-2945 157 94 205.3439 205.3439 NUM iajs-2945 157 95 table table NOUN iajs-2945 157 96 4 4 NUM iajs-2945 157 97 . . PUNCT iajs-2945 158 1 expected expect VERB iajs-2945 158 2 numerical numerical PROPN iajs-2945 158 3 simulation simulation PROPN iajs-2945 158 4 results result NOUN iajs-2945 158 5 of of ADP iajs-2945 158 6 covid-19 covid-19 PROPN iajs-2945 158 7 model model NOUN iajs-2945 158 8 from from ADP iajs-2945 158 9 2021 2021 NUM iajs-2945 158 10 to to ADP iajs-2945 158 11 2025 2025 NUM iajs-2945 158 12 model model NOUN iajs-2945 158 13 variables variable NOUN iajs-2945 158 14 step step NOUN iajs-2945 158 15 size size NOUN iajs-2945 158 16 , , PUNCT iajs-2945 158 17 h h NOUN iajs-2945 158 18 ( ( PUNCT iajs-2945 158 19 weekly weekly ADJ iajs-2945 158 20 & & CCONJ iajs-2945 158 21 monthly monthly ADJ iajs-2945 158 22 ) ) PUNCT iajs-2945 158 23 number number NOUN iajs-2945 158 24 of of ADP iajs-2945 158 25 iteration iteration NOUN iajs-2945 158 26 , , PUNCT iajs-2945 158 27 π’Ž π’Ž PROPN iajs-2945 158 28 ( ( PUNCT iajs-2945 158 29 weekly weekly ADJ iajs-2945 158 30 & & CCONJ iajs-2945 158 31 monthly monthly ADJ iajs-2945 158 32 ) ) PUNCT iajs-2945 158 33 rk4 rk4 NOUN iajs-2945 158 34 ( ( PUNCT iajs-2945 158 35 4 4 NUM iajs-2945 158 36 years year NOUN iajs-2945 158 37 ) ) PUNCT iajs-2945 158 38 mmc_rk mmc_rk PROPN iajs-2945 158 39 100 100 NUM iajs-2945 158 40 rep rep PROPN iajs-2945 158 41 . . PROPN iajs-2945 159 1 ( ( PUNCT iajs-2945 159 2 4 4 NUM iajs-2945 159 3 years year NOUN iajs-2945 159 4 ) ) PUNCT iajs-2945 160 1 mlh_rk mlh_rk PROPN iajs-2945 161 1 100 100 NUM iajs-2945 161 2 rep rep PROPN iajs-2945 161 3 . . PROPN iajs-2945 161 4 ( ( PUNCT iajs-2945 161 5 4years 4years X iajs-2945 161 6 ) ) PUNCT iajs-2945 161 7 𝑺(𝒕 𝑺(𝒕 NOUN iajs-2945 161 8 ) ) PUNCT iajs-2945 161 9 0.08 0.08 NUM iajs-2945 161 10 ( ( PUNCT iajs-2945 161 11 monthly monthly ADV iajs-2945 161 12 ) ) PUNCT iajs-2945 161 13 600 600 NUM iajs-2945 161 14 45.3077 45.3077 NUM iajs-2945 161 15 45.7295 45.7295 NUM iajs-2945 161 16 45.1721 45.1721 NUM iajs-2945 161 17 0.02 0.02 NUM iajs-2945 161 18 ( ( PUNCT iajs-2945 161 19 weekly weekly ADJ iajs-2945 161 20 ) ) PUNCT iajs-2945 161 21 2400 2400 NUM iajs-2945 161 22 45.4914 45.4914 NUM iajs-2945 161 23 45.7972 45.7972 NUM iajs-2945 161 24 45.3906 45.3906 NUM iajs-2945 161 25 𝑽(𝒕 𝑽(𝒕 NOUN iajs-2945 161 26 ) ) PUNCT iajs-2945 161 27 0.08 0.08 NUM iajs-2945 161 28 ( ( PUNCT iajs-2945 161 29 monthly monthly ADV iajs-2945 161 30 ) ) PUNCT iajs-2945 161 31 600 600 NUM iajs-2945 161 32 34.9403 34.9403 NUM iajs-2945 161 33 35.5509 35.5509 NUM iajs-2945 161 34 35.3254 35.3254 NUM iajs-2945 161 35 0.02 0.02 NUM iajs-2945 161 36 ( ( PUNCT iajs-2945 161 37 weekly weekly ADJ iajs-2945 161 38 ) ) PUNCT iajs-2945 161 39 2400 2400 NUM iajs-2945 161 40 34.8710 34.8710 NUM iajs-2945 161 41 35.6280 35.6280 NUM iajs-2945 161 42 35.1763 35.1763 NUM iajs-2945 161 43 𝑨(𝒕 𝑨(𝒕 NUM iajs-2945 161 44 ) ) PUNCT iajs-2945 161 45 0.08 0.08 NUM iajs-2945 161 46 ( ( PUNCT iajs-2945 161 47 monthly monthly ADV iajs-2945 161 48 ) ) PUNCT iajs-2945 161 49 600 600 NUM iajs-2945 161 50 13.5280 13.5280 NUM iajs-2945 161 51 13.7776 13.7776 NUM iajs-2945 161 52 13.2342 13.2342 NUM iajs-2945 161 53 0.02 0.02 NUM iajs-2945 161 54 ( ( PUNCT iajs-2945 161 55 weekly weekly ADJ iajs-2945 161 56 ) ) PUNCT iajs-2945 161 57 2400 2400 NUM iajs-2945 161 58 13.4236 13.4236 NUM iajs-2945 161 59 13.7370 13.7370 NUM iajs-2945 161 60 13.4793 13.4793 NUM iajs-2945 161 61 𝑰(𝒕 𝑰(𝒕 NOUN iajs-2945 161 62 ) ) PUNCT iajs-2945 161 63 0.08 0.08 NUM iajs-2945 161 64 ( ( PUNCT iajs-2945 161 65 monthly monthly ADV iajs-2945 161 66 ) ) PUNCT iajs-2945 161 67 600 600 NUM iajs-2945 161 68 9.3148 9.3148 NUM iajs-2945 161 69 9.3368 9.3368 NUM iajs-2945 161 70 9.3201 9.3201 NUM iajs-2945 161 71 0.02 0.02 NUM iajs-2945 161 72 ( ( PUNCT iajs-2945 161 73 weekly weekly ADJ iajs-2945 161 74 ) ) PUNCT iajs-2945 161 75 2400 2400 NUM iajs-2945 161 76 9.2985 9.2985 NUM iajs-2945 161 77 9.3130 9.3130 NUM iajs-2945 161 78 9.2956 9.2956 NUM iajs-2945 161 79 𝑹(𝒕 𝑹(𝒕 NOUN iajs-2945 161 80 ) ) PUNCT iajs-2945 161 81 0.08 0.08 NUM iajs-2945 161 82 ( ( PUNCT iajs-2945 161 83 monthly monthly ADV iajs-2945 161 84 ) ) PUNCT iajs-2945 161 85 600 600 NUM iajs-2945 161 86 500.1596 500.1596 NUM iajs-2945 161 87 500.4997 500.4997 NUM iajs-2945 161 88 499.8646 499.8646 NUM iajs-2945 161 89 0.02 0.02 NUM iajs-2945 161 90 ( ( PUNCT iajs-2945 161 91 weekly weekly ADJ iajs-2945 161 92 ) ) PUNCT iajs-2945 161 93 2400 2400 NUM iajs-2945 162 1 500.4212 500.4212 NUM iajs-2945 162 2 500.7103 500.7103 NUM iajs-2945 162 3 500.4103 500.4103 NUM iajs-2945 162 4 ihjpas ihjpa NOUN iajs-2945 162 5 . . PUNCT iajs-2945 163 1 36(3)2023 36(3)2023 NUM iajs-2945 163 2 297 297 NUM iajs-2945 163 3 table table NOUN iajs-2945 163 4 5 5 NUM iajs-2945 163 5 . . PUNCT iajs-2945 163 6 prediction prediction NOUN iajs-2945 163 7 intervals interval NOUN iajs-2945 163 8 ( ( PUNCT iajs-2945 163 9 5th 5th ADJ iajs-2945 163 10 percentile percentile ADJ iajs-2945 163 11 , , PUNCT iajs-2945 163 12 95th 95th ADJ iajs-2945 163 13 percentile percentile NOUN iajs-2945 163 14 ) ) PUNCT iajs-2945 163 15 for for ADP iajs-2945 163 16 mmc_rk mmc_rk PROPN iajs-2945 163 17 and and CCONJ iajs-2945 163 18 mlh_rk mlh_rk PROPN iajs-2945 163 19 solutions solution NOUN iajs-2945 163 20 mmc_rk mmc_rk PROPN iajs-2945 163 21 from from ADP iajs-2945 163 22 2021 2021 NUM iajs-2945 163 23 to to ADP iajs-2945 163 24 2025 2025 NUM iajs-2945 163 25 ( ( PUNCT iajs-2945 163 26 𝒕 𝒕 NOUN iajs-2945 163 27 ≀ ≀ NOUN iajs-2945 163 28 πŸ’πŸ– πŸ’πŸ– NUM iajs-2945 163 29 ) ) PUNCT iajs-2945 163 30 subpopulation subpopulation NOUN iajs-2945 163 31 ( ( PUNCT iajs-2945 163 32 100 100 NUM iajs-2945 163 33 repetitions repetition NOUN iajs-2945 163 34 ) ) PUNCT iajs-2945 163 35 ( ( PUNCT 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21.2286 21.2286 NUM iajs-2945 163 69 ) ) PUNCT iajs-2945 163 70 ( ( PUNCT iajs-2945 163 71 7.8735 7.8735 NUM iajs-2945 163 72 , , PUNCT iajs-2945 163 73 20.6545 20.6545 NUM iajs-2945 163 74 ) ) PUNCT iajs-2945 163 75 𝑰(𝒕 𝑰(𝒕 ADP iajs-2945 163 76 ) ) PUNCT iajs-2945 163 77 ( ( PUNCT iajs-2945 163 78 5.0933 5.0933 NUM iajs-2945 163 79 , , PUNCT iajs-2945 163 80 13.9210 13.9210 NUM iajs-2945 163 81 ) ) PUNCT iajs-2945 163 82 ( ( PUNCT iajs-2945 163 83 5.5697 5.5697 NUM iajs-2945 163 84 , , PUNCT iajs-2945 163 85 14.6953 14.6953 NUM iajs-2945 163 86 ) ) PUNCT iajs-2945 163 87 𝑹(𝒕 𝑹(𝒕 NUM iajs-2945 163 88 ) ) PUNCT iajs-2945 163 89 ( ( PUNCT iajs-2945 163 90 447.8911 447.8911 NUM iajs-2945 163 91 , , PUNCT iajs-2945 163 92 628.1435 628.1435 NUM iajs-2945 163 93 ) ) PUNCT iajs-2945 163 94 ( ( PUNCT iajs-2945 163 95 449.8386 449.8386 NUM iajs-2945 163 96 , , PUNCT iajs-2945 163 97 628.6205 628.6205 NUM iajs-2945 163 98 ) ) PUNCT iajs-2945 163 99 mlh_rk mlh_rk PROPN iajs-2945 164 1 from from 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34 26.3581 26.3581 NUM iajs-2945 164 35 , , PUNCT iajs-2945 164 36 56.7235 56.7235 NUM iajs-2945 164 37 ) ) PUNCT iajs-2945 164 38 ( ( PUNCT iajs-2945 164 39 24.0661 24.0661 NUM iajs-2945 164 40 , , PUNCT iajs-2945 164 41 56.6104 56.6104 NUM iajs-2945 164 42 ) ) PUNCT iajs-2945 164 43 𝑨(𝒕 𝑨(𝒕 NUM iajs-2945 164 44 ) ) PUNCT iajs-2945 164 45 ( ( PUNCT iajs-2945 164 46 6.4966 6.4966 NUM iajs-2945 164 47 , , PUNCT iajs-2945 164 48 17.3059 17.3059 NUM iajs-2945 164 49 ) ) PUNCT iajs-2945 164 50 ( ( PUNCT iajs-2945 164 51 6.5912 6.5912 NUM iajs-2945 164 52 , , PUNCT iajs-2945 164 53 17.6509 17.6509 NUM iajs-2945 164 54 ) ) PUNCT iajs-2945 164 55 𝑰(𝒕 𝑰(𝒕 ADP iajs-2945 164 56 ) ) PUNCT iajs-2945 164 57 ( ( PUNCT iajs-2945 164 58 4.2058 4.2058 NUM iajs-2945 164 59 , , PUNCT iajs-2945 164 60 12.3463 12.3463 NUM iajs-2945 164 61 ) ) PUNCT iajs-2945 164 62 ( ( PUNCT iajs-2945 164 63 4.7953 4.7953 NUM iajs-2945 164 64 , , PUNCT iajs-2945 164 65 12.5404 12.5404 NUM iajs-2945 164 66 ) ) PUNCT iajs-2945 164 67 𝑹(𝒕 𝑹(𝒕 NUM iajs-2945 164 68 ) ) PUNCT iajs-2945 164 69 ( ( PUNCT iajs-2945 164 70 414.8612 414.8612 NUM iajs-2945 164 71 , , PUNCT iajs-2945 164 72 578.4889 578.4889 NUM iajs-2945 164 73 ) ) PUNCT iajs-2945 164 74 ( ( PUNCT iajs-2945 164 75 410.9803 410.9803 NUM iajs-2945 164 76 , , PUNCT iajs-2945 164 77 570.2245 570.2245 NUM iajs-2945 164 78 ) ) PUNCT iajs-2945 164 79 table table NOUN iajs-2945 164 80 6 6 NUM iajs-2945 164 81 . . PUNCT iajs-2945 164 82 absolute absolute ADJ iajs-2945 164 83 error error NOUN iajs-2945 164 84 for for ADP iajs-2945 164 85 mmc_rk mmc_rk PROPN iajs-2945 164 86 and and CCONJ iajs-2945 164 87 mlh_rk mlh_rk PROPN iajs-2945 164 88 with with ADP iajs-2945 164 89 rk4 rk4 NOUN iajs-2945 164 90 from from ADP iajs-2945 164 91 2021 2021 NUM iajs-2945 164 92 to to ADP iajs-2945 164 93 2022 2022 NUM iajs-2945 164 94 . . PUNCT iajs-2945 165 1 model model NOUN iajs-2945 165 2 variables variable NOUN iajs-2945 165 3 step step NOUN iajs-2945 165 4 size size NOUN iajs-2945 165 5 , , PUNCT iajs-2945 165 6 h h NOUN iajs-2945 165 7 ( ( PUNCT iajs-2945 165 8 weekly weekly ADJ iajs-2945 165 9 & & CCONJ iajs-2945 165 10 monthly monthly ADJ iajs-2945 165 11 ) ) PUNCT iajs-2945 165 12 iterations iteration NOUN iajs-2945 165 13 ( ( PUNCT iajs-2945 165 14 months month NOUN iajs-2945 165 15 ) ) PUNCT iajs-2945 165 16 mmc_rk mmc_rk PROPN iajs-2945 165 17 mlh_rk mlh_rk X iajs-2945 166 1 𝑺(𝒕 𝑺(𝒕 X iajs-2945 166 2 ) ) PUNCT iajs-2945 166 3 0.08 0.08 NUM iajs-2945 166 4 ( ( PUNCT iajs-2945 166 5 monthly monthly ADJ iajs-2945 166 6 ) ) PUNCT iajs-2945 166 7 12 12 NUM iajs-2945 166 8 0.8196 0.8196 NUM iajs-2945 166 9 0.81504 0.81504 NUM iajs-2945 166 10 0.02 0.02 NUM iajs-2945 166 11 ( ( PUNCT iajs-2945 166 12 weakly weakly ADJ iajs-2945 166 13 ) ) PUNCT iajs-2945 166 14 0.3361 0.3361 NOUN iajs-2945 166 15 0.3359 0.3359 NUM iajs-2945 166 16 𝑽(𝒕 𝑽(𝒕 SYM iajs-2945 166 17 ) ) PUNCT iajs-2945 166 18 0.08 0.08 NUM iajs-2945 166 19 ( ( PUNCT iajs-2945 166 20 monthly monthly ADJ iajs-2945 166 21 ) ) PUNCT iajs-2945 166 22 12 12 NUM iajs-2945 167 1 0.9019 0.9019 NUM iajs-2945 167 2 0.8760 0.8760 NUM iajs-2945 167 3 0.02 0.02 NUM iajs-2945 167 4 ( ( PUNCT iajs-2945 167 5 weekly weekly ADJ iajs-2945 167 6 ) ) PUNCT iajs-2945 167 7 0.9802 0.9802 NUM iajs-2945 167 8 0.8000 0.8000 NUM iajs-2945 167 9 𝑨(𝒕 𝑨(𝒕 NUM iajs-2945 167 10 ) ) PUNCT iajs-2945 167 11 0.08 0.08 NUM iajs-2945 167 12 ( ( PUNCT iajs-2945 167 13 monthly monthly NOUN iajs-2945 167 14 ) ) PUNCT iajs-2945 167 15 12 12 NUM iajs-2945 168 1 0.4256 0.4256 NUM iajs-2945 168 2 0.3512 0.3512 NUM iajs-2945 168 3 0.02 0.02 NUM iajs-2945 168 4 ( ( PUNCT iajs-2945 168 5 weekly weekly ADJ iajs-2945 168 6 ) ) PUNCT iajs-2945 168 7 0.3685 0.3685 NUM iajs-2945 168 8 0.2266 0.2266 NUM iajs-2945 168 9 𝑰(𝒕 𝑰(𝒕 ADP iajs-2945 168 10 ) ) PUNCT iajs-2945 168 11 0.08 0.08 NUM iajs-2945 168 12 ( ( PUNCT iajs-2945 168 13 monthly monthly ADJ iajs-2945 168 14 ) ) PUNCT iajs-2945 168 15 12 12 NUM iajs-2945 168 16 0.2755 0.2755 NUM iajs-2945 168 17 0.04403 0.04403 NUM iajs-2945 168 18 0.02 0.02 NUM iajs-2945 168 19 ( ( PUNCT iajs-2945 168 20 weekly weekly ADJ iajs-2945 168 21 ) ) PUNCT iajs-2945 168 22 0.1744 0.1744 NUM iajs-2945 168 23 0.0539 0.0539 NUM iajs-2945 168 24 𝑹(𝒕 𝑹(𝒕 NOUN iajs-2945 168 25 ) ) PUNCT iajs-2945 168 26 0.08 0.08 NUM iajs-2945 168 27 ( ( PUNCT iajs-2945 168 28 monthly monthly ADJ iajs-2945 168 29 ) ) PUNCT iajs-2945 168 30 12 12 NUM iajs-2945 168 31 0.4641 0.4641 NUM iajs-2945 168 32 0.1750 0.1750 NUM iajs-2945 168 33 0.02 0.02 NUM iajs-2945 168 34 ( ( PUNCT iajs-2945 168 35 weekly weekly ADJ iajs-2945 168 36 ) ) PUNCT iajs-2945 168 37 0.6904 0.6904 NUM iajs-2945 168 38 0.2663 0.2663 NUM iajs-2945 168 39 table table NOUN iajs-2945 168 40 7 7 NUM iajs-2945 168 41 . . PUNCT iajs-2945 168 42 absolute absolute ADJ iajs-2945 168 43 error error NOUN iajs-2945 168 44 πΈβ„Ž πΈβ„Ž NOUN iajs-2945 168 45 = = SYM iajs-2945 168 46 |π‘‡β„Ž |π‘‡β„Ž PROPN iajs-2945 168 47 βˆ’ βˆ’ PROPN iajs-2945 168 48 π‘‡β„Ž π‘‡β„Ž ADJ iajs-2945 168 49 2 2 NUM iajs-2945 168 50 | | ADV iajs-2945 168 51 for for ADP iajs-2945 168 52 mmc_rk mmc_rk PROPN iajs-2945 168 53 and and CCONJ iajs-2945 168 54 mlh_rk mlh_rk PROPN iajs-2945 168 55 from from ADP iajs-2945 168 56 2021 2021 NUM iajs-2945 168 57 to to ADP iajs-2945 168 58 2025 2025 NUM iajs-2945 168 59 ihjpas ihjpa NOUN iajs-2945 168 60 . . PUNCT iajs-2945 169 1 36(3)2023 36(3)2023 NUM iajs-2945 169 2 298 298 NUM iajs-2945 169 3 model model NOUN iajs-2945 169 4 variables variable NOUN iajs-2945 169 5 step step NOUN iajs-2945 169 6 size size NOUN iajs-2945 169 7 , , PUNCT iajs-2945 169 8 h h NOUN iajs-2945 169 9 ( ( PUNCT iajs-2945 169 10 weekly weekly ADJ iajs-2945 169 11 & & CCONJ iajs-2945 169 12 monthly monthly ADJ iajs-2945 169 13 ) ) PUNCT iajs-2945 169 14 number number NOUN iajs-2945 169 15 of of ADP iajs-2945 169 16 iterations iteration NOUN iajs-2945 169 17 𝑬𝒉_𝑴𝑴π‘ͺ_𝑹𝑲 𝑬𝒉_𝑴𝑴π‘ͺ_𝑹𝑲 PROPN iajs-2945 169 18 100 100 NUM iajs-2945 169 19 rep rep NOUN iajs-2945 169 20 . . PROPN iajs-2945 169 21 ( ( PUNCT iajs-2945 169 22 4 4 NUM iajs-2945 169 23 years year NOUN iajs-2945 169 24 ) ) PUNCT iajs-2945 169 25 𝑬𝒉_𝑴𝑳𝑯_𝑹𝑲 𝑬𝒉_𝑴𝑳𝑯_𝑹𝑲 PROPN iajs-2945 169 26 100 100 NUM iajs-2945 169 27 rep rep NOUN iajs-2945 169 28 . . PROPN iajs-2945 169 29 ( ( PUNCT iajs-2945 169 30 4 4 NUM iajs-2945 169 31 years year NOUN iajs-2945 169 32 ) ) PUNCT iajs-2945 169 33 𝑺(𝒕 𝑺(𝒕 PART iajs-2945 169 34 ) ) PUNCT iajs-2945 169 35 0.08 0.08 NUM iajs-2945 169 36 monthly monthly ADJ iajs-2945 169 37 600 600 NUM iajs-2945 169 38 0.045088 0.045088 NUM iajs-2945 169 39 0.107386 0.107386 NUM iajs-2945 169 40 0.08/2 0.08/2 PUNCT iajs-2945 169 41 1200 1200 NUM iajs-2945 169 42 0.022554 0.022554 NUM iajs-2945 169 43 0.111144 0.111144 NUM iajs-2945 169 44 0.08/4 0.08/4 NUM iajs-2945 169 45 2400 2400 NUM iajs-2945 169 46 0.019704 0.019704 NUM iajs-2945 169 47 0.103381 0.103381 NUM iajs-2945 169 48 𝑽(𝒕 𝑽(𝒕 NOUN iajs-2945 169 49 ) ) PUNCT iajs-2945 169 50 0.08 0.08 NUM iajs-2945 169 51 monthly monthly ADJ iajs-2945 169 52 600 600 NUM iajs-2945 169 53 0.088598 0.088598 NUM iajs-2945 169 54 0.109317 0.109317 NUM iajs-2945 169 55 0.08/2 0.08/2 NOUN iajs-2945 169 56 1200 1200 NUM iajs-2945 169 57 0.104216 0.104216 NUM iajs-2945 169 58 0.039814 0.039814 NUM iajs-2945 169 59 0.08/4 0.08/4 NUM iajs-2945 169 60 2400 2400 NUM iajs-2945 169 61 0.073518 0.073518 NUM iajs-2945 169 62 0.029403 0.029403 NUM iajs-2945 169 63 𝑨(𝒕 𝑨(𝒕 NUM iajs-2945 169 64 ) ) PUNCT iajs-2945 169 65 0.08 0.08 NUM iajs-2945 169 66 monthly monthly ADJ iajs-2945 169 67 600 600 NUM iajs-2945 169 68 0.027061 0.027061 NUM iajs-2945 169 69 0.157000 0.157000 NUM iajs-2945 169 70 0.08/2 0.08/2 NOUN iajs-2945 169 71 1200 1200 NUM iajs-2945 169 72 0.013543 0.013543 NUM iajs-2945 169 73 0.048095 0.048095 NUM iajs-2945 169 74 0.08/4 0.08/4 NUM iajs-2945 169 75 2400 2400 NUM iajs-2945 169 76 0.010381 0.010381 NUM iajs-2945 169 77 0.010124 0.010124 NUM iajs-2945 169 78 𝑰(𝒕 𝑰(𝒕 ADP iajs-2945 169 79 ) ) PUNCT iajs-2945 169 80 0.08 0.08 NUM iajs-2945 169 81 monthly monthly ADJ iajs-2945 169 82 600 600 NUM iajs-2945 169 83 0.011903 0.011903 NUM iajs-2945 169 84 0.010215 0.010215 NUM iajs-2945 169 85 0.08/2 0.08/2 NUM iajs-2945 169 86 1200 1200 NUM iajs-2945 169 87 0.011887 0.011887 NUM iajs-2945 169 88 0.014358 0.014358 NUM iajs-2945 169 89 0.08/4 0.08/4 NUM iajs-2945 169 90 2400 2400 NUM iajs-2945 169 91 0.011402 0.011402 NUM iajs-2945 169 92 0.009302 0.009302 NUM iajs-2945 169 93 𝑹(𝒕 𝑹(𝒕 NUM iajs-2945 169 94 ) ) PUNCT iajs-2945 169 95 0.08 0.08 NUM iajs-2945 169 96 monthly monthly ADJ iajs-2945 169 97 600 600 NUM iajs-2945 169 98 0.332002 0.332002 NUM iajs-2945 169 99 0.645725 0.645725 NUM iajs-2945 169 100 0.08/2 0.08/2 NOUN iajs-2945 169 101 1200 1200 NUM iajs-2945 169 102 0.121379 0.121379 NUM iajs-2945 169 103 0.099979 0.099979 NUM iajs-2945 169 104 0.08/4 0.08/4 NUM iajs-2945 169 105 2400 2400 NUM iajs-2945 169 106 0.109360 0.109360 NUM iajs-2945 169 107 0.083376 0.083376 NUM iajs-2945 169 108 table table NOUN iajs-2945 169 109 3 3 NUM iajs-2945 169 110 shows show VERB iajs-2945 169 111 the the DET iajs-2945 169 112 numerical numerical PROPN iajs-2945 169 113 simulation simulation PROPN iajs-2945 169 114 solutions solution NOUN iajs-2945 169 115 of of ADP iajs-2945 169 116 mmc_rk mmc_rk PROPN iajs-2945 169 117 and and CCONJ iajs-2945 169 118 mlh_rk mlh_rk PROPN iajs-2945 169 119 for for ADP iajs-2945 169 120 one one NUM iajs-2945 169 121 year year NOUN iajs-2945 169 122 ( ( PUNCT iajs-2945 169 123 2021–2022 2021–2022 NOUN iajs-2945 169 124 ) ) PUNCT iajs-2945 169 125 with with ADP iajs-2945 169 126 100 100 NUM iajs-2945 169 127 repetitions repetition NOUN iajs-2945 169 128 in in ADP iajs-2945 169 129 the the DET iajs-2945 169 130 interval interval NOUN iajs-2945 169 131 [ [ X iajs-2945 169 132 0 0 NUM iajs-2945 169 133 , , PUNCT iajs-2945 169 134 1 1 NUM iajs-2945 169 135 ] ] PUNCT iajs-2945 169 136 and and CCONJ iajs-2945 169 137 real real ADJ iajs-2945 169 138 step step NOUN iajs-2945 169 139 sizes size NOUN iajs-2945 169 140 of of ADP iajs-2945 169 141 0.02 0.02 NUM iajs-2945 169 142 , , PUNCT iajs-2945 169 143 0.08 0.08 NUM iajs-2945 169 144 , , PUNCT iajs-2945 169 145 and and CCONJ iajs-2945 169 146 0.12 0.12 NUM iajs-2945 169 147 weekly weekly ADJ iajs-2945 169 148 and and CCONJ iajs-2945 169 149 monthly monthly ADJ iajs-2945 169 150 , , PUNCT iajs-2945 169 151 respectively respectively ADV iajs-2945 169 152 . . PUNCT iajs-2945 169 153 table table NOUN iajs-2945 169 154 4 4 NUM iajs-2945 169 155 also also ADV iajs-2945 169 156 includes include VERB iajs-2945 169 157 the the DET iajs-2945 169 158 results result NOUN iajs-2945 169 159 of of ADP iajs-2945 169 160 the the DET iajs-2945 169 161 numerical numerical ADJ iajs-2945 169 162 simulations simulation NOUN iajs-2945 169 163 mmc_rk mmc_rk PROPN iajs-2945 169 164 and and CCONJ iajs-2945 169 165 mlh_rk mlh_rk X iajs-2945 169 166 with with ADP iajs-2945 169 167 1000 1000 NUM iajs-2945 169 168 for for ADP iajs-2945 169 169 the the DET iajs-2945 169 170 societal societal ADJ iajs-2945 169 171 groups group NOUN iajs-2945 169 172 in in ADP iajs-2945 169 173 the the DET iajs-2945 169 174 monthly monthly ADJ iajs-2945 169 175 interval interval NOUN iajs-2945 169 176 [ [ X iajs-2945 169 177 0 0 NUM iajs-2945 169 178 , , PUNCT iajs-2945 169 179 48 48 NUM iajs-2945 169 180 ] ] PUNCT iajs-2945 169 181 for for ADP iajs-2945 169 182 the the DET iajs-2945 169 183 future future ADJ iajs-2945 169 184 time time NOUN iajs-2945 169 185 until until ADP iajs-2945 169 186 2025 2025 NUM iajs-2945 169 187 . . PUNCT iajs-2945 170 1 the the DET iajs-2945 170 2 expected expect VERB iajs-2945 170 3 approximate approximate ADJ iajs-2945 170 4 mmc_rk mmc_rk PROPN iajs-2945 170 5 and and CCONJ iajs-2945 170 6 mlh_rk mlh_rk PROPN iajs-2945 170 7 results result NOUN iajs-2945 170 8 have have AUX iajs-2945 170 9 been be AUX iajs-2945 170 10 calculated calculate VERB iajs-2945 170 11 in in ADP iajs-2945 170 12 the the DET iajs-2945 170 13 prediction prediction NOUN iajs-2945 170 14 intervals interval NOUN iajs-2945 170 15 that that PRON iajs-2945 170 16 contain contain VERB iajs-2945 170 17 the the DET iajs-2945 170 18 minimum minimum NOUN iajs-2945 170 19 bound bind VERB iajs-2945 170 20 ( ( PUNCT iajs-2945 170 21 5th 5th ADJ iajs-2945 170 22 percentile percentile ADJ iajs-2945 170 23 ) ) PUNCT iajs-2945 170 24 and and CCONJ iajs-2945 170 25 maximum maximum ADV iajs-2945 170 26 bound bind VERB iajs-2945 170 27 ( ( PUNCT iajs-2945 170 28 95th 95th ADJ iajs-2945 170 29 percentile percentile NOUN iajs-2945 170 30 ) ) PUNCT iajs-2945 170 31 for for ADP iajs-2945 170 32 mmc_rk mmc_rk PROPN iajs-2945 170 33 and and CCONJ iajs-2945 170 34 mlh_rk mlh_rk PROPN iajs-2945 170 35 results result NOUN iajs-2945 170 36 in in ADP iajs-2945 170 37 the the DET iajs-2945 170 38 future future NOUN iajs-2945 170 39 until until ADP iajs-2945 170 40 2025 2025 NUM iajs-2945 170 41 . . PUNCT iajs-2945 171 1 mmc_rk mmc_rk PROPN iajs-2945 171 2 and and CCONJ iajs-2945 171 3 mlh_rk mlh_rk PROPN iajs-2945 171 4 results result NOUN iajs-2945 171 5 must must AUX iajs-2945 171 6 be be AUX iajs-2945 171 7 inside inside ADP iajs-2945 171 8 the the DET iajs-2945 171 9 predicted predict VERB iajs-2945 171 10 intervals interval NOUN iajs-2945 171 11 ; ; PUNCT iajs-2945 171 12 see see VERB iajs-2945 171 13 table table NOUN iajs-2945 171 14 5 5 NUM iajs-2945 171 15 . . PUNCT iajs-2945 171 16 . . PUNCT iajs-2945 172 1 to to PART iajs-2945 172 2 compare compare VERB iajs-2945 172 3 the the DET iajs-2945 172 4 two two NUM iajs-2945 172 5 numerical numerical ADJ iajs-2945 172 6 simulation simulation NOUN iajs-2945 172 7 methods method NOUN iajs-2945 172 8 , , PUNCT iajs-2945 172 9 mmc_rk mmc_rk PROPN iajs-2945 172 10 and and CCONJ iajs-2945 172 11 mlh_rk mlh_rk PROPN iajs-2945 172 12 , , PUNCT iajs-2945 172 13 with with ADP iajs-2945 172 14 the the DET iajs-2945 172 15 numerical numerical ADJ iajs-2945 172 16 rk4 rk4 PROPN iajs-2945 172 17 method method NOUN iajs-2945 172 18 , , PUNCT iajs-2945 172 19 the the DET iajs-2945 172 20 absolute absolute ADJ iajs-2945 172 21 error error NOUN iajs-2945 172 22 for for ADP iajs-2945 172 23 , , PUNCT iajs-2945 172 24 , , PUNCT iajs-2945 172 25 , , PUNCT iajs-2945 172 26 and and CCONJ iajs-2945 172 27 is be AUX iajs-2945 172 28 calculated calculate VERB iajs-2945 172 29 as as ADP iajs-2945 172 30 a a DET iajs-2945 172 31 criterion criterion NOUN iajs-2945 172 32 for for ADP iajs-2945 172 33 comparison comparison NOUN iajs-2945 172 34 from from ADP iajs-2945 172 35 2021 2021 NUM iajs-2945 172 36 to to ADP iajs-2945 172 37 2022 2022 NUM iajs-2945 172 38 . . PUNCT iajs-2945 173 1 in in ADP iajs-2945 173 2 table table NOUN iajs-2945 173 3 6 6 NUM iajs-2945 173 4 , , PUNCT iajs-2945 173 5 it it PRON iajs-2945 173 6 is be AUX iajs-2945 173 7 clear clear ADJ iajs-2945 173 8 that that SCONJ iajs-2945 173 9 the the DET iajs-2945 173 10 mlh_rk mlh_rk PROPN iajs-2945 173 11 method method NOUN iajs-2945 173 12 is be AUX iajs-2945 173 13 more more ADV iajs-2945 173 14 accurate accurate ADJ iajs-2945 173 15 and and CCONJ iajs-2945 173 16 reliable reliable ADJ iajs-2945 173 17 than than ADP iajs-2945 173 18 the the DET iajs-2945 173 19 mmc_rk mmc_rk PROPN iajs-2945 173 20 method method NOUN iajs-2945 173 21 since since SCONJ iajs-2945 173 22 the the DET iajs-2945 173 23 absolute absolute ADJ iajs-2945 173 24 error error NOUN iajs-2945 173 25 of of ADP iajs-2945 173 26 the the DET iajs-2945 173 27 mlh_rk mlh_rk PROPN iajs-2945 173 28 results result NOUN iajs-2945 173 29 is be AUX iajs-2945 173 30 less less ADJ iajs-2945 173 31 than than SCONJ iajs-2945 173 32 the the DET iajs-2945 173 33 mmc_rk mmc_rk PROPN iajs-2945 173 34 results result VERB iajs-2945 173 35 for for ADP iajs-2945 173 36 all all DET iajs-2945 173 37 subpopulations subpopulation NOUN iajs-2945 173 38 of of ADP iajs-2945 173 39 the the DET iajs-2945 173 40 studied studied ADJ iajs-2945 173 41 model model NOUN iajs-2945 173 42 . . PUNCT iajs-2945 174 1 table table NOUN iajs-2945 174 2 7 7 NUM iajs-2945 174 3 shows show VERB iajs-2945 174 4 the the DET iajs-2945 174 5 numerical numerical ADJ iajs-2945 174 6 stability stability NOUN iajs-2945 174 7 of of ADP iajs-2945 174 8 the the DET iajs-2945 174 9 numerical numerical ADJ iajs-2945 174 10 methods method NOUN iajs-2945 174 11 used use VERB iajs-2945 174 12 in in ADP iajs-2945 174 13 the the DET iajs-2945 174 14 current current ADJ iajs-2945 174 15 study study NOUN iajs-2945 174 16 . . PUNCT iajs-2945 175 1 table table NOUN iajs-2945 175 2 7 7 NUM iajs-2945 175 3 also also ADV iajs-2945 175 4 explains explain VERB iajs-2945 175 5 how how SCONJ iajs-2945 175 6 the the DET iajs-2945 175 7 numerical numerical PROPN iajs-2945 175 8 simulation simulation PROPN iajs-2945 175 9 method method NOUN iajs-2945 175 10 ( ( PUNCT iajs-2945 175 11 mlh_rk mlh_rk NUM iajs-2945 175 12 ) ) PUNCT iajs-2945 175 13 becomes become VERB iajs-2945 175 14 more more ADV iajs-2945 175 15 convergent convergent NOUN iajs-2945 175 16 as as SCONJ iajs-2945 175 17 the the DET iajs-2945 175 18 step step NOUN iajs-2945 175 19 size size NOUN iajs-2945 175 20 is be AUX iajs-2945 175 21 reduced reduce VERB iajs-2945 175 22 , , PUNCT iajs-2945 175 23 resulting result VERB iajs-2945 175 24 in in ADP iajs-2945 175 25 a a DET iajs-2945 175 26 smaller small ADJ iajs-2945 175 27 error error NOUN iajs-2945 175 28 between between ADP iajs-2945 175 29 the the DET iajs-2945 175 30 proposed propose VERB iajs-2945 175 31 method method NOUN iajs-2945 175 32 and and CCONJ iajs-2945 175 33 the the DET iajs-2945 175 34 actual actual ADJ iajs-2945 175 35 method method NOUN iajs-2945 175 36 in in ADP iajs-2945 175 37 step step NOUN iajs-2945 175 38 size size NOUN iajs-2945 175 39 . . PUNCT iajs-2945 176 1 to to PART iajs-2945 176 2 prove prove VERB iajs-2945 176 3 the the DET iajs-2945 176 4 convergence convergence NOUN iajs-2945 176 5 of of ADP iajs-2945 176 6 the the DET iajs-2945 176 7 methods method NOUN iajs-2945 176 8 used use VERB iajs-2945 176 9 , , PUNCT iajs-2945 176 10 see see VERB iajs-2945 176 11 [ [ X iajs-2945 176 12 28 28 NUM iajs-2945 176 13 ] ] PUNCT iajs-2945 176 14 . . PUNCT iajs-2945 177 1 ihjpas ihjpas PROPN iajs-2945 177 2 . . PUNCT iajs-2945 178 1 36(3)2023 36(3)2023 NUM iajs-2945 178 2 299 299 NUM iajs-2945 178 3 figure figure NOUN iajs-2945 178 4 3 3 NUM iajs-2945 178 5 . . NOUN iajs-2945 178 6 comparison comparison NOUN iajs-2945 178 7 of of ADP iajs-2945 178 8 numerical numerical ADJ iajs-2945 178 9 and and CCONJ iajs-2945 178 10 numerical numerical PROPN iajs-2945 178 11 simulation simulation NOUN iajs-2945 178 12 solutions solution NOUN iajs-2945 178 13 by by ADP iajs-2945 178 14 using use VERB iajs-2945 178 15 rk4 rk4 NOUN iajs-2945 178 16 , , PUNCT iajs-2945 178 17 mmc_rk mmc_rk PROPN iajs-2945 178 18 and and CCONJ iajs-2945 178 19 mlh_rk mlh_rk PROPN iajs-2945 178 20 of of ADP iajs-2945 178 21 ( ( PUNCT iajs-2945 178 22 a a PRON iajs-2945 178 23 ) ) PUNCT iajs-2945 178 24 𝑆(𝑑 𝑆(𝑑 NUM iajs-2945 178 25 ) ) PUNCT iajs-2945 178 26 , , PUNCT iajs-2945 178 27 ( ( PUNCT iajs-2945 178 28 b b NOUN iajs-2945 178 29 ) ) PUNCT iajs-2945 178 30 𝑉(𝑑 𝑉(𝑑 ADP iajs-2945 178 31 ) ) PUNCT iajs-2945 178 32 , , PUNCT iajs-2945 178 33 ( ( PUNCT iajs-2945 178 34 c c X iajs-2945 178 35 ) ) PUNCT iajs-2945 178 36 𝐴(𝑑 𝐴(𝑑 NOUN iajs-2945 178 37 ) ) PUNCT iajs-2945 178 38 , , PUNCT iajs-2945 178 39 ( ( PUNCT iajs-2945 178 40 d d X iajs-2945 178 41 ) ) PUNCT iajs-2945 178 42 𝐼(𝑑 𝐼(𝑑 NUM iajs-2945 178 43 ) ) PUNCT iajs-2945 178 44 and and CCONJ iajs-2945 178 45 ( ( PUNCT iajs-2945 178 46 e e NOUN iajs-2945 178 47 ) ) PUNCT iajs-2945 178 48 𝑅(𝑑 𝑅(𝑑 NOUN iajs-2945 178 49 ) ) PUNCT iajs-2945 178 50 from from ADP iajs-2945 178 51 2021 2021 NUM iajs-2945 178 52 to to ADP iajs-2945 178 53 2025 2025 NUM iajs-2945 178 54 when when SCONJ iajs-2945 178 55 β„Ž β„Ž X iajs-2945 178 56 = = NOUN iajs-2945 178 57 0.08 0.08 NUM iajs-2945 178 58 monthly monthly ADV iajs-2945 178 59 in in ADP iajs-2945 178 60 iraq iraq PROPN iajs-2945 178 61 . . PUNCT iajs-2945 179 1 ihjpas ihjpas PROPN iajs-2945 179 2 . . PUNCT iajs-2945 180 1 36(3)2023 36(3)2023 NUM iajs-2945 180 2 300 300 NUM iajs-2945 180 3 figure figure NOUN iajs-2945 180 4 4 4 NUM iajs-2945 180 5 . . PUNCT iajs-2945 180 6 comparison comparison PROPN iajs-2945 180 7 numerical numerical PROPN iajs-2945 180 8 simulation simulation PROPN iajs-2945 180 9 mmc_rk mmc_rk PROPN iajs-2945 180 10 and and CCONJ iajs-2945 180 11 mlh_rk mlh_rk PROPN iajs-2945 180 12 results result NOUN iajs-2945 180 13 with with ADP iajs-2945 180 14 numerical numerical ADJ iajs-2945 180 15 rk4 rk4 PROPN iajs-2945 180 16 results result NOUN iajs-2945 180 17 for for ADP iajs-2945 180 18 ( ( PUNCT iajs-2945 180 19 a a PRON iajs-2945 180 20 ) ) PUNCT iajs-2945 180 21 𝑆(𝑑 𝑆(𝑑 NUM iajs-2945 180 22 ) ) PUNCT iajs-2945 180 23 , , PUNCT iajs-2945 180 24 ( ( PUNCT iajs-2945 180 25 b b NOUN iajs-2945 180 26 ) ) PUNCT iajs-2945 180 27 𝑉(𝑑 𝑉(𝑑 ADP iajs-2945 180 28 ) ) PUNCT iajs-2945 180 29 , , PUNCT iajs-2945 180 30 ( ( PUNCT iajs-2945 180 31 c c X iajs-2945 180 32 ) ) PUNCT iajs-2945 180 33 𝐴(𝑑 𝐴(𝑑 NOUN iajs-2945 180 34 ) ) PUNCT iajs-2945 180 35 , , PUNCT iajs-2945 180 36 ( ( PUNCT iajs-2945 180 37 d d X iajs-2945 180 38 ) ) PUNCT iajs-2945 180 39 𝐼(𝑑 𝐼(𝑑 NUM iajs-2945 180 40 ) ) PUNCT iajs-2945 180 41 and and CCONJ iajs-2945 180 42 ( ( PUNCT iajs-2945 180 43 e e NOUN iajs-2945 180 44 ) ) PUNCT iajs-2945 180 45 𝑅(𝑑 𝑅(𝑑 NOUN iajs-2945 180 46 ) ) PUNCT iajs-2945 180 47 from from ADP iajs-2945 180 48 2021 2021 NUM iajs-2945 180 49 to to ADP iajs-2945 180 50 2025 2025 NUM iajs-2945 180 51 when when SCONJ iajs-2945 180 52 β„Ž β„Ž X iajs-2945 180 53 = = SYM iajs-2945 180 54 0.04 0.04 NUM iajs-2945 180 55 monthly monthly ADV iajs-2945 180 56 in in ADP iajs-2945 180 57 iraq iraq PROPN iajs-2945 180 58 . . PUNCT iajs-2945 181 1 ihjpas ihjpas PROPN iajs-2945 181 2 . . PUNCT iajs-2945 182 1 36(3)2023 36(3)2023 NUM iajs-2945 182 2 301 301 NUM iajs-2945 182 3 figure figure NOUN iajs-2945 182 4 5 5 NUM iajs-2945 182 5 . . PUNCT iajs-2945 183 1 the the DET iajs-2945 183 2 numerical numerical PROPN iajs-2945 183 3 simulation simulation PROPN iajs-2945 183 4 results result VERB iajs-2945 183 5 mmc_rk mmc_rk PROPN iajs-2945 183 6 and and CCONJ iajs-2945 183 7 mlh_rk mlh_rk PROPN iajs-2945 183 8 of of ADP iajs-2945 183 9 ( ( PUNCT iajs-2945 183 10 a a PRON iajs-2945 183 11 ) ) PUNCT iajs-2945 183 12 𝑆(𝑑 𝑆(𝑑 NUM iajs-2945 183 13 ) ) PUNCT iajs-2945 183 14 , , PUNCT iajs-2945 183 15 ( ( PUNCT iajs-2945 183 16 b b NOUN iajs-2945 183 17 ) ) PUNCT iajs-2945 183 18 𝑉(𝑑 𝑉(𝑑 ADP iajs-2945 183 19 ) ) PUNCT iajs-2945 183 20 , , PUNCT iajs-2945 183 21 ( ( PUNCT iajs-2945 183 22 c c X iajs-2945 183 23 ) ) PUNCT iajs-2945 183 24 𝐴(𝑑 𝐴(𝑑 NOUN iajs-2945 183 25 ) ) PUNCT iajs-2945 183 26 , , PUNCT iajs-2945 183 27 ( ( PUNCT iajs-2945 183 28 d d X iajs-2945 183 29 ) ) PUNCT iajs-2945 183 30 𝐼(𝑑 𝐼(𝑑 NUM iajs-2945 183 31 ) ) PUNCT iajs-2945 183 32 and and CCONJ iajs-2945 183 33 ( ( PUNCT iajs-2945 183 34 e e NOUN iajs-2945 183 35 ) ) PUNCT iajs-2945 183 36 𝑅(𝑑 𝑅(𝑑 NOUN iajs-2945 183 37 ) ) PUNCT iajs-2945 183 38 from from ADP iajs-2945 183 39 20201to 20201to NOUN iajs-2945 183 40 2025 2025 NUM iajs-2945 183 41 when when SCONJ iajs-2945 183 42 β„Ž β„Ž X iajs-2945 183 43 = = SYM iajs-2945 183 44 0.02 0.02 NUM iajs-2945 183 45 weekly weekly NOUN iajs-2945 183 46 in in ADP iajs-2945 183 47 iraq iraq PROPN iajs-2945 183 48 . . PUNCT iajs-2945 184 1 ihjpas ihjpas PROPN iajs-2945 184 2 . . PUNCT iajs-2945 185 1 36(3)2023 36(3)2023 NUM iajs-2945 185 2 302 302 NUM iajs-2945 185 3 figure figure NOUN iajs-2945 185 4 6 6 NUM iajs-2945 185 5 . . PUNCT iajs-2945 186 1 curve curve NOUN iajs-2945 186 2 fitting fitting ADJ iajs-2945 186 3 for for ADP iajs-2945 186 4 infected infected ADJ iajs-2945 186 5 people people NOUN iajs-2945 186 6 𝐼(𝑑 𝐼(𝑑 NUM iajs-2945 186 7 ) ) PUNCT iajs-2945 186 8 with with ADP iajs-2945 186 9 observing observe VERB iajs-2945 186 10 data datum NOUN iajs-2945 186 11 from from ADP iajs-2945 186 12 2021 2021 NUM iajs-2945 186 13 to to ADP iajs-2945 186 14 2022 2022 NUM iajs-2945 186 15 when when SCONJ iajs-2945 186 16 β„Ž β„Ž X iajs-2945 186 17 = = NOUN iajs-2945 186 18 0.08 0.08 NUM iajs-2945 186 19 monthly monthly ADV iajs-2945 186 20 in in ADP iajs-2945 186 21 iraq iraq PROPN iajs-2945 186 22 . . PUNCT iajs-2945 187 1 fig fig NOUN iajs-2945 187 2 3 3 NUM iajs-2945 187 3 shows show VERB iajs-2945 187 4 the the DET iajs-2945 187 5 curves curve NOUN iajs-2945 187 6 of of ADP iajs-2945 187 7 the the DET iajs-2945 187 8 methods method NOUN iajs-2945 187 9 used use VERB iajs-2945 187 10 in in ADP iajs-2945 187 11 our our PRON iajs-2945 187 12 study study NOUN iajs-2945 187 13 for for ADP iajs-2945 187 14 48 48 NUM iajs-2945 187 15 months month NOUN iajs-2945 187 16 , , PUNCT iajs-2945 187 17 the the DET iajs-2945 187 18 interval interval NOUN iajs-2945 187 19 2021 2021 NUM iajs-2945 187 20 – – PUNCT iajs-2945 187 21 2025 2025 NUM iajs-2945 187 22 , , PUNCT iajs-2945 187 23 in in ADP iajs-2945 187 24 which which PRON iajs-2945 187 25 all all DET iajs-2945 187 26 groups group NOUN iajs-2945 187 27 of of ADP iajs-2945 187 28 society society NOUN iajs-2945 187 29 are be AUX iajs-2945 187 30 shown show VERB iajs-2945 187 31 according accord VERB iajs-2945 187 32 to to ADP iajs-2945 187 33 the the DET iajs-2945 187 34 impact impact NOUN iajs-2945 187 35 of of ADP iajs-2945 187 36 the the DET iajs-2945 187 37 virus virus NOUN iajs-2945 187 38 on on ADP iajs-2945 187 39 them they PRON iajs-2945 187 40 . . PUNCT iajs-2945 188 1 fig fig NOUN iajs-2945 188 2 3(a 3(a NUM iajs-2945 188 3 ) ) PUNCT iajs-2945 188 4 , , PUNCT iajs-2945 188 5 which which PRON iajs-2945 188 6 represents represent VERB iajs-2945 188 7 a a DET iajs-2945 188 8 group group NOUN iajs-2945 188 9 of of ADP iajs-2945 188 10 people people NOUN iajs-2945 188 11 who who PRON iajs-2945 188 12 are be AUX iajs-2945 188 13 not not PART iajs-2945 188 14 infected infect VERB iajs-2945 188 15 with with ADP iajs-2945 188 16 an an DET iajs-2945 188 17 epidemic epidemic NOUN iajs-2945 188 18 but but CCONJ iajs-2945 188 19 are be AUX iajs-2945 188 20 susceptible susceptible ADJ iajs-2945 188 21 to to ADP iajs-2945 188 22 infection infection NOUN iajs-2945 188 23 for for ADP iajs-2945 188 24 this this DET iajs-2945 188 25 class class NOUN iajs-2945 188 26 for for ADP iajs-2945 188 27 all all DET iajs-2945 188 28 rk4 rk4 NOUN iajs-2945 188 29 , , PUNCT iajs-2945 188 30 mmc_rk mmc_rk PROPN iajs-2945 188 31 , , PUNCT iajs-2945 188 32 and and CCONJ iajs-2945 188 33 mlh_rk mlh_rk PROPN iajs-2945 188 34 methods method NOUN iajs-2945 188 35 , , PUNCT iajs-2945 188 36 is be AUX iajs-2945 188 37 used use VERB iajs-2945 188 38 with with ADP iajs-2945 188 39 step step NOUN iajs-2945 188 40 size size NOUN iajs-2945 188 41 weekly weekly ADJ iajs-2945 188 42 and and CCONJ iajs-2945 188 43 monthly monthly ADJ iajs-2945 188 44 through through ADP iajs-2945 188 45 4 4 NUM iajs-2945 188 46 years year NOUN iajs-2945 188 47 . . PUNCT iajs-2945 189 1 there there PRON iajs-2945 189 2 is be VERB iajs-2945 189 3 a a DET iajs-2945 189 4 sudden sudden ADJ iajs-2945 189 5 drop drop NOUN iajs-2945 189 6 in in ADP iajs-2945 189 7 the the DET iajs-2945 189 8 curve curve NOUN iajs-2945 189 9 of of ADP iajs-2945 189 10 this this DET iajs-2945 189 11 group group NOUN iajs-2945 189 12 for for ADP iajs-2945 189 13 all all DET iajs-2945 189 14 the the DET iajs-2945 189 15 methods method NOUN iajs-2945 189 16 used use VERB iajs-2945 189 17 in in ADP iajs-2945 189 18 the the DET iajs-2945 189 19 study study NOUN iajs-2945 189 20 rk4 rk4 NOUN iajs-2945 189 21 , , PUNCT iajs-2945 189 22 mmc_rk mmc_rk PROPN iajs-2945 189 23 , , PUNCT iajs-2945 189 24 and and CCONJ iajs-2945 189 25 mlh_rk mlh_rk VERB iajs-2945 189 26 after after ADP iajs-2945 189 27 the the DET iajs-2945 189 28 33rd 33rd ADJ iajs-2945 189 29 month month NOUN iajs-2945 189 30 , , PUNCT iajs-2945 189 31 then then ADV iajs-2945 189 32 it it PRON iajs-2945 189 33 rises rise VERB iajs-2945 189 34 again again ADV iajs-2945 189 35 after after ADP iajs-2945 189 36 the the DET iajs-2945 189 37 35th 35th ADJ iajs-2945 189 38 month month NOUN iajs-2945 189 39 to to PART iajs-2945 189 40 stabilize stabilize VERB iajs-2945 189 41 during during ADP iajs-2945 189 42 the the DET iajs-2945 189 43 last last ADJ iajs-2945 189 44 months month NOUN iajs-2945 189 45 of of ADP iajs-2945 189 46 our our PRON iajs-2945 189 47 study study NOUN iajs-2945 189 48 . . PUNCT iajs-2945 190 1 because because SCONJ iajs-2945 190 2 of of ADP iajs-2945 190 3 continuos continuo NOUN iajs-2945 190 4 mixing mix VERB iajs-2945 190 5 between between ADP iajs-2945 190 6 the the DET iajs-2945 190 7 people people NOUN iajs-2945 190 8 and and CCONJ iajs-2945 190 9 the the DET iajs-2945 190 10 lack lack NOUN iajs-2945 190 11 of of ADP iajs-2945 190 12 commitment commitment NOUN iajs-2945 190 13 , , PUNCT iajs-2945 190 14 people people NOUN iajs-2945 190 15 in in ADP iajs-2945 190 16 the the DET iajs-2945 190 17 society society NOUN iajs-2945 190 18 can can AUX iajs-2945 190 19 not not PART iajs-2945 190 20 continous continous VERB iajs-2945 190 21 profect profect VERB iajs-2945 190 22 their their PRON iajs-2945 190 23 health health NOUN iajs-2945 190 24 properly properly ADV iajs-2945 190 25 . . PUNCT iajs-2945 191 1 therefore therefore ADV iajs-2945 191 2 , , PUNCT iajs-2945 191 3 we we PRON iajs-2945 191 4 can can AUX iajs-2945 191 5 observe observe VERB iajs-2945 191 6 the the DET iajs-2945 191 7 sudden sudden ADJ iajs-2945 191 8 descent descent NOUN iajs-2945 191 9 in in ADP iajs-2945 191 10 the the DET iajs-2945 191 11 curve curve NOUN iajs-2945 191 12 as as ADP iajs-2945 191 13 a a DET iajs-2945 191 14 result result NOUN iajs-2945 191 15 of of ADP iajs-2945 191 16 a a DET iajs-2945 191 17 large large ADJ iajs-2945 191 18 number number NOUN iajs-2945 191 19 of of ADP iajs-2945 191 20 infections infection NOUN iajs-2945 191 21 , , PUNCT iajs-2945 191 22 particularly particularly ADV iajs-2945 191 23 between between ADP iajs-2945 191 24 the the DET iajs-2945 191 25 25th 25th ADJ iajs-2945 191 26 and and CCONJ iajs-2945 191 27 35th 35th ADJ iajs-2945 191 28 month month NOUN iajs-2945 191 29 of of ADP iajs-2945 191 30 the the DET iajs-2945 191 31 study study NOUN iajs-2945 191 32 period period NOUN iajs-2945 191 33 , , PUNCT iajs-2945 191 34 to to PART iajs-2945 191 35 settle settle VERB iajs-2945 191 36 down down ADP iajs-2945 191 37 after after ADP iajs-2945 191 38 the the DET iajs-2945 191 39 end end NOUN iajs-2945 191 40 of of ADP iajs-2945 191 41 2025 2025 NUM iajs-2945 191 42 . . PUNCT iajs-2945 192 1 fig fig NOUN iajs-2945 192 2 3(b 3(b NUM iajs-2945 192 3 ) ) PUNCT iajs-2945 192 4 shows show VERB iajs-2945 192 5 a a DET iajs-2945 192 6 curved curved ADJ iajs-2945 192 7 group group NOUN iajs-2945 192 8 of of ADP iajs-2945 192 9 vaccinated vaccinated ADJ iajs-2945 192 10 people people NOUN iajs-2945 192 11 against against ADP iajs-2945 192 12 covid-19 covid-19 PROPN iajs-2945 192 13 in in ADP iajs-2945 192 14 iraq iraq PROPN iajs-2945 192 15 , , PUNCT iajs-2945 192 16 where where SCONJ iajs-2945 192 17 we we PRON iajs-2945 192 18 show show VERB iajs-2945 192 19 that that SCONJ iajs-2945 192 20 there there PRON iajs-2945 192 21 is be VERB iajs-2945 192 22 a a DET iajs-2945 192 23 simple simple ADJ iajs-2945 192 24 rise rise NOUN iajs-2945 192 25 in in ADP iajs-2945 192 26 the the DET iajs-2945 192 27 curve curve NOUN iajs-2945 192 28 for for ADP iajs-2945 192 29 all all DET iajs-2945 192 30 rk4 rk4 NOUN iajs-2945 192 31 , , PUNCT iajs-2945 192 32 mmc_rk mmc_rk PROPN iajs-2945 192 33 , , PUNCT iajs-2945 192 34 and and CCONJ iajs-2945 192 35 mlh_rk mlh_rk PROPN iajs-2945 192 36 methods method NOUN iajs-2945 192 37 used use VERB iajs-2945 192 38 in in ADP iajs-2945 192 39 the the DET iajs-2945 192 40 study study NOUN iajs-2945 192 41 from from ADP iajs-2945 192 42 the the DET iajs-2945 192 43 beginning beginning NOUN iajs-2945 192 44 of of ADP iajs-2945 192 45 the the DET iajs-2945 192 46 vaccine vaccine NOUN iajs-2945 192 47 until until ADP iajs-2945 192 48 the the DET iajs-2945 192 49 25th 25th ADJ iajs-2945 192 50 month month NOUN iajs-2945 192 51 . . PUNCT iajs-2945 193 1 the the DET iajs-2945 193 2 large large ADJ iajs-2945 193 3 number number NOUN iajs-2945 193 4 of of ADP iajs-2945 193 5 people people NOUN iajs-2945 193 6 wanting want VERB iajs-2945 193 7 to to PART iajs-2945 193 8 get get VERB iajs-2945 193 9 the the DET iajs-2945 193 10 vaccine vaccine NOUN iajs-2945 193 11 as as ADP iajs-2945 193 12 a a DET iajs-2945 193 13 result result NOUN iajs-2945 193 14 of of ADP iajs-2945 193 15 rising rise VERB iajs-2945 193 16 health health NOUN iajs-2945 193 17 and and CCONJ iajs-2945 193 18 cultural cultural ADJ iajs-2945 193 19 awareness awareness NOUN iajs-2945 193 20 has have AUX iajs-2945 193 21 resulted result VERB iajs-2945 193 22 in in ADP iajs-2945 193 23 a a DET iajs-2945 193 24 dramatic dramatic ADJ iajs-2945 193 25 increase increase NOUN iajs-2945 193 26 , , PUNCT iajs-2945 193 27 particularly particularly ADV iajs-2945 193 28 between between ADP iajs-2945 193 29 the the DET iajs-2945 193 30 27th 27th ADJ iajs-2945 193 31 and and CCONJ iajs-2945 193 32 35th 35th ADJ iajs-2945 193 33 month month NOUN iajs-2945 193 34 , , PUNCT iajs-2945 193 35 after after ADP iajs-2945 193 36 which which PRON iajs-2945 193 37 the the DET iajs-2945 193 38 curve curve NOUN iajs-2945 193 39 stabilized stabilize VERB iajs-2945 193 40 until until ADP iajs-2945 193 41 the the DET iajs-2945 193 42 end end NOUN iajs-2945 193 43 of of ADP iajs-2945 193 44 the the DET iajs-2945 193 45 study study NOUN iajs-2945 193 46 period period NOUN iajs-2945 193 47 . . PUNCT iajs-2945 194 1 fig fig NOUN iajs-2945 194 2 3(c 3(c NUM iajs-2945 194 3 ) ) PUNCT iajs-2945 194 4 depicts depict VERB iajs-2945 194 5 the the DET iajs-2945 194 6 subpopulation subpopulation NOUN iajs-2945 194 7 as as ADP iajs-2945 194 8 asymptomatic asymptomatic ADJ iajs-2945 194 9 with with ADP iajs-2945 194 10 the the DET iajs-2945 194 11 epidemic epidemic NOUN iajs-2945 194 12 but but CCONJ iajs-2945 194 13 not not PART iajs-2945 194 14 showing show VERB iajs-2945 194 15 symptoms symptom NOUN iajs-2945 194 16 of of ADP iajs-2945 194 17 infection.there infection.there NOUN iajs-2945 194 18 is be AUX iajs-2945 194 19 a a DET iajs-2945 194 20 simple simple ADJ iajs-2945 194 21 rise rise NOUN iajs-2945 194 22 in in ADP iajs-2945 194 23 the the DET iajs-2945 194 24 first first ADJ iajs-2945 194 25 study study NOUN iajs-2945 194 26 months month NOUN iajs-2945 194 27 , , PUNCT iajs-2945 194 28 bringing bring VERB iajs-2945 194 29 the the DET iajs-2945 194 30 curve curve NOUN iajs-2945 194 31 of of ADP iajs-2945 194 32 this this DET iajs-2945 194 33 group group NOUN iajs-2945 194 34 to to ADP iajs-2945 194 35 its its PRON iajs-2945 194 36 highest high ADJ iajs-2945 194 37 level level NOUN iajs-2945 194 38 between between ADP iajs-2945 194 39 the the DET iajs-2945 194 40 15th 15th ADJ iajs-2945 194 41 and and CCONJ iajs-2945 194 42 30th 30th ADJ iajs-2945 194 43 month month NOUN iajs-2945 194 44 . . PUNCT iajs-2945 195 1 because because SCONJ iajs-2945 195 2 of of ADP iajs-2945 195 3 following follow VERB iajs-2945 195 4 health health NOUN iajs-2945 195 5 prevention prevention NOUN iajs-2945 195 6 methods method NOUN iajs-2945 195 7 , , PUNCT iajs-2945 195 8 the the DET iajs-2945 195 9 instructions instruction NOUN iajs-2945 195 10 of of ADP iajs-2945 195 11 the the DET iajs-2945 195 12 world world PROPN iajs-2945 195 13 health health NOUN iajs-2945 195 14 organization organization NOUN iajs-2945 195 15 , , PUNCT iajs-2945 195 16 and and CCONJ iajs-2945 195 17 the the DET iajs-2945 195 18 demand demand NOUN iajs-2945 195 19 for for ADP iajs-2945 195 20 vaccination vaccination NOUN iajs-2945 195 21 against against ADP iajs-2945 195 22 ihjpas ihjpas PROPN iajs-2945 195 23 . . PUNCT iajs-2945 196 1 36(3)2023 36(3)2023 NUM iajs-2945 196 2 303 303 NUM iajs-2945 196 3 the the DET iajs-2945 196 4 pandemic pandemic NOUN iajs-2945 196 5 , , PUNCT iajs-2945 196 6 the the DET iajs-2945 196 7 curve curve NOUN iajs-2945 196 8 begins begin VERB iajs-2945 196 9 to to PART iajs-2945 196 10 decline decline VERB iajs-2945 196 11 gradually gradually ADV iajs-2945 196 12 until until ADP iajs-2945 196 13 the the DET iajs-2945 196 14 40th 40th ADJ iajs-2945 196 15 month month NOUN iajs-2945 196 16 and and CCONJ iajs-2945 196 17 settles settle VERB iajs-2945 196 18 at at ADP iajs-2945 196 19 the the DET iajs-2945 196 20 beginning beginning NOUN iajs-2945 196 21 of of ADP iajs-2945 196 22 the the DET iajs-2945 196 23 40th 40th ADJ iajs-2945 196 24 month month NOUN iajs-2945 196 25 until until ADP iajs-2945 196 26 the the DET iajs-2945 196 27 end end NOUN iajs-2945 196 28 of of ADP iajs-2945 196 29 the the DET iajs-2945 196 30 year year NOUN iajs-2945 196 31 2025 2025 NUM iajs-2945 196 32 . . PUNCT iajs-2945 197 1 fig fig NOUN iajs-2945 197 2 3(d 3(d NUM iajs-2945 197 3 ) ) PUNCT iajs-2945 197 4 represents represent VERB iajs-2945 197 5 the the DET iajs-2945 197 6 number number NOUN iajs-2945 197 7 of of ADP iajs-2945 197 8 people people NOUN iajs-2945 197 9 infected infect VERB iajs-2945 197 10 with with ADP iajs-2945 197 11 the the DET iajs-2945 197 12 epidemic.the epidemic.the PRON iajs-2945 197 13 curve curve NOUN iajs-2945 197 14 rose rise VERB iajs-2945 197 15 dramatically dramatically ADV iajs-2945 197 16 from from ADP iajs-2945 197 17 the the DET iajs-2945 197 18 15th 15th ADJ iajs-2945 197 19 month month NOUN iajs-2945 197 20 to to ADP iajs-2945 197 21 the the DET iajs-2945 197 22 highest high ADJ iajs-2945 197 23 level level NOUN iajs-2945 197 24 in in ADP iajs-2945 197 25 the the DET iajs-2945 197 26 25th 25th ADJ iajs-2945 197 27 month month NOUN iajs-2945 197 28 , , PUNCT iajs-2945 197 29 and and CCONJ iajs-2945 197 30 then then ADV iajs-2945 197 31 fell fall VERB iajs-2945 197 32 dramatically dramatically ADV iajs-2945 197 33 from from ADP iajs-2945 197 34 the the DET iajs-2945 197 35 33rd 33rd ADJ iajs-2945 197 36 month month NOUN iajs-2945 197 37 to to ADP iajs-2945 197 38 the the DET iajs-2945 197 39 40th 40th ADJ iajs-2945 197 40 month month NOUN iajs-2945 197 41 to to PART iajs-2945 197 42 settle settle VERB iajs-2945 197 43 as as ADP iajs-2945 197 44 a a DET iajs-2945 197 45 result result NOUN iajs-2945 197 46 of of ADP iajs-2945 197 47 increased increase VERB iajs-2945 197 48 health health NOUN iajs-2945 197 49 awareness awareness NOUN iajs-2945 197 50 and and CCONJ iajs-2945 197 51 following follow VERB iajs-2945 197 52 health health NOUN iajs-2945 197 53 guidelines guideline NOUN iajs-2945 197 54 , , PUNCT iajs-2945 197 55 and and CCONJ iajs-2945 197 56 more more ADJ iajs-2945 197 57 people people NOUN iajs-2945 197 58 are be AUX iajs-2945 197 59 convinced convince VERB iajs-2945 197 60 to to PART iajs-2945 197 61 get get VERB iajs-2945 197 62 the the DET iajs-2945 197 63 vaccine vaccine NOUN iajs-2945 197 64 . . PUNCT iajs-2945 198 1 fig fig NOUN iajs-2945 198 2 3(e 3(e NUM iajs-2945 198 3 ) ) PUNCT iajs-2945 198 4 represents represent VERB iajs-2945 198 5 the the DET iajs-2945 198 6 group group NOUN iajs-2945 198 7 of of ADP iajs-2945 198 8 people people NOUN iajs-2945 198 9 who who PRON iajs-2945 198 10 have have AUX iajs-2945 198 11 been be AUX iajs-2945 198 12 cured cure VERB iajs-2945 198 13 of of ADP iajs-2945 198 14 the the DET iajs-2945 198 15 disease disease NOUN iajs-2945 198 16 , , PUNCT iajs-2945 198 17 as as SCONJ iajs-2945 198 18 they they PRON iajs-2945 198 19 have have AUX iajs-2945 198 20 been be AUX iajs-2945 198 21 removed remove VERB iajs-2945 198 22 from from ADP iajs-2945 198 23 the the DET iajs-2945 198 24 list list NOUN iajs-2945 198 25 of of ADP iajs-2945 198 26 positive positive ADJ iajs-2945 198 27 cases case NOUN iajs-2945 198 28 . . PUNCT iajs-2945 199 1 there there PRON iajs-2945 199 2 is be VERB iajs-2945 199 3 a a DET iajs-2945 199 4 gradual gradual ADJ iajs-2945 199 5 rise rise NOUN iajs-2945 199 6 of of ADP iajs-2945 199 7 the the DET iajs-2945 199 8 curve curve NOUN iajs-2945 199 9 of of ADP iajs-2945 199 10 this this DET iajs-2945 199 11 group group NOUN iajs-2945 199 12 until until ADP iajs-2945 199 13 the the DET iajs-2945 199 14 20th 20th ADJ iajs-2945 199 15 month month NOUN iajs-2945 199 16 , , PUNCT iajs-2945 199 17 then then ADV iajs-2945 199 18 it it PRON iajs-2945 199 19 comes come VERB iajs-2945 199 20 down down ADP iajs-2945 199 21 in in ADP iajs-2945 199 22 the the DET iajs-2945 199 23 25th 25th ADJ iajs-2945 199 24 month month NOUN iajs-2945 199 25 , , PUNCT iajs-2945 199 26 then then ADV iajs-2945 199 27 it it PRON iajs-2945 199 28 rises rise VERB iajs-2945 199 29 dramatically dramatically ADV iajs-2945 199 30 to to PART iajs-2945 199 31 reach reach VERB iajs-2945 199 32 its its PRON iajs-2945 199 33 highest high ADJ iajs-2945 199 34 level level NOUN iajs-2945 199 35 in in ADP iajs-2945 199 36 the the DET iajs-2945 199 37 40th 40th ADJ iajs-2945 199 38 month month NOUN iajs-2945 199 39 due due ADP iajs-2945 199 40 to to ADP iajs-2945 199 41 following follow VERB iajs-2945 199 42 world world PROPN iajs-2945 199 43 health health NOUN iajs-2945 199 44 organization organization NOUN iajs-2945 199 45 guidelines guideline NOUN iajs-2945 199 46 , , PUNCT iajs-2945 199 47 so so SCONJ iajs-2945 199 48 more more ADJ iajs-2945 199 49 people people NOUN iajs-2945 199 50 became become VERB iajs-2945 199 51 fully fully ADV iajs-2945 199 52 vaccinated vaccinated ADJ iajs-2945 199 53 , , PUNCT iajs-2945 199 54 then then ADV iajs-2945 199 55 the the DET iajs-2945 199 56 curve curve NOUN iajs-2945 199 57 is be AUX iajs-2945 199 58 still still ADV iajs-2945 199 59 at at ADP iajs-2945 199 60 the the DET iajs-2945 199 61 same same ADJ iajs-2945 199 62 high high ADJ iajs-2945 199 63 level level NOUN iajs-2945 199 64 until until ADP iajs-2945 199 65 the the DET iajs-2945 199 66 end end NOUN iajs-2945 199 67 of of ADP iajs-2945 199 68 the the DET iajs-2945 199 69 study study NOUN iajs-2945 199 70 period period NOUN iajs-2945 199 71 . . PUNCT iajs-2945 200 1 fig fig NOUN iajs-2945 200 2 4 4 NUM iajs-2945 200 3 shows show VERB iajs-2945 200 4 the the DET iajs-2945 200 5 convergence convergence NOUN iajs-2945 200 6 of of ADP iajs-2945 200 7 the the DET iajs-2945 200 8 methods method NOUN iajs-2945 200 9 that that PRON iajs-2945 200 10 are be AUX iajs-2945 200 11 used use VERB iajs-2945 200 12 , , PUNCT iajs-2945 200 13 where where SCONJ iajs-2945 200 14 the the DET iajs-2945 200 15 result result NOUN iajs-2945 200 16 that that PRON iajs-2945 200 17 has have VERB iajs-2945 200 18 the the DET iajs-2945 200 19 smallest small ADJ iajs-2945 200 20 step step NOUN iajs-2945 200 21 size size NOUN iajs-2945 200 22 has have VERB iajs-2945 200 23 the the DET iajs-2945 200 24 greatest great ADJ iajs-2945 200 25 convergence convergence NOUN iajs-2945 200 26 . . PUNCT iajs-2945 201 1 the the DET iajs-2945 201 2 convergence convergence NOUN iajs-2945 201 3 between between ADP iajs-2945 201 4 the the DET iajs-2945 201 5 numerical numerical PROPN iajs-2945 201 6 simulation simulation PROPN iajs-2945 201 7 methods method NOUN iajs-2945 201 8 and and CCONJ iajs-2945 201 9 the the DET iajs-2945 201 10 numerical numerical PROPN iajs-2945 201 11 method method PROPN iajs-2945 201 12 runge runge NOUN iajs-2945 201 13 - - PUNCT iajs-2945 201 14 kutta kutta NOUN iajs-2945 201 15 ( ( PUNCT iajs-2945 201 16 rk4 rk4 NOUN iajs-2945 201 17 ) ) PUNCT iajs-2945 201 18 , , PUNCT iajs-2945 201 19 which which PRON iajs-2945 201 20 represented represent VERB iajs-2945 201 21 the the DET iajs-2945 201 22 exact exact ADJ iajs-2945 201 23 solution solution NOUN iajs-2945 201 24 , , PUNCT iajs-2945 201 25 in in ADP iajs-2945 201 26 figure figure NOUN iajs-2945 201 27 4 4 NUM iajs-2945 201 28 , , PUNCT iajs-2945 201 29 is be AUX iajs-2945 201 30 greater great ADJ iajs-2945 201 31 than than ADP iajs-2945 201 32 the the DET iajs-2945 201 33 convergence convergence NOUN iajs-2945 201 34 in in ADP iajs-2945 201 35 fig fig NOUN iajs-2945 201 36 3 3 NUM iajs-2945 201 37 because because SCONJ iajs-2945 201 38 the the DET iajs-2945 201 39 step step NOUN iajs-2945 201 40 size size NOUN iajs-2945 201 41 in in ADP iajs-2945 201 42 fig fig NOUN iajs-2945 201 43 4 4 NUM iajs-2945 201 44 is be AUX iajs-2945 201 45 smaller small ADJ iajs-2945 201 46 . . PUNCT iajs-2945 202 1 also also ADV iajs-2945 202 2 , , PUNCT iajs-2945 202 3 we we PRON iajs-2945 202 4 notice notice VERB iajs-2945 202 5 that that SCONJ iajs-2945 202 6 the the DET iajs-2945 202 7 mlh_rk mlh_rk PROPN iajs-2945 202 8 method method NOUN iajs-2945 202 9 is be AUX iajs-2945 202 10 more more ADV iajs-2945 202 11 convergent convergent ADJ iajs-2945 202 12 than than ADP iajs-2945 202 13 mmc_rk mmc_rk PROPN iajs-2945 202 14 to to ADP iajs-2945 202 15 rk4 rk4 PROPN iajs-2945 202 16 . . PUNCT iajs-2945 203 1 fig fig NOUN iajs-2945 203 2 5 5 NUM iajs-2945 203 3 explains explain VERB iajs-2945 203 4 the the DET iajs-2945 203 5 similarities similarity NOUN iajs-2945 203 6 in in ADP iajs-2945 203 7 the the DET iajs-2945 203 8 behavior behavior NOUN iajs-2945 203 9 of of ADP iajs-2945 203 10 the the DET iajs-2945 203 11 solution solution NOUN iajs-2945 203 12 for for ADP iajs-2945 203 13 the the DET iajs-2945 203 14 proposed propose VERB iajs-2945 203 15 numerical numerical ADJ iajs-2945 203 16 simulations simulation NOUN iajs-2945 203 17 using use VERB iajs-2945 203 18 the the DET iajs-2945 203 19 mmc_rk mmc_rk PROPN iajs-2945 203 20 and and CCONJ iajs-2945 203 21 mlh_rk mlh_rk PROPN iajs-2945 203 22 methods method NOUN iajs-2945 203 23 despite despite SCONJ iajs-2945 203 24 the the DET iajs-2945 203 25 change change NOUN iajs-2945 203 26 in in ADP iajs-2945 203 27 the the DET iajs-2945 203 28 step step NOUN iajs-2945 203 29 size size NOUN iajs-2945 203 30 ( ( PUNCT iajs-2945 203 31 weekly weekly ADJ iajs-2945 203 32 with with ADP iajs-2945 203 33 100 100 NUM iajs-2945 203 34 repetitions repetition NOUN iajs-2945 203 35 ) ) PUNCT iajs-2945 203 36 for for ADP iajs-2945 203 37 each each DET iajs-2945 203 38 subpopulation subpopulation NOUN iajs-2945 203 39 , , PUNCT iajs-2945 203 40 , , PUNCT iajs-2945 203 41 , , PUNCT iajs-2945 203 42 , , PUNCT iajs-2945 203 43 and and CCONJ iajs-2945 203 44 for for ADP iajs-2945 203 45 covid-19 covid-19 PROPN iajs-2945 203 46 model model NOUN iajs-2945 203 47 for for ADP iajs-2945 203 48 four four NUM iajs-2945 203 49 years year NOUN iajs-2945 203 50 from from ADP iajs-2945 203 51 2021 2021 NUM iajs-2945 203 52 to to ADP iajs-2945 203 53 2025 2025 NUM iajs-2945 203 54 . . PUNCT iajs-2945 204 1 finally finally ADV iajs-2945 204 2 , , PUNCT iajs-2945 204 3 fig fig NOUN iajs-2945 204 4 6 6 NUM iajs-2945 204 5 shows show VERB iajs-2945 204 6 the the DET iajs-2945 204 7 curve curve NOUN iajs-2945 204 8 fitting fitting ADJ iajs-2945 204 9 of of ADP iajs-2945 204 10 real real ADJ iajs-2945 204 11 observed observed ADJ iajs-2945 204 12 data datum NOUN iajs-2945 204 13 from from ADP iajs-2945 204 14 the the DET iajs-2945 204 15 world world PROPN iajs-2945 204 16 health health NOUN iajs-2945 204 17 organization organization NOUN iajs-2945 204 18 , , PUNCT iajs-2945 204 19 utilizing utilize VERB iajs-2945 204 20 the the DET iajs-2945 204 21 concept concept NOUN iajs-2945 204 22 of of ADP iajs-2945 204 23 linear linear ADJ iajs-2945 204 24 regression regression NOUN iajs-2945 204 25 for for ADP iajs-2945 204 26 the the DET iajs-2945 204 27 class class NOUN iajs-2945 204 28 of of ADP iajs-2945 204 29 people people NOUN iajs-2945 204 30 who who PRON iajs-2945 204 31 suffer suffer VERB iajs-2945 204 32 from from ADP iajs-2945 204 33 infection infection NOUN iajs-2945 204 34 during during ADP iajs-2945 204 35 the the DET iajs-2945 204 36 12 12 NUM iajs-2945 204 37 months month NOUN iajs-2945 204 38 from from ADP iajs-2945 204 39 2021 2021 NUM iajs-2945 204 40 to to ADP iajs-2945 204 41 2022 2022 NUM iajs-2945 204 42 using use VERB iajs-2945 204 43 the the DET iajs-2945 204 44 magic magic ADJ iajs-2945 204 45 plot plot NOUN iajs-2945 204 46 program program NOUN iajs-2945 204 47 . . PUNCT iajs-2945 205 1 6 6 X iajs-2945 205 2 . . X iajs-2945 205 3 conclusion conclusion NOUN iajs-2945 205 4 the the DET iajs-2945 205 5 epidemiological epidemiological ADJ iajs-2945 205 6 covid-19 covid-19 PROPN iajs-2945 205 7 model model NOUN iajs-2945 205 8 in in ADP iajs-2945 205 9 our our PRON iajs-2945 205 10 current current ADJ iajs-2945 205 11 study study NOUN iajs-2945 205 12 has have AUX iajs-2945 205 13 been be AUX iajs-2945 205 14 solved solve VERB iajs-2945 205 15 for for ADP iajs-2945 205 16 48 48 NUM iajs-2945 205 17 months month NOUN iajs-2945 205 18 , , PUNCT iajs-2945 205 19 from from ADP iajs-2945 205 20 2021 2021 NUM iajs-2945 205 21 to to ADP iajs-2945 205 22 2022 2022 NUM iajs-2945 205 23 . . PUNCT iajs-2945 206 1 many many ADJ iajs-2945 206 2 methods method NOUN iajs-2945 206 3 are be AUX iajs-2945 206 4 employed employ VERB iajs-2945 206 5 , , PUNCT iajs-2945 206 6 including include VERB iajs-2945 206 7 the the DET iajs-2945 206 8 numerical numerical ADJ iajs-2945 206 9 rk4 rk4 PROPN iajs-2945 206 10 method method NOUN iajs-2945 206 11 and and CCONJ iajs-2945 206 12 the the DET iajs-2945 206 13 other other ADJ iajs-2945 206 14 two two NUM iajs-2945 206 15 numerical numerical ADJ iajs-2945 206 16 simulation simulation NOUN iajs-2945 206 17 methods method NOUN iajs-2945 206 18 mmc_rk mmc_rk PROPN iajs-2945 206 19 and and CCONJ iajs-2945 206 20 mlh_rk mlh_rk PROPN iajs-2945 206 21 , , PUNCT iajs-2945 206 22 to to PART iajs-2945 206 23 solve solve VERB iajs-2945 206 24 this this DET iajs-2945 206 25 model model NOUN iajs-2945 206 26 . . PUNCT iajs-2945 207 1 in in ADP iajs-2945 207 2 this this DET iajs-2945 207 3 study study NOUN iajs-2945 207 4 , , PUNCT iajs-2945 207 5 we we PRON iajs-2945 207 6 found find VERB iajs-2945 207 7 convergence convergence NOUN iajs-2945 207 8 in in ADP iajs-2945 207 9 the the DET iajs-2945 207 10 results result NOUN iajs-2945 207 11 for for ADP iajs-2945 207 12 all all DET iajs-2945 207 13 methods method NOUN iajs-2945 207 14 that that PRON iajs-2945 207 15 we we PRON iajs-2945 207 16 used use VERB iajs-2945 207 17 , , PUNCT iajs-2945 207 18 but but CCONJ iajs-2945 207 19 the the DET iajs-2945 207 20 mlh_rk mlh_rk PROPN iajs-2945 207 21 method method NOUN iajs-2945 207 22 is be AUX iajs-2945 207 23 the the DET iajs-2945 207 24 closest close ADJ iajs-2945 207 25 to to ADP iajs-2945 207 26 the the DET iajs-2945 207 27 numerical numerical ADJ iajs-2945 207 28 method method NOUN iajs-2945 207 29 ( ( PUNCT iajs-2945 207 30 rk4 rk4 NOUN iajs-2945 207 31 ) ) PUNCT iajs-2945 207 32 ; ; PUNCT iajs-2945 207 33 the the DET iajs-2945 207 34 curve curve NOUN iajs-2945 207 35 of of ADP iajs-2945 207 36 mlh_rk mlh_rk PROPN iajs-2945 207 37 results result NOUN iajs-2945 207 38 is be AUX iajs-2945 207 39 more more ADV iajs-2945 207 40 convergent convergent NOUN iajs-2945 207 41 with with ADP iajs-2945 207 42 the the DET iajs-2945 207 43 curve curve NOUN iajs-2945 207 44 of of ADP iajs-2945 207 45 rk4 rk4 NOUN iajs-2945 207 46 results result NOUN iajs-2945 207 47 than than ADP iajs-2945 207 48 the the DET iajs-2945 207 49 curve curve NOUN iajs-2945 207 50 of of ADP iajs-2945 207 51 mmc_rk mmc_rk PROPN iajs-2945 207 52 results result NOUN iajs-2945 207 53 . . PUNCT iajs-2945 208 1 therefore therefore ADV iajs-2945 208 2 , , PUNCT iajs-2945 208 3 it it PRON iajs-2945 208 4 is be AUX iajs-2945 208 5 considered consider VERB iajs-2945 208 6 the the DET iajs-2945 208 7 most most ADV iajs-2945 208 8 efficient efficient ADJ iajs-2945 208 9 approximation approximation NOUN iajs-2945 208 10 method method NOUN iajs-2945 208 11 for for ADP iajs-2945 208 12 solving solve VERB iajs-2945 208 13 this this DET iajs-2945 208 14 model model NOUN iajs-2945 208 15 . . PUNCT iajs-2945 209 1 also also ADV iajs-2945 209 2 , , PUNCT iajs-2945 209 3 we we PRON iajs-2945 209 4 found find VERB iajs-2945 209 5 that that SCONJ iajs-2945 209 6 the the DET iajs-2945 209 7 epidemic epidemic NOUN iajs-2945 209 8 model model NOUN iajs-2945 209 9 gives give VERB iajs-2945 209 10 an an DET iajs-2945 209 11 impression impression NOUN iajs-2945 209 12 of of ADP iajs-2945 209 13 the the DET iajs-2945 209 14 impact impact NOUN iajs-2945 209 15 of of ADP iajs-2945 209 16 this this DET iajs-2945 209 17 virus virus NOUN iajs-2945 209 18 on on ADP iajs-2945 209 19 society society NOUN iajs-2945 209 20 . . PUNCT iajs-2945 210 1 the the DET iajs-2945 210 2 results result NOUN iajs-2945 210 3 showed show VERB iajs-2945 210 4 that that SCONJ iajs-2945 210 5 the the DET iajs-2945 210 6 category category NOUN iajs-2945 210 7 of of ADP iajs-2945 210 8 people people NOUN iajs-2945 210 9 not not PART iajs-2945 210 10 infected infect VERB iajs-2945 210 11 with with ADP iajs-2945 210 12 the the DET iajs-2945 210 13 epidemic epidemic NOUN iajs-2945 210 14 began begin VERB iajs-2945 210 15 to to PART iajs-2945 210 16 decrease decrease VERB iajs-2945 210 17 during during ADP iajs-2945 210 18 the the DET iajs-2945 210 19 study study NOUN iajs-2945 210 20 interval interval NOUN iajs-2945 210 21 , , PUNCT iajs-2945 210 22 while while SCONJ iajs-2945 210 23 the the DET iajs-2945 210 24 category category NOUN iajs-2945 210 25 associated associate VERB iajs-2945 210 26 with with ADP iajs-2945 210 27 vaccinated vaccinated ADJ iajs-2945 210 28 people people NOUN iajs-2945 210 29 increased increase VERB iajs-2945 210 30 . . PUNCT iajs-2945 211 1 there there PRON iajs-2945 211 2 is be VERB iajs-2945 211 3 a a DET iajs-2945 211 4 gradual gradual ADJ iajs-2945 211 5 increase increase NOUN iajs-2945 211 6 in in ADP iajs-2945 211 7 the the DET iajs-2945 211 8 category category NOUN iajs-2945 211 9 of of ADP iajs-2945 211 10 infected infected ADJ iajs-2945 211 11 people people NOUN iajs-2945 211 12 who who PRON iajs-2945 211 13 do do AUX iajs-2945 211 14 not not PART iajs-2945 211 15 show show VERB iajs-2945 211 16 symptoms symptom NOUN iajs-2945 211 17 because because SCONJ iajs-2945 211 18 education education NOUN iajs-2945 211 19 does do AUX iajs-2945 211 20 not not PART iajs-2945 211 21 adhere adhere VERB iajs-2945 211 22 to to ADP iajs-2945 211 23 health health NOUN iajs-2945 211 24 prevention prevention NOUN iajs-2945 211 25 methods method NOUN iajs-2945 211 26 , , PUNCT iajs-2945 211 27 as as ADV iajs-2945 211 28 well well ADV iajs-2945 211 29 as as ADP iajs-2945 211 30 social social ADJ iajs-2945 211 31 distancing.then distancing.then PRON iajs-2945 211 32 it it PRON iajs-2945 211 33 decreases decrease VERB iajs-2945 211 34 in in ADP iajs-2945 211 35 the the DET iajs-2945 211 36 last last ADJ iajs-2945 211 37 months month NOUN iajs-2945 211 38 of of ADP iajs-2945 211 39 the the DET iajs-2945 211 40 study study NOUN iajs-2945 211 41 period period NOUN iajs-2945 211 42 . . 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