id sid tid token lemma pos cana-4443 1 1 communications communication NOUN cana-4443 1 2 on on ADP cana-4443 1 3 applied apply VERB cana-4443 1 4 nonlinear nonlinear ADJ cana-4443 1 5 analysis analysis NOUN cana-4443 1 6 issn issn NOUN cana-4443 1 7 : : PUNCT cana-4443 1 8 1074 1074 NUM cana-4443 1 9 - - PUNCT cana-4443 1 10 133x 133x NUM cana-4443 1 11 vol vol NOUN cana-4443 1 12 32 32 NUM cana-4443 1 13 no no NOUN cana-4443 1 14 . . PUNCT cana-4443 2 1 9s 9s NUM cana-4443 2 2 ( ( PUNCT cana-4443 2 3 2025 2025 NUM cana-4443 2 4 ) ) PUNCT cana-4443 2 5 2023 2023 NUM cana-4443 3 1 https://internationalpubls.com https://internationalpubls.com X cana-4443 3 2 stability stability NOUN cana-4443 3 3 of of ADP cana-4443 3 4 malicious malicious ADJ cana-4443 3 5 object object NOUN cana-4443 3 6 in in ADP cana-4443 3 7 sieqar sieqar NOUN cana-4443 3 8 model model NOUN cana-4443 3 9 kaveri kaveri PROPN cana-4443 3 10 kanchan kanchan PROPN cana-4443 3 11 kumari kumari PROPN cana-4443 3 12 1 1 NUM cana-4443 3 13 , , PUNCT cana-4443 3 14 ashish ashish PROPN cana-4443 3 15 kumar kumar PROPN cana-4443 3 16 jha2 jha2 PROPN cana-4443 3 17 1research 1research PROPN cana-4443 3 18 scholar scholar NOUN cana-4443 3 19 , , PUNCT cana-4443 3 20 university university NOUN cana-4443 3 21 department department NOUN cana-4443 3 22 of of ADP cana-4443 3 23 mathematics mathematics PROPN cana-4443 3 24 , , PUNCT cana-4443 3 25 ranchi ranchi PROPN cana-4443 3 26 university university PROPN cana-4443 3 27 , , PUNCT cana-4443 3 28 ranchi ranchi PROPN cana-4443 3 29 2associate 2associate PROPN cana-4443 3 30 professor professor NOUN cana-4443 3 31 , , PUNCT cana-4443 3 32 , , PUNCT cana-4443 3 33 university university NOUN cana-4443 3 34 department department NOUN cana-4443 3 35 of of ADP cana-4443 3 36 mathematics mathematics PROPN cana-4443 3 37 , , PUNCT cana-4443 3 38 ranchi ranchi PROPN cana-4443 3 39 university university PROPN cana-4443 3 40 , , PUNCT cana-4443 3 41 ranchi ranchi PROPN cana-4443 3 42 1kanchan_kaveri4@yahoo.in 1kanchan_kaveri4@yahoo.in NUM cana-4443 3 43 , , PUNCT cana-4443 4 1 2jhaak25@gmail.com 2jhaak25@gmail.com NUM cana-4443 5 1 article article NOUN cana-4443 5 2 history history NOUN cana-4443 5 3 : : PUNCT cana-4443 5 4 received receive VERB cana-4443 5 5 : : PUNCT cana-4443 5 6 12 12 NUM cana-4443 5 7 - - SYM cana-4443 5 8 01 01 NUM cana-4443 5 9 - - PUNCT cana-4443 5 10 2025 2025 NUM cana-4443 5 11 revised revise VERB cana-4443 5 12 : : PUNCT cana-4443 5 13 15 15 NUM cana-4443 5 14 - - NUM cana-4443 5 15 02 02 NUM cana-4443 5 16 - - PUNCT cana-4443 5 17 2025 2025 NUM cana-4443 5 18 accepted accept VERB cana-4443 5 19 : : PUNCT cana-4443 5 20 01 01 NUM cana-4443 5 21 - - SYM cana-4443 5 22 03 03 NUM cana-4443 5 23 - - PUNCT cana-4443 5 24 2025 2025 NUM cana-4443 5 25 abstract abstract NOUN cana-4443 5 26 : : PUNCT cana-4443 5 27 the the DET cana-4443 5 28 proposed propose VERB cana-4443 5 29 model model NOUN cana-4443 5 30 is be AUX cana-4443 5 31 sieqar sieqar VERB cana-4443 5 32 ( ( PUNCT cana-4443 5 33 susceptible susceptible ADJ cana-4443 5 34 - - PUNCT cana-4443 5 35 infected infect VERB cana-4443 5 36 - - PUNCT cana-4443 5 37 exposed expose VERB cana-4443 5 38 - - PUNCT cana-4443 5 39 quarantine quarantine NOUN cana-4443 5 40 - - PUNCT cana-4443 5 41 antidotalrecovered antidotalrecovere VERB cana-4443 5 42 ) ) PUNCT cana-4443 5 43 which which PRON cana-4443 5 44 is be AUX cana-4443 5 45 extension extension NOUN cana-4443 5 46 of of ADP cana-4443 5 47 sair sair PROPN cana-4443 5 48 model model NOUN cana-4443 5 49 . . PUNCT cana-4443 6 1 in in ADP cana-4443 6 2 this this DET cana-4443 6 3 model model NOUN cana-4443 6 4 we we PRON cana-4443 6 5 discussed discuss VERB cana-4443 6 6 basic basic ADJ cana-4443 6 7 reproduction reproduction NOUN cana-4443 6 8 number number NOUN cana-4443 6 9 for for ADP cana-4443 6 10 mfe mfe PROPN cana-4443 6 11 ( ( PUNCT cana-4443 6 12 malware malware NOUN cana-4443 6 13 free free ADJ cana-4443 6 14 equilibrium equilibrium NOUN cana-4443 6 15 ) ) PUNCT cana-4443 6 16 point point NOUN cana-4443 6 17 . . PUNCT cana-4443 7 1 we we PRON cana-4443 7 2 discussed discuss VERB cana-4443 7 3 about about ADP cana-4443 7 4 local local ADJ cana-4443 7 5 stability stability NOUN cana-4443 7 6 at at ADP cana-4443 7 7 that that DET cana-4443 7 8 point point NOUN cana-4443 7 9 , , PUNCT cana-4443 7 10 also also ADV cana-4443 7 11 endemic endemic ADJ cana-4443 7 12 equilibrium equilibrium NOUN cana-4443 7 13 point point NOUN cana-4443 7 14 ids id NOUN cana-4443 7 15 discussed discuss VERB cana-4443 7 16 . . PUNCT cana-4443 8 1 keywords keyword NOUN cana-4443 8 2 : : PUNCT cana-4443 8 3 quarantine quarantine NOUN cana-4443 8 4 , , PUNCT cana-4443 8 5 antidotal antidotal ADJ cana-4443 8 6 , , PUNCT cana-4443 8 7 malware malware NOUN cana-4443 8 8 free free ADJ cana-4443 8 9 equilibrium equilibrium NOUN cana-4443 8 10 Μ§endemic Μ§endemic ADP cana-4443 8 11 equilibrium equilibrium NOUN cana-4443 8 12 , , PUNCT cana-4443 8 13 reproduction reproduction NOUN cana-4443 8 14 number number NOUN cana-4443 8 15 .. .. PUNCT cana-4443 9 1 1 1 X cana-4443 9 2 . . X cana-4443 9 3 introduction introduction NOUN cana-4443 9 4 : : PUNCT cana-4443 9 5 computer computer NOUN cana-4443 9 6 virus virus NOUN cana-4443 9 7 is be AUX cana-4443 9 8 nothing nothing PRON cana-4443 9 9 but but CCONJ cana-4443 9 10 it it PRON cana-4443 9 11 is be AUX cana-4443 9 12 a a DET cana-4443 9 13 code code NOUN cana-4443 9 14 . . PUNCT cana-4443 10 1 malware malware NOUN cana-4443 10 2 is be AUX cana-4443 10 3 computer computer NOUN cana-4443 10 4 program program NOUN cana-4443 10 5 which which PRON cana-4443 10 6 destroy destroy VERB cana-4443 10 7 the the DET cana-4443 10 8 important important ADJ cana-4443 10 9 files file NOUN cana-4443 10 10 from from ADP cana-4443 10 11 computer computer NOUN cana-4443 10 12 . . PUNCT cana-4443 11 1 computer computer NOUN cana-4443 11 2 virus virus NOUN cana-4443 11 3 is be AUX cana-4443 11 4 similar similar ADJ cana-4443 11 5 like like ADP cana-4443 11 6 biological biological NOUN cana-4443 11 7 virus[1 virus[1 NUM cana-4443 11 8 ] ] PUNCT cana-4443 11 9 . . PUNCT cana-4443 12 1 more more ADJ cana-4443 12 2 than than ADP cana-4443 12 3 1000 1000 NUM cana-4443 12 4 papers paper NOUN cana-4443 12 5 are be AUX cana-4443 12 6 discussed discuss VERB cana-4443 12 7 for for ADP cana-4443 12 8 many many ADJ cana-4443 12 9 type type NOUN cana-4443 12 10 of of ADP cana-4443 12 11 model model NOUN cana-4443 12 12 [ [ X cana-4443 12 13 2 2 NUM cana-4443 12 14 - - SYM cana-4443 12 15 3 3 NUM cana-4443 12 16 ] ] PUNCT cana-4443 12 17 . . PUNCT cana-4443 13 1 common common ADJ cana-4443 13 2 models model NOUN cana-4443 13 3 are be AUX cana-4443 13 4 susceptible susceptible ADJ cana-4443 13 5 infectioussusceptible infectioussusceptible ADJ cana-4443 13 6 ( ( PUNCT cana-4443 13 7 sis sis NOUN cana-4443 13 8 ) ) PUNCT cana-4443 13 9 model[4 model[4 PROPN cana-4443 13 10 - - PUNCT cana-4443 13 11 5 5 NUM cana-4443 13 12 ] ] PUNCT cana-4443 13 13 , , PUNCT cana-4443 13 14 susceptibleinfectedrecovered susceptibleinfectedrecovere VERB cana-4443 13 15 ( ( PUNCT cana-4443 13 16 sir sir NOUN cana-4443 13 17 ) ) PUNCT cana-4443 13 18 model[6 model[6 PROPN cana-4443 13 19 - - SYM cana-4443 13 20 7 7 NUM cana-4443 13 21 ] ] PUNCT cana-4443 13 22 , , PUNCT cana-4443 13 23 kaveri kaveri PROPN cana-4443 13 24 et.al.[8,9 et.al.[8,9 PROPN cana-4443 13 25 ] ] PUNCT cana-4443 13 26 discussed discuss VERB cana-4443 13 27 the the DET cana-4443 13 28 different different ADJ cana-4443 13 29 type type NOUN cana-4443 13 30 of of ADP cana-4443 13 31 model model NOUN cana-4443 13 32 . . PUNCT cana-4443 14 1 2000 2000 NUM cana-4443 14 2 clasification clasification NOUN cana-4443 14 3 : : PUNCT cana-4443 14 4 92d30 92d30 NUM cana-4443 14 5 2 2 NUM cana-4443 14 6 . . PUNCT cana-4443 14 7 formulation formulation NOUN cana-4443 14 8 of of ADP cana-4443 14 9 model model NOUN cana-4443 14 10 : : PUNCT cana-4443 14 11 mailto:kanchan_kaveri4@yahoo.in mailto:kanchan_kaveri4@yahoo.in PUNCT cana-4443 14 12 mailto:jhaak25@gmail.com mailto:jhaak25@gmail.com PROPN cana-4443 14 13 communications communication NOUN cana-4443 14 14 on on ADP cana-4443 14 15 applied apply VERB cana-4443 14 16 nonlinear nonlinear ADJ cana-4443 14 17 analysis analysis NOUN cana-4443 14 18 issn issn NOUN cana-4443 14 19 : : PUNCT cana-4443 14 20 1074 1074 NUM cana-4443 14 21 - - PUNCT cana-4443 14 22 133x 133x NUM cana-4443 14 23 vol vol NOUN cana-4443 14 24 32 32 NUM cana-4443 14 25 no no NOUN cana-4443 14 26 . . PUNCT cana-4443 15 1 9s 9s NUM cana-4443 15 2 ( ( PUNCT cana-4443 15 3 2025 2025 NUM cana-4443 15 4 ) ) PUNCT cana-4443 15 5 2024 2024 NUM cana-4443 16 1 https://internationalpubls.com https://internationalpubls.com X cana-4443 16 2 𝑑𝑆 𝑑𝑆 ADJ cana-4443 16 3 𝑑𝑑 𝑑𝑑 ADP cana-4443 16 4 = = PROPN cana-4443 16 5 𝑇 𝑇 PROPN cana-4443 16 6 βˆ’ βˆ’ PROPN cana-4443 16 7 𝛽𝑆𝐼 𝛽𝑆𝐼 NOUN cana-4443 16 8 + + NUM cana-4443 16 9 𝛼𝐸 𝛼𝐸 NOUN cana-4443 16 10 + + CCONJ cana-4443 16 11 𝛾𝑅 𝛾𝑅 PROPN cana-4443 16 12 βˆ’ βˆ’ PROPN cana-4443 16 13 πœ‡π‘† πœ‡π‘† PROPN cana-4443 16 14 𝑑𝐼 𝑑𝐼 NOUN cana-4443 16 15 𝑑𝑑 𝑑𝑑 ADP cana-4443 16 16 = = PROPN cana-4443 16 17 𝛽𝑆𝐼 𝛽𝑆𝐼 PROPN cana-4443 16 18 + + PROPN cana-4443 16 19 𝛿𝐸 𝛿𝐸 PROPN cana-4443 16 20 βˆ’ βˆ’ PROPN cana-4443 16 21 ( ( PUNCT cana-4443 16 22 πœ‡ πœ‡ X cana-4443 16 23 + + X cana-4443 16 24 πœ“ πœ“ NOUN cana-4443 16 25 + + CCONJ cana-4443 16 26 𝜎)𝐼 𝜎)𝐼 ADJ cana-4443 16 27 𝑑𝐸 𝑑𝐸 ADJ cana-4443 16 28 𝑑𝑑 𝑑𝑑 ADP cana-4443 16 29 = = PROPN cana-4443 16 30 𝐡 𝐡 PROPN cana-4443 16 31 βˆ’ βˆ’ PROPN cana-4443 16 32 ( ( PUNCT cana-4443 16 33 𝛼 𝛼 X cana-4443 16 34 + + X cana-4443 16 35 πœ‡ πœ‡ ADP cana-4443 16 36 + + NOUN cana-4443 16 37 𝛿 𝛿 ADJ cana-4443 16 38 + + CCONJ cana-4443 16 39 πœƒ)𝐸 πœƒ)𝐸 ADJ cana-4443 16 40 𝑑𝑄 𝑑𝑄 ADJ cana-4443 16 41 𝑑𝑑 𝑑𝑑 ADP cana-4443 16 42 = = PROPN cana-4443 16 43 𝜎𝐼 𝜎𝐼 PROPN cana-4443 16 44 βˆ’ βˆ’ PROPN cana-4443 16 45 ( ( PUNCT cana-4443 16 46 πœ‰ πœ‰ NOUN cana-4443 16 47 + + X cana-4443 16 48 πœ‡ πœ‡ X cana-4443 16 49 + + NOUN cana-4443 16 50 πœ‚)𝑄 πœ‚)𝑄 ADJ cana-4443 16 51 𝑑𝐴 𝑑𝐴 NOUN cana-4443 16 52 𝑑𝑑 𝑑𝑑 ADP cana-4443 16 53 = = PUNCT cana-4443 16 54 πœ‰π‘„ πœ‰π‘„ PROPN cana-4443 16 55 + + CCONJ cana-4443 16 56 πœƒπΈ πœƒπΈ NOUN cana-4443 16 57 βˆ’ βˆ’ PROPN cana-4443 16 58 ( ( PUNCT cana-4443 16 59 πœ‡ πœ‡ ADP cana-4443 16 60 + + X cana-4443 16 61 πœ™)𝐴 πœ™)𝐴 X cana-4443 16 62 𝑑𝑅 𝑑𝑅 VERB cana-4443 16 63 𝑑𝑑 𝑑𝑑 ADP cana-4443 16 64 = = SYM cana-4443 16 65 πœ‚π‘„ πœ‚π‘„ PROPN cana-4443 17 1 + + CCONJ cana-4443 17 2 πœ“πΌ πœ“πΌ ADJ cana-4443 17 3 + + CCONJ cana-4443 17 4 πœ™π΄ πœ™π΄ NOUN cana-4443 17 5 βˆ’ βˆ’ NOUN cana-4443 17 6 ( ( PUNCT cana-4443 17 7 πœ‡ πœ‡ X cana-4443 17 8 + + X cana-4443 17 9 𝛾)𝑅 𝛾)𝑅 X cana-4443 17 10 } } PUNCT cana-4443 17 11 … … PUNCT cana-4443 17 12 ( ( PUNCT cana-4443 17 13 i i NOUN cana-4443 17 14 ) ) PUNCT cana-4443 17 15 all all DET cana-4443 17 16 parameters parameter NOUN cana-4443 17 17 are be AUX cana-4443 17 18 positive positive ADJ cana-4443 17 19 . . PUNCT cana-4443 18 1 i.e. i.e. X cana-4443 18 2 , , PUNCT cana-4443 18 3 𝑆 𝑆 PROPN cana-4443 18 4 β‰₯ β‰₯ NOUN cana-4443 18 5 0 0 NUM cana-4443 18 6 , , PUNCT cana-4443 18 7 𝐼 𝐼 ADP cana-4443 18 8 β‰₯ β‰₯ NOUN cana-4443 18 9 0 0 NUM cana-4443 18 10 , , PUNCT cana-4443 18 11 𝐸 𝐸 PROPN cana-4443 18 12 β‰₯ β‰₯ NOUN cana-4443 18 13 0 0 NUM cana-4443 18 14 , , PUNCT cana-4443 18 15 𝑄 𝑄 PRON cana-4443 18 16 β‰₯ β‰₯ NOUN cana-4443 18 17 0 0 NUM cana-4443 18 18 , , PUNCT cana-4443 18 19 𝐴 𝐴 PROPN cana-4443 18 20 β‰₯ β‰₯ NUM cana-4443 18 21 0 0 NUM cana-4443 18 22 , , PUNCT cana-4443 18 23 𝑅 𝑅 NOUN cana-4443 18 24 β‰₯ β‰₯ NOUN cana-4443 18 25 0 0 NUM cana-4443 18 26 . . PUNCT cana-4443 19 1 ∴ ∴ NOUN cana-4443 19 2 total total ADJ cana-4443 19 3 population population NOUN cana-4443 19 4 𝑁 𝑁 PROPN cana-4443 19 5 = = PUNCT cana-4443 19 6 𝑆 𝑆 PROPN cana-4443 19 7 + + CCONJ cana-4443 19 8 𝐼 𝐼 PROPN cana-4443 19 9 + + CCONJ cana-4443 19 10 𝐸 𝐸 PROPN cana-4443 19 11 + + CCONJ cana-4443 19 12 𝑄 𝑄 PROPN cana-4443 19 13 + + CCONJ cana-4443 19 14 𝐴 𝐴 PROPN cana-4443 19 15 + + CCONJ cana-4443 19 16 𝑅. 𝑅. ADV cana-4443 19 17 then then ADV cana-4443 19 18 , , PUNCT cana-4443 19 19 𝑑𝑁 𝑑𝑁 PROPN cana-4443 19 20 𝑑𝑑 𝑑𝑑 ADP cana-4443 19 21 = = PUNCT cana-4443 19 22 𝑑𝑆 𝑑𝑆 PROPN cana-4443 19 23 𝑑𝑑 𝑑𝑑 ADP cana-4443 19 24 + + CCONJ cana-4443 19 25 𝑑𝐼 𝑑𝐼 ADJ cana-4443 19 26 𝑑𝑑 𝑑𝑑 ADP cana-4443 19 27 + + CCONJ cana-4443 19 28 𝑑𝐸 𝑑𝐸 ADV cana-4443 19 29 𝑑𝑑 𝑑𝑑 ADP cana-4443 19 30 + + ADV cana-4443 19 31 𝑑𝑄 𝑑𝑄 VERB cana-4443 19 32 𝑑𝑑 𝑑𝑑 ADP cana-4443 19 33 + + ADJ cana-4443 19 34 𝑑𝐴 𝑑𝐴 NUM cana-4443 19 35 𝑑𝑑 𝑑𝑑 ADP cana-4443 19 36 + + NOUN cana-4443 19 37 𝑑𝑅 𝑑𝑅 VERB cana-4443 19 38 𝑑𝑑 𝑑𝑑 ADP cana-4443 19 39 . . PUNCT cana-4443 20 1 β‡’ β‡’ PROPN cana-4443 20 2 𝑑𝑁 𝑑𝑁 PROPN cana-4443 20 3 𝑑𝑑 𝑑𝑑 ADP cana-4443 20 4 = = SYM cana-4443 20 5 𝑇 𝑇 PROPN cana-4443 20 6 + + CCONJ cana-4443 20 7 𝐡 𝐡 NOUN cana-4443 20 8 βˆ’ βˆ’ PROPN cana-4443 20 9 πœ‡π‘ πœ‡π‘ NOUN cana-4443 20 10 solving solve VERB cana-4443 20 11 lim lim PROPN cana-4443 20 12 π‘‘β†’βˆž π‘‘β†’βˆž NUM cana-4443 20 13 sup(𝑆 sup(𝑆 PROPN cana-4443 21 1 + + CCONJ cana-4443 21 2 𝐼 𝐼 PROPN cana-4443 21 3 + + CCONJ cana-4443 21 4 𝐸 𝐸 PROPN cana-4443 21 5 + + CCONJ cana-4443 21 6 𝑄 𝑄 PROPN cana-4443 21 7 + + CCONJ cana-4443 21 8 𝐴 𝐴 PROPN cana-4443 21 9 + + CCONJ cana-4443 21 10 𝑅 𝑅 PROPN cana-4443 21 11 ) ) PUNCT cana-4443 21 12 ≀ ≀ PUNCT cana-4443 21 13 𝑇 𝑇 PROPN cana-4443 21 14 + + CCONJ cana-4443 21 15 𝐡 𝐡 NOUN cana-4443 21 16 πœ‡ πœ‡ ADP cana-4443 21 17 hence hence ADV cana-4443 21 18 the the DET cana-4443 21 19 feasible feasible ADJ cana-4443 21 20 region region NOUN cana-4443 21 21 for for ADP cana-4443 21 22 system system NOUN cana-4443 21 23 ( ( PUNCT cana-4443 21 24 1 1 X cana-4443 21 25 ) ) PUNCT cana-4443 21 26 is be AUX cana-4443 21 27 , , PUNCT cana-4443 21 28 Ο‰ Ο‰ PROPN cana-4443 21 29 = = SYM cana-4443 21 30 { { PUNCT cana-4443 21 31 ( ( PUNCT cana-4443 21 32 𝑆 𝑆 PROPN cana-4443 21 33 , , PUNCT cana-4443 21 34 𝐼 𝐼 PROPN cana-4443 21 35 , , PUNCT cana-4443 21 36 𝐸 𝐸 PROPN cana-4443 21 37 , , PUNCT cana-4443 21 38 𝑄 𝑄 PROPN cana-4443 21 39 , , PUNCT cana-4443 21 40 𝐴 𝐴 PROPN cana-4443 21 41 , , PUNCT cana-4443 21 42 𝑅 𝑅 PROPN cana-4443 21 43 ): ): PUNCT cana-4443 21 44 𝑆 𝑆 PROPN cana-4443 21 45 , , PUNCT cana-4443 21 46 𝐼 𝐼 PROPN cana-4443 21 47 , , PUNCT cana-4443 21 48 𝐸 𝐸 PROPN cana-4443 21 49 , , PUNCT cana-4443 21 50 𝑄 𝑄 PROPN cana-4443 21 51 , , PUNCT cana-4443 21 52 𝐴 𝐴 PROPN cana-4443 21 53 , , PUNCT cana-4443 21 54 𝑅 𝑅 PROPN cana-4443 21 55 β‰₯ β‰₯ NOUN cana-4443 21 56 0 0 NUM cana-4443 21 57 ; ; PUNCT cana-4443 21 58 𝑆 𝑆 PROPN cana-4443 21 59 + + CCONJ cana-4443 21 60 𝐼 𝐼 PROPN cana-4443 21 61 + + CCONJ cana-4443 21 62 𝐸 𝐸 PROPN cana-4443 21 63 + + CCONJ cana-4443 21 64 𝑄 𝑄 PROPN cana-4443 21 65 + + CCONJ cana-4443 21 66 𝐴 𝐴 PROPN cana-4443 21 67 + + CCONJ cana-4443 21 68 𝑅 𝑅 PROPN cana-4443 21 69 ≀ ≀ ADJ cana-4443 21 70 𝑇 𝑇 NOUN cana-4443 21 71 + + CCONJ cana-4443 21 72 𝐡 𝐡 NOUN cana-4443 21 73 πœ‡ πœ‡ ADP cana-4443 21 74 } } PUNCT cana-4443 21 75 the the DET cana-4443 21 76 malware malware NOUN cana-4443 21 77 free free ADJ cana-4443 21 78 equilibrium equilibrium NOUN cana-4443 21 79 ( ( PUNCT cana-4443 21 80 mfe mfe PROPN cana-4443 21 81 ) ) PUNCT cana-4443 21 82 of of ADP cana-4443 21 83 system system NOUN cana-4443 21 84 ( ( PUNCT cana-4443 21 85 1 1 X cana-4443 21 86 ) ) PUNCT cana-4443 21 87 is be AUX cana-4443 21 88 denoted denote VERB cana-4443 21 89 by by ADP cana-4443 21 90 πΈπ‘œ πΈπ‘œ ADV cana-4443 21 91 𝑖. 𝑖. ADJ cana-4443 21 92 𝑒. 𝑒. NOUN cana-4443 21 93 , , PUNCT cana-4443 22 1 πΈπ‘œ πΈπ‘œ ADV cana-4443 22 2 = = SYM cana-4443 22 3 ( ( PUNCT cana-4443 22 4 𝑆 𝑆 PROPN cana-4443 22 5 , , PUNCT cana-4443 22 6 𝐼 𝐼 PROPN cana-4443 22 7 , , PUNCT cana-4443 22 8 𝐸 𝐸 PROPN cana-4443 22 9 , , PUNCT cana-4443 22 10 𝑄 𝑄 PROPN cana-4443 22 11 , , PUNCT cana-4443 22 12 𝐴 𝐴 PROPN cana-4443 22 13 , , PUNCT cana-4443 22 14 𝑅 𝑅 PROPN cana-4443 22 15 ) ) PUNCT cana-4443 22 16 = = PUNCT cana-4443 22 17 ( ( PUNCT cana-4443 22 18 𝑇 𝑇 PROPN cana-4443 22 19 + + CCONJ cana-4443 22 20 𝐡 𝐡 NOUN cana-4443 22 21 πœ‡ πœ‡ ADP cana-4443 22 22 , , PUNCT cana-4443 22 23 0 0 NUM cana-4443 22 24 , , PUNCT cana-4443 22 25 0 0 NUM cana-4443 22 26 , , PUNCT cana-4443 22 27 0 0 NUM cana-4443 22 28 , , PUNCT cana-4443 22 29 0 0 NUM cana-4443 22 30 , , PUNCT cana-4443 22 31 0 0 NUM cana-4443 22 32 ) ) PUNCT cana-4443 22 33 description description NOUN cana-4443 22 34 of of ADP cana-4443 22 35 parameters parameter NOUN cana-4443 22 36 used use VERB cana-4443 22 37 in in ADP cana-4443 22 38 above above ADP cana-4443 22 39 ode ode ADJ cana-4443 22 40 system system NOUN cana-4443 22 41 . . PUNCT cana-4443 23 1 𝑆 𝑆 PROPN cana-4443 23 2 is be AUX cana-4443 23 3 number number NOUN cana-4443 23 4 of of ADP cana-4443 23 5 susceptible susceptible ADJ cana-4443 23 6 nodes node NOUN cana-4443 23 7 . . PUNCT cana-4443 24 1 𝐼 𝐼 NOUN cana-4443 24 2 is be AUX cana-4443 24 3 number number NOUN cana-4443 24 4 of of ADP cana-4443 24 5 infected infected ADJ cana-4443 24 6 nodes node NOUN cana-4443 24 7 . . PUNCT cana-4443 25 1 𝐸 𝐸 PROPN cana-4443 25 2 is be AUX cana-4443 25 3 number number NOUN cana-4443 25 4 of of ADP cana-4443 25 5 exposed expose VERB cana-4443 25 6 nodes node NOUN cana-4443 25 7 . . PUNCT cana-4443 26 1 𝑄 𝑄 PRON cana-4443 26 2 is be AUX cana-4443 26 3 number number NOUN cana-4443 26 4 of of ADP cana-4443 26 5 quarantined quarantine VERB cana-4443 26 6 nodes node NOUN cana-4443 26 7 𝐴 𝐴 PROPN cana-4443 26 8 is be AUX cana-4443 26 9 number number NOUN cana-4443 26 10 of of ADP cana-4443 26 11 antidotal antidotal ADJ cana-4443 26 12 nodes node NOUN cana-4443 26 13 𝑅 𝑅 NOUN cana-4443 26 14 is be AUX cana-4443 26 15 number number NOUN cana-4443 26 16 of of ADP cana-4443 26 17 recovered recover VERB cana-4443 26 18 nodes node NOUN cana-4443 26 19 𝛽 𝛽 NOUN cana-4443 26 20 is be AUX cana-4443 26 21 coefficient coefficient NOUN cana-4443 26 22 of of ADP cana-4443 26 23 transmission transmission NOUN cana-4443 26 24 for for ADP cana-4443 26 25 susceptible susceptible ADJ cana-4443 26 26 individuals individual NOUN cana-4443 26 27 𝜎 𝜎 PRON cana-4443 26 28 is be AUX cana-4443 26 29 rate rate NOUN cana-4443 26 30 of of ADP cana-4443 26 31 quarantine quarantine NOUN cana-4443 26 32 for for ADP cana-4443 26 33 infectious infectious ADJ cana-4443 26 34 individuals individual NOUN cana-4443 26 35 communications communication NOUN cana-4443 26 36 on on ADP cana-4443 26 37 applied apply VERB cana-4443 26 38 nonlinear nonlinear ADJ cana-4443 26 39 analysis analysis NOUN cana-4443 26 40 issn issn NOUN cana-4443 26 41 : : PUNCT cana-4443 26 42 1074 1074 NUM cana-4443 26 43 - - PUNCT cana-4443 26 44 133x 133x NUM cana-4443 26 45 vol vol NOUN cana-4443 26 46 32 32 NUM cana-4443 26 47 no no NOUN cana-4443 26 48 . . PUNCT cana-4443 27 1 9s 9s NUM cana-4443 27 2 ( ( PUNCT cana-4443 27 3 2025 2025 NUM cana-4443 27 4 ) ) PUNCT cana-4443 27 5 2025 2025 NUM cana-4443 27 6 https://internationalpubls.com https://internationalpubls.com X cana-4443 28 1 πœ“ πœ“ PROPN cana-4443 28 2 is be AUX cana-4443 28 3 rate rate NOUN cana-4443 28 4 of of ADP cana-4443 28 5 recovery recovery NOUN cana-4443 28 6 for for ADP cana-4443 28 7 infectious infectious ADJ cana-4443 28 8 individuals individual NOUN cana-4443 28 9 πœ‰ πœ‰ VERB cana-4443 28 10 is be AUX cana-4443 28 11 rate rate NOUN cana-4443 28 12 of of ADP cana-4443 28 13 antidotal antidotal ADJ cana-4443 28 14 for for ADP cana-4443 28 15 quarantine quarantine NOUN cana-4443 28 16 individuals individual NOUN cana-4443 28 17 πœ™ πœ™ NOUN cana-4443 28 18 is be AUX cana-4443 28 19 rate rate NOUN cana-4443 28 20 of of ADP cana-4443 28 21 recovery recovery NOUN cana-4443 28 22 for for ADP cana-4443 28 23 antidotal antidotal ADJ cana-4443 28 24 individuals individual NOUN cana-4443 28 25 πœ‚ πœ‚ NOUN cana-4443 28 26 is be AUX cana-4443 28 27 rate rate NOUN cana-4443 28 28 of of ADP cana-4443 28 29 recovery recovery NOUN cana-4443 28 30 for for ADP cana-4443 28 31 quarantine quarantine NOUN cana-4443 28 32 individuals individual NOUN cana-4443 28 33 πœƒ πœƒ PRON cana-4443 28 34 is be AUX cana-4443 28 35 rate rate NOUN cana-4443 28 36 of of ADP cana-4443 28 37 antidotal antidotal ADJ cana-4443 28 38 for for ADP cana-4443 28 39 exposed expose VERB cana-4443 28 40 individuals individual NOUN cana-4443 28 41 𝛿 𝛿 ADJ cana-4443 28 42 is be AUX cana-4443 28 43 rate rate NOUN cana-4443 28 44 of of ADP cana-4443 28 45 infective infective ADJ cana-4443 28 46 for for ADP cana-4443 28 47 exposed expose VERB cana-4443 28 48 individuals individual NOUN cana-4443 28 49 𝛾 𝛾 NOUN cana-4443 28 50 is be AUX cana-4443 28 51 rate rate NOUN cana-4443 28 52 of of ADP cana-4443 28 53 recovered recover VERB cana-4443 28 54 individuals individual NOUN cana-4443 28 55 to to PART cana-4443 28 56 susceptible susceptible VERB cana-4443 28 57 𝛼 𝛼 NOUN cana-4443 28 58 is be AUX cana-4443 28 59 rate rate NOUN cana-4443 28 60 of of ADP cana-4443 28 61 exposed expose VERB cana-4443 28 62 individuals individual NOUN cana-4443 28 63 to to PART cana-4443 28 64 susceptible susceptible VERB cana-4443 28 65 πœ‡ πœ‡ ADP cana-4443 28 66 is be AUX cana-4443 28 67 death death NOUN cana-4443 28 68 rate rate NOUN cana-4443 28 69 due due ADP cana-4443 28 70 to to ADP cana-4443 28 71 other other ADJ cana-4443 28 72 than than ADP cana-4443 28 73 the the DET cana-4443 28 74 malicious malicious ADJ cana-4443 28 75 objects object NOUN cana-4443 28 76 basic basic ADJ cana-4443 28 77 reproduction reproduction NOUN cana-4443 28 78 number number NOUN cana-4443 28 79 : : PUNCT cana-4443 28 80 for for ADP cana-4443 28 81 convenient convenient ADJ cana-4443 28 82 we we PRON cana-4443 28 83 take take VERB cana-4443 28 84 four four NUM cana-4443 28 85 classes class NOUN cana-4443 28 86 for for ADP cana-4443 28 87 calculation calculation NOUN cana-4443 28 88 of of ADP cana-4443 28 89 basic basic ADJ cana-4443 28 90 reproduction reproduction NOUN cana-4443 28 91 number number NOUN cana-4443 28 92 , , PUNCT cana-4443 28 93 from from ADP cana-4443 28 94 ode ode PROPN cana-4443 28 95 system system NOUN cana-4443 28 96 ( ( PUNCT cana-4443 28 97 1 1 NUM cana-4443 28 98 ) ) PUNCT cana-4443 28 99 . . PUNCT cana-4443 29 1 𝑑𝐼 𝑑𝐼 ADV cana-4443 29 2 𝑑𝑑 𝑑𝑑 ADP cana-4443 29 3 = = PROPN cana-4443 29 4 𝛽𝑆𝐼 𝛽𝑆𝐼 PROPN cana-4443 29 5 + + PROPN cana-4443 29 6 𝛿𝐸 𝛿𝐸 PROPN cana-4443 30 1 βˆ’ βˆ’ PROPN cana-4443 30 2 ( ( PUNCT cana-4443 30 3 πœ‡ πœ‡ X cana-4443 30 4 + + X cana-4443 30 5 πœ“ πœ“ NOUN cana-4443 30 6 + + CCONJ cana-4443 30 7 𝜎)𝐼 𝜎)𝐼 ADJ cana-4443 30 8 𝑑𝐸 𝑑𝐸 ADJ cana-4443 30 9 𝑑𝑑 𝑑𝑑 ADP cana-4443 30 10 = = PROPN cana-4443 30 11 𝐡 𝐡 PROPN cana-4443 30 12 βˆ’ βˆ’ PROPN cana-4443 30 13 ( ( PUNCT cana-4443 30 14 𝛼 𝛼 X cana-4443 30 15 + + X cana-4443 30 16 πœ‡ πœ‡ ADP cana-4443 30 17 + + NOUN cana-4443 30 18 𝛿 𝛿 ADJ cana-4443 30 19 + + CCONJ cana-4443 30 20 πœƒ)𝐸 πœƒ)𝐸 ADJ cana-4443 30 21 𝑑𝑄 𝑑𝑄 ADJ cana-4443 30 22 𝑑𝑑 𝑑𝑑 ADP cana-4443 30 23 = = PROPN cana-4443 30 24 𝜎𝐼 𝜎𝐼 PROPN cana-4443 30 25 βˆ’ βˆ’ PROPN cana-4443 30 26 ( ( PUNCT cana-4443 30 27 πœ‰ πœ‰ NOUN cana-4443 30 28 + + X cana-4443 30 29 πœ‡ πœ‡ X cana-4443 30 30 + + NOUN cana-4443 30 31 πœ‚)𝑄 πœ‚)𝑄 ADJ cana-4443 30 32 𝑑𝐴 𝑑𝐴 NOUN cana-4443 30 33 𝑑𝑑 𝑑𝑑 ADP cana-4443 30 34 = = PUNCT cana-4443 30 35 πœ‰π‘„ πœ‰π‘„ PROPN cana-4443 30 36 + + CCONJ cana-4443 30 37 πœƒπΈ πœƒπΈ NOUN cana-4443 30 38 βˆ’ βˆ’ PROPN cana-4443 30 39 ( ( PUNCT cana-4443 30 40 πœ‡ πœ‡ X cana-4443 30 41 + + X cana-4443 30 42 πœ™)𝐴 πœ™)𝐴 NUM cana-4443 30 43 by by ADP cana-4443 30 44 using use VERB cana-4443 30 45 next next ADJ cana-4443 30 46 generation generation NOUN cana-4443 30 47 matrix matrix NOUN cana-4443 30 48 𝑑π‘₯ 𝑑π‘₯ VERB cana-4443 30 49 𝑑𝑑 𝑑𝑑 ADP cana-4443 30 50 = = PRON cana-4443 30 51 𝑓 𝑓 DET cana-4443 30 52 βˆ’ βˆ’ NOUN cana-4443 30 53 𝑣. 𝑣. NOUN cana-4443 30 54 where where SCONJ cana-4443 30 55 , , PUNCT cana-4443 30 56 𝑓 𝑓 PROPN cana-4443 30 57 = = X cana-4443 30 58 [ [ PUNCT cana-4443 30 59 𝛽𝑆𝐼 𝛽𝑆𝐼 NOUN cana-4443 30 60 0 0 NUM cana-4443 30 61 0 0 NUM cana-4443 30 62 0 0 NUM cana-4443 30 63 ] ] PUNCT cana-4443 30 64 and and CCONJ cana-4443 30 65 𝑣 𝑣 X cana-4443 30 66 = = X cana-4443 30 67 [ [ PUNCT cana-4443 30 68 ( ( PUNCT cana-4443 30 69 πœ‡ πœ‡ X cana-4443 30 70 + + X cana-4443 30 71 πœ“ πœ“ NOUN cana-4443 30 72 + + CCONJ cana-4443 31 1 𝜎)𝐼 𝜎)𝐼 ADJ cana-4443 31 2 βˆ’ βˆ’ PROPN cana-4443 31 3 𝛿𝐸 𝛿𝐸 PROPN cana-4443 31 4 ( ( PUNCT cana-4443 31 5 𝛼 𝛼 X cana-4443 31 6 + + X cana-4443 31 7 πœ‡ πœ‡ ADP cana-4443 31 8 + + NOUN cana-4443 31 9 𝛿 𝛿 ADJ cana-4443 31 10 + + CCONJ cana-4443 31 11 πœƒ)𝐸 πœƒ)𝐸 ADJ cana-4443 31 12 βˆ’ βˆ’ PROPN cana-4443 31 13 𝐡 𝐡 NOUN cana-4443 31 14 ( ( PUNCT cana-4443 31 15 πœ‰ πœ‰ X cana-4443 31 16 + + X cana-4443 31 17 πœ‡ πœ‡ X cana-4443 31 18 + + X cana-4443 31 19 πœ‚)𝑄 πœ‚)𝑄 ADJ cana-4443 31 20 βˆ’ βˆ’ PROPN cana-4443 31 21 𝜎𝐼 𝜎𝐼 ADJ cana-4443 31 22 ( ( PUNCT cana-4443 31 23 πœ‡ πœ‡ X cana-4443 31 24 + + X cana-4443 31 25 πœ™)𝐴 πœ™)𝐴 NUM cana-4443 31 26 βˆ’ βˆ’ NOUN cana-4443 31 27 πœ‰π‘„ πœ‰π‘„ NOUN cana-4443 31 28 βˆ’ βˆ’ PROPN cana-4443 32 1 πœƒπΈ πœƒπΈ NOUN cana-4443 32 2 ] ] PUNCT cana-4443 32 3 𝐹 𝐹 PROPN cana-4443 32 4 is be AUX cana-4443 32 5 jacobian jacobian ADJ cana-4443 32 6 of of ADP cana-4443 32 7 𝑓 𝑓 PRON cana-4443 32 8 at at ADP cana-4443 32 9 𝑀𝐹𝐸 𝑀𝐹𝐸 PROPN cana-4443 32 10 is be AUX cana-4443 32 11 [ [ PUNCT cana-4443 32 12 𝛽 𝛽 NOUN cana-4443 32 13 0 0 NUM cana-4443 32 14 0 0 NUM cana-4443 32 15 0 0 NUM cana-4443 32 16 0 0 NUM cana-4443 32 17 0 0 NUM cana-4443 32 18 0 0 NUM cana-4443 32 19 0 0 NUM cana-4443 32 20 0 0 NUM cana-4443 32 21 0 0 NUM cana-4443 32 22 0 0 NUM cana-4443 32 23 0 0 NUM cana-4443 32 24 0 0 NUM cana-4443 32 25 0 0 NUM cana-4443 32 26 0 0 NUM cana-4443 32 27 0 0 NUM cana-4443 32 28 ] ] X cana-4443 33 1 𝑉 𝑉 PROPN cana-4443 33 2 is be AUX cana-4443 33 3 jacobian jacobian ADJ cana-4443 33 4 of of ADP cana-4443 33 5 𝑣 𝑣 PRON cana-4443 33 6 at at ADP cana-4443 33 7 𝑀𝐹𝐸 𝑀𝐹𝐸 PROPN cana-4443 33 8 is be AUX cana-4443 33 9 [ [ PUNCT cana-4443 33 10 πœ‡ πœ‡ ADP cana-4443 33 11 + + X cana-4443 33 12 πœ“ πœ“ NOUN cana-4443 33 13 + + CCONJ cana-4443 33 14 𝜎 𝜎 PRON cana-4443 33 15 βˆ’π›Ώ βˆ’π›Ώ NOUN cana-4443 33 16 0 0 PUNCT cana-4443 34 1 𝛼 𝛼 NOUN cana-4443 35 1 + + X cana-4443 35 2 πœ‡ πœ‡ ADP cana-4443 35 3 + + NOUN cana-4443 36 1 𝛿 𝛿 ADJ cana-4443 36 2 + + NOUN cana-4443 36 3 πœƒ πœƒ NOUN cana-4443 36 4 0 0 NUM cana-4443 36 5 0 0 NUM cana-4443 36 6 0 0 NUM cana-4443 36 7 0 0 NUM cana-4443 36 8 βˆ’πœŽ βˆ’πœŽ NOUN cana-4443 36 9 0 0 NUM cana-4443 36 10 0 0 NUM cana-4443 37 1 βˆ’πœƒ βˆ’πœƒ PROPN cana-4443 37 2 πœ‰ πœ‰ PROPN cana-4443 37 3 + + X cana-4443 37 4 πœ‡ πœ‡ ADP cana-4443 37 5 + + NOUN cana-4443 37 6 πœ‚ πœ‚ NOUN cana-4443 37 7 0 0 NUM cana-4443 37 8 βˆ’πœ‰ βˆ’πœ‰ NOUN cana-4443 37 9 πœ‡ πœ‡ ADP cana-4443 37 10 + + X cana-4443 37 11 πœ™ πœ™ X cana-4443 37 12 ] ] PUNCT cana-4443 37 13 then then ADV cana-4443 37 14 , , PUNCT cana-4443 37 15 communications communication NOUN cana-4443 37 16 on on ADP cana-4443 37 17 applied apply VERB cana-4443 37 18 nonlinear nonlinear ADJ cana-4443 37 19 analysis analysis NOUN cana-4443 37 20 issn issn NOUN cana-4443 37 21 : : PUNCT cana-4443 37 22 1074 1074 NUM cana-4443 37 23 - - PUNCT cana-4443 37 24 133x 133x NUM cana-4443 37 25 vol vol NOUN cana-4443 37 26 32 32 NUM cana-4443 37 27 no no NOUN cana-4443 37 28 . . PUNCT cana-4443 38 1 9s 9s NUM cana-4443 38 2 ( ( PUNCT cana-4443 38 3 2025 2025 NUM cana-4443 38 4 ) ) PUNCT cana-4443 38 5 2026 2026 NUM cana-4443 39 1 https://internationalpubls.com https://internationalpubls.com X cana-4443 39 2 π‘‰βˆ’1 π‘‰βˆ’1 NOUN cana-4443 39 3 = = PUNCT cana-4443 39 4 [ [ PUNCT cana-4443 39 5 1 1 NUM cana-4443 39 6 πœ‡ πœ‡ ADP cana-4443 39 7 + + X cana-4443 39 8 πœ“ πœ“ NOUN cana-4443 39 9 + + CCONJ cana-4443 39 10 𝜎 𝜎 ADJ cana-4443 39 11 𝛿 𝛿 ADJ cana-4443 39 12 ( ( PUNCT cana-4443 39 13 πœ‡ πœ‡ ADP cana-4443 39 14 + + X cana-4443 39 15 πœ“ πœ“ X cana-4443 39 16 + + CCONJ cana-4443 39 17 𝜎)(𝛼 𝜎)(𝛼 NOUN cana-4443 39 18 + + CCONJ cana-4443 39 19 πœ‡ πœ‡ ADP cana-4443 39 20 + + NOUN cana-4443 39 21 𝛿 𝛿 ADJ cana-4443 39 22 + + NOUN cana-4443 39 23 πœƒ πœƒ NOUN cana-4443 39 24 ) ) PUNCT cana-4443 39 25 0 0 NUM cana-4443 39 26 1 1 NUM cana-4443 39 27 ( ( PUNCT cana-4443 39 28 𝛼 𝛼 NOUN cana-4443 39 29 + + X cana-4443 39 30 πœ‡ πœ‡ ADP cana-4443 39 31 + + NOUN cana-4443 39 32 𝛿 𝛿 ADJ cana-4443 39 33 + + NOUN cana-4443 39 34 πœƒ πœƒ NOUN cana-4443 39 35 ) ) PUNCT cana-4443 39 36 0 0 NUM cana-4443 39 37 0 0 NUM cana-4443 39 38 0 0 NUM cana-4443 39 39 0 0 NUM cana-4443 39 40 𝜎 𝜎 NOUN cana-4443 39 41 ( ( PUNCT cana-4443 39 42 πœ‡ πœ‡ X cana-4443 39 43 + + X cana-4443 39 44 πœ“ πœ“ NOUN cana-4443 39 45 + + CCONJ cana-4443 39 46 𝜎)(πœ‰ 𝜎)(πœ‰ NUM cana-4443 39 47 + + CCONJ cana-4443 39 48 πœ‡ πœ‡ X cana-4443 39 49 + + NOUN cana-4443 39 50 πœ‚ πœ‚ X cana-4443 39 51 ) ) PUNCT cana-4443 39 52 πœŽπ›Ώ πœŽπ›Ώ NOUN cana-4443 39 53 ( ( PUNCT cana-4443 39 54 πœ‡ πœ‡ ADP cana-4443 39 55 + + X cana-4443 39 56 πœ“ πœ“ X cana-4443 39 57 + + CCONJ cana-4443 39 58 𝜎)(𝛼 𝜎)(𝛼 NOUN cana-4443 39 59 + + CCONJ cana-4443 39 60 πœ‡ πœ‡ ADP cana-4443 39 61 + + NOUN cana-4443 39 62 𝛿 𝛿 ADJ cana-4443 39 63 + + X cana-4443 39 64 πœƒ)(πœ‰ πœƒ)(πœ‰ NUM cana-4443 39 65 + + CCONJ cana-4443 39 66 πœ‡ πœ‡ ADP cana-4443 39 67 + + NOUN cana-4443 39 68 πœ‚ πœ‚ NOUN cana-4443 39 69 ) ) PUNCT cana-4443 39 70 πœŽπœ‰ πœŽπœ‰ NOUN cana-4443 39 71 ( ( PUNCT cana-4443 39 72 πœ‡ πœ‡ ADP cana-4443 39 73 + + X cana-4443 39 74 πœ“ πœ“ NOUN cana-4443 39 75 + + CCONJ cana-4443 39 76 𝜎)(πœ‰ 𝜎)(πœ‰ NUM cana-4443 39 77 + + CCONJ cana-4443 39 78 πœ‡ πœ‡ X cana-4443 39 79 + + NOUN cana-4443 39 80 πœ‚)(πœ‡ πœ‚)(πœ‡ VERB cana-4443 39 81 + + CCONJ cana-4443 39 82 πœ™ πœ™ X cana-4443 39 83 ) ) PUNCT cana-4443 39 84 ( ( PUNCT cana-4443 39 85 πœ‡ πœ‡ ADP cana-4443 39 86 + + X cana-4443 39 87 πœ“ πœ“ X cana-4443 39 88 + + CCONJ cana-4443 39 89 𝜎)πœƒ(πœ‰ 𝜎)πœƒ(πœ‰ NOUN cana-4443 39 90 + + CCONJ cana-4443 39 91 πœ‡ πœ‡ X cana-4443 39 92 + + NOUN cana-4443 39 93 πœ‚ πœ‚ NOUN cana-4443 39 94 ) ) PUNCT cana-4443 39 95 + + NOUN cana-4443 39 96 π›ΏπœŽπœ‰ π›ΏπœŽπœ‰ PROPN cana-4443 39 97 ( ( PUNCT cana-4443 39 98 πœ‡ πœ‡ ADP cana-4443 39 99 + + X cana-4443 39 100 πœ“ πœ“ X cana-4443 39 101 + + CCONJ cana-4443 39 102 𝜎)(𝛼 𝜎)(𝛼 NOUN cana-4443 39 103 + + CCONJ cana-4443 39 104 πœ‡ πœ‡ ADP cana-4443 39 105 + + NOUN cana-4443 39 106 𝛿 𝛿 ADJ cana-4443 39 107 + + X cana-4443 39 108 πœƒ)(πœ‰ πœƒ)(πœ‰ NUM cana-4443 39 109 + + CCONJ cana-4443 39 110 πœ‡ πœ‡ X cana-4443 39 111 + + ADV cana-4443 39 112 πœ‚)(πœ‡ πœ‚)(πœ‡ VERB cana-4443 39 113 + + CCONJ cana-4443 39 114 πœ™ πœ™ X cana-4443 39 115 ) ) PUNCT cana-4443 39 116 1 1 NUM cana-4443 39 117 ( ( PUNCT cana-4443 39 118 πœ‰ πœ‰ NOUN cana-4443 39 119 + + X cana-4443 39 120 πœ‡ πœ‡ X cana-4443 39 121 + + NOUN cana-4443 39 122 πœ‚ πœ‚ NOUN cana-4443 39 123 ) ) PUNCT cana-4443 39 124 0 0 NUM cana-4443 39 125 πœ‰ πœ‰ X cana-4443 39 126 ( ( PUNCT cana-4443 39 127 πœ‰ πœ‰ PROPN cana-4443 39 128 + + X cana-4443 39 129 πœ‡ πœ‡ X cana-4443 39 130 + + NOUN cana-4443 39 131 πœ‚)(πœ‡ πœ‚)(πœ‡ VERB cana-4443 39 132 + + CCONJ cana-4443 39 133 πœ™ πœ™ X cana-4443 39 134 ) ) PUNCT cana-4443 39 135 1 1 NUM cana-4443 39 136 ( ( PUNCT cana-4443 39 137 πœ‡ πœ‡ X cana-4443 39 138 + + X cana-4443 39 139 πœ™ πœ™ NOUN cana-4443 39 140 ) ) PUNCT cana-4443 39 141 ] ] PUNCT cana-4443 39 142 πΉπ‘‰βˆ’1 πΉπ‘‰βˆ’1 PROPN cana-4443 39 143 = = PUNCT cana-4443 40 1 [ [ PUNCT cana-4443 40 2 𝛽 𝛽 NOUN cana-4443 40 3 πœ‡ πœ‡ ADP cana-4443 40 4 + + X cana-4443 40 5 πœ“ πœ“ NOUN cana-4443 40 6 + + CCONJ cana-4443 40 7 𝜎 𝜎 AUX cana-4443 40 8 𝛽𝛿 𝛽𝛿 INTJ cana-4443 40 9 ( ( PUNCT cana-4443 40 10 πœ‡ πœ‡ ADP cana-4443 40 11 + + X cana-4443 40 12 πœ“ πœ“ X cana-4443 40 13 + + CCONJ cana-4443 40 14 𝜎)(𝛼 𝜎)(𝛼 NOUN cana-4443 40 15 + + CCONJ cana-4443 40 16 πœ‡ πœ‡ ADP cana-4443 40 17 + + NOUN cana-4443 40 18 𝛿 𝛿 ADJ cana-4443 40 19 + + NOUN cana-4443 40 20 πœƒ πœƒ NOUN cana-4443 40 21 ) ) PUNCT cana-4443 40 22 0 0 NUM cana-4443 40 23 0 0 NUM cana-4443 40 24 0 0 NUM cana-4443 40 25 0 0 NUM cana-4443 40 26 0 0 NUM cana-4443 40 27 0 0 NUM cana-4443 40 28 0 0 NUM cana-4443 40 29 0 0 NUM cana-4443 40 30 0 0 NUM cana-4443 40 31 0 0 NUM cana-4443 40 32 0 0 NUM cana-4443 40 33 0 0 NUM cana-4443 40 34 0 0 NUM cana-4443 40 35 0 0 NUM cana-4443 40 36 ] ] X cana-4443 40 37 the the DET cana-4443 40 38 dominant dominant PROPN cana-4443 40 39 eigen eigen PROPN cana-4443 40 40 values value NOUN cana-4443 40 41 𝑅0 𝑅0 NOUN cana-4443 40 42 = = SYM cana-4443 40 43 𝛽 𝛽 NOUN cana-4443 40 44 ( ( PUNCT cana-4443 40 45 πœ‡ πœ‡ ADP cana-4443 40 46 + + X cana-4443 40 47 πœ“ πœ“ NOUN cana-4443 40 48 + + CCONJ cana-4443 40 49 𝜎 𝜎 X cana-4443 40 50 ) ) PUNCT cana-4443 40 51 3 3 NUM cana-4443 40 52 . . PUNCT cana-4443 40 53 local local ADJ cana-4443 40 54 stability stability NOUN cana-4443 40 55 at at ADP cana-4443 40 56 mfe mfe PROPN cana-4443 40 57 ( ( PUNCT cana-4443 40 58 malware malware NOUN cana-4443 40 59 free free ADJ cana-4443 40 60 equilibrium equilibrium NOUN cana-4443 40 61 ) ) PUNCT cana-4443 40 62 point point NOUN cana-4443 40 63 : : PUNCT cana-4443 40 64 for for ADP cana-4443 40 65 equilibrium equilibrium NOUN cana-4443 40 66 points point NOUN cana-4443 40 67 in in ADP cana-4443 40 68 the the DET cana-4443 40 69 steady steady ADJ cana-4443 40 70 state state NOUN cana-4443 40 71 of of ADP cana-4443 40 72 ode ode ADJ cana-4443 40 73 system system NOUN cana-4443 40 74 ( ( PUNCT cana-4443 40 75 i i NOUN cana-4443 40 76 ) ) PUNCT cana-4443 40 77 . . PUNCT cana-4443 41 1 𝑇 𝑇 PROPN cana-4443 41 2 βˆ’ βˆ’ PROPN cana-4443 41 3 𝛽𝑆𝐼 𝛽𝑆𝐼 PROPN cana-4443 41 4 + + NUM cana-4443 41 5 𝛼𝐸 𝛼𝐸 NOUN cana-4443 41 6 + + CCONJ cana-4443 41 7 𝛾𝑅 𝛾𝑅 PROPN cana-4443 41 8 βˆ’ βˆ’ NOUN cana-4443 41 9 πœ‡π‘† πœ‡π‘† NOUN cana-4443 41 10 = = SYM cana-4443 41 11 0 0 PUNCT cana-4443 41 12 𝛽𝑆𝐼 𝛽𝑆𝐼 PROPN cana-4443 41 13 + + PROPN cana-4443 41 14 𝛿𝐸 𝛿𝐸 PROPN cana-4443 41 15 βˆ’ βˆ’ PROPN cana-4443 41 16 ( ( PUNCT cana-4443 41 17 πœ‡ πœ‡ X cana-4443 41 18 + + X cana-4443 41 19 πœ“ πœ“ NOUN cana-4443 41 20 + + CCONJ cana-4443 41 21 𝜎)𝐼 𝜎)𝐼 ADJ cana-4443 41 22 = = SYM cana-4443 41 23 0 0 NUM cana-4443 41 24 𝐡 𝐡 NOUN cana-4443 41 25 βˆ’ βˆ’ PROPN cana-4443 41 26 ( ( PUNCT cana-4443 41 27 𝛼 𝛼 X cana-4443 41 28 + + X cana-4443 41 29 πœ‡ πœ‡ ADP cana-4443 41 30 + + NOUN cana-4443 41 31 𝛿 𝛿 ADJ cana-4443 41 32 + + ADJ cana-4443 41 33 πœƒ)𝐸 πœƒ)𝐸 ADJ cana-4443 41 34 = = SYM cana-4443 41 35 0 0 NUM cana-4443 41 36 𝜎𝐼 𝜎𝐼 ADJ cana-4443 41 37 βˆ’ βˆ’ PROPN cana-4443 41 38 ( ( PUNCT cana-4443 41 39 πœ‰ πœ‰ NOUN cana-4443 41 40 + + X cana-4443 41 41 πœ‡ πœ‡ X cana-4443 41 42 + + X cana-4443 41 43 πœ‚)𝑄 πœ‚)𝑄 X cana-4443 41 44 = = SYM cana-4443 41 45 0 0 NUM cana-4443 41 46 πœ‰π‘„ πœ‰π‘„ NOUN cana-4443 41 47 + + CCONJ cana-4443 41 48 πœƒπΈ πœƒπΈ NOUN cana-4443 41 49 βˆ’ βˆ’ PROPN cana-4443 41 50 ( ( PUNCT cana-4443 41 51 πœ‡ πœ‡ X cana-4443 41 52 + + X cana-4443 41 53 πœ™)𝐴 πœ™)𝐴 X cana-4443 41 54 = = SYM cana-4443 41 55 0 0 PUNCT cana-4443 42 1 πœ‚π‘„ πœ‚π‘„ ADJ cana-4443 42 2 + + CCONJ cana-4443 42 3 πœ“πΌ πœ“πΌ ADJ cana-4443 42 4 + + CCONJ cana-4443 42 5 πœ™π΄ πœ™π΄ NOUN cana-4443 42 6 βˆ’ βˆ’ NOUN cana-4443 42 7 ( ( PUNCT cana-4443 42 8 πœ‡ πœ‡ X cana-4443 42 9 + + X cana-4443 42 10 𝛾)𝑅 𝛾)𝑅 X cana-4443 42 11 = = NOUN cana-4443 42 12 0 0 NUM cana-4443 42 13 } } PUNCT cana-4443 42 14 … … PUNCT cana-4443 42 15 ( ( PUNCT cana-4443 42 16 ii ii NOUN cana-4443 42 17 ) ) PUNCT cana-4443 42 18 theorem theorem NOUN cana-4443 42 19 1 1 NUM cana-4443 42 20 : : PUNCT cana-4443 42 21 the the DET cana-4443 42 22 πΈβˆ—of πΈβˆ—of NOUN cana-4443 42 23 system system NOUN cana-4443 42 24 ( ( PUNCT cana-4443 42 25 i i NOUN cana-4443 42 26 ) ) PUNCT cana-4443 42 27 is be AUX cana-4443 42 28 locally locally ADV cana-4443 42 29 asymptotically asymptotically ADV cana-4443 42 30 stable stable ADJ cana-4443 42 31 ( ( PUNCT cana-4443 42 32 las las NOUN cana-4443 42 33 ) ) PUNCT cana-4443 42 34 if if SCONJ cana-4443 42 35 𝑅0 𝑅0 VERB cana-4443 42 36 < < X cana-4443 42 37 1 1 NUM cana-4443 42 38 . . PUNCT cana-4443 43 1 proof proof NOUN cana-4443 43 2 : : PUNCT cana-4443 43 3 the the DET cana-4443 43 4 jacobian jacobian NOUN cana-4443 43 5 of of ADP cana-4443 43 6 system system NOUN cana-4443 43 7 ( ( PUNCT cana-4443 43 8 i i NOUN cana-4443 43 9 ) ) PUNCT cana-4443 43 10 𝐽1 𝐽1 PROPN cana-4443 44 1 = = PUNCT cana-4443 45 1 [ [ PUNCT cana-4443 45 2 βˆ’πœ‡ βˆ’πœ‡ NUM cana-4443 45 3 0 0 NUM cana-4443 45 4 0 0 NUM cana-4443 45 5 0 0 NUM cana-4443 45 6 0 0 NUM cana-4443 45 7 0 0 NUM cana-4443 45 8 0 0 NUM cana-4443 46 1 π›½π‘†βˆ— π›½π‘†βˆ— NOUN cana-4443 46 2 βˆ’ βˆ’ PROPN cana-4443 46 3 ( ( PUNCT cana-4443 46 4 πœ‡ πœ‡ ADP cana-4443 46 5 + + X cana-4443 46 6 πœ“ πœ“ X cana-4443 46 7 + + CCONJ cana-4443 46 8 𝜎 𝜎 X cana-4443 46 9 ) ) PUNCT cana-4443 46 10 0 0 NUM cana-4443 47 1 𝜎 𝜎 NOUN cana-4443 47 2 0 0 X cana-4443 47 3 πœ“ πœ“ NOUN cana-4443 47 4 0 0 NUM cana-4443 47 5 𝛿 𝛿 PRON cana-4443 47 6 βˆ’(𝛼 βˆ’(𝛼 NOUN cana-4443 47 7 + + CCONJ cana-4443 47 8 πœ‡ πœ‡ ADP cana-4443 47 9 + + NOUN cana-4443 47 10 𝛿 𝛿 ADJ cana-4443 47 11 + + NOUN cana-4443 47 12 πœƒ πœƒ NOUN cana-4443 47 13 ) ) PUNCT cana-4443 47 14 0 0 NUM cana-4443 48 1 πœƒ πœƒ X cana-4443 48 2 0 0 NUM cana-4443 48 3 0 0 NUM cana-4443 48 4 0 0 NUM cana-4443 48 5 0 0 NUM cana-4443 48 6 βˆ’(πœ‰ βˆ’(πœ‰ NOUN cana-4443 48 7 + + CCONJ cana-4443 48 8 πœ‡ πœ‡ ADP cana-4443 48 9 + + NOUN cana-4443 48 10 πœ‚ πœ‚ NOUN cana-4443 48 11 ) ) PUNCT cana-4443 48 12 πœ‰ πœ‰ NOUN cana-4443 48 13 πœ‚ πœ‚ NOUN cana-4443 48 14 0 0 NUM cana-4443 48 15 0 0 NUM cana-4443 48 16 0 0 NUM cana-4443 48 17 0 0 NUM cana-4443 48 18 βˆ’(πœ‡ βˆ’(πœ‡ NOUN cana-4443 48 19 + + CCONJ cana-4443 48 20 πœ™ πœ™ NOUN cana-4443 48 21 ) ) PUNCT cana-4443 48 22 πœ™ πœ™ PROPN cana-4443 48 23 𝛾 𝛾 NOUN cana-4443 48 24 0 0 NUM cana-4443 48 25 0 0 NUM cana-4443 48 26 0 0 NUM cana-4443 48 27 0 0 NUM cana-4443 48 28 βˆ’(πœ‡ βˆ’(πœ‡ NOUN cana-4443 48 29 + + CCONJ cana-4443 48 30 𝛾 𝛾 NOUN cana-4443 48 31 ) ) PUNCT cana-4443 48 32 ] ] PUNCT cana-4443 49 1 the the DET cana-4443 49 2 characteristic characteristic ADJ cana-4443 49 3 equation equation NOUN cana-4443 49 4 of of ADP cana-4443 49 5 𝐽1 𝐽1 PROPN cana-4443 49 6 is be AUX cana-4443 49 7 |𝐽1 |𝐽1 PUNCT cana-4443 49 8 βˆ’ βˆ’ PROPN cana-4443 49 9 πœ†πΌ| πœ†πΌ| PUNCT cana-4443 49 10 = = SYM cana-4443 49 11 0 0 NUM cana-4443 49 12 β‡’ β‡’ NOUN cana-4443 49 13 | | INTJ cana-4443 49 14 | | ADV cana-4443 49 15 βˆ’(πœ‡ βˆ’(πœ‡ NOUN cana-4443 49 16 + + CCONJ cana-4443 49 17 πœ† πœ† X cana-4443 49 18 ) ) PUNCT cana-4443 49 19 0 0 NUM cana-4443 49 20 0 0 NUM cana-4443 49 21 0 0 NUM cana-4443 49 22 0 0 NUM cana-4443 49 23 0 0 NUM cana-4443 49 24 0 0 NUM cana-4443 50 1 π›½π‘†βˆ— π›½π‘†βˆ— NOUN cana-4443 50 2 βˆ’ βˆ’ PROPN cana-4443 50 3 ( ( PUNCT cana-4443 50 4 πœ‡ πœ‡ ADP cana-4443 50 5 + + X cana-4443 50 6 πœ“ πœ“ NOUN cana-4443 50 7 + + CCONJ cana-4443 50 8 𝜎 𝜎 NOUN cana-4443 50 9 + + CCONJ cana-4443 50 10 πœ† πœ† X cana-4443 50 11 ) ) PUNCT cana-4443 50 12 0 0 NUM cana-4443 51 1 𝜎 𝜎 NOUN cana-4443 51 2 0 0 X cana-4443 51 3 πœ“ πœ“ NOUN cana-4443 51 4 0 0 NUM cana-4443 51 5 𝛿 𝛿 PRON cana-4443 51 6 βˆ’(𝛼 βˆ’(𝛼 NOUN cana-4443 51 7 + + CCONJ cana-4443 51 8 πœ‡ πœ‡ ADP cana-4443 51 9 + + NOUN cana-4443 51 10 𝛿 𝛿 ADJ cana-4443 51 11 + + NOUN cana-4443 51 12 πœƒ πœƒ NOUN cana-4443 51 13 + + CCONJ cana-4443 51 14 πœ† πœ† X cana-4443 51 15 ) ) PUNCT cana-4443 51 16 0 0 NUM cana-4443 52 1 πœƒ πœƒ NOUN cana-4443 52 2 0 0 NUM cana-4443 52 3 0 0 NUM cana-4443 52 4 0 0 NUM cana-4443 52 5 0 0 NUM cana-4443 52 6 βˆ’(πœ‰ βˆ’(πœ‰ NOUN cana-4443 52 7 + + CCONJ cana-4443 52 8 πœ‡ πœ‡ ADP cana-4443 52 9 + + NOUN cana-4443 52 10 πœ‚ πœ‚ NOUN cana-4443 52 11 + + CCONJ cana-4443 52 12 πœ† πœ† X cana-4443 52 13 ) ) PUNCT cana-4443 52 14 πœ‰ πœ‰ NOUN cana-4443 52 15 πœ‚ πœ‚ NOUN cana-4443 52 16 0 0 NUM cana-4443 52 17 0 0 NUM cana-4443 52 18 0 0 NUM cana-4443 52 19 0 0 NUM cana-4443 52 20 βˆ’(πœ‡ βˆ’(πœ‡ NOUN cana-4443 53 1 + + CCONJ cana-4443 53 2 πœ™ πœ™ NOUN cana-4443 53 3 + + CCONJ cana-4443 53 4 πœ† πœ† X cana-4443 53 5 ) ) PUNCT cana-4443 53 6 πœ™ πœ™ NOUN cana-4443 53 7 𝛾 𝛾 NOUN cana-4443 53 8 0 0 NUM cana-4443 53 9 0 0 NUM cana-4443 53 10 0 0 NUM cana-4443 53 11 0 0 NUM cana-4443 53 12 βˆ’(πœ‡ βˆ’(πœ‡ NOUN cana-4443 53 13 + + CCONJ cana-4443 53 14 𝛾 𝛾 NOUN cana-4443 53 15 + + CCONJ cana-4443 53 16 πœ† πœ† X cana-4443 53 17 ) ) PUNCT cana-4443 54 1 | | ADV cana-4443 54 2 | | ADV cana-4443 54 3 = = SYM cana-4443 54 4 0 0 NUM cana-4443 55 1 the the DET cana-4443 55 2 eigen eigen PROPN cana-4443 55 3 vlues vlue NOUN cana-4443 55 4 of|𝐽1 of|𝐽1 NOUN cana-4443 56 1 βˆ’ βˆ’ PROPN cana-4443 56 2 πœ†πΌ| πœ†πΌ| NOUN cana-4443 56 3 = = SYM cana-4443 56 4 0 0 NUM cana-4443 56 5 are be AUX cana-4443 56 6 communications communication NOUN cana-4443 56 7 on on ADP cana-4443 56 8 applied apply VERB cana-4443 56 9 nonlinear nonlinear ADJ cana-4443 56 10 analysis analysis NOUN cana-4443 56 11 issn issn NOUN cana-4443 56 12 : : PUNCT cana-4443 56 13 1074 1074 NUM cana-4443 56 14 - - PUNCT cana-4443 56 15 133x 133x NUM cana-4443 56 16 vol vol NOUN cana-4443 56 17 32 32 NUM cana-4443 56 18 no no NOUN cana-4443 56 19 . . PUNCT cana-4443 57 1 9s 9s NUM cana-4443 57 2 ( ( PUNCT cana-4443 57 3 2025 2025 NUM cana-4443 57 4 ) ) PUNCT cana-4443 57 5 2027 2027 NUM cana-4443 57 6 https://internationalpubls.com https://internationalpubls.com X cana-4443 57 7 πœ†1 πœ†1 NOUN cana-4443 57 8 = = PUNCT cana-4443 58 1 βˆ’πœ‡ βˆ’πœ‡ VERB cana-4443 58 2 < < X cana-4443 58 3 0 0 NUM cana-4443 58 4 πœ†2 πœ†2 NOUN cana-4443 58 5 = = SYM cana-4443 58 6 𝛽𝑆 𝛽𝑆 PROPN cana-4443 58 7 βˆ— βˆ— NOUN cana-4443 58 8 βˆ’ βˆ’ PROPN cana-4443 58 9 ( ( PUNCT cana-4443 58 10 πœ‡ πœ‡ ADP cana-4443 58 11 + + X cana-4443 58 12 πœ“ πœ“ PROPN cana-4443 58 13 + + CCONJ cana-4443 58 14 𝜎 𝜎 X cana-4443 58 15 ) ) PUNCT cana-4443 58 16 πœ†3 πœ†3 NOUN cana-4443 58 17 = = SYM cana-4443 58 18 βˆ’(𝛼 βˆ’(𝛼 NOUN cana-4443 58 19 + + CCONJ cana-4443 58 20 πœ‡ πœ‡ ADP cana-4443 58 21 + + NOUN cana-4443 58 22 𝛿 𝛿 ADJ cana-4443 58 23 + + NOUN cana-4443 58 24 πœƒ πœƒ NOUN cana-4443 58 25 ) ) PUNCT cana-4443 58 26 < < X cana-4443 58 27 0 0 NUM cana-4443 58 28 πœ†4 πœ†4 NOUN cana-4443 58 29 = = SYM cana-4443 58 30 βˆ’(πœ‰ βˆ’(πœ‰ NOUN cana-4443 58 31 + + CCONJ cana-4443 58 32 πœ‡ πœ‡ ADP cana-4443 58 33 + + NOUN cana-4443 58 34 πœ‚ πœ‚ NOUN cana-4443 58 35 ) ) PUNCT cana-4443 58 36 < < X cana-4443 59 1 0 0 PUNCT cana-4443 59 2 πœ†5 πœ†5 ADJ cana-4443 59 3 = = PUNCT cana-4443 59 4 βˆ’(πœ‡ βˆ’(πœ‡ NOUN cana-4443 59 5 + + CCONJ cana-4443 59 6 πœ™ πœ™ NOUN cana-4443 59 7 ) ) PUNCT cana-4443 59 8 < < X cana-4443 59 9 0 0 NUM cana-4443 59 10 πœ†6 πœ†6 PROPN cana-4443 59 11 = = NOUN cana-4443 59 12 βˆ’(πœ‡ βˆ’(πœ‡ PROPN cana-4443 59 13 + + CCONJ cana-4443 59 14 𝛾 𝛾 NOUN cana-4443 59 15 ) ) PUNCT cana-4443 59 16 < < X cana-4443 59 17 0 0 PUNCT cana-4443 60 1 clearly clearly ADV cana-4443 60 2 it it PRON cana-4443 60 3 has have VERB cana-4443 60 4 five five NUM cana-4443 60 5 negative negative ADJ cana-4443 60 6 real real ADJ cana-4443 60 7 roots root NOUN cana-4443 60 8 and and CCONJ cana-4443 60 9 the the DET cana-4443 60 10 root root NOUN cana-4443 60 11 πœ†2 πœ†2 NOUN cana-4443 60 12 = = SYM cana-4443 60 13 𝛽𝑆 𝛽𝑆 PROPN cana-4443 60 14 βˆ— βˆ— NOUN cana-4443 60 15 βˆ’ βˆ’ PROPN cana-4443 60 16 ( ( PUNCT cana-4443 60 17 πœ‡ πœ‡ ADP cana-4443 60 18 + + X cana-4443 60 19 πœ“ πœ“ X cana-4443 60 20 + + X cana-4443 60 21 𝜎 𝜎 X cana-4443 60 22 ) ) PUNCT cana-4443 60 23 < < X cana-4443 60 24 0 0 PUNCT cana-4443 61 1 if if SCONJ cana-4443 61 2 π›½π‘†βˆ— π›½π‘†βˆ— VERB cana-4443 61 3 < < X cana-4443 61 4 ( ( PUNCT cana-4443 61 5 πœ‡ πœ‡ ADP cana-4443 61 6 + + X cana-4443 61 7 πœ“ πœ“ PROPN cana-4443 61 8 + + X cana-4443 61 9 𝜎 𝜎 X cana-4443 61 10 ) ) PUNCT cana-4443 61 11 . . PUNCT cana-4443 62 1 clearly clearly ADV cana-4443 62 2 all all DET cana-4443 62 3 roots root NOUN cana-4443 62 4 are be AUX cana-4443 62 5 negative negative ADJ cana-4443 62 6 real real ADJ cana-4443 62 7 roots root NOUN cana-4443 62 8 so so SCONJ cana-4443 62 9 system system NOUN cana-4443 62 10 ( ( PUNCT cana-4443 62 11 i i NOUN cana-4443 62 12 ) ) PUNCT cana-4443 62 13 is be AUX cana-4443 62 14 malware malware NOUN cana-4443 62 15 free free ADJ cana-4443 62 16 equilibrium equilibrium NOUN cana-4443 62 17 and and CCONJ cana-4443 62 18 is be AUX cana-4443 62 19 localy localy PROPN cana-4443 62 20 asymptotically asymptotically ADV cana-4443 62 21 stable stable ADJ cana-4443 62 22 . . PUNCT cana-4443 63 1 4 4 X cana-4443 63 2 . . X cana-4443 63 3 endemic endemic ADJ cana-4443 63 4 equilibrium equilibrium NOUN cana-4443 63 5 point point NOUN cana-4443 63 6 : : PUNCT cana-4443 63 7 the the DET cana-4443 63 8 endemic endemic ADJ cana-4443 63 9 equilibrium equilibrium NOUN cana-4443 63 10 ( ( PUNCT cana-4443 63 11 ee ee NOUN cana-4443 63 12 ) ) PUNCT cana-4443 63 13 point point NOUN cana-4443 63 14 π‘ƒβˆ—(π‘†βˆ— π‘ƒβˆ—(π‘†βˆ— NOUN cana-4443 63 15 , , PUNCT cana-4443 63 16 πΌβˆ— πΌβˆ— PROPN cana-4443 63 17 , , PUNCT cana-4443 63 18 πΈβˆ— πΈβˆ— NOUN cana-4443 63 19 , , PUNCT cana-4443 63 20 π‘„βˆ— π‘„βˆ— PROPN cana-4443 63 21 , , PUNCT cana-4443 63 22 π΄βˆ— π΄βˆ— NOUN cana-4443 63 23 , , PUNCT cana-4443 63 24 π‘…βˆ— π‘…βˆ— NUM cana-4443 63 25 ) ) PUNCT cana-4443 63 26 , , PUNCT cana-4443 63 27 which which PRON cana-4443 63 28 can can AUX cana-4443 63 29 be be AUX cana-4443 63 30 calculated calculate VERB cana-4443 63 31 by by ADP cana-4443 63 32 using use VERB cana-4443 63 33 system system NOUN cana-4443 63 34 ( ( PUNCT cana-4443 63 35 ii ii NOUN cana-4443 63 36 ) ) PUNCT cana-4443 63 37 thus thus ADV cana-4443 63 38 , , PUNCT cana-4443 63 39 π‘†βˆ— π‘†βˆ— X cana-4443 63 40 = = PUNCT cana-4443 63 41 { { PUNCT cana-4443 63 42 𝑇(𝛼 𝑇(𝛼 X cana-4443 64 1 + + X cana-4443 64 2 πœ‡ πœ‡ X cana-4443 64 3 + + NOUN cana-4443 64 4 𝛿 𝛿 ADJ cana-4443 64 5 + + NOUN cana-4443 64 6 πœƒ πœƒ NOUN cana-4443 64 7 ) ) PUNCT cana-4443 64 8 + + NUM cana-4443 64 9 𝛼𝛽}(πœ‰ 𝛼𝛽}(πœ‰ NUM cana-4443 64 10 + + X cana-4443 64 11 πœ‡ πœ‡ X cana-4443 64 12 + + ADV cana-4443 64 13 πœ‚)(πœ‡ πœ‚)(πœ‡ VERB cana-4443 65 1 + + CCONJ cana-4443 65 2 πœ™)(πœ‡ πœ™)(πœ‡ PUNCT cana-4443 65 3 + + SYM cana-4443 65 4 𝛾 𝛾 AUX cana-4443 65 5 ) ) PUNCT cana-4443 65 6 + + ADJ cana-4443 65 7 𝛾[πΌβˆ—(𝛼 𝛾[πΌβˆ—(𝛼 ADJ cana-4443 65 8 + + CCONJ cana-4443 65 9 πœ‡ πœ‡ X cana-4443 65 10 + + NOUN cana-4443 65 11 𝛿 𝛿 ADJ cana-4443 65 12 + + NUM cana-4443 65 13 πœƒ)[{πœ‚πœŽ πœƒ)[{πœ‚πœŽ NOUN cana-4443 65 14 + + CCONJ cana-4443 65 15 πœ“(πœ‰ πœ“(πœ‰ X cana-4443 65 16 + + CCONJ cana-4443 65 17 πœ‡ πœ‡ X cana-4443 65 18 + + ADJ cana-4443 65 19 πœ‚)}(πœ‡ πœ‚)}(πœ‡ NOUN cana-4443 65 20 + + CCONJ cana-4443 65 21 πœ™ πœ™ X cana-4443 65 22 ) ) PUNCT cana-4443 65 23 + + CCONJ cana-4443 65 24 πœ™πœ‰πœŽ πœ™πœ‰πœŽ NOUN cana-4443 65 25 ] ] X cana-4443 65 26 + + CCONJ cana-4443 66 1 πœƒπ΅(πœ‰ πœƒπ΅(πœ‰ NUM cana-4443 66 2 + + NUM cana-4443 66 3 πœ‡ πœ‡ ADP cana-4443 66 4 + + NOUN cana-4443 66 5 πœ‚ πœ‚ NOUN cana-4443 66 6 ) ) PUNCT cana-4443 66 7 ] ] PUNCT cana-4443 66 8 ( ( PUNCT cana-4443 66 9 𝛼 𝛼 X cana-4443 66 10 + + X cana-4443 66 11 πœ‡ πœ‡ ADP cana-4443 66 12 + + NOUN cana-4443 66 13 𝛿 𝛿 ADJ cana-4443 66 14 + + X cana-4443 66 15 πœƒ)(πœ‰ πœƒ)(πœ‰ NUM cana-4443 66 16 + + CCONJ cana-4443 66 17 πœ‡ πœ‡ X cana-4443 66 18 + + ADV cana-4443 66 19 πœ‚)(πœ‡ πœ‚)(πœ‡ VERB cana-4443 66 20 + + CCONJ cana-4443 66 21 πœ™)(πœ‡ πœ™)(πœ‡ PUNCT cana-4443 67 1 + + NUM cana-4443 67 2 𝛾)(π΅πΌβˆ— 𝛾)(π΅πΌβˆ— NOUN cana-4443 67 3 + + CCONJ cana-4443 67 4 πœ‡ πœ‡ NOUN cana-4443 67 5 ) ) PUNCT cana-4443 67 6 , , PUNCT cana-4443 67 7 πΌβˆ— πΌβˆ— NOUN cana-4443 67 8 = = SYM cana-4443 67 9 𝛿𝐸 𝛿𝐸 PROPN cana-4443 67 10 ( ( PUNCT cana-4443 67 11 πœ‡ πœ‡ ADP cana-4443 67 12 + + X cana-4443 67 13 πœ“ πœ“ NOUN cana-4443 67 14 + + CCONJ cana-4443 67 15 𝜎 𝜎 ADJ cana-4443 67 16 βˆ’ βˆ’ NOUN cana-4443 67 17 π›½π‘†βˆ— π›½π‘†βˆ— NOUN cana-4443 67 18 ) ) PUNCT cana-4443 67 19 , , PUNCT cana-4443 67 20 πΈβˆ— πΈβˆ— NOUN cana-4443 68 1 = = SYM cana-4443 68 2 𝐡 𝐡 NOUN cana-4443 68 3 𝛼 𝛼 NOUN cana-4443 68 4 + + X cana-4443 68 5 πœ‡ πœ‡ ADP cana-4443 68 6 + + NOUN cana-4443 68 7 𝛿 𝛿 ADJ cana-4443 68 8 + + NUM cana-4443 68 9 πœƒ πœƒ NOUN cana-4443 68 10 , , PUNCT cana-4443 68 11 π‘„βˆ— π‘„βˆ— PUNCT cana-4443 69 1 = = PUNCT cana-4443 69 2 πœŽπΌβˆ— πœŽπΌβˆ— PROPN cana-4443 69 3 ( ( PUNCT cana-4443 69 4 πœ‰ πœ‰ X cana-4443 69 5 + + X cana-4443 69 6 πœ‡ πœ‡ X cana-4443 69 7 + + NOUN cana-4443 69 8 πœ‚ πœ‚ NOUN cana-4443 69 9 ) ) PUNCT cana-4443 69 10 , , PUNCT cana-4443 69 11 π΄βˆ— π΄βˆ— X cana-4443 69 12 = = SYM cana-4443 69 13 πœ‰πœŽπΌβˆ— πœ‰πœŽπΌβˆ— PROPN cana-4443 69 14 + + CCONJ cana-4443 70 1 πœƒπ΅(πœ‰ πœƒπ΅(πœ‰ PROPN cana-4443 70 2 + + NUM cana-4443 70 3 πœ‡ πœ‡ ADP cana-4443 70 4 + + NOUN cana-4443 70 5 πœ‚ πœ‚ NOUN cana-4443 70 6 ) ) PUNCT cana-4443 70 7 ( ( PUNCT cana-4443 70 8 𝛼 𝛼 X cana-4443 70 9 + + X cana-4443 70 10 πœ‡ πœ‡ ADP cana-4443 70 11 + + NOUN cana-4443 70 12 𝛿 𝛿 ADJ cana-4443 70 13 + + X cana-4443 70 14 πœƒ)(πœ‰ πœƒ)(πœ‰ NUM cana-4443 71 1 + + CCONJ cana-4443 71 2 πœ‡ πœ‡ X cana-4443 71 3 + + ADV cana-4443 71 4 πœ‚)(πœ‡ πœ‚)(πœ‡ VERB cana-4443 71 5 + + CCONJ cana-4443 71 6 πœ™ πœ™ NOUN cana-4443 71 7 ) ) PUNCT cana-4443 71 8 , , PUNCT cana-4443 71 9 π‘…βˆ— π‘…βˆ— PUNCT cana-4443 71 10 = = SYM cana-4443 71 11 πΌβˆ—(𝛼 πΌβˆ—(𝛼 NOUN cana-4443 71 12 + + CCONJ cana-4443 71 13 πœ‡ πœ‡ ADP cana-4443 71 14 + + NOUN cana-4443 71 15 𝛿 𝛿 ADJ cana-4443 71 16 + + NUM cana-4443 71 17 πœƒ)[{πœ‚πœŽ πœƒ)[{πœ‚πœŽ NOUN cana-4443 71 18 + + CCONJ cana-4443 71 19 πœ“(πœ‰ πœ“(πœ‰ X cana-4443 71 20 + + CCONJ cana-4443 71 21 πœ‡ πœ‡ X cana-4443 71 22 + + ADJ cana-4443 71 23 πœ‚)}(πœ‡ πœ‚)}(πœ‡ NOUN cana-4443 71 24 + + CCONJ cana-4443 71 25 πœ™ πœ™ X cana-4443 71 26 ) ) PUNCT cana-4443 72 1 + + CCONJ cana-4443 72 2 πœ™πœ‰πœŽ πœ™πœ‰πœŽ NOUN cana-4443 72 3 ] ] X cana-4443 73 1 + + CCONJ cana-4443 73 2 πœƒπ΅(πœ‰ πœƒπ΅(πœ‰ NUM cana-4443 73 3 + + NUM cana-4443 73 4 πœ‡ πœ‡ ADP cana-4443 73 5 + + NOUN cana-4443 73 6 πœ‚ πœ‚ NOUN cana-4443 73 7 ) ) PUNCT cana-4443 73 8 ( ( PUNCT cana-4443 73 9 𝛼 𝛼 X cana-4443 73 10 + + X cana-4443 73 11 πœ‡ πœ‡ ADP cana-4443 73 12 + + NOUN cana-4443 73 13 𝛿 𝛿 ADJ cana-4443 73 14 + + X cana-4443 73 15 πœƒ)(πœ‰ πœƒ)(πœ‰ NUM cana-4443 73 16 + + CCONJ cana-4443 73 17 πœ‡ πœ‡ X cana-4443 73 18 + + ADV cana-4443 73 19 πœ‚)(πœ‡ πœ‚)(πœ‡ VERB cana-4443 73 20 + + CCONJ cana-4443 73 21 πœ™)(πœ‡ πœ™)(πœ‡ PUNCT cana-4443 73 22 + + SYM cana-4443 73 23 𝛾 𝛾 X cana-4443 73 24 ) ) PUNCT cana-4443 73 25 from from ADP cana-4443 73 26 above above ADP cana-4443 73 27 calculation calculation NOUN cana-4443 73 28 , , PUNCT cana-4443 73 29 the the DET cana-4443 73 30 ee ee PROPN cana-4443 73 31 state state NOUN cana-4443 73 32 exist exist VERB cana-4443 73 33 . . PUNCT cana-4443 74 1 5 5 X cana-4443 74 2 . . X cana-4443 74 3 conclusion conclusion NOUN cana-4443 74 4 : : PUNCT cana-4443 74 5 in in ADP cana-4443 74 6 above above ADP cana-4443 74 7 paper paper NOUN cana-4443 74 8 , , PUNCT cana-4443 74 9 the the DET cana-4443 74 10 proposed propose VERB cana-4443 74 11 model model NOUN cana-4443 74 12 is be AUX cana-4443 74 13 sieqar sieqar VERB cana-4443 74 14 ( ( PUNCT cana-4443 74 15 susceptible susceptible ADJ cana-4443 74 16 - - PUNCT cana-4443 74 17 infected infect VERB cana-4443 74 18 - - PUNCT cana-4443 74 19 exposedquarantine exposedquarantine NOUN cana-4443 74 20 - - PUNCT cana-4443 74 21 antidotal antidotal ADV cana-4443 74 22 - - PUNCT cana-4443 74 23 recovered recover VERB cana-4443 74 24 ) ) PUNCT cana-4443 74 25 which which PRON cana-4443 74 26 is be AUX cana-4443 74 27 extension extension NOUN cana-4443 74 28 of of ADP cana-4443 74 29 sair sair ADJ cana-4443 74 30 model.this model.this PRON cana-4443 74 31 model model NOUN cana-4443 74 32 is be AUX cana-4443 74 33 useful useful ADJ cana-4443 74 34 for for ADP cana-4443 74 35 getting get VERB cana-4443 74 36 malware malware NOUN cana-4443 74 37 free free ADJ cana-4443 74 38 equilibrium equilibrium NOUN cana-4443 74 39 ( ( PUNCT cana-4443 74 40 mfe mfe NOUN cana-4443 74 41 ) ) PUNCT cana-4443 74 42 point point NOUN cana-4443 74 43 . . PUNCT cana-4443 75 1 we we PRON cana-4443 75 2 discussed discuss VERB cana-4443 75 3 about about ADP cana-4443 75 4 local local ADJ cana-4443 75 5 stability stability NOUN cana-4443 75 6 of of ADP cana-4443 75 7 mfe mfe PROPN cana-4443 75 8 point point NOUN cana-4443 75 9 and and CCONJ cana-4443 75 10 endemic endemic ADJ cana-4443 75 11 equilibrium equilibrium NOUN cana-4443 75 12 ( ( PUNCT cana-4443 75 13 ee ee NOUN cana-4443 75 14 ) ) PUNCT cana-4443 75 15 point point NOUN cana-4443 75 16 . . PUNCT cana-4443 76 1 locally locally ADV cana-4443 76 2 asymptotically asymptotically ADV cana-4443 76 3 stable stable ADJ cana-4443 76 4 ( ( PUNCT cana-4443 76 5 las las NOUN cana-4443 76 6 ) ) PUNCT cana-4443 76 7 if if SCONJ cana-4443 76 8 𝑅0 𝑅0 VERB cana-4443 76 9 < < X cana-4443 76 10 1 1 NUM cana-4443 76 11 mfe mfe NOUN cana-4443 76 12 point point NOUN cana-4443 76 13 . . PUNCT cana-4443 77 1 in in ADP cana-4443 77 2 2 2 NUM cana-4443 77 3 - - PUNCT cana-4443 77 4 dimenssion dimenssion NOUN cana-4443 77 5 and and CCONJ cana-4443 77 6 3dimension 3dimension NUM cana-4443 77 7 several several ADJ cana-4443 77 8 graphs graph NOUN cana-4443 77 9 of of ADP cana-4443 77 10 parameters parameter NOUN cana-4443 77 11 are be AUX cana-4443 77 12 discussed discuss VERB cana-4443 77 13 . . PUNCT cana-4443 78 1 the the DET cana-4443 78 2 above above ADJ cana-4443 78 3 paper paper NOUN cana-4443 78 4 is be AUX cana-4443 78 5 useful useful ADJ cana-4443 78 6 for for ADP cana-4443 78 7 controlling control VERB cana-4443 78 8 the the DET cana-4443 78 9 virus virus NOUN cana-4443 78 10 in in ADP cana-4443 78 11 all all DET cana-4443 78 12 computer computer NOUN cana-4443 78 13 network network NOUN cana-4443 78 14 . . PUNCT cana-4443 79 1 communications communication NOUN cana-4443 79 2 on on ADP cana-4443 79 3 applied apply VERB cana-4443 79 4 nonlinear nonlinear ADJ cana-4443 79 5 analysis analysis NOUN cana-4443 79 6 issn issn NOUN cana-4443 79 7 : : PUNCT cana-4443 79 8 1074 1074 NUM cana-4443 79 9 - - PUNCT cana-4443 79 10 133x 133x NUM cana-4443 79 11 vol vol NOUN cana-4443 79 12 32 32 NUM cana-4443 79 13 no no NOUN cana-4443 79 14 . . PUNCT cana-4443 80 1 9s 9s NUM cana-4443 80 2 ( ( PUNCT cana-4443 80 3 2025 2025 NUM cana-4443 80 4 ) ) PUNCT cana-4443 80 5 2028 2028 NUM cana-4443 80 6 https://internationalpubls.com https://internationalpubls.com X cana-4443 80 7 refrences refrence VERB cana-4443 80 8 : : PUNCT cana-4443 81 1 [ [ X cana-4443 81 2 1]han 1]han NUM cana-4443 81 3 x x X cana-4443 81 4 , , PUNCT cana-4443 81 5 tan tan PROPN cana-4443 81 6 q. q. PROPN cana-4443 81 7 dynamical dynamical ADJ cana-4443 81 8 behavior behavior NOUN cana-4443 81 9 of of ADP cana-4443 81 10 computer computer NOUN cana-4443 81 11 virus virus NOUN cana-4443 81 12 on on ADP cana-4443 81 13 internet internet NOUN cana-4443 81 14 . . PUNCT cana-4443 82 1 appl appl PROPN cana-4443 82 2 math math PROPN cana-4443 82 3 comput comput PROPN cana-4443 82 4 2010 2010 NUM cana-4443 82 5 ; ; PUNCT cana-4443 82 6 217 217 NUM cana-4443 82 7 ( ( PUNCT cana-4443 82 8 6 6 NUM cana-4443 82 9 ) ) PUNCT cana-4443 82 10 ; ; PUNCT cana-4443 82 11 2520(6 2520(6 NUM cana-4443 82 12 ) ) PUNCT cana-4443 82 13 . . PUNCT cana-4443 83 1 [ [ X cana-4443 83 2 2 2 NUM cana-4443 83 3 ] ] PUNCT cana-4443 83 4 serazzi serazzi NOUN cana-4443 83 5 g g PROPN cana-4443 83 6 , , PUNCT cana-4443 83 7 zanero zanero NOUN cana-4443 83 8 s. s. PROPN cana-4443 83 9 computer computer PROPN cana-4443 83 10 virus virus PROPN cana-4443 83 11 propagation propagation NOUN cana-4443 83 12 models model NOUN cana-4443 83 13 . . PUNCT cana-4443 84 1 in in ADP cana-4443 84 2 international international ADJ cana-4443 84 3 workshop workshop NOUN cana-4443 84 4 on on ADP cana-4443 84 5 modeling modeling NOUN cana-4443 84 6 , , PUNCT cana-4443 84 7 analysis analysis NOUN cana-4443 84 8 and and CCONJ cana-4443 84 9 simulation simulation NOUN cana-4443 84 10 of of ADP cana-4443 84 11 computer computer NOUN cana-4443 84 12 and and CCONJ cana-4443 84 13 telecommunication telecommunication NOUN cana-4443 84 14 systems system NOUN cana-4443 84 15 . . PUNCT cana-4443 85 1 berlin berlin PROPN cana-4443 85 2 , , PUNCT cana-4443 85 3 heidelberg heidelberg NOUN cana-4443 85 4 : : PUNCT cana-4443 85 5 springer springer NOUN cana-4443 85 6 , , PUNCT cana-4443 85 7 2003 2003 NUM cana-4443 85 8 , , PUNCT cana-4443 85 9 p. p. NOUN cana-4443 85 10 26 26 NUM cana-4443 85 11 - - SYM cana-4443 85 12 50 50 NUM cana-4443 85 13 [ [ NUM cana-4443 85 14 3]yaun 3]yaun NUM cana-4443 85 15 h h NOUN cana-4443 85 16 , , PUNCT cana-4443 85 17 chen chen PROPN cana-4443 85 18 g. g. PROPN cana-4443 85 19 network network PROPN cana-4443 85 20 virus virus PROPN cana-4443 85 21 - - PUNCT cana-4443 85 22 epidemic epidemic NOUN cana-4443 85 23 model model NOUN cana-4443 85 24 with with ADP cana-4443 85 25 the the DET cana-4443 85 26 point point NOUN cana-4443 85 27 - - PUNCT cana-4443 85 28 to to ADP cana-4443 85 29 - - PUNCT cana-4443 85 30 group group NOUN cana-4443 85 31 information information NOUN cana-4443 85 32 propagation propagation NOUN cana-4443 85 33 . . PUNCT cana-4443 86 1 appl appl PROPN cana-4443 86 2 math math PROPN cana-4443 86 3 comput comput PROPN cana-4443 86 4 2008 2008 NUM cana-4443 86 5 ; ; PUNCT cana-4443 86 6 206(1 206(1 NUM cana-4443 86 7 ): ): PUNCT cana-4443 86 8 357 357 NUM cana-4443 86 9 - - SYM cana-4443 86 10 67 67 NUM cana-4443 86 11 . . PUNCT cana-4443 87 1 [ [ X cana-4443 87 2 4]wang 4]wang NUM cana-4443 87 3 y y PROPN cana-4443 87 4 , , PUNCT cana-4443 87 5 cao cao PROPN cana-4443 87 6 j j PROPN cana-4443 87 7 , , PUNCT cana-4443 87 8 jin jin PROPN cana-4443 87 9 z z PROPN cana-4443 87 10 , , PUNCT cana-4443 87 11 zhang zhang PROPN cana-4443 87 12 h h PROPN cana-4443 87 13 , , PUNCT cana-4443 87 14 sun sun PROPN cana-4443 87 15 gq gq PROPN cana-4443 87 16 , , PUNCT cana-4443 87 17 impact impact NOUN cana-4443 87 18 of of ADP cana-4443 87 19 media medium NOUN cana-4443 87 20 coverage coverage NOUN cana-4443 87 21 onepidemic onepidemic NOUN cana-4443 87 22 spreading spread VERB cana-4443 87 23 in in ADP cana-4443 87 24 complex complex ADJ cana-4443 87 25 networks network NOUN cana-4443 87 26 ; ; PUNCT cana-4443 87 27 physica physica NOUN cana-4443 87 28 a a PRON cana-4443 87 29 ; ; PUNCT cana-4443 87 30 statistical statistical ADJ cana-4443 87 31 mechanics mechanic NOUN cana-4443 87 32 and and CCONJ cana-4443 87 33 its its PRON cana-4443 87 34 applications application NOUN cana-4443 87 35 , , PUNCT cana-4443 87 36 2013 2013 NUM cana-4443 87 37 ; ; PUNCT cana-4443 87 38 392(23 392(23 NUM cana-4443 87 39 ): ): PUNCT cana-4443 87 40 p p NOUN cana-4443 87 41 58245835 58245835 NUM cana-4443 87 42 [ [ X cana-4443 87 43 5 5 NUM cana-4443 87 44 ] ] PUNCT cana-4443 87 45 tomovski tomovski NOUN cana-4443 87 46 i i PRON cana-4443 87 47 , , PUNCT cana-4443 87 48 trepviski trepviski VERB cana-4443 87 49 i i PRON cana-4443 87 50 , , PUNCT cana-4443 87 51 kokarev kokarev PROPN cana-4443 87 52 l l PROPN cana-4443 87 53 ; ; PUNCT cana-4443 87 54 topology topology NOUN cana-4443 87 55 independent independent ADJ cana-4443 87 56 sis sis NOUN cana-4443 87 57 process process NOUN cana-4443 87 58 : : PUNCT cana-4443 87 59 an an DET cana-4443 87 60 engineering engineering NOUN cana-4443 87 61 view view NOUN cana-4443 87 62 point point NOUN cana-4443 87 63 ; ; PUNCT cana-4443 87 64 comunications comunication NOUN cana-4443 87 65 in in ADP cana-4443 87 66 nonlinear nonlinear ADJ cana-4443 87 67 science science NOUN cana-4443 87 68 ; ; PUNCT cana-4443 87 69 2014 2014 NUM cana-4443 87 70 ; ; PUNCT cana-4443 87 71 19(3 19(3 NUM cana-4443 87 72 ) ) PUNCT cana-4443 87 73 ; ; PUNCT cana-4443 87 74 p. p. NOUN cana-4443 87 75 627 627 NUM cana-4443 87 76 - - SYM cana-4443 87 77 637 637 NUM cana-4443 87 78 [ [ X cana-4443 87 79 6 6 NUM cana-4443 87 80 ] ] X cana-4443 87 81 piqueira piqueira PROPN cana-4443 87 82 jrc jrc PROPN cana-4443 87 83 , , PUNCT cana-4443 87 84 araujo araujo PROPN cana-4443 87 85 vo vo NOUN cana-4443 87 86 ; ; PUNCT cana-4443 87 87 amodified amodifie VERB cana-4443 87 88 epidemiological epidemiological ADJ cana-4443 87 89 model model NOUN cana-4443 87 90 for for ADP cana-4443 87 91 computer computer NOUN cana-4443 87 92 viruses virus NOUN cana-4443 87 93 ; ; PUNCT cana-4443 87 94 applied apply VERB cana-4443 87 95 mathematics mathematic NOUN cana-4443 87 96 and and CCONJ cana-4443 87 97 computation computation NOUN cana-4443 87 98 ; ; PUNCT cana-4443 87 99 2009 2009 NUM cana-4443 87 100 ; ; PUNCT cana-4443 87 101 213(2);p 213(2);p X cana-4443 87 102 . . PUNCT cana-4443 87 103 355 355 NUM cana-4443 87 104 - - SYM cana-4443 87 105 360 360 NUM cana-4443 87 106 [ [ X cana-4443 87 107 7 7 NUM cana-4443 87 108 ] ] PUNCT cana-4443 87 109 tripathi tripathi NOUN cana-4443 87 110 a a PROPN cana-4443 87 111 , , PUNCT cana-4443 87 112 modeling modeling NOUN cana-4443 87 113 and and CCONJ cana-4443 87 114 analysis analysis NOUN cana-4443 87 115 of of ADP cana-4443 87 116 the the DET cana-4443 87 117 effects effect NOUN cana-4443 87 118 of of ADP cana-4443 87 119 antivirus antivirus NOUN cana-4443 87 120 software software NOUN cana-4443 87 121 on on ADP cana-4443 87 122 an an DET cana-4443 87 123 infected infected ADJ cana-4443 87 124 computer computer NOUN cana-4443 87 125 network network NOUN cana-4443 87 126 . . PUNCT cana-4443 88 1 applied apply VERB cana-4443 88 2 mathmatics mathmatic NOUN cana-4443 88 3 and and CCONJ cana-4443 88 4 computation computation NOUN cana-4443 88 5 ; ; PUNCT cana-4443 88 6 2014 2014 NUM cana-4443 88 7 ; ; PUNCT cana-4443 88 8 227;p 227;p NUM cana-4443 88 9 . . NOUN cana-4443 88 10 11 11 NUM cana-4443 88 11 - - SYM cana-4443 88 12 18 18 NUM cana-4443 89 1 [ [ SYM cana-4443 89 2 8 8 NUM cana-4443 89 3 ] ] X cana-4443 89 4 kumari kumari PROPN cana-4443 89 5 k. k. PROPN cana-4443 89 6 k. k. PROPN cana-4443 89 7 , , PUNCT cana-4443 89 8 singh singh PROPN cana-4443 89 9 a. a. PROPN cana-4443 89 10 , , PUNCT cana-4443 89 11 mahto mahto PROPN cana-4443 89 12 . . PUNCT cana-4443 90 1 s. s. PROPN cana-4443 90 2 , , PUNCT cana-4443 90 3 β€œ " PUNCT cana-4443 90 4 mathematical mathematical ADJ cana-4443 90 5 models model NOUN cana-4443 90 6 for for ADP cana-4443 90 7 stability stability NOUN cana-4443 90 8 in in ADP cana-4443 90 9 computer computer NOUN cana-4443 90 10 network network NOUN cana-4443 90 11 ” " PUNCT cana-4443 90 12 , , PUNCT cana-4443 90 13 journal journal NOUN cana-4443 90 14 of of ADP cana-4443 90 15 computer computer NOUN cana-4443 90 16 and and CCONJ cana-4443 90 17 mathematical mathematical ADJ cana-4443 90 18 sciences science NOUN cana-4443 90 19 , , PUNCT cana-4443 90 20 vol.10(1 vol.10(1 ADJ cana-4443 90 21 ) ) PUNCT cana-4443 90 22 , , PUNCT cana-4443 90 23 pp.92 pp.92 NOUN cana-4443 90 24 - - PUNCT cana-4443 90 25 98 98 NUM cana-4443 90 26 january january NOUN cana-4443 90 27 2019 2019 NUM cana-4443 90 28 . . PUNCT cana-4443 91 1 [ [ X cana-4443 91 2 9 9 NUM cana-4443 91 3 ] ] X cana-4443 91 4 kumari kumari PROPN cana-4443 91 5 k. k. PROPN cana-4443 91 6 k. k. PROPN cana-4443 91 7 , , PUNCT cana-4443 91 8 sinah sinah PROPN cana-4443 91 9 a. a. PROPN cana-4443 91 10 , , PUNCT cana-4443 91 11 mahto mahto PROPN cana-4443 91 12 . . PUNCT cana-4443 92 1 s. s. PROPN cana-4443 92 2 , , PUNCT cana-4443 92 3 β€œ " PUNCT cana-4443 92 4 time time NOUN cana-4443 92 5 delay delay VERB cana-4443 92 6 seirs seirs PROPN cana-4443 92 7 e e PROPN cana-4443 92 8 - - ADJ cana-4443 92 9 epidemic epidemic ADJ cana-4443 92 10 model model NOUN cana-4443 92 11 for for ADP cana-4443 92 12 computer computer NOUN cana-4443 92 13 network network NOUN cana-4443 92 14 ” " PUNCT cana-4443 92 15 , , PUNCT cana-4443 92 16 international international ADJ cana-4443 92 17 journal journal NOUN cana-4443 92 18 of of ADP cana-4443 92 19 mathematical mathematical ADJ cana-4443 92 20 archive-9(2 archive-9(2 NOUN cana-4443 92 21 ) ) PUNCT cana-4443 92 22 , , PUNCT cana-4443 92 23 2018 2018 NUM cana-4443 92 24 , , PUNCT cana-4443 92 25 pp.265 pp.265 NOUN cana-4443 92 26 - - PUNCT cana-4443 92 27 273 273 NUM cana-4443 92 28 . . PUNCT