id sid tid token lemma pos ijassa-1224 1 1 microsoft microsoft PROPN ijassa-1224 1 2 word word PROPN ijassa-1224 1 3 1224 1224 NUM ijassa-1224 1 4 - - PUNCT ijassa-1224 1 5 article article NOUN ijassa-1224 1 6 text-5527 text-5527 VERB ijassa-1224 1 7 - - PUNCT ijassa-1224 1 8 1 1 NUM ijassa-1224 1 9 - - PUNCT ijassa-1224 1 10 18 18 NUM ijassa-1224 1 11 - - PUNCT ijassa-1224 1 12 20230104 20230104 NUM ijassa-1224 1 13 adv adv PROPN ijassa-1224 1 14 syst syst PROPN ijassa-1224 1 15 sci sci PROPN ijassa-1224 1 16 appl appl PROPN ijassa-1224 1 17 2022 2022 NUM ijassa-1224 1 18 ; ; PUNCT ijassa-1224 1 19 04 04 NUM ijassa-1224 1 20 ; ; PUNCT ijassa-1224 1 21 144 144 NUM ijassa-1224 1 22 - - SYM ijassa-1224 1 23 161 161 NUM ijassa-1224 1 24 published publish VERB ijassa-1224 1 25 online online ADV ijassa-1224 1 26 at at ADP ijassa-1224 1 27 http://ijassa.ipu.ru http://ijassa.ipu.ru ADV ijassa-1224 1 28 . . PUNCT ijassa-1224 2 1 analysis analysis NOUN ijassa-1224 2 2 and and CCONJ ijassa-1224 2 3 dynamics dynamic NOUN ijassa-1224 2 4 of of ADP ijassa-1224 2 5 tuberculosis tuberculosis NOUN ijassa-1224 2 6 outbreak outbreak NOUN ijassa-1224 2 7 : : PUNCT ijassa-1224 2 8 a a DET ijassa-1224 2 9 mathematical mathematical ADJ ijassa-1224 2 10 modelling modelling NOUN ijassa-1224 2 11 approach approach NOUN ijassa-1224 2 12 festus festus PROPN ijassa-1224 2 13 abiodun abiodun PROPN ijassa-1224 2 14 oguntolu1 oguntolu1 PROPN ijassa-1224 2 15 , , PUNCT ijassa-1224 2 16 olumuyiwa olumuyiwa PROPN ijassa-1224 2 17 james james PROPN ijassa-1224 2 18 peter2,3 peter2,3 PROPN ijassa-1224 2 19 * * PROPN ijassa-1224 2 20 , , PUNCT ijassa-1224 2 21 kayode kayode PROPN ijassa-1224 2 22 oshinubi4 oshinubi4 PROPN ijassa-1224 2 23 , , PUNCT ijassa-1224 2 24 tawakalt tawakalt NOUN ijassa-1224 2 25 abosede abosede NOUN ijassa-1224 2 26 ayoola5 ayoola5 PROPN ijassa-1224 2 27 , , PUNCT ijassa-1224 2 28 asimiyu asimiyu PROPN ijassa-1224 2 29 olalekan olalekan PROPN ijassa-1224 2 30 oladapo5 oladapo5 PROPN ijassa-1224 2 31 , , PUNCT ijassa-1224 2 32 mayowa mayowa ADJ ijassa-1224 2 33 m. m. NOUN ijassa-1224 2 34 ojo6,7 ojo6,7 PROPN ijassa-1224 2 35 1)department 1)department NUM ijassa-1224 2 36 of of ADP ijassa-1224 2 37 mathematics mathematic NOUN ijassa-1224 2 38 , , PUNCT ijassa-1224 2 39 federal federal ADJ ijassa-1224 2 40 university university PROPN ijassa-1224 2 41 of of ADP ijassa-1224 2 42 technology technology NOUN ijassa-1224 2 43 minna minna NOUN ijassa-1224 2 44 , , PUNCT ijassa-1224 2 45 minna minna NOUN ijassa-1224 2 46 , , PUNCT ijassa-1224 2 47 nigeria nigeria PROPN ijassa-1224 2 48 2)department 2)department NUM ijassa-1224 2 49 of of ADP ijassa-1224 2 50 mathematical mathematical ADJ ijassa-1224 2 51 and and CCONJ ijassa-1224 2 52 computer computer NOUN ijassa-1224 2 53 sciences science NOUN ijassa-1224 2 54 , , PUNCT ijassa-1224 2 55 university university NOUN ijassa-1224 2 56 of of ADP ijassa-1224 2 57 medical medical ADJ ijassa-1224 2 58 sciences sciences PROPN ijassa-1224 2 59 , , PUNCT ijassa-1224 2 60 ondo ondo NOUN ijassa-1224 2 61 city city NOUN ijassa-1224 2 62 , , PUNCT ijassa-1224 2 63 ondo ondo PROPN ijassa-1224 2 64 state state PROPN ijassa-1224 2 65 , , PUNCT ijassa-1224 2 66 nigeria nigeria PROPN ijassa-1224 2 67 3)department 3)department NUM ijassa-1224 2 68 of of ADP ijassa-1224 2 69 epidemiology epidemiology NOUN ijassa-1224 2 70 and and CCONJ ijassa-1224 2 71 biostatistics biostatistic NOUN ijassa-1224 2 72 , , PUNCT ijassa-1224 2 73 school school NOUN ijassa-1224 2 74 of of ADP ijassa-1224 2 75 public public ADJ ijassa-1224 2 76 health health NOUN ijassa-1224 2 77 , , PUNCT ijassa-1224 2 78 university university NOUN ijassa-1224 2 79 of of ADP ijassa-1224 2 80 medical medical ADJ ijassa-1224 2 81 sciences sciences PROPN ijassa-1224 2 82 , , PUNCT ijassa-1224 2 83 ondo ondo NOUN ijassa-1224 2 84 city city NOUN ijassa-1224 2 85 , , PUNCT ijassa-1224 2 86 ondo ondo NOUN ijassa-1224 2 87 state state PROPN ijassa-1224 2 88 , , PUNCT ijassa-1224 2 89 nigeria nigeria PROPN ijassa-1224 2 90 . . PUNCT ijassa-1224 3 1 4)agies 4)agies NUM ijassa-1224 3 2 research research NOUN ijassa-1224 3 3 unit unit NOUN ijassa-1224 3 4 , , PUNCT ijassa-1224 3 5 universite universite PROPN ijassa-1224 3 6 grenoble grenoble PROPN ijassa-1224 3 7 alpes alpes PROPN ijassa-1224 3 8 , , PUNCT ijassa-1224 3 9 alpes alpes PROPN ijassa-1224 3 10 , , PUNCT ijassa-1224 3 11 france france PROPN ijassa-1224 3 12 5)department 5)department NUM ijassa-1224 3 13 of of ADP ijassa-1224 3 14 mathematics mathematic NOUN ijassa-1224 3 15 , , PUNCT ijassa-1224 3 16 osun osun PROPN ijassa-1224 3 17 state state PROPN ijassa-1224 3 18 university university PROPN ijassa-1224 3 19 oshogbo oshogbo NOUN ijassa-1224 3 20 , , PUNCT ijassa-1224 3 21 nigeria nigeria PROPN ijassa-1224 3 22 6)department 6)department NUM ijassa-1224 3 23 of of ADP ijassa-1224 3 24 mathematical mathematical ADJ ijassa-1224 3 25 sciences science NOUN ijassa-1224 3 26 , , PUNCT ijassa-1224 3 27 university university NOUN ijassa-1224 3 28 of of ADP ijassa-1224 3 29 south south PROPN ijassa-1224 3 30 africa africa PROPN ijassa-1224 3 31 , , PUNCT ijassa-1224 3 32 florida florida PROPN ijassa-1224 3 33 , , PUNCT ijassa-1224 3 34 south south PROPN ijassa-1224 3 35 africa africa PROPN ijassa-1224 3 36 7)thermo 7)thermo PROPN ijassa-1224 3 37 fisher fisher PROPN ijassa-1224 3 38 scientific scientific NOUN ijassa-1224 3 39 , , PUNCT ijassa-1224 3 40 microbiology microbiology NOUN ijassa-1224 3 41 division division NOUN ijassa-1224 3 42 , , PUNCT ijassa-1224 3 43 lenexa lenexa NOUN ijassa-1224 3 44 , , PUNCT ijassa-1224 3 45 kansas kansas PROPN ijassa-1224 3 46 , , PUNCT ijassa-1224 3 47 usa usa PROPN ijassa-1224 3 48 e e PROPN ijassa-1224 3 49 - - NOUN ijassa-1224 3 50 mail mail NOUN ijassa-1224 3 51 : : PUNCT ijassa-1224 3 52 peterjames4real@gmail.com peterjames4real@gmail.com NUM ijassa-1224 3 53 abstract abstract NOUN ijassa-1224 3 54 : : PUNCT ijassa-1224 3 55 tuberculosis tuberculosis NOUN ijassa-1224 3 56 ( ( PUNCT ijassa-1224 3 57 tb tb NOUN ijassa-1224 3 58 ) ) PUNCT ijassa-1224 3 59 is be AUX ijassa-1224 3 60 an an DET ijassa-1224 3 61 infectious infectious ADJ ijassa-1224 3 62 disease disease NOUN ijassa-1224 3 63 caused cause VERB ijassa-1224 3 64 by by ADP ijassa-1224 3 65 mycobacterium mycobacterium NOUN ijassa-1224 3 66 disease disease NOUN ijassa-1224 3 67 which which PRON ijassa-1224 3 68 causes cause VERB ijassa-1224 3 69 major major ADJ ijassa-1224 3 70 ill ill ADJ ijassa-1224 3 71 health health NOUN ijassa-1224 3 72 in in ADP ijassa-1224 3 73 humans human NOUN ijassa-1224 3 74 . . PUNCT ijassa-1224 4 1 control control NOUN ijassa-1224 4 2 strategies strategy NOUN ijassa-1224 4 3 like like ADP ijassa-1224 4 4 vaccines vaccine NOUN ijassa-1224 4 5 , , PUNCT ijassa-1224 4 6 early early ADJ ijassa-1224 4 7 detention detention NOUN ijassa-1224 4 8 , , PUNCT ijassa-1224 4 9 treatment treatment NOUN ijassa-1224 4 10 and and CCONJ ijassa-1224 4 11 isolation isolation NOUN ijassa-1224 4 12 are be AUX ijassa-1224 4 13 required require VERB ijassa-1224 4 14 to to PART ijassa-1224 4 15 minimize minimize VERB ijassa-1224 4 16 or or CCONJ ijassa-1224 4 17 eradicate eradicate VERB ijassa-1224 4 18 this this DET ijassa-1224 4 19 deadly deadly ADJ ijassa-1224 4 20 pandemic pandemic ADJ ijassa-1224 4 21 disease disease NOUN ijassa-1224 4 22 . . PUNCT ijassa-1224 5 1 this this DET ijassa-1224 5 2 article article NOUN ijassa-1224 5 3 presents present VERB ijassa-1224 5 4 a a DET ijassa-1224 5 5 novel novel ADJ ijassa-1224 5 6 mathematical mathematical ADJ ijassa-1224 5 7 modelling modelling NOUN ijassa-1224 5 8 approach approach NOUN ijassa-1224 5 9 to to ADP ijassa-1224 5 10 tuberculosis tuberculosis NOUN ijassa-1224 5 11 disease disease NOUN ijassa-1224 5 12 using use VERB ijassa-1224 5 13 vaccinated vaccinated ADJ ijassa-1224 5 14 - - PUNCT ijassa-1224 5 15 susceptiblelatent susceptiblelatent NOUN ijassa-1224 5 16 - - PUNCT ijassa-1224 5 17 mild mild ADJ ijassa-1224 5 18 - - PUNCT ijassa-1224 5 19 chronic chronic NOUN ijassa-1224 5 20 - - PUNCT ijassa-1224 5 21 isolated isolate VERB ijassa-1224 5 22 - - PUNCT ijassa-1224 5 23 treated treat VERB ijassa-1224 5 24 model model NOUN ijassa-1224 5 25 . . PUNCT ijassa-1224 6 1 we we PRON ijassa-1224 6 2 examined examine VERB ijassa-1224 6 3 if if SCONJ ijassa-1224 6 4 the the DET ijassa-1224 6 5 epidemiology epidemiology NOUN ijassa-1224 6 6 model model NOUN ijassa-1224 6 7 is be AUX ijassa-1224 6 8 well well ADV ijassa-1224 6 9 posed pose VERB ijassa-1224 6 10 and and CCONJ ijassa-1224 6 11 then then ADV ijassa-1224 6 12 obtained obtain VERB ijassa-1224 6 13 two two NUM ijassa-1224 6 14 equilibria equilibrium NOUN ijassa-1224 6 15 points point NOUN ijassa-1224 6 16 ( ( PUNCT ijassa-1224 6 17 disease disease NOUN ijassa-1224 6 18 free free ADJ ijassa-1224 6 19 and and CCONJ ijassa-1224 6 20 endemic endemic ADJ ijassa-1224 6 21 equilibrium equilibrium NOUN ijassa-1224 6 22 ) ) PUNCT ijassa-1224 6 23 . . PUNCT ijassa-1224 7 1 we we PRON ijassa-1224 7 2 also also ADV ijassa-1224 7 3 showed show VERB ijassa-1224 7 4 that that SCONJ ijassa-1224 7 5 tb tb ADP ijassa-1224 7 6 disease disease NOUN ijassa-1224 7 7 free free ADJ ijassa-1224 7 8 equilibrium equilibrium NOUN ijassa-1224 7 9 is be AUX ijassa-1224 7 10 locally locally ADV ijassa-1224 7 11 and and CCONJ ijassa-1224 7 12 globally globally ADV ijassa-1224 7 13 asymptotically asymptotically ADV ijassa-1224 7 14 stable stable ADJ ijassa-1224 7 15 if if SCONJ ijassa-1224 7 16 𝑅 𝑅 PROPN ijassa-1224 7 17 < < X ijassa-1224 7 18 1 1 NUM ijassa-1224 7 19 . . PUNCT ijassa-1224 8 1 we we PRON ijassa-1224 8 2 solved solve VERB ijassa-1224 8 3 the the DET ijassa-1224 8 4 model model NOUN ijassa-1224 8 5 analytically analytically ADV ijassa-1224 8 6 using use VERB ijassa-1224 8 7 homotopy homotopy NOUN ijassa-1224 8 8 perturbation perturbation NOUN ijassa-1224 8 9 method method NOUN ijassa-1224 8 10 ( ( PUNCT ijassa-1224 8 11 hpm hpm NOUN ijassa-1224 8 12 ) ) PUNCT ijassa-1224 8 13 and and CCONJ ijassa-1224 8 14 the the DET ijassa-1224 8 15 graphical graphical ADJ ijassa-1224 8 16 representations representation NOUN ijassa-1224 8 17 and and CCONJ ijassa-1224 8 18 interpretations interpretation NOUN ijassa-1224 8 19 of of ADP ijassa-1224 8 20 various various ADJ ijassa-1224 8 21 effects effect NOUN ijassa-1224 8 22 of of ADP ijassa-1224 8 23 the the DET ijassa-1224 8 24 model model NOUN ijassa-1224 8 25 parameters parameter NOUN ijassa-1224 8 26 in in ADP ijassa-1224 8 27 order order NOUN ijassa-1224 8 28 to to PART ijassa-1224 8 29 measure measure VERB ijassa-1224 8 30 the the DET ijassa-1224 8 31 impact impact NOUN ijassa-1224 8 32 for for ADP ijassa-1224 8 33 effective effective ADJ ijassa-1224 8 34 disease disease NOUN ijassa-1224 8 35 control control NOUN ijassa-1224 8 36 are be AUX ijassa-1224 8 37 presented present VERB ijassa-1224 8 38 . . PUNCT ijassa-1224 9 1 the the DET ijassa-1224 9 2 findings finding NOUN ijassa-1224 9 3 show show VERB ijassa-1224 9 4 that that SCONJ ijassa-1224 9 5 infected infected ADJ ijassa-1224 9 6 populations population NOUN ijassa-1224 9 7 will will AUX ijassa-1224 9 8 be be AUX ijassa-1224 9 9 reduced reduce VERB ijassa-1224 9 10 when when SCONJ ijassa-1224 9 11 the the DET ijassa-1224 9 12 isolation isolation NOUN ijassa-1224 9 13 and and CCONJ ijassa-1224 9 14 treatment treatment NOUN ijassa-1224 9 15 rates rate NOUN ijassa-1224 9 16 and and CCONJ ijassa-1224 9 17 their their PRON ijassa-1224 9 18 effectiveness effectiveness NOUN ijassa-1224 9 19 are be AUX ijassa-1224 9 20 high high ADJ ijassa-1224 9 21 . . PUNCT ijassa-1224 10 1 keywords keyword NOUN ijassa-1224 10 2 : : PUNCT ijassa-1224 10 3 tuberculosis tuberculosis NOUN ijassa-1224 10 4 ; ; PUNCT ijassa-1224 10 5 homotopy homotopy VERB ijassa-1224 10 6 perturbation perturbation NOUN ijassa-1224 10 7 method method NOUN ijassa-1224 10 8 ; ; PUNCT ijassa-1224 10 9 infectious infectious ADJ ijassa-1224 10 10 disease disease NOUN ijassa-1224 10 11 ; ; PUNCT ijassa-1224 10 12 basic basic ADJ ijassa-1224 10 13 reproduction reproduction NOUN ijassa-1224 10 14 number number NOUN ijassa-1224 10 15 ; ; PUNCT ijassa-1224 10 16 vaccination vaccination NOUN ijassa-1224 10 17 1 1 NUM ijassa-1224 10 18 . . PUNCT ijassa-1224 11 1 introduction introduction NOUN ijassa-1224 11 2 tuberculosis tuberculosis NOUN ijassa-1224 11 3 ( ( PUNCT ijassa-1224 11 4 tb tb NOUN ijassa-1224 11 5 ) ) PUNCT ijassa-1224 11 6 is be AUX ijassa-1224 11 7 the the DET ijassa-1224 11 8 third third ADJ ijassa-1224 11 9 greatest great ADJ ijassa-1224 11 10 killer killer NOUN ijassa-1224 11 11 worldwide worldwide ADV ijassa-1224 11 12 caused cause VERB ijassa-1224 11 13 by by ADP ijassa-1224 11 14 an an DET ijassa-1224 11 15 infectious infectious ADJ ijassa-1224 11 16 agent agent NOUN ijassa-1224 11 17 [ [ X ijassa-1224 11 18 12 12 NUM ijassa-1224 11 19 ] ] PUNCT ijassa-1224 11 20 . . PUNCT ijassa-1224 12 1 according accord VERB ijassa-1224 12 2 to to ADP ijassa-1224 12 3 world world PROPN ijassa-1224 12 4 health health NOUN ijassa-1224 12 5 organization organization NOUN ijassa-1224 12 6 ( ( PUNCT ijassa-1224 12 7 who who PRON ijassa-1224 12 8 ) ) PUNCT ijassa-1224 12 9 , , PUNCT ijassa-1224 12 10 one one NUM ijassa-1224 12 11 - - PUNCT ijassa-1224 12 12 third third NOUN ijassa-1224 12 13 of of ADP ijassa-1224 12 14 the the DET ijassa-1224 12 15 world world NOUN ijassa-1224 12 16 ’s ’s PART ijassa-1224 12 17 population population NOUN ijassa-1224 12 18 is be AUX ijassa-1224 12 19 currently currently ADV ijassa-1224 12 20 infected infect VERB ijassa-1224 12 21 by by ADP ijassa-1224 12 22 the the DET ijassa-1224 12 23 tb tb NOUN ijassa-1224 12 24 bacillus bacillus NOUN ijassa-1224 12 25 bacteria bacteria NOUN ijassa-1224 12 26 . . PUNCT ijassa-1224 13 1 being be AUX ijassa-1224 13 2 a a DET ijassa-1224 13 3 disease disease NOUN ijassa-1224 13 4 of of ADP ijassa-1224 13 5 poverty poverty NOUN ijassa-1224 13 6 , , PUNCT ijassa-1224 13 7 the the DET ijassa-1224 13 8 vast vast ADJ ijassa-1224 13 9 majority majority NOUN ijassa-1224 13 10 of of ADP ijassa-1224 13 11 tb tb ADP ijassa-1224 13 12 deaths death NOUN ijassa-1224 13 13 are be AUX ijassa-1224 13 14 in in ADP ijassa-1224 13 15 developing develop VERB ijassa-1224 13 16 countries country NOUN ijassa-1224 13 17 with with ADP ijassa-1224 13 18 more more ADJ ijassa-1224 13 19 than than ADP ijassa-1224 13 20 half half NOUN ijassa-1224 13 21 occurring occur VERB ijassa-1224 13 22 in in ADP ijassa-1224 13 23 asia asia PROPN ijassa-1224 13 24 . . PUNCT ijassa-1224 14 1 furthermore furthermore ADV ijassa-1224 14 2 , , PUNCT ijassa-1224 14 3 over over ADP ijassa-1224 14 4 95 95 NUM ijassa-1224 14 5 % % NOUN ijassa-1224 14 6 of of ADP ijassa-1224 14 7 these these DET ijassa-1224 14 8 deaths death NOUN ijassa-1224 14 9 occurred occur VERB ijassa-1224 14 10 in in ADP ijassa-1224 14 11 lowand lowand ADJ ijassa-1224 14 12 middle middle ADJ ijassa-1224 14 13 - - PUNCT ijassa-1224 14 14 income income NOUN ijassa-1224 14 15 countries country NOUN ijassa-1224 14 16 where where SCONJ ijassa-1224 14 17 the the DET ijassa-1224 14 18 cost cost NOUN ijassa-1224 14 19 of of ADP ijassa-1224 14 20 diagnosis diagnosis NOUN ijassa-1224 14 21 and and CCONJ ijassa-1224 14 22 treatment treatment NOUN ijassa-1224 14 23 is be AUX ijassa-1224 14 24 high high ADJ ijassa-1224 14 25 , , PUNCT ijassa-1224 14 26 and and CCONJ ijassa-1224 14 27 not not PART ijassa-1224 14 28 readily readily ADV ijassa-1224 14 29 accessible accessible ADJ ijassa-1224 14 30 . . PUNCT ijassa-1224 15 1 tuberculosis tuberculosis NOUN ijassa-1224 15 2 is be AUX ijassa-1224 15 3 a a DET ijassa-1224 15 4 chronic chronic ADJ ijassa-1224 15 5 bacteria bacteria NOUN ijassa-1224 15 6 infectious infectious ADJ ijassa-1224 15 7 disease disease NOUN ijassa-1224 15 8 caused cause VERB ijassa-1224 15 9 by by ADP ijassa-1224 15 10 mycobacterium mycobacterium NOUN ijassa-1224 15 11 tuberculosis tuberculosis NOUN ijassa-1224 15 12 which which PRON ijassa-1224 15 13 poses pose VERB ijassa-1224 15 14 a a DET ijassa-1224 15 15 major major ADJ ijassa-1224 15 16 health health NOUN ijassa-1224 15 17 , , PUNCT ijassa-1224 15 18 social social ADJ ijassa-1224 15 19 and and CCONJ ijassa-1224 15 20 economic economic ADJ ijassa-1224 15 21 burden burden NOUN ijassa-1224 15 22 globally globally ADV ijassa-1224 15 23 , , PUNCT ijassa-1224 15 24 especially especially ADV ijassa-1224 15 25 in in ADP ijassa-1224 15 26 lowand lowand ADJ ijassa-1224 15 27 middle middle ADJ ijassa-1224 15 28 - - PUNCT ijassa-1224 15 29 income income NOUN ijassa-1224 15 30 countries country NOUN ijassa-1224 15 31 [ [ X ijassa-1224 15 32 5 5 NUM ijassa-1224 15 33 ] ] PUNCT ijassa-1224 15 34 . . PUNCT ijassa-1224 16 1 the the DET ijassa-1224 16 2 surge surge NOUN ijassa-1224 16 3 in in ADP ijassa-1224 16 4 hiv hiv PROPN ijassa-1224 16 5 - - PUNCT ijassa-1224 16 6 tb tb ADP ijassa-1224 16 7 co co NOUN ijassa-1224 16 8 - - NOUN ijassa-1224 16 9 infection infection NOUN ijassa-1224 16 10 and and CCONJ ijassa-1224 16 11 the the DET ijassa-1224 16 12 growing grow VERB ijassa-1224 16 13 emergence emergence NOUN ijassa-1224 16 14 of of ADP ijassa-1224 16 15 multidrug multidrug NOUN ijassa-1224 16 16 - - PUNCT ijassa-1224 16 17 resistant resistant ADJ ijassa-1224 16 18 tb tb X ijassa-1224 16 19 ( ( PUNCT ijassa-1224 16 20 mdr mdr PROPN ijassa-1224 16 21 - - NOUN ijassa-1224 16 22 tb tb NOUN ijassa-1224 16 23 ) ) PUNCT ijassa-1224 16 24 and and CCONJ ijassa-1224 16 25 extensively extensively ADV ijassa-1224 16 26 drug drug NOUN ijassa-1224 16 27 - - PUNCT ijassa-1224 16 28 resistant resistant ADJ ijassa-1224 16 29 tb tb X ijassa-1224 16 30 ( ( PUNCT ijassa-1224 16 31 xdr xdr PROPN ijassa-1224 16 32 - - PUNCT ijassa-1224 16 33 tb tb NOUN ijassa-1224 16 34 ) ) PUNCT ijassa-1224 16 35 strains strain NOUN ijassa-1224 16 36 has have AUX ijassa-1224 16 37 further far ADV ijassa-1224 16 38 fueled fuel VERB ijassa-1224 16 39 tb tb ADP ijassa-1224 16 40 epidemic epidemic NOUN ijassa-1224 16 41 . . PUNCT ijassa-1224 17 1 tb tb PROPN ijassa-1224 17 2 usually usually ADV ijassa-1224 17 3 affects affect VERB ijassa-1224 17 4 the the DET ijassa-1224 17 5 lungs lung NOUN ijassa-1224 17 6 ( ( PUNCT ijassa-1224 17 7 pulmonary pulmonary NOUN ijassa-1224 17 8 tb tb NOUN ijassa-1224 17 9 ) ) PUNCT ijassa-1224 17 10 but but CCONJ ijassa-1224 17 11 it it PRON ijassa-1224 17 12 can can AUX ijassa-1224 17 13 also also ADV ijassa-1224 17 14 affect affect VERB ijassa-1224 17 15 other other ADJ ijassa-1224 17 16 sites site NOUN ijassa-1224 17 17 as as ADV ijassa-1224 17 18 well well ADV ijassa-1224 17 19 ( ( PUNCT ijassa-1224 17 20 extra extra ADJ ijassa-1224 17 21 - - ADJ ijassa-1224 17 22 pulmonary pulmonary ADJ ijassa-1224 17 23 tb tb NOUN ijassa-1224 17 24 ) ) PUNCT ijassa-1224 17 25 . . PUNCT ijassa-1224 18 1 tuberculosis tuberculosis NOUN ijassa-1224 18 2 is be AUX ijassa-1224 18 3 transmitted transmit VERB ijassa-1224 18 4 by by ADP ijassa-1224 18 5 tiny tiny ADJ ijassa-1224 18 6 analysis analysis NOUN ijassa-1224 18 7 and and CCONJ ijassa-1224 18 8 dynamics dynamic NOUN ijassa-1224 18 9 of of ADP ijassa-1224 18 10 tuberculosis tuberculosis NOUN ijassa-1224 18 11 outbreak outbreak NOUN ijassa-1224 18 12 145 145 NUM ijassa-1224 18 13 copyright copyright NOUN ijassa-1224 18 14 Β© Β© PROPN ijassa-1224 18 15 2022 2022 NUM ijassa-1224 18 16 assa assa NOUN ijassa-1224 18 17 . . PUNCT ijassa-1224 19 1 adv adv PROPN ijassa-1224 19 2 . . PUNCT ijassa-1224 20 1 in in ADP ijassa-1224 20 2 systems system NOUN ijassa-1224 20 3 science science NOUN ijassa-1224 20 4 and and CCONJ ijassa-1224 20 5 appl appl NOUN ijassa-1224 20 6 . . PUNCT ijassa-1224 21 1 ( ( PUNCT ijassa-1224 21 2 2022 2022 NUM ijassa-1224 21 3 ) ) PUNCT ijassa-1224 21 4 airborne airborne ADJ ijassa-1224 21 5 droplets droplet NOUN ijassa-1224 21 6 which which PRON ijassa-1224 21 7 are be AUX ijassa-1224 21 8 expelled expel VERB ijassa-1224 21 9 into into ADP ijassa-1224 21 10 the the DET ijassa-1224 21 11 air air NOUN ijassa-1224 21 12 when when SCONJ ijassa-1224 21 13 a a DET ijassa-1224 21 14 person person NOUN ijassa-1224 21 15 with with ADP ijassa-1224 21 16 active active ADJ ijassa-1224 21 17 pulmonary pulmonary NOUN ijassa-1224 21 18 tb tb ADP ijassa-1224 21 19 coughs cough NOUN ijassa-1224 21 20 or or CCONJ ijassa-1224 21 21 talks talk NOUN ijassa-1224 22 1 [ [ X ijassa-1224 22 2 21,22 21,22 X ijassa-1224 22 3 ] ] X ijassa-1224 22 4 . . PUNCT ijassa-1224 23 1 diagnosis diagnosis NOUN ijassa-1224 23 2 of of ADP ijassa-1224 23 3 latent latent NOUN ijassa-1224 23 4 tb tb ADP ijassa-1224 23 5 infections infection NOUN ijassa-1224 23 6 ( ( PUNCT ijassa-1224 23 7 ltbi ltbi NOUN ijassa-1224 23 8 ) ) PUNCT ijassa-1224 23 9 and and CCONJ ijassa-1224 23 10 prompt prompt ADJ ijassa-1224 23 11 treatment treatment NOUN ijassa-1224 23 12 of of ADP ijassa-1224 23 13 active active ADJ ijassa-1224 23 14 cases case NOUN ijassa-1224 23 15 remains remain VERB ijassa-1224 23 16 an an DET ijassa-1224 23 17 important important ADJ ijassa-1224 23 18 component component NOUN ijassa-1224 23 19 of of ADP ijassa-1224 23 20 effective effective ADJ ijassa-1224 23 21 tb tb ADP ijassa-1224 23 22 control control NOUN ijassa-1224 23 23 as as SCONJ ijassa-1224 23 24 shown show VERB ijassa-1224 23 25 in in ADP ijassa-1224 23 26 previous previous ADJ ijassa-1224 23 27 studies study NOUN ijassa-1224 23 28 . . PUNCT ijassa-1224 24 1 on on ADP ijassa-1224 24 2 the the DET ijassa-1224 24 3 other other ADJ ijassa-1224 24 4 hand hand NOUN ijassa-1224 24 5 , , PUNCT ijassa-1224 24 6 undetected undetecte VERB ijassa-1224 24 7 tb tb ADP ijassa-1224 24 8 infection infection NOUN ijassa-1224 24 9 and and CCONJ ijassa-1224 24 10 delay delay NOUN ijassa-1224 24 11 in in ADP ijassa-1224 24 12 the the DET ijassa-1224 24 13 treatment treatment NOUN ijassa-1224 24 14 of of ADP ijassa-1224 24 15 active active ADJ ijassa-1224 24 16 tb tb ADP ijassa-1224 24 17 cases case NOUN ijassa-1224 24 18 leads lead VERB ijassa-1224 24 19 to to ADP ijassa-1224 24 20 more more ADV ijassa-1224 24 21 severe severe ADJ ijassa-1224 24 22 disease disease NOUN ijassa-1224 24 23 conditions condition NOUN ijassa-1224 24 24 in in ADP ijassa-1224 24 25 the the DET ijassa-1224 24 26 infected infected ADJ ijassa-1224 24 27 person person NOUN ijassa-1224 24 28 which which PRON ijassa-1224 24 29 could could AUX ijassa-1224 24 30 result result VERB ijassa-1224 24 31 in in ADP ijassa-1224 24 32 wider wide ADJ ijassa-1224 24 33 disease disease NOUN ijassa-1224 24 34 spread spread VERB ijassa-1224 24 35 in in ADP ijassa-1224 24 36 the the DET ijassa-1224 24 37 community community NOUN ijassa-1224 24 38 [ [ X ijassa-1224 24 39 3 3 NUM ijassa-1224 24 40 , , PUNCT ijassa-1224 24 41 7 7 NUM ijassa-1224 24 42 , , PUNCT ijassa-1224 24 43 10 10 NUM ijassa-1224 24 44 , , PUNCT ijassa-1224 24 45 9 9 NUM ijassa-1224 24 46 ] ] PUNCT ijassa-1224 24 47 . . PUNCT ijassa-1224 25 1 some some DET ijassa-1224 25 2 researchers researcher NOUN ijassa-1224 25 3 have have AUX ijassa-1224 25 4 proposed propose VERB ijassa-1224 25 5 some some DET ijassa-1224 25 6 mathematical mathematical ADJ ijassa-1224 25 7 models model NOUN ijassa-1224 25 8 to to PART ijassa-1224 25 9 solve solve VERB ijassa-1224 25 10 problems problem NOUN ijassa-1224 25 11 arising arise VERB ijassa-1224 25 12 from from ADP ijassa-1224 25 13 tb tb ADP ijassa-1224 25 14 models model NOUN ijassa-1224 25 15 and and CCONJ ijassa-1224 25 16 we we PRON ijassa-1224 25 17 shall shall AUX ijassa-1224 25 18 discuss discuss VERB ijassa-1224 25 19 some some PRON ijassa-1224 25 20 of of ADP ijassa-1224 25 21 them they PRON ijassa-1224 25 22 as as SCONJ ijassa-1224 25 23 follows follow VERB ijassa-1224 25 24 : : PUNCT ijassa-1224 25 25 [ [ X ijassa-1224 25 26 8 8 NUM ijassa-1224 25 27 ] ] PUNCT ijassa-1224 25 28 presents present VERB ijassa-1224 25 29 a a DET ijassa-1224 25 30 susceptibleexposed susceptibleexpose VERB ijassa-1224 25 31 - - PUNCT ijassa-1224 25 32 infected infect VERB ijassa-1224 25 33 - - PUNCT ijassa-1224 25 34 recovered recover VERB ijassa-1224 25 35 ( ( PUNCT ijassa-1224 25 36 seir seir NOUN ijassa-1224 25 37 ) ) PUNCT ijassa-1224 25 38 tuberculosis tuberculosis NOUN ijassa-1224 25 39 model model NOUN ijassa-1224 25 40 which which PRON ijassa-1224 25 41 incorporated incorporate VERB ijassa-1224 25 42 treatment treatment NOUN ijassa-1224 25 43 of of ADP ijassa-1224 25 44 infectious infectious ADJ ijassa-1224 25 45 individuals individual NOUN ijassa-1224 25 46 and and CCONJ ijassa-1224 25 47 chemoprophylaxis chemoprophylaxis NOUN ijassa-1224 25 48 ( ( PUNCT ijassa-1224 25 49 treatment treatment NOUN ijassa-1224 25 50 for for ADP ijassa-1224 25 51 the the DET ijassa-1224 25 52 latently latently ADV ijassa-1224 25 53 infected infect VERB ijassa-1224 25 54 ) ) PUNCT ijassa-1224 25 55 . . PUNCT ijassa-1224 26 1 the the DET ijassa-1224 26 2 model model NOUN ijassa-1224 26 3 assumed assume VERB ijassa-1224 26 4 that that SCONJ ijassa-1224 26 5 the the DET ijassa-1224 26 6 latently latently ADV ijassa-1224 26 7 infected infect VERB ijassa-1224 26 8 individuals individual NOUN ijassa-1224 26 9 develop develop VERB ijassa-1224 26 10 the the DET ijassa-1224 26 11 active active ADJ ijassa-1224 26 12 disease disease NOUN ijassa-1224 26 13 as as ADP ijassa-1224 26 14 a a DET ijassa-1224 26 15 result result NOUN ijassa-1224 26 16 of of ADP ijassa-1224 26 17 endogenous endogenous ADJ ijassa-1224 26 18 re re NOUN ijassa-1224 26 19 - - NOUN ijassa-1224 26 20 activation activation NOUN ijassa-1224 26 21 , , PUNCT ijassa-1224 26 22 exogenous exogenous ADJ ijassa-1224 26 23 re re NOUN ijassa-1224 26 24 - - NOUN ijassa-1224 26 25 infection infection NOUN ijassa-1224 26 26 and and CCONJ ijassa-1224 26 27 disease disease NOUN ijassa-1224 26 28 relapse relapse NOUN ijassa-1224 26 29 . . PUNCT ijassa-1224 27 1 [ [ X ijassa-1224 27 2 4 4 X ijassa-1224 27 3 ] ] PUNCT ijassa-1224 27 4 presents present VERB ijassa-1224 27 5 the the DET ijassa-1224 27 6 mathematical mathematical ADJ ijassa-1224 27 7 model model NOUN ijassa-1224 27 8 of of ADP ijassa-1224 27 9 a a DET ijassa-1224 27 10 tuberculosis tuberculosis NOUN ijassa-1224 27 11 transmission transmission NOUN ijassa-1224 27 12 dynamics dynamic NOUN ijassa-1224 27 13 incorporating incorporate VERB ijassa-1224 27 14 first first ADJ ijassa-1224 27 15 and and CCONJ ijassa-1224 27 16 second second ADJ ijassa-1224 27 17 line line NOUN ijassa-1224 27 18 treatment treatment NOUN ijassa-1224 27 19 . . PUNCT ijassa-1224 28 1 [ [ X ijassa-1224 28 2 7 7 X ijassa-1224 28 3 ] ] PUNCT ijassa-1224 28 4 proposed propose VERB ijassa-1224 28 5 a a DET ijassa-1224 28 6 seven seven NUM ijassa-1224 28 7 - - PUNCT ijassa-1224 28 8 compartment compartment NOUN ijassa-1224 28 9 model model NOUN ijassa-1224 28 10 which which PRON ijassa-1224 28 11 included include VERB ijassa-1224 28 12 diagnosed diagnose VERB ijassa-1224 28 13 and and CCONJ ijassa-1224 28 14 undiagnosed undiagnosed ADJ ijassa-1224 28 15 infectious infectious ADJ ijassa-1224 28 16 population population NOUN ijassa-1224 28 17 and and CCONJ ijassa-1224 28 18 their their PRON ijassa-1224 28 19 result result NOUN ijassa-1224 28 20 shows show VERB ijassa-1224 28 21 that that SCONJ ijassa-1224 28 22 high high ADJ ijassa-1224 28 23 vaccination vaccination NOUN ijassa-1224 28 24 rate rate NOUN ijassa-1224 28 25 is be AUX ijassa-1224 28 26 required require VERB ijassa-1224 28 27 to to PART ijassa-1224 28 28 eradicate eradicate VERB ijassa-1224 28 29 tb tb NOUN ijassa-1224 28 30 . . PUNCT ijassa-1224 29 1 in in ADP ijassa-1224 29 2 [ [ X ijassa-1224 29 3 16 16 NUM ijassa-1224 29 4 ] ] PUNCT ijassa-1224 29 5 , , PUNCT ijassa-1224 29 6 the the DET ijassa-1224 29 7 authors author NOUN ijassa-1224 29 8 develop develop VERB ijassa-1224 29 9 a a DET ijassa-1224 29 10 mathematical mathematical ADJ ijassa-1224 29 11 model model NOUN ijassa-1224 29 12 for for ADP ijassa-1224 29 13 control control NOUN ijassa-1224 29 14 of of ADP ijassa-1224 29 15 tuberculosis tuberculosis NOUN ijassa-1224 29 16 epidemiology epidemiology NOUN ijassa-1224 29 17 by by ADP ijassa-1224 29 18 incorporating incorporate VERB ijassa-1224 29 19 some some DET ijassa-1224 29 20 control control NOUN ijassa-1224 29 21 strategies strategy NOUN ijassa-1224 29 22 , , PUNCT ijassa-1224 29 23 the the DET ijassa-1224 29 24 findings finding NOUN ijassa-1224 29 25 of of ADP ijassa-1224 29 26 the the DET ijassa-1224 29 27 study study NOUN ijassa-1224 29 28 show show VERB ijassa-1224 29 29 that that SCONJ ijassa-1224 29 30 using use VERB ijassa-1224 29 31 multiple multiple ADJ ijassa-1224 29 32 controls control NOUN ijassa-1224 29 33 is be AUX ijassa-1224 29 34 the the DET ijassa-1224 29 35 best good ADJ ijassa-1224 29 36 way way NOUN ijassa-1224 29 37 to to PART ijassa-1224 29 38 control control VERB ijassa-1224 29 39 the the DET ijassa-1224 29 40 spread spread NOUN ijassa-1224 29 41 of of ADP ijassa-1224 29 42 tb tb NOUN ijassa-1224 29 43 . . PUNCT ijassa-1224 30 1 several several ADJ ijassa-1224 30 2 studies study NOUN ijassa-1224 30 3 have have AUX ijassa-1224 30 4 been be AUX ijassa-1224 30 5 conducted conduct VERB ijassa-1224 30 6 utilizing utilize VERB ijassa-1224 30 7 a a DET ijassa-1224 30 8 mathematical mathematical ADJ ijassa-1224 30 9 model model NOUN ijassa-1224 30 10 method method NOUN ijassa-1224 30 11 in in ADP ijassa-1224 30 12 order order NOUN ijassa-1224 30 13 to to PART ijassa-1224 30 14 identify identify VERB ijassa-1224 30 15 ways way NOUN ijassa-1224 30 16 to to PART ijassa-1224 30 17 control control VERB ijassa-1224 30 18 diseases disease NOUN ijassa-1224 30 19 in in ADP ijassa-1224 30 20 the the DET ijassa-1224 30 21 population population NOUN ijassa-1224 30 22 [ [ X ijassa-1224 30 23 1,13 1,13 NUM ijassa-1224 30 24 , , PUNCT ijassa-1224 30 25 18 18 NUM ijassa-1224 30 26 - - SYM ijassa-1224 30 27 20 20 NUM ijassa-1224 30 28 ] ] PUNCT ijassa-1224 30 29 . . PUNCT ijassa-1224 31 1 [ [ X ijassa-1224 31 2 17 17 NUM ijassa-1224 31 3 ] ] PUNCT ijassa-1224 31 4 presented present VERB ijassa-1224 31 5 a a DET ijassa-1224 31 6 deterministic deterministic ADJ ijassa-1224 31 7 seir seir NOUN ijassa-1224 31 8 model model NOUN ijassa-1224 31 9 to to PART ijassa-1224 31 10 described describe VERB ijassa-1224 31 11 the the DET ijassa-1224 31 12 transmission transmission NOUN ijassa-1224 31 13 dynamics dynamic NOUN ijassa-1224 31 14 of of ADP ijassa-1224 31 15 tb tb NOUN ijassa-1224 31 16 in in ADP ijassa-1224 31 17 ashanti ashanti ADJ ijassa-1224 31 18 region region NOUN ijassa-1224 31 19 of of ADP ijassa-1224 31 20 ghana ghana PROPN ijassa-1224 31 21 and and CCONJ ijassa-1224 31 22 the the DET ijassa-1224 31 23 results result NOUN ijassa-1224 31 24 showed show VERB ijassa-1224 31 25 that that SCONJ ijassa-1224 31 26 the the DET ijassa-1224 31 27 region region NOUN ijassa-1224 31 28 has have VERB ijassa-1224 31 29 herd herd ADJ ijassa-1224 31 30 immunity immunity NOUN ijassa-1224 31 31 against against ADP ijassa-1224 31 32 tb tb ADP ijassa-1224 31 33 infection infection NOUN ijassa-1224 31 34 . . PUNCT ijassa-1224 32 1 in in ADP ijassa-1224 32 2 this this DET ijassa-1224 32 3 study study NOUN ijassa-1224 32 4 we we PRON ijassa-1224 32 5 consider consider VERB ijassa-1224 32 6 some some DET ijassa-1224 32 7 control control NOUN ijassa-1224 32 8 strategies strategy NOUN ijassa-1224 32 9 such such ADJ ijassa-1224 32 10 as as ADP ijassa-1224 32 11 , , PUNCT ijassa-1224 32 12 treatment treatment NOUN ijassa-1224 32 13 , , PUNCT ijassa-1224 32 14 isolation isolation NOUN ijassa-1224 32 15 and and CCONJ ijassa-1224 32 16 vaccination vaccination NOUN ijassa-1224 32 17 into into ADP ijassa-1224 32 18 the the DET ijassa-1224 32 19 mathematical mathematical ADJ ijassa-1224 32 20 formulation formulation NOUN ijassa-1224 32 21 of of ADP ijassa-1224 32 22 tb tb ADP ijassa-1224 32 23 outbreak outbreak NOUN ijassa-1224 32 24 with with ADP ijassa-1224 32 25 assumptions assumption NOUN ijassa-1224 32 26 that that SCONJ ijassa-1224 32 27 people people NOUN ijassa-1224 32 28 in in ADP ijassa-1224 32 29 each each DET ijassa-1224 32 30 compartment compartment NOUN ijassa-1224 32 31 have have AUX ijassa-1224 32 32 equal equal ADJ ijassa-1224 32 33 natural natural ADJ ijassa-1224 32 34 death death NOUN ijassa-1224 32 35 rate rate NOUN ijassa-1224 32 36 and and CCONJ ijassa-1224 32 37 infection infection NOUN ijassa-1224 32 38 does do AUX ijassa-1224 32 39 not not PART ijassa-1224 32 40 confer confer VERB ijassa-1224 32 41 immunity immunity NOUN ijassa-1224 32 42 to to ADP ijassa-1224 32 43 the the DET ijassa-1224 32 44 treated treat VERB ijassa-1224 32 45 and and CCONJ ijassa-1224 32 46 recovered recover VERB ijassa-1224 32 47 individuals individual NOUN ijassa-1224 32 48 . . PUNCT ijassa-1224 33 1 the the DET ijassa-1224 33 2 rest rest NOUN ijassa-1224 33 3 of of ADP ijassa-1224 33 4 the the DET ijassa-1224 33 5 article article NOUN ijassa-1224 33 6 is be AUX ijassa-1224 33 7 divided divide VERB ijassa-1224 33 8 as as SCONJ ijassa-1224 33 9 follows follow VERB ijassa-1224 33 10 : : PUNCT ijassa-1224 33 11 method method NOUN ijassa-1224 33 12 which which PRON ijassa-1224 33 13 includes include VERB ijassa-1224 33 14 model model NOUN ijassa-1224 33 15 formulation formulation NOUN ijassa-1224 33 16 and and CCONJ ijassa-1224 33 17 mathematical mathematical ADJ ijassa-1224 33 18 analysis analysis NOUN ijassa-1224 33 19 of of ADP ijassa-1224 33 20 the the DET ijassa-1224 33 21 model model NOUN ijassa-1224 33 22 are be AUX ijassa-1224 33 23 described describe VERB ijassa-1224 33 24 in in ADP ijassa-1224 33 25 β€œ " PUNCT ijassa-1224 33 26 section section NOUN ijassa-1224 33 27 2 2 NUM ijassa-1224 33 28 . . PUNCT ijassa-1224 34 1 next next ADV ijassa-1224 34 2 , , PUNCT ijassa-1224 34 3 section section NOUN ijassa-1224 34 4 consists consist VERB ijassa-1224 34 5 of of ADP ijassa-1224 34 6 the the DET ijassa-1224 34 7 semi semi ADJ ijassa-1224 34 8 - - ADJ ijassa-1224 34 9 analytic analytic ADJ ijassa-1224 34 10 solution solution NOUN ijassa-1224 34 11 of of ADP ijassa-1224 34 12 the the DET ijassa-1224 34 13 model model NOUN ijassa-1224 34 14 formulated formulate VERB ijassa-1224 34 15 . . PUNCT ijassa-1224 35 1 numerical numerical PROPN ijassa-1224 35 2 simulation simulation PROPN ijassa-1224 35 3 and and CCONJ ijassa-1224 35 4 graphical graphical ADJ ijassa-1224 35 5 representation representation NOUN ijassa-1224 35 6 of of ADP ijassa-1224 35 7 results result NOUN ijassa-1224 35 8 is be AUX ijassa-1224 35 9 given give VERB ijassa-1224 35 10 in in ADP ijassa-1224 35 11 4 4 NUM ijassa-1224 35 12 , , PUNCT ijassa-1224 35 13 while while SCONJ ijassa-1224 35 14 the the DET ijassa-1224 35 15 discussion discussion NOUN ijassa-1224 35 16 of of ADP ijassa-1224 35 17 the the DET ijassa-1224 35 18 results result NOUN ijassa-1224 35 19 is be AUX ijassa-1224 35 20 presented present VERB ijassa-1224 35 21 in in ADP ijassa-1224 35 22 section section NOUN ijassa-1224 35 23 5 5 NUM ijassa-1224 35 24 . . PUNCT ijassa-1224 36 1 finally finally ADV ijassa-1224 36 2 , , PUNCT ijassa-1224 36 3 in in ADP ijassa-1224 36 4 section section NOUN ijassa-1224 36 5 6 6 NUM ijassa-1224 36 6 , , PUNCT ijassa-1224 36 7 we we PRON ijassa-1224 36 8 have have AUX ijassa-1224 36 9 provided provide VERB ijassa-1224 36 10 conclusions conclusion NOUN ijassa-1224 36 11 of of ADP ijassa-1224 36 12 this this DET ijassa-1224 36 13 article article NOUN ijassa-1224 36 14 . . PUNCT ijassa-1224 37 1 2 2 X ijassa-1224 37 2 . . X ijassa-1224 37 3 method method PROPN ijassa-1224 37 4 2.1 2.1 NUM ijassa-1224 37 5 . . PUNCT ijassa-1224 37 6 model model NOUN ijassa-1224 37 7 formulation formulation NOUN ijassa-1224 37 8 in in ADP ijassa-1224 37 9 this this DET ijassa-1224 37 10 section section NOUN ijassa-1224 37 11 , , PUNCT ijassa-1224 37 12 the the DET ijassa-1224 37 13 tb tb NOUN ijassa-1224 37 14 transmission transmission NOUN ijassa-1224 37 15 model model NOUN ijassa-1224 37 16 is be AUX ijassa-1224 37 17 formulated formulate VERB ijassa-1224 37 18 . . PUNCT ijassa-1224 38 1 using use VERB ijassa-1224 38 2 a a DET ijassa-1224 38 3 compartmental compartmental ADJ ijassa-1224 38 4 approach approach NOUN ijassa-1224 38 5 , , PUNCT ijassa-1224 38 6 the the DET ijassa-1224 38 7 total total ADJ ijassa-1224 38 8 host host NOUN ijassa-1224 38 9 population population NOUN ijassa-1224 38 10 can can AUX ijassa-1224 38 11 be be AUX ijassa-1224 38 12 partitioned partition VERB ijassa-1224 38 13 into into ADP ijassa-1224 38 14 seven seven NUM ijassa-1224 38 15 compartments compartment NOUN ijassa-1224 38 16 according accord VERB ijassa-1224 38 17 to to ADP ijassa-1224 38 18 their their PRON ijassa-1224 38 19 epidemiological epidemiological ADJ ijassa-1224 38 20 status status NOUN ijassa-1224 38 21 . . PUNCT ijassa-1224 39 1 the the DET ijassa-1224 39 2 groups group NOUN ijassa-1224 39 3 are be AUX ijassa-1224 39 4 the the DET ijassa-1224 39 5 vaccinated vaccinated ADJ ijassa-1224 39 6 𝑉(𝑑 𝑉(𝑑 ADP ijassa-1224 39 7 ) ) PUNCT ijassa-1224 39 8 , , PUNCT ijassa-1224 39 9 susceptible susceptible ADJ ijassa-1224 39 10 𝑆(𝑑 𝑆(𝑑 NUM ijassa-1224 39 11 ) ) PUNCT ijassa-1224 39 12 , , PUNCT ijassa-1224 39 13 latent latent NOUN ijassa-1224 39 14 𝐸(𝑑 𝐸(𝑑 VERB ijassa-1224 39 15 ) ) PUNCT ijassa-1224 39 16 , , PUNCT ijassa-1224 39 17 mild mild ADJ ijassa-1224 39 18 tb tb ADP ijassa-1224 39 19 𝐼 𝐼 PROPN ijassa-1224 39 20 ( ( PUNCT ijassa-1224 39 21 𝑑 𝑑 NOUN ijassa-1224 39 22 ) ) PUNCT ijassa-1224 39 23 , , PUNCT ijassa-1224 39 24 chronic chronic ADJ ijassa-1224 39 25 tb tb ADP ijassa-1224 39 26 𝐼 𝐼 PROPN ijassa-1224 39 27 ( ( PUNCT ijassa-1224 39 28 𝑑 𝑑 NOUN ijassa-1224 39 29 ) ) PUNCT ijassa-1224 39 30 , , PUNCT ijassa-1224 39 31 isolated isolate VERB ijassa-1224 39 32 infectious infectious ADJ ijassa-1224 39 33 𝐽(𝑑 𝐽(𝑑 PRON ijassa-1224 39 34 ) ) PUNCT ijassa-1224 39 35 and and CCONJ ijassa-1224 39 36 treated treat VERB ijassa-1224 39 37 𝑇(𝑑 𝑇(𝑑 NUM ijassa-1224 39 38 ) ) PUNCT ijassa-1224 39 39 individual individual NOUN ijassa-1224 39 40 , , PUNCT ijassa-1224 39 41 where where SCONJ ijassa-1224 39 42 𝑑 𝑑 PROPN ijassa-1224 39 43 is be AUX ijassa-1224 39 44 the the DET ijassa-1224 39 45 time time NOUN ijassa-1224 39 46 variable variable NOUN ijassa-1224 39 47 . . PUNCT ijassa-1224 40 1 it it PRON ijassa-1224 40 2 is be AUX ijassa-1224 40 3 assumed assume VERB ijassa-1224 40 4 that that SCONJ ijassa-1224 40 5 once once SCONJ ijassa-1224 40 6 the the DET ijassa-1224 40 7 treatment treatment NOUN ijassa-1224 40 8 of of ADP ijassa-1224 40 9 active active ADJ ijassa-1224 40 10 tb tb ADP ijassa-1224 40 11 cases case NOUN ijassa-1224 40 12 is be AUX ijassa-1224 40 13 interrupted interrupt VERB ijassa-1224 40 14 , , PUNCT ijassa-1224 40 15 there there PRON ijassa-1224 40 16 is be VERB ijassa-1224 40 17 no no DET ijassa-1224 40 18 more more ADJ ijassa-1224 40 19 treatment treatment NOUN ijassa-1224 40 20 . . PUNCT ijassa-1224 41 1 vaccination vaccination NOUN ijassa-1224 41 2 reduces reduce VERB ijassa-1224 41 3 the the DET ijassa-1224 41 4 risk risk NOUN ijassa-1224 41 5 of of ADP ijassa-1224 41 6 infection infection NOUN ijassa-1224 41 7 by by ADP ijassa-1224 41 8 a a DET ijassa-1224 41 9 factor factor NOUN ijassa-1224 41 10 πœƒ πœƒ X ijassa-1224 41 11 ∈ ∈ PROPN ijassa-1224 41 12 ( ( PUNCT ijassa-1224 41 13 0,1 0,1 NUM ijassa-1224 41 14 ) ) PUNCT ijassa-1224 41 15 and and CCONJ ijassa-1224 41 16 the the DET ijassa-1224 41 17 efficacy efficacy NOUN ijassa-1224 41 18 of of ADP ijassa-1224 41 19 the the DET ijassa-1224 41 20 vaccine vaccine NOUN ijassa-1224 41 21 is be AUX ijassa-1224 41 22 πœ”. πœ”. NOUN ijassa-1224 41 23 let let VERB ijassa-1224 41 24 a a DET ijassa-1224 41 25 constant constant ADJ ijassa-1224 41 26 πœ‹ πœ‹ NOUN ijassa-1224 41 27 stands stand VERB ijassa-1224 41 28 for for ADP ijassa-1224 41 29 the the DET ijassa-1224 41 30 number number NOUN ijassa-1224 41 31 of of ADP ijassa-1224 41 32 newborn newborn ADJ ijassa-1224 41 33 babies baby NOUN ijassa-1224 41 34 into into ADP ijassa-1224 41 35 the the DET ijassa-1224 41 36 population population NOUN ijassa-1224 41 37 , , PUNCT ijassa-1224 41 38 then then ADV ijassa-1224 41 39 πœƒπœ‹ πœƒπœ‹ PROPN ijassa-1224 41 40 are be AUX ijassa-1224 41 41 the the DET ijassa-1224 41 42 individuals individual NOUN ijassa-1224 41 43 in in ADP ijassa-1224 41 44 the the DET ijassa-1224 41 45 vaccinated vaccinated ADJ ijassa-1224 41 46 class class NOUN ijassa-1224 41 47 while while SCONJ ijassa-1224 41 48 ( ( PUNCT ijassa-1224 41 49 1 1 NUM ijassa-1224 41 50 βˆ’ βˆ’ NOUN ijassa-1224 41 51 πœƒ)πœ‹ πœƒ)πœ‹ NOUN ijassa-1224 41 52 are be AUX ijassa-1224 41 53 the the DET ijassa-1224 41 54 susceptible susceptible ADJ ijassa-1224 41 55 individual individual NOUN ijassa-1224 41 56 . . PUNCT ijassa-1224 42 1 the the DET ijassa-1224 42 2 susceptible susceptible ADJ ijassa-1224 42 3 class class NOUN ijassa-1224 42 4 also also ADV ijassa-1224 42 5 increases increase VERB ijassa-1224 42 6 with with ADP ijassa-1224 42 7 a a DET ijassa-1224 42 8 waning wane VERB ijassa-1224 42 9 rate rate NOUN ijassa-1224 42 10 of of ADP ijassa-1224 42 11 vaccine vaccine NOUN ijassa-1224 42 12 at at ADP ijassa-1224 42 13 πœ” πœ” ADP ijassa-1224 42 14 , , PUNCT ijassa-1224 42 15 due due ADP ijassa-1224 42 16 to to ADP ijassa-1224 42 17 fact fact NOUN ijassa-1224 42 18 that that SCONJ ijassa-1224 42 19 vaccine vaccine NOUN ijassa-1224 42 20 does do AUX ijassa-1224 42 21 not not PART ijassa-1224 42 22 confer confer VERB ijassa-1224 42 23 a a DET ijassa-1224 42 24 total total ADJ ijassa-1224 42 25 immunity immunity NOUN ijassa-1224 42 26 . . PUNCT ijassa-1224 43 1 we we PRON ijassa-1224 43 2 assume assume VERB ijassa-1224 43 3 thatπœ‡is thatπœ‡is NOUN ijassa-1224 43 4 per per ADP ijassa-1224 43 5 capital capital NOUN ijassa-1224 43 6 natural natural ADJ ijassa-1224 43 7 death death NOUN ijassa-1224 43 8 rate rate NOUN ijassa-1224 43 9 and and CCONJ ijassa-1224 43 10 𝑑 𝑑 PROPN ijassa-1224 43 11 ( ( PUNCT ijassa-1224 43 12 𝑖 𝑖 NOUN ijassa-1224 43 13 = = NOUN ijassa-1224 43 14 1,2,3 1,2,3 NUM ijassa-1224 43 15 ) ) PUNCT ijassa-1224 43 16 is be AUX ijassa-1224 43 17 the the DET ijassa-1224 43 18 disease disease NOUN ijassa-1224 43 19 induced induce VERB ijassa-1224 43 20 death death NOUN ijassa-1224 43 21 rate rate NOUN ijassa-1224 43 22 in in ADP ijassa-1224 43 23 classes𝐼 classes𝐼 PROPN ijassa-1224 43 24 ( ( PUNCT ijassa-1224 43 25 𝑑 𝑑 NOUN ijassa-1224 43 26 ) ) PUNCT ijassa-1224 43 27 , , PUNCT ijassa-1224 43 28 𝐼 𝐼 PROPN ijassa-1224 43 29 ( ( PUNCT ijassa-1224 43 30 𝑑 𝑑 NOUN ijassa-1224 43 31 ) ) PUNCT ijassa-1224 43 32 and𝐽(𝑑 and𝐽(𝑑 PROPN ijassa-1224 43 33 ) ) PUNCT ijassa-1224 43 34 respectively respectively ADV ijassa-1224 43 35 . . PUNCT ijassa-1224 44 1 it it PRON ijassa-1224 44 2 is be AUX ijassa-1224 44 3 natural natural ADJ ijassa-1224 44 4 to to PART ijassa-1224 44 5 assume assume VERB ijassa-1224 44 6 that that SCONJ ijassa-1224 44 7 𝑑 𝑑 PROPN ijassa-1224 44 8 β‰₯ β‰₯ NOUN ijassa-1224 44 9 𝑑 𝑑 PROPN ijassa-1224 44 10 β‰₯ β‰₯ NOUN ijassa-1224 44 11 𝑑 𝑑 NOUN ijassa-1224 44 12 due due ADP ijassa-1224 44 13 to to ADP ijassa-1224 44 14 the the DET ijassa-1224 44 15 treatment treatment NOUN ijassa-1224 44 16 of of ADP ijassa-1224 44 17 active active ADJ ijassa-1224 44 18 tb tb ADP ijassa-1224 44 19 cases case NOUN ijassa-1224 44 20 reducing reduce VERB ijassa-1224 44 21 the the DET ijassa-1224 44 22 disease disease NOUN ijassa-1224 44 23 induced induce VERB ijassa-1224 44 24 death death NOUN ijassa-1224 44 25 rate rate NOUN ijassa-1224 44 26 are be AUX ijassa-1224 44 27 the the DET ijassa-1224 44 28 transmission transmission NOUN ijassa-1224 44 29 coefficients coefficient NOUN ijassa-1224 44 30 from from ADP ijassa-1224 44 31 class class NOUN ijassa-1224 44 32 𝑆(𝑑 𝑆(𝑑 NOUN ijassa-1224 44 33 ) ) PUNCT ijassa-1224 44 34 , , PUNCT ijassa-1224 44 35 𝐸(𝑑 𝐸(𝑑 VERB ijassa-1224 44 36 ) ) PUNCT ijassa-1224 44 37 and and CCONJ ijassa-1224 44 38 𝑇(𝑑 𝑇(𝑑 NOUN ijassa-1224 44 39 ) ) PUNCT ijassa-1224 44 40 respectively respectively ADV ijassa-1224 44 41 . . PUNCT ijassa-1224 45 1 we we PRON ijassa-1224 45 2 assume assume VERB ijassa-1224 45 3 that that SCONJ ijassa-1224 45 4 πœ† πœ† X ijassa-1224 45 5 > > X ijassa-1224 45 6 πœ† πœ† X ijassa-1224 45 7 > > X ijassa-1224 45 8 πœ† πœ† NOUN ijassa-1224 45 9 because because SCONJ ijassa-1224 45 10 the the DET ijassa-1224 45 11 treatment treatment NOUN ijassa-1224 45 12 of of ADP ijassa-1224 45 13 active active ADJ ijassa-1224 45 14 tb tb ADP ijassa-1224 45 15 cases case NOUN ijassa-1224 45 16 reduces reduce VERB ijassa-1224 45 17 the the DET ijassa-1224 45 18 infectivity infectivity NOUN ijassa-1224 45 19 of of ADP ijassa-1224 45 20 active active ADJ ijassa-1224 45 21 tb tb ADP ijassa-1224 45 22 cases case NOUN ijassa-1224 45 23 . . PUNCT ijassa-1224 46 1 take take VERB ijassa-1224 46 2 𝜌(0 𝜌(0 PROPN ijassa-1224 46 3 < < X ijassa-1224 46 4 𝜌 𝜌 X ijassa-1224 46 5 < < X ijassa-1224 46 6 1 1 NUM ijassa-1224 46 7 ) ) PUNCT ijassa-1224 46 8 as as ADP ijassa-1224 46 9 the the DET ijassa-1224 46 10 fraction fraction NOUN ijassa-1224 46 11 of of ADP ijassa-1224 46 12 the the DET ijassa-1224 46 13 latent latent NOUN ijassa-1224 46 14 persons person NOUN ijassa-1224 46 15 who who PRON ijassa-1224 46 16 have have VERB ijassa-1224 46 17 fast fast ADJ ijassa-1224 46 18 tb tb ADP ijassa-1224 46 19 progression progression NOUN ijassa-1224 46 20 . . PUNCT ijassa-1224 47 1 the the DET ijassa-1224 47 2 146 146 NUM ijassa-1224 47 3 f.a f.a PROPN ijassa-1224 47 4 . . PROPN ijassa-1224 48 1 oguntolu oguntolu PROPN ijassa-1224 48 2 , , PUNCT ijassa-1224 48 3 o.j o.j PROPN ijassa-1224 48 4 . . PROPN ijassa-1224 48 5 peter peter PROPN ijassa-1224 48 6 , , PUNCT ijassa-1224 48 7 k. k. PROPN ijassa-1224 48 8 oshinubi oshinubi PROPN ijassa-1224 48 9 , , PUNCT ijassa-1224 48 10 t.a t.a PROPN ijassa-1224 48 11 . . PROPN ijassa-1224 48 12 ayoola ayoola PROPN ijassa-1224 48 13 , , PUNCT ijassa-1224 48 14 a.o a.o PROPN ijassa-1224 48 15 . . PROPN ijassa-1224 48 16 oladapo oladapo PROPN ijassa-1224 48 17 , , PUNCT ijassa-1224 48 18 m.m m.m PROPN ijassa-1224 48 19 . . PROPN ijassa-1224 48 20 ojo ojo NOUN ijassa-1224 48 21 copyright copyright NOUN ijassa-1224 48 22 Β© Β© PROPN ijassa-1224 48 23 2022 2022 NUM ijassa-1224 48 24 assa assa PROPN ijassa-1224 48 25 adv adv PROPN ijassa-1224 48 26 . . PUNCT ijassa-1224 49 1 in in ADP ijassa-1224 49 2 systems system NOUN ijassa-1224 49 3 science science NOUN ijassa-1224 49 4 and and CCONJ ijassa-1224 49 5 appl appl NOUN ijassa-1224 49 6 . . PUNCT ijassa-1224 50 1 ( ( PUNCT ijassa-1224 50 2 2022 2022 NUM ijassa-1224 50 3 ) ) PUNCT ijassa-1224 50 4 proportion proportion NOUN ijassa-1224 50 5 πœ™ πœ™ NOUN ijassa-1224 50 6 of of ADP ijassa-1224 50 7 individual individual NOUN ijassa-1224 50 8 in in ADP ijassa-1224 50 9 the the DET ijassa-1224 50 10 exposed expose VERB ijassa-1224 50 11 class class NOUN ijassa-1224 50 12 will will AUX ijassa-1224 50 13 progress progress VERB ijassa-1224 50 14 to to ADP ijassa-1224 50 15 the the DET ijassa-1224 50 16 chronic chronic ADJ ijassa-1224 50 17 class class NOUN ijassa-1224 50 18 via via ADP ijassa-1224 50 19 endogenous endogenous ADJ ijassa-1224 50 20 us us PROPN ijassa-1224 50 21 reactivation reactivation NOUN ijassa-1224 50 22 . . PUNCT ijassa-1224 51 1 𝜎is 𝜎is VERB ijassa-1224 51 2 the the DET ijassa-1224 51 3 reactivation reactivation NOUN ijassa-1224 51 4 rate rate NOUN ijassa-1224 51 5 from from ADP ijassa-1224 51 6 the the DET ijassa-1224 51 7 latent latent NOUN ijassa-1224 51 8 persons person NOUN ijassa-1224 51 9 to to ADP ijassa-1224 51 10 infected infected ADJ ijassa-1224 51 11 class class NOUN ijassa-1224 51 12 . . PUNCT ijassa-1224 52 1 𝛾is 𝛾is VERB ijassa-1224 52 2 the the DET ijassa-1224 52 3 reactivation reactivation NOUN ijassa-1224 52 4 rate rate NOUN ijassa-1224 52 5 of of ADP ijassa-1224 52 6 the the DET ijassa-1224 52 7 individual individual NOUN ijassa-1224 52 8 in in ADP ijassa-1224 52 9 the the DET ijassa-1224 52 10 mild mild NOUN ijassa-1224 52 11 tb tb ADP ijassa-1224 52 12 𝐼 𝐼 PROPN ijassa-1224 52 13 ( ( PUNCT ijassa-1224 52 14 𝑑 𝑑 NOUN ijassa-1224 52 15 ) ) PUNCT ijassa-1224 52 16 to to ADP ijassa-1224 52 17 the the DET ijassa-1224 52 18 chronic chronic NOUN ijassa-1224 52 19 tb tb ADP ijassa-1224 52 20 𝐼 𝐼 PROPN ijassa-1224 52 21 ( ( PUNCT ijassa-1224 52 22 𝑑 𝑑 NOUN ijassa-1224 52 23 ) ) PUNCT ijassa-1224 52 24 . . PUNCT ijassa-1224 53 1 the the DET ijassa-1224 53 2 parameters parameter NOUN ijassa-1224 53 3 are be AUX ijassa-1224 53 4 the the DET ijassa-1224 53 5 recovery recovery NOUN ijassa-1224 53 6 rates rate NOUN ijassa-1224 53 7 of of ADP ijassa-1224 53 8 the the DET ijassa-1224 53 9 individual individual NOUN ijassa-1224 53 10 in in ADP ijassa-1224 53 11 the the DET ijassa-1224 53 12 classes class NOUN ijassa-1224 53 13 𝐼 𝐼 PROPN ijassa-1224 53 14 ( ( PUNCT ijassa-1224 53 15 𝑑 𝑑 NOUN ijassa-1224 53 16 ) ) PUNCT ijassa-1224 53 17 , , PUNCT ijassa-1224 53 18 𝐼 𝐼 PROPN ijassa-1224 53 19 ( ( PUNCT ijassa-1224 53 20 𝑑 𝑑 NOUN ijassa-1224 53 21 ) ) PUNCT ijassa-1224 53 22 and and CCONJ ijassa-1224 53 23 𝐽(𝑑 𝐽(𝑑 NUM ijassa-1224 53 24 ) ) PUNCT ijassa-1224 53 25 respectively respectively ADV ijassa-1224 53 26 . . PUNCT ijassa-1224 54 1 and and CCONJ ijassa-1224 54 2 the the DET ijassa-1224 54 3 parameter parameter NOUN ijassa-1224 54 4 is be AUX ijassa-1224 54 5 the the DET ijassa-1224 54 6 rate rate NOUN ijassa-1224 54 7 of of ADP ijassa-1224 54 8 isolation isolation NOUN ijassa-1224 54 9 of of ADP ijassa-1224 54 10 the the DET ijassa-1224 54 11 individuals individual NOUN ijassa-1224 54 12 in in ADP ijassa-1224 54 13 chronic chronic ADJ ijassa-1224 54 14 class class NOUN ijassa-1224 54 15 𝐼 𝐼 PROPN ijassa-1224 54 16 ( ( PUNCT ijassa-1224 54 17 𝑑 𝑑 NOUN ijassa-1224 54 18 ) ) PUNCT ijassa-1224 54 19 . . PUNCT ijassa-1224 55 1 in in ADP ijassa-1224 55 2 this this DET ijassa-1224 55 3 article article NOUN ijassa-1224 55 4 , , PUNCT ijassa-1224 55 5 the the DET ijassa-1224 55 6 tb tb ADP ijassa-1224 55 7 dynamic dynamic ADJ ijassa-1224 55 8 model model NOUN ijassa-1224 55 9 describing describe VERB ijassa-1224 55 10 the the DET ijassa-1224 55 11 compartment compartment NOUN ijassa-1224 55 12 is be AUX ijassa-1224 55 13 based base VERB ijassa-1224 55 14 on on ADP ijassa-1224 55 15 the the DET ijassa-1224 55 16 following follow VERB ijassa-1224 55 17 assumptions assumption NOUN ijassa-1224 55 18 : : PUNCT ijassa-1224 55 19 that that SCONJ ijassa-1224 55 20 a a DET ijassa-1224 55 21 proportion proportion NOUN ijassa-1224 55 22 of of ADP ijassa-1224 55 23 the the DET ijassa-1224 55 24 population population NOUN ijassa-1224 55 25 of of ADP ijassa-1224 55 26 newborn newborn ADJ ijassa-1224 55 27 is be AUX ijassa-1224 55 28 immunized immunize VERB ijassa-1224 55 29 against against ADP ijassa-1224 55 30 tb tb ADP ijassa-1224 55 31 infection infection NOUN ijassa-1224 55 32 through through ADP ijassa-1224 55 33 vaccination vaccination NOUN ijassa-1224 55 34 . . PUNCT ijassa-1224 56 1 that that SCONJ ijassa-1224 56 2 the the DET ijassa-1224 56 3 immunity immunity NOUN ijassa-1224 56 4 conferred confer VERB ijassa-1224 56 5 on on ADP ijassa-1224 56 6 individuals individual NOUN ijassa-1224 56 7 by by ADP ijassa-1224 56 8 treatment treatment NOUN ijassa-1224 56 9 expires expire VERB ijassa-1224 56 10 after after ADP ijassa-1224 56 11 some some DET ijassa-1224 56 12 time time NOUN ijassa-1224 56 13 at at ADP ijassa-1224 56 14 given give VERB ijassa-1224 56 15 rate rate NOUN ijassa-1224 56 16 . . PUNCT ijassa-1224 57 1 that that SCONJ ijassa-1224 57 2 people people NOUN ijassa-1224 57 3 in in ADP ijassa-1224 57 4 each each DET ijassa-1224 57 5 compartment compartment NOUN ijassa-1224 57 6 have have VERB ijassa-1224 57 7 equal equal ADJ ijassa-1224 57 8 natural natural ADJ ijassa-1224 57 9 death death NOUN ijassa-1224 57 10 rate rate NOUN ijassa-1224 57 11 of of ADP ijassa-1224 57 12 πœ‡ πœ‡ ADP ijassa-1224 57 13 that that SCONJ ijassa-1224 57 14 there there PRON ijassa-1224 57 15 are be VERB ijassa-1224 57 16 no no DET ijassa-1224 57 17 immigrants immigrant NOUN ijassa-1224 57 18 and and CCONJ ijassa-1224 57 19 emigrants emigrant NOUN ijassa-1224 57 20 . . PUNCT ijassa-1224 58 1 the the DET ijassa-1224 58 2 only only ADJ ijassa-1224 58 3 way way NOUN ijassa-1224 58 4 of of ADP ijassa-1224 58 5 entry entry NOUN ijassa-1224 58 6 into into ADP ijassa-1224 58 7 the the DET ijassa-1224 58 8 population population NOUN ijassa-1224 58 9 is be AUX ijassa-1224 58 10 through through ADP ijassa-1224 58 11 new new ADV ijassa-1224 58 12 - - PUNCT ijassa-1224 58 13 born bear VERB ijassa-1224 58 14 babies baby NOUN ijassa-1224 58 15 and and CCONJ ijassa-1224 58 16 the the DET ijassa-1224 58 17 only only ADJ ijassa-1224 58 18 way way NOUN ijassa-1224 58 19 of of ADP ijassa-1224 58 20 exit exit NOUN ijassa-1224 58 21 is be AUX ijassa-1224 58 22 through through ADP ijassa-1224 58 23 death death NOUN ijassa-1224 58 24 from from ADP ijassa-1224 58 25 natural natural ADJ ijassa-1224 58 26 causes cause NOUN ijassa-1224 58 27 or or CCONJ ijassa-1224 58 28 death death NOUN ijassa-1224 58 29 from from ADP ijassa-1224 58 30 tb tb ADP ijassa-1224 58 31 related relate VERB ijassa-1224 58 32 causes cause NOUN ijassa-1224 58 33 . . PUNCT ijassa-1224 59 1 that that SCONJ ijassa-1224 59 2 the the DET ijassa-1224 59 3 infection infection NOUN ijassa-1224 59 4 does do AUX ijassa-1224 59 5 not not PART ijassa-1224 59 6 confer confer VERB ijassa-1224 59 7 immunity immunity NOUN ijassa-1224 59 8 to to ADP ijassa-1224 59 9 the the DET ijassa-1224 59 10 treated treat VERB ijassa-1224 59 11 and and CCONJ ijassa-1224 59 12 recovered recover VERB ijassa-1224 59 13 individuals individual NOUN ijassa-1224 59 14 and and CCONJ ijassa-1224 59 15 so so ADV ijassa-1224 59 16 they they PRON ijassa-1224 59 17 go go VERB ijassa-1224 59 18 back back ADV ijassa-1224 59 19 to to ADP ijassa-1224 59 20 the the DET ijassa-1224 59 21 susceptible susceptible ADJ ijassa-1224 59 22 class class NOUN ijassa-1224 59 23 at at ADP ijassa-1224 59 24 a a DET ijassa-1224 59 25 given give VERB ijassa-1224 59 26 rates rate NOUN ijassa-1224 59 27 . . PUNCT ijassa-1224 60 1 that that SCONJ ijassa-1224 60 2 all all DET ijassa-1224 60 3 newborns newborn NOUN ijassa-1224 60 4 are be AUX ijassa-1224 60 5 previously previously ADV ijassa-1224 60 6 uninfected uninfected ADJ ijassa-1224 60 7 by by ADP ijassa-1224 60 8 tb tb X ijassa-1224 60 9 and and CCONJ ijassa-1224 60 10 therefore therefore ADV ijassa-1224 60 11 join join VERB ijassa-1224 60 12 either either CCONJ ijassa-1224 60 13 the the DET ijassa-1224 60 14 immunized immunize VERB ijassa-1224 60 15 compartment compartment NOUN ijassa-1224 60 16 or or CCONJ ijassa-1224 60 17 the the DET ijassa-1224 60 18 susceptible susceptible ADJ ijassa-1224 60 19 compartment compartment NOUN ijassa-1224 60 20 depending depend VERB ijassa-1224 60 21 on on ADP ijassa-1224 60 22 whether whether SCONJ ijassa-1224 60 23 they they PRON ijassa-1224 60 24 are be AUX ijassa-1224 60 25 vaccinated vaccinate VERB ijassa-1224 60 26 or or CCONJ ijassa-1224 60 27 not not PART ijassa-1224 60 28 . . PUNCT ijassa-1224 61 1 we we PRON ijassa-1224 61 2 combine combine VERB ijassa-1224 61 3 the the DET ijassa-1224 61 4 basic basic ADJ ijassa-1224 61 5 assumptions assumption NOUN ijassa-1224 61 6 , , PUNCT ijassa-1224 61 7 model model NOUN ijassa-1224 61 8 parameters parameter NOUN ijassa-1224 61 9 , , PUNCT ijassa-1224 61 10 variables variable NOUN ijassa-1224 61 11 and and CCONJ ijassa-1224 61 12 the the DET ijassa-1224 61 13 tb tb NOUN ijassa-1224 61 14 infection infection NOUN ijassa-1224 61 15 processes process NOUN ijassa-1224 61 16 to to PART ijassa-1224 61 17 formulate formulate VERB ijassa-1224 61 18 a a DET ijassa-1224 61 19 schematic schematic ADJ ijassa-1224 61 20 diagram diagram NOUN ijassa-1224 61 21 for for ADP ijassa-1224 61 22 tb tb ADP ijassa-1224 61 23 infection infection NOUN ijassa-1224 61 24 as as SCONJ ijassa-1224 61 25 shown show VERB ijassa-1224 61 26 in in ADP ijassa-1224 61 27 figure figure NOUN ijassa-1224 61 28 1 1 NUM ijassa-1224 61 29 . . PUNCT ijassa-1224 62 1 the the DET ijassa-1224 62 2 model model NOUN ijassa-1224 62 3 equations equation NOUN ijassa-1224 62 4 are be AUX ijassa-1224 62 5 given give VERB ijassa-1224 62 6 as as ADP ijassa-1224 62 7 follow follow NOUN ijassa-1224 62 8 = = PUNCT ijassa-1224 62 9 πœ‹πœƒ πœ‹πœƒ NOUN ijassa-1224 62 10 βˆ’ βˆ’ PROPN ijassa-1224 62 11 ( ( PUNCT ijassa-1224 62 12 πœ‡ πœ‡ X ijassa-1224 62 13 + + X ijassa-1224 62 14 πœ”)𝑉 πœ”)𝑉 NOUN ijassa-1224 62 15 , , PUNCT ijassa-1224 62 16 ( ( PUNCT ijassa-1224 62 17 1 1 X ijassa-1224 62 18 ) ) PUNCT ijassa-1224 63 1 = = SYM ijassa-1224 63 2 πœ‹(1 πœ‹(1 NOUN ijassa-1224 63 3 βˆ’ βˆ’ PROPN ijassa-1224 63 4 πœƒ πœƒ NOUN ijassa-1224 63 5 ) ) PUNCT ijassa-1224 63 6 βˆ’ βˆ’ PROPN ijassa-1224 63 7 πœ† πœ† DET ijassa-1224 63 8 𝑆 𝑆 PROPN ijassa-1224 63 9 βˆ’ βˆ’ PROPN ijassa-1224 63 10 πœ‡π‘† πœ‡π‘† PROPN ijassa-1224 63 11 + + CCONJ ijassa-1224 63 12 πœ”π‘‰ πœ”π‘‰ NOUN ijassa-1224 63 13 , , PUNCT ijassa-1224 63 14 ( ( PUNCT ijassa-1224 63 15 2 2 NUM ijassa-1224 63 16 ) ) PUNCT ijassa-1224 63 17 = = PUNCT ijassa-1224 63 18 πœ† πœ† DET ijassa-1224 63 19 𝑆 𝑆 PROPN ijassa-1224 63 20 + + CCONJ ijassa-1224 63 21 πœ† πœ† PROPN ijassa-1224 63 22 𝑇 𝑇 PROPN ijassa-1224 63 23 βˆ’ βˆ’ PROPN ijassa-1224 63 24 πœ† πœ† PROPN ijassa-1224 63 25 𝐸 𝐸 PROPN ijassa-1224 63 26 βˆ’ βˆ’ PROPN ijassa-1224 63 27 ( ( PUNCT ijassa-1224 63 28 πœ‡ πœ‡ X ijassa-1224 63 29 + + X ijassa-1224 63 30 𝜎)𝐸 𝜎)𝐸 NUM ijassa-1224 63 31 , , PUNCT ijassa-1224 63 32 ( ( PUNCT ijassa-1224 63 33 3 3 X ijassa-1224 63 34 ) ) PUNCT ijassa-1224 63 35 = = PUNCT ijassa-1224 63 36 ( ( PUNCT ijassa-1224 63 37 1 1 NUM ijassa-1224 63 38 βˆ’ βˆ’ PROPN ijassa-1224 63 39 𝜌)𝜎𝐸 𝜌)𝜎𝐸 PROPN ijassa-1224 63 40 βˆ’ βˆ’ PROPN ijassa-1224 63 41 ( ( PUNCT ijassa-1224 63 42 𝛾 𝛾 NOUN ijassa-1224 63 43 + + X ijassa-1224 63 44 πœ‡ πœ‡ ADP ijassa-1224 63 45 + + NOUN ijassa-1224 63 46 π‘Ÿ π‘Ÿ NOUN ijassa-1224 63 47 + + CCONJ ijassa-1224 63 48 𝑑 𝑑 NOUN ijassa-1224 63 49 ) ) PUNCT ijassa-1224 63 50 𝐼 𝐼 ADP ijassa-1224 63 51 + + CCONJ ijassa-1224 63 52 ( ( PUNCT ijassa-1224 63 53 1 1 NUM ijassa-1224 63 54 βˆ’ βˆ’ NOUN ijassa-1224 63 55 πœ™)πœ† πœ™)πœ† X ijassa-1224 63 56 𝐸 𝐸 PROPN ijassa-1224 63 57 , , PUNCT ijassa-1224 63 58 ( ( PUNCT ijassa-1224 63 59 4 4 NUM ijassa-1224 63 60 ) ) PUNCT ijassa-1224 63 61 = = NOUN ijassa-1224 64 1 𝜌𝜎𝐸 𝜌𝜎𝐸 NOUN ijassa-1224 64 2 + + CCONJ ijassa-1224 64 3 𝛾𝐼 𝛾𝐼 PROPN ijassa-1224 64 4 βˆ’ βˆ’ PROPN ijassa-1224 64 5 ( ( PUNCT ijassa-1224 64 6 π‘Ÿ π‘Ÿ NOUN ijassa-1224 64 7 + + CCONJ ijassa-1224 64 8 π‘Ÿ π‘Ÿ NOUN ijassa-1224 64 9 + + CCONJ ijassa-1224 64 10 πœ‡ πœ‡ ADP ijassa-1224 64 11 + + X ijassa-1224 64 12 𝑑 𝑑 NOUN ijassa-1224 64 13 ) ) PUNCT ijassa-1224 64 14 𝐼 𝐼 ADP ijassa-1224 64 15 + + PROPN ijassa-1224 64 16 πœ™πœ† πœ™πœ† PROPN ijassa-1224 64 17 𝐸 𝐸 PROPN ijassa-1224 64 18 , , PUNCT ijassa-1224 64 19 ( ( PUNCT ijassa-1224 64 20 5 5 NUM ijassa-1224 64 21 ) ) PUNCT ijassa-1224 64 22 = = NOUN ijassa-1224 65 1 π‘Ÿ π‘Ÿ X ijassa-1224 65 2 𝐼 𝐼 ADP ijassa-1224 65 3 βˆ’ βˆ’ PROPN ijassa-1224 65 4 ( ( PUNCT ijassa-1224 65 5 πœ‡ πœ‡ X ijassa-1224 65 6 + + X ijassa-1224 65 7 𝑑 𝑑 PROPN ijassa-1224 65 8 + + ADJ ijassa-1224 65 9 π‘Ÿ π‘Ÿ NOUN ijassa-1224 65 10 ) ) PUNCT ijassa-1224 65 11 𝐽 𝐽 PROPN ijassa-1224 65 12 , , PUNCT ijassa-1224 65 13 ( ( PUNCT ijassa-1224 65 14 6 6 NUM ijassa-1224 65 15 ) ) PUNCT ijassa-1224 65 16 = = NOUN ijassa-1224 66 1 π‘Ÿ π‘Ÿ X ijassa-1224 66 2 𝐽 𝐽 NOUN ijassa-1224 66 3 + + NUM ijassa-1224 66 4 π‘Ÿ π‘Ÿ X ijassa-1224 67 1 𝐼 𝐼 ADP ijassa-1224 67 2 + + NOUN ijassa-1224 67 3 π‘Ÿ π‘Ÿ NOUN ijassa-1224 67 4 𝐼 𝐼 ADP ijassa-1224 67 5 βˆ’ βˆ’ PROPN ijassa-1224 67 6 ( ( PUNCT ijassa-1224 67 7 πœ‡ πœ‡ ADP ijassa-1224 67 8 + + X ijassa-1224 67 9 πœ† πœ† X ijassa-1224 67 10 ) ) PUNCT ijassa-1224 67 11 𝑇 𝑇 PROPN ijassa-1224 67 12 , , PUNCT ijassa-1224 67 13 ( ( PUNCT ijassa-1224 67 14 7 7 X ijassa-1224 67 15 ) ) PUNCT ijassa-1224 67 16 where where SCONJ ijassa-1224 67 17 πœ† πœ† NOUN ijassa-1224 67 18 = = NOUN ijassa-1224 67 19 𝛽(𝐼 𝛽(𝐼 NOUN ijassa-1224 67 20 + + CCONJ ijassa-1224 67 21 πœ€ πœ€ X ijassa-1224 67 22 𝐼 𝐼 ADP ijassa-1224 67 23 + + CCONJ ijassa-1224 67 24 πœ€ πœ€ X ijassa-1224 67 25 𝐽),πœ† 𝐽),πœ† X ijassa-1224 67 26 = = SYM ijassa-1224 67 27 𝛼(𝐼 𝛼(𝐼 X ijassa-1224 67 28 + + PUNCT ijassa-1224 67 29 πœ€ πœ€ X ijassa-1224 67 30 𝐼 𝐼 ADP ijassa-1224 67 31 + + PROPN ijassa-1224 67 32 πœ€ πœ€ PROPN ijassa-1224 67 33 𝐽 𝐽 NOUN ijassa-1224 67 34 ) ) PUNCT ijassa-1224 67 35 and and CCONJ ijassa-1224 67 36 πœ† πœ† X ijassa-1224 67 37 = = PUNCT ijassa-1224 67 38 𝛾(𝐼 𝛾(𝐼 PROPN ijassa-1224 67 39 + + CCONJ ijassa-1224 67 40 πœ€ πœ€ X ijassa-1224 67 41 𝐼 𝐼 PROPN ijassa-1224 67 42 + + PROPN ijassa-1224 67 43 πœ€ πœ€ PROPN ijassa-1224 67 44 𝐽 𝐽 PROPN ijassa-1224 67 45 ) ) PUNCT ijassa-1224 67 46 . . PUNCT ijassa-1224 68 1 analysis analysis NOUN ijassa-1224 68 2 and and CCONJ ijassa-1224 68 3 dynamics dynamic NOUN ijassa-1224 68 4 of of ADP ijassa-1224 68 5 tuberculosis tuberculosis NOUN ijassa-1224 68 6 outbreak outbreak NOUN ijassa-1224 68 7 147 147 NUM ijassa-1224 68 8 copyright copyright NOUN ijassa-1224 68 9 Β© Β© PROPN ijassa-1224 68 10 2022 2022 NUM ijassa-1224 68 11 assa assa NOUN ijassa-1224 68 12 . . PUNCT ijassa-1224 69 1 adv adv PROPN ijassa-1224 69 2 . . PUNCT ijassa-1224 70 1 in in ADP ijassa-1224 70 2 systems system NOUN ijassa-1224 70 3 science science NOUN ijassa-1224 70 4 and and CCONJ ijassa-1224 70 5 appl appl NOUN ijassa-1224 70 6 . . PUNCT ijassa-1224 71 1 ( ( PUNCT ijassa-1224 71 2 2022 2022 NUM ijassa-1224 71 3 ) ) PUNCT ijassa-1224 71 4 figure figure NOUN ijassa-1224 71 5 1 1 NUM ijassa-1224 71 6 : : PUNCT ijassa-1224 71 7 schematic schematic ADJ ijassa-1224 71 8 representation representation NOUN ijassa-1224 71 9 of of ADP ijassa-1224 71 10 the the DET ijassa-1224 71 11 model model NOUN ijassa-1224 71 12 table table NOUN ijassa-1224 71 13 1 1 NUM ijassa-1224 71 14 . . PUNCT ijassa-1224 72 1 notation notation NOUN ijassa-1224 72 2 and and CCONJ ijassa-1224 72 3 definition definition NOUN ijassa-1224 72 4 of of ADP ijassa-1224 72 5 other other ADJ ijassa-1224 72 6 parameters parameter NOUN ijassa-1224 72 7 symbol symbol NOUN ijassa-1224 72 8 description description NOUN ijassa-1224 72 9 π‘Ÿ π‘Ÿ PRON ijassa-1224 72 10 treatment treatment NOUN ijassa-1224 72 11 rate rate NOUN ijassa-1224 72 12 of of ADP ijassa-1224 72 13 individuals individual NOUN ijassa-1224 72 14 in in ADP ijassa-1224 72 15 mild mild ADJ ijassa-1224 72 16 class class NOUN ijassa-1224 72 17 π‘Ÿ π‘Ÿ X ijassa-1224 72 18 the the DET ijassa-1224 72 19 treatment treatment NOUN ijassa-1224 72 20 rate rate NOUN ijassa-1224 72 21 for for ADP ijassa-1224 72 22 those those PRON ijassa-1224 72 23 is be AUX ijassa-1224 72 24 𝐼 𝐼 ADP ijassa-1224 72 25 class class NOUN ijassa-1224 72 26 π‘Ÿ π‘Ÿ NOUN ijassa-1224 72 27 the the DET ijassa-1224 72 28 progression progression NOUN ijassa-1224 72 29 rate rate NOUN ijassa-1224 72 30 from from ADP ijassa-1224 72 31 classes𝐼 classes𝐼 PROPN ijassa-1224 72 32 to to ADP ijassa-1224 72 33 j j PROPN ijassa-1224 72 34 π‘Ÿ π‘Ÿ X ijassa-1224 72 35 the the DET ijassa-1224 72 36 treatment treatment NOUN ijassa-1224 72 37 rate rate NOUN ijassa-1224 72 38 for for ADP ijassa-1224 72 39 those those PRON ijassa-1224 72 40 in in ADP ijassa-1224 72 41 isolated isolated ADJ ijassa-1224 72 42 class class NOUN ijassa-1224 72 43 𝛽 𝛽 NOUN ijassa-1224 72 44 transmission transmission NOUN ijassa-1224 72 45 rate rate NOUN ijassa-1224 72 46 among among ADP ijassa-1224 72 47 the the DET ijassa-1224 72 48 susceptible susceptible ADJ ijassa-1224 72 49 𝑑 𝑑 PROPN ijassa-1224 72 50 death death NOUN ijassa-1224 72 51 rate rate NOUN ijassa-1224 72 52 for for ADP ijassa-1224 72 53 mild mild ADJ ijassa-1224 72 54 tb tb ADP ijassa-1224 72 55 individual individual NOUN ijassa-1224 72 56 𝑑 𝑑 PROPN ijassa-1224 72 57 death death NOUN ijassa-1224 72 58 rate rate NOUN ijassa-1224 72 59 for for ADP ijassa-1224 72 60 chronic chronic ADJ ijassa-1224 72 61 tb tb ADP ijassa-1224 72 62 individuals individual NOUN ijassa-1224 72 63 𝑑 𝑑 NOUN ijassa-1224 72 64 death death NOUN ijassa-1224 72 65 rate rate NOUN ijassa-1224 72 66 for for ADP ijassa-1224 72 67 isolated isolated ADJ ijassa-1224 72 68 class class NOUN ijassa-1224 72 69 𝛼 𝛼 NOUN ijassa-1224 72 70 effective effective ADJ ijassa-1224 72 71 transmission transmission NOUN ijassa-1224 72 72 rate rate NOUN ijassa-1224 72 73 from from ADP ijassa-1224 72 74 latent latent ADJ ijassa-1224 72 75 class class NOUN ijassa-1224 72 76 to to ADP ijassa-1224 72 77 infected infected ADJ ijassa-1224 72 78 class class NOUN ijassa-1224 72 79 πœ€ πœ€ PROPN ijassa-1224 72 80 relative relative ADJ ijassa-1224 72 81 infectiousness infectiousness NOUN ijassa-1224 72 82 of of ADP ijassa-1224 72 83 humans human NOUN ijassa-1224 72 84 with with ADP ijassa-1224 72 85 mild mild ADJ ijassa-1224 72 86 tb tb NOUN ijassa-1224 72 87 compared compare VERB ijassa-1224 72 88 to to ADP ijassa-1224 72 89 humans human NOUN ijassa-1224 72 90 in in ADP ijassa-1224 72 91 the the DET ijassa-1224 72 92 chronic chronic ADJ ijassa-1224 72 93 class class NOUN ijassa-1224 72 94 πœ€ πœ€ PROPN ijassa-1224 72 95 relative relative ADJ ijassa-1224 72 96 infectiousness infectiousness NOUN ijassa-1224 72 97 of of ADP ijassa-1224 72 98 humans human NOUN ijassa-1224 72 99 with with ADP ijassa-1224 72 100 tb tb NOUN ijassa-1224 72 101 in in ADP ijassa-1224 72 102 the the DET ijassa-1224 72 103 isolated isolated ADJ ijassa-1224 72 104 class class NOUN ijassa-1224 72 105 compared compare VERB ijassa-1224 72 106 to to ADP ijassa-1224 72 107 humans human NOUN ijassa-1224 72 108 in in ADP ijassa-1224 72 109 the the DET ijassa-1224 72 110 chronic chronic ADJ ijassa-1224 72 111 class class NOUN ijassa-1224 72 112 πœ€ πœ€ PROPN ijassa-1224 72 113 relative relative ADJ ijassa-1224 72 114 infectiousness infectiousness NOUN ijassa-1224 72 115 of of ADP ijassa-1224 72 116 humans human NOUN ijassa-1224 72 117 with with ADP ijassa-1224 72 118 mild mild ADJ ijassa-1224 72 119 tb tb ADP ijassa-1224 72 120 due due ADP ijassa-1224 72 121 to to ADP ijassa-1224 72 122 endogenous endogenous ADJ ijassa-1224 72 123 reactivation reactivation NOUN ijassa-1224 72 124 compared compare VERB ijassa-1224 72 125 to to ADP ijassa-1224 72 126 humans human NOUN ijassa-1224 72 127 in in ADP ijassa-1224 72 128 the the DET ijassa-1224 72 129 chronic chronic ADJ ijassa-1224 72 130 class class NOUN ijassa-1224 72 131 . . PUNCT ijassa-1224 73 1 πœ€ πœ€ PROPN ijassa-1224 73 2 relative relative ADJ ijassa-1224 73 3 infectiousness infectiousness NOUN ijassa-1224 73 4 of of ADP ijassa-1224 73 5 humans human NOUN ijassa-1224 73 6 on on ADP ijassa-1224 73 7 isolation isolation NOUN ijassa-1224 73 8 after after ADP ijassa-1224 73 9 endogenous endogenous ADJ ijassa-1224 73 10 reactivation reactivation NOUN ijassa-1224 73 11 compared compare VERB ijassa-1224 73 12 to to ADP ijassa-1224 73 13 humans human NOUN ijassa-1224 73 14 in in ADP ijassa-1224 73 15 the the DET ijassa-1224 73 16 chronic chronic ADJ ijassa-1224 73 17 class class NOUN ijassa-1224 73 18 πœ€ πœ€ PROPN ijassa-1224 73 19 relative relative ADJ ijassa-1224 73 20 infectiousness infectiousness NOUN ijassa-1224 73 21 of of ADP ijassa-1224 73 22 humans human NOUN ijassa-1224 73 23 with with ADP ijassa-1224 73 24 mild mild ADJ ijassa-1224 73 25 tb tb ADP ijassa-1224 73 26 due due ADP ijassa-1224 73 27 to to PART ijassa-1224 73 28 exogenous exogenous ADJ ijassa-1224 73 29 re re NOUN ijassa-1224 73 30 - - NOUN ijassa-1224 73 31 infection infection NOUN ijassa-1224 73 32 compared compare VERB ijassa-1224 73 33 to to ADP ijassa-1224 73 34 humans human NOUN ijassa-1224 73 35 in in ADP ijassa-1224 73 36 the the DET ijassa-1224 73 37 chronic chronic ADJ ijassa-1224 73 38 class class NOUN ijassa-1224 73 39 πœ€ πœ€ PROPN ijassa-1224 73 40 relative relative ADJ ijassa-1224 73 41 infectiousness infectiousness NOUN ijassa-1224 73 42 of of ADP ijassa-1224 73 43 humans human NOUN ijassa-1224 73 44 on on ADP ijassa-1224 73 45 isolation isolation NOUN ijassa-1224 73 46 after after ADP ijassa-1224 73 47 exogenous exogenous ADJ ijassa-1224 73 48 re re NOUN ijassa-1224 73 49 - - NOUN ijassa-1224 73 50 infection infection NOUN ijassa-1224 73 51 compared compare VERB ijassa-1224 73 52 to to ADP ijassa-1224 73 53 humans human NOUN ijassa-1224 73 54 in in ADP ijassa-1224 73 55 the the DET ijassa-1224 73 56 chronic chronic ADJ ijassa-1224 73 57 class class NOUN ijassa-1224 73 58 𝜌 𝜌 ADP ijassa-1224 73 59 fraction fraction NOUN ijassa-1224 73 60 of of ADP ijassa-1224 73 61 the the DET ijassa-1224 73 62 latent latent NOUN ijassa-1224 73 63 persons person NOUN ijassa-1224 73 64 who who PRON ijassa-1224 73 65 have have VERB ijassa-1224 73 66 fast fast ADJ ijassa-1224 73 67 tb tb ADP ijassa-1224 73 68 progression progression NOUN ijassa-1224 73 69 𝜎 𝜎 PROPN ijassa-1224 73 70 reactivation reactivation NOUN ijassa-1224 73 71 rate rate NOUN ijassa-1224 73 72 from from ADP ijassa-1224 73 73 the the DET ijassa-1224 73 74 latent latent NOUN ijassa-1224 73 75 individuals individual NOUN ijassa-1224 73 76 πœ™ πœ™ DET ijassa-1224 73 77 proportion proportion NOUN ijassa-1224 73 78 of of ADP ijassa-1224 73 79 individual individual NOUN ijassa-1224 73 80 in in ADP ijassa-1224 73 81 the the DET ijassa-1224 73 82 exposed expose VERB ijassa-1224 73 83 class class NOUN ijassa-1224 73 84 𝛾 𝛾 ADP ijassa-1224 73 85 reactivation reactivation NOUN ijassa-1224 73 86 rate rate NOUN ijassa-1224 73 87 of of ADP ijassa-1224 73 88 the the DET ijassa-1224 73 89 individual individual NOUN ijassa-1224 73 90 in in ADP ijassa-1224 73 91 the the DET ijassa-1224 73 92 mild mild ADJ ijassa-1224 73 93 tb tb ADP ijassa-1224 73 94 class class NOUN ijassa-1224 73 95 πœ‡ πœ‡ ADP ijassa-1224 73 96 natural natural ADJ ijassa-1224 73 97 death death NOUN ijassa-1224 73 98 rate rate NOUN ijassa-1224 73 99 2.2 2.2 NUM ijassa-1224 73 100 . . PUNCT ijassa-1224 74 1 the the DET ijassa-1224 74 2 positive positive ADJ ijassa-1224 74 3 invariant invariant ADJ ijassa-1224 74 4 region region NOUN ijassa-1224 74 5 the the DET ijassa-1224 74 6 entire entire ADJ ijassa-1224 74 7 population population NOUN ijassa-1224 74 8 size size NOUN ijassa-1224 74 9 𝑁 𝑁 PROPN ijassa-1224 74 10 can can AUX ijassa-1224 74 11 be be AUX ijassa-1224 74 12 determined determine VERB ijassa-1224 74 13 from from ADP ijassa-1224 74 14 by by ADP ijassa-1224 74 15 adding add VERB ijassa-1224 74 16 equations equation NOUN ijassa-1224 74 17 ( ( PUNCT ijassa-1224 74 18 1)–(7 1)–(7 NUM ijassa-1224 74 19 ) ) PUNCT ijassa-1224 74 20 . . PUNCT ijassa-1224 75 1 hence hence ADV ijassa-1224 75 2 , , PUNCT ijassa-1224 75 3 𝑁(𝑑 𝑁(𝑑 NOUN ijassa-1224 75 4 ) ) PUNCT ijassa-1224 75 5 = = PUNCT ijassa-1224 75 6 𝑆(𝑑 𝑆(𝑑 X ijassa-1224 75 7 ) ) PUNCT ijassa-1224 75 8 + + PUNCT ijassa-1224 75 9 𝑉(𝑑 𝑉(𝑑 ADP ijassa-1224 75 10 ) ) PUNCT ijassa-1224 75 11 + + PUNCT ijassa-1224 75 12 𝐸(𝑑 𝐸(𝑑 VERB ijassa-1224 75 13 ) ) PUNCT ijassa-1224 75 14 + + CCONJ ijassa-1224 75 15 𝐼 𝐼 PROPN ijassa-1224 75 16 ( ( PUNCT ijassa-1224 75 17 𝑑 𝑑 NOUN ijassa-1224 75 18 ) ) PUNCT ijassa-1224 75 19 + + CCONJ ijassa-1224 75 20 𝐼 𝐼 PROPN ijassa-1224 75 21 ( ( PUNCT ijassa-1224 75 22 𝑑 𝑑 NOUN ijassa-1224 75 23 ) ) PUNCT ijassa-1224 75 24 + + PUNCT ijassa-1224 75 25 𝐽(𝑑 𝐽(𝑑 X ijassa-1224 75 26 ) ) PUNCT ijassa-1224 75 27 + + CCONJ ijassa-1224 75 28 𝑇(𝑑 𝑇(𝑑 X ijassa-1224 75 29 ) ) PUNCT ijassa-1224 75 30 then then ADV ijassa-1224 75 31 , , PUNCT ijassa-1224 75 32 = = PUNCT ijassa-1224 75 33 πœ‹ πœ‹ PRON ijassa-1224 75 34 βˆ’ βˆ’ PROPN ijassa-1224 75 35 πœ‡π‘(𝑑 πœ‡π‘(𝑑 NUM ijassa-1224 75 36 ) ) PUNCT ijassa-1224 75 37 βˆ’ βˆ’ PROPN ijassa-1224 75 38 𝑑 𝑑 PRON ijassa-1224 75 39 𝑁 𝑁 PROPN ijassa-1224 75 40 βˆ’ βˆ’ NOUN ijassa-1224 75 41 𝑑 𝑑 NOUN ijassa-1224 75 42 𝑁 𝑁 PROPN ijassa-1224 75 43 βˆ’ βˆ’ NOUN ijassa-1224 75 44 𝑑 𝑑 PROPN ijassa-1224 75 45 𝑁 𝑁 PROPN ijassa-1224 75 46 ( ( PUNCT ijassa-1224 75 47 8) 8) NUM ijassa-1224 75 48 in in ADP ijassa-1224 75 49 the the DET ijassa-1224 75 50 absence absence NOUN ijassa-1224 75 51 of of ADP ijassa-1224 75 52 the the DET ijassa-1224 75 53 disease disease NOUN ijassa-1224 75 54 ( ( PUNCT ijassa-1224 75 55 𝑑 𝑑 NOUN ijassa-1224 75 56 = = X ijassa-1224 75 57 𝑑 𝑑 NOUN ijassa-1224 75 58 = = X ijassa-1224 75 59 𝑑 𝑑 NOUN ijassa-1224 75 60 = = NOUN ijassa-1224 75 61 0 0 NUM ijassa-1224 75 62 ) ) PUNCT ijassa-1224 75 63 then then ADV ijassa-1224 75 64 ( ( PUNCT ijassa-1224 75 65 8) 8) NUM ijassa-1224 75 66 gives give VERB ijassa-1224 75 67 148 148 NUM ijassa-1224 75 68 f.a f.a PROPN ijassa-1224 75 69 . . PROPN ijassa-1224 76 1 oguntolu oguntolu PROPN ijassa-1224 76 2 , , PUNCT ijassa-1224 76 3 o.j o.j PROPN ijassa-1224 76 4 . . PROPN ijassa-1224 76 5 peter peter PROPN ijassa-1224 76 6 , , PUNCT ijassa-1224 76 7 k. k. PROPN ijassa-1224 76 8 oshinubi oshinubi PROPN ijassa-1224 76 9 , , PUNCT ijassa-1224 76 10 t.a t.a PROPN ijassa-1224 76 11 . . PROPN ijassa-1224 76 12 ayoola ayoola PROPN ijassa-1224 76 13 , , PUNCT ijassa-1224 76 14 a.o a.o PROPN ijassa-1224 76 15 . . PROPN ijassa-1224 76 16 oladapo oladapo PROPN ijassa-1224 76 17 , , PUNCT ijassa-1224 76 18 m.m m.m PROPN ijassa-1224 76 19 . . PROPN ijassa-1224 76 20 ojo ojo NOUN ijassa-1224 76 21 copyright copyright NOUN ijassa-1224 76 22 Β© Β© PROPN ijassa-1224 76 23 2022 2022 NUM ijassa-1224 76 24 assa assa PROPN ijassa-1224 76 25 adv adv PROPN ijassa-1224 76 26 . . PUNCT ijassa-1224 77 1 in in ADP ijassa-1224 77 2 systems system NOUN ijassa-1224 77 3 science science NOUN ijassa-1224 77 4 and and CCONJ ijassa-1224 77 5 appl appl NOUN ijassa-1224 77 6 . . PUNCT ijassa-1224 78 1 ( ( PUNCT ijassa-1224 78 2 2022 2022 NUM ijassa-1224 78 3 ) ) PUNCT ijassa-1224 79 1 = = NOUN ijassa-1224 79 2 πœ‹ πœ‹ PRON ijassa-1224 79 3 βˆ’ βˆ’ PROPN ijassa-1224 79 4 πœ‡π‘ πœ‡π‘ NOUN ijassa-1224 79 5 ( ( PUNCT ijassa-1224 79 6 9 9 NUM ijassa-1224 79 7 ) ) PUNCT ijassa-1224 79 8 theorem theorem NOUN ijassa-1224 79 9 1 1 NUM ijassa-1224 79 10 : : PUNCT ijassa-1224 79 11 the the DET ijassa-1224 79 12 system system NOUN ijassa-1224 79 13 ( ( PUNCT ijassa-1224 79 14 1 1 NUM ijassa-1224 79 15 ) ) PUNCT ijassa-1224 79 16 to to ADP ijassa-1224 79 17 ( ( PUNCT ijassa-1224 79 18 7 7 X ijassa-1224 79 19 ) ) PUNCT ijassa-1224 79 20 has have VERB ijassa-1224 79 21 solution solution NOUN ijassa-1224 79 22 which which PRON ijassa-1224 79 23 are be AUX ijassa-1224 79 24 contained contain VERB ijassa-1224 79 25 in in ADP ijassa-1224 79 26 the the DET ijassa-1224 79 27 feasible feasible ADJ ijassa-1224 79 28 region region NOUN ijassa-1224 79 29 Ο‰ Ο‰ PROPN ijassa-1224 79 30 for for ADP ijassa-1224 79 31 all all DET ijassa-1224 79 32 𝑑 𝑑 NOUN ijassa-1224 79 33 > > X ijassa-1224 79 34 0 0 X ijassa-1224 79 35 . . PUNCT ijassa-1224 80 1 proof proof NOUN ijassa-1224 80 2 . . PUNCT ijassa-1224 81 1 let let VERB ijassa-1224 81 2 𝛺 𝛺 PROPN ijassa-1224 81 3 = = SYM ijassa-1224 81 4 ( ( PUNCT ijassa-1224 81 5 𝑆 𝑆 PROPN ijassa-1224 81 6 , , PUNCT ijassa-1224 81 7 𝑉 𝑉 PROPN ijassa-1224 81 8 , , PUNCT ijassa-1224 81 9 𝐸 𝐸 PROPN ijassa-1224 81 10 , , PUNCT ijassa-1224 81 11 𝐼 𝐼 PROPN ijassa-1224 81 12 𝐼 𝐼 PROPN ijassa-1224 81 13 , , PUNCT ijassa-1224 81 14 𝐽 𝐽 PROPN ijassa-1224 81 15 , , PUNCT ijassa-1224 81 16 𝑇 𝑇 PROPN ijassa-1224 81 17 ) ) PUNCT ijassa-1224 81 18 ∈ ∈ PROPN ijassa-1224 81 19 𝑅 𝑅 PROPN ijassa-1224 81 20 be be AUX ijassa-1224 81 21 any any DET ijassa-1224 81 22 solution solution NOUN ijassa-1224 81 23 of of ADP ijassa-1224 81 24 the the DET ijassa-1224 81 25 system system NOUN ijassa-1224 81 26 ( ( PUNCT ijassa-1224 81 27 1)–(7 1)–(7 NUM ijassa-1224 81 28 ) ) PUNCT ijassa-1224 81 29 with with ADP ijassa-1224 81 30 non non ADJ ijassa-1224 81 31 - - ADJ ijassa-1224 81 32 negative negative ADJ ijassa-1224 81 33 initial initial ADJ ijassa-1224 81 34 condition condition NOUN ijassa-1224 81 35 . . PUNCT ijassa-1224 82 1 using use VERB ijassa-1224 82 2 theorem theorem NOUN ijassa-1224 82 3 of of ADP ijassa-1224 82 4 differential differential ADJ ijassa-1224 82 5 inequality inequality NOUN ijassa-1224 82 6 , , PUNCT ijassa-1224 82 7 equation equation NOUN ijassa-1224 82 8 ( ( PUNCT ijassa-1224 82 9 9 9 X ijassa-1224 82 10 ) ) PUNCT ijassa-1224 82 11 gives give VERB ijassa-1224 82 12 ≀ ≀ NOUN ijassa-1224 82 13 πœ‹ πœ‹ PRON ijassa-1224 82 14 βˆ’ βˆ’ PROPN ijassa-1224 82 15 πœ‡π‘ πœ‡π‘ NOUN ijassa-1224 82 16 , , PUNCT ijassa-1224 82 17 then then ADV ijassa-1224 82 18 0 0 NUM ijassa-1224 82 19 ≀ ≀ NOUN ijassa-1224 82 20 𝑁 𝑁 PROPN ijassa-1224 82 21 ≀ ≀ NOUN ijassa-1224 82 22 , , PUNCT ijassa-1224 82 23 hence hence ADV ijassa-1224 82 24 πœ‹ πœ‹ NOUN ijassa-1224 82 25 βˆ’ βˆ’ PROPN ijassa-1224 82 26 πœ‡π‘ πœ‡π‘ NOUN ijassa-1224 82 27 β‰₯ β‰₯ NUM ijassa-1224 82 28 π‘˜π‘’ π‘˜π‘’ NOUN ijassa-1224 82 29 , , PUNCT ijassa-1224 82 30 where where SCONJ ijassa-1224 82 31 π‘˜ π‘˜ NOUN ijassa-1224 82 32 is be AUX ijassa-1224 82 33 constant constant ADJ ijassa-1224 82 34 . . PUNCT ijassa-1224 83 1 thus thus ADV ijassa-1224 83 2 , , PUNCT ijassa-1224 83 3 the the DET ijassa-1224 83 4 feasible feasible ADJ ijassa-1224 83 5 set set NOUN ijassa-1224 83 6 of of ADP ijassa-1224 83 7 the the DET ijassa-1224 83 8 model model NOUN ijassa-1224 83 9 is be AUX ijassa-1224 83 10 given give VERB ijassa-1224 83 11 by by ADP ijassa-1224 83 12 𝛺 𝛺 PROPN ijassa-1224 83 13 = = SYM ijassa-1224 83 14 ( ( PUNCT ijassa-1224 83 15 𝑆 𝑆 PROPN ijassa-1224 83 16 , , PUNCT ijassa-1224 83 17 𝑉 𝑉 PROPN ijassa-1224 83 18 , , PUNCT ijassa-1224 83 19 𝐼 𝐼 PROPN ijassa-1224 83 20 , , PUNCT ijassa-1224 83 21 𝐼 𝐼 PROPN ijassa-1224 83 22 , , PUNCT ijassa-1224 83 23 𝐽 𝐽 PROPN ijassa-1224 83 24 , , PUNCT ijassa-1224 83 25 𝑇 𝑇 PROPN ijassa-1224 83 26 ) ) PUNCT ijassa-1224 83 27 ∈ ∈ PROPN ijassa-1224 83 28 𝑅 𝑅 PROPN ijassa-1224 83 29 : : PUNCT ijassa-1224 83 30 𝑆 𝑆 PROPN ijassa-1224 83 31 , , PUNCT ijassa-1224 83 32 𝑉 𝑉 PROPN ijassa-1224 83 33 , , PUNCT ijassa-1224 83 34 𝐼 𝐼 PROPN ijassa-1224 83 35 , , PUNCT ijassa-1224 83 36 𝐼 𝐼 PROPN ijassa-1224 83 37 , , PUNCT ijassa-1224 83 38 𝐽 𝐽 PROPN ijassa-1224 83 39 , , PUNCT ijassa-1224 83 40 𝑇 𝑇 PROPN ijassa-1224 83 41 β‰₯ β‰₯ NOUN ijassa-1224 83 42 0 0 NUM ijassa-1224 83 43 , , PUNCT ijassa-1224 83 44 𝑁 𝑁 PROPN ijassa-1224 83 45 ≀ ≀ NOUN ijassa-1224 83 46 , , PUNCT ijassa-1224 83 47 which which PRON ijassa-1224 83 48 is be AUX ijassa-1224 83 49 positive positive ADJ ijassa-1224 83 50 invariant invariant ADJ ijassa-1224 83 51 ( ( PUNCT ijassa-1224 83 52 i.e. i.e. X ijassa-1224 83 53 , , PUNCT ijassa-1224 83 54 solution solution NOUN ijassa-1224 83 55 remain remain VERB ijassa-1224 83 56 positive positive ADJ ijassa-1224 83 57 for for ADP ijassa-1224 83 58 all all DET ijassa-1224 83 59 time time NOUN ijassa-1224 83 60 𝑑 𝑑 NOUN ijassa-1224 83 61 ) ) PUNCT ijassa-1224 83 62 and and CCONJ ijassa-1224 83 63 the the DET ijassa-1224 83 64 model model NOUN ijassa-1224 83 65 is be AUX ijassa-1224 83 66 epidemiologically epidemiologically ADV ijassa-1224 83 67 meaningful meaningful ADJ ijassa-1224 83 68 and and CCONJ ijassa-1224 83 69 mathematically mathematically ADV ijassa-1224 83 70 well well ADV ijassa-1224 83 71 pose pose VERB ijassa-1224 83 72 . . PUNCT ijassa-1224 84 1 β–‘ β–‘ PUNCT ijassa-1224 84 2 2.3 2.3 NUM ijassa-1224 84 3 . . PUNCT ijassa-1224 84 4 positivity positivity NOUN ijassa-1224 84 5 of of ADP ijassa-1224 84 6 solutions solution NOUN ijassa-1224 84 7 since since SCONJ ijassa-1224 84 8 equations equation NOUN ijassa-1224 84 9 ( ( PUNCT ijassa-1224 84 10 1)–(7 1)–(7 NUM ijassa-1224 84 11 ) ) PUNCT ijassa-1224 84 12 represent represent VERB ijassa-1224 84 13 the the DET ijassa-1224 84 14 population population NOUN ijassa-1224 84 15 in in ADP ijassa-1224 84 16 each each DET ijassa-1224 84 17 compartment compartment NOUN ijassa-1224 84 18 and and CCONJ ijassa-1224 84 19 all all DET ijassa-1224 84 20 model model NOUN ijassa-1224 84 21 parameters parameter NOUN ijassa-1224 84 22 are be AUX ijassa-1224 84 23 all all ADV ijassa-1224 84 24 positive positive ADJ ijassa-1224 84 25 , , PUNCT ijassa-1224 84 26 then then ADV ijassa-1224 84 27 it it PRON ijassa-1224 84 28 lies lie VERB ijassa-1224 84 29 in in ADP ijassa-1224 84 30 a a DET ijassa-1224 84 31 region region NOUN ijassa-1224 84 32 Ο‰ Ο‰ NUM ijassa-1224 84 33 defined define VERB ijassa-1224 84 34 by by ADP ijassa-1224 84 35 𝛺 𝛺 PROPN ijassa-1224 84 36 = = SYM ijassa-1224 84 37 ( ( PUNCT ijassa-1224 84 38 𝑆 𝑆 PROPN ijassa-1224 84 39 , , PUNCT ijassa-1224 84 40 𝑉 𝑉 PROPN ijassa-1224 84 41 , , PUNCT ijassa-1224 84 42 𝐼 𝐼 PROPN ijassa-1224 84 43 , , PUNCT ijassa-1224 84 44 𝐼 𝐼 PROPN ijassa-1224 84 45 , , PUNCT ijassa-1224 84 46 𝐽 𝐽 PROPN ijassa-1224 84 47 , , PUNCT ijassa-1224 84 48 𝑇 𝑇 PROPN ijassa-1224 84 49 ) ) PUNCT ijassa-1224 84 50 ∈ ∈ PROPN ijassa-1224 84 51 𝑅 𝑅 PROPN ijassa-1224 84 52 : : PUNCT ijassa-1224 84 53 𝑆 𝑆 PROPN ijassa-1224 84 54 , , PUNCT ijassa-1224 84 55 𝑉 𝑉 PROPN ijassa-1224 84 56 , , PUNCT ijassa-1224 84 57 𝐼 𝐼 PROPN ijassa-1224 84 58 , , PUNCT ijassa-1224 84 59 𝐼 𝐼 PROPN ijassa-1224 84 60 , , PUNCT ijassa-1224 84 61 𝐽 𝐽 PROPN ijassa-1224 84 62 , , PUNCT ijassa-1224 84 63 𝑇 𝑇 PROPN ijassa-1224 84 64 β‰₯ β‰₯ NOUN ijassa-1224 84 65 0 0 NUM ijassa-1224 84 66 , , PUNCT ijassa-1224 84 67 𝑁 𝑁 PROPN ijassa-1224 84 68 ≀ ≀ NOUN ijassa-1224 84 69 . . PUNCT ijassa-1224 85 1 theorem theorem NOUN ijassa-1224 85 2 2 2 NUM ijassa-1224 85 3 : : PUNCT ijassa-1224 85 4 let let VERB ijassa-1224 85 5 the the DET ijassa-1224 85 6 initial initial ADJ ijassa-1224 85 7 value value NOUN ijassa-1224 85 8 for for ADP ijassa-1224 85 9 the the DET ijassa-1224 85 10 model model NOUN ijassa-1224 85 11 equation equation NOUN ijassa-1224 85 12 be be AUX ijassa-1224 85 13 given give VERB ijassa-1224 85 14 as as ADP ijassa-1224 85 15 𝑆(0 𝑆(0 NUM ijassa-1224 85 16 ) ) PUNCT ijassa-1224 85 17 , , PUNCT ijassa-1224 85 18 𝑉(0 𝑉(0 NUM ijassa-1224 85 19 ) ) PUNCT ijassa-1224 85 20 , , PUNCT ijassa-1224 85 21 𝐸(0 𝐸(0 NUM ijassa-1224 85 22 ) ) PUNCT ijassa-1224 85 23 , , PUNCT ijassa-1224 85 24 𝐼 𝐼 PROPN ijassa-1224 85 25 ( ( PUNCT ijassa-1224 85 26 0 0 NUM ijassa-1224 85 27 ) ) PUNCT ijassa-1224 85 28 , , PUNCT ijassa-1224 85 29 𝐼 𝐼 PROPN ijassa-1224 85 30 ( ( PUNCT ijassa-1224 85 31 0 0 NUM ijassa-1224 85 32 ) ) PUNCT ijassa-1224 85 33 , , PUNCT ijassa-1224 85 34 𝐽(0 𝐽(0 NUM ijassa-1224 85 35 ) ) PUNCT ijassa-1224 85 36 , , PUNCT ijassa-1224 85 37 𝑇(0 𝑇(0 NOUN ijassa-1224 85 38 ) ) PUNCT ijassa-1224 85 39 ∈ ∈ PROPN ijassa-1224 86 1 𝑛 𝑛 ADP ijassa-1224 86 2 then then ADV ijassa-1224 86 3 the the DET ijassa-1224 86 4 solution solution NOUN ijassa-1224 86 5 set set VERB ijassa-1224 86 6 { { PUNCT ijassa-1224 86 7 𝑆(𝑑 𝑆(𝑑 NUM ijassa-1224 86 8 ) ) PUNCT ijassa-1224 86 9 , , PUNCT ijassa-1224 86 10 𝑉(𝑑 𝑉(𝑑 ADP ijassa-1224 86 11 ) ) PUNCT ijassa-1224 86 12 , , PUNCT ijassa-1224 86 13 𝐸(0 𝐸(0 NUM ijassa-1224 86 14 ) ) PUNCT ijassa-1224 86 15 , , PUNCT ijassa-1224 86 16 𝐼 𝐼 PROPN ijassa-1224 86 17 ( ( PUNCT ijassa-1224 86 18 𝑑 𝑑 NOUN ijassa-1224 86 19 ) ) PUNCT ijassa-1224 86 20 , , PUNCT ijassa-1224 86 21 𝐼 𝐼 PROPN ijassa-1224 86 22 ( ( PUNCT ijassa-1224 86 23 𝑑 𝑑 NOUN ijassa-1224 86 24 ) ) PUNCT ijassa-1224 86 25 , , PUNCT ijassa-1224 86 26 𝐽(𝑑 𝐽(𝑑 NOUN ijassa-1224 86 27 ) ) PUNCT ijassa-1224 86 28 , , PUNCT ijassa-1224 86 29 𝑇(𝑑 𝑇(𝑑 NOUN ijassa-1224 86 30 ) ) PUNCT ijassa-1224 86 31 } } PUNCT ijassa-1224 86 32 of of ADP ijassa-1224 86 33 the the DET ijassa-1224 86 34 system system NOUN ijassa-1224 86 35 ( ( PUNCT ijassa-1224 86 36 1)–(7 1)–(7 NUM ijassa-1224 86 37 ) ) PUNCT ijassa-1224 86 38 is be AUX ijassa-1224 86 39 positive positive ADJ ijassa-1224 86 40 for for ADP ijassa-1224 86 41 all all DET ijassa-1224 86 42 𝑑 𝑑 X ijassa-1224 86 43 > > X ijassa-1224 86 44 0 0 X ijassa-1224 86 45 . . PUNCT ijassa-1224 87 1 proof proof NOUN ijassa-1224 87 2 . . PUNCT ijassa-1224 88 1 from from ADP ijassa-1224 88 2 equation equation NOUN ijassa-1224 88 3 ( ( PUNCT ijassa-1224 88 4 2 2 NUM ijassa-1224 88 5 ) ) PUNCT ijassa-1224 88 6 = = SYM ijassa-1224 88 7 πœ‹(1 πœ‹(1 NOUN ijassa-1224 88 8 βˆ’ βˆ’ PROPN ijassa-1224 89 1 πœƒ πœƒ NOUN ijassa-1224 89 2 ) ) PUNCT ijassa-1224 90 1 + + CCONJ ijassa-1224 90 2 πœ”π‘‰ πœ”π‘‰ NOUN ijassa-1224 90 3 βˆ’ βˆ’ NOUN ijassa-1224 90 4 ( ( PUNCT ijassa-1224 90 5 πœ† πœ† ADP ijassa-1224 90 6 + + PUNCT ijassa-1224 90 7 πœ‡)𝑆 πœ‡)𝑆 ADV ijassa-1224 90 8 then then ADV ijassa-1224 90 9 , , PUNCT ijassa-1224 90 10 β‰₯ β‰₯ NOUN ijassa-1224 90 11 βˆ’(πœ† βˆ’(πœ† NOUN ijassa-1224 90 12 + + CCONJ ijassa-1224 90 13 πœ‡)𝑆 πœ‡)𝑆 ADJ ijassa-1224 90 14 on on ADP ijassa-1224 90 15 integrating integrate VERB ijassa-1224 90 16 it it PRON ijassa-1224 90 17 gives give VERB ijassa-1224 90 18 ∫ ∫ PROPN ijassa-1224 90 19 β‰₯ β‰₯ NOUN ijassa-1224 90 20 βˆ’ βˆ’ PROPN ijassa-1224 90 21 ∫(πœ† ∫(πœ† PROPN ijassa-1224 90 22 + + CCONJ ijassa-1224 90 23 πœ‡ πœ‡ NOUN ijassa-1224 90 24 ) ) PUNCT ijassa-1224 90 25 𝑑𝑑. 𝑑𝑑. NOUN ijassa-1224 90 26 hence hence ADV ijassa-1224 90 27 , , PUNCT ijassa-1224 90 28 𝑆(𝑑 𝑆(𝑑 NUM ijassa-1224 90 29 ) ) PUNCT ijassa-1224 90 30 β‰₯ β‰₯ NOUN ijassa-1224 90 31 𝑆(0)𝑒 𝑆(0)𝑒 NOUN ijassa-1224 90 32 ( ( PUNCT ijassa-1224 90 33 ) ) PUNCT ijassa-1224 90 34 . . PUNCT ijassa-1224 91 1 applying apply VERB ijassa-1224 91 2 the the DET ijassa-1224 91 3 same same ADJ ijassa-1224 91 4 approach approach NOUN ijassa-1224 91 5 to to ADP ijassa-1224 91 6 other other ADJ ijassa-1224 91 7 equations equation NOUN ijassa-1224 91 8 in in ADP ijassa-1224 91 9 the the DET ijassa-1224 91 10 model model NOUN ijassa-1224 91 11 equations equation NOUN ijassa-1224 91 12 , , PUNCT ijassa-1224 91 13 we we PRON ijassa-1224 91 14 have have VERB ijassa-1224 91 15 : : PUNCT ijassa-1224 91 16 𝑉(𝑑 𝑉(𝑑 NUM ijassa-1224 91 17 ) ) PUNCT ijassa-1224 91 18 β‰₯ β‰₯ NOUN ijassa-1224 91 19 𝑉(0)𝑒 𝑉(0)𝑒 NOUN ijassa-1224 91 20 ( ( PUNCT ijassa-1224 91 21 ) ) PUNCT ijassa-1224 91 22 , , PUNCT ijassa-1224 91 23 𝐸(𝑑 𝐸(𝑑 NUM ijassa-1224 91 24 ) ) PUNCT ijassa-1224 91 25 β‰₯ β‰₯ NOUN ijassa-1224 91 26 𝐸(0)𝑒 𝐸(0)𝑒 NOUN ijassa-1224 91 27 ( ( PUNCT ijassa-1224 91 28 ) ) PUNCT ijassa-1224 91 29 , , PUNCT ijassa-1224 91 30 𝐼 𝐼 PROPN ijassa-1224 91 31 ( ( PUNCT ijassa-1224 91 32 𝑑 𝑑 NOUN ijassa-1224 91 33 ) ) PUNCT ijassa-1224 91 34 β‰₯ β‰₯ NOUN ijassa-1224 92 1 𝐼 𝐼 PROPN ijassa-1224 92 2 ( ( PUNCT ijassa-1224 92 3 0)𝑒 0)𝑒 PROPN ijassa-1224 92 4 ( ( PUNCT ijassa-1224 92 5 ) ) PUNCT ijassa-1224 92 6 , , PUNCT ijassa-1224 92 7 𝐼 𝐼 PROPN ijassa-1224 92 8 ( ( PUNCT ijassa-1224 92 9 𝑑 𝑑 NOUN ijassa-1224 92 10 ) ) PUNCT ijassa-1224 92 11 β‰₯ β‰₯ NOUN ijassa-1224 92 12 𝐼 𝐼 PROPN ijassa-1224 92 13 ( ( PUNCT ijassa-1224 92 14 0)𝑒 0)𝑒 PROPN ijassa-1224 92 15 ( ( PUNCT ijassa-1224 92 16 ) ) PUNCT ijassa-1224 92 17 , , PUNCT ijassa-1224 92 18 𝐽(𝑑 𝐽(𝑑 PRON ijassa-1224 92 19 ) ) PUNCT ijassa-1224 92 20 β‰₯ β‰₯ NOUN ijassa-1224 92 21 𝐽(0)𝑒 𝐽(0)𝑒 NOUN ijassa-1224 92 22 ( ( PUNCT ijassa-1224 92 23 ) ) PUNCT ijassa-1224 92 24 , , PUNCT ijassa-1224 92 25 𝑇(𝑑 𝑇(𝑑 X ijassa-1224 92 26 ) ) PUNCT ijassa-1224 92 27 β‰₯ β‰₯ NOUN ijassa-1224 92 28 𝑇(0)𝑒 𝑇(0)𝑒 NOUN ijassa-1224 92 29 ( ( PUNCT ijassa-1224 92 30 ) ) PUNCT ijassa-1224 92 31 . . PUNCT ijassa-1224 93 1 therefore therefore ADV ijassa-1224 93 2 , , PUNCT ijassa-1224 93 3 the the DET ijassa-1224 93 4 solution solution NOUN ijassa-1224 93 5 to to ADP ijassa-1224 93 6 the the DET ijassa-1224 93 7 model model NOUN ijassa-1224 93 8 equations equation NOUN ijassa-1224 93 9 is be AUX ijassa-1224 93 10 positive positive ADJ ijassa-1224 93 11 for for ADP ijassa-1224 93 12 all all DET ijassa-1224 93 13 𝑑 𝑑 X ijassa-1224 93 14 > > X ijassa-1224 93 15 0 0 NUM ijassa-1224 93 16 . . PUNCT ijassa-1224 94 1 β–‘ β–‘ SYM ijassa-1224 94 2 2.4 2.4 NUM ijassa-1224 94 3 . . PUNCT ijassa-1224 95 1 equilibrium equilibrium NOUN ijassa-1224 95 2 points point NOUN ijassa-1224 95 3 of of ADP ijassa-1224 95 4 the the DET ijassa-1224 95 5 model model NOUN ijassa-1224 95 6 the the DET ijassa-1224 95 7 equilibrium equilibrium NOUN ijassa-1224 95 8 state state NOUN ijassa-1224 95 9 is be AUX ijassa-1224 95 10 the the DET ijassa-1224 95 11 point point NOUN ijassa-1224 95 12 in in ADP ijassa-1224 95 13 which which PRON ijassa-1224 95 14 there there PRON ijassa-1224 95 15 is be VERB ijassa-1224 95 16 zero zero NUM ijassa-1224 95 17 disturbance disturbance NOUN ijassa-1224 95 18 on on ADP ijassa-1224 95 19 the the DET ijassa-1224 95 20 system system NOUN ijassa-1224 95 21 under under ADP ijassa-1224 95 22 consideration consideration NOUN ijassa-1224 95 23 . . PUNCT ijassa-1224 96 1 that that PRON ijassa-1224 96 2 is is ADV ijassa-1224 96 3 , , PUNCT ijassa-1224 96 4 the the DET ijassa-1224 96 5 rate rate NOUN ijassa-1224 96 6 of of ADP ijassa-1224 96 7 change change NOUN ijassa-1224 96 8 of of ADP ijassa-1224 96 9 the the DET ijassa-1224 96 10 model model NOUN ijassa-1224 96 11 variables variable NOUN ijassa-1224 96 12 with with ADP ijassa-1224 96 13 time time NOUN ijassa-1224 96 14 is be AUX ijassa-1224 96 15 zero zero NUM ijassa-1224 96 16 . . PUNCT ijassa-1224 97 1 thus thus ADV ijassa-1224 97 2 , , PUNCT ijassa-1224 97 3 at at ADP ijassa-1224 97 4 equilibrium equilibrium NOUN ijassa-1224 97 5 , , PUNCT ijassa-1224 97 6 = = PUNCT ijassa-1224 97 7 = = PUNCT ijassa-1224 98 1 = = PUNCT ijassa-1224 98 2 = = PUNCT ijassa-1224 98 3 = = PUNCT ijassa-1224 98 4 = = PUNCT ijassa-1224 98 5 = = SYM ijassa-1224 98 6 0 0 NUM ijassa-1224 98 7 ( ( PUNCT ijassa-1224 98 8 10 10 NUM ijassa-1224 98 9 ) ) PUNCT ijassa-1224 98 10 let let VERB ijassa-1224 98 11 πΈβˆ— πΈβˆ— NOUN ijassa-1224 98 12 = = SYM ijassa-1224 98 13 ( ( PUNCT ijassa-1224 98 14 𝑉 𝑉 PROPN ijassa-1224 98 15 , , PUNCT ijassa-1224 98 16 𝑆 𝑆 PROPN ijassa-1224 98 17 , , PUNCT ijassa-1224 98 18 𝐸 𝐸 PROPN ijassa-1224 98 19 , , PUNCT ijassa-1224 98 20 𝐼 𝐼 PROPN ijassa-1224 98 21 , , PUNCT ijassa-1224 98 22 𝐼 𝐼 PROPN ijassa-1224 98 23 , , PUNCT ijassa-1224 98 24 𝐽 𝐽 PROPN ijassa-1224 98 25 , , PUNCT ijassa-1224 98 26 𝑇 𝑇 PROPN ijassa-1224 98 27 ) ) PUNCT ijassa-1224 98 28 = = PUNCT ijassa-1224 98 29 ( ( PUNCT ijassa-1224 98 30 π‘‰βˆ— π‘‰βˆ— PROPN ijassa-1224 98 31 , , PUNCT ijassa-1224 98 32 π‘†βˆ— π‘†βˆ— X ijassa-1224 98 33 , , PUNCT ijassa-1224 98 34 πΈβˆ— πΈβˆ— NOUN ijassa-1224 98 35 , , PUNCT ijassa-1224 98 36 𝐼 𝐼 PROPN ijassa-1224 98 37 βˆ— βˆ— NOUN ijassa-1224 98 38 , , PUNCT ijassa-1224 98 39 𝐼 𝐼 ADP ijassa-1224 98 40 βˆ— βˆ— NOUN ijassa-1224 98 41 , , PUNCT ijassa-1224 98 42 π½βˆ— π½βˆ— NOUN ijassa-1224 98 43 , , PUNCT ijassa-1224 98 44 π‘‡βˆ— π‘‡βˆ— PROPN ijassa-1224 98 45 ) ) PUNCT ijassa-1224 98 46 be be VERB ijassa-1224 98 47 arbitrarily arbitrarily ADV ijassa-1224 98 48 equilibrium equilibrium NOUN ijassa-1224 98 49 point point NOUN ijassa-1224 98 50 substituting substitute VERB ijassa-1224 98 51 equations equation NOUN ijassa-1224 98 52 ( ( PUNCT ijassa-1224 98 53 10 10 NUM ijassa-1224 98 54 ) ) PUNCT ijassa-1224 98 55 into into ADP ijassa-1224 98 56 equations equation NOUN ijassa-1224 98 57 ( ( PUNCT ijassa-1224 98 58 1)–(7 1)–(7 NUM ijassa-1224 98 59 ) ) PUNCT ijassa-1224 99 1 gives give VERB ijassa-1224 99 2 : : PUNCT ijassa-1224 99 3 πœ‹πœƒ πœ‹πœƒ NOUN ijassa-1224 99 4 βˆ’ βˆ’ PROPN ijassa-1224 99 5 ( ( PUNCT ijassa-1224 99 6 πœ‡ πœ‡ X ijassa-1224 99 7 + + X ijassa-1224 99 8 πœ”)𝑉 πœ”)𝑉 X ijassa-1224 99 9 = = SYM ijassa-1224 99 10 0 0 NUM ijassa-1224 99 11 , , PUNCT ijassa-1224 99 12 ( ( PUNCT ijassa-1224 99 13 11 11 NUM ijassa-1224 99 14 ) ) PUNCT ijassa-1224 99 15 πœ‹(1 πœ‹(1 NOUN ijassa-1224 100 1 βˆ’ βˆ’ PROPN ijassa-1224 100 2 πœƒ πœƒ NOUN ijassa-1224 100 3 ) ) PUNCT ijassa-1224 101 1 βˆ’ βˆ’ PROPN ijassa-1224 101 2 πœ† πœ† DET ijassa-1224 101 3 𝑆 𝑆 PROPN ijassa-1224 101 4 βˆ’ βˆ’ PROPN ijassa-1224 101 5 πœ‡π‘† πœ‡π‘† NOUN ijassa-1224 102 1 + + CCONJ ijassa-1224 102 2 πœ”π‘‰ πœ”π‘‰ NOUN ijassa-1224 102 3 = = SYM ijassa-1224 102 4 0 0 NUM ijassa-1224 102 5 , , PUNCT ijassa-1224 102 6 ( ( PUNCT ijassa-1224 102 7 12 12 NUM ijassa-1224 102 8 ) ) PUNCT ijassa-1224 102 9 analysis analysis NOUN ijassa-1224 102 10 and and CCONJ ijassa-1224 102 11 dynamics dynamic NOUN ijassa-1224 102 12 of of ADP ijassa-1224 102 13 tuberculosis tuberculosis NOUN ijassa-1224 102 14 outbreak outbreak NOUN ijassa-1224 102 15 149 149 NUM ijassa-1224 102 16 copyright copyright NOUN ijassa-1224 102 17 Β© Β© PROPN ijassa-1224 102 18 2022 2022 NUM ijassa-1224 102 19 assa assa NOUN ijassa-1224 102 20 . . PUNCT ijassa-1224 103 1 adv adv PROPN ijassa-1224 103 2 . . PUNCT ijassa-1224 104 1 in in ADP ijassa-1224 104 2 systems system NOUN ijassa-1224 104 3 science science NOUN ijassa-1224 104 4 and and CCONJ ijassa-1224 104 5 appl appl NOUN ijassa-1224 104 6 . . PUNCT ijassa-1224 105 1 ( ( PUNCT ijassa-1224 105 2 2022 2022 NUM ijassa-1224 105 3 ) ) PUNCT ijassa-1224 106 1 πœ† πœ† DET ijassa-1224 106 2 𝑆 𝑆 PROPN ijassa-1224 106 3 + + CCONJ ijassa-1224 106 4 πœ† πœ† PROPN ijassa-1224 106 5 𝑇 𝑇 PROPN ijassa-1224 106 6 βˆ’ βˆ’ PROPN ijassa-1224 106 7 πœ† πœ† PROPN ijassa-1224 106 8 𝐸 𝐸 PROPN ijassa-1224 106 9 βˆ’ βˆ’ PROPN ijassa-1224 106 10 ( ( PUNCT ijassa-1224 106 11 πœ‡ πœ‡ X ijassa-1224 106 12 + + X ijassa-1224 106 13 𝜎)𝐸 𝜎)𝐸 ADV ijassa-1224 106 14 = = SYM ijassa-1224 106 15 0 0 NUM ijassa-1224 106 16 , , PUNCT ijassa-1224 106 17 ( ( PUNCT ijassa-1224 106 18 13 13 NUM ijassa-1224 106 19 ) ) PUNCT ijassa-1224 106 20 ( ( PUNCT ijassa-1224 106 21 1 1 NUM ijassa-1224 106 22 βˆ’ βˆ’ PROPN ijassa-1224 106 23 𝜌)𝜎𝐸 𝜌)𝜎𝐸 PROPN ijassa-1224 106 24 βˆ’ βˆ’ PROPN ijassa-1224 106 25 ( ( PUNCT ijassa-1224 106 26 𝛾 𝛾 NOUN ijassa-1224 106 27 + + X ijassa-1224 106 28 πœ‡ πœ‡ ADP ijassa-1224 106 29 + + NOUN ijassa-1224 106 30 π‘Ÿ π‘Ÿ NOUN ijassa-1224 106 31 + + CCONJ ijassa-1224 106 32 𝑑 𝑑 NOUN ijassa-1224 106 33 ) ) PUNCT ijassa-1224 106 34 𝐼 𝐼 ADP ijassa-1224 106 35 + + CCONJ ijassa-1224 106 36 ( ( PUNCT ijassa-1224 106 37 1 1 NUM ijassa-1224 106 38 βˆ’ βˆ’ NOUN ijassa-1224 106 39 πœ™)πœ† πœ™)πœ† X ijassa-1224 106 40 𝐸 𝐸 PROPN ijassa-1224 106 41 = = SYM ijassa-1224 106 42 0 0 NUM ijassa-1224 106 43 , , PUNCT ijassa-1224 106 44 ( ( PUNCT ijassa-1224 106 45 14 14 NUM ijassa-1224 106 46 ) ) PUNCT ijassa-1224 106 47 𝜌𝜎𝐸 𝜌𝜎𝐸 NOUN ijassa-1224 106 48 + + CCONJ ijassa-1224 106 49 𝛾𝐼 𝛾𝐼 PROPN ijassa-1224 106 50 βˆ’ βˆ’ PROPN ijassa-1224 106 51 ( ( PUNCT ijassa-1224 106 52 π‘Ÿ π‘Ÿ NOUN ijassa-1224 106 53 + + CCONJ ijassa-1224 106 54 π‘Ÿ π‘Ÿ NOUN ijassa-1224 106 55 + + CCONJ ijassa-1224 106 56 πœ‡ πœ‡ ADP ijassa-1224 106 57 + + X ijassa-1224 106 58 𝑑 𝑑 NOUN ijassa-1224 106 59 ) ) PUNCT ijassa-1224 106 60 𝐼 𝐼 ADP ijassa-1224 106 61 + + CCONJ ijassa-1224 106 62 πœ™πœ† πœ™πœ† NOUN ijassa-1224 106 63 𝐸 𝐸 NOUN ijassa-1224 106 64 = = SYM ijassa-1224 106 65 0 0 NUM ijassa-1224 106 66 , , PUNCT ijassa-1224 106 67 ( ( PUNCT ijassa-1224 106 68 15 15 NUM ijassa-1224 106 69 ) ) PUNCT ijassa-1224 106 70 π‘Ÿ π‘Ÿ NOUN ijassa-1224 107 1 𝐼 𝐼 ADP ijassa-1224 107 2 βˆ’ βˆ’ PROPN ijassa-1224 107 3 ( ( PUNCT ijassa-1224 107 4 πœ‡ πœ‡ X ijassa-1224 107 5 + + X ijassa-1224 107 6 𝑑 𝑑 PROPN ijassa-1224 107 7 + + ADJ ijassa-1224 107 8 π‘Ÿ π‘Ÿ NOUN ijassa-1224 107 9 ) ) PUNCT ijassa-1224 107 10 𝐽 𝐽 PROPN ijassa-1224 107 11 = = NOUN ijassa-1224 107 12 0 0 PROPN ijassa-1224 107 13 , , PUNCT ijassa-1224 107 14 ( ( PUNCT ijassa-1224 107 15 16 16 NUM ijassa-1224 107 16 ) ) PUNCT ijassa-1224 107 17 π‘Ÿ π‘Ÿ NOUN ijassa-1224 107 18 𝐽 𝐽 VERB ijassa-1224 107 19 + + NUM ijassa-1224 107 20 π‘Ÿ π‘Ÿ X ijassa-1224 107 21 𝐼 𝐼 ADP ijassa-1224 107 22 + + NOUN ijassa-1224 107 23 π‘Ÿ π‘Ÿ NOUN ijassa-1224 107 24 𝐼 𝐼 ADP ijassa-1224 107 25 βˆ’ βˆ’ PROPN ijassa-1224 107 26 ( ( PUNCT ijassa-1224 107 27 πœ‡ πœ‡ ADP ijassa-1224 107 28 + + X ijassa-1224 107 29 πœ† πœ† X ijassa-1224 107 30 ) ) PUNCT ijassa-1224 107 31 𝑇 𝑇 NOUN ijassa-1224 107 32 = = SYM ijassa-1224 107 33 0 0 PROPN ijassa-1224 107 34 . . PUNCT ijassa-1224 107 35 ( ( PUNCT ijassa-1224 107 36 17 17 NUM ijassa-1224 107 37 ) ) PUNCT ijassa-1224 107 38 from from ADP ijassa-1224 107 39 equation equation NOUN ijassa-1224 107 40 ( ( PUNCT ijassa-1224 107 41 11 11 NUM ijassa-1224 107 42 ) ) PUNCT ijassa-1224 107 43 we we PRON ijassa-1224 107 44 have have VERB ijassa-1224 107 45 𝑉 𝑉 PROPN ijassa-1224 107 46 = = PUNCT ijassa-1224 107 47 ( ( PUNCT ijassa-1224 107 48 ) ) PUNCT ijassa-1224 107 49 . . PUNCT ijassa-1224 108 1 ( ( PUNCT ijassa-1224 108 2 18 18 NUM ijassa-1224 108 3 ) ) PUNCT ijassa-1224 108 4 substitute substitute NOUN ijassa-1224 108 5 equation equation NOUN ijassa-1224 108 6 ( ( PUNCT ijassa-1224 108 7 18 18 NUM ijassa-1224 108 8 ) ) PUNCT ijassa-1224 108 9 into into ADP ijassa-1224 108 10 equation equation NOUN ijassa-1224 108 11 ( ( PUNCT ijassa-1224 108 12 12 12 NUM ijassa-1224 108 13 ) ) PUNCT ijassa-1224 108 14 we we PRON ijassa-1224 108 15 have have VERB ijassa-1224 108 16 πœ‹(1 πœ‹(1 NOUN ijassa-1224 108 17 βˆ’ βˆ’ PROPN ijassa-1224 108 18 πœƒ πœƒ NOUN ijassa-1224 108 19 ) ) PUNCT ijassa-1224 109 1 + + CCONJ ijassa-1224 109 2 = = SYM ijassa-1224 109 3 𝑆. 𝑆. PROPN ijassa-1224 109 4 ( ( PUNCT ijassa-1224 109 5 19 19 NUM ijassa-1224 109 6 ) ) PUNCT ijassa-1224 109 7 from from ADP ijassa-1224 109 8 equation equation NOUN ijassa-1224 109 9 ( ( PUNCT ijassa-1224 109 10 16 16 NUM ijassa-1224 109 11 ) ) PUNCT ijassa-1224 109 12 we we PRON ijassa-1224 109 13 have have VERB ijassa-1224 109 14 𝐽 𝐽 NOUN ijassa-1224 109 15 = = PUNCT ijassa-1224 109 16 𝐾 𝐾 PROPN ijassa-1224 109 17 𝐼 𝐼 PROPN ijassa-1224 109 18 where where SCONJ ijassa-1224 109 19 𝐾 𝐾 PROPN ijassa-1224 109 20 = = X ijassa-1224 109 21 . . PUNCT ijassa-1224 110 1 from from ADP ijassa-1224 110 2 ( ( PUNCT ijassa-1224 110 3 15 15 NUM ijassa-1224 110 4 ) ) PUNCT ijassa-1224 110 5 we we PRON ijassa-1224 110 6 have have AUX ijassa-1224 110 7 [ [ X ijassa-1224 110 8 ( ( PUNCT ijassa-1224 110 9 1 1 NUM ijassa-1224 110 10 βˆ’ βˆ’ NOUN ijassa-1224 110 11 𝜌)𝜎 𝜌)𝜎 ADJ ijassa-1224 110 12 + + CCONJ ijassa-1224 110 13 ( ( PUNCT ijassa-1224 110 14 1 1 NUM ijassa-1224 110 15 βˆ’ βˆ’ NOUN ijassa-1224 110 16 πœ™)πœ† πœ™)πœ† X ijassa-1224 110 17 ] ] X ijassa-1224 110 18 𝐸 𝐸 X ijassa-1224 110 19 = = PUNCT ijassa-1224 111 1 [ [ X ijassa-1224 111 2 π‘Ÿ π‘Ÿ NOUN ijassa-1224 111 3 + + NOUN ijassa-1224 111 4 π‘Ÿ π‘Ÿ NOUN ijassa-1224 112 1 + + CCONJ ijassa-1224 112 2 πœ‡ πœ‡ ADP ijassa-1224 112 3 + + X ijassa-1224 112 4 𝑑 𝑑 X ijassa-1224 112 5 ] ] X ijassa-1224 112 6 𝐼 𝐼 ADP ijassa-1224 112 7 β‡’ β‡’ NOUN ijassa-1224 112 8 𝐸 𝐸 PROPN ijassa-1224 112 9 = = SYM ijassa-1224 112 10 𝐾 𝐾 PROPN ijassa-1224 112 11 𝐼 𝐼 PROPN ijassa-1224 112 12 where where SCONJ ijassa-1224 112 13 𝐾 𝐾 PROPN ijassa-1224 112 14 = = PRON ijassa-1224 112 15 ( ( PUNCT ijassa-1224 112 16 ) ) PUNCT ijassa-1224 112 17 ( ( PUNCT ijassa-1224 112 18 ) ) PUNCT ijassa-1224 112 19 , , PUNCT ijassa-1224 112 20 from from ADP ijassa-1224 112 21 equation equation NOUN ijassa-1224 112 22 ( ( PUNCT ijassa-1224 112 23 16 16 NUM ijassa-1224 112 24 ) ) PUNCT ijassa-1224 112 25 we we PRON ijassa-1224 112 26 have have VERB ijassa-1224 112 27 ( ( PUNCT ijassa-1224 112 28 π‘Ÿ π‘Ÿ NOUN ijassa-1224 112 29 + + NOUN ijassa-1224 112 30 π‘Ÿ π‘Ÿ NOUN ijassa-1224 112 31 + + CCONJ ijassa-1224 112 32 πœ‡ πœ‡ ADP ijassa-1224 112 33 + + X ijassa-1224 112 34 𝑑 𝑑 NOUN ijassa-1224 112 35 ) ) PUNCT ijassa-1224 112 36 𝐼 𝐼 NOUN ijassa-1224 112 37 = = SYM ijassa-1224 112 38 𝜌𝜎𝐸 𝜌𝜎𝐸 PROPN ijassa-1224 112 39 + + CCONJ ijassa-1224 112 40 πœ™πœ† πœ™πœ† VERB ijassa-1224 112 41 𝐸 𝐸 PROPN ijassa-1224 112 42 + + CCONJ ijassa-1224 112 43 𝛾𝐼 𝛾𝐼 PROPN ijassa-1224 112 44 , , PUNCT ijassa-1224 112 45 then then ADV ijassa-1224 112 46 𝐼 𝐼 PROPN ijassa-1224 112 47 = = SYM ijassa-1224 112 48 𝐾 𝐾 PROPN ijassa-1224 113 1 𝐼 𝐼 PROPN ijassa-1224 113 2 where where SCONJ ijassa-1224 113 3 𝐾 𝐾 PROPN ijassa-1224 113 4 = = SYM ijassa-1224 113 5 ( ( PUNCT ijassa-1224 113 6 ) ) PUNCT ijassa-1224 113 7 further further ADJ ijassa-1224 113 8 substitution substitution NOUN ijassa-1224 113 9 gives give VERB ijassa-1224 113 10 𝐽 𝐽 PROPN ijassa-1224 113 11 = = SYM ijassa-1224 113 12 𝐾 𝐾 PROPN ijassa-1224 113 13 𝐾 𝐾 PROPN ijassa-1224 113 14 𝐼 𝐼 PROPN ijassa-1224 113 15 and and CCONJ ijassa-1224 113 16 from from ADP ijassa-1224 113 17 equation equation NOUN ijassa-1224 113 18 ( ( PUNCT ijassa-1224 113 19 17 17 NUM ijassa-1224 113 20 ) ) PUNCT ijassa-1224 113 21 we we PRON ijassa-1224 113 22 have have VERB ijassa-1224 113 23 : : PUNCT ijassa-1224 113 24 𝑇 𝑇 PROPN ijassa-1224 113 25 = = PRON ijassa-1224 113 26 . . PUNCT ijassa-1224 114 1 then then ADV ijassa-1224 114 2 𝑇 𝑇 PROPN ijassa-1224 114 3 = = SYM ijassa-1224 114 4 𝐾 𝐾 PROPN ijassa-1224 114 5 𝐼 𝐼 PROPN ijassa-1224 114 6 where where SCONJ ijassa-1224 114 7 𝐾 𝐾 PROPN ijassa-1224 114 8 = = SYM ijassa-1224 114 9 ( ( PUNCT ijassa-1224 114 10 ) ) PUNCT ijassa-1224 114 11 , , PUNCT ijassa-1224 114 12 πœ† πœ† X ijassa-1224 114 13 = = NOUN ijassa-1224 114 14 𝛽(𝐼 𝛽(𝐼 NOUN ijassa-1224 114 15 + + CCONJ ijassa-1224 114 16 πœ€ πœ€ X ijassa-1224 114 17 𝐼 𝐼 ADP ijassa-1224 114 18 + + PROPN ijassa-1224 114 19 πœ€ πœ€ PROPN ijassa-1224 114 20 𝐽 𝐽 NOUN ijassa-1224 114 21 ) ) PUNCT ijassa-1224 114 22 πœ† πœ† X ijassa-1224 114 23 = = SYM ijassa-1224 114 24 𝛼(𝐼 𝛼(𝐼 X ijassa-1224 114 25 + + PUNCT ijassa-1224 114 26 πœ€ πœ€ X ijassa-1224 114 27 𝐼 𝐼 ADP ijassa-1224 114 28 + + PROPN ijassa-1224 114 29 πœ€ πœ€ PROPN ijassa-1224 114 30 𝐽 𝐽 NOUN ijassa-1224 114 31 ) ) PUNCT ijassa-1224 114 32 πœ† πœ† X ijassa-1224 115 1 = = SYM ijassa-1224 115 2 𝛾 𝛾 X ijassa-1224 115 3 ( ( PUNCT ijassa-1224 115 4 𝐼 𝐼 PROPN ijassa-1224 115 5 + + NOUN ijassa-1224 115 6 πœ€ πœ€ X ijassa-1224 115 7 𝐼 𝐼 ADP ijassa-1224 115 8 + + PROPN ijassa-1224 115 9 πœ€ πœ€ PROPN ijassa-1224 115 10 𝐽 𝐽 NOUN ijassa-1224 115 11 ) ) PUNCT ijassa-1224 115 12 and and CCONJ ijassa-1224 115 13 𝐽 𝐽 NOUN ijassa-1224 115 14 = = SYM ijassa-1224 115 15 𝐾 𝐾 PROPN ijassa-1224 115 16 𝐾 𝐾 PROPN ijassa-1224 115 17 𝐼 𝐼 PROPN ijassa-1224 115 18 𝐼 𝐼 PROPN ijassa-1224 115 19 = = SYM ijassa-1224 115 20 𝐾 𝐾 PROPN ijassa-1224 115 21 𝐼 𝐼 PROPN ijassa-1224 115 22 by by ADP ijassa-1224 115 23 combining combine VERB ijassa-1224 115 24 both both DET ijassa-1224 115 25 equations equation NOUN ijassa-1224 115 26 : : PUNCT ijassa-1224 115 27 πœ† πœ† X ijassa-1224 115 28 = = SYM ijassa-1224 115 29 𝛽𝐼 𝛽𝐼 PROPN ijassa-1224 115 30 ( ( PUNCT ijassa-1224 115 31 𝐾 𝐾 PROPN ijassa-1224 115 32 + + NOUN ijassa-1224 115 33 πœ€ πœ€ X ijassa-1224 115 34 𝐾 𝐾 PROPN ijassa-1224 115 35 𝐾 𝐾 PROPN ijassa-1224 115 36 + + CCONJ ijassa-1224 115 37 πœ€ πœ€ PROPN ijassa-1224 115 38 ) ) PUNCT ijassa-1224 115 39 πœ† πœ† X ijassa-1224 115 40 = = PUNCT ijassa-1224 115 41 𝛼𝐼 𝛼𝐼 PROPN ijassa-1224 115 42 ( ( PUNCT ijassa-1224 115 43 𝐾 𝐾 NOUN ijassa-1224 115 44 + + NOUN ijassa-1224 115 45 πœ€ πœ€ X ijassa-1224 115 46 𝐾 𝐾 PROPN ijassa-1224 115 47 𝐾 𝐾 PROPN ijassa-1224 115 48 + + CCONJ ijassa-1224 115 49 πœ€ πœ€ PROPN ijassa-1224 115 50 ) ) PUNCT ijassa-1224 115 51 πœ† πœ† X ijassa-1224 116 1 = = PUNCT ijassa-1224 116 2 𝛾 𝛾 ADP ijassa-1224 116 3 𝐼 𝐼 PROPN ijassa-1224 116 4 ( ( PUNCT ijassa-1224 116 5 𝐾 𝐾 PROPN ijassa-1224 116 6 + + NOUN ijassa-1224 116 7 πœ€ πœ€ X ijassa-1224 116 8 𝐾 𝐾 PROPN ijassa-1224 116 9 𝐾 𝐾 PROPN ijassa-1224 116 10 + + CCONJ ijassa-1224 116 11 πœ€ πœ€ ADJ ijassa-1224 116 12 ) ) PUNCT ijassa-1224 116 13 ⎭ ⎭ PROPN ijassa-1224 116 14 βŽͺ βŽͺ NOUN ijassa-1224 116 15 ⎬ ⎬ NOUN ijassa-1224 116 16 βŽͺ βŽͺ NOUN ijassa-1224 116 17 ⎫ ⎫ NOUN ijassa-1224 116 18 further further ADJ ijassa-1224 116 19 substitution substitution NOUN ijassa-1224 116 20 gives give VERB ijassa-1224 116 21 [ [ PUNCT ijassa-1224 116 22 𝛽𝐾 𝛽𝐾 PROPN ijassa-1224 116 23 𝑆 𝑆 PROPN ijassa-1224 116 24 + + CCONJ ijassa-1224 116 25 𝛾 𝛾 PROPN ijassa-1224 116 26 𝐾 𝐾 NOUN ijassa-1224 116 27 βˆ’ βˆ’ PROPN ijassa-1224 116 28 𝛼𝐾 𝛼𝐾 NOUN ijassa-1224 116 29 𝐾 𝐾 PROPN ijassa-1224 116 30 𝐼 𝐼 PROPN ijassa-1224 116 31 βˆ’ βˆ’ PROPN ijassa-1224 116 32 ( ( PUNCT ijassa-1224 116 33 πœ‡ πœ‡ X ijassa-1224 116 34 + + X ijassa-1224 116 35 𝜎)𝐾 𝜎)𝐾 X ijassa-1224 116 36 ] ] X ijassa-1224 116 37 𝐼 𝐼 PROPN ijassa-1224 116 38 = = SYM ijassa-1224 116 39 0 0 X ijassa-1224 116 40 . . PUNCT ijassa-1224 117 1 therefore therefore ADV ijassa-1224 117 2 , , PUNCT ijassa-1224 117 3 𝐼 𝐼 PROPN ijassa-1224 117 4 = = PUNCT ijassa-1224 117 5 0 0 NUM ijassa-1224 117 6 or or CCONJ ijassa-1224 117 7 𝛽𝐾 𝛽𝐾 PROPN ijassa-1224 117 8 𝑆 𝑆 PROPN ijassa-1224 117 9 + + CCONJ ijassa-1224 117 10 𝛾 𝛾 PROPN ijassa-1224 117 11 𝐾 𝐾 NOUN ijassa-1224 117 12 βˆ’ βˆ’ PROPN ijassa-1224 117 13 𝛼𝐾 𝛼𝐾 NOUN ijassa-1224 117 14 𝐾 𝐾 PROPN ijassa-1224 117 15 𝐼 𝐼 PROPN ijassa-1224 117 16 βˆ’ βˆ’ PROPN ijassa-1224 117 17 ( ( PUNCT ijassa-1224 117 18 πœ‡ πœ‡ X ijassa-1224 117 19 + + X ijassa-1224 117 20 𝜎)𝐾 𝜎)𝐾 X ijassa-1224 117 21 = = SYM ijassa-1224 117 22 0 0 NUM ijassa-1224 117 23 where where SCONJ ijassa-1224 117 24 𝐾 𝐾 PROPN ijassa-1224 117 25 = = SYM ijassa-1224 117 26 𝐾 𝐾 PROPN ijassa-1224 117 27 + + PROPN ijassa-1224 117 28 πœ€ πœ€ PROPN ijassa-1224 117 29 + + NUM ijassa-1224 117 30 πœ€ πœ€ X ijassa-1224 117 31 𝐾 𝐾 PROPN ijassa-1224 117 32 𝐾 𝐾 PROPN ijassa-1224 117 33 𝐾 𝐾 PROPN ijassa-1224 117 34 = = SYM ijassa-1224 117 35 𝐾 𝐾 PROPN ijassa-1224 117 36 + + PROPN ijassa-1224 117 37 πœ€ πœ€ PROPN ijassa-1224 117 38 + + NUM ijassa-1224 117 39 πœ€ πœ€ X ijassa-1224 117 40 𝐾 𝐾 PROPN ijassa-1224 117 41 𝐾 𝐾 PROPN ijassa-1224 117 42 𝐾 𝐾 PROPN ijassa-1224 117 43 = = SYM ijassa-1224 117 44 𝐾 𝐾 PROPN ijassa-1224 117 45 + + PROPN ijassa-1224 117 46 πœ€ πœ€ PROPN ijassa-1224 117 47 + + NUM ijassa-1224 117 48 πœ€ πœ€ X ijassa-1224 117 49 𝐾 𝐾 PROPN ijassa-1224 117 50 𝐾 𝐾 PROPN ijassa-1224 117 51 and and CCONJ ijassa-1224 117 52 πœ† πœ† PROPN ijassa-1224 117 53 = = SYM ijassa-1224 117 54 𝛽𝐾 𝛽𝐾 PROPN ijassa-1224 118 1 𝐼 𝐼 ADP ijassa-1224 118 2 πœ† πœ† NOUN ijassa-1224 118 3 = = PUNCT ijassa-1224 118 4 𝛼𝐾 𝛼𝐾 NOUN ijassa-1224 118 5 𝐼 𝐼 ADP ijassa-1224 118 6 πœ† πœ† NOUN ijassa-1224 118 7 = = SYM ijassa-1224 118 8 𝛾 𝛾 PROPN ijassa-1224 119 1 𝐾 𝐾 PROPN ijassa-1224 119 2 𝐼 𝐼 PROPN ijassa-1224 119 3 ⎭ ⎭ PROPN ijassa-1224 119 4 βŽͺ βŽͺ NOUN ijassa-1224 119 5 ⎬ ⎬ PROPN ijassa-1224 119 6 βŽͺ βŽͺ NOUN ijassa-1224 119 7 ⎫ ⎫ PROPN ijassa-1224 119 8 . . PUNCT ijassa-1224 120 1 ( ( PUNCT ijassa-1224 120 2 20 20 NUM ijassa-1224 120 3 ) ) PUNCT ijassa-1224 120 4 2.5 2.5 NUM ijassa-1224 120 5 . . PUNCT ijassa-1224 121 1 disease disease NOUN ijassa-1224 121 2 free free ADJ ijassa-1224 121 3 equilibrium equilibrium NOUN ijassa-1224 121 4 ( ( PUNCT ijassa-1224 121 5 d.f.e d.f.e ADJ ijassa-1224 121 6 ) ) PUNCT ijassa-1224 121 7 the the DET ijassa-1224 121 8 disease disease NOUN ijassa-1224 121 9 - - PUNCT ijassa-1224 121 10 free free ADJ ijassa-1224 121 11 equilibrium equilibrium NOUN ijassa-1224 121 12 state state NOUN ijassa-1224 121 13 is be AUX ijassa-1224 121 14 the the DET ijassa-1224 121 15 point point NOUN ijassa-1224 121 16 at at ADP ijassa-1224 121 17 which which PRON ijassa-1224 121 18 there there PRON ijassa-1224 121 19 exist exist VERB ijassa-1224 121 20 no no DET ijassa-1224 121 21 infection infection NOUN ijassa-1224 121 22 in in ADP ijassa-1224 121 23 the the DET ijassa-1224 121 24 given give VERB ijassa-1224 121 25 population population NOUN ijassa-1224 121 26 . . PUNCT ijassa-1224 122 1 at at ADP ijassa-1224 122 2 disease disease NOUN ijassa-1224 122 3 free free ADJ ijassa-1224 122 4 equilibrium equilibrium NOUN ijassa-1224 122 5 , , PUNCT ijassa-1224 122 6 we we PRON ijassa-1224 122 7 let let VERB ijassa-1224 122 8 ( ( PUNCT ijassa-1224 122 9 𝑉 𝑉 PROPN ijassa-1224 122 10 , , PUNCT ijassa-1224 122 11 𝑆 𝑆 PROPN ijassa-1224 122 12 , , PUNCT ijassa-1224 122 13 𝐸 𝐸 PROPN ijassa-1224 122 14 , , PUNCT ijassa-1224 122 15 𝐼 𝐼 PROPN ijassa-1224 122 16 , , PUNCT ijassa-1224 122 17 𝐼 𝐼 PROPN ijassa-1224 122 18 , , PUNCT ijassa-1224 122 19 𝐽 𝐽 PROPN ijassa-1224 122 20 , , PUNCT ijassa-1224 122 21 𝑇 𝑇 PROPN ijassa-1224 122 22 ) ) PUNCT ijassa-1224 122 23 = = SYM ijassa-1224 122 24 πΈβˆ— πΈβˆ— NOUN ijassa-1224 122 25 = = SYM ijassa-1224 122 26 ( ( PUNCT ijassa-1224 122 27 π‘‰βˆ— π‘‰βˆ— PROPN ijassa-1224 122 28 , , PUNCT ijassa-1224 122 29 π‘†βˆ— π‘†βˆ— X ijassa-1224 122 30 , , PUNCT ijassa-1224 122 31 πΈβˆ— πΈβˆ— NOUN ijassa-1224 122 32 , , PUNCT ijassa-1224 122 33 πΌβˆ— πΌβˆ— NOUN ijassa-1224 122 34 , , PUNCT ijassa-1224 122 35 πΌβˆ— πΌβˆ— PROPN ijassa-1224 122 36 , , PUNCT ijassa-1224 122 37 π½βˆ— π½βˆ— NOUN ijassa-1224 122 38 , , PUNCT ijassa-1224 122 39 π‘‡βˆ— π‘‡βˆ— PROPN ijassa-1224 122 40 ) ) PUNCT ijassa-1224 122 41 . . PUNCT ijassa-1224 123 1 lemma lemma PROPN ijassa-1224 123 2 1 1 NUM ijassa-1224 123 3 : : SYM ijassa-1224 123 4 150 150 NUM ijassa-1224 123 5 f.a f.a PROPN ijassa-1224 123 6 . . PROPN ijassa-1224 124 1 oguntolu oguntolu PROPN ijassa-1224 124 2 , , PUNCT ijassa-1224 124 3 o.j o.j PROPN ijassa-1224 124 4 . . PROPN ijassa-1224 124 5 peter peter PROPN ijassa-1224 124 6 , , PUNCT ijassa-1224 124 7 k. k. PROPN ijassa-1224 124 8 oshinubi oshinubi PROPN ijassa-1224 124 9 , , PUNCT ijassa-1224 124 10 t.a t.a PROPN ijassa-1224 124 11 . . PROPN ijassa-1224 124 12 ayoola ayoola PROPN ijassa-1224 124 13 , , PUNCT ijassa-1224 124 14 a.o a.o PROPN ijassa-1224 124 15 . . PROPN ijassa-1224 124 16 oladapo oladapo PROPN ijassa-1224 124 17 , , PUNCT ijassa-1224 124 18 m.m m.m PROPN ijassa-1224 124 19 . . PROPN ijassa-1224 124 20 ojo ojo NOUN ijassa-1224 124 21 copyright copyright NOUN ijassa-1224 124 22 Β© Β© PROPN ijassa-1224 124 23 2022 2022 NUM ijassa-1224 124 24 assa assa PROPN ijassa-1224 124 25 adv adv PROPN ijassa-1224 124 26 . . PUNCT ijassa-1224 125 1 in in ADP ijassa-1224 125 2 systems system NOUN ijassa-1224 125 3 science science NOUN ijassa-1224 125 4 and and CCONJ ijassa-1224 125 5 appl appl NOUN ijassa-1224 125 6 . . PUNCT ijassa-1224 126 1 ( ( PUNCT ijassa-1224 126 2 2022 2022 NUM ijassa-1224 126 3 ) ) PUNCT ijassa-1224 126 4 the the DET ijassa-1224 126 5 d.f.e d.f.e NOUN ijassa-1224 126 6 of of ADP ijassa-1224 126 7 the the DET ijassa-1224 126 8 model model NOUN ijassa-1224 126 9 exists exist VERB ijassa-1224 126 10 and and CCONJ ijassa-1224 126 11 is be AUX ijassa-1224 126 12 given give VERB ijassa-1224 126 13 by by ADP ijassa-1224 126 14 𝐸 𝐸 PROPN ijassa-1224 126 15 = = SYM ijassa-1224 126 16 ( ( PUNCT ijassa-1224 126 17 π‘‰βˆ— π‘‰βˆ— PROPN ijassa-1224 126 18 , , PUNCT ijassa-1224 126 19 π‘†βˆ— π‘†βˆ— X ijassa-1224 126 20 , , PUNCT ijassa-1224 126 21 πΈβˆ— πΈβˆ— NOUN ijassa-1224 126 22 , , PUNCT ijassa-1224 126 23 πΌβˆ— πΌβˆ— NOUN ijassa-1224 126 24 , , PUNCT ijassa-1224 126 25 πΌβˆ— πΌβˆ— PROPN ijassa-1224 126 26 , , PUNCT ijassa-1224 126 27 π½βˆ— π½βˆ— NOUN ijassa-1224 126 28 , , PUNCT ijassa-1224 126 29 π‘‡βˆ— π‘‡βˆ— NOUN ijassa-1224 126 30 ) ) PUNCT ijassa-1224 127 1 = = PRON ijassa-1224 128 1 πœ‹πœƒ πœ‹πœƒ X ijassa-1224 128 2 ( ( PUNCT ijassa-1224 128 3 πœ‡ πœ‡ X ijassa-1224 128 4 + + NOUN ijassa-1224 128 5 πœ” πœ” NOUN ijassa-1224 128 6 ) ) PUNCT ijassa-1224 128 7 , , PUNCT ijassa-1224 128 8 πœ‹(πœ‡ πœ‹(πœ‡ PROPN ijassa-1224 128 9 + + PUNCT ijassa-1224 128 10 πœ” πœ” PRON ijassa-1224 128 11 βˆ’ βˆ’ NOUN ijassa-1224 128 12 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 128 13 ) ) PUNCT ijassa-1224 128 14 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 129 1 + + CCONJ ijassa-1224 129 2 πœ” πœ” X ijassa-1224 129 3 ) ) PUNCT ijassa-1224 130 1 , , PUNCT ijassa-1224 130 2 0,0,0,0,0 0,0,0,0,0 NOUN ijassa-1224 130 3 . . PUNCT ijassa-1224 131 1 proof proof NOUN ijassa-1224 131 2 . . PUNCT ijassa-1224 132 1 suppose suppose VERB ijassa-1224 132 2 𝐼 𝐼 ADP ijassa-1224 132 3 = = PROPN ijassa-1224 132 4 0 0 PROPN ijassa-1224 132 5 . . PUNCT ijassa-1224 133 1 then then ADV ijassa-1224 133 2 equation equation NOUN ijassa-1224 133 3 ( ( PUNCT ijassa-1224 133 4 20 20 NUM ijassa-1224 133 5 ) ) PUNCT ijassa-1224 133 6 becomes become VERB ijassa-1224 133 7 πœ† πœ† NOUN ijassa-1224 133 8 = = NOUN ijassa-1224 133 9 0 0 NUM ijassa-1224 134 1 πœ† πœ† X ijassa-1224 134 2 = = NOUN ijassa-1224 134 3 0 0 PUNCT ijassa-1224 134 4 πœ† πœ† X ijassa-1224 134 5 = = SYM ijassa-1224 134 6 0 0 PROPN ijassa-1224 134 7 and and CCONJ ijassa-1224 134 8 also also ADV ijassa-1224 134 9 π½βˆ— π½βˆ— ADP ijassa-1224 135 1 = = SYM ijassa-1224 135 2 0 0 NUM ijassa-1224 135 3 πΈβˆ— πΈβˆ— NOUN ijassa-1224 135 4 = = NOUN ijassa-1224 135 5 0 0 NUM ijassa-1224 135 6 πΌβˆ— πΌβˆ— NOUN ijassa-1224 135 7 = = SYM ijassa-1224 135 8 0 0 PUNCT ijassa-1224 135 9 π‘‡βˆ— π‘‡βˆ— NOUN ijassa-1224 136 1 = = NOUN ijassa-1224 136 2 0 0 PROPN ijassa-1224 136 3 . . PUNCT ijassa-1224 137 1 from from ADP ijassa-1224 137 2 ( ( PUNCT ijassa-1224 137 3 19 19 NUM ijassa-1224 137 4 ) ) PUNCT ijassa-1224 137 5 π‘†βˆ— π‘†βˆ— X ijassa-1224 137 6 = = PUNCT ijassa-1224 137 7 πœ‹(πœ‡ πœ‹(πœ‡ PROPN ijassa-1224 137 8 + + CCONJ ijassa-1224 137 9 πœ” πœ” PRON ijassa-1224 137 10 βˆ’ βˆ’ NOUN ijassa-1224 137 11 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 137 12 ) ) PUNCT ijassa-1224 137 13 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 137 14 + + CCONJ ijassa-1224 137 15 πœ” πœ” X ijassa-1224 137 16 ) ) PUNCT ijassa-1224 137 17 . . PUNCT ijassa-1224 138 1 thus thus ADV ijassa-1224 138 2 , , PUNCT ijassa-1224 138 3 the the DET ijassa-1224 138 4 lemma lemma PROPN ijassa-1224 138 5 is be AUX ijassa-1224 138 6 proved prove VERB ijassa-1224 138 7 and and CCONJ ijassa-1224 138 8 ⎝ ⎝ PUNCT ijassa-1224 138 9 ⎜ ⎜ PROPN ijassa-1224 138 10 ⎜ ⎜ PROPN ijassa-1224 138 11 ⎜ ⎜ PROPN ijassa-1224 138 12 ⎜ ⎜ PROPN ijassa-1224 138 13 ⎜ ⎜ PROPN ijassa-1224 138 14 βŽ› βŽ› X ijassa-1224 138 15 π‘‰βˆ— π‘‰βˆ— X ijassa-1224 138 16 π‘†βˆ— π‘†βˆ— VERB ijassa-1224 138 17 πΈβˆ— πΈβˆ— NOUN ijassa-1224 139 1 𝐼 𝐼 ADP ijassa-1224 139 2 βˆ— βˆ— NOUN ijassa-1224 139 3 𝐼 𝐼 ADP ijassa-1224 139 4 βˆ— βˆ— NOUN ijassa-1224 140 1 π½βˆ— π½βˆ— PRON ijassa-1224 140 2 π‘‡βˆ— π‘‡βˆ— NOUN ijassa-1224 140 3 ⎠ ⎠ NOUN ijassa-1224 140 4 ⎟ ⎟ X ijassa-1224 140 5 ⎟ ⎟ X ijassa-1224 140 6 ⎟ ⎟ X ijassa-1224 140 7 ⎟ ⎟ X ijassa-1224 140 8 ⎟ ⎟ PROPN ijassa-1224 140 9 ⎞ ⎞ VERB ijassa-1224 140 10 = = SYM ijassa-1224 140 11 ⎝ ⎝ PROPN ijassa-1224 140 12 ⎜ ⎜ PROPN ijassa-1224 140 13 ⎜ ⎜ PROPN ijassa-1224 140 14 ⎜ ⎜ PROPN ijassa-1224 140 15 ⎜ ⎜ PROPN ijassa-1224 140 16 ⎜ ⎜ PROPN ijassa-1224 140 17 βŽ› βŽ› X ijassa-1224 140 18 ( ( PUNCT ijassa-1224 140 19 ) ) PUNCT ijassa-1224 140 20 ( ( PUNCT ijassa-1224 140 21 ) ) PUNCT ijassa-1224 140 22 ( ( PUNCT ijassa-1224 140 23 ) ) PUNCT ijassa-1224 140 24 0 0 NUM ijassa-1224 141 1 0 0 NUM ijassa-1224 141 2 0 0 NUM ijassa-1224 141 3 0 0 NUM ijassa-1224 141 4 0 0 NUM ijassa-1224 141 5 ⎠ ⎠ NOUN ijassa-1224 141 6 ⎟ ⎟ X ijassa-1224 141 7 ⎟ ⎟ X ijassa-1224 141 8 ⎟ ⎟ X ijassa-1224 141 9 ⎟ ⎟ X ijassa-1224 141 10 ⎟ ⎟ PROPN ijassa-1224 141 11 ⎞ ⎞ VERB ijassa-1224 141 12 . . PUNCT ijassa-1224 142 1 ( ( PUNCT ijassa-1224 142 2 21 21 NUM ijassa-1224 142 3 ) ) PUNCT ijassa-1224 142 4 the the DET ijassa-1224 142 5 above above ADJ ijassa-1224 142 6 equation equation NOUN ijassa-1224 142 7 is be AUX ijassa-1224 142 8 the the DET ijassa-1224 142 9 disease disease NOUN ijassa-1224 142 10 - - PUNCT ijassa-1224 142 11 free free ADJ ijassa-1224 142 12 equilibrium equilibrium NOUN ijassa-1224 142 13 . . PUNCT ijassa-1224 143 1 2.7 2.7 NUM ijassa-1224 143 2 . . PUNCT ijassa-1224 143 3 effective effective ADJ ijassa-1224 143 4 reproduction reproduction NOUN ijassa-1224 143 5 number number NOUN ijassa-1224 143 6 in in ADP ijassa-1224 143 7 biomathematics biomathematic NOUN ijassa-1224 143 8 , , PUNCT ijassa-1224 143 9 the the DET ijassa-1224 143 10 basic basic ADJ ijassa-1224 143 11 reproduction reproduction NOUN ijassa-1224 143 12 number number NOUN ijassa-1224 143 13 ( ( PUNCT ijassa-1224 143 14 r0 r0 NOUN ijassa-1224 143 15 ) ) PUNCT ijassa-1224 143 16 is be AUX ijassa-1224 143 17 the the DET ijassa-1224 143 18 average average ADJ ijassa-1224 143 19 number number NOUN ijassa-1224 143 20 of of ADP ijassa-1224 143 21 infected infected ADJ ijassa-1224 143 22 contacts contact NOUN ijassa-1224 143 23 per per ADP ijassa-1224 143 24 infected infected ADJ ijassa-1224 143 25 individual individual NOUN ijassa-1224 143 26 . . PUNCT ijassa-1224 144 1 it it PRON ijassa-1224 144 2 is be AUX ijassa-1224 144 3 one one NUM ijassa-1224 144 4 of of ADP ijassa-1224 144 5 the the DET ijassa-1224 144 6 fundamental fundamental ADJ ijassa-1224 144 7 concepts concept NOUN ijassa-1224 144 8 to to PART ijassa-1224 144 9 determine determine VERB ijassa-1224 144 10 the the DET ijassa-1224 144 11 future future NOUN ijassa-1224 144 12 of of ADP ijassa-1224 144 13 an an DET ijassa-1224 144 14 epidemics epidemic NOUN ijassa-1224 144 15 in in ADP ijassa-1224 144 16 a a DET ijassa-1224 144 17 population population NOUN ijassa-1224 144 18 . . PUNCT ijassa-1224 145 1 when when SCONJ ijassa-1224 145 2 𝑅 𝑅 PROPN ijassa-1224 145 3 < < X ijassa-1224 145 4 1 1 NUM ijassa-1224 145 5 the the DET ijassa-1224 145 6 infection infection NOUN ijassa-1224 145 7 will will AUX ijassa-1224 145 8 die die VERB ijassa-1224 145 9 out out ADP ijassa-1224 145 10 in in ADP ijassa-1224 145 11 the the DET ijassa-1224 145 12 long long ADJ ijassa-1224 145 13 run run NOUN ijassa-1224 145 14 , , PUNCT ijassa-1224 145 15 but but CCONJ ijassa-1224 145 16 if if SCONJ ijassa-1224 145 17 𝑅 𝑅 PROPN ijassa-1224 145 18 > > X ijassa-1224 145 19 1 1 NUM ijassa-1224 145 20 . . PUNCT ijassa-1224 146 1 the the DET ijassa-1224 146 2 infection infection NOUN ijassa-1224 146 3 will will AUX ijassa-1224 146 4 be be AUX ijassa-1224 146 5 able able ADJ ijassa-1224 146 6 to to PART ijassa-1224 146 7 spread spread VERB ijassa-1224 146 8 in in ADP ijassa-1224 146 9 a a DET ijassa-1224 146 10 population population NOUN ijassa-1224 146 11 . . PUNCT ijassa-1224 147 1 in in ADP ijassa-1224 147 2 this this DET ijassa-1224 147 3 model model NOUN ijassa-1224 147 4 , , PUNCT ijassa-1224 147 5 the the DET ijassa-1224 147 6 spectral spectral ADJ ijassa-1224 147 7 radius radius NOUN ijassa-1224 147 8 of of ADP ijassa-1224 147 9 the the DET ijassa-1224 147 10 equation equation NOUN ijassa-1224 147 11 is be AUX ijassa-1224 147 12 given give VERB ijassa-1224 147 13 as as ADP ijassa-1224 147 14 largest large ADJ ijassa-1224 147 15 eigenvalue eigenvalue NOUN ijassa-1224 147 16 given give VERB ijassa-1224 147 17 as as ADP ijassa-1224 147 18 𝑅 𝑅 PROPN ijassa-1224 147 19 = = PUNCT ijassa-1224 147 20 πœŒπ‘“π‘£ πœŒπ‘“π‘£ PROPN ijassa-1224 147 21 following follow VERB ijassa-1224 147 22 the the DET ijassa-1224 147 23 procedure procedure NOUN ijassa-1224 147 24 in in ADP ijassa-1224 147 25 [ [ X ijassa-1224 147 26 14 14 NUM ijassa-1224 147 27 , , PUNCT ijassa-1224 147 28 15 15 NUM ijassa-1224 147 29 ] ] PUNCT ijassa-1224 147 30 , , PUNCT ijassa-1224 147 31 the the DET ijassa-1224 147 32 next next ADJ ijassa-1224 147 33 generation generation NOUN ijassa-1224 147 34 matrix matrix NOUN ijassa-1224 147 35 operator operator NOUN ijassa-1224 147 36 is be AUX ijassa-1224 147 37 used use VERB ijassa-1224 147 38 to to PART ijassa-1224 147 39 estimate estimate VERB ijassa-1224 147 40 the the DET ijassa-1224 147 41 effective effective ADJ ijassa-1224 147 42 reproduction reproduction NOUN ijassa-1224 147 43 number number NOUN ijassa-1224 147 44 such such ADJ ijassa-1224 147 45 that that SCONJ ijassa-1224 147 46 the the DET ijassa-1224 147 47 jacobian jacobian ADJ ijassa-1224 147 48 matrices matrix NOUN ijassa-1224 147 49 for for ADP ijassa-1224 147 50 the the DET ijassa-1224 147 51 new new ADJ ijassa-1224 147 52 infection infection NOUN ijassa-1224 147 53 terms term NOUN ijassa-1224 147 54 and and CCONJ ijassa-1224 147 55 the the DET ijassa-1224 147 56 remaining remain VERB ijassa-1224 147 57 transfer transfer NOUN ijassa-1224 147 58 terms term NOUN ijassa-1224 147 59 are be AUX ijassa-1224 147 60 obtained obtain VERB ijassa-1224 147 61 below below ADP ijassa-1224 147 62 𝐹 𝐹 PROPN ijassa-1224 147 63 = = PUNCT ijassa-1224 147 64 πœ† πœ† PROPN ijassa-1224 147 65 𝑆 𝑆 PROPN ijassa-1224 147 66 + + CCONJ ijassa-1224 147 67 πœ† πœ† PROPN ijassa-1224 147 68 𝑇 𝑇 PROPN ijassa-1224 147 69 ( ( PUNCT ijassa-1224 147 70 1 1 NUM ijassa-1224 147 71 βˆ’ βˆ’ NOUN ijassa-1224 147 72 πœ™)πœ† πœ™)πœ† X ijassa-1224 147 73 𝐸 𝐸 PROPN ijassa-1224 147 74 ( ( PUNCT ijassa-1224 147 75 πœ™πœ† πœ™πœ† NOUN ijassa-1224 147 76 ) ) PUNCT ijassa-1224 147 77 𝐸 𝐸 PROPN ijassa-1224 147 78 0 0 NUM ijassa-1224 147 79 𝑉 𝑉 NOUN ijassa-1224 147 80 = = NOUN ijassa-1224 147 81 ⎝ ⎝ X ijassa-1224 147 82 βŽ› βŽ› NOUN ijassa-1224 147 83 ( ( PUNCT ijassa-1224 147 84 πœ‡ πœ‡ X ijassa-1224 147 85 + + X ijassa-1224 147 86 𝜎)𝐸 𝜎)𝐸 ADV ijassa-1224 147 87 ( ( PUNCT ijassa-1224 147 88 𝛾 𝛾 ADP ijassa-1224 147 89 + + PRON ijassa-1224 147 90 π‘Ÿ π‘Ÿ NOUN ijassa-1224 148 1 + + CCONJ ijassa-1224 148 2 𝑑 𝑑 PROPN ijassa-1224 148 3 + + ADJ ijassa-1224 148 4 πœ‡)𝐼 πœ‡)𝐼 ADJ ijassa-1224 148 5 βˆ’ βˆ’ PROPN ijassa-1224 148 6 ( ( PUNCT ijassa-1224 148 7 1 1 NUM ijassa-1224 148 8 βˆ’ βˆ’ PROPN ijassa-1224 148 9 𝜌)𝜎𝐸 𝜌)𝜎𝐸 PROPN ijassa-1224 148 10 ( ( PUNCT ijassa-1224 148 11 π‘Ÿ π‘Ÿ NOUN ijassa-1224 148 12 + + NOUN ijassa-1224 148 13 π‘Ÿ π‘Ÿ NOUN ijassa-1224 148 14 + + CCONJ ijassa-1224 148 15 𝑑 𝑑 PROPN ijassa-1224 148 16 + + ADJ ijassa-1224 148 17 πœ‡)𝐼 πœ‡)𝐼 ADJ ijassa-1224 148 18 βˆ’ βˆ’ NOUN ijassa-1224 148 19 𝛾 𝛾 NOUN ijassa-1224 149 1 𝐼 𝐼 ADP ijassa-1224 149 2 βˆ’ βˆ’ PROPN ijassa-1224 149 3 𝜌𝜎𝐸 𝜌𝜎𝐸 PROPN ijassa-1224 149 4 ( ( PUNCT ijassa-1224 149 5 πœ‡ πœ‡ X ijassa-1224 149 6 + + X ijassa-1224 149 7 𝑑 𝑑 PROPN ijassa-1224 149 8 + + ADJ ijassa-1224 149 9 π‘Ÿ π‘Ÿ NOUN ijassa-1224 149 10 ) ) PUNCT ijassa-1224 149 11 𝐽 𝐽 PROPN ijassa-1224 149 12 βˆ’ βˆ’ NOUN ijassa-1224 150 1 π‘Ÿ π‘Ÿ CCONJ ijassa-1224 150 2 𝐼 𝐼 ADP ijassa-1224 150 3 ⎠ ⎠ NOUN ijassa-1224 150 4 ⎞ ⎞ NOUN ijassa-1224 150 5 𝐹(𝐷𝐹𝐸 𝐹(𝐷𝐹𝐸 PUNCT ijassa-1224 150 6 ) ) PUNCT ijassa-1224 150 7 = = PUNCT ijassa-1224 150 8 ⎝ ⎝ X ijassa-1224 150 9 ⎜ ⎜ PROPN ijassa-1224 150 10 βŽ› βŽ› X ijassa-1224 150 11 0 0 NUM ijassa-1224 150 12 π›½πœ€ π›½πœ€ ADP ijassa-1224 150 13 πœ‹(πœ‡ πœ‹(πœ‡ PROPN ijassa-1224 150 14 + + CCONJ ijassa-1224 150 15 πœ” πœ” PRON ijassa-1224 150 16 βˆ’ βˆ’ NOUN ijassa-1224 150 17 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 150 18 ) ) PUNCT ijassa-1224 150 19 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 151 1 + + CCONJ ijassa-1224 151 2 πœ” πœ” X ijassa-1224 151 3 ) ) PUNCT ijassa-1224 151 4 π›½πœ‹(πœ‡ π›½πœ‹(πœ‡ NUM ijassa-1224 152 1 + + CCONJ ijassa-1224 152 2 πœ” πœ” PRON ijassa-1224 152 3 βˆ’ βˆ’ NOUN ijassa-1224 152 4 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 152 5 ) ) PUNCT ijassa-1224 152 6 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 153 1 + + CCONJ ijassa-1224 153 2 πœ” πœ” X ijassa-1224 153 3 ) ) PUNCT ijassa-1224 153 4 π›½πœ€ π›½πœ€ ADP ijassa-1224 153 5 πœ‹(πœ‡ πœ‹(πœ‡ PROPN ijassa-1224 153 6 + + CCONJ ijassa-1224 153 7 πœ” πœ” PRON ijassa-1224 153 8 βˆ’ βˆ’ NOUN ijassa-1224 153 9 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 153 10 ) ) PUNCT ijassa-1224 153 11 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 154 1 + + CCONJ ijassa-1224 154 2 πœ” πœ” X ijassa-1224 154 3 ) ) PUNCT ijassa-1224 154 4 0 0 NUM ijassa-1224 155 1 0 0 NUM ijassa-1224 155 2 0 0 NUM ijassa-1224 155 3 0 0 NUM ijassa-1224 155 4 0 0 NUM ijassa-1224 155 5 0 0 NUM ijassa-1224 155 6 0 0 NUM ijassa-1224 155 7 0 0 NUM ijassa-1224 155 8 0 0 NUM ijassa-1224 155 9 0 0 NUM ijassa-1224 155 10 0 0 NUM ijassa-1224 155 11 0 0 NUM ijassa-1224 155 12 ⎠ ⎠ NOUN ijassa-1224 155 13 ⎟ ⎟ X ijassa-1224 155 14 ⎞ ⎞ VERB ijassa-1224 155 15 analysis analysis NOUN ijassa-1224 155 16 and and CCONJ ijassa-1224 155 17 dynamics dynamic NOUN ijassa-1224 155 18 of of ADP ijassa-1224 155 19 tuberculosis tuberculosis NOUN ijassa-1224 155 20 outbreak outbreak NOUN ijassa-1224 155 21 151 151 NUM ijassa-1224 155 22 copyright copyright NOUN ijassa-1224 155 23 Β© Β© PROPN ijassa-1224 155 24 2022 2022 NUM ijassa-1224 155 25 assa assa NOUN ijassa-1224 155 26 . . PUNCT ijassa-1224 156 1 adv adv PROPN ijassa-1224 156 2 . . PUNCT ijassa-1224 157 1 in in ADP ijassa-1224 157 2 systems system NOUN ijassa-1224 157 3 science science NOUN ijassa-1224 157 4 and and CCONJ ijassa-1224 157 5 appl appl NOUN ijassa-1224 157 6 . . PUNCT ijassa-1224 158 1 ( ( PUNCT ijassa-1224 158 2 2022 2022 NUM ijassa-1224 158 3 ) ) PUNCT ijassa-1224 158 4 𝑉 𝑉 PROPN ijassa-1224 158 5 = = SYM ijassa-1224 158 6 ⎝ ⎝ X ijassa-1224 158 7 βŽ› βŽ› NOUN ijassa-1224 158 8 ( ( PUNCT ijassa-1224 158 9 πœ‡ πœ‡ X ijassa-1224 158 10 + + X ijassa-1224 158 11 𝜎 𝜎 X ijassa-1224 158 12 ) ) PUNCT ijassa-1224 158 13 0 0 NUM ijassa-1224 158 14 0 0 NUM ijassa-1224 158 15 0 0 NUM ijassa-1224 159 1 βˆ’(1 βˆ’(1 NOUN ijassa-1224 159 2 βˆ’ βˆ’ NOUN ijassa-1224 159 3 𝜌)𝜎 𝜌)𝜎 PUNCT ijassa-1224 159 4 ( ( PUNCT ijassa-1224 159 5 𝛾 𝛾 NOUN ijassa-1224 159 6 + + X ijassa-1224 159 7 πœ‡ πœ‡ ADP ijassa-1224 159 8 + + NOUN ijassa-1224 159 9 π‘Ÿ π‘Ÿ NOUN ijassa-1224 159 10 + + CCONJ ijassa-1224 159 11 𝑑 𝑑 PROPN ijassa-1224 159 12 ) ) PUNCT ijassa-1224 159 13 0 0 NUM ijassa-1224 159 14 0 0 NUM ijassa-1224 160 1 βˆ’πœŒπœŽ βˆ’πœŒπœŽ PROPN ijassa-1224 160 2 βˆ’π›Ύ βˆ’π›Ύ ADJ ijassa-1224 160 3 ( ( PUNCT ijassa-1224 160 4 π‘Ÿ π‘Ÿ NOUN ijassa-1224 160 5 + + ADP ijassa-1224 160 6 π‘Ÿ π‘Ÿ NOUN ijassa-1224 160 7 + + CCONJ ijassa-1224 160 8 𝑑 𝑑 PROPN ijassa-1224 160 9 + + X ijassa-1224 160 10 πœ‡ πœ‡ X ijassa-1224 160 11 ) ) PUNCT ijassa-1224 160 12 0 0 NUM ijassa-1224 160 13 0 0 NUM ijassa-1224 160 14 0 0 NUM ijassa-1224 160 15 βˆ’π‘Ÿ βˆ’π‘Ÿ NOUN ijassa-1224 160 16 ( ( PUNCT ijassa-1224 160 17 πœ‡ πœ‡ ADP ijassa-1224 160 18 + + NOUN ijassa-1224 160 19 π‘Ÿ π‘Ÿ NOUN ijassa-1224 160 20 + + CCONJ ijassa-1224 160 21 𝑑 𝑑 NOUN ijassa-1224 160 22 ) ) PUNCT ijassa-1224 160 23 ⎠ ⎠ NOUN ijassa-1224 160 24 ⎞ ⎞ NOUN ijassa-1224 160 25 let let VERB ijassa-1224 160 26 𝑉 𝑉 VERB ijassa-1224 160 27 = = NOUN ijassa-1224 160 28 𝑄 𝑄 PROPN ijassa-1224 160 29 0 0 NUM ijassa-1224 160 30 0 0 NUM ijassa-1224 160 31 0 0 NUM ijassa-1224 160 32 βˆ’πΆ βˆ’πΆ ADP ijassa-1224 160 33 𝑄 𝑄 PROPN ijassa-1224 160 34 0 0 NUM ijassa-1224 160 35 0 0 NUM ijassa-1224 161 1 βˆ’πΆ βˆ’πΆ ADP ijassa-1224 161 2 βˆ’π›Ύ βˆ’π›Ύ ADJ ijassa-1224 161 3 𝑄 𝑄 PROPN ijassa-1224 161 4 0 0 NUM ijassa-1224 161 5 0 0 NUM ijassa-1224 161 6 0 0 NUM ijassa-1224 162 1 βˆ’π‘Ÿ βˆ’π‘Ÿ NOUN ijassa-1224 162 2 𝑄 𝑄 PRON ijassa-1224 162 3 where where SCONJ ijassa-1224 162 4 𝑄 𝑄 PROPN ijassa-1224 162 5 ( ( PUNCT ijassa-1224 162 6 πœ‡ πœ‡ X ijassa-1224 162 7 + + X ijassa-1224 162 8 𝜎 𝜎 X ijassa-1224 162 9 ) ) PUNCT ijassa-1224 162 10 , , PUNCT ijassa-1224 162 11 𝑄 𝑄 PROPN ijassa-1224 162 12 = = SYM ijassa-1224 162 13 𝛾 𝛾 PART ijassa-1224 163 1 + + X ijassa-1224 163 2 πœ‡ πœ‡ X ijassa-1224 163 3 + + NOUN ijassa-1224 163 4 π‘Ÿ π‘Ÿ NOUN ijassa-1224 163 5 + + CCONJ ijassa-1224 163 6 𝑑 𝑑 NOUN ijassa-1224 163 7 , , PUNCT ijassa-1224 163 8 𝑄 𝑄 PROPN ijassa-1224 163 9 = = PUNCT ijassa-1224 163 10 π‘Ÿ π‘Ÿ NOUN ijassa-1224 164 1 + + SYM ijassa-1224 164 2 π‘Ÿ π‘Ÿ NOUN ijassa-1224 164 3 + + CCONJ ijassa-1224 164 4 𝑑 𝑑 PROPN ijassa-1224 164 5 + + X ijassa-1224 164 6 πœ‡ πœ‡ ADP ijassa-1224 164 7 , , PUNCT ijassa-1224 164 8 𝑄 𝑄 PROPN ijassa-1224 164 9 = = PUNCT ijassa-1224 164 10 𝑑 𝑑 PROPN ijassa-1224 164 11 + + ADJ ijassa-1224 164 12 π‘Ÿ π‘Ÿ NOUN ijassa-1224 164 13 + + CCONJ ijassa-1224 164 14 πœ‡ πœ‡ ADP ijassa-1224 164 15 , , PUNCT ijassa-1224 164 16 therefore therefore ADV ijassa-1224 164 17 𝑉 𝑉 PROPN ijassa-1224 164 18 = = SYM ijassa-1224 164 19 ⎝ ⎝ NUM ijassa-1224 164 20 ⎜ ⎜ PROPN ijassa-1224 164 21 ⎜ ⎜ PROPN ijassa-1224 164 22 ⎜ ⎜ PROPN ijassa-1224 164 23 ⎜ ⎜ PROPN ijassa-1224 164 24 ⎜ ⎜ PROPN ijassa-1224 164 25 βŽ› βŽ› X ijassa-1224 164 26 1 1 NUM ijassa-1224 164 27 ( ( PUNCT ijassa-1224 164 28 πœ‡ πœ‡ X ijassa-1224 164 29 + + X ijassa-1224 164 30 𝜎 𝜎 X ijassa-1224 164 31 ) ) PUNCT ijassa-1224 164 32 0 0 NUM ijassa-1224 164 33 0 0 NUM ijassa-1224 164 34 0 0 NUM ijassa-1224 165 1 ( ( PUNCT ijassa-1224 165 2 1 1 NUM ijassa-1224 165 3 βˆ’ βˆ’ NOUN ijassa-1224 165 4 𝜌)𝜎 𝜌)𝜎 ADJ ijassa-1224 165 5 𝑄 𝑄 NOUN ijassa-1224 165 6 𝑄 𝑄 NOUN ijassa-1224 165 7 1 1 NUM ijassa-1224 165 8 𝑄 𝑄 NOUN ijassa-1224 165 9 0 0 NUM ijassa-1224 165 10 0 0 NUM ijassa-1224 166 1 ( ( PUNCT ijassa-1224 166 2 1 1 NUM ijassa-1224 166 3 βˆ’ βˆ’ PROPN ijassa-1224 166 4 𝜌)π›ΎπœŽ 𝜌)π›ΎπœŽ PROPN ijassa-1224 166 5 + + CCONJ ijassa-1224 166 6 πœŒπœŽπ‘„ πœŒπœŽπ‘„ PRON ijassa-1224 166 7 𝑄 𝑄 PRON ijassa-1224 166 8 𝑄 𝑄 PRON ijassa-1224 166 9 𝑄 𝑄 PRON ijassa-1224 166 10 𝛾 𝛾 VERB ijassa-1224 166 11 𝑄 𝑄 PRON ijassa-1224 166 12 𝑄 𝑄 PROPN ijassa-1224 166 13 1 1 NUM ijassa-1224 166 14 𝑄 𝑄 NOUN ijassa-1224 166 15 0 0 NUM ijassa-1224 167 1 π‘Ÿ π‘Ÿ NOUN ijassa-1224 168 1 [ [ X ijassa-1224 168 2 ( ( PUNCT ijassa-1224 168 3 1 1 NUM ijassa-1224 168 4 βˆ’ βˆ’ PROPN ijassa-1224 168 5 𝜌)π›ΎπœŽ 𝜌)π›ΎπœŽ PROPN ijassa-1224 168 6 + + CCONJ ijassa-1224 168 7 πœŒπœŽπ‘„ πœŒπœŽπ‘„ X ijassa-1224 168 8 ] ] PUNCT ijassa-1224 168 9 𝑄 𝑄 PROPN ijassa-1224 168 10 𝑄 𝑄 NOUN ijassa-1224 168 11 𝑄 𝑄 NOUN ijassa-1224 168 12 𝑄 𝑄 PRON ijassa-1224 168 13 π‘Ÿ π‘Ÿ NOUN ijassa-1224 168 14 𝛾 𝛾 ADP ijassa-1224 168 15 𝑄 𝑄 PRON ijassa-1224 168 16 𝑄 𝑄 PRON ijassa-1224 168 17 𝑄 𝑄 PRON ijassa-1224 168 18 π‘Ÿ π‘Ÿ NOUN ijassa-1224 168 19 𝑄 𝑄 NOUN ijassa-1224 168 20 𝑄 𝑄 PROPN ijassa-1224 168 21 1 1 NUM ijassa-1224 168 22 𝑄 𝑄 NOUN ijassa-1224 168 23 ⎠ ⎠ NOUN ijassa-1224 168 24 ⎟ ⎟ X ijassa-1224 168 25 ⎟ ⎟ X ijassa-1224 168 26 ⎟ ⎟ X ijassa-1224 168 27 ⎟ ⎟ X ijassa-1224 168 28 ⎟ ⎟ PROPN ijassa-1224 168 29 ⎞ ⎞ VERB ijassa-1224 168 30 𝐹𝑉 𝐹𝑉 PROPN ijassa-1224 168 31 = = SYM ijassa-1224 168 32 ⎝ ⎝ X ijassa-1224 168 33 ⎜ ⎜ PROPN ijassa-1224 168 34 βŽ› βŽ› NOUN ijassa-1224 168 35 π›½πœ€ π›½πœ€ ADP ijassa-1224 168 36 𝜎π‘₯(1 𝜎π‘₯(1 PROPN ijassa-1224 168 37 βˆ’ βˆ’ PROPN ijassa-1224 168 38 𝜌 𝜌 X ijassa-1224 168 39 ) ) PUNCT ijassa-1224 168 40 𝑄 𝑄 PROPN ijassa-1224 168 41 𝑄 𝑄 PROPN ijassa-1224 168 42 + + CCONJ ijassa-1224 168 43 𝛽π‘₯𝜎[(1 𝛽π‘₯𝜎[(1 PROPN ijassa-1224 168 44 βˆ’ βˆ’ PROPN ijassa-1224 168 45 𝜌)𝛾 𝜌)𝛾 PUNCT ijassa-1224 168 46 + + PUNCT ijassa-1224 168 47 πœŒπ‘„ πœŒπ‘„ PROPN ijassa-1224 168 48 ] ] PUNCT ijassa-1224 168 49 𝑄 𝑄 PROPN ijassa-1224 168 50 𝑄 𝑄 NOUN ijassa-1224 168 51 𝑄 𝑄 PRON ijassa-1224 169 1 + + CCONJ ijassa-1224 169 2 π›½πœ€ π›½πœ€ ADP ijassa-1224 169 3 π‘₯π‘Ÿ π‘₯π‘Ÿ X ijassa-1224 169 4 𝜎[(1 𝜎[(1 INTJ ijassa-1224 169 5 βˆ’ βˆ’ PROPN ijassa-1224 169 6 𝜌)𝛾 𝜌)𝛾 X ijassa-1224 170 1 + + PUNCT ijassa-1224 170 2 πœŒπ‘„ πœŒπ‘„ PROPN ijassa-1224 170 3 ] ] PUNCT ijassa-1224 170 4 𝑄 𝑄 PROPN ijassa-1224 170 5 𝑄 𝑄 NOUN ijassa-1224 170 6 𝑄 𝑄 PRON ijassa-1224 170 7 𝑄 𝑄 PRON ijassa-1224 170 8 π›½πœ€ π›½πœ€ ADP ijassa-1224 170 9 π‘₯ π‘₯ DET ijassa-1224 170 10 𝑄 𝑄 PROPN ijassa-1224 171 1 + + CCONJ ijassa-1224 171 2 𝛽π‘₯𝛾 𝛽π‘₯𝛾 NOUN ijassa-1224 171 3 𝑄 𝑄 PROPN ijassa-1224 171 4 𝑄 𝑄 PRON ijassa-1224 172 1 + + CCONJ ijassa-1224 172 2 π›½πœ€ π›½πœ€ ADP ijassa-1224 172 3 π‘₯π‘Ÿ π‘₯π‘Ÿ NOUN ijassa-1224 172 4 𝛾 𝛾 ADP ijassa-1224 172 5 𝑄 𝑄 PRON ijassa-1224 172 6 𝑄 𝑄 PROPN ijassa-1224 172 7 𝑄 𝑄 PROPN ijassa-1224 172 8 𝛽π‘₯ 𝛽π‘₯ VERB ijassa-1224 172 9 𝑄 𝑄 PRON ijassa-1224 172 10 + + CCONJ ijassa-1224 172 11 π›½πœ€ π›½πœ€ ADP ijassa-1224 172 12 π‘₯π‘Ÿ π‘₯π‘Ÿ NOUN ijassa-1224 172 13 𝑄 𝑄 PRON ijassa-1224 173 1 𝑄 𝑄 PRON ijassa-1224 173 2 π›½πœ€ π›½πœ€ ADP ijassa-1224 173 3 π‘₯ π‘₯ PRON ijassa-1224 173 4 𝑄 𝑄 ADV ijassa-1224 173 5 0 0 NUM ijassa-1224 173 6 0 0 NUM ijassa-1224 173 7 0 0 NUM ijassa-1224 173 8 0 0 NUM ijassa-1224 173 9 0 0 NUM ijassa-1224 173 10 0 0 NUM ijassa-1224 173 11 0 0 NUM ijassa-1224 173 12 0 0 NUM ijassa-1224 173 13 0 0 NUM ijassa-1224 173 14 0 0 NUM ijassa-1224 173 15 0 0 NUM ijassa-1224 173 16 0 0 NUM ijassa-1224 173 17 ⎠ ⎠ NOUN ijassa-1224 173 18 ⎟ ⎟ X ijassa-1224 173 19 ⎞ ⎞ NOUN ijassa-1224 173 20 , , PUNCT ijassa-1224 173 21 ( ( PUNCT ijassa-1224 173 22 22 22 NUM ijassa-1224 173 23 ) ) PUNCT ijassa-1224 173 24 where where SCONJ ijassa-1224 173 25 π‘₯ π‘₯ NOUN ijassa-1224 173 26 = = PRON ijassa-1224 173 27 ( ( PUNCT ijassa-1224 173 28 ) ) PUNCT ijassa-1224 173 29 ( ( PUNCT ijassa-1224 173 30 ) ) PUNCT ijassa-1224 173 31 . . PUNCT ijassa-1224 174 1 from from ADP ijassa-1224 174 2 ( ( PUNCT ijassa-1224 174 3 22 22 NUM ijassa-1224 174 4 ) ) PUNCT ijassa-1224 174 5 , , PUNCT ijassa-1224 174 6 we we PRON ijassa-1224 174 7 calculate calculate VERB ijassa-1224 174 8 the the DET ijassa-1224 174 9 eigen eigen NOUN ijassa-1224 174 10 - - PUNCT ijassa-1224 174 11 values value NOUN ijassa-1224 174 12 to to PART ijassa-1224 174 13 determine determine VERB ijassa-1224 174 14 the the DET ijassa-1224 174 15 basic basic ADJ ijassa-1224 174 16 reproduction reproduction NOUN ijassa-1224 174 17 number number NOUN ijassa-1224 174 18 , , PUNCT ijassa-1224 174 19 𝑅 𝑅 NOUN ijassa-1224 174 20 by by ADP ijassa-1224 174 21 taking take VERB ijassa-1224 174 22 the the DET ijassa-1224 174 23 spectral spectral ADJ ijassa-1224 174 24 radius radius NOUN ijassa-1224 174 25 ( ( PUNCT ijassa-1224 174 26 dominant dominant PROPN ijassa-1224 174 27 eigenvalue eigenvalue NOUN ijassa-1224 174 28 ) ) PUNCT ijassa-1224 174 29 of of ADP ijassa-1224 174 30 the the DET ijassa-1224 174 31 matrix matrix NOUN ijassa-1224 174 32 𝐹𝑉 𝐹𝑉 PROPN ijassa-1224 174 33 , , PUNCT ijassa-1224 174 34 this this PRON ijassa-1224 174 35 is be AUX ijassa-1224 174 36 computed compute VERB ijassa-1224 174 37 by by ADP ijassa-1224 174 38 |𝐽 |𝐽 PROPN ijassa-1224 175 1 βˆ’ βˆ’ PROPN ijassa-1224 175 2 πœ†πΌ| πœ†πΌ| SYM ijassa-1224 175 3 = = SYM ijassa-1224 175 4 0 0 NUM ijassa-1224 175 5 , , PUNCT ijassa-1224 175 6 hence hence ADV ijassa-1224 175 7 the the DET ijassa-1224 175 8 matrix matrix NOUN ijassa-1224 175 9 becomes become VERB ijassa-1224 175 10 |𝐽 |𝐽 PROPN ijassa-1224 176 1 βˆ’ βˆ’ PROPN ijassa-1224 176 2 πœ†πΌ| πœ†πΌ| NUM ijassa-1224 176 3 = = SYM ijassa-1224 176 4 𝑇 𝑇 PROPN ijassa-1224 176 5 βˆ’ βˆ’ PROPN ijassa-1224 176 6 πœ† πœ† DET ijassa-1224 176 7 𝑇 𝑇 PROPN ijassa-1224 176 8 𝑇 𝑇 PROPN ijassa-1224 176 9 𝑇 𝑇 PROPN ijassa-1224 176 10 0 0 NUM ijassa-1224 176 11 βˆ’πœ† βˆ’πœ† NOUN ijassa-1224 176 12 0 0 NUM ijassa-1224 176 13 0 0 NUM ijassa-1224 176 14 0 0 NUM ijassa-1224 176 15 0 0 NUM ijassa-1224 177 1 βˆ’πœ† βˆ’πœ† NOUN ijassa-1224 177 2 0 0 NUM ijassa-1224 177 3 0 0 NUM ijassa-1224 177 4 0 0 NUM ijassa-1224 177 5 0 0 NUM ijassa-1224 177 6 βˆ’πœ† βˆ’πœ† NOUN ijassa-1224 178 1 = = NOUN ijassa-1224 178 2 0 0 NUM ijassa-1224 178 3 where where SCONJ ijassa-1224 178 4 𝑇 𝑇 PROPN ijassa-1224 178 5 = = PRON ijassa-1224 178 6 π›½πœ€ π›½πœ€ ADP ijassa-1224 178 7 𝜎π‘₯(1 𝜎π‘₯(1 PROPN ijassa-1224 178 8 βˆ’ βˆ’ PROPN ijassa-1224 178 9 𝜌 𝜌 X ijassa-1224 178 10 ) ) PUNCT ijassa-1224 178 11 𝑄 𝑄 PROPN ijassa-1224 178 12 𝑄 𝑄 PROPN ijassa-1224 178 13 + + CCONJ ijassa-1224 178 14 𝛽π‘₯𝜎[(1 𝛽π‘₯𝜎[(1 PROPN ijassa-1224 178 15 βˆ’ βˆ’ PROPN ijassa-1224 178 16 𝜌)𝛾 𝜌)𝛾 PUNCT ijassa-1224 179 1 + + PUNCT ijassa-1224 179 2 πœŒπ‘„ πœŒπ‘„ PROPN ijassa-1224 179 3 ] ] PUNCT ijassa-1224 179 4 𝑄 𝑄 PROPN ijassa-1224 179 5 𝑄 𝑄 PROPN ijassa-1224 179 6 𝑄 𝑄 PRON ijassa-1224 180 1 + + CCONJ ijassa-1224 180 2 𝛽π‘₯πœ€ 𝛽π‘₯πœ€ VERB ijassa-1224 180 3 π‘Ÿ π‘Ÿ X ijassa-1224 180 4 𝜎[(1 𝜎[(1 ADJ ijassa-1224 180 5 βˆ’ βˆ’ PROPN ijassa-1224 180 6 𝜌)𝛾 𝜌)𝛾 X ijassa-1224 181 1 + + PUNCT ijassa-1224 181 2 πœŒπ‘„ πœŒπ‘„ PROPN ijassa-1224 181 3 ] ] PUNCT ijassa-1224 181 4 𝑄 𝑄 PROPN ijassa-1224 181 5 𝑄 𝑄 NOUN ijassa-1224 181 6 𝑄 𝑄 NOUN ijassa-1224 181 7 𝑄 𝑄 NOUN ijassa-1224 181 8 𝑇 𝑇 NOUN ijassa-1224 181 9 = = PUNCT ijassa-1224 181 10 π›½πœ€ π›½πœ€ ADP ijassa-1224 181 11 π‘₯ π‘₯ DET ijassa-1224 181 12 𝑄 𝑄 PROPN ijassa-1224 182 1 + + CCONJ ijassa-1224 182 2 𝛽π‘₯𝛾 𝛽π‘₯𝛾 NOUN ijassa-1224 182 3 𝑄 𝑄 PROPN ijassa-1224 182 4 𝑄 𝑄 PRON ijassa-1224 183 1 + + CCONJ ijassa-1224 183 2 π›½πœ€ π›½πœ€ ADP ijassa-1224 183 3 π‘₯π‘Ÿ π‘₯π‘Ÿ NOUN ijassa-1224 183 4 𝛾 𝛾 ADP ijassa-1224 183 5 𝑄 𝑄 NOUN ijassa-1224 183 6 𝑄 𝑄 PROPN ijassa-1224 183 7 𝑄 𝑄 PROPN ijassa-1224 183 8 , , PUNCT ijassa-1224 183 9 𝑇 𝑇 PROPN ijassa-1224 183 10 = = SYM ijassa-1224 183 11 𝛽π‘₯ 𝛽π‘₯ PROPN ijassa-1224 183 12 𝑄 𝑄 PROPN ijassa-1224 183 13 + + CCONJ ijassa-1224 183 14 π›½πœ€ π›½πœ€ ADP ijassa-1224 183 15 π‘₯π‘Ÿ π‘₯π‘Ÿ NOUN ijassa-1224 183 16 𝑄 𝑄 PROPN ijassa-1224 183 17 𝑄 𝑄 PROPN ijassa-1224 183 18 , , PUNCT ijassa-1224 183 19 𝑇 𝑇 PROPN ijassa-1224 183 20 = = SYM ijassa-1224 183 21 π›½πœ€ π›½πœ€ ADP ijassa-1224 183 22 π‘₯ π‘₯ DET ijassa-1224 183 23 𝑄 𝑄 PROPN ijassa-1224 183 24 and and CCONJ ijassa-1224 184 1 152 152 NUM ijassa-1224 184 2 f.a f.a PROPN ijassa-1224 184 3 . . PROPN ijassa-1224 185 1 oguntolu oguntolu PROPN ijassa-1224 185 2 , , PUNCT ijassa-1224 185 3 o.j o.j PROPN ijassa-1224 185 4 . . PROPN ijassa-1224 185 5 peter peter PROPN ijassa-1224 185 6 , , PUNCT ijassa-1224 185 7 k. k. PROPN ijassa-1224 185 8 oshinubi oshinubi PROPN ijassa-1224 185 9 , , PUNCT ijassa-1224 185 10 t.a t.a PROPN ijassa-1224 185 11 . . PROPN ijassa-1224 185 12 ayoola ayoola PROPN ijassa-1224 185 13 , , PUNCT ijassa-1224 185 14 a.o a.o PROPN ijassa-1224 185 15 . . PROPN ijassa-1224 185 16 oladapo oladapo PROPN ijassa-1224 185 17 , , PUNCT ijassa-1224 185 18 m.m m.m PROPN ijassa-1224 185 19 . . PROPN ijassa-1224 185 20 ojo ojo NOUN ijassa-1224 185 21 copyright copyright NOUN ijassa-1224 185 22 Β© Β© PROPN ijassa-1224 185 23 2022 2022 NUM ijassa-1224 185 24 assa assa PROPN ijassa-1224 185 25 adv adv PROPN ijassa-1224 185 26 . . PUNCT ijassa-1224 186 1 in in ADP ijassa-1224 186 2 systems system NOUN ijassa-1224 186 3 science science NOUN ijassa-1224 186 4 and and CCONJ ijassa-1224 186 5 appl appl NOUN ijassa-1224 186 6 . . PUNCT ijassa-1224 187 1 ( ( PUNCT ijassa-1224 187 2 2022 2022 NUM ijassa-1224 187 3 ) ) PUNCT ijassa-1224 187 4 π‘₯ π‘₯ NOUN ijassa-1224 188 1 = = PUNCT ijassa-1224 188 2 πœ‹(πœ‡ πœ‹(πœ‡ PROPN ijassa-1224 188 3 + + CCONJ ijassa-1224 188 4 πœ” πœ” PRON ijassa-1224 188 5 βˆ’ βˆ’ NOUN ijassa-1224 188 6 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 188 7 ) ) PUNCT ijassa-1224 188 8 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 189 1 + + CCONJ ijassa-1224 189 2 πœ” πœ” X ijassa-1224 189 3 ) ) PUNCT ijassa-1224 189 4 . . PUNCT ijassa-1224 190 1 this this PRON ijassa-1224 190 2 implies imply VERB ijassa-1224 190 3 that that SCONJ ijassa-1224 190 4 πœ† πœ† ADP ijassa-1224 190 5 = = SYM ijassa-1224 190 6 𝑇 𝑇 PROPN ijassa-1224 190 7 = = SYM ijassa-1224 190 8 π›½πœ€ π›½πœ€ ADP ijassa-1224 190 9 𝜎π‘₯(1 𝜎π‘₯(1 PROPN ijassa-1224 190 10 βˆ’ βˆ’ PROPN ijassa-1224 190 11 𝜌 𝜌 X ijassa-1224 190 12 ) ) PUNCT ijassa-1224 190 13 𝑄 𝑄 PROPN ijassa-1224 190 14 𝑄 𝑄 PROPN ijassa-1224 190 15 + + CCONJ ijassa-1224 190 16 𝛽π‘₯𝜎[(1 𝛽π‘₯𝜎[(1 PROPN ijassa-1224 190 17 βˆ’ βˆ’ PROPN ijassa-1224 190 18 𝜌)𝛾 𝜌)𝛾 PUNCT ijassa-1224 190 19 + + PUNCT ijassa-1224 190 20 πœŒπ‘„ πœŒπ‘„ PROPN ijassa-1224 190 21 ] ] PUNCT ijassa-1224 190 22 𝑄 𝑄 PROPN ijassa-1224 190 23 𝑄 𝑄 NOUN ijassa-1224 190 24 𝑄 𝑄 PRON ijassa-1224 190 25 + + CCONJ ijassa-1224 190 26 π›½πœ€ π›½πœ€ ADP ijassa-1224 190 27 π‘₯π‘Ÿ π‘₯π‘Ÿ X ijassa-1224 190 28 𝜎[(1 𝜎[(1 INTJ ijassa-1224 190 29 βˆ’ βˆ’ PROPN ijassa-1224 190 30 𝜌)𝛾 𝜌)𝛾 X ijassa-1224 190 31 + + PUNCT ijassa-1224 190 32 πœŒπ‘„ πœŒπ‘„ PROPN ijassa-1224 190 33 ] ] PUNCT ijassa-1224 190 34 𝑄 𝑄 PROPN ijassa-1224 190 35 𝑄 𝑄 NOUN ijassa-1224 190 36 𝑄 𝑄 NOUN ijassa-1224 190 37 𝑄 𝑄 PRON ijassa-1224 190 38 πœ† πœ† NOUN ijassa-1224 190 39 = = SYM ijassa-1224 190 40 0 0 NUM ijassa-1224 190 41 , , PUNCT ijassa-1224 190 42 πœ† πœ† NOUN ijassa-1224 190 43 = = SYM ijassa-1224 190 44 0 0 NUM ijassa-1224 190 45 , , PUNCT ijassa-1224 190 46 πœ† πœ† NOUN ijassa-1224 190 47 = = SYM ijassa-1224 190 48 0 0 X ijassa-1224 190 49 . . PUNCT ijassa-1224 190 50 therefore therefore ADV ijassa-1224 190 51 𝑅 𝑅 PROPN ijassa-1224 190 52 = = PROPN ijassa-1224 190 53 π›½πœŽπ‘₯[(1 π›½πœŽπ‘₯[(1 PROPN ijassa-1224 190 54 βˆ’ βˆ’ PROPN ijassa-1224 190 55 𝜌)(πœ€ 𝜌)(πœ€ PUNCT ijassa-1224 190 56 𝑄 𝑄 PROPN ijassa-1224 190 57 + + CCONJ ijassa-1224 190 58 𝛾 𝛾 NOUN ijassa-1224 190 59 ) ) PUNCT ijassa-1224 191 1 + + CCONJ ijassa-1224 191 2 πœŒπ‘„ πœŒπ‘„ NOUN ijassa-1224 191 3 ] ] PUNCT ijassa-1224 191 4 𝑄 𝑄 PROPN ijassa-1224 191 5 𝑄 𝑄 NOUN ijassa-1224 191 6 𝑄 𝑄 PRON ijassa-1224 191 7 + + CCONJ ijassa-1224 191 8 π›½πœ€ π›½πœ€ ADP ijassa-1224 191 9 π‘₯π‘Ÿ π‘₯π‘Ÿ X ijassa-1224 191 10 𝜎[(1 𝜎[(1 INTJ ijassa-1224 191 11 βˆ’ βˆ’ PROPN ijassa-1224 191 12 𝜌)𝛾 𝜌)𝛾 X ijassa-1224 191 13 + + PUNCT ijassa-1224 191 14 πœŒπ‘„ πœŒπ‘„ PROPN ijassa-1224 191 15 ] ] PUNCT ijassa-1224 191 16 𝑄 𝑄 PROPN ijassa-1224 191 17 𝑄 𝑄 NOUN ijassa-1224 191 18 𝑄 𝑄 NOUN ijassa-1224 191 19 𝑄 𝑄 NOUN ijassa-1224 191 20 = = PUNCT ijassa-1224 191 21 π›½πœŽπœ‹(πœ‡ π›½πœŽπœ‹(πœ‡ PROPN ijassa-1224 191 22 + + CCONJ ijassa-1224 191 23 πœ” πœ” X ijassa-1224 191 24 βˆ’ βˆ’ NOUN ijassa-1224 191 25 πœ‡πœƒ)([(1 πœ‡πœƒ)([(1 PRON ijassa-1224 191 26 βˆ’ βˆ’ NOUN ijassa-1224 191 27 𝜌)(πœ€ 𝜌)(πœ€ PUNCT ijassa-1224 191 28 𝑄 𝑄 PROPN ijassa-1224 191 29 + + CCONJ ijassa-1224 191 30 𝛾 𝛾 NOUN ijassa-1224 191 31 ) ) PUNCT ijassa-1224 192 1 + + CCONJ ijassa-1224 192 2 πœŒπ‘„ πœŒπ‘„ NOUN ijassa-1224 192 3 ] ] X ijassa-1224 192 4 𝑄 𝑄 PROPN ijassa-1224 192 5 + + NOUN ijassa-1224 192 6 πœ€ πœ€ X ijassa-1224 192 7 π‘Ÿ π‘Ÿ X ijassa-1224 192 8 [ [ X ijassa-1224 192 9 ( ( PUNCT ijassa-1224 192 10 1 1 NUM ijassa-1224 192 11 βˆ’ βˆ’ NOUN ijassa-1224 192 12 𝜌)𝛾 𝜌)𝛾 NOUN ijassa-1224 192 13 + + CCONJ ijassa-1224 192 14 πœŒπ‘„ πœŒπ‘„ NOUN ijassa-1224 192 15 ] ] PUNCT ijassa-1224 192 16 ) ) PUNCT ijassa-1224 192 17 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 193 1 + + CCONJ ijassa-1224 193 2 πœ”)(πœ‡ πœ”)(πœ‡ PUNCT ijassa-1224 194 1 + + CCONJ ijassa-1224 194 2 𝜎)𝑄 𝜎)𝑄 ADJ ijassa-1224 194 3 𝑄 𝑄 NOUN ijassa-1224 194 4 𝑄 𝑄 PROPN ijassa-1224 194 5 where where SCONJ ijassa-1224 194 6 𝑄 𝑄 PROPN ijassa-1224 194 7 = = SYM ijassa-1224 194 8 𝛾 𝛾 PART ijassa-1224 194 9 + + X ijassa-1224 194 10 πœ‡ πœ‡ X ijassa-1224 194 11 + + NOUN ijassa-1224 194 12 π‘Ÿ π‘Ÿ NOUN ijassa-1224 194 13 + + CCONJ ijassa-1224 194 14 𝑑 𝑑 NOUN ijassa-1224 194 15 , , PUNCT ijassa-1224 194 16 𝑄 𝑄 PROPN ijassa-1224 194 17 = = PUNCT ijassa-1224 194 18 π‘Ÿ π‘Ÿ NOUN ijassa-1224 194 19 + + SYM ijassa-1224 194 20 π‘Ÿ π‘Ÿ NOUN ijassa-1224 194 21 + + CCONJ ijassa-1224 194 22 𝑑 𝑑 PROPN ijassa-1224 194 23 + + X ijassa-1224 194 24 πœ‡ πœ‡ ADP ijassa-1224 194 25 , , PUNCT ijassa-1224 194 26 𝑄 𝑄 PROPN ijassa-1224 194 27 = = PUNCT ijassa-1224 194 28 𝑑 𝑑 PROPN ijassa-1224 194 29 + + NOUN ijassa-1224 194 30 π‘Ÿ π‘Ÿ NOUN ijassa-1224 194 31 + + CCONJ ijassa-1224 194 32 πœ‡. πœ‡. NOUN ijassa-1224 194 33 2.8 2.8 NUM ijassa-1224 194 34 . . PUNCT ijassa-1224 195 1 local local ADJ ijassa-1224 195 2 stability stability NOUN ijassa-1224 195 3 of of ADP ijassa-1224 195 4 disease disease NOUN ijassa-1224 195 5 - - PUNCT ijassa-1224 195 6 free free ADJ ijassa-1224 195 7 equilibrium equilibrium NOUN ijassa-1224 195 8 theorem theorem VERB ijassa-1224 195 9 3 3 NUM ijassa-1224 195 10 : : PUNCT ijassa-1224 195 11 the the DET ijassa-1224 195 12 disease disease NOUN ijassa-1224 195 13 equilibrium equilibrium NOUN ijassa-1224 195 14 of of ADP ijassa-1224 195 15 the the DET ijassa-1224 195 16 model model NOUN ijassa-1224 195 17 equations equation NOUN ijassa-1224 195 18 ( ( PUNCT ijassa-1224 195 19 1)–(7 1)–(7 NUM ijassa-1224 195 20 ) ) PUNCT ijassa-1224 195 21 is be AUX ijassa-1224 195 22 locally locally ADV ijassa-1224 195 23 asymptotically asymptotically ADV ijassa-1224 195 24 stable stable ADJ ijassa-1224 195 25 ( ( PUNCT ijassa-1224 195 26 las las NOUN ijassa-1224 195 27 ) ) PUNCT ijassa-1224 195 28 if if SCONJ ijassa-1224 195 29 𝑅 𝑅 PROPN ijassa-1224 195 30 < < X ijassa-1224 195 31 1 1 NUM ijassa-1224 195 32 . . PUNCT ijassa-1224 195 33 proof proof NOUN ijassa-1224 195 34 . . PUNCT ijassa-1224 196 1 using use VERB ijassa-1224 196 2 jacobian jacobian ADJ ijassa-1224 196 3 stability stability NOUN ijassa-1224 196 4 techniques technique NOUN ijassa-1224 196 5 , , PUNCT ijassa-1224 196 6 the the DET ijassa-1224 196 7 jacobian jacobian ADJ ijassa-1224 196 8 matrix matrix NOUN ijassa-1224 196 9 at at ADP ijassa-1224 196 10 d.f.e d.f.e NOUN ijassa-1224 196 11 is be AUX ijassa-1224 196 12 given give VERB ijassa-1224 196 13 by by ADP ijassa-1224 196 14 : : PUNCT ijassa-1224 196 15 𝐽(𝐸 𝐽(𝐸 ADJ ijassa-1224 196 16 ) ) PUNCT ijassa-1224 196 17 = = SYM ijassa-1224 197 1 ⎝ ⎝ PROPN ijassa-1224 197 2 ⎜ ⎜ PROPN ijassa-1224 197 3 ⎜ ⎜ PROPN ijassa-1224 197 4 ⎜ ⎜ PROPN ijassa-1224 197 5 ⎜ ⎜ PROPN ijassa-1224 197 6 ⎜ ⎜ PROPN ijassa-1224 197 7 βŽ› βŽ› NOUN ijassa-1224 197 8 βˆ’(πœ‡ βˆ’(πœ‡ NOUN ijassa-1224 197 9 + + CCONJ ijassa-1224 197 10 πœ” πœ” X ijassa-1224 197 11 ) ) PUNCT ijassa-1224 197 12 0 0 NUM ijassa-1224 197 13 0 0 NUM ijassa-1224 197 14 0 0 NUM ijassa-1224 197 15 0 0 NUM ijassa-1224 197 16 0 0 NUM ijassa-1224 197 17 0 0 NUM ijassa-1224 197 18 πœ” πœ” PRON ijassa-1224 197 19 βˆ’πœ‡ βˆ’πœ‡ VERB ijassa-1224 197 20 0 0 NUM ijassa-1224 197 21 0 0 NUM ijassa-1224 197 22 0 0 NUM ijassa-1224 197 23 0 0 NUM ijassa-1224 197 24 0 0 NUM ijassa-1224 197 25 0 0 NUM ijassa-1224 197 26 0 0 NUM ijassa-1224 197 27 βˆ’(πœ‡ βˆ’(πœ‡ NOUN ijassa-1224 197 28 + + CCONJ ijassa-1224 197 29 𝜎 𝜎 X ijassa-1224 197 30 ) ) PUNCT ijassa-1224 197 31 π›½πœ€ π›½πœ€ ADP ijassa-1224 197 32 πœ‹(πœ‡ πœ‹(πœ‡ PROPN ijassa-1224 197 33 + + CCONJ ijassa-1224 197 34 πœ” πœ” PRON ijassa-1224 197 35 βˆ’ βˆ’ NOUN ijassa-1224 197 36 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 197 37 ) ) PUNCT ijassa-1224 197 38 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 198 1 + + CCONJ ijassa-1224 198 2 πœ” πœ” X ijassa-1224 198 3 ) ) PUNCT ijassa-1224 198 4 π›½πœ€ π›½πœ€ ADP ijassa-1224 198 5 πœ‹(πœ‡ πœ‹(πœ‡ PROPN ijassa-1224 198 6 + + CCONJ ijassa-1224 198 7 πœ” πœ” PRON ijassa-1224 198 8 βˆ’ βˆ’ NOUN ijassa-1224 198 9 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 198 10 ) ) PUNCT ijassa-1224 198 11 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 199 1 + + CCONJ ijassa-1224 199 2 πœ” πœ” X ijassa-1224 199 3 ) ) PUNCT ijassa-1224 199 4 π›½πœ€ π›½πœ€ ADP ijassa-1224 199 5 πœ‹(πœ‡ πœ‹(πœ‡ PROPN ijassa-1224 199 6 + + CCONJ ijassa-1224 199 7 πœ” πœ” PRON ijassa-1224 199 8 βˆ’ βˆ’ NOUN ijassa-1224 199 9 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 199 10 ) ) PUNCT ijassa-1224 199 11 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 200 1 + + CCONJ ijassa-1224 200 2 πœ” πœ” X ijassa-1224 200 3 ) ) PUNCT ijassa-1224 200 4 0 0 NUM ijassa-1224 201 1 0 0 NUM ijassa-1224 201 2 0 0 NUM ijassa-1224 201 3 ( ( PUNCT ijassa-1224 201 4 1 1 NUM ijassa-1224 201 5 βˆ’ βˆ’ NOUN ijassa-1224 201 6 𝜌)𝜎 𝜌)𝜎 ADJ ijassa-1224 201 7 βˆ’(𝛾 βˆ’(𝛾 NOUN ijassa-1224 201 8 + + X ijassa-1224 201 9 πœ‡ πœ‡ ADP ijassa-1224 201 10 + + X ijassa-1224 201 11 𝑑 𝑑 PROPN ijassa-1224 201 12 + + NUM ijassa-1224 201 13 π‘Ÿ π‘Ÿ NOUN ijassa-1224 201 14 ) ) PUNCT ijassa-1224 201 15 0 0 NUM ijassa-1224 202 1 0 0 NUM ijassa-1224 202 2 0 0 NUM ijassa-1224 202 3 0 0 NUM ijassa-1224 202 4 0 0 NUM ijassa-1224 202 5 𝜌𝜎 𝜌𝜎 NOUN ijassa-1224 202 6 𝛾 𝛾 ADP ijassa-1224 202 7 βˆ’(π‘Ÿ βˆ’(π‘Ÿ NOUN ijassa-1224 203 1 + + CCONJ ijassa-1224 203 2 π‘Ÿ π‘Ÿ NOUN ijassa-1224 203 3 + + CCONJ ijassa-1224 203 4 πœ‡ πœ‡ ADP ijassa-1224 203 5 + + X ijassa-1224 203 6 𝑑 𝑑 NOUN ijassa-1224 203 7 ) ) PUNCT ijassa-1224 203 8 0 0 NUM ijassa-1224 203 9 0 0 NUM ijassa-1224 203 10 0 0 NUM ijassa-1224 203 11 0 0 NUM ijassa-1224 203 12 0 0 NUM ijassa-1224 203 13 0 0 NUM ijassa-1224 204 1 π‘Ÿ π‘Ÿ NOUN ijassa-1224 204 2 βˆ’(πœ‡ βˆ’(πœ‡ ADJ ijassa-1224 204 3 + + CCONJ ijassa-1224 204 4 𝑑 𝑑 PROPN ijassa-1224 204 5 + + NUM ijassa-1224 204 6 π‘Ÿ π‘Ÿ NOUN ijassa-1224 204 7 ) ) PUNCT ijassa-1224 204 8 0 0 NUM ijassa-1224 205 1 0 0 NUM ijassa-1224 205 2 0 0 NUM ijassa-1224 205 3 0 0 NUM ijassa-1224 205 4 π‘Ÿ π‘Ÿ NOUN ijassa-1224 205 5 π‘Ÿ π‘Ÿ NOUN ijassa-1224 205 6 π‘Ÿ π‘Ÿ X ijassa-1224 205 7 βˆ’πœ‡βŽ  βˆ’πœ‡βŽ  X ijassa-1224 205 8 ⎟ ⎟ PROPN ijassa-1224 205 9 ⎟ ⎟ X ijassa-1224 205 10 ⎟ ⎟ X ijassa-1224 205 11 ⎟ ⎟ X ijassa-1224 205 12 ⎟ ⎟ PROPN ijassa-1224 205 13 ⎞ ⎞ VERB ijassa-1224 205 14 . . PUNCT ijassa-1224 206 1 let let VERB ijassa-1224 206 2 𝑄 𝑄 PRON ijassa-1224 206 3 = = SYM ijassa-1224 206 4 ( ( PUNCT ijassa-1224 206 5 πœ‡ πœ‡ X ijassa-1224 206 6 + + X ijassa-1224 206 7 𝜎 𝜎 X ijassa-1224 206 8 ) ) PUNCT ijassa-1224 206 9 , , PUNCT ijassa-1224 206 10 𝑄 𝑄 PROPN ijassa-1224 206 11 = = PUNCT ijassa-1224 206 12 ( ( PUNCT ijassa-1224 206 13 𝛾 𝛾 NOUN ijassa-1224 206 14 + + X ijassa-1224 206 15 πœ‡ πœ‡ ADP ijassa-1224 206 16 + + X ijassa-1224 206 17 𝑑 𝑑 PROPN ijassa-1224 206 18 + + ADJ ijassa-1224 206 19 π‘Ÿ π‘Ÿ NOUN ijassa-1224 206 20 ) ) PUNCT ijassa-1224 206 21 , , PUNCT ijassa-1224 207 1 𝑄 𝑄 PROPN ijassa-1224 207 2 = = PUNCT ijassa-1224 207 3 βˆ’(π‘Ÿ βˆ’(π‘Ÿ NOUN ijassa-1224 207 4 + + CCONJ ijassa-1224 207 5 π‘Ÿ π‘Ÿ NOUN ijassa-1224 208 1 + + X ijassa-1224 208 2 πœ‡ πœ‡ ADP ijassa-1224 208 3 + + X ijassa-1224 208 4 𝑑 𝑑 NOUN ijassa-1224 208 5 ) ) PUNCT ijassa-1224 208 6 , , PUNCT ijassa-1224 208 7 𝑄 𝑄 PROPN ijassa-1224 208 8 = = SYM ijassa-1224 208 9 ( ( PUNCT ijassa-1224 208 10 πœ‡ πœ‡ X ijassa-1224 208 11 + + X ijassa-1224 208 12 𝑑 𝑑 PROPN ijassa-1224 208 13 + + ADJ ijassa-1224 208 14 π‘Ÿ π‘Ÿ NOUN ijassa-1224 208 15 ) ) PUNCT ijassa-1224 208 16 , , PUNCT ijassa-1224 208 17 𝑄 𝑄 PROPN ijassa-1224 208 18 = = SYM ijassa-1224 208 19 ( ( PUNCT ijassa-1224 208 20 πœ‡ πœ‡ X ijassa-1224 208 21 + + NOUN ijassa-1224 208 22 πœ” πœ” NOUN ijassa-1224 208 23 ) ) PUNCT ijassa-1224 208 24 , , PUNCT ijassa-1224 208 25 𝐡 𝐡 NOUN ijassa-1224 208 26 = = SYM ijassa-1224 208 27 ( ( PUNCT ijassa-1224 208 28 ) ) PUNCT ijassa-1224 208 29 ( ( PUNCT ijassa-1224 208 30 ) ) PUNCT ijassa-1224 208 31 , , PUNCT ijassa-1224 208 32 𝐡 𝐡 NOUN ijassa-1224 208 33 = = SYM ijassa-1224 208 34 ( ( PUNCT ijassa-1224 208 35 ) ) PUNCT ijassa-1224 208 36 ( ( PUNCT ijassa-1224 208 37 ) ) PUNCT ijassa-1224 208 38 , , PUNCT ijassa-1224 208 39 𝐡 𝐡 NOUN ijassa-1224 208 40 = = SYM ijassa-1224 208 41 ( ( PUNCT ijassa-1224 208 42 ) ) PUNCT ijassa-1224 208 43 ( ( PUNCT ijassa-1224 208 44 ) ) PUNCT ijassa-1224 208 45 , , PUNCT ijassa-1224 208 46 𝐢 𝐢 PROPN ijassa-1224 208 47 = = SYM ijassa-1224 208 48 ( ( PUNCT ijassa-1224 208 49 1 1 NUM ijassa-1224 208 50 βˆ’ βˆ’ NOUN ijassa-1224 208 51 𝜌)𝜎 𝜌)𝜎 ADJ ijassa-1224 208 52 ⎭ ⎭ PROPN ijassa-1224 208 53 βŽͺ βŽͺ NOUN ijassa-1224 208 54 βŽͺ βŽͺ NOUN ijassa-1224 208 55 βŽͺ βŽͺ NOUN ijassa-1224 208 56 βŽͺ βŽͺ NOUN ijassa-1224 208 57 ⎬ ⎬ PROPN ijassa-1224 208 58 βŽͺ βŽͺ NOUN ijassa-1224 208 59 βŽͺ βŽͺ NOUN ijassa-1224 208 60 βŽͺ βŽͺ NOUN ijassa-1224 208 61 βŽͺ βŽͺ NOUN ijassa-1224 208 62 ⎫ ⎫ PROPN ijassa-1224 208 63 , , PUNCT ijassa-1224 208 64 ( ( PUNCT ijassa-1224 208 65 23 23 X ijassa-1224 208 66 ) ) PUNCT ijassa-1224 208 67 analysis analysis NOUN ijassa-1224 208 68 and and CCONJ ijassa-1224 208 69 dynamics dynamic NOUN ijassa-1224 208 70 of of ADP ijassa-1224 208 71 tuberculosis tuberculosis NOUN ijassa-1224 208 72 outbreak outbreak NOUN ijassa-1224 208 73 153 153 NUM ijassa-1224 208 74 copyright copyright NOUN ijassa-1224 208 75 Β© Β© PROPN ijassa-1224 208 76 2022 2022 NUM ijassa-1224 208 77 assa assa NOUN ijassa-1224 208 78 . . PUNCT ijassa-1224 209 1 adv adv PROPN ijassa-1224 209 2 . . PUNCT ijassa-1224 210 1 in in ADP ijassa-1224 210 2 systems system NOUN ijassa-1224 210 3 science science NOUN ijassa-1224 210 4 and and CCONJ ijassa-1224 210 5 appl appl NOUN ijassa-1224 210 6 . . PUNCT ijassa-1224 211 1 ( ( PUNCT ijassa-1224 211 2 2022 2022 NUM ijassa-1224 211 3 ) ) PUNCT ijassa-1224 211 4 𝐽(𝐸 𝐽(𝐸 NOUN ijassa-1224 211 5 ) ) PUNCT ijassa-1224 212 1 = = SYM ijassa-1224 212 2 ⎝ ⎝ PROPN ijassa-1224 212 3 ⎜ ⎜ PROPN ijassa-1224 212 4 ⎜ ⎜ PROPN ijassa-1224 212 5 ⎜ ⎜ PROPN ijassa-1224 212 6 βŽ› βŽ› VERB ijassa-1224 212 7 βˆ’π‘„ βˆ’π‘„ NOUN ijassa-1224 212 8 0 0 NUM ijassa-1224 212 9 0 0 NUM ijassa-1224 212 10 0 0 NUM ijassa-1224 212 11 0 0 NUM ijassa-1224 212 12 0 0 NUM ijassa-1224 212 13 0 0 NUM ijassa-1224 212 14 πœ” πœ” PRON ijassa-1224 212 15 βˆ’πœ‡ βˆ’πœ‡ VERB ijassa-1224 212 16 0 0 NUM ijassa-1224 212 17 0 0 NUM ijassa-1224 212 18 0 0 NUM ijassa-1224 212 19 0 0 NUM ijassa-1224 212 20 0 0 NUM ijassa-1224 212 21 0 0 NUM ijassa-1224 212 22 0 0 NUM ijassa-1224 213 1 βˆ’π‘„ βˆ’π‘„ PROPN ijassa-1224 213 2 𝐡 𝐡 NOUN ijassa-1224 213 3 βˆ— βˆ— NOUN ijassa-1224 213 4 𝐡 𝐡 NOUN ijassa-1224 213 5 𝐡 𝐡 NOUN ijassa-1224 213 6 0 0 NUM ijassa-1224 213 7 0 0 NUM ijassa-1224 213 8 0 0 NUM ijassa-1224 213 9 𝐢 𝐢 PROPN ijassa-1224 213 10 𝑄 𝑄 PROPN ijassa-1224 213 11 0 0 NUM ijassa-1224 213 12 0 0 NUM ijassa-1224 213 13 0 0 NUM ijassa-1224 213 14 0 0 NUM ijassa-1224 213 15 0 0 NUM ijassa-1224 213 16 𝜌𝜎 𝜌𝜎 NOUN ijassa-1224 213 17 𝛾 𝛾 ADP ijassa-1224 213 18 βˆ’π‘„ βˆ’π‘„ PROPN ijassa-1224 213 19 0 0 NUM ijassa-1224 213 20 0 0 NUM ijassa-1224 213 21 0 0 NUM ijassa-1224 213 22 0 0 NUM ijassa-1224 213 23 0 0 NUM ijassa-1224 213 24 0 0 NUM ijassa-1224 214 1 π‘Ÿ π‘Ÿ NOUN ijassa-1224 215 1 βˆ’π‘„ βˆ’π‘„ ADP ijassa-1224 215 2 0 0 NUM ijassa-1224 215 3 0 0 NUM ijassa-1224 215 4 0 0 NUM ijassa-1224 215 5 0 0 NUM ijassa-1224 215 6 π‘Ÿ π‘Ÿ NOUN ijassa-1224 215 7 π‘Ÿ π‘Ÿ NOUN ijassa-1224 215 8 π‘Ÿ π‘Ÿ X ijassa-1224 215 9 βˆ’πœ‡βŽ  βˆ’πœ‡βŽ  X ijassa-1224 215 10 ⎟ ⎟ PROPN ijassa-1224 215 11 ⎟ ⎟ X ijassa-1224 215 12 ⎟ ⎟ PROPN ijassa-1224 215 13 ⎞ ⎞ VERB ijassa-1224 215 14 . . PUNCT ijassa-1224 216 1 then then ADV ijassa-1224 216 2 , , PUNCT ijassa-1224 216 3 |𝐽 |𝐽 PROPN ijassa-1224 216 4 βˆ’ βˆ’ PROPN ijassa-1224 216 5 πœ†πΌ| πœ†πΌ| NUM ijassa-1224 216 6 = = SYM ijassa-1224 216 7 ⎝ ⎝ PROPN ijassa-1224 216 8 ⎜ ⎜ PROPN ijassa-1224 216 9 ⎜ ⎜ PROPN ijassa-1224 216 10 ⎜ ⎜ PROPN ijassa-1224 216 11 βŽ› βŽ› NOUN ijassa-1224 216 12 βˆ’π‘„ βˆ’π‘„ NOUN ijassa-1224 216 13 βˆ’ βˆ’ NOUN ijassa-1224 216 14 πœ† πœ† ADV ijassa-1224 216 15 0 0 NUM ijassa-1224 216 16 0 0 NUM ijassa-1224 216 17 0 0 NUM ijassa-1224 216 18 0 0 NUM ijassa-1224 216 19 0 0 NUM ijassa-1224 216 20 0 0 NUM ijassa-1224 216 21 0 0 NUM ijassa-1224 217 1 βˆ’πœ‡π‘„ βˆ’πœ‡π‘„ NOUN ijassa-1224 217 2 βˆ’ βˆ’ NOUN ijassa-1224 217 3 πœ† πœ† ADP ijassa-1224 217 4 0 0 NUM ijassa-1224 217 5 0 0 NUM ijassa-1224 217 6 0 0 NUM ijassa-1224 217 7 0 0 NUM ijassa-1224 217 8 0 0 NUM ijassa-1224 217 9 0 0 NUM ijassa-1224 217 10 0 0 NUM ijassa-1224 218 1 βˆ’π‘„ βˆ’π‘„ NOUN ijassa-1224 218 2 βˆ’ βˆ’ NOUN ijassa-1224 218 3 πœ† πœ† DET ijassa-1224 218 4 𝐡 𝐡 NOUN ijassa-1224 218 5 𝐡 𝐡 NOUN ijassa-1224 218 6 𝐡 𝐡 NOUN ijassa-1224 218 7 0 0 NUM ijassa-1224 218 8 0 0 NUM ijassa-1224 218 9 0 0 NUM ijassa-1224 218 10 0 0 NUM ijassa-1224 219 1 𝑄 𝑄 NOUN ijassa-1224 219 2 βˆ’ βˆ’ PROPN ijassa-1224 219 3 πœ† πœ† DET ijassa-1224 219 4 𝐢 𝐢 PROPN ijassa-1224 219 5 𝐡 𝐡 PROPN ijassa-1224 219 6 𝐢 𝐢 PROPN ijassa-1224 219 7 𝐡 𝐡 PROPN ijassa-1224 219 8 0 0 NUM ijassa-1224 219 9 0 0 NUM ijassa-1224 219 10 0 0 NUM ijassa-1224 219 11 0 0 NUM ijassa-1224 219 12 0 0 NUM ijassa-1224 220 1 𝑄 𝑄 NOUN ijassa-1224 220 2 βˆ’ βˆ’ PROPN ijassa-1224 220 3 πœ† πœ† DET ijassa-1224 220 4 𝑄 𝑄 PROPN ijassa-1224 220 5 0 0 NUM ijassa-1224 220 6 0 0 NUM ijassa-1224 220 7 0 0 NUM ijassa-1224 220 8 0 0 NUM ijassa-1224 220 9 0 0 NUM ijassa-1224 220 10 0 0 NUM ijassa-1224 220 11 βˆ’π‘„ βˆ’π‘„ NOUN ijassa-1224 220 12 βˆ’ βˆ’ NOUN ijassa-1224 221 1 πœ† πœ† ADV ijassa-1224 221 2 0 0 NUM ijassa-1224 221 3 0 0 NUM ijassa-1224 221 4 0 0 NUM ijassa-1224 221 5 0 0 NUM ijassa-1224 221 6 0 0 NUM ijassa-1224 221 7 0 0 NUM ijassa-1224 221 8 0 0 NUM ijassa-1224 222 1 βˆ’π‘„ βˆ’π‘„ PROPN ijassa-1224 222 2 𝑄 𝑄 PROPN ijassa-1224 222 3 βˆ’ βˆ’ PROPN ijassa-1224 222 4 πœ†βŽ  πœ†βŽ  NOUN ijassa-1224 222 5 ⎟ ⎟ PROPN ijassa-1224 222 6 ⎟ ⎟ PROPN ijassa-1224 222 7 ⎟ ⎟ PROPN ijassa-1224 222 8 ⎞ ⎞ VERB ijassa-1224 222 9 and and CCONJ ijassa-1224 222 10 𝑄 𝑄 PROPN ijassa-1224 222 11 = = SYM ijassa-1224 222 12 𝐢 𝐢 PROPN ijassa-1224 222 13 𝐡 𝐡 NOUN ijassa-1224 222 14 βˆ’ βˆ’ NOUN ijassa-1224 222 15 𝑄 𝑄 PROPN ijassa-1224 222 16 𝑄 𝑄 PROPN ijassa-1224 222 17 , , PUNCT ijassa-1224 222 18 𝑄 𝑄 PROPN ijassa-1224 222 19 = = SYM ijassa-1224 222 20 ( ( PUNCT ijassa-1224 222 21 𝐢 𝐢 PROPN ijassa-1224 222 22 𝐡 𝐡 NOUN ijassa-1224 222 23 βˆ’ βˆ’ NOUN ijassa-1224 222 24 𝑄 𝑄 PROPN ijassa-1224 222 25 𝑄 𝑄 PROPN ijassa-1224 222 26 ) ) PUNCT ijassa-1224 222 27 ( ( PUNCT ijassa-1224 222 28 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 222 29 βˆ’ βˆ’ NOUN ijassa-1224 222 30 𝑄 𝑄 PROPN ijassa-1224 222 31 𝑄 𝑄 PROPN ijassa-1224 222 32 ) ) PUNCT ijassa-1224 222 33 βˆ’ βˆ’ PROPN ijassa-1224 223 1 ( ( PUNCT ijassa-1224 223 2 𝛾𝑄 𝛾𝑄 PROPN ijassa-1224 223 3 βˆ’ βˆ’ PROPN ijassa-1224 223 4 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 223 5 ) ) PUNCT ijassa-1224 223 6 𝐢 𝐢 PROPN ijassa-1224 223 7 𝐡 𝐡 PROPN ijassa-1224 223 8 , , PUNCT ijassa-1224 223 9 𝑄 𝑄 PROPN ijassa-1224 223 10 = = SYM ijassa-1224 223 11 ( ( PUNCT ijassa-1224 223 12 𝐢 𝐢 PROPN ijassa-1224 223 13 𝐡 𝐡 NOUN ijassa-1224 223 14 βˆ’ βˆ’ NOUN ijassa-1224 223 15 𝑄 𝑄 PROPN ijassa-1224 223 16 𝑄 𝑄 PROPN ijassa-1224 223 17 ) ) PUNCT ijassa-1224 223 18 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 223 19 βˆ’ βˆ’ PROPN ijassa-1224 223 20 ( ( PUNCT ijassa-1224 223 21 𝛾𝑄 𝛾𝑄 NOUN ijassa-1224 223 22 βˆ’ βˆ’ PROPN ijassa-1224 223 23 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 223 24 ) ) PUNCT ijassa-1224 223 25 𝐢 𝐢 PROPN ijassa-1224 223 26 𝐡 𝐡 PROPN ijassa-1224 223 27 , , PUNCT ijassa-1224 223 28 𝑄 𝑄 PROPN ijassa-1224 223 29 = = SYM ijassa-1224 223 30 βˆ’([(𝐢 βˆ’([(𝐢 ADP ijassa-1224 223 31 𝐡 𝐡 NOUN ijassa-1224 223 32 βˆ’ βˆ’ NOUN ijassa-1224 223 33 𝑄 𝑄 PROPN ijassa-1224 223 34 𝑄 𝑄 PROPN ijassa-1224 223 35 ) ) PUNCT ijassa-1224 223 36 ( ( PUNCT ijassa-1224 223 37 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 223 38 βˆ’ βˆ’ NOUN ijassa-1224 223 39 𝑄 𝑄 PROPN ijassa-1224 223 40 𝑄 𝑄 PROPN ijassa-1224 223 41 ) ) PUNCT ijassa-1224 223 42 βˆ’ βˆ’ PROPN ijassa-1224 223 43 ( ( PUNCT ijassa-1224 223 44 𝛾𝑄 𝛾𝑄 PROPN ijassa-1224 223 45 βˆ’ βˆ’ PROPN ijassa-1224 223 46 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 223 47 ) ) PUNCT ijassa-1224 223 48 𝐢 𝐢 PROPN ijassa-1224 223 49 𝐡 𝐡 NOUN ijassa-1224 223 50 ] ] PUNCT ijassa-1224 223 51 𝑄 𝑄 PROPN ijassa-1224 223 52 ) ) PUNCT ijassa-1224 223 53 , , PUNCT ijassa-1224 224 1 + + NOUN ijassa-1224 224 2 π‘Ÿ π‘Ÿ X ijassa-1224 224 3 [ [ X ijassa-1224 224 4 ( ( PUNCT ijassa-1224 224 5 𝐢 𝐢 PROPN ijassa-1224 224 6 𝐡 𝐡 NOUN ijassa-1224 224 7 βˆ’ βˆ’ NOUN ijassa-1224 224 8 𝑄 𝑄 PROPN ijassa-1224 224 9 𝑄 𝑄 PROPN ijassa-1224 224 10 ) ) PUNCT ijassa-1224 224 11 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 224 12 βˆ’ βˆ’ PROPN ijassa-1224 225 1 ( ( PUNCT ijassa-1224 225 2 𝛾𝑄 𝛾𝑄 NOUN ijassa-1224 225 3 βˆ’ βˆ’ PROPN ijassa-1224 225 4 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 225 5 ) ) PUNCT ijassa-1224 225 6 𝐢 𝐢 PROPN ijassa-1224 225 7 𝐡 𝐡 PROPN ijassa-1224 225 8 ] ] PUNCT ijassa-1224 225 9 , , PUNCT ijassa-1224 225 10 𝑄 𝑄 PROPN ijassa-1224 225 11 = = PUNCT ijassa-1224 225 12 πœ‡(𝐢 πœ‡(𝐢 NUM ijassa-1224 225 13 𝐡 𝐡 NOUN ijassa-1224 225 14 βˆ’ βˆ’ NOUN ijassa-1224 225 15 𝑄 𝑄 PROPN ijassa-1224 225 16 𝑄 𝑄 PROPN ijassa-1224 225 17 ) ) PUNCT ijassa-1224 226 1 [ [ X ijassa-1224 226 2 ( ( PUNCT ijassa-1224 226 3 𝐢 𝐢 PROPN ijassa-1224 226 4 𝐡 𝐡 NOUN ijassa-1224 226 5 βˆ’ βˆ’ NOUN ijassa-1224 226 6 𝑄 𝑄 PROPN ijassa-1224 226 7 𝑄 𝑄 PROPN ijassa-1224 226 8 ) ) PUNCT ijassa-1224 226 9 ( ( PUNCT ijassa-1224 226 10 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 226 11 βˆ’ βˆ’ NOUN ijassa-1224 226 12 𝑄 𝑄 PROPN ijassa-1224 226 13 𝑄 𝑄 PROPN ijassa-1224 226 14 ) ) PUNCT ijassa-1224 226 15 βˆ’ βˆ’ PROPN ijassa-1224 226 16 ( ( PUNCT ijassa-1224 226 17 𝛾𝑄 𝛾𝑄 PROPN ijassa-1224 226 18 βˆ’ βˆ’ PROPN ijassa-1224 226 19 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 226 20 ) ) PUNCT ijassa-1224 226 21 𝐢 𝐢 PROPN ijassa-1224 226 22 𝐡 𝐡 PROPN ijassa-1224 226 23 ] ] PUNCT ijassa-1224 226 24 where where SCONJ ijassa-1224 226 25 βˆ’ βˆ’ PROPN ijassa-1224 226 26 𝑄 𝑄 NOUN ijassa-1224 227 1 βˆ’ βˆ’ VERB ijassa-1224 227 2 πœ† πœ† NOUN ijassa-1224 227 3 = = SYM ijassa-1224 227 4 0 0 NUM ijassa-1224 227 5 , , PUNCT ijassa-1224 227 6 βˆ’πœ‡π‘„ βˆ’πœ‡π‘„ NOUN ijassa-1224 227 7 βˆ’ βˆ’ NOUN ijassa-1224 227 8 πœ† πœ† NOUN ijassa-1224 227 9 = = SYM ijassa-1224 227 10 0 0 NUM ijassa-1224 227 11 , , PUNCT ijassa-1224 227 12 βˆ’π‘„ βˆ’π‘„ NOUN ijassa-1224 227 13 βˆ’ βˆ’ NOUN ijassa-1224 227 14 πœ† πœ† NOUN ijassa-1224 227 15 = = SYM ijassa-1224 227 16 0 0 NUM ijassa-1224 227 17 , , PUNCT ijassa-1224 227 18 𝑄 𝑄 PROPN ijassa-1224 227 19 βˆ’ βˆ’ NOUN ijassa-1224 228 1 πœ† πœ† NOUN ijassa-1224 228 2 = = SYM ijassa-1224 228 3 0 0 NUM ijassa-1224 228 4 , , PUNCT ijassa-1224 228 5 𝑄 𝑄 PROPN ijassa-1224 228 6 βˆ’ βˆ’ NOUN ijassa-1224 229 1 πœ† πœ† NOUN ijassa-1224 229 2 = = SYM ijassa-1224 229 3 0 0 NUM ijassa-1224 229 4 , , PUNCT ijassa-1224 229 5 βˆ’π‘„ βˆ’π‘„ PROPN ijassa-1224 229 6 𝑄 𝑄 NOUN ijassa-1224 229 7 βˆ’ βˆ’ VERB ijassa-1224 229 8 πœ† πœ† NOUN ijassa-1224 229 9 = = NOUN ijassa-1224 229 10 0⎭ 0⎭ NUM ijassa-1224 229 11 βŽͺ βŽͺ NOUN ijassa-1224 229 12 ⎬ ⎬ PROPN ijassa-1224 229 13 βŽͺ βŽͺ NOUN ijassa-1224 229 14 ⎫ ⎫ PROPN ijassa-1224 229 15 . . PUNCT ijassa-1224 230 1 ( ( PUNCT ijassa-1224 230 2 24 24 NUM ijassa-1224 230 3 ) ) PUNCT ijassa-1224 230 4 from from ADP ijassa-1224 230 5 equation equation NOUN ijassa-1224 230 6 ( ( PUNCT ijassa-1224 230 7 24 24 NUM ijassa-1224 230 8 ) ) PUNCT ijassa-1224 230 9 πœ† πœ† X ijassa-1224 231 1 = = SYM ijassa-1224 231 2 βˆ’π‘„ βˆ’π‘„ PROPN ijassa-1224 231 3 , , PUNCT ijassa-1224 231 4 πœ† πœ† PROPN ijassa-1224 231 5 = = PUNCT ijassa-1224 231 6 βˆ’ βˆ’ PROPN ijassa-1224 232 1 [ [ X ijassa-1224 232 2 ( ( PUNCT ijassa-1224 232 3 𝐢 𝐢 PROPN ijassa-1224 232 4 𝐡 𝐡 NOUN ijassa-1224 232 5 βˆ’ βˆ’ NOUN ijassa-1224 232 6 𝑄 𝑄 PROPN ijassa-1224 232 7 𝑄 𝑄 PROPN ijassa-1224 232 8 ) ) PUNCT ijassa-1224 232 9 ( ( PUNCT ijassa-1224 232 10 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 232 11 βˆ’ βˆ’ NOUN ijassa-1224 232 12 𝑄 𝑄 PROPN ijassa-1224 232 13 𝑄 𝑄 PROPN ijassa-1224 232 14 ) ) PUNCT ijassa-1224 232 15 βˆ’ βˆ’ PROPN ijassa-1224 232 16 ( ( PUNCT ijassa-1224 232 17 𝛾𝑄 𝛾𝑄 PROPN ijassa-1224 232 18 βˆ’ βˆ’ PROPN ijassa-1224 232 19 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 232 20 ) ) PUNCT ijassa-1224 232 21 𝐢 𝐢 PROPN ijassa-1224 232 22 𝐡 𝐡 NOUN ijassa-1224 232 23 ] ] X ijassa-1224 232 24 𝑄 𝑄 PROPN ijassa-1224 232 25 + + NOUN ijassa-1224 232 26 π‘Ÿ π‘Ÿ NOUN ijassa-1224 233 1 [ [ X ijassa-1224 233 2 ( ( PUNCT ijassa-1224 233 3 𝐢 𝐢 PROPN ijassa-1224 233 4 𝐡 𝐡 NOUN ijassa-1224 233 5 βˆ’ βˆ’ NOUN ijassa-1224 233 6 𝑄 𝑄 PROPN ijassa-1224 233 7 𝑄 𝑄 PROPN ijassa-1224 233 8 ) ) PUNCT ijassa-1224 233 9 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 233 10 βˆ’ βˆ’ PROPN ijassa-1224 234 1 ( ( PUNCT ijassa-1224 234 2 𝛾𝑄 𝛾𝑄 NOUN ijassa-1224 234 3 βˆ’ βˆ’ PROPN ijassa-1224 234 4 𝜌𝜎𝐡 𝜌𝜎𝐡 NOUN ijassa-1224 234 5 ) ) PUNCT ijassa-1224 234 6 𝐢 𝐢 PROPN ijassa-1224 234 7 𝐡 𝐡 PROPN ijassa-1224 234 8 ] ] PUNCT ijassa-1224 234 9 . . PUNCT ijassa-1224 235 1 ( ( PUNCT ijassa-1224 235 2 25 25 NUM ijassa-1224 235 3 ) ) PUNCT ijassa-1224 235 4 substitute substitute NOUN ijassa-1224 235 5 equation equation NOUN ijassa-1224 235 6 ( ( PUNCT ijassa-1224 235 7 23 23 NUM ijassa-1224 235 8 ) ) PUNCT ijassa-1224 235 9 into into ADP ijassa-1224 235 10 equation equation NOUN ijassa-1224 235 11 ( ( PUNCT ijassa-1224 235 12 25 25 NUM ijassa-1224 235 13 ) ) PUNCT ijassa-1224 235 14 , , PUNCT ijassa-1224 235 15 we we PRON ijassa-1224 235 16 have have VERB ijassa-1224 235 17 = = PUNCT ijassa-1224 235 18 βˆ’π›½π›Ώπœ‹(πœ‡ βˆ’π›½π›Ώπœ‹(πœ‡ NOUN ijassa-1224 235 19 + + CCONJ ijassa-1224 235 20 πœ” πœ” PRON ijassa-1224 235 21 βˆ’ βˆ’ NOUN ijassa-1224 235 22 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 235 23 ) ) PUNCT ijassa-1224 235 24 ( ( PUNCT ijassa-1224 235 25 1 1 NUM ijassa-1224 235 26 βˆ’ βˆ’ NOUN ijassa-1224 235 27 𝜌)(πœ€ 𝜌)(πœ€ PUNCT ijassa-1224 235 28 𝑄 𝑄 PROPN ijassa-1224 236 1 + + NUM ijassa-1224 236 2 𝛾)𝑄 𝛾)𝑄 X ijassa-1224 237 1 + + CCONJ ijassa-1224 237 2 πœŒπ‘„ πœŒπ‘„ PUNCT ijassa-1224 237 3 𝑄 𝑄 PROPN ijassa-1224 237 4 + + CCONJ ijassa-1224 237 5 π‘Ÿ π‘Ÿ NOUN ijassa-1224 237 6 πœ€ πœ€ X ijassa-1224 237 7 ( ( PUNCT ijassa-1224 237 8 1 1 NUM ijassa-1224 237 9 βˆ’ βˆ’ NOUN ijassa-1224 237 10 𝜌)𝛾 𝜌)𝛾 X ijassa-1224 237 11 + + CCONJ ijassa-1224 237 12 πœŒπ‘„ πœŒπ‘„ NOUN ijassa-1224 237 13 πœ‡(πœ‡ πœ‡(πœ‡ PROPN ijassa-1224 237 14 + + PUNCT ijassa-1224 237 15 πœ”)𝑄 πœ”)𝑄 ADJ ijassa-1224 237 16 𝑄 𝑄 NOUN ijassa-1224 237 17 𝑄 𝑄 PROPN ijassa-1224 237 18 𝑄 𝑄 PROPN ijassa-1224 237 19 . . PUNCT ijassa-1224 238 1 therefore therefore ADV ijassa-1224 238 2 , , PUNCT ijassa-1224 238 3 𝑅 𝑅 PROPN ijassa-1224 238 4 = = SYM ijassa-1224 238 5 π›½π›Ώπœ‹(πœ‡ π›½π›Ώπœ‹(πœ‡ PROPN ijassa-1224 238 6 + + PUNCT ijassa-1224 238 7 πœ” πœ” PRON ijassa-1224 238 8 βˆ’ βˆ’ NOUN ijassa-1224 238 9 πœ‡πœƒ πœ‡πœƒ NOUN ijassa-1224 238 10 ) ) PUNCT ijassa-1224 238 11 ( ( PUNCT ijassa-1224 238 12 ) ) PUNCT ijassa-1224 238 13 ( ( PUNCT ijassa-1224 238 14 ) ) PUNCT ijassa-1224 238 15 ( ( PUNCT ijassa-1224 238 16 ) ) PUNCT ijassa-1224 238 17 ( ( PUNCT ijassa-1224 238 18 ) ) PUNCT ijassa-1224 238 19 . . PUNCT ijassa-1224 239 1 ( ( PUNCT ijassa-1224 239 2 26 26 NUM ijassa-1224 239 3 ) ) PUNCT ijassa-1224 239 4 154 154 NUM ijassa-1224 239 5 f.a f.a PROPN ijassa-1224 239 6 . . PROPN ijassa-1224 240 1 oguntolu oguntolu PROPN ijassa-1224 240 2 , , PUNCT ijassa-1224 240 3 o.j o.j PROPN ijassa-1224 240 4 . . PROPN ijassa-1224 240 5 peter peter PROPN ijassa-1224 240 6 , , PUNCT ijassa-1224 240 7 k. k. PROPN ijassa-1224 240 8 oshinubi oshinubi PROPN ijassa-1224 240 9 , , PUNCT ijassa-1224 240 10 t.a t.a PROPN ijassa-1224 240 11 . . PROPN ijassa-1224 240 12 ayoola ayoola PROPN ijassa-1224 240 13 , , PUNCT ijassa-1224 240 14 a.o a.o PROPN ijassa-1224 240 15 . . PROPN ijassa-1224 240 16 oladapo oladapo PROPN ijassa-1224 240 17 , , PUNCT ijassa-1224 240 18 m.m m.m PROPN ijassa-1224 240 19 . . PROPN ijassa-1224 240 20 ojo ojo NOUN ijassa-1224 240 21 copyright copyright NOUN ijassa-1224 240 22 Β© Β© PROPN ijassa-1224 240 23 2022 2022 NUM ijassa-1224 240 24 assa assa PROPN ijassa-1224 240 25 adv adv PROPN ijassa-1224 240 26 . . PUNCT ijassa-1224 241 1 in in ADP ijassa-1224 241 2 systems system NOUN ijassa-1224 241 3 science science NOUN ijassa-1224 241 4 and and CCONJ ijassa-1224 241 5 appl appl NOUN ijassa-1224 241 6 . . PUNCT ijassa-1224 242 1 ( ( PUNCT ijassa-1224 242 2 2022 2022 NUM ijassa-1224 242 3 ) ) PUNCT ijassa-1224 242 4 the the DET ijassa-1224 242 5 dfe dfe PROPN ijassa-1224 242 6 is be AUX ijassa-1224 242 7 locally locally ADV ijassa-1224 242 8 asymptotically asymptotically ADV ijassa-1224 242 9 stable stable ADJ ijassa-1224 242 10 since since SCONJ ijassa-1224 242 11 all all DET ijassa-1224 242 12 the the DET ijassa-1224 242 13 eigenvalues eigenvalue NOUN ijassa-1224 242 14 of of ADP ijassa-1224 242 15 ( ( PUNCT ijassa-1224 242 16 26 26 NUM ijassa-1224 242 17 ) ) PUNCT ijassa-1224 242 18 are be AUX ijassa-1224 242 19 negatives negative NOUN ijassa-1224 242 20 for for ADP ijassa-1224 242 21 𝑅 𝑅 PROPN ijassa-1224 242 22 < < X ijassa-1224 242 23 1 1 NUM ijassa-1224 242 24 , , PUNCT ijassa-1224 242 25 hence hence ADV ijassa-1224 242 26 the the DET ijassa-1224 242 27 proof proof NOUN ijassa-1224 242 28 is be AUX ijassa-1224 242 29 established establish VERB ijassa-1224 242 30 . . PUNCT ijassa-1224 243 1 β–‘ β–‘ PUNCT ijassa-1224 243 2 3 3 X ijassa-1224 243 3 . . PUNCT ijassa-1224 243 4 numerical numerical PROPN ijassa-1224 243 5 method method PROPN ijassa-1224 243 6 3.1 3.1 NUM ijassa-1224 243 7 . . PUNCT ijassa-1224 244 1 homotopy homotopy NOUN ijassa-1224 244 2 perturbation perturbation NOUN ijassa-1224 244 3 method method NOUN ijassa-1224 244 4 ( ( PUNCT ijassa-1224 244 5 hpm hpm NOUN ijassa-1224 244 6 ) ) PUNCT ijassa-1224 244 7 the the DET ijassa-1224 244 8 fundamental fundamental ADJ ijassa-1224 244 9 of of ADP ijassa-1224 244 10 homotopy homotopy NOUN ijassa-1224 244 11 perturbation perturbation NOUN ijassa-1224 244 12 method method NOUN ijassa-1224 244 13 ( ( PUNCT ijassa-1224 244 14 hpm hpm NOUN ijassa-1224 244 15 ) ) PUNCT ijassa-1224 244 16 was be AUX ijassa-1224 244 17 first first ADV ijassa-1224 244 18 proposed propose VERB ijassa-1224 244 19 by by ADP ijassa-1224 244 20 [ [ X ijassa-1224 244 21 11 11 NUM ijassa-1224 244 22 ] ] PUNCT ijassa-1224 244 23 . . PUNCT ijassa-1224 245 1 the the DET ijassa-1224 245 2 homotopy homotopy NOUN ijassa-1224 245 3 perturbation perturbation NOUN ijassa-1224 245 4 method method NOUN ijassa-1224 245 5 , , PUNCT ijassa-1224 245 6 which which PRON ijassa-1224 245 7 provides provide VERB ijassa-1224 245 8 analytical analytical ADJ ijassa-1224 245 9 approximate approximate ADJ ijassa-1224 245 10 solution solution NOUN ijassa-1224 245 11 , , PUNCT ijassa-1224 245 12 is be AUX ijassa-1224 245 13 applied apply VERB ijassa-1224 245 14 to to ADP ijassa-1224 245 15 various various ADJ ijassa-1224 245 16 linear linear ADJ ijassa-1224 245 17 and and CCONJ ijassa-1224 245 18 non non ADJ ijassa-1224 245 19 - - ADJ ijassa-1224 245 20 linear linear ADJ ijassa-1224 245 21 equations equation NOUN ijassa-1224 245 22 . . PUNCT ijassa-1224 246 1 [ [ X ijassa-1224 246 2 2 2 NUM ijassa-1224 246 3 , , PUNCT ijassa-1224 246 4 18 18 NUM ijassa-1224 246 5 ] ] PUNCT ijassa-1224 246 6 used use VERB ijassa-1224 246 7 homotopy homotopy NOUN ijassa-1224 246 8 perturbation perturbation NOUN ijassa-1224 246 9 method method NOUN ijassa-1224 246 10 to to PART ijassa-1224 246 11 solve solve VERB ijassa-1224 246 12 a a DET ijassa-1224 246 13 susceptible susceptible ADJ ijassa-1224 246 14 - - PUNCT ijassa-1224 246 15 infected infect VERB ijassa-1224 246 16 - - PUNCT ijassa-1224 246 17 recovered recover VERB ijassa-1224 246 18 ( ( PUNCT ijassa-1224 246 19 sir sir NOUN ijassa-1224 246 20 ) ) PUNCT ijassa-1224 246 21 model model NOUN ijassa-1224 246 22 of of ADP ijassa-1224 246 23 infectious infectious ADJ ijassa-1224 246 24 diseases disease NOUN ijassa-1224 246 25 . . PUNCT ijassa-1224 247 1 the the DET ijassa-1224 247 2 homotopy homotopy NOUN ijassa-1224 247 3 perturbation perturbation NOUN ijassa-1224 247 4 method method NOUN ijassa-1224 247 5 is be AUX ijassa-1224 247 6 a a DET ijassa-1224 247 7 series series NOUN ijassa-1224 247 8 expansion expansion NOUN ijassa-1224 247 9 method method NOUN ijassa-1224 247 10 used use VERB ijassa-1224 247 11 in in ADP ijassa-1224 247 12 the the DET ijassa-1224 247 13 solution solution NOUN ijassa-1224 247 14 of of ADP ijassa-1224 247 15 nonlinear nonlinear ADJ ijassa-1224 247 16 partial partial ADJ ijassa-1224 247 17 differential differential NOUN ijassa-1224 247 18 equations equation NOUN ijassa-1224 247 19 [ [ X ijassa-1224 247 20 18 18 NUM ijassa-1224 247 21 ] ] PUNCT ijassa-1224 247 22 . . PUNCT ijassa-1224 248 1 to to PART ijassa-1224 248 2 show show VERB ijassa-1224 248 3 the the DET ijassa-1224 248 4 simple simple ADJ ijassa-1224 248 5 concepts concept NOUN ijassa-1224 248 6 of of ADP ijassa-1224 248 7 this this DET ijassa-1224 248 8 method method NOUN ijassa-1224 248 9 , , PUNCT ijassa-1224 248 10 we we PRON ijassa-1224 248 11 consider consider VERB ijassa-1224 248 12 the the DET ijassa-1224 248 13 following follow VERB ijassa-1224 248 14 non non ADJ ijassa-1224 248 15 - - ADJ ijassa-1224 248 16 linear linear ADJ ijassa-1224 248 17 differential differential ADJ ijassa-1224 248 18 equation equation NOUN ijassa-1224 248 19 given give VERB ijassa-1224 248 20 as as ADP ijassa-1224 248 21 equations equation NOUN ijassa-1224 248 22 according accord VERB ijassa-1224 248 23 to to ADP ijassa-1224 248 24 [ [ X ijassa-1224 248 25 2 2 NUM ijassa-1224 248 26 ] ] PUNCT ijassa-1224 248 27 . . PUNCT ijassa-1224 249 1 𝐴 𝐴 PROPN ijassa-1224 249 2 ( ( PUNCT ijassa-1224 249 3 π‘ˆ π‘ˆ PROPN ijassa-1224 249 4 ) ) PUNCT ijassa-1224 249 5 βˆ’ βˆ’ PROPN ijassa-1224 249 6 𝑓(π‘Ÿ 𝑓(π‘Ÿ NOUN ijassa-1224 249 7 ) ) PUNCT ijassa-1224 249 8 = = SYM ijassa-1224 249 9 0 0 NUM ijassa-1224 249 10 , , PUNCT ijassa-1224 249 11 π‘Ÿ π‘Ÿ X ijassa-1224 249 12 ∈ ∈ NOUN ijassa-1224 249 13 𝛺 𝛺 PROPN ijassa-1224 249 14 ( ( PUNCT ijassa-1224 249 15 27 27 NUM ijassa-1224 249 16 ) ) PUNCT ijassa-1224 249 17 subject subject NOUN ijassa-1224 249 18 to to ADP ijassa-1224 249 19 the the DET ijassa-1224 249 20 boundary boundary ADJ ijassa-1224 249 21 condition condition NOUN ijassa-1224 249 22 𝐡 𝐡 PROPN ijassa-1224 249 23 π‘ˆ π‘ˆ PROPN ijassa-1224 249 24 , , PUNCT ijassa-1224 249 25 = = NOUN ijassa-1224 249 26 0 0 NUM ijassa-1224 249 27 , , PUNCT ijassa-1224 249 28 π‘Ÿ π‘Ÿ NOUN ijassa-1224 249 29 ∈ ∈ PROPN ijassa-1224 249 30 𝛀 𝛀 PROPN ijassa-1224 249 31 ( ( PUNCT ijassa-1224 249 32 28 28 NUM ijassa-1224 249 33 ) ) PUNCT ijassa-1224 249 34 where where SCONJ ijassa-1224 249 35 a3 a3 NOUN ijassa-1224 249 36 is be AUX ijassa-1224 249 37 a a DET ijassa-1224 249 38 general general ADJ ijassa-1224 249 39 differential differential NOUN ijassa-1224 249 40 operator operator NOUN ijassa-1224 249 41 , , PUNCT ijassa-1224 249 42 b3 b3 PROPN ijassa-1224 249 43 a a DET ijassa-1224 249 44 boundary boundary ADJ ijassa-1224 249 45 operator operator NOUN ijassa-1224 249 46 , , PUNCT ijassa-1224 249 47 𝑓(π‘Ÿ 𝑓(π‘Ÿ PROPN ijassa-1224 249 48 ) ) PUNCT ijassa-1224 249 49 is be AUX ijassa-1224 249 50 a a DET ijassa-1224 249 51 known know VERB ijassa-1224 249 52 analytical analytical ADJ ijassa-1224 249 53 function function NOUN ijassa-1224 249 54 and and CCONJ ijassa-1224 249 55 Ξ³ Ξ³ NOUN ijassa-1224 249 56 is be AUX ijassa-1224 249 57 the the DET ijassa-1224 249 58 boundary boundary NOUN ijassa-1224 249 59 of of ADP ijassa-1224 249 60 the the DET ijassa-1224 249 61 domain domain NOUN ijassa-1224 249 62 𝛺. 𝛺. PROPN ijassa-1224 249 63 the the DET ijassa-1224 249 64 operator operator NOUN ijassa-1224 249 65 a3 a3 NOUN ijassa-1224 249 66 can can AUX ijassa-1224 249 67 be be AUX ijassa-1224 249 68 divided divide VERB ijassa-1224 249 69 into into ADP ijassa-1224 249 70 two two NUM ijassa-1224 249 71 parts part NOUN ijassa-1224 249 72 l l NOUN ijassa-1224 249 73 and and CCONJ ijassa-1224 249 74 n n CCONJ ijassa-1224 249 75 , , PUNCT ijassa-1224 249 76 where where SCONJ ijassa-1224 249 77 l l NOUN ijassa-1224 249 78 is be AUX ijassa-1224 249 79 the the DET ijassa-1224 249 80 linear linear ADJ ijassa-1224 249 81 part part NOUN ijassa-1224 249 82 , , PUNCT ijassa-1224 249 83 and and CCONJ ijassa-1224 249 84 n n PRON ijassa-1224 249 85 is be AUX ijassa-1224 249 86 the the DET ijassa-1224 249 87 nonlinear nonlinear ADJ ijassa-1224 249 88 part part NOUN ijassa-1224 249 89 . . PUNCT ijassa-1224 250 1 equation equation NOUN ijassa-1224 250 2 ( ( PUNCT ijassa-1224 250 3 27 27 NUM ijassa-1224 250 4 ) ) PUNCT ijassa-1224 250 5 can can AUX ijassa-1224 250 6 be be AUX ijassa-1224 250 7 written write VERB ijassa-1224 250 8 as as ADP ijassa-1224 250 9 : : PUNCT ijassa-1224 250 10 𝐿(π‘ˆ 𝐿(π‘ˆ NOUN ijassa-1224 250 11 ) ) PUNCT ijassa-1224 250 12 + + CCONJ ijassa-1224 250 13 𝑁(π‘ˆ 𝑁(π‘ˆ NOUN ijassa-1224 250 14 ) ) PUNCT ijassa-1224 250 15 βˆ’ βˆ’ ADP ijassa-1224 250 16 𝑓(π‘Ÿ 𝑓(π‘Ÿ NOUN ijassa-1224 250 17 ) ) PUNCT ijassa-1224 250 18 = = SYM ijassa-1224 250 19 0 0 NUM ijassa-1224 250 20 , , PUNCT ijassa-1224 250 21 π‘Ÿ π‘Ÿ X ijassa-1224 250 22 ∈ ∈ PROPN ijassa-1224 250 23 𝛺. 𝛺. VERB ijassa-1224 250 24 the the DET ijassa-1224 250 25 homotopy homotopy NOUN ijassa-1224 250 26 perturbation perturbation NOUN ijassa-1224 250 27 structure structure NOUN ijassa-1224 250 28 is be AUX ijassa-1224 250 29 shown show VERB ijassa-1224 250 30 as as SCONJ ijassa-1224 250 31 follows follow VERB ijassa-1224 250 32 𝐻(𝑉 𝐻(𝑉 NUM ijassa-1224 250 33 , , PUNCT ijassa-1224 250 34 β„Ž β„Ž PROPN ijassa-1224 250 35 ) ) PUNCT ijassa-1224 250 36 = = SYM ijassa-1224 250 37 ( ( PUNCT ijassa-1224 250 38 1 1 NUM ijassa-1224 250 39 βˆ’ βˆ’ NOUN ijassa-1224 250 40 β„Ž)[𝐿(𝑉 β„Ž)[𝐿(𝑉 NOUN ijassa-1224 250 41 ) ) PUNCT ijassa-1224 250 42 βˆ’ βˆ’ PROPN ijassa-1224 250 43 𝐿(π‘ˆ 𝐿(π‘ˆ NOUN ijassa-1224 250 44 ) ) PUNCT ijassa-1224 250 45 ] ] PUNCT ijassa-1224 251 1 + + NUM ijassa-1224 251 2 β„Ž[𝐴(𝑉 β„Ž[𝐴(𝑉 NOUN ijassa-1224 251 3 ) ) PUNCT ijassa-1224 251 4 βˆ’ βˆ’ PROPN ijassa-1224 251 5 𝑓(π‘Ÿ 𝑓(π‘Ÿ NOUN ijassa-1224 251 6 ) ) PUNCT ijassa-1224 251 7 ] ] PUNCT ijassa-1224 252 1 = = SYM ijassa-1224 252 2 0 0 PUNCT ijassa-1224 252 3 ( ( PUNCT ijassa-1224 252 4 29 29 NUM ijassa-1224 252 5 ) ) PUNCT ijassa-1224 252 6 where where SCONJ ijassa-1224 252 7 𝑉(π‘Ÿ 𝑉(π‘Ÿ ADV ijassa-1224 252 8 , , PUNCT ijassa-1224 252 9 𝑃 𝑃 NOUN ijassa-1224 252 10 ): ): PUNCT ijassa-1224 252 11 𝛺 𝛺 PROPN ijassa-1224 252 12 ∈ ∈ PROPN ijassa-1224 253 1 [ [ X ijassa-1224 253 2 0,1 0,1 NUM ijassa-1224 253 3 ] ] PUNCT ijassa-1224 253 4 β†’ β†’ SYM ijassa-1224 253 5 𝑅. 𝑅. X ijassa-1224 253 6 ( ( PUNCT ijassa-1224 253 7 30 30 NUM ijassa-1224 253 8 ) ) PUNCT ijassa-1224 253 9 in in ADP ijassa-1224 253 10 equation equation NOUN ijassa-1224 253 11 ( ( PUNCT ijassa-1224 253 12 29 29 NUM ijassa-1224 253 13 ) ) PUNCT ijassa-1224 253 14 𝑃 𝑃 NOUN ijassa-1224 253 15 ∈ ∈ NOUN ijassa-1224 254 1 [ [ X ijassa-1224 254 2 0,1 0,1 NUM ijassa-1224 254 3 ] ] PUNCT ijassa-1224 254 4 is be AUX ijassa-1224 254 5 an an DET ijassa-1224 254 6 embedding embed VERB ijassa-1224 254 7 parameter parameter NOUN ijassa-1224 254 8 and and CCONJ ijassa-1224 254 9 π‘ˆ π‘ˆ PROPN ijassa-1224 254 10 is be AUX ijassa-1224 254 11 the the DET ijassa-1224 254 12 approximation approximation NOUN ijassa-1224 254 13 that that PRON ijassa-1224 254 14 satisfies satisfy VERB ijassa-1224 254 15 the the DET ijassa-1224 254 16 boundary boundary ADJ ijassa-1224 254 17 condition condition NOUN ijassa-1224 254 18 . . PUNCT ijassa-1224 255 1 it it PRON ijassa-1224 255 2 can can AUX ijassa-1224 255 3 be be AUX ijassa-1224 255 4 assumed assume VERB ijassa-1224 255 5 that that SCONJ ijassa-1224 255 6 the the DET ijassa-1224 255 7 solution solution NOUN ijassa-1224 255 8 of of ADP ijassa-1224 255 9 the the DET ijassa-1224 255 10 equation equation NOUN ijassa-1224 255 11 ( ( PUNCT ijassa-1224 255 12 30 30 NUM ijassa-1224 255 13 ) ) PUNCT ijassa-1224 255 14 can can AUX ijassa-1224 255 15 be be AUX ijassa-1224 255 16 written write VERB ijassa-1224 255 17 as as ADP ijassa-1224 255 18 power power NOUN ijassa-1224 255 19 series series NOUN ijassa-1224 255 20 in in ADP ijassa-1224 255 21 h h NOUN ijassa-1224 255 22 given give VERB ijassa-1224 255 23 as as ADP ijassa-1224 255 24 equations equation NOUN ijassa-1224 255 25 ( ( PUNCT ijassa-1224 255 26 31 31 NUM ijassa-1224 255 27 ) ) PUNCT ijassa-1224 255 28 to to ADP ijassa-1224 255 29 ( ( PUNCT ijassa-1224 255 30 32 32 NUM ijassa-1224 255 31 ): ): PUNCT ijassa-1224 255 32 𝑉 𝑉 PROPN ijassa-1224 255 33 = = SYM ijassa-1224 255 34 𝑉 𝑉 PROPN ijassa-1224 255 35 + + CCONJ ijassa-1224 255 36 β„Žπ‘‰ β„Žπ‘‰ ADJ ijassa-1224 255 37 + + NUM ijassa-1224 255 38 β„Ž β„Ž X ijassa-1224 255 39 𝑉 𝑉 PROPN ijassa-1224 255 40 + + PROPN ijassa-1224 255 41 . . PROPN ijassa-1224 255 42 .. .. PUNCT ijassa-1224 256 1 ( ( PUNCT ijassa-1224 256 2 31 31 NUM ijassa-1224 256 3 ) ) PUNCT ijassa-1224 256 4 and and CCONJ ijassa-1224 256 5 the the DET ijassa-1224 256 6 best good ADJ ijassa-1224 256 7 approximation approximation NOUN ijassa-1224 256 8 for for ADP ijassa-1224 256 9 the the DET ijassa-1224 256 10 solution solution NOUN ijassa-1224 256 11 is be AUX ijassa-1224 256 12 : : PUNCT ijassa-1224 256 13 π‘ˆ π‘ˆ PROPN ijassa-1224 256 14 = = PUNCT ijassa-1224 256 15 π‘™π‘–π‘š π‘™π‘–π‘š VERB ijassa-1224 256 16 𝑣 𝑣 NOUN ijassa-1224 256 17 = = PUNCT ijassa-1224 256 18 𝑣 𝑣 PROPN ijassa-1224 256 19 + + CCONJ ijassa-1224 256 20 β„Žπ‘£ β„Žπ‘£ VERB ijassa-1224 256 21 + + NUM ijassa-1224 256 22 β„Ž β„Ž X ijassa-1224 256 23 𝑣 𝑣 NOUN ijassa-1224 256 24 + + NUM ijassa-1224 256 25 β‹― β‹― VERB ijassa-1224 256 26 β„Ž β„Ž NOUN ijassa-1224 256 27 β†’ β†’ SYM ijassa-1224 256 28 1 1 NUM ijassa-1224 256 29 . . PUNCT ijassa-1224 257 1 ( ( PUNCT ijassa-1224 257 2 32 32 NUM ijassa-1224 257 3 ) ) PUNCT ijassa-1224 257 4 the the DET ijassa-1224 257 5 series series NOUN ijassa-1224 257 6 ( ( PUNCT ijassa-1224 257 7 31 31 NUM ijassa-1224 257 8 ) ) PUNCT ijassa-1224 257 9 is be AUX ijassa-1224 257 10 convergent convergent ADJ ijassa-1224 257 11 for for ADP ijassa-1224 257 12 most most ADJ ijassa-1224 257 13 cases case NOUN ijassa-1224 257 14 . . PUNCT ijassa-1224 258 1 however however ADV ijassa-1224 258 2 , , PUNCT ijassa-1224 258 3 the the DET ijassa-1224 258 4 convergent convergent NOUN ijassa-1224 258 5 rate rate NOUN ijassa-1224 258 6 depends depend VERB ijassa-1224 258 7 on on ADP ijassa-1224 258 8 the the DET ijassa-1224 258 9 nonlinear nonlinear ADJ ijassa-1224 258 10 operator operator NOUN ijassa-1224 258 11 a a DET ijassa-1224 258 12 ( ( PUNCT ijassa-1224 258 13 v v NOUN ijassa-1224 258 14 ) ) PUNCT ijassa-1224 258 15 3.2 3.2 NUM ijassa-1224 258 16 . . PUNCT ijassa-1224 259 1 solution solution NOUN ijassa-1224 259 2 of of ADP ijassa-1224 259 3 the the DET ijassa-1224 259 4 model model NOUN ijassa-1224 259 5 equations equation NOUN ijassa-1224 259 6 using use VERB ijassa-1224 259 7 hpm hpm NOUN ijassa-1224 259 8 from from ADP ijassa-1224 259 9 differential differential ADJ ijassa-1224 259 10 equations equation NOUN ijassa-1224 259 11 1 1 NUM ijassa-1224 259 12 to to ADP ijassa-1224 259 13 7 7 NUM ijassa-1224 259 14 + + CCONJ ijassa-1224 259 15 ( ( PUNCT ijassa-1224 259 16 πœ‡ πœ‡ X ijassa-1224 259 17 + + X ijassa-1224 259 18 πœ† πœ† X ijassa-1224 259 19 ) ) PUNCT ijassa-1224 259 20 𝑆 𝑆 PROPN ijassa-1224 259 21 βˆ’ βˆ’ PROPN ijassa-1224 259 22 πœ”π‘‰ πœ”π‘‰ PROPN ijassa-1224 259 23 βˆ’ βˆ’ PROPN ijassa-1224 259 24 πœ‹(1 πœ‹(1 NOUN ijassa-1224 259 25 βˆ’ βˆ’ PROPN ijassa-1224 259 26 πœƒ πœƒ NOUN ijassa-1224 259 27 ) ) PUNCT ijassa-1224 259 28 = = SYM ijassa-1224 259 29 0 0 NUM ijassa-1224 259 30 , , PUNCT ijassa-1224 259 31 ( ( PUNCT ijassa-1224 259 32 33 33 NUM ijassa-1224 259 33 ) ) PUNCT ijassa-1224 260 1 + + CCONJ ijassa-1224 260 2 ( ( PUNCT ijassa-1224 260 3 πœ‡ πœ‡ X ijassa-1224 260 4 + + X ijassa-1224 260 5 πœ”)𝑉 πœ”)𝑉 X ijassa-1224 260 6 βˆ’ βˆ’ X ijassa-1224 260 7 πœƒπœ‹ πœƒπœ‹ X ijassa-1224 260 8 = = SYM ijassa-1224 260 9 0 0 NUM ijassa-1224 260 10 , , PUNCT ijassa-1224 260 11 ( ( PUNCT ijassa-1224 260 12 34 34 NUM ijassa-1224 260 13 ) ) PUNCT ijassa-1224 260 14 + + CCONJ ijassa-1224 260 15 ( ( PUNCT ijassa-1224 260 16 𝜎 𝜎 NOUN ijassa-1224 260 17 + + X ijassa-1224 260 18 πœ† πœ† NOUN ijassa-1224 260 19 + + CCONJ ijassa-1224 260 20 πœ‡)𝐸 πœ‡)𝐸 ADJ ijassa-1224 260 21 βˆ’ βˆ’ PROPN ijassa-1224 260 22 πœ† πœ† DET ijassa-1224 260 23 𝑇 𝑇 PROPN ijassa-1224 260 24 βˆ’ βˆ’ PROPN ijassa-1224 260 25 πœ† πœ† DET ijassa-1224 260 26 𝑆 𝑆 PROPN ijassa-1224 260 27 = = SYM ijassa-1224 260 28 0 0 PROPN ijassa-1224 260 29 , , PUNCT ijassa-1224 260 30 ( ( PUNCT ijassa-1224 260 31 35 35 NUM ijassa-1224 260 32 ) ) PUNCT ijassa-1224 260 33 analysis analysis NOUN ijassa-1224 260 34 and and CCONJ ijassa-1224 260 35 dynamics dynamic NOUN ijassa-1224 260 36 of of ADP ijassa-1224 260 37 tuberculosis tuberculosis NOUN ijassa-1224 260 38 outbreak outbreak NOUN ijassa-1224 260 39 155 155 NUM ijassa-1224 260 40 copyright copyright NOUN ijassa-1224 260 41 Β© Β© PROPN ijassa-1224 260 42 2022 2022 NUM ijassa-1224 260 43 assa assa NOUN ijassa-1224 260 44 . . PUNCT ijassa-1224 261 1 adv adv PROPN ijassa-1224 261 2 . . PUNCT ijassa-1224 262 1 in in ADP ijassa-1224 262 2 systems system NOUN ijassa-1224 262 3 science science NOUN ijassa-1224 262 4 and and CCONJ ijassa-1224 262 5 appl appl NOUN ijassa-1224 262 6 . . PUNCT ijassa-1224 263 1 ( ( PUNCT ijassa-1224 263 2 2022 2022 NUM ijassa-1224 263 3 ) ) PUNCT ijassa-1224 264 1 + + CCONJ ijassa-1224 264 2 ( ( PUNCT ijassa-1224 264 3 𝛾 𝛾 PART ijassa-1224 264 4 + + X ijassa-1224 264 5 πœ‡ πœ‡ ADP ijassa-1224 264 6 + + NOUN ijassa-1224 264 7 π‘Ÿ π‘Ÿ NOUN ijassa-1224 264 8 + + CCONJ ijassa-1224 264 9 𝑑 𝑑 NOUN ijassa-1224 264 10 ) ) PUNCT ijassa-1224 264 11 𝐼 𝐼 ADP ijassa-1224 264 12 βˆ’ βˆ’ PROPN ijassa-1224 264 13 ( ( PUNCT ijassa-1224 264 14 1 1 NUM ijassa-1224 264 15 βˆ’ βˆ’ PROPN ijassa-1224 264 16 𝜌)𝜎𝐸 𝜌)𝜎𝐸 PROPN ijassa-1224 264 17 βˆ’ βˆ’ PROPN ijassa-1224 264 18 ( ( PUNCT ijassa-1224 264 19 1 1 NUM ijassa-1224 264 20 βˆ’ βˆ’ NOUN ijassa-1224 264 21 πœ™)πœ† πœ™)πœ† X ijassa-1224 264 22 𝐸 𝐸 PROPN ijassa-1224 264 23 = = SYM ijassa-1224 264 24 0 0 NUM ijassa-1224 264 25 , , PUNCT ijassa-1224 264 26 ( ( PUNCT ijassa-1224 264 27 36 36 NUM ijassa-1224 264 28 ) ) PUNCT ijassa-1224 264 29 + + CCONJ ijassa-1224 264 30 ( ( PUNCT ijassa-1224 264 31 πœ‡ πœ‡ X ijassa-1224 264 32 + + X ijassa-1224 264 33 𝑑 𝑑 PROPN ijassa-1224 264 34 + + NUM ijassa-1224 264 35 π‘Ÿ π‘Ÿ NOUN ijassa-1224 264 36 + + SYM ijassa-1224 264 37 π‘Ÿ π‘Ÿ NOUN ijassa-1224 264 38 ) ) PUNCT ijassa-1224 265 1 𝐼 𝐼 ADP ijassa-1224 265 2 βˆ’ βˆ’ PROPN ijassa-1224 265 3 𝜌𝜎𝐸 𝜌𝜎𝐸 NOUN ijassa-1224 265 4 βˆ’ βˆ’ PROPN ijassa-1224 265 5 𝛾𝐼 𝛾𝐼 PROPN ijassa-1224 265 6 βˆ’ βˆ’ PROPN ijassa-1224 265 7 πœ™πœ† πœ™πœ† PROPN ijassa-1224 265 8 𝐸 𝐸 PROPN ijassa-1224 265 9 = = SYM ijassa-1224 265 10 0 0 NUM ijassa-1224 265 11 , , PUNCT ijassa-1224 265 12 ( ( PUNCT ijassa-1224 265 13 37 37 NUM ijassa-1224 265 14 ) ) PUNCT ijassa-1224 265 15 + + CCONJ ijassa-1224 265 16 ( ( PUNCT ijassa-1224 265 17 πœ‡ πœ‡ X ijassa-1224 265 18 + + X ijassa-1224 265 19 𝑑 𝑑 PROPN ijassa-1224 265 20 + + ADJ ijassa-1224 265 21 π‘Ÿ π‘Ÿ NOUN ijassa-1224 265 22 ) ) PUNCT ijassa-1224 265 23 𝐽 𝐽 PROPN ijassa-1224 266 1 βˆ’ βˆ’ NOUN ijassa-1224 267 1 π‘Ÿ π‘Ÿ NOUN ijassa-1224 267 2 𝐼 𝐼 PROPN ijassa-1224 267 3 = = SYM ijassa-1224 267 4 0 0 NUM ijassa-1224 267 5 , , PUNCT ijassa-1224 267 6 ( ( PUNCT ijassa-1224 267 7 38 38 NUM ijassa-1224 267 8 ) ) PUNCT ijassa-1224 268 1 + + CCONJ ijassa-1224 268 2 ( ( PUNCT ijassa-1224 268 3 πœ‡ πœ‡ X ijassa-1224 268 4 + + X ijassa-1224 268 5 πœ† πœ† X ijassa-1224 268 6 ) ) PUNCT ijassa-1224 268 7 𝑇 𝑇 PROPN ijassa-1224 268 8 βˆ’ βˆ’ PROPN ijassa-1224 268 9 π‘Ÿ π‘Ÿ NOUN ijassa-1224 268 10 𝐽 𝐽 PRON ijassa-1224 268 11 βˆ’ βˆ’ VERB ijassa-1224 269 1 π‘Ÿ π‘Ÿ X ijassa-1224 269 2 𝐼 𝐼 ADP ijassa-1224 269 3 βˆ’ βˆ’ PROPN ijassa-1224 269 4 π‘Ÿ π‘Ÿ NOUN ijassa-1224 269 5 𝐼 𝐼 PROPN ijassa-1224 269 6 = = SYM ijassa-1224 269 7 0 0 PROPN ijassa-1224 269 8 . . PUNCT ijassa-1224 269 9 ( ( PUNCT ijassa-1224 269 10 39 39 NUM ijassa-1224 269 11 ) ) PUNCT ijassa-1224 269 12 with with ADP ijassa-1224 269 13 the the DET ijassa-1224 269 14 initial initial ADJ ijassa-1224 269 15 condition condition NOUN ijassa-1224 269 16 given give VERB ijassa-1224 269 17 as as ADP ijassa-1224 269 18 𝑆(0 𝑆(0 NUM ijassa-1224 269 19 ) ) PUNCT ijassa-1224 269 20 = = SYM ijassa-1224 269 21 𝑆 𝑆 PROPN ijassa-1224 269 22 , , PUNCT ijassa-1224 269 23 𝑉(0 𝑉(0 NUM ijassa-1224 269 24 ) ) PUNCT ijassa-1224 269 25 = = SYM ijassa-1224 269 26 𝑉 𝑉 PROPN ijassa-1224 269 27 , , PUNCT ijassa-1224 269 28 𝐸(0 𝐸(0 NUM ijassa-1224 269 29 ) ) PUNCT ijassa-1224 269 30 = = SYM ijassa-1224 269 31 𝐸 𝐸 PROPN ijassa-1224 269 32 , , PUNCT ijassa-1224 269 33 𝐼 𝐼 PROPN ijassa-1224 269 34 ( ( PUNCT ijassa-1224 269 35 0 0 NUM ijassa-1224 269 36 ) ) PUNCT ijassa-1224 269 37 = = SYM ijassa-1224 269 38 𝐼 𝐼 PROPN ijassa-1224 269 39 , , PUNCT ijassa-1224 269 40 𝐼 𝐼 PROPN ijassa-1224 269 41 ( ( PUNCT ijassa-1224 269 42 0 0 NUM ijassa-1224 269 43 ) ) PUNCT ijassa-1224 269 44 = = SYM ijassa-1224 269 45 𝐼 𝐼 PROPN ijassa-1224 269 46 , , PUNCT ijassa-1224 269 47 𝐽(0 𝐽(0 NUM ijassa-1224 269 48 ) ) PUNCT ijassa-1224 269 49 = = SYM ijassa-1224 269 50 𝐽 𝐽 PROPN ijassa-1224 269 51 , , PUNCT ijassa-1224 269 52 𝑇(0 𝑇(0 PROPN ijassa-1224 269 53 ) ) PUNCT ijassa-1224 269 54 = = SYM ijassa-1224 269 55 𝑇 𝑇 PROPN ijassa-1224 269 56 . . PUNCT ijassa-1224 270 1 ( ( PUNCT ijassa-1224 270 2 40 40 NUM ijassa-1224 270 3 ) ) PUNCT ijassa-1224 270 4 let let VERB ijassa-1224 270 5 𝑆 𝑆 PROPN ijassa-1224 270 6 = = SYM ijassa-1224 270 7 𝑠 𝑠 PROPN ijassa-1224 271 1 + + CCONJ ijassa-1224 271 2 β„Žπ‘  β„Žπ‘  VERB ijassa-1224 271 3 + + NUM ijassa-1224 271 4 β„Ž β„Ž X ijassa-1224 271 5 𝑠 𝑠 PROPN ijassa-1224 271 6 + + PROPN ijassa-1224 271 7 . . PUNCT ijassa-1224 271 8 . . PUNCT ijassa-1224 271 9 . . PUNCT ijassa-1224 272 1 , , PUNCT ijassa-1224 272 2 ( ( PUNCT ijassa-1224 272 3 41 41 NUM ijassa-1224 272 4 ) ) PUNCT ijassa-1224 272 5 𝑉 𝑉 PROPN ijassa-1224 272 6 = = PUNCT ijassa-1224 272 7 𝑒 𝑒 PROPN ijassa-1224 272 8 + + X ijassa-1224 272 9 β„Žπ‘’ β„Žπ‘’ NOUN ijassa-1224 272 10 + + NUM ijassa-1224 272 11 β„Ž β„Ž X ijassa-1224 272 12 𝑒 𝑒 PRON ijassa-1224 272 13 + + PROPN ijassa-1224 272 14 . . PUNCT ijassa-1224 272 15 . . PUNCT ijassa-1224 272 16 . . PUNCT ijassa-1224 273 1 , , PUNCT ijassa-1224 273 2 ( ( PUNCT ijassa-1224 273 3 42 42 X ijassa-1224 273 4 ) ) PUNCT ijassa-1224 273 5 𝐸 𝐸 PROPN ijassa-1224 273 6 = = SYM ijassa-1224 273 7 𝑣 𝑣 PROPN ijassa-1224 273 8 + + CCONJ ijassa-1224 273 9 β„Žπ‘£ β„Žπ‘£ VERB ijassa-1224 273 10 + + NUM ijassa-1224 273 11 β„Ž β„Ž X ijassa-1224 273 12 𝑣 𝑣 PRON ijassa-1224 273 13 + + PROPN ijassa-1224 273 14 . . PUNCT ijassa-1224 273 15 . . PUNCT ijassa-1224 273 16 . . PUNCT ijassa-1224 274 1 , , PUNCT ijassa-1224 274 2 ( ( PUNCT ijassa-1224 274 3 43 43 NUM ijassa-1224 274 4 ) ) PUNCT ijassa-1224 274 5 𝐼 𝐼 NOUN ijassa-1224 274 6 = = PUNCT ijassa-1224 274 7 𝑀 𝑀 PROPN ijassa-1224 274 8 + + NUM ijassa-1224 274 9 β„Žπ‘€ β„Žπ‘€ NOUN ijassa-1224 274 10 + + CCONJ ijassa-1224 274 11 β„Ž β„Ž PART ijassa-1224 274 12 𝑀 𝑀 ADP ijassa-1224 274 13 + + PROPN ijassa-1224 274 14 β‹― β‹― NOUN ijassa-1224 274 15 , , PUNCT ijassa-1224 274 16 ( ( PUNCT ijassa-1224 274 17 44 44 NUM ijassa-1224 274 18 ) ) PUNCT ijassa-1224 274 19 𝐼 𝐼 PROPN ijassa-1224 274 20 = = PUNCT ijassa-1224 274 21 π‘₯ π‘₯ PROPN ijassa-1224 275 1 + + NUM ijassa-1224 275 2 β„Žπ‘₯ β„Žπ‘₯ PRON ijassa-1224 275 3 + + NOUN ijassa-1224 275 4 β„Ž β„Ž X ijassa-1224 275 5 π‘₯ π‘₯ NOUN ijassa-1224 275 6 + + NOUN ijassa-1224 275 7 . . PUNCT ijassa-1224 275 8 . . PUNCT ijassa-1224 276 1 . . PUNCT ijassa-1224 277 1 , , PUNCT ijassa-1224 277 2 ( ( PUNCT ijassa-1224 277 3 45 45 NUM ijassa-1224 277 4 ) ) PUNCT ijassa-1224 277 5 𝐽 𝐽 NOUN ijassa-1224 277 6 = = SYM ijassa-1224 277 7 𝑦 𝑦 PROPN ijassa-1224 277 8 + + NUM ijassa-1224 277 9 β„Žπ‘¦ β„Žπ‘¦ PROPN ijassa-1224 277 10 + + NOUN ijassa-1224 277 11 β„Ž β„Ž X ijassa-1224 277 12 𝑦 𝑦 NOUN ijassa-1224 277 13 + + PROPN ijassa-1224 277 14 . . PUNCT ijassa-1224 277 15 . . PUNCT ijassa-1224 277 16 . . PUNCT ijassa-1224 278 1 , , PUNCT ijassa-1224 278 2 ( ( PUNCT ijassa-1224 278 3 46 46 X ijassa-1224 278 4 ) ) PUNCT ijassa-1224 278 5 𝑇 𝑇 NOUN ijassa-1224 278 6 = = SYM ijassa-1224 278 7 𝑧 𝑧 PROPN ijassa-1224 279 1 + + X ijassa-1224 279 2 β„Žπ‘§ β„Žπ‘§ PRON ijassa-1224 279 3 + + PUNCT ijassa-1224 279 4 β„Ž β„Ž X ijassa-1224 279 5 𝑧 𝑧 PROPN ijassa-1224 279 6 + + PROPN ijassa-1224 279 7 . . PROPN ijassa-1224 279 8 … … PUNCT ijassa-1224 279 9 ( ( PUNCT ijassa-1224 279 10 47 47 NUM ijassa-1224 279 11 ) ) PUNCT ijassa-1224 279 12 applying apply VERB ijassa-1224 279 13 hpm hpm NOUN ijassa-1224 279 14 into into ADP ijassa-1224 279 15 equation equation NOUN ijassa-1224 279 16 ( ( PUNCT ijassa-1224 279 17 33 33 NUM ijassa-1224 279 18 ) ) PUNCT ijassa-1224 279 19 ( ( PUNCT ijassa-1224 279 20 1 1 NUM ijassa-1224 279 21 βˆ’ βˆ’ NUM ijassa-1224 279 22 β„Ž β„Ž NOUN ijassa-1224 279 23 ) ) PUNCT ijassa-1224 279 24 + + CCONJ ijassa-1224 280 1 β„Ž β„Ž X ijassa-1224 280 2 + + CCONJ ijassa-1224 280 3 ( ( PUNCT ijassa-1224 280 4 πœ‡ πœ‡ X ijassa-1224 280 5 + + X ijassa-1224 280 6 πœ† πœ† X ijassa-1224 280 7 ) ) PUNCT ijassa-1224 280 8 𝑆 𝑆 PROPN ijassa-1224 280 9 βˆ’ βˆ’ PROPN ijassa-1224 280 10 πœ”π‘‰ πœ”π‘‰ PROPN ijassa-1224 280 11 βˆ’ βˆ’ PROPN ijassa-1224 280 12 πœ‹(1 πœ‹(1 NOUN ijassa-1224 280 13 βˆ’ βˆ’ PROPN ijassa-1224 281 1 πœƒ πœƒ NOUN ijassa-1224 281 2 ) ) PUNCT ijassa-1224 281 3 = = SYM ijassa-1224 281 4 0 0 X ijassa-1224 281 5 . . PUNCT ijassa-1224 282 1 ( ( PUNCT ijassa-1224 282 2 48 48 NUM ijassa-1224 282 3 ) ) PUNCT ijassa-1224 282 4 substitute substitute NOUN ijassa-1224 282 5 equation equation NOUN ijassa-1224 282 6 ( ( PUNCT ijassa-1224 282 7 41 41 NUM ijassa-1224 282 8 ) ) PUNCT ijassa-1224 282 9 and and CCONJ ijassa-1224 282 10 ( ( PUNCT ijassa-1224 282 11 42 42 NUM ijassa-1224 282 12 ) ) PUNCT ijassa-1224 282 13 into into ADP ijassa-1224 282 14 ( ( PUNCT ijassa-1224 282 15 48 48 NUM ijassa-1224 282 16 ) ) PUNCT ijassa-1224 282 17 ( ( PUNCT ijassa-1224 282 18 𝑠 𝑠 X ijassa-1224 282 19 + + CCONJ ijassa-1224 282 20 β„Žπ‘  β„Žπ‘  VERB ijassa-1224 282 21 + + NUM ijassa-1224 282 22 β„Ž β„Ž X ijassa-1224 282 23 𝑠 𝑠 PROPN ijassa-1224 282 24 + + PROPN ijassa-1224 282 25 . . PUNCT ijassa-1224 282 26 . . PUNCT ijassa-1224 282 27 . . PUNCT ijassa-1224 282 28 ) ) PUNCT ijassa-1224 283 1 + + CCONJ ijassa-1224 283 2 β„Ž β„Ž X ijassa-1224 283 3 ( ( PUNCT ijassa-1224 283 4 πœ‡ πœ‡ ADP ijassa-1224 283 5 + + X ijassa-1224 283 6 πœ† πœ† X ijassa-1224 283 7 ) ) PUNCT ijassa-1224 283 8 ( ( PUNCT ijassa-1224 283 9 𝑠 𝑠 PROPN ijassa-1224 283 10 + + CCONJ ijassa-1224 283 11 β„Žπ‘  β„Žπ‘  VERB ijassa-1224 283 12 + + NUM ijassa-1224 283 13 β„Ž β„Ž X ijassa-1224 283 14 𝑠 𝑠 PROPN ijassa-1224 283 15 + + PROPN ijassa-1224 283 16 . . PUNCT ijassa-1224 283 17 . . PUNCT ijassa-1224 283 18 . . PUNCT ijassa-1224 283 19 ) ) PUNCT ijassa-1224 284 1 βˆ’ βˆ’ NOUN ijassa-1224 285 1 πœ” πœ” X ijassa-1224 285 2 ( ( PUNCT ijassa-1224 285 3 𝑒 𝑒 X ijassa-1224 285 4 + + PROPN ijassa-1224 285 5 β„Žπ‘’ β„Žπ‘’ NOUN ijassa-1224 285 6 + + NUM ijassa-1224 285 7 β„Ž β„Ž X ijassa-1224 285 8 𝑒 𝑒 PRON ijassa-1224 285 9 + + PROPN ijassa-1224 285 10 . . PUNCT ijassa-1224 285 11 . . PUNCT ijassa-1224 285 12 . . PUNCT ijassa-1224 285 13 ) ) PUNCT ijassa-1224 286 1 βˆ’ βˆ’ PROPN ijassa-1224 287 1 πœ‹(1 πœ‹(1 NOUN ijassa-1224 287 2 βˆ’ βˆ’ PROPN ijassa-1224 287 3 πœƒ πœƒ NOUN ijassa-1224 287 4 ) ) PUNCT ijassa-1224 287 5 = = SYM ijassa-1224 287 6 0 0 X ijassa-1224 287 7 . . X ijassa-1224 288 1 collecting collect VERB ijassa-1224 288 2 the the DET ijassa-1224 288 3 coefficient coefficient NOUN ijassa-1224 288 4 of of ADP ijassa-1224 288 5 power power NOUN ijassa-1224 288 6 of of ADP ijassa-1224 288 7 h h NOUN ijassa-1224 288 8 , , PUNCT ijassa-1224 288 9 we we PRON ijassa-1224 288 10 have have VERB ijassa-1224 288 11 β„Ž β„Ž NOUN ijassa-1224 288 12 : : PUNCT ijassa-1224 288 13 𝑠 𝑠 PROPN ijassa-1224 288 14 = = SYM ijassa-1224 288 15 0 0 PROPN ijassa-1224 288 16 , , PUNCT ijassa-1224 288 17 ( ( PUNCT ijassa-1224 288 18 49 49 NUM ijassa-1224 288 19 ) ) PUNCT ijassa-1224 288 20 β„Ž β„Ž NOUN ijassa-1224 288 21 : : PUNCT ijassa-1224 289 1 𝑠 𝑠 PROPN ijassa-1224 289 2 + + CCONJ ijassa-1224 289 3 ( ( PUNCT ijassa-1224 289 4 πœ‡ πœ‡ X ijassa-1224 289 5 + + X ijassa-1224 289 6 πœ† πœ† X ijassa-1224 289 7 ) ) PUNCT ijassa-1224 289 8 𝑠 𝑠 PROPN ijassa-1224 289 9 βˆ’ βˆ’ PROPN ijassa-1224 289 10 πœ”π‘’ πœ”π‘’ VERB ijassa-1224 289 11 βˆ’ βˆ’ PROPN ijassa-1224 289 12 πœ‹(1 πœ‹(1 PROPN ijassa-1224 289 13 βˆ’ βˆ’ PROPN ijassa-1224 290 1 πœƒ πœƒ NOUN ijassa-1224 290 2 ) ) PUNCT ijassa-1224 290 3 = = SYM ijassa-1224 290 4 0 0 NUM ijassa-1224 290 5 , , PUNCT ijassa-1224 290 6 ( ( PUNCT ijassa-1224 290 7 50 50 NUM ijassa-1224 290 8 ) ) PUNCT ijassa-1224 290 9 β„Ž β„Ž NOUN ijassa-1224 290 10 : : PUNCT ijassa-1224 290 11 𝑠 𝑠 PROPN ijassa-1224 291 1 + + CCONJ ijassa-1224 291 2 ( ( PUNCT ijassa-1224 291 3 πœ‡ πœ‡ X ijassa-1224 291 4 + + X ijassa-1224 291 5 πœ† πœ† X ijassa-1224 291 6 ) ) PUNCT ijassa-1224 291 7 𝑠 𝑠 PROPN ijassa-1224 291 8 βˆ’ βˆ’ NOUN ijassa-1224 291 9 πœ”π‘’ πœ”π‘’ VERB ijassa-1224 291 10 = = PUNCT ijassa-1224 291 11 0 0 PROPN ijassa-1224 291 12 . . PUNCT ijassa-1224 292 1 ( ( PUNCT ijassa-1224 292 2 51 51 NUM ijassa-1224 292 3 ) ) PUNCT ijassa-1224 292 4 from from ADP ijassa-1224 292 5 equation equation NOUN ijassa-1224 292 6 ( ( PUNCT ijassa-1224 292 7 49 49 NUM ijassa-1224 292 8 ) ) PUNCT ijassa-1224 292 9 𝑠 𝑠 PROPN ijassa-1224 292 10 = = SYM ijassa-1224 292 11 0 0 NUM ijassa-1224 292 12 , , PUNCT ijassa-1224 292 13 integrating integrate VERB ijassa-1224 292 14 both both DET ijassa-1224 292 15 side side NOUN ijassa-1224 292 16 𝑠 𝑠 PROPN ijassa-1224 292 17 = = SYM ijassa-1224 292 18 𝐷 𝐷 PROPN ijassa-1224 292 19 and and CCONJ ijassa-1224 292 20 applying apply VERB ijassa-1224 292 21 initial initial ADJ ijassa-1224 292 22 condition condition NOUN ijassa-1224 292 23 𝑠 𝑠 PROPN ijassa-1224 292 24 ( ( PUNCT ijassa-1224 292 25 0 0 NUM ijassa-1224 292 26 ) ) PUNCT ijassa-1224 292 27 = = SYM ijassa-1224 292 28 𝑆 𝑆 PROPN ijassa-1224 292 29 = = SYM ijassa-1224 292 30 𝑠 𝑠 PROPN ijassa-1224 292 31 , , PUNCT ijassa-1224 292 32 𝐷 𝐷 PROPN ijassa-1224 292 33 = = SYM ijassa-1224 292 34 𝑆 𝑆 PROPN ijassa-1224 292 35 and and CCONJ ijassa-1224 292 36 𝑠 𝑠 PROPN ijassa-1224 292 37 = = SYM ijassa-1224 292 38 𝑆 𝑆 PROPN ijassa-1224 292 39 . . PUNCT ijassa-1224 293 1 from from ADP ijassa-1224 293 2 equation equation NOUN ijassa-1224 293 3 ( ( PUNCT ijassa-1224 293 4 51 51 NUM ijassa-1224 293 5 ) ) PUNCT ijassa-1224 293 6 𝑠 𝑠 PROPN ijassa-1224 293 7 = = SYM ijassa-1224 293 8 πœ‹(1 πœ‹(1 PROPN ijassa-1224 293 9 βˆ’ βˆ’ PROPN ijassa-1224 293 10 πœƒ πœƒ NOUN ijassa-1224 293 11 ) ) PUNCT ijassa-1224 293 12 + + CCONJ ijassa-1224 293 13 πœ”π‘£ πœ”π‘£ ADP ijassa-1224 293 14 βˆ’ βˆ’ PROPN ijassa-1224 293 15 ( ( PUNCT ijassa-1224 293 16 πœ‡ πœ‡ ADP ijassa-1224 293 17 + + X ijassa-1224 293 18 πœ† πœ† X ijassa-1224 293 19 ) ) PUNCT ijassa-1224 293 20 𝑠 𝑠 PROPN ijassa-1224 293 21 . . PUNCT ijassa-1224 294 1 integrate integrate VERB ijassa-1224 294 2 both both DET ijassa-1224 294 3 sides side NOUN ijassa-1224 294 4 and and CCONJ ijassa-1224 294 5 applying apply VERB ijassa-1224 294 6 the the DET ijassa-1224 294 7 initial initial ADJ ijassa-1224 294 8 condition condition NOUN ijassa-1224 294 9 we we PRON ijassa-1224 294 10 get get VERB ijassa-1224 294 11 : : PUNCT ijassa-1224 294 12 𝑠 𝑠 PROPN ijassa-1224 294 13 ( ( PUNCT ijassa-1224 294 14 𝑑 𝑑 NOUN ijassa-1224 294 15 ) ) PUNCT ijassa-1224 294 16 = = SYM ijassa-1224 294 17 ( ( PUNCT ijassa-1224 294 18 πœ‹(1 πœ‹(1 NOUN ijassa-1224 294 19 βˆ’ βˆ’ PROPN ijassa-1224 294 20 πœƒ πœƒ NOUN ijassa-1224 294 21 ) ) PUNCT ijassa-1224 295 1 + + CCONJ ijassa-1224 295 2 πœ”π‘£ πœ”π‘£ ADP ijassa-1224 295 3 βˆ’ βˆ’ PROPN ijassa-1224 295 4 ( ( PUNCT ijassa-1224 295 5 πœ‡ πœ‡ ADP ijassa-1224 295 6 + + X ijassa-1224 295 7 πœ† πœ† X ijassa-1224 295 8 ) ) PUNCT ijassa-1224 295 9 𝑠 𝑠 NOUN ijassa-1224 295 10 ) ) PUNCT ijassa-1224 295 11 𝑑. 𝑑. NOUN ijassa-1224 295 12 ( ( PUNCT ijassa-1224 295 13 52 52 NUM ijassa-1224 295 14 ) ) PUNCT ijassa-1224 295 15 substitute substitute NOUN ijassa-1224 295 16 equations equation NOUN ijassa-1224 295 17 ( ( PUNCT ijassa-1224 295 18 41 41 NUM ijassa-1224 295 19 ) ) PUNCT ijassa-1224 295 20 and and CCONJ ijassa-1224 295 21 ( ( PUNCT ijassa-1224 295 22 42 42 NUM ijassa-1224 295 23 ) ) PUNCT ijassa-1224 295 24 into into ADP ijassa-1224 295 25 ( ( PUNCT ijassa-1224 295 26 52 52 NUM ijassa-1224 295 27 ) ) PUNCT ijassa-1224 295 28 𝑠 𝑠 PROPN ijassa-1224 295 29 ( ( PUNCT ijassa-1224 295 30 𝑑 𝑑 NOUN ijassa-1224 295 31 ) ) PUNCT ijassa-1224 295 32 = = SYM ijassa-1224 295 33 ( ( PUNCT ijassa-1224 295 34 πœ‹(1 πœ‹(1 NOUN ijassa-1224 295 35 βˆ’ βˆ’ PROPN ijassa-1224 295 36 πœƒ πœƒ NOUN ijassa-1224 295 37 ) ) PUNCT ijassa-1224 295 38 + + CCONJ ijassa-1224 295 39 πœ”πΈ πœ”πΈ PROPN ijassa-1224 295 40 βˆ’ βˆ’ PROPN ijassa-1224 295 41 ( ( PUNCT ijassa-1224 295 42 πœ‡ πœ‡ ADP ijassa-1224 295 43 + + X ijassa-1224 295 44 πœ† πœ† X ijassa-1224 295 45 ) ) PUNCT ijassa-1224 295 46 𝑆 𝑆 NOUN ijassa-1224 295 47 ) ) PUNCT ijassa-1224 295 48 𝑑. 𝑑. NOUN ijassa-1224 295 49 ( ( PUNCT ijassa-1224 295 50 53 53 NUM ijassa-1224 295 51 ) ) PUNCT ijassa-1224 295 52 applying apply VERB ijassa-1224 295 53 hpm hpm NOUN ijassa-1224 295 54 to to ADP ijassa-1224 295 55 equation equation NOUN ijassa-1224 295 56 ( ( PUNCT ijassa-1224 295 57 34 34 NUM ijassa-1224 295 58 ) ) PUNCT ijassa-1224 295 59 ( ( PUNCT ijassa-1224 295 60 1 1 NUM ijassa-1224 295 61 βˆ’ βˆ’ NUM ijassa-1224 295 62 β„Ž β„Ž NOUN ijassa-1224 295 63 ) ) PUNCT ijassa-1224 295 64 + + CCONJ ijassa-1224 295 65 β„Ž β„Ž X ijassa-1224 295 66 + + CCONJ ijassa-1224 295 67 ( ( PUNCT ijassa-1224 295 68 πœ‡ πœ‡ X ijassa-1224 295 69 + + X ijassa-1224 295 70 πœ”)𝑉 πœ”)𝑉 NOUN ijassa-1224 295 71 βˆ’ βˆ’ NOUN ijassa-1224 295 72 πœ‹πœƒ πœ‹πœƒ NOUN ijassa-1224 295 73 = = NOUN ijassa-1224 295 74 0 0 PROPN ijassa-1224 295 75 . . PUNCT ijassa-1224 296 1 ( ( PUNCT ijassa-1224 296 2 54 54 NUM ijassa-1224 296 3 ) ) PUNCT ijassa-1224 296 4 substitute substitute NOUN ijassa-1224 296 5 equation equation NOUN ijassa-1224 296 6 ( ( PUNCT ijassa-1224 296 7 42 42 NUM ijassa-1224 296 8 ) ) PUNCT ijassa-1224 296 9 into into ADP ijassa-1224 296 10 ( ( PUNCT ijassa-1224 296 11 54 54 NUM ijassa-1224 296 12 ) ) PUNCT ijassa-1224 296 13 156 156 NUM ijassa-1224 296 14 f.a f.a PROPN ijassa-1224 296 15 . . PROPN ijassa-1224 296 16 oguntolu oguntolu PROPN ijassa-1224 296 17 , , PUNCT ijassa-1224 296 18 o.j o.j PROPN ijassa-1224 296 19 . . PROPN ijassa-1224 296 20 peter peter PROPN ijassa-1224 296 21 , , PUNCT ijassa-1224 296 22 k. k. PROPN ijassa-1224 296 23 oshinubi oshinubi PROPN ijassa-1224 296 24 , , PUNCT ijassa-1224 296 25 t.a t.a PROPN ijassa-1224 296 26 . . PROPN ijassa-1224 296 27 ayoola ayoola PROPN ijassa-1224 296 28 , , PUNCT ijassa-1224 296 29 a.o a.o PROPN ijassa-1224 296 30 . . PROPN ijassa-1224 296 31 oladapo oladapo PROPN ijassa-1224 296 32 , , PUNCT ijassa-1224 296 33 m.m m.m PROPN ijassa-1224 296 34 . . PROPN ijassa-1224 296 35 ojo ojo NOUN ijassa-1224 296 36 copyright copyright NOUN ijassa-1224 296 37 Β© Β© PROPN ijassa-1224 296 38 2022 2022 NUM ijassa-1224 296 39 assa assa PROPN ijassa-1224 296 40 adv adv PROPN ijassa-1224 296 41 . . PUNCT ijassa-1224 297 1 in in ADP ijassa-1224 297 2 systems system NOUN ijassa-1224 297 3 science science NOUN ijassa-1224 297 4 and and CCONJ ijassa-1224 297 5 appl appl NOUN ijassa-1224 297 6 . . PUNCT ijassa-1224 298 1 ( ( PUNCT ijassa-1224 298 2 2022 2022 NUM ijassa-1224 298 3 ) ) PUNCT ijassa-1224 298 4 ( ( PUNCT ijassa-1224 298 5 𝑒 𝑒 X ijassa-1224 298 6 + + X ijassa-1224 298 7 β„Žπ‘’ β„Žπ‘’ NOUN ijassa-1224 298 8 + + NUM ijassa-1224 298 9 β„Ž β„Ž X ijassa-1224 298 10 𝑒 𝑒 PRON ijassa-1224 298 11 + + PROPN ijassa-1224 298 12 . . PUNCT ijassa-1224 298 13 . . PUNCT ijassa-1224 298 14 . . PUNCT ijassa-1224 298 15 ) ) PUNCT ijassa-1224 299 1 + + CCONJ ijassa-1224 299 2 β„Ž[(πœ‡ β„Ž[(πœ‡ ADV ijassa-1224 299 3 + + PUNCT ijassa-1224 299 4 πœ”)(𝑒 πœ”)(𝑒 PUNCT ijassa-1224 299 5 + + CCONJ ijassa-1224 299 6 β„Žπ‘’ β„Žπ‘’ NOUN ijassa-1224 299 7 + + NUM ijassa-1224 299 8 β„Ž β„Ž X ijassa-1224 299 9 𝑒 𝑒 PRON ijassa-1224 299 10 + + PROPN ijassa-1224 299 11 . . PUNCT ijassa-1224 299 12 . . PUNCT ijassa-1224 299 13 . . PUNCT ijassa-1224 299 14 ) ) PUNCT ijassa-1224 300 1 βˆ’ βˆ’ PRON ijassa-1224 300 2 πœ‹πœƒ πœ‹πœƒ NOUN ijassa-1224 300 3 ] ] X ijassa-1224 300 4 = = SYM ijassa-1224 300 5 0 0 X ijassa-1224 300 6 . . PUNCT ijassa-1224 301 1 collecting collect VERB ijassa-1224 301 2 the the DET ijassa-1224 301 3 coefficient coefficient NOUN ijassa-1224 301 4 of of ADP ijassa-1224 301 5 power power NOUN ijassa-1224 301 6 of of ADP ijassa-1224 301 7 β„Ž β„Ž PROPN ijassa-1224 301 8 , , PUNCT ijassa-1224 301 9 we we PRON ijassa-1224 301 10 have have VERB ijassa-1224 301 11 β„Ž β„Ž NOUN ijassa-1224 301 12 : : PUNCT ijassa-1224 301 13 𝑒 𝑒 X ijassa-1224 301 14 = = SYM ijassa-1224 301 15 0 0 NUM ijassa-1224 301 16 , , PUNCT ijassa-1224 301 17 ( ( PUNCT ijassa-1224 301 18 55 55 NUM ijassa-1224 301 19 ) ) PUNCT ijassa-1224 301 20 β„Ž β„Ž NOUN ijassa-1224 301 21 : : PUNCT ijassa-1224 301 22 𝑒 𝑒 X ijassa-1224 301 23 + + X ijassa-1224 301 24 ( ( PUNCT ijassa-1224 301 25 πœ‡ πœ‡ X ijassa-1224 301 26 + + X ijassa-1224 301 27 πœ”)𝑒 πœ”)𝑒 PUNCT ijassa-1224 301 28 βˆ’ βˆ’ NOUN ijassa-1224 301 29 πœ‹πœƒ πœ‹πœƒ NOUN ijassa-1224 301 30 = = SYM ijassa-1224 301 31 0 0 NUM ijassa-1224 301 32 , , PUNCT ijassa-1224 301 33 ( ( PUNCT ijassa-1224 301 34 56 56 NUM ijassa-1224 301 35 ) ) PUNCT ijassa-1224 301 36 β„Ž β„Ž NOUN ijassa-1224 301 37 : : PUNCT ijassa-1224 301 38 𝑒 𝑒 X ijassa-1224 301 39 + + X ijassa-1224 301 40 ( ( PUNCT ijassa-1224 301 41 πœ‡ πœ‡ X ijassa-1224 301 42 + + X ijassa-1224 301 43 πœ”)𝑒 πœ”)𝑒 PUNCT ijassa-1224 302 1 = = SYM ijassa-1224 302 2 0 0 X ijassa-1224 302 3 . . PUNCT ijassa-1224 302 4 ( ( PUNCT ijassa-1224 302 5 57 57 NUM ijassa-1224 302 6 ) ) PUNCT ijassa-1224 302 7 from from ADP ijassa-1224 302 8 equation equation NOUN ijassa-1224 302 9 ( ( PUNCT ijassa-1224 302 10 56 56 NUM ijassa-1224 302 11 ) ) PUNCT ijassa-1224 302 12 𝑒 𝑒 NOUN ijassa-1224 302 13 = = PUNCT ijassa-1224 302 14 πœ‹πœƒ πœ‹πœƒ NOUN ijassa-1224 302 15 βˆ’ βˆ’ PROPN ijassa-1224 302 16 ( ( PUNCT ijassa-1224 302 17 πœ‡ πœ‡ X ijassa-1224 302 18 + + X ijassa-1224 302 19 πœ”)𝑒 πœ”)𝑒 PUNCT ijassa-1224 302 20 . . PUNCT ijassa-1224 303 1 integrate integrate VERB ijassa-1224 303 2 both both DET ijassa-1224 303 3 sides side NOUN ijassa-1224 303 4 and and CCONJ ijassa-1224 303 5 applying apply VERB ijassa-1224 303 6 the the DET ijassa-1224 303 7 initial initial ADJ ijassa-1224 303 8 condition condition NOUN ijassa-1224 303 9 we we PRON ijassa-1224 303 10 have have VERB ijassa-1224 303 11 : : PUNCT ijassa-1224 303 12 𝑒 𝑒 X ijassa-1224 303 13 ( ( PUNCT ijassa-1224 303 14 𝑑 𝑑 NOUN ijassa-1224 303 15 ) ) PUNCT ijassa-1224 303 16 = = SYM ijassa-1224 303 17 ( ( PUNCT ijassa-1224 303 18 πœ‹πœƒ πœ‹πœƒ NOUN ijassa-1224 303 19 βˆ’ βˆ’ PROPN ijassa-1224 303 20 ( ( PUNCT ijassa-1224 303 21 πœ‡ πœ‡ X ijassa-1224 303 22 + + X ijassa-1224 303 23 πœ”)𝑒 πœ”)𝑒 PUNCT ijassa-1224 303 24 ) ) PUNCT ijassa-1224 303 25 𝑑. 𝑑. NOUN ijassa-1224 303 26 ( ( PUNCT ijassa-1224 303 27 58 58 NUM ijassa-1224 303 28 ) ) PUNCT ijassa-1224 303 29 substitute substitute NOUN ijassa-1224 303 30 equation equation NOUN ijassa-1224 303 31 ( ( PUNCT ijassa-1224 303 32 42 42 NUM ijassa-1224 303 33 ) ) PUNCT ijassa-1224 303 34 into into ADP ijassa-1224 303 35 ( ( PUNCT ijassa-1224 303 36 60 60 NUM ijassa-1224 303 37 ) ) PUNCT ijassa-1224 303 38 𝑒 𝑒 PROPN ijassa-1224 303 39 ( ( PUNCT ijassa-1224 303 40 𝑑 𝑑 NOUN ijassa-1224 303 41 ) ) PUNCT ijassa-1224 303 42 = = SYM ijassa-1224 303 43 ( ( PUNCT ijassa-1224 303 44 πœ‹πœƒ πœ‹πœƒ NOUN ijassa-1224 303 45 βˆ’ βˆ’ PROPN ijassa-1224 303 46 ( ( PUNCT ijassa-1224 303 47 πœ‡ πœ‡ X ijassa-1224 303 48 + + X ijassa-1224 303 49 πœ”)𝑉 πœ”)𝑉 NOUN ijassa-1224 303 50 ) ) PUNCT ijassa-1224 303 51 𝑑. 𝑑. NOUN ijassa-1224 303 52 ( ( PUNCT ijassa-1224 303 53 59 59 NUM ijassa-1224 303 54 ) ) PUNCT ijassa-1224 303 55 from from ADP ijassa-1224 303 56 equation equation NOUN ijassa-1224 303 57 ( ( PUNCT ijassa-1224 303 58 51 51 NUM ijassa-1224 303 59 ) ) PUNCT ijassa-1224 303 60 𝑠 𝑠 PROPN ijassa-1224 304 1 = = PUNCT ijassa-1224 304 2 πœ”π‘’ πœ”π‘’ PROPN ijassa-1224 304 3 βˆ’ βˆ’ PROPN ijassa-1224 304 4 ( ( PUNCT ijassa-1224 304 5 πœ‡ πœ‡ ADP ijassa-1224 304 6 + + X ijassa-1224 304 7 πœ† πœ† X ijassa-1224 304 8 ) ) PUNCT ijassa-1224 304 9 𝑠 𝑠 PROPN ijassa-1224 304 10 . . PUNCT ijassa-1224 305 1 ( ( PUNCT ijassa-1224 305 2 60 60 NUM ijassa-1224 305 3 ) ) PUNCT ijassa-1224 305 4 substitute substitute NOUN ijassa-1224 305 5 equation equation NOUN ijassa-1224 305 6 ( ( PUNCT ijassa-1224 305 7 59 59 NUM ijassa-1224 305 8 ) ) PUNCT ijassa-1224 305 9 and and CCONJ ijassa-1224 305 10 ( ( PUNCT ijassa-1224 305 11 53 53 NUM ijassa-1224 305 12 ) ) PUNCT ijassa-1224 305 13 into into ADP ijassa-1224 305 14 ( ( PUNCT ijassa-1224 305 15 60 60 NUM ijassa-1224 305 16 ) ) PUNCT ijassa-1224 305 17 𝑠 𝑠 PROPN ijassa-1224 305 18 = = SYM ijassa-1224 305 19 πœ”(πœ‹πœƒ πœ”(πœ‹πœƒ PROPN ijassa-1224 305 20 βˆ’ βˆ’ PROPN ijassa-1224 305 21 ( ( PUNCT ijassa-1224 305 22 πœ‡ πœ‡ X ijassa-1224 305 23 + + X ijassa-1224 305 24 πœ”)𝑉 πœ”)𝑉 NOUN ijassa-1224 305 25 ) ) PUNCT ijassa-1224 305 26 𝑑 𝑑 NOUN ijassa-1224 305 27 βˆ’ βˆ’ PROPN ijassa-1224 305 28 ( ( PUNCT ijassa-1224 305 29 πœ‡ πœ‡ ADP ijassa-1224 305 30 + + X ijassa-1224 305 31 πœ† πœ† X ijassa-1224 305 32 ) ) PUNCT ijassa-1224 305 33 ( ( PUNCT ijassa-1224 305 34 πœ‹(1 πœ‹(1 NOUN ijassa-1224 305 35 βˆ’ βˆ’ PROPN ijassa-1224 305 36 πœƒ πœƒ NOUN ijassa-1224 305 37 ) ) PUNCT ijassa-1224 306 1 + + CCONJ ijassa-1224 306 2 πœ”πΈ πœ”πΈ PROPN ijassa-1224 306 3 βˆ’ βˆ’ PROPN ijassa-1224 306 4 ( ( PUNCT ijassa-1224 306 5 πœ‡ πœ‡ ADP ijassa-1224 306 6 + + X ijassa-1224 306 7 πœ† πœ† X ijassa-1224 306 8 ) ) PUNCT ijassa-1224 306 9 𝑆 𝑆 PROPN ijassa-1224 306 10 ) ) PUNCT ijassa-1224 306 11 𝑑 𝑑 PROPN ijassa-1224 306 12 , , PUNCT ijassa-1224 306 13 𝑠 𝑠 X ijassa-1224 306 14 = = PUNCT ijassa-1224 306 15 πœ”(πœ‹πœƒ πœ”(πœ‹πœƒ PROPN ijassa-1224 306 16 βˆ’ βˆ’ PROPN ijassa-1224 306 17 ( ( PUNCT ijassa-1224 306 18 πœ‡ πœ‡ X ijassa-1224 306 19 + + X ijassa-1224 306 20 πœ”)𝑉 πœ”)𝑉 NOUN ijassa-1224 306 21 ) ) PUNCT ijassa-1224 306 22 βˆ’ βˆ’ PROPN ijassa-1224 306 23 ( ( PUNCT ijassa-1224 306 24 πœ‡ πœ‡ ADP ijassa-1224 306 25 + + X ijassa-1224 306 26 πœ† πœ† X ijassa-1224 306 27 ) ) PUNCT ijassa-1224 306 28 ( ( PUNCT ijassa-1224 306 29 πœ‹(1 πœ‹(1 NOUN ijassa-1224 306 30 βˆ’ βˆ’ PROPN ijassa-1224 306 31 πœƒ πœƒ NOUN ijassa-1224 306 32 ) ) PUNCT ijassa-1224 307 1 + + CCONJ ijassa-1224 307 2 πœ”πΈ πœ”πΈ AUX ijassa-1224 307 3 βˆ’ βˆ’ PROPN ijassa-1224 307 4 ( ( PUNCT ijassa-1224 307 5 πœ‡ πœ‡ ADP ijassa-1224 307 6 + + X ijassa-1224 307 7 πœ† πœ† X ijassa-1224 307 8 ) ) PUNCT ijassa-1224 307 9 𝑆 𝑆 PROPN ijassa-1224 307 10 ) ) PUNCT ijassa-1224 307 11 𝑑. 𝑑. NOUN ijassa-1224 307 12 integrating integrate VERB ijassa-1224 307 13 both both DET ijassa-1224 307 14 sides side NOUN ijassa-1224 307 15 and and CCONJ ijassa-1224 307 16 applying apply VERB ijassa-1224 307 17 the the DET ijassa-1224 307 18 initial initial ADJ ijassa-1224 307 19 condition condition NOUN ijassa-1224 308 1 𝑠 𝑠 PROPN ijassa-1224 308 2 ( ( PUNCT ijassa-1224 308 3 𝑑 𝑑 NOUN ijassa-1224 308 4 ) ) PUNCT ijassa-1224 308 5 = = PUNCT ijassa-1224 308 6 πœ”(πœ‹πœƒ πœ”(πœ‹πœƒ PROPN ijassa-1224 308 7 βˆ’ βˆ’ PROPN ijassa-1224 308 8 ( ( PUNCT ijassa-1224 308 9 πœ‡ πœ‡ X ijassa-1224 308 10 + + X ijassa-1224 308 11 πœ”)𝑉 πœ”)𝑉 NOUN ijassa-1224 308 12 ) ) PUNCT ijassa-1224 308 13 βˆ’ βˆ’ PROPN ijassa-1224 308 14 ( ( PUNCT ijassa-1224 308 15 πœ‡ πœ‡ ADP ijassa-1224 308 16 + + X ijassa-1224 308 17 πœ† πœ† X ijassa-1224 308 18 ) ) PUNCT ijassa-1224 308 19 ( ( PUNCT ijassa-1224 308 20 πœ‹(1 πœ‹(1 NOUN ijassa-1224 308 21 βˆ’ βˆ’ PROPN ijassa-1224 308 22 πœƒ πœƒ NOUN ijassa-1224 308 23 ) ) PUNCT ijassa-1224 308 24 + + CCONJ ijassa-1224 308 25 πœ”πΈ πœ”πΈ PROPN ijassa-1224 308 26 βˆ’ βˆ’ PROPN ijassa-1224 308 27 ( ( PUNCT ijassa-1224 308 28 πœ‡ πœ‡ ADP ijassa-1224 308 29 + + X ijassa-1224 308 30 πœ† πœ† X ijassa-1224 308 31 ) ) PUNCT ijassa-1224 308 32 𝑆 𝑆 PROPN ijassa-1224 308 33 ) ) PUNCT ijassa-1224 308 34 . . PUNCT ijassa-1224 309 1 ( ( PUNCT ijassa-1224 309 2 61 61 NUM ijassa-1224 309 3 ) ) PUNCT ijassa-1224 309 4 substitute substitute NOUN ijassa-1224 309 5 the the DET ijassa-1224 309 6 initial initial ADJ ijassa-1224 309 7 condition condition NOUN ijassa-1224 309 8 and and CCONJ ijassa-1224 309 9 equation equation NOUN ijassa-1224 309 10 ( ( PUNCT ijassa-1224 309 11 53 53 NUM ijassa-1224 309 12 ) ) PUNCT ijassa-1224 309 13 and and CCONJ ijassa-1224 309 14 ( ( PUNCT ijassa-1224 309 15 61 61 NUM ijassa-1224 309 16 ) ) PUNCT ijassa-1224 309 17 into into ADP ijassa-1224 309 18 ( ( PUNCT ijassa-1224 309 19 41 41 NUM ijassa-1224 309 20 ) ) PUNCT ijassa-1224 309 21 𝑆(𝑑 𝑆(𝑑 NOUN ijassa-1224 309 22 ) ) PUNCT ijassa-1224 309 23 = = SYM ijassa-1224 310 1 𝑠 𝑠 PROPN ijassa-1224 311 1 + + CCONJ ijassa-1224 311 2 β„Žπ‘  β„Žπ‘  VERB ijassa-1224 311 3 + + NUM ijassa-1224 311 4 β„Ž β„Ž X ijassa-1224 311 5 𝑠 𝑠 PROPN ijassa-1224 311 6 + + PROPN ijassa-1224 311 7 . . PUNCT ijassa-1224 311 8 . . PUNCT ijassa-1224 312 1 . . PUNCT ijassa-1224 313 1 , , PUNCT ijassa-1224 313 2 𝑆(𝑑 𝑆(𝑑 NUM ijassa-1224 313 3 ) ) PUNCT ijassa-1224 313 4 = = SYM ijassa-1224 313 5 lim lim NOUN ijassa-1224 313 6 { { PUNCT ijassa-1224 313 7 β†’ β†’ SYM ijassa-1224 313 8 } } PUNCT ijassa-1224 313 9 ( ( PUNCT ijassa-1224 313 10 𝑠 𝑠 PROPN ijassa-1224 313 11 + + CCONJ ijassa-1224 313 12 β„Žπ‘  β„Žπ‘  VERB ijassa-1224 313 13 + + NUM ijassa-1224 313 14 β„Ž β„Ž X ijassa-1224 313 15 𝑠 𝑠 PROPN ijassa-1224 313 16 + + NUM ijassa-1224 313 17 β‹― β‹― PROPN ijassa-1224 313 18 ) ) PUNCT ijassa-1224 313 19 , , PUNCT ijassa-1224 313 20 𝑆(𝑑 𝑆(𝑑 NOUN ijassa-1224 313 21 ) ) PUNCT ijassa-1224 313 22 = = SYM ijassa-1224 313 23 𝑠 𝑠 PROPN ijassa-1224 314 1 + + NUM ijassa-1224 314 2 𝑠 𝑠 PROPN ijassa-1224 315 1 + + NOUN ijassa-1224 315 2 𝑠 𝑠 PROPN ijassa-1224 316 1 + + PROPN ijassa-1224 316 2 . . PUNCT ijassa-1224 316 3 . . PUNCT ijassa-1224 317 1 . . PUNCT ijassa-1224 318 1 , , PUNCT ijassa-1224 318 2 hence hence ADV ijassa-1224 318 3 , , PUNCT ijassa-1224 318 4 𝑆(𝑑 𝑆(𝑑 NOUN ijassa-1224 318 5 ) ) PUNCT ijassa-1224 318 6 = = SYM ijassa-1224 318 7 𝑆 𝑆 PROPN ijassa-1224 318 8 + + CCONJ ijassa-1224 318 9 ( ( PUNCT ijassa-1224 318 10 πœ‹(1 πœ‹(1 NOUN ijassa-1224 318 11 βˆ’ βˆ’ PROPN ijassa-1224 318 12 πœƒ πœƒ NOUN ijassa-1224 318 13 ) ) PUNCT ijassa-1224 319 1 + + CCONJ ijassa-1224 319 2 πœ”πΈ πœ”πΈ PROPN ijassa-1224 319 3 βˆ’ βˆ’ PROPN ijassa-1224 319 4 ( ( PUNCT ijassa-1224 319 5 πœ‡ πœ‡ ADP ijassa-1224 319 6 + + X ijassa-1224 319 7 πœ† πœ† X ijassa-1224 319 8 ) ) PUNCT ijassa-1224 319 9 𝑆 𝑆 PROPN ijassa-1224 319 10 ) ) PUNCT ijassa-1224 319 11 𝑑 𝑑 PROPN ijassa-1224 319 12 + + PROPN ijassa-1224 319 13 πœ”(πœ‹πœƒ πœ”(πœ‹πœƒ X ijassa-1224 319 14 βˆ’ βˆ’ PROPN ijassa-1224 319 15 ( ( PUNCT ijassa-1224 319 16 πœ‡ πœ‡ X ijassa-1224 319 17 + + X ijassa-1224 319 18 πœ”)𝑉 πœ”)𝑉 NOUN ijassa-1224 319 19 ) ) PUNCT ijassa-1224 319 20 βˆ’ βˆ’ PROPN ijassa-1224 320 1 ( ( PUNCT ijassa-1224 320 2 πœ‡ πœ‡ ADP ijassa-1224 320 3 + + X ijassa-1224 320 4 πœ† πœ† X ijassa-1224 320 5 ) ) PUNCT ijassa-1224 320 6 ( ( PUNCT ijassa-1224 320 7 πœ‹(1 πœ‹(1 NOUN ijassa-1224 320 8 βˆ’ βˆ’ PROPN ijassa-1224 320 9 πœƒ πœƒ NOUN ijassa-1224 320 10 ) ) PUNCT ijassa-1224 320 11 + + CCONJ ijassa-1224 320 12 πœ”πΈ πœ”πΈ PROPN ijassa-1224 320 13 βˆ’ βˆ’ PROPN ijassa-1224 320 14 ( ( PUNCT ijassa-1224 320 15 πœ‡ πœ‡ ADP ijassa-1224 320 16 + + X ijassa-1224 320 17 πœ† πœ† X ijassa-1224 320 18 ) ) PUNCT ijassa-1224 320 19 𝑆 𝑆 PROPN ijassa-1224 320 20 ) ) PUNCT ijassa-1224 320 21 𝑑 𝑑 PROPN ijassa-1224 320 22 2 2 NUM ijassa-1224 320 23 . . PUNCT ijassa-1224 321 1 following follow VERB ijassa-1224 321 2 the the DET ijassa-1224 321 3 same same ADJ ijassa-1224 321 4 process process NOUN ijassa-1224 321 5 for for ADP ijassa-1224 321 6 other other ADJ ijassa-1224 321 7 equations equation NOUN ijassa-1224 321 8 , , PUNCT ijassa-1224 321 9 we we PRON ijassa-1224 321 10 have have VERB ijassa-1224 321 11 : : PUNCT ijassa-1224 321 12 𝑉(𝑑 𝑉(𝑑 NUM ijassa-1224 321 13 ) ) PUNCT ijassa-1224 321 14 = = SYM ijassa-1224 321 15 𝑉 𝑉 PROPN ijassa-1224 321 16 + + CCONJ ijassa-1224 321 17 ( ( PUNCT ijassa-1224 321 18 πœ‹πœƒ πœ‹πœƒ PROPN ijassa-1224 321 19 βˆ’ βˆ’ PROPN ijassa-1224 321 20 ( ( PUNCT ijassa-1224 321 21 πœ‡ πœ‡ X ijassa-1224 321 22 + + X ijassa-1224 321 23 πœ”)𝑉 πœ”)𝑉 NOUN ijassa-1224 321 24 ) ) PUNCT ijassa-1224 321 25 𝑑 𝑑 PROPN ijassa-1224 322 1 + + X ijassa-1224 322 2 ( ( PUNCT ijassa-1224 322 3 πœ‡ πœ‡ X ijassa-1224 322 4 + + X ijassa-1224 322 5 πœ”)(πœ‹πœƒ πœ”)(πœ‹πœƒ NOUN ijassa-1224 322 6 βˆ’ βˆ’ NOUN ijassa-1224 322 7 ( ( PUNCT ijassa-1224 322 8 πœ‡ πœ‡ X ijassa-1224 322 9 + + X ijassa-1224 322 10 πœ”)𝑉 πœ”)𝑉 NOUN ijassa-1224 322 11 ) ) PUNCT ijassa-1224 322 12 𝑑 𝑑 PROPN ijassa-1224 322 13 2 2 NUM ijassa-1224 322 14 , , PUNCT ijassa-1224 322 15 𝐸(𝑑 𝐸(𝑑 NUM ijassa-1224 322 16 ) ) PUNCT ijassa-1224 322 17 = = SYM ijassa-1224 322 18 𝐸 𝐸 PROPN ijassa-1224 322 19 + + CCONJ ijassa-1224 322 20 πœ† πœ† PROPN ijassa-1224 322 21 𝑇 𝑇 PROPN ijassa-1224 322 22 + + CCONJ ijassa-1224 322 23 πœ† πœ† PROPN ijassa-1224 322 24 𝑆 𝑆 PROPN ijassa-1224 322 25 βˆ’ βˆ’ PROPN ijassa-1224 322 26 ( ( PUNCT ijassa-1224 322 27 𝜎 𝜎 PROPN ijassa-1224 323 1 + + X ijassa-1224 323 2 πœ† πœ† NOUN ijassa-1224 323 3 + + CCONJ ijassa-1224 323 4 πœ‡)𝐸 πœ‡)𝐸 ADJ ijassa-1224 323 5 𝑑 𝑑 NOUN ijassa-1224 323 6 + + X ijassa-1224 323 7 πœ† πœ† NOUN ijassa-1224 323 8 ( ( PUNCT ijassa-1224 323 9 π‘Ÿ π‘Ÿ X ijassa-1224 323 10 𝐽 𝐽 PROPN ijassa-1224 323 11 + + NUM ijassa-1224 323 12 π‘Ÿ π‘Ÿ X ijassa-1224 323 13 𝐼 𝐼 ADP ijassa-1224 323 14 + + NOUN ijassa-1224 323 15 π‘Ÿ π‘Ÿ NOUN ijassa-1224 323 16 𝐼 𝐼 ADP ijassa-1224 323 17 βˆ’ βˆ’ PROPN ijassa-1224 323 18 ( ( PUNCT ijassa-1224 323 19 πœ‡ πœ‡ ADP ijassa-1224 323 20 + + X ijassa-1224 323 21 πœ† πœ† X ijassa-1224 323 22 ) ) PUNCT ijassa-1224 323 23 𝑇 𝑇 PROPN ijassa-1224 323 24 ) ) PUNCT ijassa-1224 324 1 + + CCONJ ijassa-1224 324 2 πœ† πœ† X ijassa-1224 324 3 ( ( PUNCT ijassa-1224 324 4 πœ‹(1 πœ‹(1 NOUN ijassa-1224 324 5 βˆ’ βˆ’ PROPN ijassa-1224 324 6 πœƒ πœƒ NOUN ijassa-1224 324 7 ) ) PUNCT ijassa-1224 324 8 + + CCONJ ijassa-1224 324 9 πœ”πΈ πœ”πΈ PROPN ijassa-1224 324 10 βˆ’ βˆ’ PROPN ijassa-1224 324 11 ( ( PUNCT ijassa-1224 324 12 πœ‡ πœ‡ ADP ijassa-1224 324 13 + + X ijassa-1224 324 14 πœ† πœ† X ijassa-1224 324 15 ) ) PUNCT ijassa-1224 324 16 𝑆 𝑆 PROPN ijassa-1224 324 17 ) ) PUNCT ijassa-1224 324 18 βˆ’(πœ† βˆ’(πœ† PROPN ijassa-1224 324 19 + + CCONJ ijassa-1224 324 20 πœ‡ πœ‡ X ijassa-1224 324 21 + + NOUN ijassa-1224 324 22 𝜎)(πœ† 𝜎)(πœ† PROPN ijassa-1224 324 23 𝑇 𝑇 NOUN ijassa-1224 324 24 + + CCONJ ijassa-1224 324 25 πœ† πœ† PROPN ijassa-1224 324 26 𝑆 𝑆 PROPN ijassa-1224 324 27 βˆ’ βˆ’ PROPN ijassa-1224 324 28 ( ( PUNCT ijassa-1224 324 29 𝜎 𝜎 PROPN ijassa-1224 325 1 + + X ijassa-1224 325 2 πœ† πœ† NOUN ijassa-1224 325 3 + + CCONJ ijassa-1224 325 4 πœ‡)𝐸 πœ‡)𝐸 ADJ ijassa-1224 325 5 ) ) PUNCT ijassa-1224 325 6 𝑑 𝑑 PROPN ijassa-1224 325 7 2 2 NUM ijassa-1224 325 8 , , PUNCT ijassa-1224 325 9 𝐼 𝐼 PROPN ijassa-1224 325 10 ( ( PUNCT ijassa-1224 325 11 𝑑 𝑑 NOUN ijassa-1224 325 12 ) ) PUNCT ijassa-1224 325 13 = = SYM ijassa-1224 325 14 𝐼 𝐼 PROPN ijassa-1224 325 15 + + CCONJ ijassa-1224 325 16 ( ( PUNCT ijassa-1224 325 17 1 1 NUM ijassa-1224 325 18 βˆ’ βˆ’ PROPN ijassa-1224 325 19 𝜌)𝜎𝐸 𝜌)𝜎𝐸 PROPN ijassa-1224 325 20 + + CCONJ ijassa-1224 325 21 ( ( PUNCT ijassa-1224 325 22 1 1 NUM ijassa-1224 325 23 βˆ’ βˆ’ NOUN ijassa-1224 325 24 πœ™)πœ† πœ™)πœ† X ijassa-1224 325 25 𝐸 𝐸 PROPN ijassa-1224 325 26 βˆ’ βˆ’ PROPN ijassa-1224 325 27 ( ( PUNCT ijassa-1224 325 28 𝛾 𝛾 NOUN ijassa-1224 325 29 + + X ijassa-1224 325 30 πœ‡ πœ‡ ADP ijassa-1224 325 31 + + NOUN ijassa-1224 325 32 π‘Ÿ π‘Ÿ NOUN ijassa-1224 325 33 + + CCONJ ijassa-1224 325 34 𝑑 𝑑 NOUN ijassa-1224 325 35 ) ) PUNCT ijassa-1224 325 36 𝐼 𝐼 ADP ijassa-1224 325 37 𝑑 𝑑 PROPN ijassa-1224 325 38 + + X ijassa-1224 325 39 ( ( PUNCT ijassa-1224 325 40 1 1 NUM ijassa-1224 325 41 βˆ’ βˆ’ NOUN ijassa-1224 325 42 𝜌)𝜎 𝜌)𝜎 ADJ ijassa-1224 325 43 + + CCONJ ijassa-1224 325 44 ( ( PUNCT ijassa-1224 325 45 1 1 NUM ijassa-1224 325 46 βˆ’ βˆ’ PROPN ijassa-1224 325 47 πœƒ πœƒ NOUN ijassa-1224 325 48 ) ) PUNCT ijassa-1224 325 49 ( ( PUNCT ijassa-1224 325 50 πœ† πœ† PROPN ijassa-1224 325 51 𝑇 𝑇 PROPN ijassa-1224 325 52 + + CCONJ ijassa-1224 325 53 πœ† πœ† PROPN ijassa-1224 325 54 𝑆 𝑆 PROPN ijassa-1224 325 55 βˆ’ βˆ’ PROPN ijassa-1224 325 56 ( ( PUNCT ijassa-1224 325 57 𝜎 𝜎 PROPN ijassa-1224 326 1 + + X ijassa-1224 326 2 πœ† πœ† NOUN ijassa-1224 326 3 + + CCONJ ijassa-1224 326 4 πœ‡)𝐸 πœ‡)𝐸 NOUN ijassa-1224 326 5 ) ) PUNCT ijassa-1224 327 1 βˆ’ βˆ’ PROPN ijassa-1224 327 2 ( ( PUNCT ijassa-1224 327 3 𝛾 𝛾 ADP ijassa-1224 327 4 + + PRON ijassa-1224 327 5 π‘Ÿ π‘Ÿ NOUN ijassa-1224 328 1 + + CCONJ ijassa-1224 328 2 𝑑 𝑑 PROPN ijassa-1224 328 3 + + X ijassa-1224 328 4 πœ‡ πœ‡ X ijassa-1224 328 5 ) ) PUNCT ijassa-1224 328 6 ( ( PUNCT ijassa-1224 328 7 1 1 NUM ijassa-1224 328 8 βˆ’ βˆ’ NOUN ijassa-1224 328 9 𝜌)𝜎 𝜌)𝜎 ADJ ijassa-1224 328 10 + + CCONJ ijassa-1224 328 11 ( ( PUNCT ijassa-1224 328 12 1 1 NUM ijassa-1224 328 13 βˆ’ βˆ’ NOUN ijassa-1224 328 14 πœ™)πœ† πœ™)πœ† X ijassa-1224 328 15 𝐸 𝐸 PROPN ijassa-1224 328 16 βˆ’ βˆ’ PROPN ijassa-1224 328 17 ( ( PUNCT ijassa-1224 328 18 𝛾 𝛾 NOUN ijassa-1224 328 19 + + X ijassa-1224 328 20 πœ‡ πœ‡ ADP ijassa-1224 328 21 + + NOUN ijassa-1224 328 22 π‘Ÿ π‘Ÿ NOUN ijassa-1224 328 23 + + CCONJ ijassa-1224 328 24 𝑑 𝑑 NOUN ijassa-1224 328 25 ) ) PUNCT ijassa-1224 328 26 𝐼 𝐼 ADP ijassa-1224 328 27 𝑑 𝑑 PROPN ijassa-1224 328 28 2 2 NUM ijassa-1224 328 29 , , PUNCT ijassa-1224 328 30 analysis analysis NOUN ijassa-1224 328 31 and and CCONJ ijassa-1224 328 32 dynamics dynamic NOUN ijassa-1224 328 33 of of ADP ijassa-1224 328 34 tuberculosis tuberculosis NOUN ijassa-1224 328 35 outbreak outbreak NOUN ijassa-1224 328 36 157 157 NUM ijassa-1224 328 37 copyright copyright NOUN ijassa-1224 328 38 Β© Β© PROPN ijassa-1224 328 39 2022 2022 NUM ijassa-1224 328 40 assa assa NOUN ijassa-1224 328 41 . . PUNCT ijassa-1224 329 1 adv adv PROPN ijassa-1224 329 2 . . PUNCT ijassa-1224 330 1 in in ADP ijassa-1224 330 2 systems system NOUN ijassa-1224 330 3 science science NOUN ijassa-1224 330 4 and and CCONJ ijassa-1224 330 5 appl appl NOUN ijassa-1224 330 6 . . PUNCT ijassa-1224 331 1 ( ( PUNCT ijassa-1224 331 2 2022 2022 NUM ijassa-1224 331 3 ) ) PUNCT ijassa-1224 332 1 𝐼 𝐼 PROPN ijassa-1224 332 2 ( ( PUNCT ijassa-1224 332 3 𝑑 𝑑 NOUN ijassa-1224 332 4 ) ) PUNCT ijassa-1224 332 5 = = SYM ijassa-1224 332 6 𝐼 𝐼 PROPN ijassa-1224 332 7 + + CCONJ ijassa-1224 332 8 ( ( PUNCT ijassa-1224 332 9 πœ™πœ† πœ™πœ† NOUN ijassa-1224 332 10 𝐸 𝐸 PROPN ijassa-1224 332 11 + + CCONJ ijassa-1224 332 12 𝜌𝜎𝐸 𝜌𝜎𝐸 PROPN ijassa-1224 332 13 + + CCONJ ijassa-1224 332 14 𝛾𝐼 𝛾𝐼 PROPN ijassa-1224 332 15 βˆ’ βˆ’ PROPN ijassa-1224 332 16 ( ( PUNCT ijassa-1224 332 17 πœ‡ πœ‡ ADP ijassa-1224 332 18 + + X ijassa-1224 332 19 𝑑 𝑑 PROPN ijassa-1224 332 20 + + NUM ijassa-1224 332 21 π‘Ÿ π‘Ÿ NOUN ijassa-1224 332 22 + + NUM ijassa-1224 332 23 π‘Ÿ π‘Ÿ NOUN ijassa-1224 332 24 ) ) PUNCT ijassa-1224 332 25 π‘₯𝐼 π‘₯𝐼 PUNCT ijassa-1224 332 26 ) ) PUNCT ijassa-1224 333 1 𝑑 𝑑 PROPN ijassa-1224 333 2 + + X ijassa-1224 333 3 ( ( PUNCT ijassa-1224 333 4 𝜌𝜎 𝜌𝜎 VERB ijassa-1224 333 5 + + CCONJ ijassa-1224 333 6 πœ™πœ† πœ™πœ† NOUN ijassa-1224 333 7 ) ) PUNCT ijassa-1224 333 8 ( ( PUNCT ijassa-1224 333 9 πœ† πœ† PROPN ijassa-1224 333 10 𝑇 𝑇 PROPN ijassa-1224 333 11 + + CCONJ ijassa-1224 333 12 πœ† πœ† PROPN ijassa-1224 333 13 𝑆 𝑆 PROPN ijassa-1224 333 14 βˆ’ βˆ’ PROPN ijassa-1224 333 15 ( ( PUNCT ijassa-1224 333 16 𝜎 𝜎 PROPN ijassa-1224 334 1 + + X ijassa-1224 334 2 πœ† πœ† NOUN ijassa-1224 334 3 + + X ijassa-1224 334 4 πœ‡)𝐸 πœ‡)𝐸 NOUN ijassa-1224 334 5 ) ) PUNCT ijassa-1224 335 1 + + CCONJ ijassa-1224 335 2 𝛾 𝛾 X ijassa-1224 335 3 ( ( PUNCT ijassa-1224 335 4 1 1 NUM ijassa-1224 335 5 βˆ’ βˆ’ PROPN ijassa-1224 335 6 𝜌)𝜎𝐸 𝜌)𝜎𝐸 PROPN ijassa-1224 335 7 + + CCONJ ijassa-1224 335 8 ( ( PUNCT ijassa-1224 335 9 1 1 NUM ijassa-1224 335 10 βˆ’ βˆ’ NOUN ijassa-1224 335 11 πœ™)πœ† πœ™)πœ† X ijassa-1224 335 12 𝐸 𝐸 PROPN ijassa-1224 335 13 βˆ’ βˆ’ PROPN ijassa-1224 335 14 ( ( PUNCT ijassa-1224 335 15 𝛾 𝛾 NOUN ijassa-1224 335 16 + + X ijassa-1224 335 17 πœ‡ πœ‡ ADP ijassa-1224 335 18 + + NOUN ijassa-1224 335 19 π‘Ÿ π‘Ÿ NOUN ijassa-1224 335 20 + + CCONJ ijassa-1224 335 21 𝑑 𝑑 NOUN ijassa-1224 335 22 ) ) PUNCT ijassa-1224 335 23 𝐼 𝐼 ADP ijassa-1224 335 24 βˆ’ βˆ’ PROPN ijassa-1224 335 25 ( ( PUNCT ijassa-1224 335 26 πœ‡ πœ‡ X ijassa-1224 335 27 + + X ijassa-1224 335 28 𝑑 𝑑 PROPN ijassa-1224 335 29 + + NUM ijassa-1224 335 30 π‘Ÿ π‘Ÿ NOUN ijassa-1224 335 31 + + CCONJ ijassa-1224 335 32 π‘Ÿ π‘Ÿ NOUN ijassa-1224 335 33 ) ) PUNCT ijassa-1224 335 34 ( ( PUNCT ijassa-1224 335 35 πœ™πœ† πœ™πœ† NOUN ijassa-1224 335 36 𝐸 𝐸 PROPN ijassa-1224 335 37 + + CCONJ ijassa-1224 335 38 𝜌𝜎𝐸 𝜌𝜎𝐸 PROPN ijassa-1224 335 39 + + CCONJ ijassa-1224 335 40 𝛾𝐼 𝛾𝐼 PROPN ijassa-1224 335 41 βˆ’ βˆ’ PROPN ijassa-1224 335 42 ( ( PUNCT ijassa-1224 335 43 πœ‡ πœ‡ ADP ijassa-1224 335 44 + + X ijassa-1224 335 45 𝑑 𝑑 PROPN ijassa-1224 335 46 + + NUM ijassa-1224 335 47 π‘Ÿ π‘Ÿ NOUN ijassa-1224 335 48 + + NUM ijassa-1224 335 49 π‘Ÿ π‘Ÿ NOUN ijassa-1224 335 50 ) ) PUNCT ijassa-1224 335 51 π‘₯𝐼 π‘₯𝐼 NUM ijassa-1224 335 52 ) ) PUNCT ijassa-1224 336 1 𝑑 𝑑 PROPN ijassa-1224 336 2 2 2 NUM ijassa-1224 336 3 , , PUNCT ijassa-1224 336 4 𝐽(𝑑 𝐽(𝑑 PRON ijassa-1224 336 5 ) ) PUNCT ijassa-1224 336 6 = = SYM ijassa-1224 336 7 𝐽 𝐽 PROPN ijassa-1224 337 1 + + NUM ijassa-1224 337 2 π‘Ÿ π‘Ÿ X ijassa-1224 337 3 𝐼 𝐼 ADP ijassa-1224 337 4 βˆ’ βˆ’ PROPN ijassa-1224 337 5 ( ( PUNCT ijassa-1224 337 6 πœ‡ πœ‡ X ijassa-1224 337 7 + + X ijassa-1224 337 8 𝑑 𝑑 PROPN ijassa-1224 337 9 + + ADJ ijassa-1224 337 10 π‘Ÿ π‘Ÿ NOUN ijassa-1224 337 11 ) ) PUNCT ijassa-1224 337 12 𝐽 𝐽 PROPN ijassa-1224 338 1 𝑑 𝑑 NOUN ijassa-1224 338 2 + + ADP ijassa-1224 338 3 π‘Ÿ π‘Ÿ NOUN ijassa-1224 338 4 ( ( PUNCT ijassa-1224 338 5 πœ™πœ† πœ™πœ† NOUN ijassa-1224 338 6 𝐸 𝐸 PROPN ijassa-1224 338 7 + + CCONJ ijassa-1224 338 8 𝜌𝜎𝐸 𝜌𝜎𝐸 PROPN ijassa-1224 339 1 + + CCONJ ijassa-1224 339 2 𝛾𝐼 𝛾𝐼 PROPN ijassa-1224 339 3 βˆ’ βˆ’ PROPN ijassa-1224 339 4 ( ( PUNCT ijassa-1224 339 5 πœ‡ πœ‡ ADP ijassa-1224 339 6 + + X ijassa-1224 339 7 𝑑 𝑑 PROPN ijassa-1224 339 8 + + NUM ijassa-1224 339 9 π‘Ÿ π‘Ÿ NOUN ijassa-1224 339 10 + + NUM ijassa-1224 339 11 π‘Ÿ π‘Ÿ NOUN ijassa-1224 339 12 ) ) PUNCT ijassa-1224 339 13 π‘₯𝐼 π‘₯𝐼 X ijassa-1224 339 14 ) ) PUNCT ijassa-1224 340 1 βˆ’(πœ‡ βˆ’(πœ‡ NOUN ijassa-1224 341 1 + + CCONJ ijassa-1224 341 2 𝑑 𝑑 PROPN ijassa-1224 341 3 + + ADJ ijassa-1224 341 4 π‘Ÿ π‘Ÿ NOUN ijassa-1224 341 5 ) ) PUNCT ijassa-1224 341 6 ( ( PUNCT ijassa-1224 341 7 π‘Ÿ π‘Ÿ X ijassa-1224 341 8 𝐼 𝐼 ADP ijassa-1224 341 9 βˆ’ βˆ’ PROPN ijassa-1224 341 10 ( ( PUNCT ijassa-1224 341 11 πœ‡ πœ‡ X ijassa-1224 341 12 + + X ijassa-1224 341 13 𝑑 𝑑 PROPN ijassa-1224 341 14 + + ADJ ijassa-1224 341 15 π‘Ÿ π‘Ÿ NOUN ijassa-1224 341 16 ) ) PUNCT ijassa-1224 341 17 𝐽 𝐽 PROPN ijassa-1224 341 18 ) ) PUNCT ijassa-1224 341 19 𝑑 𝑑 PROPN ijassa-1224 341 20 2 2 NUM ijassa-1224 341 21 , , PUNCT ijassa-1224 341 22 𝑇(𝑑 𝑇(𝑑 NOUN ijassa-1224 341 23 ) ) PUNCT ijassa-1224 341 24 = = SYM ijassa-1224 341 25 𝑇 𝑇 PROPN ijassa-1224 341 26 + + CCONJ ijassa-1224 341 27 ( ( PUNCT ijassa-1224 341 28 π‘Ÿ π‘Ÿ X ijassa-1224 341 29 𝐽 𝐽 PROPN ijassa-1224 341 30 + + NUM ijassa-1224 341 31 π‘Ÿ π‘Ÿ X ijassa-1224 341 32 𝐼 𝐼 ADP ijassa-1224 341 33 + + NOUN ijassa-1224 341 34 π‘Ÿ π‘Ÿ NOUN ijassa-1224 341 35 𝐼 𝐼 ADP ijassa-1224 341 36 βˆ’ βˆ’ PROPN ijassa-1224 341 37 ( ( PUNCT ijassa-1224 341 38 πœ‡ πœ‡ ADP ijassa-1224 341 39 + + X ijassa-1224 341 40 πœ† πœ† X ijassa-1224 341 41 ) ) PUNCT ijassa-1224 341 42 𝑇 𝑇 PROPN ijassa-1224 341 43 ) ) PUNCT ijassa-1224 341 44 𝑑 𝑑 PROPN ijassa-1224 341 45 + + CCONJ ijassa-1224 341 46 ⎝ ⎝ NUM ijassa-1224 341 47 ⎜ ⎜ PROPN ijassa-1224 341 48 ⎜ ⎜ PROPN ijassa-1224 341 49 ⎜ ⎜ PROPN ijassa-1224 341 50 ⎜ ⎜ PROPN ijassa-1224 341 51 βŽ› βŽ› NOUN ijassa-1224 341 52 π‘Ÿ π‘Ÿ NOUN ijassa-1224 341 53 ( ( PUNCT ijassa-1224 341 54 π‘Ÿ π‘Ÿ X ijassa-1224 341 55 𝐼 𝐼 ADP ijassa-1224 341 56 βˆ’ βˆ’ PROPN ijassa-1224 341 57 ( ( PUNCT ijassa-1224 341 58 πœ‡ πœ‡ X ijassa-1224 341 59 + + X ijassa-1224 341 60 𝑑 𝑑 PROPN ijassa-1224 341 61 + + ADJ ijassa-1224 341 62 π‘Ÿ π‘Ÿ NOUN ijassa-1224 341 63 ) ) PUNCT ijassa-1224 341 64 𝐽 𝐽 PROPN ijassa-1224 341 65 ) ) PUNCT ijassa-1224 342 1 + + CCONJ ijassa-1224 342 2 π‘Ÿ π‘Ÿ X ijassa-1224 342 3 πœ™πœ† πœ™πœ† VERB ijassa-1224 342 4 𝐸 𝐸 PROPN ijassa-1224 342 5 + + CCONJ ijassa-1224 342 6 𝜌𝜎𝐸 𝜌𝜎𝐸 PROPN ijassa-1224 342 7 + + CCONJ ijassa-1224 342 8 𝛾𝐼 𝛾𝐼 PROPN ijassa-1224 342 9 βˆ’ βˆ’ PROPN ijassa-1224 342 10 ( ( PUNCT ijassa-1224 342 11 πœ‡ πœ‡ ADP ijassa-1224 342 12 + + X ijassa-1224 342 13 𝑑 𝑑 PROPN ijassa-1224 342 14 + + NUM ijassa-1224 342 15 π‘Ÿ π‘Ÿ NOUN ijassa-1224 342 16 + + NUM ijassa-1224 342 17 π‘Ÿ π‘Ÿ NOUN ijassa-1224 342 18 ) ) PUNCT ijassa-1224 342 19 π‘₯𝐼 π‘₯𝐼 PROPN ijassa-1224 343 1 + + CCONJ ijassa-1224 343 2 π‘Ÿ π‘Ÿ NOUN ijassa-1224 343 3 ( ( PUNCT ijassa-1224 343 4 1 1 NUM ijassa-1224 343 5 βˆ’ βˆ’ PROPN ijassa-1224 343 6 𝜌)𝜎𝐸 𝜌)𝜎𝐸 PROPN ijassa-1224 343 7 + + CCONJ ijassa-1224 343 8 ( ( PUNCT ijassa-1224 343 9 1 1 NUM ijassa-1224 343 10 βˆ’ βˆ’ NOUN ijassa-1224 343 11 πœ™)πœ† πœ™)πœ† X ijassa-1224 343 12 𝐸 𝐸 PROPN ijassa-1224 343 13 βˆ’ βˆ’ PROPN ijassa-1224 343 14 ( ( PUNCT ijassa-1224 343 15 𝛾 𝛾 NOUN ijassa-1224 343 16 + + X ijassa-1224 343 17 πœ‡ πœ‡ ADP ijassa-1224 343 18 + + NOUN ijassa-1224 343 19 π‘Ÿ π‘Ÿ NOUN ijassa-1224 343 20 + + CCONJ ijassa-1224 343 21 𝑑 𝑑 NOUN ijassa-1224 343 22 ) ) PUNCT ijassa-1224 343 23 𝐼 𝐼 ADP ijassa-1224 343 24 βˆ’(πœ‡ βˆ’(πœ‡ NOUN ijassa-1224 343 25 + + CCONJ ijassa-1224 343 26 πœ† πœ† X ijassa-1224 343 27 ) ) PUNCT ijassa-1224 343 28 π‘Ÿ π‘Ÿ X ijassa-1224 343 29 𝐽 𝐽 VERB ijassa-1224 344 1 + + NUM ijassa-1224 344 2 π‘Ÿ π‘Ÿ X ijassa-1224 344 3 𝐼 𝐼 ADP ijassa-1224 344 4 + + NOUN ijassa-1224 344 5 π‘Ÿ π‘Ÿ NOUN ijassa-1224 344 6 𝐼 𝐼 ADP ijassa-1224 344 7 βˆ’(πœ‡ βˆ’(πœ‡ NOUN ijassa-1224 344 8 + + CCONJ ijassa-1224 344 9 πœ† πœ† X ijassa-1224 344 10 ) ) PUNCT ijassa-1224 344 11 𝑇 𝑇 NOUN ijassa-1224 344 12 ⎠ ⎠ NOUN ijassa-1224 344 13 ⎟ ⎟ X ijassa-1224 344 14 ⎟ ⎟ X ijassa-1224 344 15 ⎟ ⎟ X ijassa-1224 344 16 ⎟ ⎟ PROPN ijassa-1224 344 17 ⎞ ⎞ VERB ijassa-1224 344 18 𝑑 𝑑 PROPN ijassa-1224 344 19 2 2 NUM ijassa-1224 344 20 . . PUNCT ijassa-1224 345 1 4 4 X ijassa-1224 345 2 . . NOUN ijassa-1224 345 3 results result VERB ijassa-1224 345 4 4.1 4.1 NUM ijassa-1224 345 5 . . PUNCT ijassa-1224 346 1 numerical numerical ADJ ijassa-1224 346 2 parameters parameter NOUN ijassa-1224 346 3 in in ADP ijassa-1224 346 4 this this DET ijassa-1224 346 5 section section NOUN ijassa-1224 346 6 , , PUNCT ijassa-1224 346 7 we we PRON ijassa-1224 346 8 give give VERB ijassa-1224 346 9 the the DET ijassa-1224 346 10 values value NOUN ijassa-1224 346 11 and and CCONJ ijassa-1224 346 12 source source NOUN ijassa-1224 346 13 of of ADP ijassa-1224 346 14 the the DET ijassa-1224 346 15 parameters parameter NOUN ijassa-1224 346 16 used use VERB ijassa-1224 346 17 for for ADP ijassa-1224 346 18 simulating simulate VERB ijassa-1224 346 19 the the DET ijassa-1224 346 20 model model NOUN ijassa-1224 346 21 . . PUNCT ijassa-1224 347 1 we we PRON ijassa-1224 347 2 used use VERB ijassa-1224 347 3 the the DET ijassa-1224 347 4 following following ADJ ijassa-1224 347 5 initial initial ADJ ijassa-1224 347 6 values value NOUN ijassa-1224 347 7 for for ADP ijassa-1224 347 8 𝑆(𝑑 𝑆(𝑑 ADJ ijassa-1224 347 9 ) ) PUNCT ijassa-1224 347 10 = = SYM ijassa-1224 347 11 160,840,589 160,840,589 NUM ijassa-1224 347 12 , , PUNCT ijassa-1224 347 13 𝐸(𝑑 𝐸(𝑑 NUM ijassa-1224 347 14 ) ) PUNCT ijassa-1224 347 15 = = SYM ijassa-1224 347 16 1,700,000 1,700,000 NUM ijassa-1224 347 17 , , PUNCT ijassa-1224 347 18 𝐼 𝐼 PROPN ijassa-1224 347 19 ( ( PUNCT ijassa-1224 347 20 𝑑 𝑑 NOUN ijassa-1224 347 21 ) ) PUNCT ijassa-1224 347 22 = = SYM ijassa-1224 347 23 90000 90000 NUM ijassa-1224 347 24 , , PUNCT ijassa-1224 347 25 𝐼 𝐼 PROPN ijassa-1224 347 26 ( ( PUNCT ijassa-1224 347 27 𝑑 𝑑 NOUN ijassa-1224 347 28 ) ) PUNCT ijassa-1224 347 29 = = NOUN ijassa-1224 347 30 10,400,000 10,400,000 NUM ijassa-1224 347 31 , , PUNCT ijassa-1224 347 32 𝐽(𝑑 𝐽(𝑑 PRON ijassa-1224 347 33 ) ) PUNCT ijassa-1224 347 34 = = SYM ijassa-1224 347 35 1,000,000 1,000,000 NUM ijassa-1224 347 36 , , PUNCT ijassa-1224 347 37 𝑇(𝑑 𝑇(𝑑 NOUN ijassa-1224 347 38 ) ) PUNCT ijassa-1224 347 39 = = NOUN ijassa-1224 347 40 1,109,000 1,109,000 NUM ijassa-1224 347 41 and and CCONJ ijassa-1224 347 42 𝑉(𝑑 𝑉(𝑑 ADP ijassa-1224 347 43 ) ) PUNCT ijassa-1224 347 44 = = SYM ijassa-1224 347 45 8,000,000 8,000,000 NUM ijassa-1224 347 46 . . PUNCT ijassa-1224 348 1 𝑁 𝑁 PROPN ijassa-1224 348 2 = = SYM ijassa-1224 348 3 𝑆(𝑑 𝑆(𝑑 X ijassa-1224 348 4 ) ) PUNCT ijassa-1224 348 5 + + PUNCT ijassa-1224 348 6 𝐸(𝑑 𝐸(𝑑 VERB ijassa-1224 348 7 ) ) PUNCT ijassa-1224 348 8 + + CCONJ ijassa-1224 348 9 𝐼 𝐼 PROPN ijassa-1224 348 10 ( ( PUNCT ijassa-1224 348 11 𝑑 𝑑 NOUN ijassa-1224 348 12 ) ) PUNCT ijassa-1224 348 13 + + CCONJ ijassa-1224 348 14 𝐼 𝐼 PROPN ijassa-1224 348 15 ( ( PUNCT ijassa-1224 348 16 𝑑 𝑑 NOUN ijassa-1224 348 17 ) ) PUNCT ijassa-1224 348 18 + + PUNCT ijassa-1224 348 19 𝐽(𝑑 𝐽(𝑑 X ijassa-1224 348 20 ) ) PUNCT ijassa-1224 348 21 + + CCONJ ijassa-1224 348 22 𝑇(𝑑 𝑇(𝑑 X ijassa-1224 348 23 ) ) PUNCT ijassa-1224 348 24 + + PUNCT ijassa-1224 348 25 𝑉(𝑑 𝑉(𝑑 ADP ijassa-1224 348 26 ) ) PUNCT ijassa-1224 348 27 = = NOUN ijassa-1224 348 28 206,139,589 206,139,589 NUM ijassa-1224 348 29 . . PUNCT ijassa-1224 348 30 table table NOUN ijassa-1224 348 31 2 2 NUM ijassa-1224 348 32 . . PUNCT ijassa-1224 349 1 the the DET ijassa-1224 349 2 parameters parameter NOUN ijassa-1224 349 3 value value NOUN ijassa-1224 349 4 used use VERB ijassa-1224 349 5 for for ADP ijassa-1224 349 6 the the DET ijassa-1224 349 7 model model NOUN ijassa-1224 349 8 parameters parameter NOUN ijassa-1224 349 9 value value VERB ijassa-1224 349 10 source source NOUN ijassa-1224 349 11 πœ‹ πœ‹ PROPN ijassa-1224 349 12 2,895,131 2,895,131 NUM ijassa-1224 349 13 estimated estimate VERB ijassa-1224 349 14 πœ‡ πœ‡ ADP ijassa-1224 349 15 0.018 0.018 NUM ijassa-1224 349 16 estimated estimate VERB ijassa-1224 349 17 𝑑 𝑑 AUX ijassa-1224 349 18 0.0365 0.0365 NUM ijassa-1224 349 19 assumed assume VERB ijassa-1224 349 20 𝑑 𝑑 PROPN ijassa-1224 349 21 0.68 0.68 NUM ijassa-1224 349 22 [ [ X ijassa-1224 349 23 21 21 NUM ijassa-1224 349 24 ] ] X ijassa-1224 349 25 𝑑 𝑑 NOUN ijassa-1224 349 26 0.1 0.1 NUM ijassa-1224 349 27 [ [ X ijassa-1224 349 28 22 22 NUM ijassa-1224 349 29 ] ] PUNCT ijassa-1224 349 30 π‘Ÿ π‘Ÿ DET ijassa-1224 349 31 0.02 0.02 NUM ijassa-1224 349 32 assumed assume VERB ijassa-1224 349 33 π‘Ÿ π‘Ÿ X ijassa-1224 349 34 0.02 0.02 NUM ijassa-1224 349 35 assumed assume VERB ijassa-1224 349 36 π‘Ÿ π‘Ÿ NOUN ijassa-1224 349 37 0.00375 0.00375 NUM ijassa-1224 349 38 [ [ X ijassa-1224 349 39 21 21 NUM ijassa-1224 349 40 ] ] X ijassa-1224 349 41 πœƒ πœƒ NUM ijassa-1224 349 42 0.020 0.020 NUM ijassa-1224 349 43 [ [ X ijassa-1224 349 44 22 22 NUM ijassa-1224 349 45 ] ] PUNCT ijassa-1224 349 46 𝜌 𝜌 ADP ijassa-1224 349 47 0.075 0.075 NUM ijassa-1224 349 48 [ [ X ijassa-1224 349 49 22 22 NUM ijassa-1224 349 50 ] ] PUNCT ijassa-1224 349 51 πœ™ πœ™ PRON ijassa-1224 349 52 0.3 0.3 NUM ijassa-1224 349 53 assumed assume VERB ijassa-1224 349 54 πœ† πœ† ADP ijassa-1224 349 55 0.2 0.2 NUM ijassa-1224 349 56 assumed assume VERB ijassa-1224 349 57 πœ† πœ† ADP ijassa-1224 349 58 0.2 0.2 NUM ijassa-1224 349 59 assumed assume VERB ijassa-1224 349 60 𝜎 𝜎 PROPN ijassa-1224 349 61 0.01 0.01 NUM ijassa-1224 349 62 assumed assume VERB ijassa-1224 349 63 4.2 4.2 NUM ijassa-1224 349 64 . . PUNCT ijassa-1224 350 1 graphical graphical ADJ ijassa-1224 350 2 representation representation NOUN ijassa-1224 350 3 of of ADP ijassa-1224 350 4 solutions solution NOUN ijassa-1224 350 5 of of ADP ijassa-1224 350 6 the the DET ijassa-1224 350 7 model model NOUN ijassa-1224 350 8 equation equation NOUN ijassa-1224 350 9 the the DET ijassa-1224 350 10 graphical graphical ADJ ijassa-1224 350 11 representations representation NOUN ijassa-1224 350 12 are be AUX ijassa-1224 350 13 from from ADP ijassa-1224 350 14 the the DET ijassa-1224 350 15 analytical analytical ADJ ijassa-1224 350 16 solutions solution NOUN ijassa-1224 350 17 of of ADP ijassa-1224 350 18 the the DET ijassa-1224 350 19 model model NOUN ijassa-1224 350 20 equations equation NOUN ijassa-1224 350 21 . . PUNCT ijassa-1224 351 1 they they PRON ijassa-1224 351 2 are be AUX ijassa-1224 351 3 plotted plot VERB ijassa-1224 351 4 using use VERB ijassa-1224 351 5 maple maple NOUN ijassa-1224 351 6 software software NOUN ijassa-1224 351 7 . . PUNCT ijassa-1224 352 1 158 158 NUM ijassa-1224 352 2 f.a f.a PROPN ijassa-1224 352 3 . . PROPN ijassa-1224 353 1 oguntolu oguntolu PROPN ijassa-1224 353 2 , , PUNCT ijassa-1224 353 3 o.j o.j PROPN ijassa-1224 353 4 . . PROPN ijassa-1224 353 5 peter peter PROPN ijassa-1224 353 6 , , PUNCT ijassa-1224 353 7 k. k. PROPN ijassa-1224 353 8 oshinubi oshinubi PROPN ijassa-1224 353 9 , , PUNCT ijassa-1224 353 10 t.a t.a PROPN ijassa-1224 353 11 . . PROPN ijassa-1224 353 12 ayoola ayoola PROPN ijassa-1224 353 13 , , PUNCT ijassa-1224 353 14 a.o a.o PROPN ijassa-1224 353 15 . . PROPN ijassa-1224 353 16 oladapo oladapo PROPN ijassa-1224 353 17 , , PUNCT ijassa-1224 353 18 m.m m.m PROPN ijassa-1224 353 19 . . PROPN ijassa-1224 353 20 ojo ojo NOUN ijassa-1224 353 21 copyright copyright NOUN ijassa-1224 353 22 Β© Β© PROPN ijassa-1224 353 23 2022 2022 NUM ijassa-1224 353 24 assa assa PROPN ijassa-1224 353 25 adv adv PROPN ijassa-1224 353 26 . . PUNCT ijassa-1224 354 1 in in ADP ijassa-1224 354 2 systems system NOUN ijassa-1224 354 3 science science NOUN ijassa-1224 354 4 and and CCONJ ijassa-1224 354 5 appl appl NOUN ijassa-1224 354 6 . . PUNCT ijassa-1224 355 1 ( ( PUNCT ijassa-1224 355 2 2022 2022 NUM ijassa-1224 355 3 ) ) PUNCT ijassa-1224 355 4 ( ( PUNCT ijassa-1224 355 5 a a X ijassa-1224 355 6 ) ) PUNCT ijassa-1224 355 7 ( ( PUNCT ijassa-1224 355 8 b b X ijassa-1224 355 9 ) ) PUNCT ijassa-1224 355 10 ( ( PUNCT ijassa-1224 355 11 c c X ijassa-1224 355 12 ) ) PUNCT ijassa-1224 355 13 ( ( PUNCT ijassa-1224 355 14 d d X ijassa-1224 355 15 ) ) PUNCT ijassa-1224 355 16 ( ( PUNCT ijassa-1224 355 17 e e NOUN ijassa-1224 355 18 ) ) PUNCT ijassa-1224 355 19 ( ( PUNCT ijassa-1224 355 20 f f X ijassa-1224 355 21 ) ) PUNCT ijassa-1224 355 22 ( ( PUNCT ijassa-1224 355 23 g g NOUN ijassa-1224 355 24 ) ) PUNCT ijassa-1224 355 25 fig fig NOUN ijassa-1224 355 26 . . PUNCT ijassa-1224 356 1 2 2 X ijassa-1224 356 2 . . X ijassa-1224 356 3 ( ( PUNCT ijassa-1224 356 4 a a X ijassa-1224 356 5 ) ) PUNCT ijassa-1224 356 6 effect effect NOUN ijassa-1224 356 7 of of ADP ijassa-1224 356 8 waning wane VERB ijassa-1224 356 9 rate rate NOUN ijassa-1224 356 10 of of ADP ijassa-1224 356 11 vaccine vaccine NOUN ijassa-1224 356 12 on on ADP ijassa-1224 356 13 the the DET ijassa-1224 356 14 chronic chronic ADJ ijassa-1224 356 15 class class NOUN ijassa-1224 356 16 . . PUNCT ijassa-1224 357 1 ( ( PUNCT ijassa-1224 357 2 b b X ijassa-1224 357 3 ) ) PUNCT ijassa-1224 357 4 effect effect NOUN ijassa-1224 357 5 of of ADP ijassa-1224 357 6 waning wane VERB ijassa-1224 357 7 rate rate NOUN ijassa-1224 357 8 of of ADP ijassa-1224 357 9 vaccine vaccine NOUN ijassa-1224 357 10 on on ADP ijassa-1224 357 11 vaccinated vaccinated ADJ ijassa-1224 357 12 class class NOUN ijassa-1224 357 13 . . PUNCT ijassa-1224 358 1 ( ( PUNCT ijassa-1224 358 2 c c X ijassa-1224 358 3 ) ) PUNCT ijassa-1224 358 4 effect effect NOUN ijassa-1224 358 5 of of ADP ijassa-1224 358 6 isolation isolation NOUN ijassa-1224 358 7 rate rate NOUN ijassa-1224 358 8 on on ADP ijassa-1224 358 9 the the DET ijassa-1224 358 10 isolated isolated ADJ ijassa-1224 358 11 compartment compartment NOUN ijassa-1224 358 12 . . PUNCT ijassa-1224 359 1 ( ( PUNCT ijassa-1224 359 2 d d X ijassa-1224 359 3 ) ) PUNCT ijassa-1224 359 4 treated treat VERB ijassa-1224 359 5 individual individual NOUN ijassa-1224 359 6 against against ADP ijassa-1224 359 7 time time NOUN ijassa-1224 359 8 for for ADP ijassa-1224 359 9 different different ADJ ijassa-1224 359 10 values value NOUN ijassa-1224 359 11 of of ADP ijassa-1224 359 12 recovery recovery NOUN ijassa-1224 359 13 rate rate NOUN ijassa-1224 359 14 for for ADP ijassa-1224 359 15 chronic chronic ADJ ijassa-1224 359 16 class class NOUN ijassa-1224 359 17 . . PUNCT ijassa-1224 360 1 ( ( PUNCT ijassa-1224 360 2 e e NOUN ijassa-1224 360 3 ) ) PUNCT ijassa-1224 360 4 effect effect NOUN ijassa-1224 360 5 of of ADP ijassa-1224 360 6 recovery recovery NOUN ijassa-1224 360 7 rate rate NOUN ijassa-1224 360 8 for for ADP ijassa-1224 360 9 those those PRON ijassa-1224 360 10 in in ADP ijassa-1224 360 11 isolated isolated ADJ ijassa-1224 360 12 class class NOUN ijassa-1224 360 13 . . PUNCT ijassa-1224 361 1 ( ( PUNCT ijassa-1224 361 2 f f X ijassa-1224 361 3 ) ) PUNCT ijassa-1224 361 4 impact impact NOUN ijassa-1224 361 5 of of ADP ijassa-1224 361 6 effective effective ADJ ijassa-1224 361 7 interaction interaction NOUN ijassa-1224 361 8 between between ADP ijassa-1224 361 9 susceptible susceptible ADJ ijassa-1224 361 10 and and CCONJ ijassa-1224 361 11 infected infected ADJ ijassa-1224 361 12 classes class NOUN ijassa-1224 361 13 . . PUNCT ijassa-1224 362 1 ( ( PUNCT ijassa-1224 362 2 g g NOUN ijassa-1224 362 3 ) ) PUNCT ijassa-1224 362 4 mild mild ADJ ijassa-1224 362 5 tb tb ADP ijassa-1224 362 6 individual individual NOUN ijassa-1224 362 7 against against ADP ijassa-1224 362 8 time time NOUN ijassa-1224 362 9 for for ADP ijassa-1224 362 10 different different ADJ ijassa-1224 362 11 values value NOUN ijassa-1224 362 12 of of ADP ijassa-1224 362 13 transmission transmission NOUN ijassa-1224 362 14 rate rate NOUN ijassa-1224 362 15 . . PUNCT ijassa-1224 363 1 analysis analysis NOUN ijassa-1224 363 2 and and CCONJ ijassa-1224 363 3 dynamics dynamic NOUN ijassa-1224 363 4 of of ADP ijassa-1224 363 5 tuberculosis tuberculosis NOUN ijassa-1224 363 6 outbreak outbreak NOUN ijassa-1224 363 7 159 159 NUM ijassa-1224 363 8 copyright copyright NOUN ijassa-1224 363 9 Β© Β© PROPN ijassa-1224 363 10 2022 2022 NUM ijassa-1224 363 11 assa assa NOUN ijassa-1224 363 12 . . PUNCT ijassa-1224 364 1 adv adv PROPN ijassa-1224 364 2 . . PUNCT ijassa-1224 365 1 in in ADP ijassa-1224 365 2 systems system NOUN ijassa-1224 365 3 science science NOUN ijassa-1224 365 4 and and CCONJ ijassa-1224 365 5 appl appl NOUN ijassa-1224 365 6 . . PUNCT ijassa-1224 366 1 ( ( PUNCT ijassa-1224 366 2 2022 2022 NUM ijassa-1224 366 3 ) ) PUNCT ijassa-1224 366 4 5 5 NUM ijassa-1224 366 5 . . PUNCT ijassa-1224 366 6 discussion discussion NOUN ijassa-1224 366 7 figure figure NOUN ijassa-1224 366 8 2a 2a NUM ijassa-1224 366 9 is be AUX ijassa-1224 366 10 the the DET ijassa-1224 366 11 graph graph NOUN ijassa-1224 366 12 of of ADP ijassa-1224 366 13 chronic chronic ADJ ijassa-1224 366 14 infected infect VERB ijassa-1224 366 15 individuals individual NOUN ijassa-1224 366 16 against against ADP ijassa-1224 366 17 time time NOUN ijassa-1224 366 18 for for ADP ijassa-1224 366 19 different different ADJ ijassa-1224 366 20 values value NOUN ijassa-1224 366 21 of of ADP ijassa-1224 366 22 waning wane VERB ijassa-1224 366 23 rate rate NOUN ijassa-1224 366 24 of of ADP ijassa-1224 366 25 vaccine vaccine NOUN ijassa-1224 366 26 . . PUNCT ijassa-1224 367 1 we we PRON ijassa-1224 367 2 carried carry VERB ijassa-1224 367 3 out out ADP ijassa-1224 367 4 simulations simulation NOUN ijassa-1224 367 5 by by ADP ijassa-1224 367 6 varying vary VERB ijassa-1224 367 7 waning wane VERB ijassa-1224 367 8 rate rate NOUN ijassa-1224 367 9 of of ADP ijassa-1224 367 10 vaccine vaccine NOUN ijassa-1224 367 11 as as ADP ijassa-1224 367 12 0.2 0.2 NUM ijassa-1224 367 13 , , PUNCT ijassa-1224 367 14 0.4 0.4 NUM ijassa-1224 367 15 and and CCONJ ijassa-1224 367 16 0.6 0.6 NUM ijassa-1224 367 17 . . PUNCT ijassa-1224 368 1 it it PRON ijassa-1224 368 2 could could AUX ijassa-1224 368 3 be be AUX ijassa-1224 368 4 observed observe VERB ijassa-1224 368 5 that that SCONJ ijassa-1224 368 6 different different ADJ ijassa-1224 368 7 level level NOUN ijassa-1224 368 8 of of ADP ijassa-1224 368 9 waning wane VERB ijassa-1224 368 10 rate rate NOUN ijassa-1224 368 11 does do AUX ijassa-1224 368 12 not not PART ijassa-1224 368 13 have have VERB ijassa-1224 368 14 effect effect NOUN ijassa-1224 368 15 on on ADP ijassa-1224 368 16 the the DET ijassa-1224 368 17 infected infected ADJ ijassa-1224 368 18 population population NOUN ijassa-1224 368 19 . . PUNCT ijassa-1224 369 1 for for ADP ijassa-1224 369 2 different different ADJ ijassa-1224 369 3 level level NOUN ijassa-1224 369 4 of of ADP ijassa-1224 369 5 waning wane VERB ijassa-1224 369 6 rate rate NOUN ijassa-1224 369 7 , , PUNCT ijassa-1224 369 8 the the DET ijassa-1224 369 9 tb tb NOUN ijassa-1224 369 10 infection infection NOUN ijassa-1224 369 11 continues continue VERB ijassa-1224 369 12 to to PART ijassa-1224 369 13 persist persist VERB ijassa-1224 369 14 in in ADP ijassa-1224 369 15 the the DET ijassa-1224 369 16 given give VERB ijassa-1224 369 17 population population NOUN ijassa-1224 369 18 . . PUNCT ijassa-1224 370 1 figure figure NOUN ijassa-1224 370 2 2b 2b NUM ijassa-1224 370 3 is be AUX ijassa-1224 370 4 the the DET ijassa-1224 370 5 graph graph NOUN ijassa-1224 370 6 of of ADP ijassa-1224 370 7 vaccinated vaccinated ADJ ijassa-1224 370 8 individuals individual NOUN ijassa-1224 370 9 against against ADP ijassa-1224 370 10 time time NOUN ijassa-1224 370 11 for for ADP ijassa-1224 370 12 different different ADJ ijassa-1224 370 13 values value NOUN ijassa-1224 370 14 of of ADP ijassa-1224 370 15 waning wane VERB ijassa-1224 370 16 rate rate NOUN ijassa-1224 370 17 of of ADP ijassa-1224 370 18 vaccine vaccine NOUN ijassa-1224 370 19 . . PUNCT ijassa-1224 371 1 it it PRON ijassa-1224 371 2 was be AUX ijassa-1224 371 3 observed observe VERB ijassa-1224 371 4 that that SCONJ ijassa-1224 371 5 the the DET ijassa-1224 371 6 vaccinated vaccinated ADJ ijassa-1224 371 7 population population NOUN ijassa-1224 371 8 decreases decrease VERB ijassa-1224 371 9 with with ADP ijassa-1224 371 10 increase increase NOUN ijassa-1224 371 11 in in ADP ijassa-1224 371 12 the the DET ijassa-1224 371 13 vaccination vaccination NOUN ijassa-1224 371 14 rate rate NOUN ijassa-1224 371 15 . . PUNCT ijassa-1224 372 1 therefore therefore ADV ijassa-1224 372 2 , , PUNCT ijassa-1224 372 3 high high ADJ ijassa-1224 372 4 waning wane VERB ijassa-1224 372 5 rate rate NOUN ijassa-1224 372 6 of of ADP ijassa-1224 372 7 vaccine vaccine NOUN ijassa-1224 372 8 reduces reduce VERB ijassa-1224 372 9 the the DET ijassa-1224 372 10 vaccinated vaccinated ADJ ijassa-1224 372 11 population population NOUN ijassa-1224 372 12 and and CCONJ ijassa-1224 372 13 thus thus ADV ijassa-1224 372 14 puts put VERB ijassa-1224 372 15 them they PRON ijassa-1224 372 16 at at ADP ijassa-1224 372 17 the the DET ijassa-1224 372 18 risk risk NOUN ijassa-1224 372 19 of of ADP ijassa-1224 372 20 contracting contract VERB ijassa-1224 372 21 the the DET ijassa-1224 372 22 disease disease NOUN ijassa-1224 372 23 . . PUNCT ijassa-1224 373 1 figure figure NOUN ijassa-1224 373 2 2c 2c NOUN ijassa-1224 373 3 is be AUX ijassa-1224 373 4 the the DET ijassa-1224 373 5 graph graph NOUN ijassa-1224 373 6 of of ADP ijassa-1224 373 7 isolated isolated ADJ ijassa-1224 373 8 infectious infectious ADJ ijassa-1224 373 9 individuals individual NOUN ijassa-1224 373 10 against against ADP ijassa-1224 373 11 time time NOUN ijassa-1224 373 12 at at ADP ijassa-1224 373 13 different different ADJ ijassa-1224 373 14 values value NOUN ijassa-1224 373 15 of of ADP ijassa-1224 373 16 progression progression NOUN ijassa-1224 373 17 rate rate NOUN ijassa-1224 373 18 from from ADP ijassa-1224 373 19 chronic chronic ADJ ijassa-1224 373 20 tb tb ADP ijassa-1224 373 21 class class NOUN ijassa-1224 373 22 to to ADP ijassa-1224 373 23 isolated isolated ADJ ijassa-1224 373 24 infected infected ADJ ijassa-1224 373 25 class class NOUN ijassa-1224 373 26 . . PUNCT ijassa-1224 374 1 it it PRON ijassa-1224 374 2 was be AUX ijassa-1224 374 3 observed observe VERB ijassa-1224 374 4 that that SCONJ ijassa-1224 374 5 the the DET ijassa-1224 374 6 number number NOUN ijassa-1224 374 7 of of ADP ijassa-1224 374 8 isolated isolated ADJ ijassa-1224 374 9 individuals individual NOUN ijassa-1224 374 10 increases increase VERB ijassa-1224 374 11 as as ADP ijassa-1224 374 12 progression progression NOUN ijassa-1224 374 13 rate rate NOUN ijassa-1224 374 14 from from ADP ijassa-1224 374 15 chronic chronic ADJ ijassa-1224 374 16 tb tb ADP ijassa-1224 374 17 class class NOUN ijassa-1224 374 18 to to ADP ijassa-1224 374 19 isolated isolated ADJ ijassa-1224 374 20 infected infected ADJ ijassa-1224 374 21 class class NOUN ijassa-1224 374 22 increases increase NOUN ijassa-1224 374 23 . . PUNCT ijassa-1224 375 1 figure figure NOUN ijassa-1224 375 2 2d 2d PROPN ijassa-1224 375 3 is be AUX ijassa-1224 375 4 the the DET ijassa-1224 375 5 graph graph NOUN ijassa-1224 375 6 of of ADP ijassa-1224 375 7 treated treat VERB ijassa-1224 375 8 tb tb ADP ijassa-1224 375 9 individuals individual NOUN ijassa-1224 375 10 against against ADP ijassa-1224 375 11 time time NOUN ijassa-1224 375 12 . . PUNCT ijassa-1224 376 1 it it PRON ijassa-1224 376 2 was be AUX ijassa-1224 376 3 observed observe VERB ijassa-1224 376 4 that that SCONJ ijassa-1224 376 5 the the DET ijassa-1224 376 6 number number NOUN ijassa-1224 376 7 of of ADP ijassa-1224 376 8 treated treat VERB ijassa-1224 376 9 tb tb ADP ijassa-1224 376 10 individual individual ADJ ijassa-1224 376 11 increases increase NOUN ijassa-1224 376 12 as as ADP ijassa-1224 376 13 the the DET ijassa-1224 376 14 recovery recovery NOUN ijassa-1224 376 15 rate rate NOUN ijassa-1224 376 16 among among ADP ijassa-1224 376 17 the the DET ijassa-1224 376 18 chronic chronic NOUN ijassa-1224 376 19 tb tb ADP ijassa-1224 376 20 individual individual ADJ ijassa-1224 376 21 increases increase NOUN ijassa-1224 376 22 . . PUNCT ijassa-1224 377 1 this this PRON ijassa-1224 377 2 implies imply VERB ijassa-1224 377 3 that that PRON ijassa-1224 377 4 increase increase NOUN ijassa-1224 377 5 in in ADP ijassa-1224 377 6 the the DET ijassa-1224 377 7 progression progression NOUN ijassa-1224 377 8 rate rate NOUN ijassa-1224 377 9 will will AUX ijassa-1224 377 10 lead lead VERB ijassa-1224 377 11 to to PART ijassa-1224 377 12 increase increase VERB ijassa-1224 377 13 in in ADP ijassa-1224 377 14 number number NOUN ijassa-1224 377 15 of of ADP ijassa-1224 377 16 individuals individual NOUN ijassa-1224 377 17 with with ADP ijassa-1224 377 18 chronic chronic ADJ ijassa-1224 377 19 tb tb ADP ijassa-1224 377 20 disease disease NOUN ijassa-1224 377 21 . . PUNCT ijassa-1224 378 1 figure figure NOUN ijassa-1224 378 2 2e 2e PROPN ijassa-1224 378 3 is be AUX ijassa-1224 378 4 the the DET ijassa-1224 378 5 graph graph NOUN ijassa-1224 378 6 of of ADP ijassa-1224 378 7 recovered recovered ADJ ijassa-1224 378 8 individual individual NOUN ijassa-1224 378 9 against against ADP ijassa-1224 378 10 time time NOUN ijassa-1224 378 11 . . PUNCT ijassa-1224 379 1 the the PRON ijassa-1224 379 2 lower low ADJ ijassa-1224 379 3 the the DET ijassa-1224 379 4 treated treat VERB ijassa-1224 379 5 rate rate NOUN ijassa-1224 379 6 the the PRON ijassa-1224 379 7 lower low ADJ ijassa-1224 379 8 the the DET ijassa-1224 379 9 number number NOUN ijassa-1224 379 10 of of ADP ijassa-1224 379 11 recovered recovered ADJ ijassa-1224 379 12 individuals individual NOUN ijassa-1224 379 13 . . PUNCT ijassa-1224 380 1 the the DET ijassa-1224 380 2 lowest low ADJ ijassa-1224 380 3 percentage percentage NOUN ijassa-1224 380 4 almost almost ADV ijassa-1224 380 5 decrease decrease VERB ijassa-1224 380 6 to to ADP ijassa-1224 380 7 zero zero NUM ijassa-1224 380 8 . . PUNCT ijassa-1224 381 1 this this PRON ijassa-1224 381 2 shows show VERB ijassa-1224 381 3 that that SCONJ ijassa-1224 381 4 as as SCONJ ijassa-1224 381 5 the the DET ijassa-1224 381 6 recovered recover VERB ijassa-1224 381 7 are be AUX ijassa-1224 381 8 treated treat VERB ijassa-1224 381 9 , , PUNCT ijassa-1224 381 10 they they PRON ijassa-1224 381 11 move move VERB ijassa-1224 381 12 to to AUX ijassa-1224 381 13 chronic chronic ADJ ijassa-1224 381 14 tb tb ADP ijassa-1224 381 15 population population NOUN ijassa-1224 381 16 . . PUNCT ijassa-1224 382 1 figure figure NOUN ijassa-1224 382 2 2f 2f NUM ijassa-1224 382 3 is be AUX ijassa-1224 382 4 the the DET ijassa-1224 382 5 graph graph NOUN ijassa-1224 382 6 of of ADP ijassa-1224 382 7 exposed expose VERB ijassa-1224 382 8 individual individual NOUN ijassa-1224 382 9 against against ADP ijassa-1224 382 10 time time NOUN ijassa-1224 382 11 for for ADP ijassa-1224 382 12 different different ADJ ijassa-1224 382 13 values value NOUN ijassa-1224 382 14 of of ADP ijassa-1224 382 15 contact contact NOUN ijassa-1224 382 16 rate rate NOUN ijassa-1224 382 17 . . PUNCT ijassa-1224 383 1 we we PRON ijassa-1224 383 2 can can AUX ijassa-1224 383 3 observe observe VERB ijassa-1224 383 4 that that SCONJ ijassa-1224 383 5 infected infect VERB ijassa-1224 383 6 individuals individual NOUN ijassa-1224 383 7 increase increase VERB ijassa-1224 383 8 as as ADP ijassa-1224 383 9 contact contact NOUN ijassa-1224 383 10 rate rate NOUN ijassa-1224 383 11 increases increase NOUN ijassa-1224 383 12 . . PUNCT ijassa-1224 384 1 the the DET ijassa-1224 384 2 figure figure NOUN ijassa-1224 384 3 illustrates illustrate VERB ijassa-1224 384 4 the the DET ijassa-1224 384 5 great great ADJ ijassa-1224 384 6 influence influence NOUN ijassa-1224 384 7 of of ADP ijassa-1224 384 8 effective effective ADJ ijassa-1224 384 9 contact contact NOUN ijassa-1224 384 10 rate rate NOUN ijassa-1224 384 11 on on ADP ijassa-1224 384 12 the the DET ijassa-1224 384 13 exposed expose VERB ijassa-1224 384 14 population population NOUN ijassa-1224 384 15 . . PUNCT ijassa-1224 385 1 figure figure NOUN ijassa-1224 385 2 2 2 NUM ijassa-1224 385 3 g g NOUN ijassa-1224 385 4 is be AUX ijassa-1224 385 5 the the DET ijassa-1224 385 6 graph graph NOUN ijassa-1224 385 7 of of ADP ijassa-1224 385 8 mild mild ADJ ijassa-1224 385 9 tb tb ADP ijassa-1224 385 10 individual individual NOUN ijassa-1224 385 11 against against ADP ijassa-1224 385 12 time time NOUN ijassa-1224 385 13 . . PUNCT ijassa-1224 386 1 it it PRON ijassa-1224 386 2 was be AUX ijassa-1224 386 3 observed observe VERB ijassa-1224 386 4 that that SCONJ ijassa-1224 386 5 the the DET ijassa-1224 386 6 number number NOUN ijassa-1224 386 7 of of ADP ijassa-1224 386 8 mild mild ADJ ijassa-1224 386 9 tb tb ADP ijassa-1224 386 10 individual individual ADJ ijassa-1224 386 11 increases increase NOUN ijassa-1224 386 12 as as ADP ijassa-1224 386 13 the the DET ijassa-1224 386 14 transmission transmission NOUN ijassa-1224 386 15 rate rate NOUN ijassa-1224 386 16 from from ADP ijassa-1224 386 17 the the DET ijassa-1224 386 18 exposed expose VERB ijassa-1224 386 19 to to ADP ijassa-1224 386 20 the the DET ijassa-1224 386 21 chronic chronic ADJ ijassa-1224 386 22 individuals individual NOUN ijassa-1224 386 23 increases increase VERB ijassa-1224 386 24 . . PUNCT ijassa-1224 387 1 6 6 X ijassa-1224 387 2 . . X ijassa-1224 387 3 conclusion conclusion NOUN ijassa-1224 387 4 in in ADP ijassa-1224 387 5 this this DET ijassa-1224 387 6 study study NOUN ijassa-1224 387 7 , , PUNCT ijassa-1224 387 8 a a DET ijassa-1224 387 9 mathematical mathematical ADJ ijassa-1224 387 10 model model NOUN ijassa-1224 387 11 of of ADP ijassa-1224 387 12 tuberculosis tuberculosis NOUN ijassa-1224 387 13 transmission transmission NOUN ijassa-1224 387 14 dynamics dynamic NOUN ijassa-1224 387 15 incorporating incorporate VERB ijassa-1224 387 16 treatment treatment NOUN ijassa-1224 387 17 , , PUNCT ijassa-1224 387 18 isolation isolation NOUN ijassa-1224 387 19 and and CCONJ ijassa-1224 387 20 vaccination vaccination NOUN ijassa-1224 387 21 using use VERB ijassa-1224 387 22 the the DET ijassa-1224 387 23 system system NOUN ijassa-1224 387 24 of of ADP ijassa-1224 387 25 first first ADJ ijassa-1224 387 26 order order NOUN ijassa-1224 387 27 ordinary ordinary ADJ ijassa-1224 387 28 differential differential ADJ ijassa-1224 387 29 equations equation NOUN ijassa-1224 387 30 was be AUX ijassa-1224 387 31 developed develop VERB ijassa-1224 387 32 and and CCONJ ijassa-1224 387 33 analyzed analyze VERB ijassa-1224 387 34 . . PUNCT ijassa-1224 388 1 it it PRON ijassa-1224 388 2 was be AUX ijassa-1224 388 3 discovered discover VERB ijassa-1224 388 4 that that SCONJ ijassa-1224 388 5 the the DET ijassa-1224 388 6 model model NOUN ijassa-1224 388 7 has have VERB ijassa-1224 388 8 two two NUM ijassa-1224 388 9 equilibria equilibrium NOUN ijassa-1224 388 10 . . PUNCT ijassa-1224 389 1 the the DET ijassa-1224 389 2 equilibrium equilibrium NOUN ijassa-1224 389 3 states state NOUN ijassa-1224 389 4 were be AUX ijassa-1224 389 5 obtained obtain VERB ijassa-1224 389 6 and and CCONJ ijassa-1224 389 7 analyzed analyze VERB ijassa-1224 389 8 for for ADP ijassa-1224 389 9 their their PRON ijassa-1224 389 10 stability stability NOUN ijassa-1224 389 11 relatively relatively ADV ijassa-1224 389 12 to to ADP ijassa-1224 389 13 the the DET ijassa-1224 389 14 effective effective ADJ ijassa-1224 389 15 reproduction reproduction NOUN ijassa-1224 389 16 number number NOUN ijassa-1224 389 17 . . PUNCT ijassa-1224 390 1 the the DET ijassa-1224 390 2 result result NOUN ijassa-1224 390 3 shows show VERB ijassa-1224 390 4 that that SCONJ ijassa-1224 390 5 , , PUNCT ijassa-1224 390 6 the the DET ijassa-1224 390 7 disease disease NOUN ijassa-1224 390 8 - - PUNCT ijassa-1224 390 9 free free ADJ ijassa-1224 390 10 equilibrium equilibrium NOUN ijassa-1224 390 11 was be AUX ijassa-1224 390 12 stable stable ADJ ijassa-1224 390 13 . . PUNCT ijassa-1224 391 1 we we PRON ijassa-1224 391 2 are be AUX ijassa-1224 391 3 able able ADJ ijassa-1224 391 4 to to PART ijassa-1224 391 5 show show VERB ijassa-1224 391 6 that that SCONJ ijassa-1224 391 7 the the DET ijassa-1224 391 8 tuberculosis tuberculosis NOUN ijassa-1224 391 9 infectious infectious ADJ ijassa-1224 391 10 free free ADJ ijassa-1224 391 11 equilibrium equilibrium NOUN ijassa-1224 391 12 is be AUX ijassa-1224 391 13 locally locally ADV ijassa-1224 391 14 and and CCONJ ijassa-1224 391 15 globally globally ADV ijassa-1224 391 16 asymptotically asymptotically ADV ijassa-1224 391 17 stable stable ADJ ijassa-1224 391 18 if if SCONJ ijassa-1224 391 19 𝑅 𝑅 PROPN ijassa-1224 391 20 < < X ijassa-1224 391 21 1 1 NUM ijassa-1224 391 22 . . PUNCT ijassa-1224 392 1 the the DET ijassa-1224 392 2 analytical analytical ADJ ijassa-1224 392 3 solution solution NOUN ijassa-1224 392 4 was be AUX ijassa-1224 392 5 obtained obtain VERB ijassa-1224 392 6 using use VERB ijassa-1224 392 7 homotopy homotopy NOUN ijassa-1224 392 8 perturbation perturbation NOUN ijassa-1224 392 9 method method NOUN ijassa-1224 392 10 and and CCONJ ijassa-1224 392 11 effective effective ADJ ijassa-1224 392 12 reproduction reproduction NOUN ijassa-1224 392 13 number number NOUN ijassa-1224 392 14 was be AUX ijassa-1224 392 15 computed compute VERB ijassa-1224 392 16 in in ADP ijassa-1224 392 17 order order NOUN ijassa-1224 392 18 to to PART ijassa-1224 392 19 measure measure VERB ijassa-1224 392 20 the the DET ijassa-1224 392 21 relative relative ADJ ijassa-1224 392 22 impact impact NOUN ijassa-1224 392 23 for for ADP ijassa-1224 392 24 individual individual ADJ ijassa-1224 392 25 or or CCONJ ijassa-1224 392 26 combined combine VERB ijassa-1224 392 27 intervention intervention NOUN ijassa-1224 392 28 for for ADP ijassa-1224 392 29 effective effective ADJ ijassa-1224 392 30 disease disease NOUN ijassa-1224 392 31 control control NOUN ijassa-1224 392 32 . . PUNCT ijassa-1224 393 1 the the DET ijassa-1224 393 2 graphs graph NOUN ijassa-1224 393 3 illustrate illustrate VERB ijassa-1224 393 4 the the DET ijassa-1224 393 5 impact impact NOUN ijassa-1224 393 6 of of ADP ijassa-1224 393 7 a a DET ijassa-1224 393 8 combined combine VERB ijassa-1224 393 9 effect effect NOUN ijassa-1224 393 10 of of ADP ijassa-1224 393 11 contact contact NOUN ijassa-1224 393 12 rate rate NOUN ijassa-1224 393 13 , , PUNCT ijassa-1224 393 14 waning wane VERB ijassa-1224 393 15 rate rate NOUN ijassa-1224 393 16 of of ADP ijassa-1224 393 17 vaccine vaccine NOUN ijassa-1224 393 18 and and CCONJ ijassa-1224 393 19 rate rate NOUN ijassa-1224 393 20 of of ADP ijassa-1224 393 21 isolation isolation NOUN ijassa-1224 393 22 . . PUNCT ijassa-1224 394 1 one one PRON ijassa-1224 394 2 can can AUX ijassa-1224 394 3 observe observe VERB ijassa-1224 394 4 that that SCONJ ijassa-1224 394 5 this this DET ijassa-1224 394 6 combines combine VERB ijassa-1224 394 7 effects effect NOUN ijassa-1224 394 8 reduce reduce VERB ijassa-1224 394 9 the the DET ijassa-1224 394 10 size size NOUN ijassa-1224 394 11 of of ADP ijassa-1224 394 12 infected infected ADJ ijassa-1224 394 13 compartments compartment NOUN ijassa-1224 394 14 . . PUNCT ijassa-1224 395 1 thus thus ADV ijassa-1224 395 2 , , PUNCT ijassa-1224 395 3 the the DET ijassa-1224 395 4 simultaneous simultaneous ADJ ijassa-1224 395 5 increase increase NOUN ijassa-1224 395 6 of of ADP ijassa-1224 395 7 effectiveness effectiveness NOUN ijassa-1224 395 8 of of ADP ijassa-1224 395 9 vaccination vaccination NOUN ijassa-1224 395 10 rate rate NOUN ijassa-1224 395 11 , , PUNCT ijassa-1224 395 12 isolation isolation NOUN ijassa-1224 395 13 rate rate NOUN ijassa-1224 395 14 and and CCONJ ijassa-1224 395 15 treatment treatment NOUN ijassa-1224 395 16 rate rate NOUN ijassa-1224 395 17 are be AUX ijassa-1224 395 18 effective effective ADJ ijassa-1224 395 19 control control NOUN ijassa-1224 395 20 measures measure NOUN ijassa-1224 395 21 against against ADP ijassa-1224 395 22 tb tb ADP ijassa-1224 395 23 infection infection NOUN ijassa-1224 395 24 . . PUNCT ijassa-1224 396 1 the the DET ijassa-1224 396 2 model model NOUN ijassa-1224 396 3 shows show VERB ijassa-1224 396 4 that that SCONJ ijassa-1224 396 5 the the DET ijassa-1224 396 6 spread spread NOUN ijassa-1224 396 7 of of ADP ijassa-1224 396 8 tuberculosis tuberculosis NOUN ijassa-1224 396 9 infection infection NOUN ijassa-1224 396 10 depends depend VERB ijassa-1224 396 11 largely largely ADV ijassa-1224 396 12 on on ADP ijassa-1224 396 13 the the DET ijassa-1224 396 14 contact contact NOUN ijassa-1224 396 15 rate rate NOUN ijassa-1224 396 16 , , PUNCT ijassa-1224 396 17 hence hence ADV ijassa-1224 396 18 the the DET ijassa-1224 396 19 ministry ministry PROPN ijassa-1224 396 20 of of ADP ijassa-1224 396 21 health health PROPN ijassa-1224 396 22 and and CCONJ ijassa-1224 396 23 other other ADJ ijassa-1224 396 24 health health NOUN ijassa-1224 396 25 workers worker NOUN ijassa-1224 396 26 should should AUX ijassa-1224 396 27 emphasize emphasize VERB ijassa-1224 396 28 on on ADP ijassa-1224 396 29 the the DET ijassa-1224 396 30 improvement improvement NOUN ijassa-1224 396 31 in in ADP ijassa-1224 396 32 early early ADJ ijassa-1224 396 33 detection detection NOUN ijassa-1224 396 34 of of ADP ijassa-1224 396 35 tuberculosis tuberculosis NOUN ijassa-1224 396 36 infection infection NOUN ijassa-1224 396 37 cases case NOUN ijassa-1224 396 38 , , PUNCT ijassa-1224 396 39 so so SCONJ ijassa-1224 396 40 that that SCONJ ijassa-1224 396 41 transmission transmission NOUN ijassa-1224 396 42 can can AUX ijassa-1224 396 43 be be AUX ijassa-1224 396 44 minimized minimize VERB ijassa-1224 396 45 . . PUNCT ijassa-1224 397 1 infected infect VERB ijassa-1224 397 2 individuals individual NOUN ijassa-1224 397 3 should should AUX ijassa-1224 397 4 be be AUX ijassa-1224 397 5 isolated isolate VERB ijassa-1224 397 6 and and CCONJ ijassa-1224 397 7 treated treat VERB ijassa-1224 397 8 immediately immediately ADV ijassa-1224 397 9 and and CCONJ ijassa-1224 397 10 individuals individual NOUN ijassa-1224 397 11 infected infect VERB ijassa-1224 397 12 with with ADP ijassa-1224 397 13 tuberculosis tuberculosis NOUN ijassa-1224 397 14 should should AUX ijassa-1224 397 15 be be AUX ijassa-1224 397 16 given give VERB ijassa-1224 397 17 antiretroviral antiretroviral ADJ ijassa-1224 397 18 drugs drug NOUN ijassa-1224 397 19 immediately immediately ADV ijassa-1224 397 20 . . PUNCT ijassa-1224 398 1 in in ADP ijassa-1224 398 2 future future ADJ ijassa-1224 398 3 work work NOUN ijassa-1224 398 4 , , PUNCT ijassa-1224 398 5 we we PRON ijassa-1224 398 6 intent intent VERB ijassa-1224 398 7 to to PART ijassa-1224 398 8 incorporate incorporate VERB ijassa-1224 398 9 optimal optimal ADJ ijassa-1224 398 10 control control NOUN ijassa-1224 398 11 strategy strategy NOUN ijassa-1224 398 12 into into ADP ijassa-1224 398 13 the the DET ijassa-1224 398 14 model model NOUN ijassa-1224 398 15 for for ADP ijassa-1224 398 16 greater great ADJ ijassa-1224 398 17 insight insight NOUN ijassa-1224 398 18 into into ADP ijassa-1224 398 19 the the DET ijassa-1224 398 20 dynamics dynamic NOUN ijassa-1224 398 21 . . PUNCT ijassa-1224 399 1 160 160 NUM ijassa-1224 399 2 f.a f.a PROPN ijassa-1224 399 3 . . PROPN ijassa-1224 400 1 oguntolu oguntolu PROPN ijassa-1224 400 2 , , PUNCT ijassa-1224 400 3 o.j o.j PROPN ijassa-1224 400 4 . . PROPN ijassa-1224 400 5 peter peter PROPN ijassa-1224 400 6 , , PUNCT ijassa-1224 400 7 k. k. PROPN ijassa-1224 400 8 oshinubi oshinubi PROPN ijassa-1224 400 9 , , PUNCT ijassa-1224 400 10 t.a t.a PROPN ijassa-1224 400 11 . . PROPN ijassa-1224 400 12 ayoola ayoola PROPN ijassa-1224 400 13 , , PUNCT ijassa-1224 400 14 a.o a.o PROPN ijassa-1224 400 15 . . PROPN ijassa-1224 400 16 oladapo oladapo PROPN ijassa-1224 400 17 , , PUNCT ijassa-1224 400 18 m.m m.m PROPN ijassa-1224 400 19 . . PROPN ijassa-1224 400 20 ojo ojo NOUN ijassa-1224 400 21 copyright copyright NOUN ijassa-1224 400 22 Β© Β© PROPN ijassa-1224 400 23 2022 2022 NUM ijassa-1224 400 24 assa assa PROPN ijassa-1224 400 25 adv adv PROPN ijassa-1224 400 26 . . PUNCT ijassa-1224 401 1 in in ADP ijassa-1224 401 2 systems system NOUN ijassa-1224 401 3 science science NOUN ijassa-1224 401 4 and and CCONJ ijassa-1224 401 5 appl appl NOUN ijassa-1224 401 6 . . PUNCT ijassa-1224 402 1 ( ( PUNCT ijassa-1224 402 2 2022 2022 NUM ijassa-1224 402 3 ) ) PUNCT ijassa-1224 402 4 references reference NOUN ijassa-1224 402 5 1 1 NUM ijassa-1224 402 6 . . X ijassa-1224 402 7 abioye abioye PROPN ijassa-1224 402 8 , , PUNCT ijassa-1224 402 9 a.i a.i PROPN ijassa-1224 402 10 . . PROPN ijassa-1224 402 11 , , PUNCT ijassa-1224 402 12 peter peter PROPN ijassa-1224 402 13 , , PUNCT ijassa-1224 402 14 o.j o.j PROPN ijassa-1224 402 15 . . PROPN ijassa-1224 402 16 , , PUNCT ijassa-1224 402 17 ogunseye ogunseye PROPN ijassa-1224 402 18 , , PUNCT ijassa-1224 402 19 h.a h.a PROPN ijassa-1224 402 20 . . PROPN ijassa-1224 402 21 , , PUNCT ijassa-1224 402 22 oguntolu oguntolu PROPN ijassa-1224 402 23 , , PUNCT ijassa-1224 402 24 f.a f.a PROPN ijassa-1224 402 25 . . PROPN ijassa-1224 402 26 , , PUNCT ijassa-1224 402 27 oshinubi oshinubi PROPN ijassa-1224 402 28 , , PUNCT ijassa-1224 402 29 k. k. PROPN ijassa-1224 402 30 et et PROPN ijassa-1224 402 31 al al PROPN ijassa-1224 402 32 . . PROPN ijassa-1224 402 33 ( ( PUNCT ijassa-1224 402 34 2021 2021 NUM ijassa-1224 402 35 ) ) PUNCT ijassa-1224 402 36 . . PUNCT ijassa-1224 403 1 mathematical mathematical ADJ ijassa-1224 403 2 model model NOUN ijassa-1224 403 3 of of ADP ijassa-1224 403 4 covid-19 covid-19 PROPN ijassa-1224 403 5 in in ADP ijassa-1224 403 6 nigeria nigeria PROPN ijassa-1224 403 7 with with ADP ijassa-1224 403 8 optimal optimal ADJ ijassa-1224 403 9 control control NOUN ijassa-1224 403 10 . . PUNCT ijassa-1224 404 1 results result NOUN ijassa-1224 404 2 in in ADP ijassa-1224 404 3 physics physics NOUN ijassa-1224 404 4 , , PUNCT ijassa-1224 404 5 28 28 NUM ijassa-1224 404 6 , , PUNCT ijassa-1224 404 7 104598 104598 NUM ijassa-1224 404 8 . . PUNCT ijassa-1224 405 1 2 2 X ijassa-1224 405 2 . . X ijassa-1224 405 3 abubakar abubakar PROPN ijassa-1224 405 4 , , PUNCT ijassa-1224 405 5 s. s. PROPN ijassa-1224 405 6 , , PUNCT ijassa-1224 405 7 akinwande akinwande PROPN ijassa-1224 405 8 , , PUNCT ijassa-1224 405 9 n.i n.i PROPN ijassa-1224 405 10 . . PROPN ijassa-1224 405 11 , , PUNCT ijassa-1224 405 12 jimoh jimoh PROPN ijassa-1224 405 13 , , PUNCT ijassa-1224 405 14 o.r o.r PROPN ijassa-1224 405 15 . . PROPN ijassa-1224 405 16 , , PUNCT ijassa-1224 405 17 oguntolu oguntolu PROPN ijassa-1224 405 18 , , PUNCT ijassa-1224 405 19 f.a f.a PROPN ijassa-1224 405 20 . . PROPN ijassa-1224 405 21 & & CCONJ ijassa-1224 405 22 ogwumu ogwumu PROPN ijassa-1224 405 23 , , PUNCT ijassa-1224 405 24 o.d o.d PROPN ijassa-1224 405 25 . . PROPN ijassa-1224 405 26 ( ( PUNCT ijassa-1224 405 27 2013 2013 NUM ijassa-1224 405 28 ) ) PUNCT ijassa-1224 405 29 . . PUNCT ijassa-1224 406 1 approximate approximate ADJ ijassa-1224 406 2 solution solution NOUN ijassa-1224 406 3 of of ADP ijassa-1224 406 4 sir sir NOUN ijassa-1224 406 5 infectious infectious ADJ ijassa-1224 406 6 disease disease NOUN ijassa-1224 406 7 model model NOUN ijassa-1224 406 8 using use VERB ijassa-1224 406 9 homotopy homotopy NOUN ijassa-1224 406 10 perturbation perturbation NOUN ijassa-1224 406 11 method method NOUN ijassa-1224 406 12 ( ( PUNCT ijassa-1224 406 13 hpm hpm NOUN ijassa-1224 406 14 ) ) PUNCT ijassa-1224 406 15 . . PUNCT ijassa-1224 407 1 pacific pacific PROPN ijassa-1224 407 2 journal journal PROPN ijassa-1224 407 3 of of ADP ijassa-1224 407 4 science science NOUN ijassa-1224 407 5 and and CCONJ ijassa-1224 407 6 technology technology NOUN ijassa-1224 407 7 , , PUNCT ijassa-1224 407 8 14(2 14(2 NUM ijassa-1224 407 9 ) ) PUNCT ijassa-1224 407 10 , , PUNCT ijassa-1224 407 11 163–169 163–169 NUM ijassa-1224 407 12 . . NOUN ijassa-1224 407 13 3 3 NUM ijassa-1224 407 14 al al PROPN ijassa-1224 407 15 - - PUNCT ijassa-1224 407 16 darraji darraji PROPN ijassa-1224 407 17 , , PUNCT ijassa-1224 407 18 h.a.a h.a.a PROPN ijassa-1224 407 19 . . PUNCT ijassa-1224 407 20 , , PUNCT ijassa-1224 407 21 altice altice PROPN ijassa-1224 407 22 , , PUNCT ijassa-1224 407 23 f.l f.l PROPN ijassa-1224 407 24 . . PROPN ijassa-1224 407 25 & & CCONJ ijassa-1224 407 26 kamarulzaman kamarulzaman PROPN ijassa-1224 407 27 , , PUNCT ijassa-1224 407 28 a. a. NOUN ijassa-1224 407 29 ( ( PUNCT ijassa-1224 407 30 2016 2016 NUM ijassa-1224 407 31 ) ) PUNCT ijassa-1224 407 32 . . PUNCT ijassa-1224 408 1 undiagnosed undiagnosed ADJ ijassa-1224 408 2 pulmonary pulmonary ADJ ijassa-1224 408 3 tuberculosis tuberculosis NOUN ijassa-1224 408 4 among among ADP ijassa-1224 408 5 prisoners prisoner NOUN ijassa-1224 408 6 in in ADP ijassa-1224 408 7 malaysia malaysia PROPN ijassa-1224 408 8 : : PUNCT ijassa-1224 408 9 an an DET ijassa-1224 408 10 overlooked overlook VERB ijassa-1224 408 11 risk risk NOUN ijassa-1224 408 12 for for ADP ijassa-1224 408 13 tuberculosis tuberculosis NOUN ijassa-1224 408 14 in in ADP ijassa-1224 408 15 the the DET ijassa-1224 408 16 community community NOUN ijassa-1224 408 17 . . PUNCT ijassa-1224 409 1 tropical tropical ADJ ijassa-1224 409 2 medicine medicine NOUN ijassa-1224 409 3 and and CCONJ ijassa-1224 409 4 international international ADJ ijassa-1224 409 5 health health NOUN ijassa-1224 409 6 , , PUNCT ijassa-1224 409 7 4(4 4(4 NUM ijassa-1224 409 8 ) ) PUNCT ijassa-1224 409 9 , , PUNCT ijassa-1224 409 10 401–871 401–871 NUM ijassa-1224 409 11 . . PUNCT ijassa-1224 410 1 4 4 X ijassa-1224 410 2 . . X ijassa-1224 410 3 andrawus andrawus PROPN ijassa-1224 410 4 , , PUNCT ijassa-1224 410 5 j. j. PROPN ijassa-1224 410 6 , , PUNCT ijassa-1224 410 7 eguda eguda NOUN ijassa-1224 410 8 , , PUNCT ijassa-1224 410 9 f. f. PROPN ijassa-1224 410 10 , , PUNCT ijassa-1224 410 11 usman usman PROPN ijassa-1224 410 12 , , PUNCT ijassa-1224 410 13 i. i. PROPN ijassa-1224 410 14 , , PUNCT ijassa-1224 410 15 maiwa maiwa PROPN ijassa-1224 410 16 , , PUNCT ijassa-1224 410 17 s. s. PROPN ijassa-1224 410 18 , , PUNCT ijassa-1224 410 19 dibal dibal PROPN ijassa-1224 410 20 , , PUNCT ijassa-1224 410 21 i. i. PROPN ijassa-1224 410 22 et et PROPN ijassa-1224 410 23 al al PROPN ijassa-1224 410 24 . . PROPN ijassa-1224 411 1 ( ( PUNCT ijassa-1224 411 2 2020 2020 NUM ijassa-1224 411 3 ) ) PUNCT ijassa-1224 411 4 . . PUNCT ijassa-1224 412 1 a a DET ijassa-1224 412 2 mathematical mathematical ADJ ijassa-1224 412 3 model model NOUN ijassa-1224 412 4 of of ADP ijassa-1224 412 5 a a DET ijassa-1224 412 6 tuberculosis tuberculosis NOUN ijassa-1224 412 7 transmission transmission NOUN ijassa-1224 412 8 dynamics dynamic NOUN ijassa-1224 412 9 incorporating incorporate VERB ijassa-1224 412 10 first first ADJ ijassa-1224 412 11 and and CCONJ ijassa-1224 412 12 second second ADJ ijassa-1224 412 13 line line NOUN ijassa-1224 412 14 treatment treatment NOUN ijassa-1224 412 15 . . PUNCT ijassa-1224 413 1 journal journal PROPN ijassa-1224 413 2 applied apply VERB ijassa-1224 413 3 science science NOUN ijassa-1224 413 4 environment environment NOUN ijassa-1224 413 5 management management NOUN ijassa-1224 413 6 , , PUNCT ijassa-1224 413 7 24(5 24(5 NOUN ijassa-1224 413 8 ) ) PUNCT ijassa-1224 413 9 , , PUNCT ijassa-1224 413 10 917–922 917–922 NUM ijassa-1224 413 11 . . NOUN ijassa-1224 414 1 5 5 NUM ijassa-1224 414 2 . . X ijassa-1224 414 3 asefa asefa PROPN ijassa-1224 414 4 , , PUNCT ijassa-1224 414 5 a. a. PROPN ijassa-1224 414 6 & & CCONJ ijassa-1224 414 7 teshome teshome PROPN ijassa-1224 414 8 , , PUNCT ijassa-1224 414 9 w. w. PROPN ijassa-1224 414 10 ( ( PUNCT ijassa-1224 414 11 2014 2014 NUM ijassa-1224 414 12 ) ) PUNCT ijassa-1224 414 13 . . PUNCT ijassa-1224 415 1 total total ADJ ijassa-1224 415 2 delay delay NOUN ijassa-1224 415 3 in in ADP ijassa-1224 415 4 treatment treatment NOUN ijassa-1224 415 5 among among ADP ijassa-1224 415 6 smear smear NOUN ijassa-1224 415 7 positive positive ADJ ijassa-1224 415 8 pulmonary pulmonary ADJ ijassa-1224 415 9 tuberculosis tuberculosis NOUN ijassa-1224 415 10 patients patient NOUN ijassa-1224 415 11 in in ADP ijassa-1224 415 12 five five NUM ijassa-1224 415 13 primary primary ADJ ijassa-1224 415 14 health health NOUN ijassa-1224 415 15 centers center NOUN ijassa-1224 415 16 , , PUNCT ijassa-1224 415 17 southern southern ADJ ijassa-1224 415 18 ethiopia ethiopia PROPN ijassa-1224 415 19 : : PUNCT ijassa-1224 415 20 a a DET ijassa-1224 415 21 cross cross ADJ ijassa-1224 415 22 sectional sectional ADJ ijassa-1224 415 23 study study NOUN ijassa-1224 415 24 . . PUNCT ijassa-1224 416 1 plos plos PROPN ijassa-1224 416 2 one one NUM ijassa-1224 416 3 , , PUNCT ijassa-1224 416 4 9(7 9(7 NUM ijassa-1224 416 5 ) ) PUNCT ijassa-1224 416 6 , , PUNCT ijassa-1224 416 7 102–117 102–117 NUM ijassa-1224 416 8 . . NOUN ijassa-1224 417 1 6 6 NUM ijassa-1224 417 2 . . X ijassa-1224 417 3 ayinla ayinla PROPN ijassa-1224 417 4 , , PUNCT ijassa-1224 417 5 a.y a.y PROPN ijassa-1224 417 6 . . PROPN ijassa-1224 417 7 , , PUNCT ijassa-1224 417 8 othman othman PROPN ijassa-1224 417 9 , , PUNCT ijassa-1224 417 10 w.a.m w.a.m PROPN ijassa-1224 417 11 . . PROPN ijassa-1224 417 12 & & CCONJ ijassa-1224 417 13 rabiu rabiu PROPN ijassa-1224 417 14 , , PUNCT ijassa-1224 417 15 m.a m.a PROPN ijassa-1224 417 16 . . PROPN ijassa-1224 417 17 ( ( PUNCT ijassa-1224 417 18 2021 2021 NUM ijassa-1224 417 19 ) ) PUNCT ijassa-1224 417 20 . . PUNCT ijassa-1224 418 1 a a DET ijassa-1224 418 2 mathematical mathematical ADJ ijassa-1224 418 3 model model NOUN ijassa-1224 418 4 of of ADP ijassa-1224 418 5 the the DET ijassa-1224 418 6 tuberculosis tuberculosis NOUN ijassa-1224 418 7 epidemic epidemic NOUN ijassa-1224 418 8 . . PUNCT ijassa-1224 419 1 acta acta PROPN ijassa-1224 419 2 biotheor biotheor PROPN ijassa-1224 419 3 , , PUNCT ijassa-1224 419 4 69 69 NUM ijassa-1224 419 5 , , PUNCT ijassa-1224 419 6 225–255 225–255 NUM ijassa-1224 419 7 . . PUNCT ijassa-1224 420 1 7 7 X ijassa-1224 420 2 . . X ijassa-1224 420 3 bam bam NOUN ijassa-1224 420 4 , , PUNCT ijassa-1224 420 5 t.s t.s PROPN ijassa-1224 420 6 . . PROPN ijassa-1224 420 7 , , PUNCT ijassa-1224 420 8 enarson enarson PROPN ijassa-1224 420 9 , , PUNCT ijassa-1224 420 10 d.a d.a PROPN ijassa-1224 420 11 . . PROPN ijassa-1224 420 12 & & CCONJ ijassa-1224 420 13 hinderaker hinderaker PROPN ijassa-1224 420 14 , , PUNCT ijassa-1224 420 15 s.g s.g PROPN ijassa-1224 420 16 . . PROPN ijassa-1224 420 17 ( ( PUNCT ijassa-1224 420 18 2012 2012 NUM ijassa-1224 420 19 ) ) PUNCT ijassa-1224 420 20 . . PUNCT ijassa-1224 421 1 longer long ADV ijassa-1224 421 2 delay delay VERB ijassa-1224 421 3 in in ADP ijassa-1224 421 4 accessing access VERB ijassa-1224 421 5 treatment treatment NOUN ijassa-1224 421 6 among among ADP ijassa-1224 421 7 current current ADJ ijassa-1224 421 8 smokers smoker NOUN ijassa-1224 421 9 with with ADP ijassa-1224 421 10 new new ADJ ijassa-1224 421 11 sputum sputum PROPN ijassa-1224 421 12 smear smear NOUN ijassa-1224 421 13 - - PUNCT ijassa-1224 421 14 positive positive ADJ ijassa-1224 421 15 tuberculosis tuberculosis NOUN ijassa-1224 421 16 in in ADP ijassa-1224 421 17 nepal nepal ADJ ijassa-1224 421 18 . . PUNCT ijassa-1224 422 1 union union PROPN ijassa-1224 422 2 . . PUNCT ijassa-1224 423 1 journal journal NOUN ijassa-1224 423 2 of of ADP ijassa-1224 423 3 tuberculosis tuberculosis NOUN ijassa-1224 423 4 lung lung NOUN ijassa-1224 423 5 diseases disease NOUN ijassa-1224 423 6 , , PUNCT ijassa-1224 423 7 16(6 16(6 NUM ijassa-1224 423 8 ) ) PUNCT ijassa-1224 423 9 , , PUNCT ijassa-1224 423 10 822–827 822–827 NUM ijassa-1224 423 11 . . PUNCT ijassa-1224 424 1 8 8 NUM ijassa-1224 424 2 bhunu bhunu ADJ ijassa-1224 424 3 , , PUNCT ijassa-1224 424 4 c.p c.p PROPN ijassa-1224 424 5 . . PROPN ijassa-1224 424 6 , , PUNCT ijassa-1224 424 7 garira garira PROPN ijassa-1224 424 8 , , PUNCT ijassa-1224 424 9 w. w. PROPN ijassa-1224 424 10 , , PUNCT ijassa-1224 424 11 mukandavire mukandavire NOUN ijassa-1224 424 12 , , PUNCT ijassa-1224 424 13 z. z. PROPN ijassa-1224 424 14 & & CCONJ ijassa-1224 424 15 zimba zimba PROPN ijassa-1224 424 16 , , PUNCT ijassa-1224 424 17 m. m. NOUN ijassa-1224 424 18 ( ( PUNCT ijassa-1224 424 19 2008 2008 NUM ijassa-1224 424 20 ) ) PUNCT ijassa-1224 424 21 . . PUNCT ijassa-1224 425 1 tuberculosis tuberculosis NOUN ijassa-1224 425 2 transmission transmission NOUN ijassa-1224 425 3 model model NOUN ijassa-1224 425 4 with with ADP ijassa-1224 425 5 chemoprophylaxis chemoprophylaxis NOUN ijassa-1224 425 6 and and CCONJ ijassa-1224 425 7 treatment treatment NOUN ijassa-1224 425 8 . . PUNCT ijassa-1224 426 1 bulletin bulletin NOUN ijassa-1224 426 2 of of ADP ijassa-1224 426 3 mathematical mathematical ADJ ijassa-1224 426 4 biology biology NOUN ijassa-1224 426 5 , , PUNCT ijassa-1224 426 6 70 70 NUM ijassa-1224 426 7 , , PUNCT ijassa-1224 426 8 1163–1191 1163–1191 NUM ijassa-1224 426 9 . . NOUN ijassa-1224 426 10 9 9 NUM ijassa-1224 426 11 . . X ijassa-1224 426 12 castillo castillo PROPN ijassa-1224 426 13 - - PUNCT ijassa-1224 426 14 chavez chavez PROPN ijassa-1224 426 15 , , PUNCT ijassa-1224 426 16 c. c. PROPN ijassa-1224 426 17 , , PUNCT ijassa-1224 426 18 & & CCONJ ijassa-1224 426 19 feng feng PROPN ijassa-1224 426 20 , , PUNCT ijassa-1224 426 21 z. z. PROPN ijassa-1224 426 22 ( ( PUNCT ijassa-1224 426 23 1997 1997 NUM ijassa-1224 426 24 ) ) PUNCT ijassa-1224 426 25 . . PUNCT ijassa-1224 427 1 to to PART ijassa-1224 427 2 treat treat VERB ijassa-1224 427 3 or or CCONJ ijassa-1224 427 4 not not PART ijassa-1224 427 5 to to PART ijassa-1224 427 6 treat treat VERB ijassa-1224 427 7 : : PUNCT ijassa-1224 427 8 the the DET ijassa-1224 427 9 case case NOUN ijassa-1224 427 10 of of ADP ijassa-1224 427 11 tuberculosis tuberculosis NOUN ijassa-1224 427 12 . . PUNCT ijassa-1224 428 1 j. j. PROPN ijassa-1224 428 2 math math PROPN ijassa-1224 428 3 . . PUNCT ijassa-1224 429 1 biol biol PROPN ijassa-1224 429 2 . . PUNCT ijassa-1224 430 1 35 35 NUM ijassa-1224 430 2 , , PUNCT ijassa-1224 430 3 629–659 629–659 NUM ijassa-1224 430 4 . . NOUN ijassa-1224 431 1 10 10 NUM ijassa-1224 431 2 . . PUNCT ijassa-1224 432 1 centers center NOUN ijassa-1224 432 2 for for ADP ijassa-1224 432 3 disease disease NOUN ijassa-1224 432 4 control control NOUN ijassa-1224 432 5 and and CCONJ ijassa-1224 432 6 prevention prevention NOUN ijassa-1224 432 7 ( ( PUNCT ijassa-1224 432 8 2016 2016 NUM ijassa-1224 432 9 ): ): PUNCT ijassa-1224 432 10 testing test VERB ijassa-1224 432 11 for for ADP ijassa-1224 432 12 tb tb ADP ijassa-1224 432 13 infection infection NOUN ijassa-1224 432 14 . . PUNCT ijassa-1224 433 1 [ [ X ijassa-1224 433 2 online online X ijassa-1224 433 3 ] ] X ijassa-1224 433 4 . . PUNCT ijassa-1224 434 1 available available ADJ ijassa-1224 434 2 http://www.cdc.gov/tb/topic/testing/. http://www.cdc.gov/tb/topic/testing/. PROPN ijassa-1224 434 3 11 11 NUM ijassa-1224 435 1 he he PRON ijassa-1224 435 2 , , PUNCT ijassa-1224 435 3 j.h j.h PROPN ijassa-1224 435 4 . . PROPN ijassa-1224 435 5 ( ( PUNCT ijassa-1224 435 6 1999 1999 NUM ijassa-1224 435 7 ) ) PUNCT ijassa-1224 435 8 . . PUNCT ijassa-1224 436 1 homotopy homotopy VERB ijassa-1224 436 2 perturbation perturbation NOUN ijassa-1224 436 3 technique technique NOUN ijassa-1224 436 4 . . PUNCT ijassa-1224 437 1 computer computer NOUN ijassa-1224 437 2 methods method NOUN ijassa-1224 437 3 in in ADP ijassa-1224 437 4 applied applied ADJ ijassa-1224 437 5 mechanics mechanic NOUN ijassa-1224 437 6 and and CCONJ ijassa-1224 437 7 engineering engineering NOUN ijassa-1224 437 8 , , PUNCT ijassa-1224 437 9 178 178 NUM ijassa-1224 437 10 , , PUNCT ijassa-1224 437 11 257–262 257–262 NUM ijassa-1224 437 12 . . PUNCT ijassa-1224 438 1 12 12 NUM ijassa-1224 438 2 . . PUNCT ijassa-1224 439 1 herzog herzog PROPN ijassa-1224 439 2 , , PUNCT ijassa-1224 439 3 b. b. PROPN ijassa-1224 439 4 ( ( PUNCT ijassa-1224 439 5 1998 1998 NUM ijassa-1224 439 6 ) ) PUNCT ijassa-1224 439 7 . . PUNCT ijassa-1224 440 1 history history NOUN ijassa-1224 440 2 of of ADP ijassa-1224 440 3 tuberculosis tuberculosis NOUN ijassa-1224 440 4 . . PUNCT ijassa-1224 441 1 respiration respiration NOUN ijassa-1224 441 2 , , PUNCT ijassa-1224 441 3 65(1 65(1 NOUN ijassa-1224 441 4 ) ) PUNCT ijassa-1224 441 5 , , PUNCT ijassa-1224 441 6 5–15 5–15 PROPN ijassa-1224 441 7 . . PROPN ijassa-1224 442 1 13 13 NUM ijassa-1224 442 2 . . PUNCT ijassa-1224 443 1 james james PROPN ijassa-1224 443 2 peter peter PROPN ijassa-1224 443 3 , , PUNCT ijassa-1224 443 4 o. o. PROPN ijassa-1224 443 5 , , PUNCT ijassa-1224 443 6 ojo ojo PROPN ijassa-1224 443 7 , , PUNCT ijassa-1224 443 8 m.m m.m PROPN ijassa-1224 443 9 . . PROPN ijassa-1224 443 10 , , PUNCT ijassa-1224 443 11 viriyapong viriyapong PROPN ijassa-1224 443 12 , , PUNCT ijassa-1224 443 13 r. r. PROPN ijassa-1224 443 14 , , PUNCT ijassa-1224 443 15 & & CCONJ ijassa-1224 443 16 abiodun abiodun PROPN ijassa-1224 443 17 oguntolu oguntolu PROPN ijassa-1224 443 18 , , PUNCT ijassa-1224 443 19 f. f. PROPN ijassa-1224 443 20 ( ( PUNCT ijassa-1224 443 21 2022 2022 NUM ijassa-1224 443 22 ) ) PUNCT ijassa-1224 443 23 . . PUNCT ijassa-1224 444 1 mathematical mathematical ADJ ijassa-1224 444 2 model model NOUN ijassa-1224 444 3 of of ADP ijassa-1224 444 4 measles measle NOUN ijassa-1224 444 5 transmission transmission NOUN ijassa-1224 444 6 dynamics dynamic NOUN ijassa-1224 444 7 using use VERB ijassa-1224 444 8 real real ADJ ijassa-1224 444 9 data datum NOUN ijassa-1224 444 10 from from ADP ijassa-1224 444 11 nigeria nigeria PROPN ijassa-1224 444 12 . . PUNCT ijassa-1224 445 1 journal journal PROPN ijassa-1224 445 2 of of ADP ijassa-1224 445 3 difference difference NOUN ijassa-1224 445 4 equations equation NOUN ijassa-1224 445 5 and and CCONJ ijassa-1224 445 6 applications application NOUN ijassa-1224 445 7 , , PUNCT ijassa-1224 445 8 28(6 28(6 NUM ijassa-1224 445 9 ) ) PUNCT ijassa-1224 445 10 , , PUNCT ijassa-1224 445 11 753–770 753–770 NUM ijassa-1224 445 12 . . PUNCT ijassa-1224 445 13 14 14 NUM ijassa-1224 445 14 . . X ijassa-1224 446 1 ojo ojo PROPN ijassa-1224 446 2 , , PUNCT ijassa-1224 446 3 m.m m.m PROPN ijassa-1224 446 4 . . PROPN ijassa-1224 446 5 , , PUNCT ijassa-1224 446 6 benson benson PROPN ijassa-1224 446 7 , , PUNCT ijassa-1224 446 8 t.o t.o PROPN ijassa-1224 446 9 . . PROPN ijassa-1224 446 10 , , PUNCT ijassa-1224 446 11 peter peter PROPN ijassa-1224 446 12 , , PUNCT ijassa-1224 446 13 o.j o.j PROPN ijassa-1224 446 14 . . PROPN ijassa-1224 446 15 & & CCONJ ijassa-1224 446 16 goufo goufo PROPN ijassa-1224 446 17 , , PUNCT ijassa-1224 446 18 e.d e.d PROPN ijassa-1224 446 19 . . PROPN ijassa-1224 446 20 ( ( PUNCT ijassa-1224 446 21 2022 2022 NUM ijassa-1224 446 22 ) ) PUNCT ijassa-1224 446 23 . . PUNCT ijassa-1224 447 1 nonlinear nonlinear ADJ ijassa-1224 447 2 optimal optimal ADJ ijassa-1224 447 3 control control NOUN ijassa-1224 447 4 strategies strategy NOUN ijassa-1224 447 5 for for ADP ijassa-1224 447 6 a a DET ijassa-1224 447 7 mathematical mathematical ADJ ijassa-1224 447 8 model model NOUN ijassa-1224 447 9 of of ADP ijassa-1224 447 10 covid-19 covid-19 PROPN ijassa-1224 447 11 and and CCONJ ijassa-1224 447 12 influenza influenza NOUN ijassa-1224 447 13 co co NOUN ijassa-1224 447 14 - - NOUN ijassa-1224 447 15 infection infection NOUN ijassa-1224 447 16 . . PUNCT ijassa-1224 448 1 physica physica PROPN ijassa-1224 448 2 a a DET ijassa-1224 448 3 : : PUNCT ijassa-1224 448 4 statistical statistical ADJ ijassa-1224 448 5 mechanics mechanic NOUN ijassa-1224 448 6 and and CCONJ ijassa-1224 448 7 its its PRON ijassa-1224 448 8 applications application NOUN ijassa-1224 448 9 , , PUNCT ijassa-1224 448 10 607 607 NUM ijassa-1224 448 11 , , PUNCT ijassa-1224 448 12 128173 128173 NUM ijassa-1224 448 13 . . PUNCT ijassa-1224 449 1 https://doi.org/10.1016/j.physa.2022.128173 https://doi.org/10.1016/j.physa.2022.128173 PROPN ijassa-1224 449 2 15 15 NUM ijassa-1224 449 3 . . PUNCT ijassa-1224 450 1 ojo ojo PROPN ijassa-1224 450 2 , , PUNCT ijassa-1224 450 3 m.m m.m PROPN ijassa-1224 450 4 . . PROPN ijassa-1224 450 5 , , PUNCT ijassa-1224 450 6 & & CCONJ ijassa-1224 450 7 goufo goufo PROPN ijassa-1224 450 8 , , PUNCT ijassa-1224 450 9 e.f.d e.f.d NOUN ijassa-1224 450 10 . . PUNCT ijassa-1224 450 11 ( ( PUNCT ijassa-1224 450 12 2022 2022 NUM ijassa-1224 450 13 ) ) PUNCT ijassa-1224 450 14 . . PUNCT ijassa-1224 451 1 the the DET ijassa-1224 451 2 impact impact NOUN ijassa-1224 451 3 of of ADP ijassa-1224 451 4 covid-19 covid-19 PROPN ijassa-1224 451 5 on on ADP ijassa-1224 451 6 a a DET ijassa-1224 451 7 malaria malaria NOUN ijassa-1224 451 8 dominated dominate VERB ijassa-1224 451 9 region region NOUN ijassa-1224 451 10 : : PUNCT ijassa-1224 451 11 a a DET ijassa-1224 451 12 mathematical mathematical ADJ ijassa-1224 451 13 analysis analysis NOUN ijassa-1224 451 14 and and CCONJ ijassa-1224 451 15 simulations simulation NOUN ijassa-1224 451 16 . . PUNCT ijassa-1224 452 1 alexandria alexandria PROPN ijassa-1224 452 2 engineering engineering PROPN ijassa-1224 452 3 journal journal PROPN ijassa-1224 452 4 , , PUNCT ijassa-1224 452 5 65 65 NUM ijassa-1224 452 6 , , PUNCT ijassa-1224 452 7 23–39 23–39 NUM ijassa-1224 452 8 . . PUNCT ijassa-1224 453 1 16 16 NUM ijassa-1224 453 2 ojo ojo NOUN ijassa-1224 453 3 , , PUNCT ijassa-1224 453 4 m.m m.m PROPN ijassa-1224 453 5 . . PROPN ijassa-1224 453 6 , , PUNCT ijassa-1224 453 7 peter peter PROPN ijassa-1224 453 8 , , PUNCT ijassa-1224 453 9 o.j o.j PROPN ijassa-1224 453 10 . . PROPN ijassa-1224 453 11 , , PUNCT ijassa-1224 453 12 goufo goufo PROPN ijassa-1224 453 13 , , PUNCT ijassa-1224 453 14 e.d e.d PROPN ijassa-1224 453 15 . . PROPN ijassa-1224 453 16 , , PUNCT ijassa-1224 453 17 panigoro panigoro ADV ijassa-1224 453 18 , , PUNCT ijassa-1224 453 19 h.s h.s PROPN ijassa-1224 453 20 . . PROPN ijassa-1224 453 21 & & CCONJ ijassa-1224 453 22 oguntolu oguntolu PROPN ijassa-1224 453 23 , , PUNCT ijassa-1224 453 24 f.a f.a PROPN ijassa-1224 453 25 . . PROPN ijassa-1224 453 26 ( ( PUNCT ijassa-1224 453 27 2022 2022 NUM ijassa-1224 453 28 ) ) PUNCT ijassa-1224 453 29 . . PUNCT ijassa-1224 454 1 mathematical mathematical ADJ ijassa-1224 454 2 model model NOUN ijassa-1224 454 3 for for ADP ijassa-1224 454 4 control control NOUN ijassa-1224 454 5 of of ADP ijassa-1224 454 6 tuberculosis tuberculosis NOUN ijassa-1224 454 7 epidemiology epidemiology NOUN ijassa-1224 454 8 . . PUNCT ijassa-1224 455 1 journal journal PROPN ijassa-1224 455 2 of of ADP ijassa-1224 455 3 applied apply VERB ijassa-1224 455 4 mathematics mathematic NOUN ijassa-1224 455 5 and and CCONJ ijassa-1224 455 6 computing computing NOUN ijassa-1224 455 7 , , PUNCT ijassa-1224 455 8 https://doi.org/10.1007/s12190-022-01734-x https://doi.org/10.1007/s12190-022-01734-x ADP ijassa-1224 455 9 analysis analysis NOUN ijassa-1224 455 10 and and CCONJ ijassa-1224 455 11 dynamics dynamic NOUN ijassa-1224 455 12 of of ADP ijassa-1224 455 13 tuberculosis tuberculosis NOUN ijassa-1224 455 14 outbreak outbreak NOUN ijassa-1224 455 15 161 161 NUM ijassa-1224 455 16 copyright copyright NOUN ijassa-1224 455 17 Β© Β© PROPN ijassa-1224 455 18 2022 2022 NUM ijassa-1224 455 19 assa assa NOUN ijassa-1224 455 20 . . PUNCT ijassa-1224 456 1 adv adv PROPN ijassa-1224 456 2 . . PUNCT ijassa-1224 457 1 in in ADP ijassa-1224 457 2 systems system NOUN ijassa-1224 457 3 science science NOUN ijassa-1224 457 4 and and CCONJ ijassa-1224 457 5 appl appl NOUN ijassa-1224 457 6 . . PUNCT ijassa-1224 458 1 ( ( PUNCT ijassa-1224 458 2 2022 2022 NUM ijassa-1224 458 3 ) ) PUNCT ijassa-1224 458 4 17 17 NUM ijassa-1224 458 5 . . PUNCT ijassa-1224 459 1 okuonghae okuonghae PROPN ijassa-1224 459 2 , , PUNCT ijassa-1224 459 3 d. d. PROPN ijassa-1224 459 4 & & CCONJ ijassa-1224 459 5 aihie aihie PROPN ijassa-1224 459 6 , , PUNCT ijassa-1224 459 7 v. v. PROPN ijassa-1224 459 8 ( ( PUNCT ijassa-1224 459 9 2010 2010 NUM ijassa-1224 459 10 ) ) PUNCT ijassa-1224 459 11 . . PUNCT ijassa-1224 460 1 optimal optimal ADJ ijassa-1224 460 2 control control NOUN ijassa-1224 460 3 measures measure NOUN ijassa-1224 460 4 for for ADP ijassa-1224 460 5 tuberculosis tuberculosis NOUN ijassa-1224 460 6 mathematical mathematical ADJ ijassa-1224 460 7 models model NOUN ijassa-1224 460 8 including include VERB ijassa-1224 460 9 immigration immigration NOUN ijassa-1224 460 10 and and CCONJ ijassa-1224 460 11 isolation isolation NOUN ijassa-1224 460 12 of of ADP ijassa-1224 460 13 infective infective ADJ ijassa-1224 460 14 . . PUNCT ijassa-1224 461 1 journal journal PROPN ijassa-1224 461 2 . . PUNCT ijassa-1224 462 1 biology biology NOUN ijassa-1224 462 2 system system NOUN ijassa-1224 462 3 , , PUNCT ijassa-1224 462 4 18(1 18(1 NOUN ijassa-1224 462 5 ) ) PUNCT ijassa-1224 462 6 , , PUNCT ijassa-1224 462 7 17–54 17–54 NUM ijassa-1224 462 8 . . PUNCT ijassa-1224 463 1 18 18 NUM ijassa-1224 463 2 peter peter PROPN ijassa-1224 463 3 , , PUNCT ijassa-1224 463 4 o.j o.j PROPN ijassa-1224 463 5 . . PROPN ijassa-1224 463 6 , , PUNCT ijassa-1224 463 7 & & CCONJ ijassa-1224 463 8 awoniran awoniran PROPN ijassa-1224 463 9 , , PUNCT ijassa-1224 463 10 a.f a.f PROPN ijassa-1224 463 11 . . PROPN ijassa-1224 463 12 ( ( PUNCT ijassa-1224 463 13 2018 2018 NUM ijassa-1224 463 14 ) ) PUNCT ijassa-1224 463 15 . . PUNCT ijassa-1224 464 1 homotopy homotopy VERB ijassa-1224 464 2 perturbation perturbation NOUN ijassa-1224 464 3 method method NOUN ijassa-1224 464 4 for for ADP ijassa-1224 464 5 solving solve VERB ijassa-1224 464 6 sir sir NOUN ijassa-1224 464 7 infectious infectious ADJ ijassa-1224 464 8 disease disease NOUN ijassa-1224 464 9 model model NOUN ijassa-1224 464 10 by by ADP ijassa-1224 464 11 incorporating incorporate VERB ijassa-1224 464 12 vaccination vaccination NOUN ijassa-1224 464 13 . . PUNCT ijassa-1224 465 1 the the DET ijassa-1224 465 2 pacific pacific PROPN ijassa-1224 465 3 journal journal PROPN ijassa-1224 465 4 of of ADP ijassa-1224 465 5 science science NOUN ijassa-1224 465 6 and and CCONJ ijassa-1224 465 7 technology technology NOUN ijassa-1224 465 8 , , PUNCT ijassa-1224 465 9 19(1 19(1 NUM ijassa-1224 465 10 ) ) PUNCT ijassa-1224 465 11 , , PUNCT ijassa-1224 465 12 133–140 133–140 NUM ijassa-1224 465 13 . . PUNCT ijassa-1224 465 14 19 19 NUM ijassa-1224 465 15 peter peter PROPN ijassa-1224 465 16 , , PUNCT ijassa-1224 465 17 o.j o.j PROPN ijassa-1224 465 18 . . PROPN ijassa-1224 465 19 , , PUNCT ijassa-1224 465 20 abioye abioye PROPN ijassa-1224 465 21 , , PUNCT ijassa-1224 465 22 a.i a.i PROPN ijassa-1224 465 23 . . PROPN ijassa-1224 465 24 , , PUNCT ijassa-1224 465 25 oguntolu oguntolu PROPN ijassa-1224 465 26 , , PUNCT ijassa-1224 465 27 f.a f.a PROPN ijassa-1224 465 28 . . PROPN ijassa-1224 465 29 , , PUNCT ijassa-1224 465 30 owolabi owolabi NOUN ijassa-1224 465 31 , , PUNCT ijassa-1224 465 32 t.a t.a PROPN ijassa-1224 465 33 . . PROPN ijassa-1224 465 34 , , PUNCT ijassa-1224 465 35 ajisope ajisope NOUN ijassa-1224 465 36 , , PUNCT ijassa-1224 465 37 m.o m.o PROPN ijassa-1224 465 38 . . PROPN ijassa-1224 465 39 et et PROPN ijassa-1224 465 40 al al PROPN ijassa-1224 465 41 . . PROPN ijassa-1224 465 42 ( ( PUNCT ijassa-1224 465 43 2020 2020 NUM ijassa-1224 465 44 ) ) PUNCT ijassa-1224 465 45 . . PUNCT ijassa-1224 466 1 modelling modelling NOUN ijassa-1224 466 2 and and CCONJ ijassa-1224 466 3 optimal optimal ADJ ijassa-1224 466 4 control control NOUN ijassa-1224 466 5 analysis analysis NOUN ijassa-1224 466 6 of of ADP ijassa-1224 466 7 lassa lassa ADJ ijassa-1224 466 8 fever fever NOUN ijassa-1224 466 9 disease disease NOUN ijassa-1224 466 10 . . PUNCT ijassa-1224 467 1 informatics informatic NOUN ijassa-1224 467 2 in in ADP ijassa-1224 467 3 medicine medicine NOUN ijassa-1224 467 4 unlocked unlock VERB ijassa-1224 467 5 , , PUNCT ijassa-1224 467 6 20 20 NUM ijassa-1224 467 7 , , PUNCT ijassa-1224 467 8 100419 100419 NUM ijassa-1224 467 9 . . PUNCT ijassa-1224 468 1 20 20 NUM ijassa-1224 468 2 peter peter PROPN ijassa-1224 468 3 , , PUNCT ijassa-1224 468 4 o.j o.j PROPN ijassa-1224 468 5 . . PROPN ijassa-1224 468 6 , , PUNCT ijassa-1224 468 7 qureshi qureshi PROPN ijassa-1224 468 8 , , PUNCT ijassa-1224 468 9 s. s. PROPN ijassa-1224 468 10 , , PUNCT ijassa-1224 468 11 yusuf yusuf PROPN ijassa-1224 468 12 , , PUNCT ijassa-1224 468 13 a. a. PROPN ijassa-1224 468 14 , , PUNCT ijassa-1224 468 15 al al PROPN ijassa-1224 468 16 - - PUNCT ijassa-1224 468 17 shomrani shomrani PROPN ijassa-1224 468 18 , , PUNCT ijassa-1224 468 19 m. m. NOUN ijassa-1224 468 20 , , PUNCT ijassa-1224 468 21 & & CCONJ ijassa-1224 468 22 idowu idowu PROPN ijassa-1224 468 23 , , PUNCT ijassa-1224 468 24 a.a a.a PROPN ijassa-1224 468 25 . . PROPN ijassa-1224 468 26 ( ( PUNCT ijassa-1224 468 27 2021 2021 NUM ijassa-1224 468 28 ) ) PUNCT ijassa-1224 468 29 . . PUNCT ijassa-1224 469 1 a a DET ijassa-1224 469 2 new new ADJ ijassa-1224 469 3 mathematical mathematical ADJ ijassa-1224 469 4 model model NOUN ijassa-1224 469 5 of of ADP ijassa-1224 469 6 covid-19 covid-19 PROPN ijassa-1224 469 7 using use VERB ijassa-1224 469 8 real real ADJ ijassa-1224 469 9 data datum NOUN ijassa-1224 469 10 from from ADP ijassa-1224 469 11 pakistan pakistan PROPN ijassa-1224 469 12 . . PUNCT ijassa-1224 470 1 results result NOUN ijassa-1224 470 2 in in ADP ijassa-1224 470 3 physics physics NOUN ijassa-1224 470 4 , , PUNCT ijassa-1224 470 5 24 24 NUM ijassa-1224 470 6 , , PUNCT ijassa-1224 470 7 104098 104098 NUM ijassa-1224 470 8 . . PUNCT ijassa-1224 471 1 21 21 NUM ijassa-1224 471 2 wang wang PROPN ijassa-1224 471 3 , , PUNCT ijassa-1224 471 4 m. m. NOUN ijassa-1224 471 5 , , PUNCT ijassa-1224 471 6 fitzgerald fitzgerald PROPN ijassa-1224 471 7 , , PUNCT ijassa-1224 471 8 j.m j.m PROPN ijassa-1224 471 9 . . PROPN ijassa-1224 471 10 & & CCONJ ijassa-1224 471 11 richardson richardson PROPN ijassa-1224 471 12 , , PUNCT ijassa-1224 471 13 k. k. PROPN ijassa-1224 471 14 ( ( PUNCT ijassa-1224 471 15 2011 2011 NUM ijassa-1224 471 16 ) ) PUNCT ijassa-1224 471 17 . . PUNCT ijassa-1224 471 18 is be AUX ijassa-1224 471 19 the the DET ijassa-1224 471 20 delay delay NOUN ijassa-1224 471 21 in in ADP ijassa-1224 471 22 diagnosis diagnosis NOUN ijassa-1224 471 23 of of ADP ijassa-1224 471 24 pulmonary pulmonary ADJ ijassa-1224 471 25 tuberculosis tuberculosis NOUN ijassa-1224 471 26 related relate VERB ijassa-1224 471 27 to to ADP ijassa-1224 471 28 exposure exposure NOUN ijassa-1224 471 29 to to ADP ijassa-1224 471 30 fluoroquinolones fluoroquinolone NOUN ijassa-1224 471 31 or or CCONJ ijassa-1224 471 32 any any DET ijassa-1224 471 33 antibiotic antibiotic ADJ ijassa-1224 471 34 ? ? PUNCT ijassa-1224 472 1 union union NOUN ijassa-1224 472 2 : : PUNCT ijassa-1224 473 1 int int NOUN ijassa-1224 473 2 . . PUNCT ijassa-1224 474 1 journal journal NOUN ijassa-1224 474 2 of of ADP ijassa-1224 474 3 tuberculosis tuberculosis NOUN ijassa-1224 474 4 lung lung NOUN ijassa-1224 474 5 diseases disease NOUN ijassa-1224 474 6 , , PUNCT ijassa-1224 474 7 15(8 15(8 NOUN ijassa-1224 474 8 ) ) PUNCT ijassa-1224 474 9 , , PUNCT ijassa-1224 474 10 1062–1068 1062–1068 NUM ijassa-1224 474 11 . . X ijassa-1224 475 1 22 22 NUM ijassa-1224 475 2 world world PROPN ijassa-1224 475 3 health health NOUN ijassa-1224 475 4 organization organization NOUN ijassa-1224 475 5 ( ( PUNCT ijassa-1224 475 6 2019 2019 NUM ijassa-1224 475 7 , , PUNCT ijassa-1224 475 8 august august PROPN ijassa-1224 475 9 25 25 NUM ijassa-1224 475 10 ) ) PUNCT ijassa-1224 475 11 . . PUNCT ijassa-1224 476 1 tuberculosis tuberculosis INTJ ijassa-1224 476 2 fact fact NOUN ijassa-1224 476 3 sheet sheet NOUN ijassa-1224 476 4 n n ADV ijassa-1224 476 5 104 104 NUM ijassa-1224 476 6 . . PUNCT ijassa-1224 477 1 [ [ X ijassa-1224 477 2 online online X ijassa-1224 477 3 ] ] X ijassa-1224 477 4 available available ADJ ijassa-1224 477 5 http://www.who.int/ http://www.who.int/ PROPN ijassa-1224 477 6 mediacentre mediacentre NOUN ijassa-1224 477 7 / / SYM ijassa-1224 477 8 factsheets factsheet NOUN ijassa-1224 477 9 / / SYM ijassa-1224 477 10 fs104 fs104 NOUN ijassa-1224 477 11 / / SYM ijassa-1224 477 12 en/ en/ NOUN ijassa-1224 477 13 index.html index.html NOUN