id sid tid token lemma pos cana-4541 1 1 communications communication NOUN cana-4541 1 2 on on ADP cana-4541 1 3 applied apply VERB cana-4541 1 4 nonlinear nonlinear ADJ cana-4541 1 5 analysis analysis NOUN cana-4541 1 6 issn issn NOUN cana-4541 1 7 : : PUNCT cana-4541 1 8 1074 1074 NUM cana-4541 1 9 - - PUNCT cana-4541 1 10 133x 133x NUM cana-4541 1 11 vol vol NOUN cana-4541 1 12 32 32 NUM cana-4541 1 13 no no NOUN cana-4541 1 14 . . PUNCT cana-4541 2 1 9s 9s NUM cana-4541 2 2 ( ( PUNCT cana-4541 2 3 2025 2025 NUM cana-4541 2 4 ) ) PUNCT cana-4541 2 5 2478 2478 NUM cana-4541 2 6 https://internationalpubls.com https://internationalpubls.com X cana-4541 2 7 on on ADP cana-4541 2 8 fractional fractional ADJ cana-4541 2 9 epidemic epidemic NOUN cana-4541 2 10 model model NOUN cana-4541 2 11 order order NOUN cana-4541 2 12 shigella shigella PROPN cana-4541 2 13 1mampi 1mampi PROPN cana-4541 2 14 saha saha PROPN cana-4541 2 15 , , PUNCT cana-4541 2 16 2kaveri 2kaveri NUM cana-4541 2 17 kanchan kanchan PROPN cana-4541 2 18 kumari kumari PROPN cana-4541 2 19 , , PUNCT cana-4541 2 20 3om 3om ADJ cana-4541 2 21 prakash prakash PROPN cana-4541 2 22 , , PUNCT cana-4541 2 23 4asha 4asha PROPN cana-4541 2 24 lata lata VERB cana-4541 2 25 keshri keshri PROPN cana-4541 2 26 1assistant 1assistant NUM cana-4541 2 27 professor professor NOUN cana-4541 2 28 , , PUNCT cana-4541 2 29 rtc rtc PROPN cana-4541 2 30 institute institute PROPN cana-4541 2 31 of of ADP cana-4541 2 32 technology technology PROPN cana-4541 2 33 , , PUNCT cana-4541 2 34 ranchi ranchi PROPN cana-4541 2 35 , , PUNCT cana-4541 2 36 india india PROPN cana-4541 2 37 sajalmampi@gmail.com sajalmampi@gmail.com X cana-4541 3 1 2research 2research NUM cana-4541 3 2 scholar scholar NOUN cana-4541 3 3 , , PUNCT cana-4541 3 4 department department NOUN cana-4541 3 5 of of ADP cana-4541 3 6 mathematics mathematics PROPN cana-4541 3 7 , , PUNCT cana-4541 3 8 ranchi ranchi PROPN cana-4541 3 9 university university PROPN cana-4541 3 10 , , PUNCT cana-4541 3 11 ranchi ranchi PROPN cana-4541 3 12 , , PUNCT cana-4541 3 13 india india PROPN cana-4541 3 14 kanchan_kaveri4@yahoo.in kanchan_kaveri4@yahoo.in PROPN cana-4541 4 1 3research 3research NUM cana-4541 4 2 scholar scholar NOUN cana-4541 4 3 , , PUNCT cana-4541 4 4 department department NOUN cana-4541 4 5 of of ADP cana-4541 4 6 mathematics mathematics PROPN cana-4541 4 7 , , PUNCT cana-4541 4 8 ranchi ranchi PROPN cana-4541 4 9 university university PROPN cana-4541 4 10 , , PUNCT cana-4541 4 11 ranchi ranchi PROPN cana-4541 4 12 , , PUNCT cana-4541 4 13 india india PROPN cana-4541 4 14 prakashcool.om12@gmail.com prakashcool.om12@gmail.com PROPN cana-4541 4 15 4 4 NUM cana-4541 4 16 associate associate NOUN cana-4541 4 17 professor professor NOUN cana-4541 4 18 , , PUNCT cana-4541 4 19 department department NOUN cana-4541 4 20 of of ADP cana-4541 4 21 mathematics mathematics PROPN cana-4541 4 22 , , PUNCT cana-4541 4 23 ranchi ranchi PROPN cana-4541 4 24 university university PROPN cana-4541 4 25 , , PUNCT cana-4541 4 26 ranchi ranchi PROPN cana-4541 4 27 , , PUNCT cana-4541 4 28 india india PROPN cana-4541 4 29 ashlata.math@ranchiuniversity.ac.in ashlata.math@ranchiuniversity.ac.in PART cana-4541 4 30 article article NOUN cana-4541 4 31 history history NOUN cana-4541 4 32 : : PUNCT cana-4541 4 33 received receive VERB cana-4541 4 34 : : PUNCT cana-4541 4 35 12 12 NUM cana-4541 4 36 - - SYM cana-4541 4 37 01 01 NUM cana-4541 4 38 - - PUNCT cana-4541 4 39 2025 2025 NUM cana-4541 4 40 revised revise VERB cana-4541 4 41 : : PUNCT cana-4541 4 42 15 15 NUM cana-4541 4 43 - - NUM cana-4541 4 44 02 02 NUM cana-4541 4 45 - - PUNCT cana-4541 4 46 2025 2025 NUM cana-4541 4 47 accepted accept VERB cana-4541 4 48 : : PUNCT cana-4541 4 49 01 01 NUM cana-4541 4 50 - - SYM cana-4541 4 51 03 03 NUM cana-4541 4 52 - - PUNCT cana-4541 4 53 2025 2025 NUM cana-4541 4 54 abstract abstract NOUN cana-4541 4 55 : : PUNCT cana-4541 4 56 introduction introduction NOUN cana-4541 4 57 : : PUNCT cana-4541 4 58 we we PRON cana-4541 4 59 have have AUX cana-4541 4 60 adapted adapt VERB cana-4541 4 61 the the DET cana-4541 4 62 continuous continuous ADJ cana-4541 4 63 mathematical mathematical ADJ cana-4541 4 64 framework framework NOUN cana-4541 4 65 developed develop VERB cana-4541 4 66 to to PART cana-4541 4 67 examine examine VERB cana-4541 4 68 the the DET cana-4541 4 69 dynamics dynamic NOUN cana-4541 4 70 of of ADP cana-4541 4 71 a a DET cana-4541 4 72 shigella shigella NOUN cana-4541 4 73 epidemic epidemic NOUN cana-4541 4 74 at at ADP cana-4541 4 75 a a DET cana-4541 4 76 constant constant ADJ cana-4541 4 77 recruitment recruitment NOUN cana-4541 4 78 rate rate NOUN cana-4541 4 79 . . PUNCT cana-4541 5 1 they they PRON cana-4541 5 2 divided divide VERB cana-4541 5 3 the the DET cana-4541 5 4 population population NOUN cana-4541 5 5 into into ADP cana-4541 5 6 seven seven NUM cana-4541 5 7 groups group NOUN cana-4541 5 8 in in ADP cana-4541 5 9 their their PRON cana-4541 5 10 model model NOUN cana-4541 5 11 : : PUNCT cana-4541 5 12 susceptible susceptible ADJ cana-4541 5 13 ( ( PUNCT cana-4541 5 14 s s NOUN cana-4541 5 15 ) ) PUNCT cana-4541 5 16 , , PUNCT cana-4541 5 17 vaccination(v vaccination(v PROPN cana-4541 5 18 ) ) PUNCT cana-4541 5 19 , , PUNCT cana-4541 5 20 exposΓ©(e exposΓ©(e PROPN cana-4541 5 21 ) ) PUNCT cana-4541 5 22 , , PUNCT cana-4541 5 23 infected infect VERB cana-4541 5 24 ( ( PUNCT cana-4541 5 25 i i NOUN cana-4541 5 26 ) ) PUNCT cana-4541 5 27 , , PUNCT cana-4541 5 28 isolated isolate VERB cana-4541 5 29 ( ( PUNCT cana-4541 5 30 g g NOUN cana-4541 5 31 ) ) PUNCT cana-4541 5 32 , , PUNCT cana-4541 5 33 hospitalized(h hospitalized(h NOUN cana-4541 5 34 ) ) PUNCT cana-4541 5 35 and and CCONJ cana-4541 5 36 recovered recover VERB cana-4541 5 37 ( ( PUNCT cana-4541 5 38 r r NOUN cana-4541 5 39 ) ) PUNCT cana-4541 5 40 , , PUNCT cana-4541 5 41 each each PRON cana-4541 5 42 with with ADP cana-4541 5 43 its its PRON cana-4541 5 44 own own ADJ cana-4541 5 45 set set NOUN cana-4541 5 46 of of ADP cana-4541 5 47 parameters parameter NOUN cana-4541 5 48 . . PUNCT cana-4541 6 1 we we PRON cana-4541 6 2 examined examine VERB cana-4541 6 3 a a DET cana-4541 6 4 mathematical mathematical ADJ cana-4541 6 5 model model NOUN cana-4541 6 6 of of ADP cana-4541 6 7 a a DET cana-4541 6 8 shigella shigella ADJ cana-4541 6 9 outbreak outbreak NOUN cana-4541 6 10 in in ADP cana-4541 6 11 a a DET cana-4541 6 12 community community NOUN cana-4541 6 13 with with ADP cana-4541 6 14 a a DET cana-4541 6 15 constant constant ADJ cana-4541 6 16 population population NOUN cana-4541 6 17 using use VERB cana-4541 6 18 the the DET cana-4541 6 19 sveighr sveighr NOUN cana-4541 6 20 compartmental compartmental PROPN cana-4541 6 21 nonlinear nonlinear PROPN cana-4541 6 22 deterministic deterministic ADJ cana-4541 6 23 approach approach NOUN cana-4541 6 24 . . PUNCT cana-4541 7 1 the the DET cana-4541 7 2 model model NOUN cana-4541 7 3 was be AUX cana-4541 7 4 subjected subject VERB cana-4541 7 5 to to ADP cana-4541 7 6 analytical analytical ADJ cana-4541 7 7 investigations investigation NOUN cana-4541 7 8 utilizing utilize VERB cana-4541 7 9 the the DET cana-4541 7 10 linearized linearize VERB cana-4541 7 11 stability stability NOUN cana-4541 7 12 method method NOUN cana-4541 7 13 . . PUNCT cana-4541 8 1 the the DET cana-4541 8 2 greatest great ADJ cana-4541 8 3 eigenvalue eigenvalue NOUN cana-4541 8 4 of of ADP cana-4541 8 5 the the DET cana-4541 8 6 next next ADJ cana-4541 8 7 - - PUNCT cana-4541 8 8 generation generation NOUN cana-4541 8 9 matrix matrix NOUN cana-4541 8 10 yields yield VERB cana-4541 8 11 the the DET cana-4541 8 12 fundamental fundamental ADJ cana-4541 8 13 reproductive reproductive ADJ cana-4541 8 14 number number NOUN cana-4541 8 15 r0 r0 NOUN cana-4541 8 16 , , PUNCT cana-4541 8 17 which which PRON cana-4541 8 18 controls control VERB cana-4541 8 19 the the DET cana-4541 8 20 spread spread NOUN cana-4541 8 21 of of ADP cana-4541 8 22 the the DET cana-4541 8 23 disease disease NOUN cana-4541 8 24 . . PUNCT cana-4541 9 1 the the DET cana-4541 9 2 generalized generalize VERB cana-4541 9 3 routh routh PROPN cana-4541 9 4 - - PUNCT cana-4541 9 5 hurwitz hurwitz PROPN cana-4541 9 6 and and CCONJ cana-4541 9 7 jacobian jacobian ADJ cana-4541 9 8 criterion criterion NOUN cana-4541 9 9 are be AUX cana-4541 9 10 used use VERB cana-4541 9 11 to to PART cana-4541 9 12 determine determine VERB cana-4541 9 13 the the DET cana-4541 9 14 threshold threshold NOUN cana-4541 9 15 value value NOUN cana-4541 9 16 r0 r0 NOUN cana-4541 9 17 . . PUNCT cana-4541 10 1 the the DET cana-4541 10 2 model model NOUN cana-4541 10 3 is be AUX cana-4541 10 4 unstable unstable ADJ cana-4541 10 5 if if SCONJ cana-4541 10 6 , , PUNCT cana-4541 10 7 r0 r0 NOUN cana-4541 10 8 > > X cana-4541 10 9 1 1 NUM cana-4541 10 10 , , PUNCT cana-4541 10 11 and and CCONJ cana-4541 10 12 stable stable ADJ cana-4541 10 13 if if SCONJ cana-4541 10 14 , , PUNCT cana-4541 10 15 r0 r0 NOUN cana-4541 10 16 < < X cana-4541 10 17 1 1 NUM cana-4541 10 18 . . PUNCT cana-4541 11 1 additionally additionally ADV cana-4541 11 2 , , PUNCT cana-4541 11 3 we we PRON cana-4541 11 4 determine determine VERB cana-4541 11 5 the the DET cana-4541 11 6 endemic endemic ADJ cana-4541 11 7 and and CCONJ cana-4541 11 8 disease disease NOUN cana-4541 11 9 - - PUNCT cana-4541 11 10 free free ADJ cana-4541 11 11 equilibrium equilibrium NOUN cana-4541 11 12 points point NOUN cana-4541 11 13 , , PUNCT cana-4541 11 14 which which PRON cana-4541 11 15 are be AUX cana-4541 11 16 helpful helpful ADJ cana-4541 11 17 for for ADP cana-4541 11 18 a a DET cana-4541 11 19 faster fast ADJ cana-4541 11 20 recovery recovery NOUN cana-4541 11 21 . . PUNCT cana-4541 12 1 we we PRON cana-4541 12 2 have have AUX cana-4541 12 3 created create VERB cana-4541 12 4 graphs graph NOUN cana-4541 12 5 in in ADP cana-4541 12 6 matlab matlab PROPN cana-4541 12 7 to to PART cana-4541 12 8 provide provide VERB cana-4541 12 9 a a DET cana-4541 12 10 more more ADV cana-4541 12 11 accurate accurate ADJ cana-4541 12 12 model model NOUN cana-4541 12 13 representation representation NOUN cana-4541 12 14 . . PUNCT cana-4541 13 1 objectives objective NOUN cana-4541 13 2 : : PUNCT cana-4541 13 3 to to PART cana-4541 13 4 describe describe VERB cana-4541 13 5 the the DET cana-4541 13 6 disease disease NOUN cana-4541 13 7 shigella shigella ADV cana-4541 13 8 with with ADP cana-4541 13 9 the the DET cana-4541 13 10 help help NOUN cana-4541 13 11 of of ADP cana-4541 13 12 sveigher sveigher NOUN cana-4541 13 13 compartmental compartmental ADJ cana-4541 13 14 nonlinear nonlinear ADJ cana-4541 13 15 deterministic deterministic ADJ cana-4541 13 16 approach approach NOUN cana-4541 13 17 through through ADP cana-4541 13 18 factorial factorial ADJ cana-4541 13 19 differential differential NOUN cana-4541 13 20 method method NOUN cana-4541 13 21 and and CCONJ cana-4541 13 22 compare compare VERB cana-4541 13 23 it it PRON cana-4541 13 24 to to ADP cana-4541 13 25 classical classical ADJ cana-4541 13 26 differential differential NOUN cana-4541 13 27 method method NOUN cana-4541 13 28 and and CCONJ cana-4541 13 29 see see VERB cana-4541 13 30 the the DET cana-4541 13 31 results result NOUN cana-4541 13 32 . . PUNCT cana-4541 14 1 results result NOUN cana-4541 14 2 : : PUNCT cana-4541 14 3 from from ADP cana-4541 14 4 the the DET cana-4541 14 5 above above ADJ cana-4541 14 6 studies study NOUN cana-4541 14 7 we we PRON cana-4541 14 8 conclude conclude VERB cana-4541 14 9 that that SCONJ cana-4541 14 10 fractional fractional ADJ cana-4541 14 11 differential differential NOUN cana-4541 14 12 method method NOUN cana-4541 14 13 is be AUX cana-4541 14 14 more more ADV cana-4541 14 15 effective effective ADJ cana-4541 14 16 than than ADP cana-4541 14 17 classical classical ADJ cana-4541 14 18 differential differential NOUN cana-4541 14 19 method method NOUN cana-4541 14 20 . . PUNCT cana-4541 15 1 conclusion conclusion NOUN cana-4541 15 2 : : PUNCT cana-4541 15 3 in in ADP cana-4541 15 4 this this DET cana-4541 15 5 paper paper NOUN cana-4541 15 6 , , PUNCT cana-4541 15 7 we we PRON cana-4541 15 8 discuss discuss VERB cana-4541 15 9 sveighr sveighr NOUN cana-4541 15 10 epidemic epidemic NOUN cana-4541 15 11 model model NOUN cana-4541 15 12 for for ADP cana-4541 15 13 disease disease NOUN cana-4541 15 14 shigella shigella PROPN cana-4541 15 15 . . PUNCT cana-4541 16 1 this this DET cana-4541 16 2 sveighr sveighr PROPN cana-4541 16 3 model model NOUN cana-4541 16 4 controlss controlss PROPN cana-4541 16 5 the the DET cana-4541 16 6 spreading spreading NOUN cana-4541 16 7 of of ADP cana-4541 16 8 the the DET cana-4541 16 9 mailto:sajalmampi@gmail.com mailto:sajalmampi@gmail.com NOUN cana-4541 16 10 mailto:kanchan_kaveri4@yahoo.in mailto:kanchan_kaveri4@yahoo.in NOUN cana-4541 16 11 mailto:prakashcool.om12@gmail.com mailto:prakashcool.om12@gmail.com NOUN cana-4541 16 12 mailto:ashlata.math@ranchiuniversity.ac.in mailto:ashlata.math@ranchiuniversity.ac.in PART cana-4541 16 13 communications communication NOUN cana-4541 16 14 on on ADP cana-4541 16 15 applied apply VERB cana-4541 16 16 nonlinear nonlinear ADJ cana-4541 16 17 analysis analysis NOUN cana-4541 16 18 issn issn NOUN cana-4541 16 19 : : PUNCT cana-4541 16 20 1074 1074 NUM cana-4541 16 21 - - PUNCT cana-4541 16 22 133x 133x NUM cana-4541 16 23 vol vol NOUN cana-4541 16 24 32 32 NUM cana-4541 16 25 no no NOUN cana-4541 16 26 . . PUNCT cana-4541 17 1 9s 9s NUM cana-4541 17 2 ( ( PUNCT cana-4541 17 3 2025 2025 NUM cana-4541 17 4 ) ) PUNCT cana-4541 17 5 2479 2479 NUM cana-4541 17 6 https://internationalpubls.com https://internationalpubls.com X cana-4541 17 7 disease disease NOUN cana-4541 17 8 in in ADP cana-4541 17 9 human human ADJ cana-4541 17 10 population population NOUN cana-4541 17 11 . . PUNCT cana-4541 18 1 by by ADP cana-4541 18 2 using use VERB cana-4541 18 3 routh routh PROPN cana-4541 18 4 - - PUNCT cana-4541 18 5 hurwitz hurwitz PROPN cana-4541 18 6 criteria criterion NOUN cana-4541 18 7 we we PRON cana-4541 18 8 find find VERB cana-4541 18 9 all all DET cana-4541 18 10 the the DET cana-4541 18 11 eigen eigen PROPN cana-4541 18 12 values value NOUN cana-4541 18 13 for for ADP cana-4541 18 14 endemic endemic ADJ cana-4541 18 15 point point NOUN cana-4541 18 16 are be AUX cana-4541 18 17 negative negative ADJ cana-4541 18 18 which which PRON cana-4541 18 19 shows show VERB cana-4541 18 20 that that SCONJ cana-4541 18 21 the the DET cana-4541 18 22 above above ADJ cana-4541 18 23 model model NOUN cana-4541 18 24 sveighr sveighr PROPN cana-4541 18 25 ( ( PUNCT cana-4541 18 26 susceptible susceptible ADJ cana-4541 18 27 vacation vacation NOUN cana-4541 18 28 infectious infectious ADJ cana-4541 18 29 isolated isolated ADJ cana-4541 18 30 hospitalization hospitalization NOUN cana-4541 18 31 recovered recover VERB cana-4541 18 32 ) ) PUNCT cana-4541 18 33 is be AUX cana-4541 18 34 stable stable ADJ cana-4541 18 35 . . PUNCT cana-4541 19 1 extending extend VERB cana-4541 19 2 our our PRON cana-4541 19 3 work work NOUN cana-4541 19 4 , , PUNCT cana-4541 19 5 we we PRON cana-4541 19 6 can can AUX cana-4541 19 7 also also ADV cana-4541 19 8 use use VERB cana-4541 19 9 harmonic harmonic ADJ cana-4541 19 10 mean mean NOUN cana-4541 19 11 type type NOUN cana-4541 19 12 incidence incidence NOUN cana-4541 19 13 rate rate NOUN cana-4541 19 14 for for ADP cana-4541 19 15 better well ADJ cana-4541 19 16 stability stability NOUN cana-4541 19 17 and and CCONJ cana-4541 19 18 control control VERB cana-4541 19 19 the the DET cana-4541 19 20 disease disease NOUN cana-4541 19 21 . . PUNCT cana-4541 20 1 key key ADJ cana-4541 20 2 word word NOUN cana-4541 20 3 : : PUNCT cana-4541 20 4 mathematical mathematical ADJ cana-4541 20 5 model model NOUN cana-4541 20 6 , , PUNCT cana-4541 20 7 stability stability NOUN cana-4541 20 8 analysis analysis NOUN cana-4541 20 9 , , PUNCT cana-4541 20 10 endemic endemic ADJ cana-4541 20 11 equilibrium equilibrium NOUN cana-4541 20 12 ; ; PUNCT cana-4541 20 13 routh routh PROPN cana-4541 20 14 - - PUNCT cana-4541 20 15 hurwitz hurwitz PROPN cana-4541 20 16 criteria criterion NOUN cana-4541 20 17 , , PUNCT cana-4541 20 18 reproduction reproduction NOUN cana-4541 20 19 number number NOUN cana-4541 20 20 . . PUNCT cana-4541 21 1 ams am NOUN cana-4541 21 2 classification classification NOUN cana-4541 21 3 2010 2010 NUM cana-4541 21 4 : : PUNCT cana-4541 21 5 93a30 93a30 NUM cana-4541 21 6 , , PUNCT cana-4541 21 7 92b05 92b05 NUM cana-4541 21 8 , , PUNCT cana-4541 21 9 92d30 92d30 NUM cana-4541 21 10 1 1 NUM cana-4541 21 11 . . PUNCT cana-4541 22 1 introduction introduction NOUN cana-4541 22 2 gram gram NOUN cana-4541 22 3 - - PUNCT cana-4541 22 4 negative negative ADJ cana-4541 22 5 , , PUNCT cana-4541 22 6 non non ADJ cana-4541 22 7 - - ADJ cana-4541 22 8 spore spore ADJ cana-4541 22 9 - - PUNCT cana-4541 22 10 forming form VERB cana-4541 22 11 shigella shigella PROPN cana-4541 22 12 bacteria bacteria NOUN cana-4541 22 13 are be AUX cana-4541 22 14 the the DET cana-4541 22 15 main main ADJ cana-4541 22 16 cause cause NOUN cana-4541 22 17 of of ADP cana-4541 22 18 shigella shigella ADJ cana-4541 22 19 infection infection NOUN cana-4541 22 20 , , PUNCT cana-4541 22 21 commonly commonly ADV cana-4541 22 22 referred refer VERB cana-4541 22 23 to to ADP cana-4541 22 24 as as ADP cana-4541 22 25 shigellosis shigellosis NOUN cana-4541 22 26 , , PUNCT cana-4541 22 27 a a DET cana-4541 22 28 diarrheal diarrheal ADJ cana-4541 22 29 illness illness NOUN cana-4541 22 30 . . PUNCT cana-4541 23 1 it it PRON cana-4541 23 2 is be AUX cana-4541 23 3 via via ADP cana-4541 23 4 fecal fecal ADJ cana-4541 23 5 - - PUNCT cana-4541 23 6 oral oral ADJ cana-4541 23 7 matter matter NOUN cana-4541 23 8 , , PUNCT cana-4541 23 9 which which PRON cana-4541 23 10 is be AUX cana-4541 23 11 typically typically ADV cana-4541 23 12 brought bring VERB cana-4541 23 13 on on ADP cana-4541 23 14 by by ADP cana-4541 23 15 contaminated contaminate VERB cana-4541 23 16 food food NOUN cana-4541 23 17 , , PUNCT cana-4541 23 18 water water NOUN cana-4541 23 19 , , PUNCT cana-4541 23 20 or or CCONJ cana-4541 23 21 close close ADJ cana-4541 23 22 contact contact NOUN cana-4541 23 23 with with ADP cana-4541 23 24 infected infected ADJ cana-4541 23 25 people people NOUN cana-4541 23 26 . . PUNCT cana-4541 24 1 these these DET cana-4541 24 2 bacteria bacteria NOUN cana-4541 24 3 infect infect VERB cana-4541 24 4 the the DET cana-4541 24 5 intestinal intestinal ADJ cana-4541 24 6 lining lining NOUN cana-4541 24 7 . . PUNCT cana-4541 25 1 tenesmus tenesmus NOUN cana-4541 25 2 , , PUNCT cana-4541 25 3 fever fever NOUN cana-4541 25 4 , , PUNCT cana-4541 25 5 abdominal abdominal ADJ cana-4541 25 6 pain pain NOUN cana-4541 25 7 , , PUNCT cana-4541 25 8 and and CCONJ cana-4541 25 9 diarrhea diarrhea NOUN cana-4541 25 10 - - PUNCT cana-4541 25 11 often often ADV cana-4541 25 12 bloody bloody ADJ cana-4541 25 13 - - PUNCT cana-4541 25 14 are be AUX cana-4541 25 15 among among ADP cana-4541 25 16 the the DET cana-4541 25 17 symptoms symptom NOUN cana-4541 25 18 that that PRON cana-4541 25 19 start start VERB cana-4541 25 20 to to PART cana-4541 25 21 show show VERB cana-4541 25 22 up up ADP cana-4541 25 23 1 1 NUM cana-4541 25 24 - - SYM cana-4541 25 25 2 2 NUM cana-4541 25 26 days day NOUN cana-4541 25 27 after after ADP cana-4541 25 28 exposure exposure NOUN cana-4541 25 29 and and CCONJ cana-4541 25 30 can can AUX cana-4541 25 31 linger linger VERB cana-4541 25 32 for for ADP cana-4541 25 33 up up ADP cana-4541 25 34 to to PART cana-4541 25 35 a a DET cana-4541 25 36 week week NOUN cana-4541 25 37 . . PUNCT cana-4541 26 1 serious serious ADJ cana-4541 26 2 side side NOUN cana-4541 26 3 effects effect NOUN cana-4541 26 4 include include VERB cana-4541 26 5 hemolytic hemolytic ADJ cana-4541 26 6 uremic uremic ADJ cana-4541 26 7 syndrome syndrome NOUN cana-4541 26 8 , , PUNCT cana-4541 26 9 sepsis sepsis NOUN cana-4541 26 10 , , PUNCT cana-4541 26 11 and and CCONJ cana-4541 26 12 reactive reactive ADJ cana-4541 26 13 arthritis arthritis NOUN cana-4541 26 14 could could AUX cana-4541 26 15 happen happen VERB cana-4541 26 16 . . PUNCT cana-4541 27 1 the the DET cana-4541 27 2 majority majority NOUN cana-4541 27 3 of of ADP cana-4541 27 4 cases case NOUN cana-4541 27 5 go go VERB cana-4541 27 6 away away ADV cana-4541 27 7 without without ADP cana-4541 27 8 special special ADJ cana-4541 27 9 care care NOUN cana-4541 27 10 , , PUNCT cana-4541 27 11 but but CCONJ cana-4541 27 12 rest rest NOUN cana-4541 27 13 and and CCONJ cana-4541 27 14 hydration hydration NOUN cana-4541 27 15 are be AUX cana-4541 27 16 crucial crucial ADJ cana-4541 27 17 . . PUNCT cana-4541 28 1 antibiotics antibiotic NOUN cana-4541 28 2 such such ADJ cana-4541 28 3 as as ADP cana-4541 28 4 azithromycin azithromycin PROPN cana-4541 28 5 or or CCONJ cana-4541 28 6 ciprofloxacin ciprofloxacin NOUN cana-4541 28 7 may may AUX cana-4541 28 8 be be AUX cana-4541 28 9 necessary necessary ADJ cana-4541 28 10 in in ADP cana-4541 28 11 severe severe ADJ cana-4541 28 12 cases case NOUN cana-4541 28 13 , , PUNCT cana-4541 28 14 though though SCONJ cana-4541 28 15 resistance resistance NOUN cana-4541 28 16 is be AUX cana-4541 28 17 becoming become VERB cana-4541 28 18 a a DET cana-4541 28 19 bigger big ADJ cana-4541 28 20 problem problem NOUN cana-4541 28 21 . . PUNCT cana-4541 29 1 although although SCONJ cana-4541 29 2 there there PRON cana-4541 29 3 is be VERB cana-4541 29 4 n't not PART cana-4541 29 5 a a DET cana-4541 29 6 licensed licensed ADJ cana-4541 29 7 vaccine vaccine NOUN cana-4541 29 8 at at ADP cana-4541 29 9 the the DET cana-4541 29 10 moment moment NOUN cana-4541 29 11 , , PUNCT cana-4541 29 12 a a DET cana-4541 29 13 number number NOUN cana-4541 29 14 of of ADP cana-4541 29 15 possibilities possibility NOUN cana-4541 29 16 are be AUX cana-4541 29 17 being be AUX cana-4541 29 18 developed develop VERB cana-4541 29 19 , , PUNCT cana-4541 29 20 such such ADJ cana-4541 29 21 as as ADP cana-4541 29 22 conjugate conjugate ADJ cana-4541 29 23 and and CCONJ cana-4541 29 24 live live ADJ cana-4541 29 25 attenuated attenuated ADJ cana-4541 29 26 vaccines vaccine NOUN cana-4541 29 27 . . PUNCT cana-4541 30 1 reducing reduce VERB cana-4541 30 2 transmission transmission NOUN cana-4541 30 3 still still ADV cana-4541 30 4 requires require VERB cana-4541 30 5 preventive preventive ADJ cana-4541 30 6 actions action NOUN cana-4541 30 7 like like ADP cana-4541 30 8 better well ADJ cana-4541 30 9 sanitation sanitation NOUN cana-4541 30 10 and and CCONJ cana-4541 30 11 hand hand NOUN cana-4541 30 12 hygiene hygiene NOUN cana-4541 30 13 . . PUNCT cana-4541 31 1 fractional fractional ADJ cana-4541 31 2 calculus calculus NOUN cana-4541 31 3 investigates investigate VERB cana-4541 31 4 function function VERB cana-4541 31 5 derivatives derivative NOUN cana-4541 31 6 and and CCONJ cana-4541 31 7 integrals integral NOUN cana-4541 31 8 . . PUNCT cana-4541 32 1 however however ADV cana-4541 32 2 , , PUNCT cana-4541 32 3 in in ADP cana-4541 32 4 this this DET cana-4541 32 5 area area NOUN cana-4541 32 6 of of ADP cana-4541 32 7 mathematics mathematic NOUN cana-4541 32 8 , , PUNCT cana-4541 32 9 we we PRON cana-4541 32 10 are be AUX cana-4541 32 11 examining examine VERB cana-4541 32 12 integrals integral NOUN cana-4541 32 13 and and CCONJ cana-4541 32 14 derivatives derivative NOUN cana-4541 32 15 of of ADP cana-4541 32 16 non non ADJ cana-4541 32 17 - - ADJ cana-4541 32 18 integer integer ADJ cana-4541 32 19 order order NOUN cana-4541 32 20 rather rather ADV cana-4541 32 21 than than ADP cana-4541 32 22 the the DET cana-4541 32 23 typical typical ADJ cana-4541 32 24 integer integer NOUN cana-4541 32 25 order order NOUN cana-4541 32 26 . . PUNCT cana-4541 33 1 these these PRON cana-4541 33 2 might might AUX cana-4541 33 3 be be AUX cana-4541 33 4 of of ADP cana-4541 33 5 real real ADJ cana-4541 33 6 or or CCONJ cana-4541 33 7 complex complex ADJ cana-4541 33 8 order order NOUN cana-4541 33 9 and and CCONJ cana-4541 33 10 are be AUX cana-4541 33 11 referred refer VERB cana-4541 33 12 to to ADP cana-4541 33 13 as as ADP cana-4541 33 14 fractional fractional ADJ cana-4541 33 15 - - PUNCT cana-4541 33 16 order order NOUN cana-4541 33 17 derivatives derivative NOUN cana-4541 33 18 and and CCONJ cana-4541 33 19 fractional fractional ADJ cana-4541 33 20 integrals integral NOUN cana-4541 33 21 . . PUNCT cana-4541 34 1 a a DET cana-4541 34 2 mathematical mathematical ADJ cana-4541 34 3 tool tool NOUN cana-4541 34 4 that that PRON cana-4541 34 5 unifies unify VERB cana-4541 34 6 and and CCONJ cana-4541 34 7 generalizes generalize VERB cana-4541 34 8 the the DET cana-4541 34 9 derivative derivative ADJ cana-4541 34 10 and and CCONJ cana-4541 34 11 integral integral ADJ cana-4541 34 12 of of ADP cana-4541 34 13 integer integer NOUN cana-4541 34 14 order order NOUN cana-4541 34 15 to to ADP cana-4541 34 16 any any DET cana-4541 34 17 arbitrary arbitrary ADJ cana-4541 34 18 order order NOUN cana-4541 34 19 is be AUX cana-4541 34 20 generally generally ADV cana-4541 34 21 referred refer VERB cana-4541 34 22 to to ADP cana-4541 34 23 as as ADP cana-4541 34 24 fractional fractional ADJ cana-4541 34 25 calculus calculus NOUN cana-4541 34 26 . . PUNCT cana-4541 35 1 leibniz leibniz PROPN cana-4541 35 2 initially initially ADV cana-4541 35 3 addressed address VERB cana-4541 35 4 the the DET cana-4541 35 5 theory theory NOUN cana-4541 35 6 of of ADP cana-4541 35 7 fractional fractional ADJ cana-4541 35 8 derivative derivative NOUN cana-4541 35 9 in in ADP cana-4541 35 10 1695 1695 NUM cana-4541 35 11 . . PUNCT cana-4541 36 1 because because SCONJ cana-4541 36 2 of of ADP cana-4541 36 3 this this PRON cana-4541 36 4 , , PUNCT cana-4541 36 5 mathematicians mathematician NOUN cana-4541 36 6 from from ADP cana-4541 36 7 the the DET cana-4541 36 8 18th 18th NOUN cana-4541 36 9 to to ADP cana-4541 36 10 the the DET cana-4541 36 11 19th 19th ADJ cana-4541 36 12 centuries century NOUN cana-4541 36 13 were be AUX cana-4541 36 14 interested interested ADJ cana-4541 36 15 in in ADP cana-4541 36 16 studying study VERB cana-4541 36 17 this this DET cana-4541 36 18 field field NOUN cana-4541 36 19 . . PUNCT cana-4541 37 1 a a DET cana-4541 37 2 well well ADV cana-4541 37 3 known know VERB cana-4541 37 4 scientist scientist NOUN cana-4541 37 5 , , PUNCT cana-4541 37 6 abel abel PROPN cana-4541 37 7 , , PUNCT cana-4541 37 8 in in ADP cana-4541 37 9 1823 1823 NUM cana-4541 37 10 was be AUX cana-4541 37 11 the the DET cana-4541 37 12 first first ADJ cana-4541 37 13 scientist scientist NOUN cana-4541 37 14 to to PART cana-4541 37 15 apply apply VERB cana-4541 37 16 fractional fractional ADJ cana-4541 37 17 calculus calculus NOUN cana-4541 37 18 for for ADP cana-4541 37 19 investigating investigate VERB cana-4541 37 20 tautochrone tautochrone NOUN cana-4541 37 21 problems problem NOUN cana-4541 37 22 . . PUNCT cana-4541 38 1 fractional fractional ADJ cana-4541 38 2 calculus calculus NOUN cana-4541 38 3 has have AUX cana-4541 38 4 been be AUX cana-4541 38 5 the the DET cana-4541 38 6 subject subject NOUN cana-4541 38 7 of of ADP cana-4541 38 8 worldwide worldwide ADJ cana-4541 38 9 attention attention NOUN cana-4541 38 10 in in ADP cana-4541 38 11 the the DET cana-4541 38 12 last last ADJ cana-4541 38 13 decades decade NOUN cana-4541 38 14 due due ADP cana-4541 38 15 to to ADP cana-4541 38 16 its its PRON cana-4541 38 17 broad broad ADJ cana-4541 38 18 range range NOUN cana-4541 38 19 in in ADP cana-4541 38 20 biology biology NOUN cana-4541 38 21 , , PUNCT cana-4541 38 22 physics physics NOUN cana-4541 38 23 , , PUNCT cana-4541 38 24 chemistry chemistry NOUN cana-4541 38 25 , , PUNCT cana-4541 38 26 engineering engineering NOUN cana-4541 38 27 , , PUNCT cana-4541 38 28 modeling modeling NOUN cana-4541 38 29 etc etc X cana-4541 38 30 . . X cana-4541 38 31 fractional fractional ADJ cana-4541 38 32 differential differential ADJ cana-4541 38 33 equations equation NOUN cana-4541 38 34 system system NOUN cana-4541 38 35 allows allow VERB cana-4541 38 36 more more ADJ cana-4541 38 37 degree degree NOUN cana-4541 38 38 of of ADP cana-4541 38 39 freedom freedom NOUN cana-4541 38 40 , , PUNCT cana-4541 38 41 memory memory NOUN cana-4541 38 42 effect effect NOUN cana-4541 38 43 , , PUNCT cana-4541 38 44 more more ADV cana-4541 38 45 adequate adequate ADJ cana-4541 38 46 , , PUNCT cana-4541 38 47 more more ADV cana-4541 38 48 realistic realistic ADJ cana-4541 38 49 interpretation interpretation NOUN cana-4541 38 50 of of ADP cana-4541 38 51 natural natural ADJ cana-4541 38 52 phenomena phenomenon NOUN cana-4541 38 53 than than ADP cana-4541 38 54 integer integer NOUN cana-4541 38 55 - - PUNCT cana-4541 38 56 order order NOUN cana-4541 38 57 derivatives derivative NOUN cana-4541 38 58 in in ADP cana-4541 38 59 the the DET cana-4541 38 60 model model NOUN cana-4541 38 61 . . PUNCT cana-4541 39 1 they they PRON cana-4541 39 2 have have AUX cana-4541 39 3 become become VERB cana-4541 39 4 an an DET cana-4541 39 5 excellent excellent ADJ cana-4541 39 6 tool tool NOUN cana-4541 39 7 in in ADP cana-4541 39 8 modeling model VERB cana-4541 39 9 epidemiology epidemiology NOUN cana-4541 39 10 . . PUNCT cana-4541 40 1 hence hence ADV cana-4541 40 2 , , PUNCT cana-4541 40 3 fractional fractional ADJ cana-4541 40 4 derivatives derivative NOUN cana-4541 40 5 based base VERB cana-4541 40 6 on on ADP cana-4541 40 7 epidemic epidemic NOUN cana-4541 40 8 system system NOUN cana-4541 40 9 have have AUX cana-4541 40 10 also also ADV cana-4541 40 11 been be AUX cana-4541 40 12 used use VERB cana-4541 40 13 to to PART cana-4541 40 14 deal deal VERB cana-4541 40 15 with with ADP cana-4541 40 16 some some DET cana-4541 40 17 epidemic epidemic NOUN cana-4541 40 18 behaviors behavior NOUN cana-4541 40 19 . . PUNCT cana-4541 41 1 the the DET cana-4541 41 2 statically statically ADV cana-4541 41 3 data datum NOUN cana-4541 41 4 gathered gather VERB cana-4541 41 5 during during ADP cana-4541 41 6 an an DET cana-4541 41 7 actual actual ADJ cana-4541 41 8 disease disease NOUN cana-4541 41 9 epidemic epidemic NOUN cana-4541 41 10 can can AUX cana-4541 41 11 not not PART cana-4541 41 12 be be AUX cana-4541 41 13 adequately adequately ADV cana-4541 41 14 reproduced reproduce VERB cana-4541 41 15 by by ADP cana-4541 41 16 traditional traditional ADJ cana-4541 41 17 first first ADJ cana-4541 41 18 - - PUNCT cana-4541 41 19 order order NOUN cana-4541 41 20 differential differential ADJ cana-4541 41 21 equations equation NOUN cana-4541 41 22 , , PUNCT cana-4541 41 23 and and CCONJ cana-4541 41 24 they they PRON cana-4541 41 25 also also ADV cana-4541 41 26 do do AUX cana-4541 41 27 not not PART cana-4541 41 28 yield yield VERB cana-4541 41 29 satisfactory satisfactory ADJ cana-4541 41 30 results result NOUN cana-4541 41 31 . . PUNCT cana-4541 42 1 the the DET cana-4541 42 2 research research NOUN cana-4541 42 3 has have AUX cana-4541 42 4 examined examine VERB cana-4541 42 5 a a DET cana-4541 42 6 more more ADV cana-4541 42 7 specific specific ADJ cana-4541 42 8 and and CCONJ cana-4541 42 9 complex complex ADJ cana-4541 42 10 set set NOUN cana-4541 42 11 of of ADP cana-4541 42 12 differential differential ADJ cana-4541 42 13 equations equation NOUN cana-4541 42 14 in in ADP cana-4541 42 15 order order NOUN cana-4541 42 16 to to PART cana-4541 42 17 provide provide VERB cana-4541 42 18 communications communication NOUN cana-4541 42 19 on on ADP cana-4541 42 20 applied apply VERB cana-4541 42 21 nonlinear nonlinear ADJ cana-4541 42 22 analysis analysis NOUN cana-4541 42 23 issn issn NOUN cana-4541 42 24 : : PUNCT cana-4541 42 25 1074 1074 NUM cana-4541 42 26 - - PUNCT cana-4541 42 27 133x 133x NUM cana-4541 42 28 vol vol NOUN cana-4541 42 29 32 32 NUM cana-4541 42 30 no no NOUN cana-4541 42 31 . . PUNCT cana-4541 43 1 9s 9s NUM cana-4541 43 2 ( ( PUNCT cana-4541 43 3 2025 2025 NUM cana-4541 43 4 ) ) PUNCT cana-4541 43 5 2480 2480 NUM cana-4541 43 6 https://internationalpubls.com https://internationalpubls.com X cana-4541 43 7 better well ADJ cana-4541 43 8 conclusions conclusion NOUN cana-4541 43 9 that that PRON cana-4541 43 10 are be AUX cana-4541 43 11 more more ADV cana-4541 43 12 in in ADP cana-4541 43 13 line line NOUN cana-4541 43 14 with with ADP cana-4541 43 15 reality reality NOUN cana-4541 43 16 . . PUNCT cana-4541 44 1 we we PRON cana-4541 44 2 suggest suggest VERB cana-4541 44 3 a a DET cana-4541 44 4 significantly significantly ADV cana-4541 44 5 altered alter VERB cana-4541 44 6 system system NOUN cana-4541 44 7 of of ADP cana-4541 44 8 equations equation NOUN cana-4541 44 9 that that PRON cana-4541 44 10 makes make VERB cana-4541 44 11 use use NOUN cana-4541 44 12 of of ADP cana-4541 44 13 the the DET cana-4541 44 14 fractional fractional ADJ cana-4541 44 15 order order NOUN cana-4541 44 16 differential differential NOUN cana-4541 44 17 equation equation NOUN cana-4541 44 18 . . PUNCT cana-4541 45 1 hypotheses hypothesis NOUN cana-4541 45 2 of of ADP cana-4541 45 3 the the DET cana-4541 45 4 model model NOUN cana-4541 45 5 i. i. PROPN cana-4541 45 6 the the DET cana-4541 45 7 recruitment recruitment NOUN cana-4541 45 8 process process NOUN cana-4541 45 9 is be AUX cana-4541 45 10 constant constant ADJ cana-4541 45 11 and and CCONJ cana-4541 45 12 solely solely ADV cana-4541 45 13 based base VERB cana-4541 45 14 on on ADP cana-4541 45 15 birth birth NOUN cana-4541 45 16 . . PUNCT cana-4541 46 1 ii ii X cana-4541 46 2 . . PUNCT cana-4541 47 1 every every DET cana-4541 47 2 person person NOUN cana-4541 47 3 is be AUX cana-4541 47 4 susceptible susceptible ADJ cana-4541 47 5 from from ADP cana-4541 47 6 birth birth NOUN cana-4541 47 7 . . PUNCT cana-4541 48 1 iii iii X cana-4541 48 2 . . PUNCT cana-4541 48 3 contact contact NOUN cana-4541 48 4 with with ADP cana-4541 48 5 the the DET cana-4541 48 6 excrement excrement NOUN cana-4541 48 7 of of ADP cana-4541 48 8 diseased diseased ADJ cana-4541 48 9 people people NOUN cana-4541 48 10 and and CCONJ cana-4541 48 11 tainted taint VERB cana-4541 48 12 food food NOUN cana-4541 48 13 or or CCONJ cana-4541 48 14 water water NOUN cana-4541 48 15 can can AUX cana-4541 48 16 infect infect VERB cana-4541 48 17 a a DET cana-4541 48 18 person person NOUN cana-4541 48 19 . . PUNCT cana-4541 49 1 iv iv X cana-4541 49 2 . . PUNCT cana-4541 49 3 infected infected ADJ cana-4541 49 4 people people NOUN cana-4541 49 5 can can AUX cana-4541 49 6 pass pass VERB cana-4541 49 7 either either CCONJ cana-4541 49 8 naturally naturally ADV cana-4541 49 9 or or CCONJ cana-4541 49 10 as as ADP cana-4541 49 11 a a DET cana-4541 49 12 result result NOUN cana-4541 49 13 of of ADP cana-4541 49 14 the the DET cana-4541 49 15 illness illness NOUN cana-4541 49 16 . . PUNCT cana-4541 50 1 v. v. CCONJ cana-4541 50 2 only only ADJ cana-4541 50 3 susceptible susceptible ADJ cana-4541 50 4 adults adult NOUN cana-4541 50 5 and and CCONJ cana-4541 50 6 children child NOUN cana-4541 50 7 between between ADP cana-4541 50 8 the the DET cana-4541 50 9 ages age NOUN cana-4541 50 10 of of ADP cana-4541 50 11 0 0 NUM cana-4541 50 12 and and CCONJ cana-4541 50 13 6 6 NUM cana-4541 50 14 months month NOUN cana-4541 50 15 are be AUX cana-4541 50 16 eligible eligible ADJ cana-4541 50 17 for for ADP cana-4541 50 18 immunization immunization NOUN cana-4541 50 19 . . PUNCT cana-4541 51 1 vi vi X cana-4541 51 2 . . PUNCT cana-4541 52 1 no no DET cana-4541 52 2 long long ADJ cana-4541 52 3 - - PUNCT cana-4541 52 4 term term NOUN cana-4541 52 5 recovery recovery NOUN cana-4541 52 6 is be AUX cana-4541 52 7 possible possible ADJ cana-4541 52 8 . . PUNCT cana-4541 53 1 vii vii PROPN cana-4541 53 2 . . PUNCT cana-4541 54 1 the the DET cana-4541 54 2 population population NOUN cana-4541 54 3 is be AUX cana-4541 54 4 homogeneously homogeneously ADV cana-4541 54 5 mixed mixed ADJ cana-4541 54 6 . . PUNCT cana-4541 55 1 viii viii PROPN cana-4541 55 2 . . PUNCT cana-4541 56 1 people people NOUN cana-4541 56 2 engage engage VERB cana-4541 56 3 with with ADP cana-4541 56 4 one one NUM cana-4541 56 5 another another DET cana-4541 56 6 in in ADP cana-4541 56 7 a a DET cana-4541 56 8 panmictic panmictic ADJ cana-4541 56 9 manner manner NOUN cana-4541 56 10 2 2 NUM cana-4541 56 11 . . PUNCT cana-4541 56 12 model model NOUN cana-4541 56 13 derivation derivation NOUN cana-4541 56 14 : : PUNCT cana-4541 56 15 𝑑𝑆 𝑑𝑆 ADJ cana-4541 56 16 𝑑𝑑 𝑑𝑑 ADP cana-4541 56 17 = = SYM cana-4541 56 18 Ξ» Ξ» PROPN cana-4541 56 19 βˆ’ βˆ’ NOUN cana-4541 56 20 𝛾1𝑆 𝛾1𝑆 NOUN cana-4541 56 21 βˆ’ βˆ’ PROPN cana-4541 56 22 𝛾2𝑆 𝛾2𝑆 NOUN cana-4541 56 23 βˆ’ βˆ’ PROPN cana-4541 56 24 𝑑𝑆 𝑑𝑆 PROPN cana-4541 56 25 𝑑𝑉 𝑑𝑉 ADP cana-4541 56 26 𝑑𝑑 𝑑𝑑 ADP cana-4541 56 27 = = PUNCT cana-4541 56 28 𝛾2𝑆 𝛾2𝑆 NOUN cana-4541 56 29 + + NUM cana-4541 56 30 𝜏2𝐼 𝜏2𝐼 NOUN cana-4541 56 31 βˆ’ βˆ’ NOUN cana-4541 56 32 𝑑𝑉 𝑑𝑉 ADP cana-4541 56 33 𝑑𝐸 𝑑𝐸 ADJ cana-4541 56 34 𝑑𝑑 𝑑𝑑 ADP cana-4541 56 35 = = PUNCT cana-4541 56 36 𝛾1𝑆 𝛾1𝑆 NOUN cana-4541 56 37 βˆ’ βˆ’ PROPN cana-4541 56 38 𝛿1𝐸 𝛿1𝐸 NOUN cana-4541 56 39 βˆ’ βˆ’ PROPN cana-4541 56 40 𝛿2𝐸 𝛿2𝐸 NOUN cana-4541 56 41 βˆ’ βˆ’ PROPN cana-4541 56 42 𝑑𝐸 𝑑𝐸 PROPN cana-4541 56 43 𝑑𝐼 𝑑𝐼 NOUN cana-4541 56 44 𝑑𝑑 𝑑𝑑 ADP cana-4541 56 45 = = PROPN cana-4541 56 46 𝛿1𝐸 𝛿1𝐸 NOUN cana-4541 56 47 βˆ’ βˆ’ PROPN cana-4541 56 48 𝜏1𝐼 𝜏1𝐼 AUX cana-4541 56 49 βˆ’ βˆ’ PROPN cana-4541 56 50 𝜏2𝐼 𝜏2𝐼 NOUN cana-4541 56 51 βˆ’ βˆ’ PROPN cana-4541 56 52 𝜏3𝐼 𝜏3𝐼 NOUN cana-4541 56 53 βˆ’ βˆ’ PROPN cana-4541 56 54 𝑑𝐼 𝑑𝐼 ADJ cana-4541 56 55 𝑑𝐺 𝑑𝐺 NOUN cana-4541 56 56 𝑑𝑑 𝑑𝑑 ADP cana-4541 56 57 = = PUNCT cana-4541 56 58 𝛿2𝐸 𝛿2𝐸 NOUN cana-4541 56 59 + + NUM cana-4541 56 60 𝜏3𝐼 𝜏3𝐼 NOUN cana-4541 56 61 βˆ’ βˆ’ NOUN cana-4541 56 62 𝜁1𝐺 𝜁1𝐺 ADJ cana-4541 56 63 βˆ’ βˆ’ PROPN cana-4541 56 64 𝜁2𝐺 𝜁2𝐺 PUNCT cana-4541 56 65 βˆ’ βˆ’ PROPN cana-4541 56 66 𝑑𝐺 𝑑𝐺 PROPN cana-4541 56 67 𝑑𝐻 𝑑𝐻 ADJ cana-4541 56 68 𝑑𝑑 𝑑𝑑 ADP cana-4541 56 69 = = PUNCT cana-4541 56 70 𝜏1𝐼 𝜏1𝐼 X cana-4541 56 71 + + CCONJ cana-4541 56 72 𝜁1𝐺 𝜁1𝐺 ADV cana-4541 56 73 βˆ’ βˆ’ PROPN cana-4541 56 74 πœ‰π» πœ‰π» ADJ cana-4541 56 75 βˆ’ βˆ’ PROPN cana-4541 56 76 𝑑𝐻 𝑑𝐻 ADJ cana-4541 56 77 𝑑𝑅 𝑑𝑅 NOUN cana-4541 56 78 𝑑𝑑 𝑑𝑑 ADP cana-4541 56 79 = = PROPN cana-4541 56 80 πœ‰π» πœ‰π» PROPN cana-4541 56 81 + + CCONJ cana-4541 56 82 𝜁2𝐺 𝜁2𝐺 PUNCT cana-4541 56 83 βˆ’ βˆ’ PROPN cana-4541 56 84 𝑑𝑅 𝑑𝑅 NOUN cana-4541 56 85 } } PUNCT cana-4541 56 86 … … PUNCT cana-4541 56 87 . . PUNCT cana-4541 57 1 ( ( PUNCT cana-4541 57 2 1 1 X cana-4541 57 3 ) ) PUNCT cana-4541 57 4 𝑉 𝑉 NOUN cana-4541 57 5 𝑑𝑉 𝑑𝑉 ADP cana-4541 57 6 𝑑𝐻 𝑑𝐻 ADJ cana-4541 57 7 𝐸 𝐸 ADJ cana-4541 57 8 𝛾1𝑆 𝛾1𝑆 NOUN cana-4541 57 9 𝐼 𝐼 ADP cana-4541 57 10 𝐻 𝐻 PROPN cana-4541 57 11 𝑅 𝑅 PROPN cana-4541 57 12 𝐺 𝐺 NOUN cana-4541 57 13 Ξ» Ξ» PROPN cana-4541 57 14 𝑆 𝑆 PROPN cana-4541 57 15 𝑑𝐸 𝑑𝐸 PROPN cana-4541 57 16 𝑑𝐼 𝑑𝐼 PROPN cana-4541 57 17 𝑑𝑆 𝑑𝑆 ADJ cana-4541 57 18 𝑑𝐺 𝑑𝐺 NOUN cana-4541 57 19 𝑑𝑅 𝑑𝑅 NOUN cana-4541 57 20 𝛿1𝐸 𝛿1𝐸 NOUN cana-4541 57 21 𝛿2𝐸 𝛿2𝐸 NOUN cana-4541 57 22 𝜏1𝐼 𝜏1𝐼 ADJ cana-4541 57 23 𝜏3𝐼 𝜏3𝐼 NOUN cana-4541 57 24 𝜁1𝐺 𝜁1𝐺 ADJ cana-4541 57 25 𝜁2𝐺 𝜁2𝐺 NOUN cana-4541 57 26 πœ‰π» πœ‰π» ADJ cana-4541 57 27 𝜏2𝐼 𝜏2𝐼 NOUN cana-4541 57 28 𝛾2𝑆 𝛾2𝑆 NOUN cana-4541 57 29 communications communication NOUN cana-4541 57 30 on on ADP cana-4541 57 31 applied apply VERB cana-4541 57 32 nonlinear nonlinear ADJ cana-4541 57 33 analysis analysis NOUN cana-4541 57 34 issn issn NOUN cana-4541 57 35 : : PUNCT cana-4541 57 36 1074 1074 NUM cana-4541 57 37 - - PUNCT cana-4541 57 38 133x 133x NUM cana-4541 57 39 vol vol NOUN cana-4541 57 40 32 32 NUM cana-4541 57 41 no no NOUN cana-4541 57 42 . . PUNCT cana-4541 58 1 9s 9s NUM cana-4541 58 2 ( ( PUNCT cana-4541 58 3 2025 2025 NUM cana-4541 58 4 ) ) PUNCT cana-4541 58 5 2481 2481 NUM cana-4541 59 1 https://internationalpubls.com https://internationalpubls.com X cana-4541 59 2 condition condition NOUN cana-4541 59 3 : : PUNCT cana-4541 59 4 𝑆 𝑆 PROPN cana-4541 59 5 + + CCONJ cana-4541 59 6 𝑉 𝑉 PROPN cana-4541 59 7 + + NOUN cana-4541 59 8 𝐸 𝐸 PROPN cana-4541 59 9 + + CCONJ cana-4541 59 10 𝐼 𝐼 PROPN cana-4541 59 11 + + CCONJ cana-4541 59 12 𝐺 𝐺 NOUN cana-4541 59 13 + + CCONJ cana-4541 59 14 𝐻 𝐻 PROPN cana-4541 59 15 + + PROPN cana-4541 59 16 𝑅 𝑅 NOUN cana-4541 59 17 = = PUNCT cana-4541 59 18 𝑁 𝑁 PROPN cana-4541 59 19 where where SCONJ cana-4541 59 20 , , PUNCT cana-4541 59 21 and and CCONJ cana-4541 59 22 variables variable NOUN cana-4541 59 23 description description NOUN cana-4541 59 24 𝑆 𝑆 PROPN cana-4541 59 25 the the DET cana-4541 59 26 total total ADJ cana-4541 59 27 number number NOUN cana-4541 59 28 of of ADP cana-4541 59 29 susceptible susceptible ADJ cana-4541 59 30 population population NOUN cana-4541 59 31 at at ADP cana-4541 59 32 time time NOUN cana-4541 59 33 ( ( PUNCT cana-4541 59 34 𝑑 𝑑 NOUN cana-4541 59 35 ) ) PUNCT cana-4541 59 36 𝑉 𝑉 VERB cana-4541 59 37 the the DET cana-4541 59 38 total total ADJ cana-4541 59 39 number number NOUN cana-4541 59 40 of of ADP cana-4541 59 41 vaccination vaccination NOUN cana-4541 59 42 population population NOUN cana-4541 59 43 at at ADP cana-4541 59 44 time time NOUN cana-4541 59 45 ( ( PUNCT cana-4541 59 46 𝑑 𝑑 NOUN cana-4541 59 47 ) ) PUNCT cana-4541 59 48 𝐸 𝐸 VERB cana-4541 59 49 the the DET cana-4541 59 50 total total ADJ cana-4541 59 51 number number NOUN cana-4541 59 52 of of ADP cana-4541 59 53 exposed expose VERB cana-4541 59 54 population population NOUN cana-4541 59 55 at at ADP cana-4541 59 56 time time NOUN cana-4541 59 57 ( ( PUNCT cana-4541 59 58 𝑑 𝑑 NOUN cana-4541 59 59 ) ) PUNCT cana-4541 59 60 𝐼 𝐼 ADP cana-4541 59 61 the the DET cana-4541 59 62 total total ADJ cana-4541 59 63 number number NOUN cana-4541 59 64 of of ADP cana-4541 59 65 infective infective ADJ cana-4541 59 66 population population NOUN cana-4541 59 67 at at ADP cana-4541 59 68 time time NOUN cana-4541 59 69 ( ( PUNCT cana-4541 59 70 𝑑 𝑑 NOUN cana-4541 59 71 ) ) PUNCT cana-4541 59 72 𝐺 𝐺 NOUN cana-4541 59 73 the the DET cana-4541 59 74 total total ADJ cana-4541 59 75 number number NOUN cana-4541 59 76 of of ADP cana-4541 59 77 isolated isolated ADJ cana-4541 59 78 population population NOUN cana-4541 59 79 at at ADP cana-4541 59 80 time time NOUN cana-4541 59 81 ( ( PUNCT cana-4541 59 82 𝑑 𝑑 NOUN cana-4541 59 83 ) ) PUNCT cana-4541 59 84 𝐻 𝐻 NOUN cana-4541 59 85 the the DET cana-4541 59 86 total total ADJ cana-4541 59 87 number number NOUN cana-4541 59 88 of of ADP cana-4541 59 89 hospitalized hospitalize VERB cana-4541 59 90 population population NOUN cana-4541 59 91 at at ADP cana-4541 59 92 time time NOUN cana-4541 59 93 ( ( PUNCT cana-4541 59 94 𝑑 𝑑 NOUN cana-4541 59 95 ) ) PUNCT cana-4541 59 96 𝑅 𝑅 NOUN cana-4541 59 97 the the DET cana-4541 59 98 total total ADJ cana-4541 59 99 number number NOUN cana-4541 59 100 of of ADP cana-4541 59 101 recovered recovered ADJ cana-4541 59 102 population population NOUN cana-4541 59 103 at at ADP cana-4541 59 104 time time NOUN cana-4541 59 105 ( ( PUNCT cana-4541 59 106 𝑑 𝑑 NOUN cana-4541 59 107 ) ) PUNCT cana-4541 59 108 parameters parameter NOUN cana-4541 59 109 description description NOUN cana-4541 59 110 values value NOUN cana-4541 59 111 Ξ» Ξ» VERB cana-4541 59 112 all all DET cana-4541 59 113 the the DET cana-4541 59 114 new new ADJ cana-4541 59 115 immigrants immigrant NOUN cana-4541 59 116 are be AUX cana-4541 59 117 susceptible susceptible ADJ cana-4541 59 118 and and CCONJ cana-4541 59 119 join join VERB cana-4541 59 120 the the DET cana-4541 59 121 group group NOUN cana-4541 59 122 at at ADP cana-4541 59 123 a a DET cana-4541 59 124 constant constant ADJ cana-4541 59 125 rate rate NOUN cana-4541 59 126 𝑁 𝑁 PROPN cana-4541 59 127 the the DET cana-4541 59 128 human human ADJ cana-4541 59 129 population population NOUN cana-4541 59 130 10000 10000 NUM cana-4541 59 131 𝛾1 𝛾1 NOUN cana-4541 59 132 the the DET cana-4541 59 133 exposed expose VERB cana-4541 59 134 rate rate NOUN cana-4541 59 135 by by ADP cana-4541 59 136 susceptible susceptible ADJ cana-4541 59 137 population population NOUN cana-4541 59 138 0.25 0.25 NUM cana-4541 59 139 𝛾2 𝛾2 VERB cana-4541 59 140 the the DET cana-4541 59 141 vaccination vaccination NOUN cana-4541 59 142 rate rate NOUN cana-4541 59 143 by by ADP cana-4541 59 144 susceptible susceptible ADJ cana-4541 59 145 population population NOUN cana-4541 59 146 0.75 0.75 NUM cana-4541 59 147 𝛿1 𝛿1 NOUN cana-4541 59 148 the the DET cana-4541 59 149 infected infect VERB cana-4541 59 150 rate rate NOUN cana-4541 59 151 by by ADP cana-4541 59 152 exposed expose VERB cana-4541 59 153 population population NOUN cana-4541 59 154 0.5 0.5 NUM cana-4541 59 155 𝛿2 𝛿2 VERB cana-4541 59 156 the the DET cana-4541 59 157 isolated isolated ADJ cana-4541 59 158 rate rate NOUN cana-4541 59 159 by by ADP cana-4541 59 160 exposed expose VERB cana-4541 59 161 population population NOUN cana-4541 59 162 0.2 0.2 NUM cana-4541 59 163 𝜏1 𝜏1 NOUN cana-4541 59 164 the the DET cana-4541 59 165 hospitable hospitable ADJ cana-4541 59 166 rate rate NOUN cana-4541 59 167 by by ADP cana-4541 59 168 infected infect VERB cana-4541 59 169 population population NOUN cana-4541 59 170 0.15 0.15 NUM cana-4541 59 171 𝜏2 𝜏2 VERB cana-4541 59 172 the the DET cana-4541 59 173 vaccination vaccination NOUN cana-4541 59 174 rate rate NOUN cana-4541 59 175 by by ADP cana-4541 59 176 infected infect VERB cana-4541 59 177 population population NOUN cana-4541 59 178 0.25 0.25 NUM cana-4541 59 179 𝜏3 𝜏3 NOUN cana-4541 59 180 the the DET cana-4541 59 181 isolated isolated ADJ cana-4541 59 182 rate rate NOUN cana-4541 59 183 by by ADP cana-4541 59 184 infected infected ADJ cana-4541 59 185 population population NOUN cana-4541 60 1 0.2 0.2 NUM cana-4541 60 2 𝜁1 𝜁1 ADV cana-4541 60 3 the the DET cana-4541 60 4 hospitable hospitable ADJ cana-4541 60 5 rate rate NOUN cana-4541 60 6 by by ADP cana-4541 60 7 isolated isolated ADJ cana-4541 60 8 population population NOUN cana-4541 60 9 0.25 0.25 NUM cana-4541 60 10 𝜁2 𝜁2 NOUN cana-4541 60 11 the the DET cana-4541 60 12 recovery recovery NOUN cana-4541 60 13 rate rate NOUN cana-4541 60 14 by by ADP cana-4541 60 15 isolated isolated ADJ cana-4541 60 16 population population NOUN cana-4541 60 17 0.20 0.20 NUM cana-4541 60 18 πœ‰ πœ‰ ADP cana-4541 60 19 the the DET cana-4541 60 20 recovery recovery NOUN cana-4541 60 21 rate rate NOUN cana-4541 60 22 by by ADP cana-4541 60 23 hospitable hospitable ADJ cana-4541 60 24 population population NOUN cana-4541 60 25 0.25 0.25 NUM cana-4541 60 26 𝑑 𝑑 NOUN cana-4541 60 27 the the DET cana-4541 60 28 natural natural ADJ cana-4541 60 29 death death NOUN cana-4541 60 30 rate rate NOUN cana-4541 60 31 0.000457 0.000457 NUM cana-4541 60 32 𝛽 𝛽 NOUN cana-4541 60 33 the the DET cana-4541 60 34 order order NOUN cana-4541 60 35 of of ADP cana-4541 60 36 fractional fractional ADJ cana-4541 60 37 0 0 PUNCT cana-4541 60 38 < < X cana-4541 60 39 𝛽 𝛽 NOUN cana-4541 60 40 ≀ ≀ ADV cana-4541 60 41 1 1 NUM cana-4541 60 42 communications communication NOUN cana-4541 60 43 on on ADP cana-4541 60 44 applied apply VERB cana-4541 60 45 nonlinear nonlinear ADJ cana-4541 60 46 analysis analysis NOUN cana-4541 60 47 issn issn NOUN cana-4541 60 48 : : PUNCT cana-4541 60 49 1074 1074 NUM cana-4541 60 50 - - PUNCT cana-4541 60 51 133x 133x NUM cana-4541 60 52 vol vol NOUN cana-4541 60 53 32 32 NUM cana-4541 61 1 no no NOUN cana-4541 61 2 . . PUNCT cana-4541 62 1 9s 9s NUM cana-4541 62 2 ( ( PUNCT cana-4541 62 3 2025 2025 NUM cana-4541 62 4 ) ) PUNCT cana-4541 62 5 2482 2482 NUM cana-4541 62 6 https://internationalpubls.com https://internationalpubls.com X cana-4541 63 1 many many ADJ cana-4541 63 2 definitions definition NOUN cana-4541 63 3 of of ADP cana-4541 63 4 fractional fractional ADJ cana-4541 63 5 derivatives derivative NOUN cana-4541 63 6 [ [ X cana-4541 63 7 3,4 3,4 NUM cana-4541 63 8 ] ] PUNCT cana-4541 63 9 are be AUX cana-4541 63 10 used use VERB cana-4541 63 11 . . PUNCT cana-4541 64 1 the the DET cana-4541 64 2 riemann riemann PROPN cana-4541 64 3 – – PUNCT cana-4541 64 4 liouville liouville VERB cana-4541 64 5 derivatives derivative NOUN cana-4541 64 6 of of ADP cana-4541 64 7 𝑖th 𝑖th NOUN cana-4541 64 8 order order NOUN cana-4541 64 9 is be AUX cana-4541 64 10 defined define VERB cana-4541 64 11 as as ADP cana-4541 64 12 π’Ÿ0 π’Ÿ0 PROPN cana-4541 64 13 + + SYM cana-4541 64 14 𝛽 𝛽 PROPN cana-4541 64 15 𝑅𝐿 𝑅𝐿 PROPN cana-4541 64 16 𝑓(𝑑 𝑓(𝑑 PROPN cana-4541 64 17 ) ) PUNCT cana-4541 64 18 = = SYM cana-4541 64 19 1 1 NUM cana-4541 64 20 Ξ³(𝑛 Ξ³(𝑛 PROPN cana-4541 64 21 βˆ’ βˆ’ NUM cana-4541 64 22 𝑖 𝑖 SYM cana-4541 64 23 ) ) PUNCT cana-4541 64 24 ( ( PUNCT cana-4541 64 25 𝑑 𝑑 PROPN cana-4541 64 26 𝑑𝑑 𝑑𝑑 ADP cana-4541 64 27 ) ) PUNCT cana-4541 64 28 𝑛 𝑛 DET cana-4541 64 29 ∫ ∫ PROPN cana-4541 64 30 𝑓(𝑠 𝑓(𝑠 NOUN cana-4541 64 31 ) ) PUNCT cana-4541 64 32 ( ( PUNCT cana-4541 64 33 𝑑 𝑑 PROPN cana-4541 64 34 βˆ’ βˆ’ PROPN cana-4541 64 35 𝑠)π‘–βˆ’π‘›+1 𝑠)π‘–βˆ’π‘›+1 PROPN cana-4541 64 36 𝑑 𝑑 PROPN cana-4541 64 37 0 0 NUM cana-4541 64 38 𝑑𝑠 𝑑𝑠 ADP cana-4541 64 39 where where SCONJ cana-4541 64 40 , , PUNCT cana-4541 64 41 𝑛 𝑛 PROPN cana-4541 64 42 = = PUNCT cana-4541 65 1 [ [ X cana-4541 65 2 𝑖 𝑖 X cana-4541 65 3 ] ] X cana-4541 65 4 + + CCONJ cana-4541 65 5 1 1 NUM cana-4541 65 6 … … PUNCT cana-4541 65 7 ( ( PUNCT cana-4541 65 8 2 2 X cana-4541 65 9 ) ) PUNCT cana-4541 65 10 an an DET cana-4541 65 11 alternative alternative ADJ cana-4541 65 12 definition definition NOUN cana-4541 65 13 by by ADP cana-4541 65 14 caputo caputo PROPN cana-4541 65 15 was be AUX cana-4541 65 16 as as SCONJ cana-4541 65 17 follows follow VERB cana-4541 65 18 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 65 19 𝛽 𝛽 NOUN cana-4541 65 20 𝑓(𝑑 𝑓(𝑑 PROPN cana-4541 65 21 ) ) PUNCT cana-4541 65 22 = = SYM cana-4541 65 23 1 1 NUM cana-4541 65 24 Ξ³(𝑛 Ξ³(𝑛 PROPN cana-4541 65 25 βˆ’ βˆ’ NUM cana-4541 65 26 𝑖 𝑖 SYM cana-4541 65 27 ) ) PUNCT cana-4541 65 28 ∫ ∫ PROPN cana-4541 65 29 𝑓(𝑛)(𝑠 𝑓(𝑛)(𝑠 NOUN cana-4541 65 30 ) ) PUNCT cana-4541 65 31 ( ( PUNCT cana-4541 65 32 𝑑 𝑑 PROPN cana-4541 65 33 βˆ’ βˆ’ PROPN cana-4541 65 34 𝑠)π‘–βˆ’π‘›+1 𝑠)π‘–βˆ’π‘›+1 PROPN cana-4541 65 35 𝑑 𝑑 PROPN cana-4541 65 36 0 0 NUM cana-4541 65 37 𝑑𝑠 𝑑𝑠 ADP cana-4541 65 38 where where SCONJ cana-4541 65 39 , , PUNCT cana-4541 65 40 𝑛 𝑛 PROPN cana-4541 65 41 = = PUNCT cana-4541 66 1 [ [ X cana-4541 66 2 𝑖 𝑖 X cana-4541 66 3 ] ] X cana-4541 66 4 + + CCONJ cana-4541 66 5 1 1 NUM cana-4541 66 6 … … PUNCT cana-4541 66 7 ( ( PUNCT cana-4541 66 8 3 3 X cana-4541 66 9 ) ) PUNCT cana-4541 66 10 in in ADP cana-4541 66 11 this this DET cana-4541 66 12 paper paper NOUN cana-4541 66 13 we we PRON cana-4541 66 14 will will AUX cana-4541 66 15 use use VERB cana-4541 66 16 caputo caputo PROPN cana-4541 66 17 fractional fractional PROPN cana-4541 66 18 derivative derivative NOUN cana-4541 66 19 for for ADP cana-4541 66 20 the the DET cana-4541 66 21 system system NOUN cana-4541 66 22 ( ( PUNCT cana-4541 66 23 1 1 X cana-4541 66 24 ) ) PUNCT cana-4541 66 25 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 66 26 𝛽 𝛽 NOUN cana-4541 66 27 𝑆 𝑆 PROPN cana-4541 66 28 = = SYM cana-4541 66 29 Ξ» Ξ» PROPN cana-4541 66 30 βˆ’ βˆ’ PROPN cana-4541 66 31 ( ( PUNCT cana-4541 66 32 𝛾1 𝛾1 NOUN cana-4541 66 33 + + CCONJ cana-4541 66 34 𝛾2 𝛾2 VERB cana-4541 66 35 + + CCONJ cana-4541 66 36 𝑑)𝑆 𝑑)𝑆 VERB cana-4541 66 37 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 66 38 𝛽 𝛽 PROPN cana-4541 66 39 𝑉 𝑉 ADJ cana-4541 66 40 = = PUNCT cana-4541 66 41 𝛾2𝑆 𝛾2𝑆 NOUN cana-4541 66 42 + + NUM cana-4541 66 43 𝜏2𝐼 𝜏2𝐼 NOUN cana-4541 66 44 βˆ’ βˆ’ NOUN cana-4541 66 45 𝑑𝑉 𝑑𝑉 ADP cana-4541 66 46 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 66 47 𝛽 𝛽 NOUN cana-4541 66 48 𝐸 𝐸 ADJ cana-4541 66 49 = = PUNCT cana-4541 66 50 𝛾1𝑆 𝛾1𝑆 NOUN cana-4541 67 1 βˆ’ βˆ’ PROPN cana-4541 67 2 ( ( PUNCT cana-4541 67 3 𝛿1 𝛿1 NOUN cana-4541 67 4 + + CCONJ cana-4541 67 5 𝛿2 𝛿2 NOUN cana-4541 67 6 + + CCONJ cana-4541 67 7 𝑑)𝐸 𝑑)𝐸 PRON cana-4541 67 8 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 67 9 𝛽 𝛽 NOUN cana-4541 67 10 𝐼 𝐼 PROPN cana-4541 67 11 = = PROPN cana-4541 67 12 𝛿1𝐸 𝛿1𝐸 NOUN cana-4541 67 13 βˆ’ βˆ’ PROPN cana-4541 67 14 ( ( PUNCT cana-4541 67 15 𝜏1 𝜏1 NOUN cana-4541 67 16 + + CCONJ cana-4541 67 17 𝜏2 𝜏2 NOUN cana-4541 67 18 + + CCONJ cana-4541 67 19 𝜏3 𝜏3 NOUN cana-4541 67 20 + + NOUN cana-4541 67 21 𝑑)𝐼 𝑑)𝐼 NUM cana-4541 67 22 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 67 23 𝛽 𝛽 PROPN cana-4541 67 24 𝐺 𝐺 NOUN cana-4541 67 25 = = PUNCT cana-4541 67 26 𝛿2𝐸 𝛿2𝐸 NOUN cana-4541 67 27 + + NUM cana-4541 67 28 𝜏3𝐼 𝜏3𝐼 NOUN cana-4541 67 29 βˆ’ βˆ’ PROPN cana-4541 67 30 ( ( PUNCT cana-4541 67 31 𝜁1 𝜁1 PROPN cana-4541 67 32 + + CCONJ cana-4541 67 33 𝜁2 𝜁2 NOUN cana-4541 67 34 + + CCONJ cana-4541 67 35 𝑑)𝐺 𝑑)𝐺 VERB cana-4541 67 36 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 67 37 𝛽 𝛽 NOUN cana-4541 67 38 𝐻 𝐻 NOUN cana-4541 67 39 = = PUNCT cana-4541 67 40 𝜏1𝐼 𝜏1𝐼 X cana-4541 67 41 + + CCONJ cana-4541 67 42 𝜁1𝐺 𝜁1𝐺 NOUN cana-4541 67 43 βˆ’ βˆ’ PROPN cana-4541 67 44 ( ( PUNCT cana-4541 67 45 πœ‰ πœ‰ X cana-4541 67 46 + + CCONJ cana-4541 67 47 𝑑)𝐻 𝑑)𝐻 VERB cana-4541 67 48 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 67 49 𝛽 𝛽 PROPN cana-4541 67 50 𝑅 𝑅 PROPN cana-4541 67 51 = = PROPN cana-4541 67 52 πœ‰π» πœ‰π» PROPN cana-4541 67 53 + + CCONJ cana-4541 67 54 𝜁2𝐺 𝜁2𝐺 PUNCT cana-4541 67 55 βˆ’ βˆ’ PROPN cana-4541 67 56 𝑑𝑅 𝑑𝑅 NOUN cana-4541 67 57 } } PUNCT cana-4541 67 58 … … PUNCT cana-4541 67 59 . . PUNCT cana-4541 68 1 ( ( PUNCT cana-4541 68 2 4 4 X cana-4541 68 3 ) ) PUNCT cana-4541 68 4 all all DET cana-4541 68 5 parameters parameter NOUN cana-4541 68 6 are be AUX cana-4541 68 7 assumed assume VERB cana-4541 68 8 to to PART cana-4541 68 9 be be AUX cana-4541 68 10 non non ADJ cana-4541 68 11 - - ADJ cana-4541 68 12 negative negative ADJ cana-4541 68 13 from from ADP cana-4541 68 14 system system NOUN cana-4541 68 15 ( ( PUNCT cana-4541 68 16 4 4 NUM cana-4541 68 17 ) ) PUNCT cana-4541 68 18 , , PUNCT cana-4541 68 19 where where SCONJ cana-4541 68 20 𝑑 𝑑 PROPN cana-4541 68 21 β‰₯ β‰₯ VERB cana-4541 68 22 0 0 NUM cana-4541 69 1 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 69 2 𝛽 𝛽 NOUN cana-4541 69 3 𝑁 𝑁 PROPN cana-4541 69 4 = = SYM cana-4541 69 5 Ξ» Ξ» PROPN cana-4541 69 6 βˆ’ βˆ’ PROPN cana-4541 69 7 𝑑𝑁 𝑑𝑁 NOUN cana-4541 69 8 … … PUNCT cana-4541 69 9 ( ( PUNCT cana-4541 69 10 5 5 X cana-4541 69 11 ) ) PUNCT cana-4541 69 12 we we PRON cana-4541 69 13 solve solve VERB cana-4541 69 14 the the DET cana-4541 69 15 equation equation NOUN cana-4541 69 16 ( ( PUNCT cana-4541 69 17 5 5 NUM cana-4541 69 18 ) ) PUNCT cana-4541 69 19 by by ADP cana-4541 69 20 using use VERB cana-4541 69 21 mittage mittage NOUN cana-4541 69 22 - - PUNCT cana-4541 69 23 leffler leffler NOUN cana-4541 69 24 function function NOUN cana-4541 69 25 , , PUNCT cana-4541 69 26 which which PRON cana-4541 69 27 is be AUX cana-4541 69 28 defined define VERB cana-4541 69 29 as as ADP cana-4541 69 30 𝐸𝛽,𝛾(𝑧 𝐸𝛽,𝛾(𝑧 NOUN cana-4541 69 31 ) ) PUNCT cana-4541 69 32 ~ ~ PUNCT cana-4541 70 1 βˆ’βˆ‘ βˆ’βˆ‘ PROPN cana-4541 70 2 𝑧𝑖 𝑧𝑖 INTJ cana-4541 70 3 Ξ³(𝛾 Ξ³(𝛾 PROPN cana-4541 70 4 βˆ’ βˆ’ PROPN cana-4541 70 5 𝛽𝑖 𝛽𝑖 ADJ cana-4541 70 6 ) ) PUNCT cana-4541 70 7 𝑛 𝑛 PRON cana-4541 70 8 𝑖=1 𝑖=1 PROPN cana-4541 70 9 + + NUM cana-4541 70 10 𝑂(|𝑧|βˆ’1βˆ’π‘› 𝑂(|𝑧|βˆ’1βˆ’π‘› NOUN cana-4541 70 11 ) ) PUNCT cana-4541 70 12 , , PUNCT cana-4541 70 13 ( ( PUNCT cana-4541 70 14 |𝑧| |𝑧| PROPN cana-4541 70 15 β†’ β†’ SYM cana-4541 70 16 ∞ ∞ PROPN cana-4541 70 17 , , PUNCT cana-4541 70 18 π›½πœ‹ π›½πœ‹ PROPN cana-4541 70 19 2 2 NUM cana-4541 70 20 < < X cana-4541 70 21 |arg |arg NOUN cana-4541 70 22 ( ( PUNCT cana-4541 70 23 𝑧)| 𝑧)| PROPN cana-4541 70 24 ≀ ≀ PROPN cana-4541 70 25 πœ‹ πœ‹ NOUN cana-4541 70 26 ) ) PUNCT cana-4541 70 27 let let VERB cana-4541 70 28 Ο‰ Ο‰ NOUN cana-4541 70 29 = = PRON cana-4541 70 30 { { PUNCT cana-4541 70 31 ( ( PUNCT cana-4541 70 32 𝑆 𝑆 PROPN cana-4541 70 33 , , PUNCT cana-4541 70 34 𝑉 𝑉 PROPN cana-4541 70 35 , , PUNCT cana-4541 70 36 𝐸 𝐸 PROPN cana-4541 70 37 , , PUNCT cana-4541 70 38 𝐼 𝐼 PROPN cana-4541 70 39 , , PUNCT cana-4541 70 40 𝐺 𝐺 PROPN cana-4541 70 41 , , PUNCT cana-4541 70 42 𝐻 𝐻 PROPN cana-4541 70 43 , , PUNCT cana-4541 70 44 𝑅 𝑅 PROPN cana-4541 70 45 ) ) PUNCT cana-4541 70 46 ∈ ∈ PROPN cana-4541 70 47 𝑅7 𝑅7 VERB cana-4541 71 1 + + ADJ cana-4541 71 2 : : PUNCT cana-4541 71 3 𝑆 𝑆 PROPN cana-4541 71 4 , , PUNCT cana-4541 71 5 𝑉 𝑉 PROPN cana-4541 71 6 , , PUNCT cana-4541 71 7 𝐸 𝐸 PROPN cana-4541 71 8 , , PUNCT cana-4541 71 9 𝐼 𝐼 PROPN cana-4541 71 10 , , PUNCT cana-4541 71 11 𝐺 𝐺 PROPN cana-4541 71 12 , , PUNCT cana-4541 71 13 𝐻 𝐻 PROPN cana-4541 71 14 , , PUNCT cana-4541 71 15 𝑅 𝑅 PROPN cana-4541 71 16 β‰₯ β‰₯ NOUN cana-4541 71 17 0 0 NUM cana-4541 71 18 , , PUNCT cana-4541 71 19 𝑆 𝑆 PROPN cana-4541 71 20 + + CCONJ cana-4541 71 21 𝑉 𝑉 PROPN cana-4541 71 22 + + NOUN cana-4541 71 23 𝐸 𝐸 PROPN cana-4541 71 24 + + CCONJ cana-4541 71 25 𝐼 𝐼 PROPN cana-4541 71 26 + + CCONJ cana-4541 71 27 𝐺 𝐺 NOUN cana-4541 71 28 + + CCONJ cana-4541 71 29 𝐻 𝐻 PROPN cana-4541 71 30 + + PROPN cana-4541 71 31 𝑅 𝑅 PROPN cana-4541 71 32 = = PUNCT cana-4541 71 33 Ξ»/𝑁 Ξ»/𝑁 PROPN cana-4541 71 34 } } PUNCT cana-4541 71 35 where where SCONJ cana-4541 71 36 Ο‰ Ο‰ PROPN cana-4541 71 37 is be AUX cana-4541 71 38 a a DET cana-4541 71 39 closed closed ADJ cana-4541 71 40 set set NOUN cana-4541 71 41 . . PUNCT cana-4541 72 1 after after ADP cana-4541 72 2 evaluating evaluate VERB cana-4541 72 3 the the DET cana-4541 72 4 equation equation NOUN cana-4541 72 5 ( ( PUNCT cana-4541 72 6 5 5 NUM cana-4541 72 7 ) ) PUNCT cana-4541 72 8 , , PUNCT cana-4541 72 9 we we PRON cana-4541 72 10 get get VERB cana-4541 72 11 𝑁(𝑑 𝑁(𝑑 PRON cana-4541 72 12 ) ) PUNCT cana-4541 72 13 = = PUNCT cana-4541 72 14 𝑁(0)𝐸𝛽,1(βˆ’π‘π‘‘ 𝑁(0)𝐸𝛽,1(βˆ’π‘π‘‘ ADP cana-4541 72 15 𝛽 𝛽 NOUN cana-4541 72 16 ) ) PUNCT cana-4541 73 1 + + CCONJ cana-4541 73 2 λ𝑑𝛽𝐸𝛽,𝛽+1(βˆ’π‘π‘‘ λ𝑑𝛽𝐸𝛽,𝛽+1(βˆ’π‘π‘‘ NOUN cana-4541 73 3 𝛽 𝛽 NOUN cana-4541 73 4 ) ) PUNCT cana-4541 73 5 . . PUNCT cana-4541 74 1 3 3 X cana-4541 74 2 . . X cana-4541 74 3 equilibrium equilibrium NOUN cana-4541 74 4 points point NOUN cana-4541 74 5 : : PUNCT cana-4541 74 6 let let VERB cana-4541 74 7 as as SCONJ cana-4541 74 8 assume assume VERB cana-4541 74 9 that that SCONJ cana-4541 74 10 all all DET cana-4541 74 11 equilibrium equilibrium NOUN cana-4541 74 12 points point NOUN cana-4541 74 13 are be AUX cana-4541 74 14 as as SCONJ cana-4541 74 15 follows follow VERB cana-4541 74 16 : : PUNCT cana-4541 75 1 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 75 2 𝛽 𝛽 NOUN cana-4541 75 3 𝑆 𝑆 PROPN cana-4541 75 4 = = SYM cana-4541 75 5 0 0 PROPN cana-4541 75 6 , , PUNCT cana-4541 75 7 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 75 8 𝛽 𝛽 PROPN cana-4541 75 9 𝑉 𝑉 PROPN cana-4541 75 10 = = NOUN cana-4541 75 11 0 0 NUM cana-4541 75 12 , , PUNCT cana-4541 75 13 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 75 14 𝛽 𝛽 NOUN cana-4541 75 15 𝐸 𝐸 NOUN cana-4541 75 16 = = SYM cana-4541 75 17 0 0 NUM cana-4541 75 18 , , PUNCT cana-4541 75 19 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 75 20 𝛽 𝛽 NOUN cana-4541 75 21 𝐼 𝐼 NOUN cana-4541 75 22 = = SYM cana-4541 75 23 0 0 NUM cana-4541 75 24 , , PUNCT cana-4541 75 25 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 75 26 𝛽 𝛽 PROPN cana-4541 75 27 𝐺 𝐺 NOUN cana-4541 75 28 = = NOUN cana-4541 75 29 0 0 PROPN cana-4541 75 30 , , PUNCT cana-4541 75 31 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 75 32 𝛽 𝛽 NOUN cana-4541 75 33 𝐻 𝐻 NOUN cana-4541 75 34 = = SYM cana-4541 75 35 0 0 NUM cana-4541 75 36 , , PUNCT cana-4541 75 37 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 75 38 𝛽 𝛽 PROPN cana-4541 75 39 𝑅 𝑅 PROPN cana-4541 75 40 = = PROPN cana-4541 75 41 0 0 NUM cana-4541 75 42 … … PUNCT cana-4541 75 43 ( ( PUNCT cana-4541 75 44 6 6 NUM cana-4541 75 45 ) ) PUNCT cana-4541 75 46 the the DET cana-4541 75 47 disease disease NOUN cana-4541 75 48 free free ADJ cana-4541 75 49 equilibrium equilibrium NOUN cana-4541 75 50 𝐸0 𝐸0 NOUN cana-4541 75 51 = = SYM cana-4541 75 52 ( ( PUNCT cana-4541 75 53 Ξ»/𝑁 Ξ»/𝑁 PROPN cana-4541 75 54 , , PUNCT cana-4541 75 55 0,0,0,0,0,0 0,0,0,0,0,0 NOUN cana-4541 75 56 ) ) PUNCT cana-4541 75 57 the the DET cana-4541 75 58 basic basic ADJ cana-4541 75 59 reproduction reproduction NOUN cana-4541 75 60 number number NOUN cana-4541 75 61 of of ADP cana-4541 75 62 the the DET cana-4541 75 63 disease disease NOUN cana-4541 75 64 is be AUX cana-4541 75 65 𝑅0 𝑅0 NOUN cana-4541 75 66 which which PRON cana-4541 75 67 is be AUX cana-4541 75 68 defined define VERB cana-4541 75 69 as as ADP cana-4541 75 70 communications communication NOUN cana-4541 75 71 on on ADP cana-4541 75 72 applied apply VERB cana-4541 75 73 nonlinear nonlinear ADJ cana-4541 75 74 analysis analysis NOUN cana-4541 75 75 issn issn NOUN cana-4541 75 76 : : PUNCT cana-4541 75 77 1074 1074 NUM cana-4541 75 78 - - PUNCT cana-4541 75 79 133x 133x NUM cana-4541 75 80 vol vol NOUN cana-4541 75 81 32 32 NUM cana-4541 76 1 no no NOUN cana-4541 76 2 . . PUNCT cana-4541 77 1 9s 9s NUM cana-4541 77 2 ( ( PUNCT cana-4541 77 3 2025 2025 NUM cana-4541 77 4 ) ) PUNCT cana-4541 77 5 2483 2483 NUM cana-4541 77 6 https://internationalpubls.com https://internationalpubls.com X cana-4541 77 7 𝑅0 𝑅0 NOUN cana-4541 77 8 = = SYM cana-4541 77 9 Ξ» Ξ» PROPN cana-4541 77 10 ( ( PUNCT cana-4541 77 11 𝛿1 𝛿1 NOUN cana-4541 77 12 + + CCONJ cana-4541 77 13 𝛿2 𝛿2 NOUN cana-4541 77 14 + + CCONJ cana-4541 77 15 𝑑)(𝜏1 𝑑)(𝜏1 PROPN cana-4541 77 16 + + CCONJ cana-4541 77 17 𝜏2 𝜏2 ADJ cana-4541 77 18 + + CCONJ cana-4541 77 19 𝜏3 𝜏3 NOUN cana-4541 77 20 + + CCONJ cana-4541 77 21 𝑑 𝑑 NOUN cana-4541 77 22 ) ) PUNCT cana-4541 77 23 if if SCONJ cana-4541 77 24 𝑅0 𝑅0 PROPN cana-4541 77 25 > > X cana-4541 77 26 1 1 NUM cana-4541 77 27 , , PUNCT cana-4541 77 28 then then ADV cana-4541 77 29 model model NOUN cana-4541 77 30 contains contain VERB cana-4541 77 31 a a DET cana-4541 77 32 unique unique ADJ cana-4541 77 33 positive positive ADJ cana-4541 77 34 equilibrium equilibrium NOUN cana-4541 77 35 point point NOUN cana-4541 77 36 𝐸1 𝐸1 NOUN cana-4541 77 37 = = SYM cana-4541 77 38 ( ( PUNCT cana-4541 77 39 𝑆′ 𝑆′ PROPN cana-4541 77 40 , , PUNCT cana-4541 77 41 𝑉′ 𝑉′ NOUN cana-4541 77 42 , , PUNCT cana-4541 77 43 𝐸′ 𝐸′ NOUN cana-4541 77 44 , , PUNCT cana-4541 77 45 𝐼′ 𝐼′ ADJ cana-4541 77 46 , , PUNCT cana-4541 77 47 𝐺′ 𝐺′ ADV cana-4541 77 48 , , PUNCT cana-4541 77 49 𝐻′ 𝐻′ ADV cana-4541 77 50 , , PUNCT cana-4541 77 51 𝑅′ 𝑅′ NUM cana-4541 77 52 ) ) PUNCT cana-4541 77 53 where where SCONJ cana-4541 77 54 , , PUNCT cana-4541 77 55 𝑆′ 𝑆′ PROPN cana-4541 77 56 = = SYM cana-4541 77 57 Ξ» Ξ» PROPN cana-4541 77 58 𝛾1 𝛾1 NOUN cana-4541 77 59 + + CCONJ cana-4541 77 60 𝛾2 𝛾2 VERB cana-4541 77 61 + + CCONJ cana-4541 77 62 𝑑 𝑑 NOUN cana-4541 77 63 𝑉′ 𝑉′ ADV cana-4541 77 64 = = PUNCT cana-4541 77 65 Ξ»{𝛾2(𝛿1 Ξ»{𝛾2(𝛿1 X cana-4541 77 66 + + CCONJ cana-4541 77 67 𝛿2 𝛿2 NOUN cana-4541 77 68 + + CCONJ cana-4541 77 69 𝑑)(𝜏1 𝑑)(𝜏1 PROPN cana-4541 77 70 + + CCONJ cana-4541 77 71 𝜏2 𝜏2 ADJ cana-4541 77 72 + + CCONJ cana-4541 77 73 𝜏3 𝜏3 NOUN cana-4541 77 74 + + CCONJ cana-4541 77 75 𝑑 𝑑 NOUN cana-4541 77 76 ) ) PUNCT cana-4541 78 1 + + NUM cana-4541 78 2 𝜏2𝛾1𝛿1 𝜏2𝛾1𝛿1 NOUN cana-4541 78 3 } } PUNCT cana-4541 78 4 ( ( PUNCT cana-4541 78 5 𝛾1 𝛾1 NOUN cana-4541 78 6 + + CCONJ cana-4541 78 7 𝛾2 𝛾2 VERB cana-4541 78 8 + + CCONJ cana-4541 78 9 𝑑)(𝛿1 𝑑)(𝛿1 NOUN cana-4541 78 10 + + CCONJ cana-4541 78 11 𝛿2 𝛿2 NOUN cana-4541 78 12 + + CCONJ cana-4541 78 13 𝑑)(𝜏1 𝑑)(𝜏1 PROPN cana-4541 78 14 + + CCONJ cana-4541 78 15 𝜏2 𝜏2 ADJ cana-4541 78 16 + + CCONJ cana-4541 78 17 𝜏3 𝜏3 NOUN cana-4541 78 18 + + CCONJ cana-4541 78 19 𝑑 𝑑 NOUN cana-4541 78 20 ) ) PUNCT cana-4541 78 21 𝐸′ 𝐸′ PROPN cana-4541 78 22 = = SYM cana-4541 78 23 𝛾1Ξ» 𝛾1Ξ» X cana-4541 78 24 ( ( PUNCT cana-4541 78 25 𝛾1 𝛾1 NOUN cana-4541 78 26 + + CCONJ cana-4541 78 27 𝛾2 𝛾2 VERB cana-4541 78 28 + + CCONJ cana-4541 78 29 𝑑)(𝛿1 𝑑)(𝛿1 NOUN cana-4541 78 30 + + CCONJ cana-4541 78 31 𝛿2 𝛿2 NOUN cana-4541 78 32 + + CCONJ cana-4541 78 33 𝑑 𝑑 NOUN cana-4541 78 34 ) ) PUNCT cana-4541 78 35 𝐼′ 𝐼′ PUNCT cana-4541 78 36 = = SYM cana-4541 78 37 𝛿1𝛾1Ξ» 𝛿1𝛾1Ξ» PUNCT cana-4541 78 38 ( ( PUNCT cana-4541 78 39 𝛾1 𝛾1 NOUN cana-4541 78 40 + + CCONJ cana-4541 78 41 𝛾2 𝛾2 VERB cana-4541 78 42 + + CCONJ cana-4541 78 43 𝑑)(𝛿1 𝑑)(𝛿1 NOUN cana-4541 78 44 + + CCONJ cana-4541 78 45 𝛿2 𝛿2 NOUN cana-4541 78 46 + + CCONJ cana-4541 78 47 𝑑)(𝜏1 𝑑)(𝜏1 PROPN cana-4541 78 48 + + CCONJ cana-4541 78 49 𝜏2 𝜏2 ADJ cana-4541 78 50 + + CCONJ cana-4541 78 51 𝜏3 𝜏3 NOUN cana-4541 78 52 + + CCONJ cana-4541 78 53 𝑑 𝑑 NOUN cana-4541 78 54 ) ) PUNCT cana-4541 78 55 𝐺′ 𝐺′ PROPN cana-4541 78 56 = = SYM cana-4541 78 57 𝛾1Ξ»{𝛿2(𝜏1 𝛾1Ξ»{𝛿2(𝜏1 VERB cana-4541 78 58 + + CCONJ cana-4541 78 59 𝜏2 𝜏2 ADJ cana-4541 78 60 + + CCONJ cana-4541 78 61 𝜏3 𝜏3 NOUN cana-4541 78 62 + + CCONJ cana-4541 78 63 𝑑 𝑑 NOUN cana-4541 78 64 ) ) PUNCT cana-4541 79 1 + + CCONJ cana-4541 79 2 𝜏3𝛿1 𝜏3𝛿1 NOUN cana-4541 79 3 } } PUNCT cana-4541 79 4 ( ( PUNCT cana-4541 79 5 𝛾1 𝛾1 NOUN cana-4541 79 6 + + CCONJ cana-4541 79 7 𝛾2 𝛾2 VERB cana-4541 79 8 + + CCONJ cana-4541 79 9 𝑑)(𝛿1 𝑑)(𝛿1 NOUN cana-4541 79 10 + + CCONJ cana-4541 79 11 𝛿2 𝛿2 NOUN cana-4541 79 12 + + CCONJ cana-4541 79 13 𝑑)(𝜏1 𝑑)(𝜏1 PROPN cana-4541 79 14 + + CCONJ cana-4541 79 15 𝜏2 𝜏2 ADJ cana-4541 79 16 + + CCONJ cana-4541 79 17 𝜏3 𝜏3 NOUN cana-4541 79 18 + + CCONJ cana-4541 79 19 𝑑 𝑑 NOUN cana-4541 79 20 ) ) PUNCT cana-4541 79 21 𝐻′ 𝐻′ ADV cana-4541 79 22 = = SYM cana-4541 79 23 { { PUNCT cana-4541 79 24 𝛾1𝛿1(𝜁1 𝛾1𝛿1(𝜁1 NOUN cana-4541 79 25 + + PUNCT cana-4541 79 26 𝜁2 𝜁2 NOUN cana-4541 79 27 + + CCONJ cana-4541 79 28 𝑑 𝑑 NOUN cana-4541 79 29 ) ) PUNCT cana-4541 79 30 + + CCONJ cana-4541 79 31 𝜁1[𝛿2(𝜏1 𝜁1[𝛿2(𝜏1 VERB cana-4541 79 32 + + CCONJ cana-4541 79 33 𝜏2 𝜏2 NOUN cana-4541 79 34 + + CCONJ cana-4541 79 35 𝜏3 𝜏3 NOUN cana-4541 79 36 + + CCONJ cana-4541 79 37 𝑑 𝑑 NOUN cana-4541 79 38 ) ) PUNCT cana-4541 79 39 + + PUNCT cana-4541 79 40 𝜏3𝛿1 𝜏3𝛿1 ADP cana-4541 79 41 ] ] X cana-4541 79 42 } } PUNCT cana-4541 79 43 ( ( PUNCT cana-4541 79 44 𝛾1 𝛾1 NOUN cana-4541 79 45 + + CCONJ cana-4541 79 46 𝛾2 𝛾2 VERB cana-4541 79 47 + + CCONJ cana-4541 79 48 𝑑)(𝛿1 𝑑)(𝛿1 NOUN cana-4541 79 49 + + CCONJ cana-4541 79 50 𝛿2 𝛿2 NOUN cana-4541 79 51 + + CCONJ cana-4541 79 52 𝑑)(𝜏1 𝑑)(𝜏1 PROPN cana-4541 79 53 + + CCONJ cana-4541 79 54 𝜏2 𝜏2 ADJ cana-4541 79 55 + + CCONJ cana-4541 79 56 𝜏3 𝜏3 NOUN cana-4541 79 57 + + CCONJ cana-4541 79 58 𝑑 𝑑 NOUN cana-4541 79 59 ) ) PUNCT cana-4541 79 60 𝑅′ 𝑅′ PROPN cana-4541 79 61 = = SYM cana-4541 79 62 𝜁1𝐻′ 𝜁1𝐻′ NOUN cana-4541 79 63 + + CCONJ cana-4541 79 64 𝜁2𝐺′ 𝜁2𝐺′ X cana-4541 79 65 𝑑 𝑑 NOUN cana-4541 79 66 if if SCONJ cana-4541 79 67 𝑅0 𝑅0 PROPN cana-4541 79 68 < < X cana-4541 79 69 1 1 NUM cana-4541 79 70 , , PUNCT cana-4541 79 71 then then ADV cana-4541 79 72 model model NOUN cana-4541 79 73 is be AUX cana-4541 79 74 stable stable ADJ cana-4541 79 75 . . PUNCT cana-4541 80 1 the the DET cana-4541 80 2 jacobian jacobian ADJ cana-4541 80 3 matrix matrix NOUN cana-4541 80 4 𝐽(𝐸0 𝐽(𝐸0 NOUN cana-4541 80 5 ) ) PUNCT cana-4541 80 6 for for ADP cana-4541 80 7 system system NOUN cana-4541 80 8 ( ( PUNCT cana-4541 80 9 4 4 NUM cana-4541 80 10 ) ) PUNCT cana-4541 80 11 for for ADP cana-4541 80 12 diseases disease NOUN cana-4541 80 13 free free ADJ cana-4541 80 14 equilibrium equilibrium NOUN cana-4541 80 15 point point NOUN cana-4541 80 16 is be AUX cana-4541 80 17 as as SCONJ cana-4541 80 18 follows follow VERB cana-4541 80 19 : : PUNCT cana-4541 80 20 𝐽(𝐸0 𝐽(𝐸0 NUM cana-4541 80 21 ) ) PUNCT cana-4541 80 22 = = PUNCT cana-4541 81 1 [ [ PUNCT cana-4541 81 2 βˆ’(𝛾1 βˆ’(𝛾1 NUM cana-4541 81 3 + + CCONJ cana-4541 81 4 𝛾2 𝛾2 VERB cana-4541 81 5 + + CCONJ cana-4541 81 6 𝑑 𝑑 NOUN cana-4541 81 7 ) ) PUNCT cana-4541 81 8 0 0 NUM cana-4541 81 9 0 0 NUM cana-4541 81 10 𝛾2 𝛾2 VERB cana-4541 81 11 βˆ’π‘‘ βˆ’π‘‘ ADJ cana-4541 81 12 0 0 NUM cana-4541 82 1 𝛾1 𝛾1 NOUN cana-4541 82 2 0 0 NUM cana-4541 82 3 βˆ’(𝛿1 βˆ’(𝛿1 X cana-4541 83 1 + + CCONJ cana-4541 83 2 𝛿2 𝛿2 NOUN cana-4541 83 3 + + CCONJ cana-4541 83 4 𝑑 𝑑 NOUN cana-4541 83 5 ) ) PUNCT cana-4541 83 6 0 0 PUNCT cana-4541 84 1 𝜏2 𝜏2 ADJ cana-4541 84 2 0 0 NUM cana-4541 84 3 0 0 NUM cana-4541 84 4 0 0 NUM cana-4541 84 5 0 0 NUM cana-4541 84 6 0 0 NUM cana-4541 84 7 0 0 NUM cana-4541 84 8 0 0 NUM cana-4541 84 9 0 0 NUM cana-4541 84 10 0 0 NUM cana-4541 84 11 0 0 NUM cana-4541 84 12 0 0 NUM cana-4541 84 13 0 0 NUM cana-4541 84 14 𝛿1 𝛿1 NOUN cana-4541 84 15 βˆ’(𝜏1 βˆ’(𝜏1 PUNCT cana-4541 84 16 + + CCONJ cana-4541 84 17 𝜏2 𝜏2 ADJ cana-4541 84 18 + + CCONJ cana-4541 84 19 𝜏3 𝜏3 NOUN cana-4541 84 20 + + CCONJ cana-4541 84 21 𝑑 𝑑 NOUN cana-4541 84 22 ) ) PUNCT cana-4541 84 23 0 0 NUM cana-4541 84 24 0 0 NUM cana-4541 84 25 0 0 NUM cana-4541 84 26 0 0 NUM cana-4541 84 27 0 0 NUM cana-4541 84 28 𝛿2 𝛿2 NOUN cana-4541 84 29 0 0 NUM cana-4541 84 30 0 0 NUM cana-4541 84 31 0 0 NUM cana-4541 84 32 0 0 NUM cana-4541 84 33 0 0 NUM cana-4541 84 34 0 0 NUM cana-4541 84 35 𝜏3 𝜏3 NOUN cana-4541 84 36 𝜏1 𝜏1 NOUN cana-4541 84 37 0 0 NUM cana-4541 84 38 βˆ’(𝜁1 βˆ’(𝜁1 NUM cana-4541 84 39 + + CCONJ cana-4541 84 40 𝜁2 𝜁2 NOUN cana-4541 84 41 + + CCONJ cana-4541 84 42 𝑑 𝑑 NOUN cana-4541 84 43 ) ) PUNCT cana-4541 84 44 0 0 NUM cana-4541 84 45 0 0 NUM cana-4541 85 1 𝜁1 𝜁1 ADJ cana-4541 85 2 βˆ’(πœ‰ βˆ’(πœ‰ NOUN cana-4541 85 3 + + CCONJ cana-4541 85 4 𝑑 𝑑 NOUN cana-4541 85 5 ) ) PUNCT cana-4541 85 6 0 0 NUM cana-4541 85 7 𝜁2 𝜁2 NOUN cana-4541 85 8 πœ‰ πœ‰ NOUN cana-4541 85 9 βˆ’π‘‘ βˆ’π‘‘ VERB cana-4541 85 10 ] ] PUNCT cana-4541 85 11 the the DET cana-4541 85 12 characteristic characteristic ADJ cana-4541 85 13 equation equation NOUN cana-4541 85 14 |𝐽(𝐸0 |𝐽(𝐸0 X cana-4541 85 15 ) ) PUNCT cana-4541 85 16 βˆ’ βˆ’ PROPN cana-4541 86 1 πœ†πΌ| πœ†πΌ| NOUN cana-4541 86 2 = = NOUN cana-4541 86 3 0 0 NUM cana-4541 86 4 |𝐽(𝐸0 |𝐽(𝐸0 NOUN cana-4541 86 5 ) ) PUNCT cana-4541 86 6 βˆ’ βˆ’ PROPN cana-4541 87 1 πœ†πΌ| πœ†πΌ| NOUN cana-4541 87 2 = = SYM cana-4541 87 3 ( ( PUNCT cana-4541 87 4 𝛾1 𝛾1 PROPN cana-4541 87 5 + + CCONJ cana-4541 87 6 𝛾2 𝛾2 VERB cana-4541 87 7 + + CCONJ cana-4541 87 8 𝑑 𝑑 PROPN cana-4541 87 9 + + X cana-4541 87 10 πœ†)(𝑑 πœ†)(𝑑 CCONJ cana-4541 87 11 + + NUM cana-4541 87 12 πœ†)(𝛿1 πœ†)(𝛿1 NOUN cana-4541 88 1 + + CCONJ cana-4541 88 2 𝛿2 𝛿2 NOUN cana-4541 88 3 + + CCONJ cana-4541 88 4 𝑑 𝑑 PROPN cana-4541 88 5 + + CCONJ cana-4541 88 6 πœ†)(𝜏1 πœ†)(𝜏1 VERB cana-4541 88 7 + + NUM cana-4541 88 8 𝜏2 𝜏2 NOUN cana-4541 88 9 + + CCONJ cana-4541 88 10 𝜏3 𝜏3 NOUN cana-4541 88 11 + + CCONJ cana-4541 88 12 𝑑 𝑑 PROPN cana-4541 88 13 + + CCONJ cana-4541 88 14 πœ†)(𝜁1 πœ†)(𝜁1 NOUN cana-4541 88 15 + + CCONJ cana-4541 88 16 𝜁2 𝜁2 NOUN cana-4541 88 17 + + CCONJ cana-4541 88 18 𝑑 𝑑 PROPN cana-4541 88 19 + + X cana-4541 88 20 πœ†)(πœ‰ πœ†)(πœ‰ PUNCT cana-4541 89 1 + + CCONJ cana-4541 89 2 𝑑 𝑑 PROPN cana-4541 89 3 + + X cana-4541 89 4 πœ†)(𝑑 πœ†)(𝑑 CCONJ cana-4541 89 5 + + CCONJ cana-4541 89 6 πœ† πœ† X cana-4541 89 7 ) ) PUNCT cana-4541 89 8 = = SYM cana-4541 89 9 0 0 NOUN cana-4541 90 1 the the DET cana-4541 90 2 characteristic characteristic ADJ cana-4541 90 3 root root NOUN cana-4541 90 4 for for ADP cana-4541 90 5 |𝐽(𝐸0 |𝐽(𝐸0 NOUN cana-4541 90 6 ) ) PUNCT cana-4541 90 7 βˆ’ βˆ’ PROPN cana-4541 91 1 πœ†πΌ| πœ†πΌ| NOUN cana-4541 91 2 = = SYM cana-4541 91 3 0 0 NUM cana-4541 91 4 are be AUX cana-4541 91 5 πœ†1 πœ†1 ADJ cana-4541 91 6 = = PUNCT cana-4541 91 7 βˆ’(𝛾1 βˆ’(𝛾1 NUM cana-4541 91 8 + + CCONJ cana-4541 91 9 𝛾2 𝛾2 VERB cana-4541 91 10 + + CCONJ cana-4541 91 11 𝑑 𝑑 NOUN cana-4541 91 12 ) ) PUNCT cana-4541 91 13 , , PUNCT cana-4541 91 14 πœ†2 πœ†2 NOUN cana-4541 91 15 = = PUNCT cana-4541 91 16 βˆ’π‘‘ βˆ’π‘‘ VERB cana-4541 91 17 , , PUNCT cana-4541 91 18 πœ†3 πœ†3 NOUN cana-4541 91 19 = = SYM cana-4541 91 20 βˆ’(𝛿1 βˆ’(𝛿1 X cana-4541 92 1 + + CCONJ cana-4541 92 2 𝛿2 𝛿2 NOUN cana-4541 92 3 + + CCONJ cana-4541 92 4 𝑑 𝑑 NOUN cana-4541 92 5 ) ) PUNCT cana-4541 92 6 , , PUNCT cana-4541 92 7 πœ†4 πœ†4 NOUN cana-4541 92 8 = = PUNCT cana-4541 92 9 βˆ’(𝜏1 βˆ’(𝜏1 PUNCT cana-4541 92 10 + + CCONJ cana-4541 92 11 𝜏2 𝜏2 ADJ cana-4541 92 12 + + CCONJ cana-4541 92 13 𝜏3 𝜏3 NOUN cana-4541 92 14 + + CCONJ cana-4541 92 15 𝑑 𝑑 NOUN cana-4541 92 16 ) ) PUNCT cana-4541 92 17 , , PUNCT cana-4541 92 18 πœ†5 πœ†5 ADV cana-4541 92 19 = = PUNCT cana-4541 92 20 βˆ’(𝜁1 βˆ’(𝜁1 NUM cana-4541 92 21 + + CCONJ cana-4541 92 22 𝜁2 𝜁2 NOUN cana-4541 92 23 + + CCONJ cana-4541 92 24 𝑑 𝑑 NOUN cana-4541 92 25 ) ) PUNCT cana-4541 92 26 , , PUNCT cana-4541 92 27 πœ†6 πœ†6 PROPN cana-4541 92 28 = = PUNCT cana-4541 92 29 βˆ’(πœ‰ βˆ’(πœ‰ PROPN cana-4541 92 30 + + CCONJ cana-4541 92 31 𝑑 𝑑 NOUN cana-4541 92 32 ) ) PUNCT cana-4541 92 33 , , PUNCT cana-4541 92 34 πœ†7 πœ†7 PROPN cana-4541 92 35 = = PUNCT cana-4541 92 36 βˆ’π‘‘ βˆ’π‘‘ VERB cana-4541 92 37 according accord VERB cana-4541 92 38 to to ADP cana-4541 92 39 the the DET cana-4541 92 40 generalized generalize VERB cana-4541 92 41 routh routh PROPN cana-4541 92 42 - - PUNCT cana-4541 92 43 hurwitz hurwitz PROPN cana-4541 92 44 and and CCONJ cana-4541 92 45 jacobian jacobian ADJ cana-4541 92 46 criterion criterion NOUN cana-4541 92 47 when when SCONJ cana-4541 92 48 all all DET cana-4541 92 49 the the DET cana-4541 92 50 roots root NOUN cana-4541 92 51 are be AUX cana-4541 92 52 negative negative ADJ cana-4541 92 53 then then ADV cana-4541 92 54 point point NOUN cana-4541 92 55 𝐸0 𝐸0 PROPN cana-4541 92 56 is be AUX cana-4541 92 57 disease disease NOUN cana-4541 92 58 free free ADJ cana-4541 92 59 equilibrium equilibrium NOUN cana-4541 92 60 point point NOUN cana-4541 92 61 , , PUNCT cana-4541 92 62 which which PRON cana-4541 92 63 is be AUX cana-4541 92 64 stable stable ADJ cana-4541 92 65 . . PUNCT cana-4541 93 1 communications communication NOUN cana-4541 93 2 on on ADP cana-4541 93 3 applied apply VERB cana-4541 93 4 nonlinear nonlinear ADJ cana-4541 93 5 analysis analysis NOUN cana-4541 93 6 issn issn NOUN cana-4541 93 7 : : PUNCT cana-4541 93 8 1074 1074 NUM cana-4541 93 9 - - PUNCT cana-4541 93 10 133x 133x NUM cana-4541 93 11 vol vol NOUN cana-4541 93 12 32 32 NUM cana-4541 93 13 no no NOUN cana-4541 93 14 . . PUNCT cana-4541 94 1 9s 9s NUM cana-4541 94 2 ( ( PUNCT cana-4541 94 3 2025 2025 NUM cana-4541 94 4 ) ) PUNCT cana-4541 94 5 2484 2484 NUM cana-4541 94 6 https://internationalpubls.com https://internationalpubls.com X cana-4541 94 7 4 4 X cana-4541 94 8 . . PUNCT cana-4541 94 9 numerical numerical ADJ cana-4541 94 10 methods method NOUN cana-4541 94 11 : : PUNCT cana-4541 94 12 the the DET cana-4541 94 13 generalized generalized PROPN cana-4541 94 14 adams adams PROPN cana-4541 94 15 bashforth bashforth PROPN cana-4541 94 16 moulton moulton PROPN cana-4541 94 17 method method NOUN cana-4541 94 18 can can AUX cana-4541 94 19 be be AUX cana-4541 94 20 adopted adopt VERB cana-4541 94 21 to to ADP cana-4541 94 22 the the DET cana-4541 94 23 numerical numerical ADJ cana-4541 94 24 solutions solution NOUN cana-4541 94 25 of of ADP cana-4541 94 26 system system NOUN cana-4541 94 27 ( ( PUNCT cana-4541 94 28 4 4 NUM cana-4541 94 29 ) ) PUNCT cana-4541 94 30 . . PUNCT cana-4541 95 1 evaluate evaluate VERB cana-4541 95 2 the the DET cana-4541 95 3 following following ADJ cana-4541 95 4 nonlinear nonlinear ADJ cana-4541 95 5 fractional fractional ADJ cana-4541 95 6 differential differential ADJ cana-4541 95 7 equation equation NOUN cana-4541 95 8 to to PART cana-4541 95 9 obtain obtain VERB cana-4541 95 10 the the DET cana-4541 95 11 algorithm algorithm NOUN cana-4541 95 12 's 's PART cana-4541 95 13 approximate approximate ADJ cana-4541 95 14 solution solution NOUN cana-4541 95 15 : : PUNCT cana-4541 96 1 π’Ÿπ‘‘ π’Ÿπ‘‘ PROPN cana-4541 96 2 𝛽 𝛽 PROPN cana-4541 96 3 𝑦(𝑑 𝑦(𝑑 PROPN cana-4541 96 4 ) ) PUNCT cana-4541 96 5 = = PUNCT cana-4541 97 1 𝑓(𝑑 𝑓(𝑑 NOUN cana-4541 97 2 , , PUNCT cana-4541 97 3 𝑦(𝑑 𝑦(𝑑 NUM cana-4541 97 4 ) ) PUNCT cana-4541 97 5 ) ) PUNCT cana-4541 97 6 , , PUNCT cana-4541 97 7 0 0 NUM cana-4541 97 8 ≀ ≀ NUM cana-4541 97 9 𝑑 𝑑 X cana-4541 97 10 < < X cana-4541 97 11 𝑏 𝑏 X cana-4541 97 12 < < X cana-4541 97 13 ∞ ∞ PROPN cana-4541 97 14 π‘¦β„Ž(0 π‘¦β„Ž(0 NOUN cana-4541 97 15 ) ) PUNCT cana-4541 97 16 = = PUNCT cana-4541 97 17 𝑦0 𝑦0 NOUN cana-4541 97 18 β„Ž β„Ž NOUN cana-4541 97 19 , , PUNCT cana-4541 97 20 β„Ž β„Ž X cana-4541 97 21 = = NOUN cana-4541 97 22 0,1,2 0,1,2 NUM cana-4541 97 23 , , PUNCT cana-4541 97 24 … … PUNCT cana-4541 97 25 , , PUNCT cana-4541 97 26 𝑝 𝑝 NOUN cana-4541 97 27 βˆ’ βˆ’ PROPN cana-4541 97 28 1 1 NUM cana-4541 97 29 , , PUNCT cana-4541 97 30 where where SCONJ cana-4541 97 31 𝑝 𝑝 ADP cana-4541 97 32 = = PUNCT cana-4541 98 1 [ [ X cana-4541 98 2 𝛽 𝛽 X cana-4541 98 3 ] ] PUNCT cana-4541 98 4 } } PUNCT cana-4541 98 5 ( ( PUNCT cana-4541 98 6 7 7 X cana-4541 98 7 ) ) PUNCT cana-4541 98 8 this this DET cana-4541 98 9 equation equation NOUN cana-4541 98 10 is be AUX cana-4541 98 11 equivalent equivalent ADJ cana-4541 98 12 to to ADP cana-4541 98 13 volterra volterra PROPN cana-4541 98 14 integral integral ADJ cana-4541 98 15 equation equation NOUN cana-4541 98 16 : : PUNCT cana-4541 98 17 𝑦(𝑑 𝑦(𝑑 NUM cana-4541 98 18 ) ) PUNCT cana-4541 98 19 = = SYM cana-4541 99 1 βˆ‘π‘¦0 βˆ‘π‘¦0 PROPN cana-4541 99 2 β„Ž β„Ž ADP cana-4541 99 3 π‘βˆ’1 π‘βˆ’1 PROPN cana-4541 99 4 β„Ž=0 β„Ž=0 X cana-4541 99 5 π‘‘β„Ž π‘‘β„Ž ADJ cana-4541 99 6 β„Ž β„Ž NOUN cana-4541 99 7 ! ! PUNCT cana-4541 100 1 + + CCONJ cana-4541 100 2 1 1 NUM cana-4541 100 3 𝛀(𝛽 𝛀(𝛽 NUM cana-4541 100 4 ) ) PUNCT cana-4541 100 5 ∫ ∫ PROPN cana-4541 100 6 ( ( PUNCT cana-4541 100 7 𝑑 𝑑 PROPN cana-4541 100 8 βˆ’ βˆ’ PROPN cana-4541 100 9 𝑠)π›½βˆ’1 𝑠)π›½βˆ’1 PROPN cana-4541 100 10 𝑑 𝑑 PROPN cana-4541 100 11 0 0 NUM cana-4541 100 12 𝑓(𝑠 𝑓(𝑠 PROPN cana-4541 100 13 , , PUNCT cana-4541 100 14 𝑦(𝑠))𝑑𝑠 𝑦(𝑠))𝑑𝑠 PROPN cana-4541 100 15 … … PUNCT cana-4541 100 16 ( ( PUNCT cana-4541 100 17 8) 8) NUM cana-4541 100 18 by by ADP cana-4541 100 19 applying apply VERB cana-4541 100 20 the the DET cana-4541 100 21 predictor predictor NOUN cana-4541 100 22 - - PUNCT cana-4541 100 23 correctors corrector NOUN cana-4541 100 24 scheme scheme VERB cana-4541 100 25 to to ADP cana-4541 100 26 the the DET cana-4541 100 27 fractional fractional ADJ cana-4541 100 28 order order NOUN cana-4541 100 29 shigella shigella PROPN cana-4541 100 30 epidemic epidemic NOUN cana-4541 100 31 model model NOUN cana-4541 100 32 and and CCONJ cana-4541 100 33 set set VERB cana-4541 100 34 π‘˜ π‘˜ PRON cana-4541 100 35 = = PUNCT cana-4541 100 36 𝑇/𝑁 𝑇/𝑁 NOUN cana-4541 100 37 , , PUNCT cana-4541 100 38 ( ( PUNCT cana-4541 100 39 8) 8) NUM cana-4541 100 40 can can AUX cana-4541 100 41 be be AUX cana-4541 100 42 discretized discretize VERB cana-4541 100 43 as as SCONJ cana-4541 100 44 follows follow VERB cana-4541 100 45 : : PUNCT cana-4541 100 46 π‘†π‘š+1 π‘†π‘š+1 VERB cana-4541 100 47 = = NOUN cana-4541 100 48 𝑆0 𝑆0 X cana-4541 100 49 + + CCONJ cana-4541 101 1 π‘˜π›½ π‘˜π›½ PROPN cana-4541 101 2 𝛀(𝛽 𝛀(𝛽 X cana-4541 101 3 + + NOUN cana-4541 101 4 2 2 NUM cana-4541 101 5 ) ) PUNCT cana-4541 101 6 ( ( PUNCT cana-4541 101 7 Ξ» Ξ» X cana-4541 101 8 βˆ’ βˆ’ PROPN cana-4541 101 9 ( ( PUNCT cana-4541 101 10 𝛾1 𝛾1 NOUN cana-4541 101 11 + + CCONJ cana-4541 101 12 𝛾2 𝛾2 VERB cana-4541 101 13 + + CCONJ cana-4541 101 14 𝑑)π‘†π‘š+1 𝑑)π‘†π‘š+1 PROPN cana-4541 101 15 π‘ž π‘ž X cana-4541 101 16 ) ) PUNCT cana-4541 101 17 + + CCONJ cana-4541 102 1 π‘˜π›½ π‘˜π›½ AUX cana-4541 102 2 𝛀(𝛽 𝛀(𝛽 X cana-4541 102 3 + + NOUN cana-4541 102 4 2 2 X cana-4541 102 5 ) ) PUNCT cana-4541 102 6 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 102 7 π‘š π‘š PRON cana-4541 102 8 𝑖=0 𝑖=0 PROPN cana-4541 102 9 ( ( PUNCT cana-4541 102 10 Ξ» Ξ» X cana-4541 102 11 βˆ’ βˆ’ PROPN cana-4541 102 12 ( ( PUNCT cana-4541 102 13 𝛾1 𝛾1 NOUN cana-4541 102 14 + + CCONJ cana-4541 102 15 𝛾2 𝛾2 VERB cana-4541 102 16 + + CCONJ cana-4541 102 17 𝑑)𝑆𝑖 𝑑)𝑆𝑖 NUM cana-4541 102 18 ) ) PUNCT cana-4541 102 19 π‘‰π‘š+1 π‘‰π‘š+1 NOUN cana-4541 103 1 = = PUNCT cana-4541 103 2 𝑉0 𝑉0 NOUN cana-4541 104 1 + + CCONJ cana-4541 104 2 π‘˜π›½ π‘˜π›½ PROPN cana-4541 104 3 𝛀(𝛽 𝛀(𝛽 X cana-4541 104 4 + + NOUN cana-4541 104 5 2 2 NUM cana-4541 104 6 ) ) PUNCT cana-4541 104 7 ( ( PUNCT cana-4541 104 8 𝛾3π‘†π‘š+1 𝛾3π‘†π‘š+1 NUM cana-4541 104 9 π‘ž π‘ž X cana-4541 104 10 + + X cana-4541 104 11 𝜏2πΌπ‘š+1 𝜏2πΌπ‘š+1 NUM cana-4541 104 12 π‘ž π‘ž X cana-4541 104 13 βˆ’ βˆ’ PROPN cana-4541 104 14 π‘‘π‘‰π‘š+1 π‘‘π‘‰π‘š+1 PROPN cana-4541 104 15 π‘ž π‘ž X cana-4541 104 16 ) ) PUNCT cana-4541 105 1 + + CCONJ cana-4541 105 2 π‘˜π›½ π‘˜π›½ AUX cana-4541 105 3 𝛀(𝛽 𝛀(𝛽 X cana-4541 105 4 + + NOUN cana-4541 105 5 2 2 X cana-4541 105 6 ) ) PUNCT cana-4541 105 7 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 105 8 π‘š π‘š PRON cana-4541 105 9 𝑖=0 𝑖=0 PROPN cana-4541 105 10 ( ( PUNCT cana-4541 105 11 𝛾3𝑆𝑖 𝛾3𝑆𝑖 VERB cana-4541 105 12 + + X cana-4541 105 13 𝜏2𝐼𝑖 𝜏2𝐼𝑖 VERB cana-4541 105 14 βˆ’ βˆ’ NOUN cana-4541 105 15 𝑑𝑉𝑖 𝑑𝑉𝑖 NOUN cana-4541 105 16 ) ) PUNCT cana-4541 105 17 πΈπ‘š+1 πΈπ‘š+1 NOUN cana-4541 106 1 = = SYM cana-4541 106 2 𝐸0 𝐸0 NOUN cana-4541 107 1 + + CCONJ cana-4541 107 2 π‘˜π›½ π‘˜π›½ AUX cana-4541 107 3 𝛀(𝛽 𝛀(𝛽 X cana-4541 107 4 + + NOUN cana-4541 107 5 2 2 NUM cana-4541 107 6 ) ) PUNCT cana-4541 107 7 ( ( PUNCT cana-4541 107 8 𝛾1π‘†π‘š+1 𝛾1π‘†π‘š+1 VERB cana-4541 107 9 π‘ž π‘ž X cana-4541 107 10 βˆ’ βˆ’ PROPN cana-4541 107 11 ( ( PUNCT cana-4541 107 12 𝛿1 𝛿1 NOUN cana-4541 107 13 + + CCONJ cana-4541 107 14 𝛿2 𝛿2 NOUN cana-4541 107 15 + + CCONJ cana-4541 107 16 𝑑)πΈπ‘š+1 𝑑)πΈπ‘š+1 VERB cana-4541 107 17 π‘ž π‘ž X cana-4541 107 18 ) ) PUNCT cana-4541 108 1 + + CCONJ cana-4541 109 1 π‘˜π›½ π‘˜π›½ AUX cana-4541 109 2 𝛀(𝛽 𝛀(𝛽 X cana-4541 109 3 + + NOUN cana-4541 109 4 2 2 X cana-4541 109 5 ) ) PUNCT cana-4541 109 6 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 109 7 π‘š π‘š PRON cana-4541 109 8 𝑖=0 𝑖=0 PROPN cana-4541 109 9 ( ( PUNCT cana-4541 109 10 𝛾1𝑆𝑖 𝛾1𝑆𝑖 PROPN cana-4541 109 11 βˆ’ βˆ’ PROPN cana-4541 110 1 ( ( PUNCT cana-4541 110 2 𝛿1 𝛿1 NOUN cana-4541 110 3 + + CCONJ cana-4541 110 4 𝛿2 𝛿2 NOUN cana-4541 110 5 + + CCONJ cana-4541 110 6 𝑑)𝐸𝑖 𝑑)𝐸𝑖 VERB cana-4541 110 7 ) ) PUNCT cana-4541 110 8 πΌπ‘š+1 πΌπ‘š+1 NOUN cana-4541 111 1 = = SYM cana-4541 111 2 𝐼0 𝐼0 PROPN cana-4541 111 3 + + CCONJ cana-4541 111 4 π‘˜π›½ π‘˜π›½ X cana-4541 111 5 𝛀(𝛽 𝛀(𝛽 X cana-4541 111 6 + + NOUN cana-4541 111 7 2 2 NUM cana-4541 111 8 ) ) PUNCT cana-4541 111 9 ( ( PUNCT cana-4541 111 10 𝛿1πΈπ‘š+1 𝛿1πΈπ‘š+1 NUM cana-4541 111 11 π‘ž π‘ž PART cana-4541 111 12 βˆ’ βˆ’ PROPN cana-4541 112 1 ( ( PUNCT cana-4541 112 2 𝜏1 𝜏1 NOUN cana-4541 112 3 + + CCONJ cana-4541 112 4 𝜏2 𝜏2 NOUN cana-4541 112 5 + + CCONJ cana-4541 112 6 𝜏3 𝜏3 NOUN cana-4541 112 7 + + CCONJ cana-4541 112 8 𝑑)πΌπ‘š+1 𝑑)πΌπ‘š+1 PROPN cana-4541 112 9 π‘ž π‘ž X cana-4541 112 10 ) ) PUNCT cana-4541 113 1 + + CCONJ cana-4541 113 2 π‘˜π›½ π‘˜π›½ AUX cana-4541 113 3 𝛀(𝛽 𝛀(𝛽 X cana-4541 113 4 + + NOUN cana-4541 113 5 2 2 X cana-4541 113 6 ) ) PUNCT cana-4541 113 7 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 113 8 π‘š π‘š PRON cana-4541 113 9 𝑖=0 𝑖=0 PROPN cana-4541 113 10 ( ( PUNCT cana-4541 113 11 𝛿1𝐸𝑖 𝛿1𝐸𝑖 PROPN cana-4541 113 12 βˆ’ βˆ’ PROPN cana-4541 113 13 ( ( PUNCT cana-4541 113 14 𝜏1 𝜏1 NOUN cana-4541 113 15 + + CCONJ cana-4541 113 16 𝜏2 𝜏2 PROPN cana-4541 113 17 + + CCONJ cana-4541 113 18 𝜏3 𝜏3 NOUN cana-4541 113 19 + + CCONJ cana-4541 113 20 𝑑)𝐼𝑖 𝑑)𝐼𝑖 NOUN cana-4541 113 21 ) ) PUNCT cana-4541 113 22 πΊπ‘š+1 πΊπ‘š+1 ADJ cana-4541 113 23 = = PUNCT cana-4541 114 1 𝐺0 𝐺0 PROPN cana-4541 115 1 + + CCONJ cana-4541 115 2 π‘˜π›½ π‘˜π›½ X cana-4541 115 3 𝛀(𝛽 𝛀(𝛽 X cana-4541 115 4 + + NOUN cana-4541 115 5 2 2 NUM cana-4541 115 6 ) ) PUNCT cana-4541 115 7 ( ( PUNCT cana-4541 115 8 𝛿2πΈπ‘š+1 𝛿2πΈπ‘š+1 NUM cana-4541 115 9 π‘ž π‘ž X cana-4541 115 10 + + CCONJ cana-4541 115 11 𝜏3πΌπ‘š+1 𝜏3πΌπ‘š+1 VERB cana-4541 115 12 π‘ž π‘ž X cana-4541 115 13 βˆ’ βˆ’ PROPN cana-4541 115 14 ( ( PUNCT cana-4541 115 15 𝜁1 𝜁1 ADJ cana-4541 115 16 + + CCONJ cana-4541 115 17 𝜁2 𝜁2 NOUN cana-4541 115 18 + + CCONJ cana-4541 115 19 𝑑)πΊπ‘š+1 𝑑)πΊπ‘š+1 PROPN cana-4541 115 20 π‘ž π‘ž X cana-4541 115 21 ) ) PUNCT cana-4541 116 1 + + CCONJ cana-4541 117 1 π‘˜π›½ π‘˜π›½ AUX cana-4541 117 2 𝛀(𝛽 𝛀(𝛽 X cana-4541 117 3 + + NOUN cana-4541 117 4 2 2 X cana-4541 117 5 ) ) PUNCT cana-4541 117 6 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 117 7 π‘š π‘š ADP cana-4541 117 8 𝑖=0 𝑖=0 PROPN cana-4541 117 9 ( ( PUNCT cana-4541 117 10 𝛿2𝐸𝑖 𝛿2𝐸𝑖 PROPN cana-4541 117 11 + + CCONJ cana-4541 117 12 𝜏3𝐼𝑖 𝜏3𝐼𝑖 VERB cana-4541 117 13 βˆ’ βˆ’ PROPN cana-4541 117 14 ( ( PUNCT cana-4541 117 15 𝜁1 𝜁1 ADJ cana-4541 117 16 + + CCONJ cana-4541 117 17 𝜁2 𝜁2 NOUN cana-4541 117 18 + + CCONJ cana-4541 117 19 𝑑)𝐺𝑖 𝑑)𝐺𝑖 NOUN cana-4541 117 20 ) ) PUNCT cana-4541 117 21 π»π‘š+1 π»π‘š+1 PUNCT cana-4541 118 1 = = PUNCT cana-4541 118 2 𝐻0 𝐻0 PROPN cana-4541 118 3 + + CCONJ cana-4541 118 4 π‘˜π›½ π‘˜π›½ PROPN cana-4541 118 5 𝛀(𝛽 𝛀(𝛽 X cana-4541 118 6 + + NOUN cana-4541 118 7 2 2 NUM cana-4541 118 8 ) ) PUNCT cana-4541 118 9 ( ( PUNCT cana-4541 118 10 𝜏1πΌπ‘š+1 𝜏1πΌπ‘š+1 NUM cana-4541 118 11 π‘ž π‘ž X cana-4541 118 12 + + SYM cana-4541 118 13 𝜁1πΊπ‘š+1 𝜁1πΊπ‘š+1 VERB cana-4541 118 14 π‘ž π‘ž X cana-4541 118 15 βˆ’ βˆ’ PROPN cana-4541 118 16 ( ( PUNCT cana-4541 118 17 πœ‰ πœ‰ X cana-4541 118 18 + + CCONJ cana-4541 118 19 𝑑)π»π‘š+1 𝑑)π»π‘š+1 NOUN cana-4541 118 20 π‘ž π‘ž X cana-4541 118 21 ) ) PUNCT cana-4541 119 1 + + CCONJ cana-4541 119 2 π‘˜π›½ π‘˜π›½ AUX cana-4541 119 3 𝛀(𝛽 𝛀(𝛽 X cana-4541 119 4 + + NOUN cana-4541 119 5 2 2 X cana-4541 119 6 ) ) PUNCT cana-4541 119 7 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 119 8 π‘š π‘š PRON cana-4541 119 9 𝑖=0 𝑖=0 PROPN cana-4541 119 10 ( ( PUNCT cana-4541 119 11 𝜏1𝐼𝑖 𝜏1𝐼𝑖 NOUN cana-4541 119 12 + + CCONJ cana-4541 119 13 𝜁1𝐺𝑖 𝜁1𝐺𝑖 NOUN cana-4541 119 14 βˆ’ βˆ’ PROPN cana-4541 119 15 ( ( PUNCT cana-4541 119 16 πœ‰ πœ‰ NOUN cana-4541 119 17 + + X cana-4541 119 18 𝑑)𝐻𝑖 𝑑)𝐻𝑖 NOUN cana-4541 119 19 ) ) PUNCT cana-4541 119 20 π‘…π‘š+1 π‘…π‘š+1 ADJ cana-4541 119 21 = = NOUN cana-4541 119 22 𝑅0 𝑅0 NOUN cana-4541 119 23 + + CCONJ cana-4541 119 24 π‘˜π›½ π‘˜π›½ PROPN cana-4541 119 25 𝛀(𝛽 𝛀(𝛽 X cana-4541 119 26 + + NOUN cana-4541 119 27 2 2 NUM cana-4541 119 28 ) ) PUNCT cana-4541 119 29 ( ( PUNCT cana-4541 119 30 πœ‰π»π‘š+1 πœ‰π»π‘š+1 PROPN cana-4541 119 31 π‘ž π‘ž X cana-4541 119 32 + + ADJ cana-4541 119 33 𝜁2πΊπ‘š+1 𝜁2πΊπ‘š+1 NUM cana-4541 119 34 π‘ž π‘ž PRON cana-4541 119 35 βˆ’ βˆ’ PROPN cana-4541 119 36 π‘‘π‘…π‘š+1 π‘‘π‘…π‘š+1 ADJ cana-4541 119 37 π‘ž π‘ž X cana-4541 119 38 ) ) PUNCT cana-4541 120 1 + + CCONJ cana-4541 120 2 π‘˜π›½ π‘˜π›½ AUX cana-4541 120 3 𝛀(𝛽 𝛀(𝛽 X cana-4541 120 4 + + NOUN cana-4541 120 5 2 2 X cana-4541 120 6 ) ) PUNCT cana-4541 120 7 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 120 8 π‘š π‘š PRON cana-4541 120 9 𝑖=0 𝑖=0 PROPN cana-4541 120 10 ( ( PUNCT cana-4541 120 11 πœ‰π»π‘– πœ‰π»π‘– NOUN cana-4541 120 12 + + CCONJ cana-4541 120 13 𝜁2𝐺𝑖 𝜁2𝐺𝑖 NOUN cana-4541 120 14 βˆ’ βˆ’ NOUN cana-4541 120 15 𝑑𝑅𝑖 𝑑𝑅𝑖 NOUN cana-4541 120 16 ) ) PUNCT cana-4541 120 17 } } PUNCT cana-4541 120 18 ( ( PUNCT cana-4541 120 19 9 9 NUM cana-4541 120 20 ) ) PUNCT cana-4541 120 21 where where SCONJ cana-4541 120 22 , , PUNCT cana-4541 120 23 communications communication NOUN cana-4541 120 24 on on ADP cana-4541 120 25 applied apply VERB cana-4541 120 26 nonlinear nonlinear ADJ cana-4541 120 27 analysis analysis NOUN cana-4541 120 28 issn issn NOUN cana-4541 120 29 : : PUNCT cana-4541 120 30 1074 1074 NUM cana-4541 120 31 - - PUNCT cana-4541 120 32 133x 133x NUM cana-4541 120 33 vol vol NOUN cana-4541 120 34 32 32 NUM cana-4541 120 35 no no NOUN cana-4541 120 36 . . PUNCT cana-4541 121 1 9s 9s NUM cana-4541 121 2 ( ( PUNCT cana-4541 121 3 2025 2025 NUM cana-4541 121 4 ) ) PUNCT cana-4541 121 5 2485 2485 NUM cana-4541 122 1 https://internationalpubls.com https://internationalpubls.com X cana-4541 122 2 π‘†π‘š+1 π‘†π‘š+1 VERB cana-4541 122 3 π‘ž π‘ž X cana-4541 122 4 = = PUNCT cana-4541 122 5 𝑆0 𝑆0 X cana-4541 122 6 + + CCONJ cana-4541 122 7 1 1 NUM cana-4541 122 8 𝛀(𝛽 𝛀(𝛽 NUM cana-4541 122 9 ) ) PUNCT cana-4541 122 10 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 122 11 π‘š π‘š PROPN cana-4541 122 12 𝑖=0 𝑖=0 PROPN cana-4541 122 13 ( ( PUNCT cana-4541 122 14 Ξ» Ξ» X cana-4541 122 15 βˆ’ βˆ’ PROPN cana-4541 122 16 ( ( PUNCT cana-4541 122 17 𝛾1 𝛾1 NOUN cana-4541 122 18 + + CCONJ cana-4541 122 19 𝛾2 𝛾2 VERB cana-4541 122 20 + + CCONJ cana-4541 122 21 𝑑)𝑆𝑖 𝑑)𝑆𝑖 NUM cana-4541 122 22 ) ) PUNCT cana-4541 122 23 π‘‰π‘š+1 π‘‰π‘š+1 VERB cana-4541 123 1 π‘ž π‘ž NOUN cana-4541 123 2 = = X cana-4541 123 3 𝑉0 𝑉0 PROPN cana-4541 123 4 + + CCONJ cana-4541 123 5 1 1 NUM cana-4541 123 6 𝛀(𝛽 𝛀(𝛽 NUM cana-4541 123 7 ) ) PUNCT cana-4541 123 8 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 123 9 π‘š π‘š PROPN cana-4541 123 10 𝑖=0 𝑖=0 PROPN cana-4541 123 11 ( ( PUNCT cana-4541 123 12 𝛾3𝑆𝑖 𝛾3𝑆𝑖 VERB cana-4541 123 13 + + X cana-4541 123 14 𝜏2𝐼𝑖 𝜏2𝐼𝑖 VERB cana-4541 123 15 βˆ’ βˆ’ NOUN cana-4541 123 16 𝑑𝑉𝑖 𝑑𝑉𝑖 NOUN cana-4541 123 17 ) ) PUNCT cana-4541 123 18 πΈπ‘š+1 πΈπ‘š+1 NOUN cana-4541 124 1 π‘ž π‘ž X cana-4541 124 2 = = X cana-4541 124 3 𝐸0 𝐸0 ADJ cana-4541 124 4 + + CCONJ cana-4541 124 5 1 1 NUM cana-4541 124 6 𝛀(𝛽 𝛀(𝛽 NUM cana-4541 124 7 ) ) PUNCT cana-4541 124 8 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 124 9 π‘š π‘š PROPN cana-4541 124 10 𝑖=0 𝑖=0 PROPN cana-4541 124 11 ( ( PUNCT cana-4541 124 12 𝛾1𝑆𝑖 𝛾1𝑆𝑖 PROPN cana-4541 124 13 βˆ’ βˆ’ PROPN cana-4541 125 1 ( ( PUNCT cana-4541 125 2 𝛿1 𝛿1 NOUN cana-4541 125 3 + + CCONJ cana-4541 125 4 𝛿2 𝛿2 NOUN cana-4541 125 5 + + CCONJ cana-4541 125 6 𝑑)𝐸𝑖 𝑑)𝐸𝑖 VERB cana-4541 125 7 ) ) PUNCT cana-4541 125 8 πΌπ‘š+1 πΌπ‘š+1 NOUN cana-4541 125 9 π‘ž π‘ž NOUN cana-4541 125 10 = = PUNCT cana-4541 125 11 𝐼0 𝐼0 PROPN cana-4541 125 12 + + CCONJ cana-4541 125 13 1 1 NUM cana-4541 125 14 𝛀(𝛽 𝛀(𝛽 NUM cana-4541 125 15 ) ) PUNCT cana-4541 125 16 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 125 17 π‘š π‘š PROPN cana-4541 125 18 𝑖=0 𝑖=0 PROPN cana-4541 125 19 ( ( PUNCT cana-4541 125 20 𝛿1𝐸𝑖 𝛿1𝐸𝑖 PROPN cana-4541 125 21 βˆ’ βˆ’ PROPN cana-4541 125 22 ( ( PUNCT cana-4541 125 23 𝜏1 𝜏1 NOUN cana-4541 125 24 + + CCONJ cana-4541 125 25 𝜏2 𝜏2 PROPN cana-4541 125 26 + + CCONJ cana-4541 125 27 𝜏3 𝜏3 NOUN cana-4541 125 28 + + CCONJ cana-4541 125 29 𝑑)𝐼𝑖 𝑑)𝐼𝑖 NOUN cana-4541 125 30 ) ) PUNCT cana-4541 125 31 πΊπ‘š+1 πΊπ‘š+1 VERB cana-4541 126 1 π‘ž π‘ž X cana-4541 126 2 = = PUNCT cana-4541 126 3 𝐺0 𝐺0 PROPN cana-4541 126 4 + + SYM cana-4541 126 5 1 1 NUM cana-4541 126 6 𝛀(𝛽 𝛀(𝛽 NUM cana-4541 126 7 ) ) PUNCT cana-4541 126 8 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 126 9 π‘š π‘š PROPN cana-4541 126 10 𝑖=0 𝑖=0 PROPN cana-4541 126 11 ( ( PUNCT cana-4541 126 12 𝛿2𝐸𝑖 𝛿2𝐸𝑖 PROPN cana-4541 126 13 + + CCONJ cana-4541 126 14 𝜏3𝐼𝑖 𝜏3𝐼𝑖 VERB cana-4541 126 15 βˆ’ βˆ’ PROPN cana-4541 126 16 ( ( PUNCT cana-4541 126 17 𝜁1 𝜁1 ADJ cana-4541 126 18 + + CCONJ cana-4541 126 19 𝜁2 𝜁2 NOUN cana-4541 126 20 + + CCONJ cana-4541 126 21 𝑑)𝐺𝑖 𝑑)𝐺𝑖 NOUN cana-4541 126 22 ) ) PUNCT cana-4541 126 23 π»π‘š+1 π»π‘š+1 VERB cana-4541 126 24 π‘ž π‘ž X cana-4541 126 25 = = PUNCT cana-4541 126 26 𝐻0 𝐻0 PROPN cana-4541 126 27 + + CCONJ cana-4541 126 28 1 1 NUM cana-4541 126 29 𝛀(𝛽 𝛀(𝛽 NUM cana-4541 126 30 ) ) PUNCT cana-4541 126 31 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 126 32 π‘š π‘š PROPN cana-4541 126 33 𝑖=0 𝑖=0 PROPN cana-4541 126 34 ( ( PUNCT cana-4541 126 35 𝜏1𝐼𝑖 𝜏1𝐼𝑖 NOUN cana-4541 126 36 + + CCONJ cana-4541 126 37 𝜁1𝐺𝑖 𝜁1𝐺𝑖 NOUN cana-4541 126 38 βˆ’ βˆ’ PROPN cana-4541 126 39 ( ( PUNCT cana-4541 126 40 πœ‰ πœ‰ NOUN cana-4541 126 41 + + X cana-4541 126 42 𝑑)𝐻𝑖 𝑑)𝐻𝑖 NOUN cana-4541 126 43 ) ) PUNCT cana-4541 126 44 π‘…π‘š+1 π‘…π‘š+1 ADJ cana-4541 126 45 π‘ž π‘ž X cana-4541 126 46 = = NOUN cana-4541 126 47 𝑅0 𝑅0 PROPN cana-4541 126 48 + + CCONJ cana-4541 126 49 1 1 NUM cana-4541 126 50 𝛀(𝛽 𝛀(𝛽 NUM cana-4541 126 51 ) ) PUNCT cana-4541 126 52 βˆ‘π‘π‘–,π‘š+1 βˆ‘π‘π‘–,π‘š+1 NOUN cana-4541 126 53 π‘š π‘š PROPN cana-4541 126 54 𝑖=0 𝑖=0 PROPN cana-4541 126 55 ( ( PUNCT cana-4541 126 56 πœ‰π»π‘– πœ‰π»π‘– NOUN cana-4541 126 57 + + CCONJ cana-4541 126 58 𝜁2𝐺𝑖 𝜁2𝐺𝑖 NOUN cana-4541 126 59 βˆ’ βˆ’ NOUN cana-4541 126 60 𝑑𝑅𝑖 𝑑𝑅𝑖 NOUN cana-4541 126 61 ) ) PUNCT cana-4541 126 62 } } PUNCT cana-4541 126 63 ( ( PUNCT cana-4541 126 64 10 10 NUM cana-4541 126 65 ) ) PUNCT cana-4541 126 66 𝑏𝑖,π‘š+1 𝑏𝑖,π‘š+1 NOUN cana-4541 127 1 = = PUNCT cana-4541 127 2 { { PUNCT cana-4541 127 3 𝑛𝛽 𝑛𝛽 INTJ cana-4541 127 4 βˆ’ βˆ’ PROPN cana-4541 127 5 ( ( PUNCT cana-4541 127 6 π‘š π‘š PROPN cana-4541 127 7 βˆ’ βˆ’ PROPN cana-4541 127 8 𝛽)(π‘š 𝛽)(π‘š PUNCT cana-4541 127 9 + + CCONJ cana-4541 127 10 1 1 NUM cana-4541 127 11 ) ) PUNCT cana-4541 127 12 , , PUNCT cana-4541 127 13 𝑖 𝑖 NOUN cana-4541 127 14 = = SYM cana-4541 127 15 0 0 PUNCT cana-4541 127 16 ( ( PUNCT cana-4541 127 17 𝑛 𝑛 PROPN cana-4541 127 18 βˆ’ βˆ’ PROPN cana-4541 127 19 𝑖 𝑖 SYM cana-4541 127 20 + + NOUN cana-4541 127 21 2)𝛽+1 2)𝛽+1 NUM cana-4541 127 22 + + CCONJ cana-4541 127 23 ( ( PUNCT cana-4541 127 24 𝑛 𝑛 DET cana-4541 127 25 βˆ’ βˆ’ PROPN cana-4541 127 26 𝑖)𝛽+1 𝑖)𝛽+1 PROPN cana-4541 127 27 , , PUNCT cana-4541 127 28 1 1 NUM cana-4541 127 29 ≀ ≀ NUM cana-4541 127 30 𝑖 𝑖 SYM cana-4541 127 31 ≀ ≀ NUM cana-4541 127 32 π‘š π‘š ADP cana-4541 127 33 βˆ’2(𝑛 βˆ’2(𝑛 NOUN cana-4541 127 34 βˆ’ βˆ’ PROPN cana-4541 127 35 𝑖 𝑖 SYM cana-4541 127 36 + + NOUN cana-4541 127 37 2)𝛽+1 2)𝛽+1 NUM cana-4541 127 38 , , PUNCT cana-4541 127 39 𝑖 𝑖 X cana-4541 127 40 = = PUNCT cana-4541 127 41 π‘š π‘š PROPN cana-4541 127 42 + + SYM cana-4541 127 43 1 1 NUM cana-4541 127 44 𝑐𝑖,π‘š+1 𝑐𝑖,π‘š+1 NOUN cana-4541 127 45 = = PUNCT cana-4541 127 46 π‘˜π›½ π‘˜π›½ PROPN cana-4541 127 47 𝛽 𝛽 NOUN cana-4541 127 48 ( ( PUNCT cana-4541 127 49 ( ( PUNCT cana-4541 127 50 𝑛 𝑛 PROPN cana-4541 127 51 βˆ’ βˆ’ PROPN cana-4541 127 52 𝑖 𝑖 SYM cana-4541 127 53 + + NUM cana-4541 127 54 2)𝛽 2)𝛽 NUM cana-4541 127 55 + + CCONJ cana-4541 127 56 ( ( PUNCT cana-4541 127 57 𝑛 𝑛 DET cana-4541 127 58 βˆ’ βˆ’ NOUN cana-4541 127 59 𝑖)𝛽 𝑖)𝛽 NUM cana-4541 127 60 ) ) PUNCT cana-4541 127 61 , , PUNCT cana-4541 127 62 1 1 NUM cana-4541 127 63 ≀ ≀ NUM cana-4541 127 64 𝑖 𝑖 SYM cana-4541 127 65 ≀ ≀ NOUN cana-4541 127 66 π‘š π‘š X cana-4541 127 67 } } PUNCT cana-4541 127 68 ( ( PUNCT cana-4541 127 69 11 11 NUM cana-4541 127 70 ) ) SYM cana-4541 127 71 5 5 NUM cana-4541 127 72 . . PUNCT cana-4541 127 73 simulation simulation NOUN cana-4541 127 74 : : PUNCT cana-4541 127 75 𝐚𝐭 𝐚𝐭 ADP cana-4541 127 76 𝜷 𝜷 X cana-4541 127 77 = = PUNCT cana-4541 127 78 𝟏 𝟏 NUM cana-4541 127 79 𝐚𝐭 𝐚𝐭 ADP cana-4541 127 80 𝜷 𝜷 NOUN cana-4541 127 81 = = PUNCT cana-4541 127 82 𝟎. 𝟎. PUNCT cana-4541 127 83 πŸ— πŸ— NUM cana-4541 127 84 figure figure NOUN cana-4541 127 85 1 1 NUM cana-4541 127 86 figure figure NOUN cana-4541 127 87 2 2 NUM cana-4541 127 88 communications communication NOUN cana-4541 127 89 on on ADP cana-4541 127 90 applied apply VERB cana-4541 127 91 nonlinear nonlinear ADJ cana-4541 127 92 analysis analysis NOUN cana-4541 127 93 issn issn NOUN cana-4541 127 94 : : PUNCT cana-4541 127 95 1074 1074 NUM cana-4541 127 96 - - PUNCT cana-4541 127 97 133x 133x NUM cana-4541 127 98 vol vol NOUN cana-4541 127 99 32 32 NUM cana-4541 127 100 no no NOUN cana-4541 127 101 . . PUNCT cana-4541 128 1 9s 9s NUM cana-4541 128 2 ( ( PUNCT cana-4541 128 3 2025 2025 NUM cana-4541 128 4 ) ) PUNCT cana-4541 128 5 2486 2486 NUM cana-4541 128 6 https://internationalpubls.com https://internationalpubls.com X cana-4541 129 1 𝐚𝐭 𝐚𝐭 ADP cana-4541 129 2 𝜷 𝜷 NOUN cana-4541 129 3 = = PUNCT cana-4541 129 4 𝟎. 𝟎. X cana-4541 129 5 πŸ– πŸ– NUM cana-4541 129 6 figure figure NOUN cana-4541 129 7 3 3 NUM cana-4541 129 8 in in ADP cana-4541 129 9 figure figure NOUN cana-4541 129 10 , , PUNCT cana-4541 129 11 blue blue ADJ cana-4541 129 12 line line NOUN cana-4541 129 13 represents represent VERB cana-4541 129 14 susceptible susceptible ADJ cana-4541 129 15 , , PUNCT cana-4541 129 16 orange orange ADJ cana-4541 129 17 dash dash NOUN cana-4541 129 18 line line NOUN cana-4541 129 19 represents represent VERB cana-4541 129 20 infectious infectious ADJ cana-4541 129 21 and and CCONJ cana-4541 129 22 pink pink ADJ cana-4541 129 23 dash dash NOUN cana-4541 129 24 line line NOUN cana-4541 129 25 represents represent VERB cana-4541 129 26 hospitalization hospitalization NOUN cana-4541 129 27 . . PUNCT cana-4541 130 1 in in ADP cana-4541 130 2 all all DET cana-4541 130 3 the the DET cana-4541 130 4 three three NUM cana-4541 130 5 figures figure NOUN cana-4541 130 6 , , PUNCT cana-4541 130 7 parameters parameter NOUN cana-4541 130 8 used use VERB cana-4541 130 9 are be AUX cana-4541 130 10 same same ADJ cana-4541 130 11 except except SCONJ cana-4541 130 12 𝛽. 𝛽. NOUN cana-4541 130 13 figure figure NOUN cana-4541 130 14 1 1 NUM cana-4541 130 15 shows show VERB cana-4541 130 16 sharp sharp ADJ cana-4541 130 17 fall fall NOUN cana-4541 130 18 in in ADP cana-4541 130 19 the the DET cana-4541 130 20 values value NOUN cana-4541 130 21 of of ADP cana-4541 130 22 s s PRON cana-4541 130 23 in in ADP cana-4541 130 24 a a DET cana-4541 130 25 relatively relatively ADV cana-4541 130 26 small small ADJ cana-4541 130 27 period period NOUN cana-4541 130 28 of of ADP cana-4541 130 29 time time NOUN cana-4541 130 30 compared compare VERB cana-4541 130 31 to to PART cana-4541 130 32 figure figure VERB cana-4541 130 33 2 2 NUM cana-4541 130 34 and and CCONJ cana-4541 130 35 figure figure VERB cana-4541 130 36 3 3 NUM cana-4541 130 37 . . PUNCT cana-4541 131 1 while while SCONJ cana-4541 131 2 , , PUNCT cana-4541 131 3 in in ADP cana-4541 131 4 figure figure NOUN cana-4541 131 5 1 1 NUM cana-4541 131 6 both both DET cana-4541 131 7 values value NOUN cana-4541 131 8 of of ADP cana-4541 131 9 i i PRON cana-4541 131 10 and and CCONJ cana-4541 131 11 v v NOUN cana-4541 131 12 show show VERB cana-4541 131 13 striking strike VERB cana-4541 131 14 rise rise NOUN cana-4541 131 15 during during ADP cana-4541 131 16 the the DET cana-4541 131 17 period period NOUN cana-4541 131 18 of of ADP cana-4541 131 19 30 30 NUM cana-4541 131 20 days day NOUN cana-4541 131 21 , , PUNCT cana-4541 131 22 there there PRON cana-4541 131 23 is be VERB cana-4541 131 24 no no DET cana-4541 131 25 notable notable ADJ cana-4541 131 26 changes change NOUN cana-4541 131 27 in in ADP cana-4541 131 28 the the DET cana-4541 131 29 value value NOUN cana-4541 131 30 of of ADP cana-4541 131 31 i i PRON cana-4541 131 32 and and CCONJ cana-4541 131 33 v v VERB cana-4541 131 34 in in ADP cana-4541 131 35 figure figure NOUN cana-4541 131 36 2 2 NUM cana-4541 131 37 and and CCONJ cana-4541 131 38 3 3 NUM cana-4541 131 39 . . PUNCT cana-4541 132 1 nevertheless nevertheless ADV cana-4541 132 2 , , PUNCT cana-4541 132 3 the the DET cana-4541 132 4 conversion conversion NOUN cana-4541 132 5 of of ADP cana-4541 132 6 a a DET cana-4541 132 7 classical classical ADJ cana-4541 132 8 model model NOUN cana-4541 132 9 into into ADP cana-4541 132 10 a a DET cana-4541 132 11 fractional fractional ADJ cana-4541 132 12 model model NOUN cana-4541 132 13 makes make VERB cana-4541 132 14 it it PRON cana-4541 132 15 highly highly ADV cana-4541 132 16 perceptive perceptive ADJ cana-4541 132 17 to to ADP cana-4541 132 18 the the DET cana-4541 132 19 order order NOUN cana-4541 132 20 of of ADP cana-4541 132 21 differentiation differentiation NOUN cana-4541 132 22 𝛽 𝛽 PROPN cana-4541 132 23 i.e i.e PROPN cana-4541 132 24 , , PUNCT cana-4541 132 25 a a DET cana-4541 132 26 minute minute NOUN cana-4541 132 27 change change NOUN cana-4541 132 28 can can AUX cana-4541 132 29 bring bring VERB cana-4541 132 30 about about ADP cana-4541 132 31 great great ADJ cana-4541 132 32 changes change NOUN cana-4541 132 33 in in ADP cana-4541 132 34 the the DET cana-4541 132 35 final final ADJ cana-4541 132 36 result result NOUN cana-4541 132 37 . . PUNCT cana-4541 133 1 it it PRON cana-4541 133 2 is be AUX cana-4541 133 3 evident evident ADJ cana-4541 133 4 from from ADP cana-4541 133 5 the the DET cana-4541 133 6 numerical numerical ADJ cana-4541 133 7 values value NOUN cana-4541 133 8 from from ADP cana-4541 133 9 figure figure NOUN cana-4541 133 10 2 2 NUM cana-4541 133 11 and and CCONJ cana-4541 133 12 3 3 NUM cana-4541 133 13 that that SCONJ cana-4541 133 14 it it PRON cana-4541 133 15 depends depend VERB cana-4541 133 16 continuously continuously ADV cana-4541 133 17 on on ADP cana-4541 133 18 the the DET cana-4541 133 19 fractional fractional ADJ cana-4541 133 20 derivative derivative ADJ cana-4541 133 21 𝛽. 𝛽. NOUN cana-4541 133 22 it it PRON cana-4541 133 23 is be AUX cana-4541 133 24 apparent apparent ADJ cana-4541 133 25 that that SCONJ cana-4541 133 26 figure figure NOUN cana-4541 133 27 2 2 NUM cana-4541 133 28 and and CCONJ cana-4541 133 29 3 3 NUM cana-4541 133 30 are be AUX cana-4541 133 31 more more ADV cana-4541 133 32 realistic realistic ADJ cana-4541 133 33 than than ADP cana-4541 133 34 figure figure NOUN cana-4541 133 35 1 1 NUM cana-4541 133 36 owing owe VERB cana-4541 133 37 to to ADP cana-4541 133 38 the the DET cana-4541 133 39 fact fact NOUN cana-4541 133 40 that that SCONJ cana-4541 133 41 it it PRON cana-4541 133 42 takes take VERB cana-4541 133 43 significant significant ADJ cana-4541 133 44 time time NOUN cana-4541 133 45 for for SCONJ cana-4541 133 46 the the DET cana-4541 133 47 rate rate NOUN cana-4541 133 48 of of ADP cana-4541 133 49 susceptibility susceptibility NOUN cana-4541 133 50 or or CCONJ cana-4541 133 51 recovery recovery NOUN cana-4541 133 52 to to PART cana-4541 133 53 decrease decrease VERB cana-4541 133 54 or or CCONJ cana-4541 133 55 increase increase VERB cana-4541 133 56 . . PUNCT cana-4541 134 1 6 6 X cana-4541 134 2 . . X cana-4541 134 3 reference reference NOUN cana-4541 134 4 : : PUNCT cana-4541 135 1 [ [ X cana-4541 135 2 1 1 X cana-4541 135 3 ] ] X cana-4541 135 4 al al PROPN cana-4541 135 5 - - PUNCT cana-4541 135 6 sulami sulami PROPN cana-4541 135 7 h. h. PROPN cana-4541 135 8 , , PUNCT cana-4541 135 9 el el PROPN cana-4541 135 10 - - PUNCT cana-4541 135 11 shahed shahe VERB cana-4541 135 12 m. m. NOUN cana-4541 135 13 , , PUNCT cana-4541 135 14 nieto nieto PROPN cana-4541 135 15 j. j. PROPN cana-4541 135 16 j. j. PROPN cana-4541 135 17 and and CCONJ cana-4541 135 18 shammakh shammakh VERB cana-4541 135 19 w. w. PROPN cana-4541 135 20 , , PUNCT cana-4541 135 21 β€œ " PUNCT cana-4541 135 22 on on ADP cana-4541 135 23 fractional fractional ADJ cana-4541 135 24 order order NOUN cana-4541 135 25 dengue dengue NOUN cana-4541 135 26 epidemic epidemic NOUN cana-4541 135 27 model model NOUN cana-4541 135 28 ” " PUNCT cana-4541 135 29 , , PUNCT cana-4541 135 30 mathematical mathematical ADJ cana-4541 135 31 problem problem NOUN cana-4541 135 32 in in ADP cana-4541 135 33 engineering engineering NOUN cana-4541 135 34 , , PUNCT cana-4541 135 35 2014,pp-1 2014,pp-1 NUM cana-4541 135 36 - - SYM cana-4541 135 37 6 6 NUM cana-4541 135 38 . . PUNCT cana-4541 136 1 [ [ X cana-4541 136 2 2 2 NUM cana-4541 136 3 ] ] PUNCT cana-4541 136 4 defterli defterli PROPN cana-4541 136 5 o. o. PROPN cana-4541 136 6 , , PUNCT cana-4541 136 7 β€œ " PUNCT cana-4541 136 8 modeling model VERB cana-4541 136 9 the the DET cana-4541 136 10 impact impact NOUN cana-4541 136 11 of of ADP cana-4541 136 12 temperature temperature NOUN cana-4541 136 13 on on ADP cana-4541 136 14 fractional fractional ADJ cana-4541 136 15 order order NOUN cana-4541 136 16 dengue dengue NOUN cana-4541 136 17 model model NOUN cana-4541 136 18 with with ADP cana-4541 136 19 vertical vertical ADJ cana-4541 136 20 transmission transmission NOUN cana-4541 136 21 ” " PUNCT cana-4541 136 22 , , PUNCT cana-4541 136 23 an an DET cana-4541 136 24 international international ADJ cana-4541 136 25 journal journal NOUN cana-4541 136 26 of of ADP cana-4541 136 27 optimization optimization NOUN cana-4541 136 28 and and CCONJ cana-4541 136 29 control control NOUN cana-4541 136 30 : : PUNCT cana-4541 136 31 theories theory NOUN cana-4541 136 32 & & CCONJ cana-4541 136 33 applications application NOUN cana-4541 136 34 , , PUNCT cana-4541 136 35 vol vol NOUN cana-4541 136 36 . . PUNCT cana-4541 136 37 10(1 10(1 NUM cana-4541 136 38 ) ) PUNCT cana-4541 136 39 , , PUNCT cana-4541 136 40 2020 2020 NUM cana-4541 136 41 pp-85 pp-85 PROPN cana-4541 136 42 - - PUNCT cana-4541 136 43 93 93 NUM cana-4541 136 44 . . PUNCT cana-4541 137 1 [ [ X cana-4541 137 2 3 3 X cana-4541 137 3 ] ] X cana-4541 137 4 gorenflo gorenflo NOUN cana-4541 137 5 r. r. PROPN cana-4541 137 6 , , PUNCT cana-4541 137 7 loutschko loutschko PROPN cana-4541 137 8 j. j. PROPN cana-4541 137 9 and and CCONJ cana-4541 137 10 luchko luchko PROPN cana-4541 137 11 y. y. PROPN cana-4541 137 12 , , PUNCT cana-4541 137 13 β€œ " PUNCT cana-4541 137 14 computation computation NOUN cana-4541 137 15 of of ADP cana-4541 137 16 the the DET cana-4541 137 17 mittagelefflerfunction mittagelefflerfunction NOUN cana-4541 137 18 𝐸𝛼,𝛽(𝑧 𝐸𝛼,𝛽(𝑧 PROPN cana-4541 137 19 ) ) PUNCT cana-4541 137 20 and and CCONJ cana-4541 137 21 its its PRON cana-4541 137 22 derivatives derivative NOUN cana-4541 137 23 ” " PUNCT cana-4541 137 24 , , PUNCT cana-4541 137 25 [ [ X cana-4541 137 26 4 4 X cana-4541 137 27 ] ] X cana-4541 137 28 hamdan hamdan PROPN cana-4541 137 29 n. n. PROPN cana-4541 137 30 i. i. PROPN cana-4541 137 31 and and CCONJ cana-4541 137 32 kilicman kilicman PROPN cana-4541 137 33 a. a. PROPN cana-4541 137 34 , , PUNCT cana-4541 137 35 β€œ " PUNCT cana-4541 137 36 a a DET cana-4541 137 37 fractional fractional ADJ cana-4541 137 38 order order NOUN cana-4541 137 39 sir sir NOUN cana-4541 137 40 epidemic epidemic NOUN cana-4541 137 41 model model NOUN cana-4541 137 42 for for ADP cana-4541 137 43 dengue dengue NOUN cana-4541 137 44 transmission transmission NOUN cana-4541 137 45 ” " PUNCT cana-4541 137 46 , , PUNCT cana-4541 137 47 chaos chaos NOUN cana-4541 137 48 , , PUNCT cana-4541 137 49 solitons soliton NOUN cana-4541 137 50 and and CCONJ cana-4541 137 51 fractals fractal NOUN cana-4541 137 52 114(2018 114(2018 NOUN cana-4541 137 53 ) ) PUNCT cana-4541 137 54 , , PUNCT cana-4541 137 55 pp-55 pp-55 NOUN cana-4541 137 56 - - PUNCT cana-4541 137 57 62 62 NUM cana-4541 137 58 . . PUNCT cana-4541 138 1 [ [ X cana-4541 138 2 5 5 X cana-4541 138 3 ] ] PUNCT cana-4541 138 4 kilbas kilbas PROPN cana-4541 138 5 a. a. PROPN cana-4541 138 6 a. a. PROPN cana-4541 138 7 , , PUNCT cana-4541 138 8 srivastava srivastava PROPN cana-4541 138 9 h. h. PROPN cana-4541 138 10 m. m. PROPN cana-4541 138 11 and and CCONJ cana-4541 138 12 trujillo trujillo PROPN cana-4541 138 13 j. j. PROPN cana-4541 138 14 j. j. PROPN cana-4541 138 15 , , PUNCT cana-4541 138 16 theory theory NOUN cana-4541 138 17 and and CCONJ cana-4541 138 18 application application NOUN cana-4541 138 19 fractional fractional ADJ cana-4541 138 20 differential differential NOUN cana-4541 138 21 equation equation NOUN cana-4541 138 22 , , PUNCT cana-4541 138 23 elseviesr elseviesr PROPN cana-4541 138 24 , , PUNCT cana-4541 138 25 amsterclam amsterclam VERB cana-4541 138 26 the the DET cana-4541 138 27 netherlands netherlands PROPN cana-4541 138 28 , , PUNCT cana-4541 138 29 2006 2006 NUM cana-4541 138 30 . . PUNCT cana-4541 139 1 [ [ X cana-4541 139 2 6 6 NUM cana-4541 139 3 ] ] X cana-4541 139 4 kumari kumari PROPN cana-4541 139 5 k. k. PROPN cana-4541 139 6 k. k. PROPN cana-4541 139 7 , , PUNCT cana-4541 139 8 singh singh PROPN cana-4541 139 9 a.k a.k PROPN cana-4541 139 10 . . PROPN cana-4541 139 11 , , PUNCT cana-4541 139 12 mahto mahto PROPN cana-4541 139 13 . . PUNCT cana-4541 140 1 s. s. PROPN cana-4541 140 2 , , PUNCT cana-4541 140 3 β€œ " PUNCT cana-4541 140 4 mathematical mathematical ADJ cana-4541 140 5 models model NOUN cana-4541 140 6 for for ADP cana-4541 140 7 stability stability NOUN cana-4541 140 8 in in ADP cana-4541 140 9 computer computer NOUN cana-4541 140 10 network network NOUN cana-4541 140 11 ” " PUNCT cana-4541 140 12 , , PUNCT cana-4541 140 13 journal journal NOUN cana-4541 140 14 of of ADP cana-4541 140 15 computer computer NOUN cana-4541 140 16 and and CCONJ cana-4541 140 17 mathematical mathematical ADJ cana-4541 140 18 sciences science NOUN cana-4541 140 19 , , PUNCT cana-4541 140 20 vol.10(1 vol.10(1 ADJ cana-4541 140 21 ) ) PUNCT cana-4541 140 22 , , PUNCT cana-4541 140 23 january january PROPN cana-4541 140 24 2019 2019 NUM cana-4541 140 25 , , PUNCT cana-4541 140 26 pp.9298 pp.9298 X cana-4541 140 27 . . PUNCT cana-4541 141 1 [ [ X cana-4541 141 2 7 7 X cana-4541 141 3 ] ] X cana-4541 141 4 kumari kumari PROPN cana-4541 141 5 k. k. PROPN cana-4541 141 6 k. k. PROPN cana-4541 141 7 , , PUNCT cana-4541 141 8 sinhg sinhg PROPN cana-4541 141 9 a.k a.k PROPN cana-4541 141 10 . . PROPN cana-4541 141 11 , , PUNCT cana-4541 141 12 mahto mahto PROPN cana-4541 141 13 . . PUNCT cana-4541 142 1 s. s. PROPN cana-4541 142 2 , , PUNCT cana-4541 142 3 β€œ " PUNCT cana-4541 142 4 time time NOUN cana-4541 142 5 delay delay VERB cana-4541 142 6 seirs seirs PROPN cana-4541 142 7 e e PROPN cana-4541 142 8 - - ADJ cana-4541 142 9 epidemic epidemic ADJ cana-4541 142 10 model model NOUN cana-4541 142 11 for for ADP cana-4541 142 12 computer computer NOUN cana-4541 142 13 network network NOUN cana-4541 142 14 ” " PUNCT cana-4541 142 15 , , PUNCT cana-4541 142 16 international international ADJ cana-4541 142 17 journal journal NOUN cana-4541 142 18 of of ADP cana-4541 142 19 mathematical mathematical ADJ cana-4541 142 20 archive-9(2 archive-9(2 NOUN cana-4541 142 21 ) ) PUNCT cana-4541 142 22 , , PUNCT cana-4541 142 23 2018 2018 NUM cana-4541 142 24 , , PUNCT cana-4541 142 25 pp.265 pp.265 NOUN cana-4541 142 26 - - PUNCT cana-4541 142 27 273 273 NUM cana-4541 142 28 [ [ NOUN cana-4541 142 29 8 8 NUM cana-4541 142 30 ] ] SYM cana-4541 142 31 podlubny podlubny NOUN cana-4541 142 32 i. i. PROPN cana-4541 142 33 , , PUNCT cana-4541 142 34 fractional fractional ADJ cana-4541 142 35 differential differential NOUN cana-4541 142 36 equations equation NOUN cana-4541 142 37 , , PUNCT cana-4541 142 38 academic academic ADJ cana-4541 142 39 press press NOUN cana-4541 142 40 , , PUNCT cana-4541 142 41 new new PROPN cana-4541 142 42 york york PROPN cana-4541 142 43 , , PUNCT cana-4541 142 44 ny ny PROPN cana-4541 142 45 , , PUNCT cana-4541 142 46 usa usa PROPN cana-4541 142 47 , , PUNCT cana-4541 142 48 1999 1999 NUM cana-4541 142 49 . . PUNCT