一类带时滞且具有预防接种免疫力的SIR传染病模型的稳定性与Hopf分岔分析.pdf

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1、˜a‘ž¢…äký“«•¼åSIRD/¾.•½5†Hopf©©ÛStabilityandHopfbifurcationforaSIRepidemiologicalmodelwithvaccinalimmunityanddelaysystemƉ;’µA^êÆïÄ)µpç•“µo)ÇU9ŒÆnÆ"˜cÊn›FÕM5(²<(²¤¥ÆØ©´<3“•e?1ïÄóŠÚïĤJ§Ø©¥AO±I5Ú—ƒ?§Ø©¥Ø•¹Ù¦<®²uL½>LïĤJ§•Ø•¹•¼U9ŒÆ½Ù¦˜

2、ÅƽyÖ¦^Lá"†·˜ÓóŠÓ“éïĤ‰?Ûzþ®3Ø©¥Š²(`²¿L«¿"ÆØ©Šö¶µiFÏ:cFÆØ©‡¦^ÇÖÆØ©Šö)U9ŒÆk'3!¦^ÆØ©5½"AÇU9ŒÆŒ±òÆØ©ܽܩSN?k'êâ¥?1u¢§¿æ^K

3、“«•¼åSIRD/¾.•½59Hopf©œ¹.©SN©•üÜ©:Äk´ïL§,Ùg´©ÛT.þ²ï:Ú/•¾²ï:•½5ÚHopf©œ¹.3ïL§¥,·‚¿©•Ä˜½«+O•!;¾D/„Ý!ý“«!g,k!Ͼk!£•œ¹!;¾dÏÏõ«Ïƒ,¦·‚¤ï.U•bƒ/‡A©¤ïįKý¢œ¹.©¤ï.•:8>>dS(t)>>=(+)S(t)S(t)I(t);>>dt>>dt>>>>>:dR(t)

4、=S(t)+I(t)R(t):dtï,©'%¯K´dÏÏé.•½5Ú©K•,¤

5、^•£Ú•{k:•½5Ú©nØ!AŠ{!¥%6/!5‰.•{.•,ÏLî—Øy,Ñ:(1).þ²ï:Ú/•¾²ï:•3^‡;(2).þ²ï:•½5ÚHopf©œ¹;(3)./•¾²ï:•½5ÚHopf©œ¹;(4)./•¾²ï:Hopf©±Ï)•½5Ú©••OŽúª.'…c:ž¢¶Ã¾²ï:¶/•¾²ï:¶•½5¶Hopf©©AbstractInthispaper,stability

6、andHopfbifurcationofaSIRepidemicmodelwithvaccinalimmunityanddelaywillbeconsidered.Theletterdividesintotwoparts:theprogressofmodelingrstly;thenanalysisofthestabilitiesandHopfbifurcationsofthedisease-freeequilibriumpointandtheendemicequilibriumpoint.Whenwebuildth

7、emodel,denitepopulationincrease,thespreadofdiseaseamongthem,vaccination,naturalcauses,deathbydisease,cureconditionandtheincubationperiodforthediseasewillbeconsidered.Inthisway,themodelcanbemoreclosetotherealityweconcerned.Themodelweestablishedisasfollows:8>>dS(

8、t)>>=(+)S(t)S(t)I(t);>>dt>>dt>>>>>:dR(t)=S(t)+I(t)R(t);dtThenthefulltextcaresabouthowincubationperiodeectsthestabilityandHopfbifurcationofthemodel.Inthearticlewemakeuseofthestabilityandbifurcationtheory,eigenvaluemethod

9、andnormalformtheory.Atlast,throughthestrictreasoning,wehave:(1)Existenceconditionsofthedisease-freeequilibriumpointandtheendemicequilibriumpoint;(2)StabilityandHopfbi