具有非線性發(fā)生率的傳染病模型.pdf

1、西南大學(xué)碩士學(xué)位論文具有非線性發(fā)生率的傳染病模型姓名：周銳申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王穩(wěn)地20070501SomeEpidemiologicalModelswithControlMeasuresAbstractMajorlAppliedmathematicsSpecialityIBiologicalmathematicsSupervisorIWangWendiAuthortZhonRni(20040807)Theaimo

2、fthisworkistoconst州∞veralmathematicalmodelsinepidemiologyandtoanalyzetheasymptoticbehaviorofthesemodelsInthefirstpart，80meepidemicmodelswithnonlinearincidencerate8“studiedtoconsidereffectsofprotectionmeasutr∞andintervent

3、ionpoliciesInthefirsttwosections，weconsiderSIRSepidemiologicalmodelswithnonlinearincidencerates桷and雨鬻刁，AthresholdforthediseasetobeepidemicortobeeradicatedisestablishedThebehaviorofsolutionandthethresholdconditionsofexist

4、enceandlocallyasymptoticstabilityfileobtainedThesumeientconditionsontheglobalasymptoticstabilityofthediseasefresequilibriumandtheendemicequilibriumInthethirdsection。aspeciesmechanicsepidemicalmodelwithnonlinearratewascon

5、sideredThesu伍cientconditionsontheglobalasymptoticstabilityoftheextinctequilibriumandthesurvivalequilibriumaleobtainedInthefourthsection，westudytheglobaldynamicsofnepidemicmodelwith8completeformofthenoumonotonicincidencer

6、ateof|411bycarryingoutthequalitativeanalysisofthemodel，itisshownthatthemodeladmitsrichdynamicalbehaviorsIthassaddlenodebifurcationsofendemicequilibria，Hopfbifurcations，thesaddlenodebifurcationofnonhyperbolicperiodicorbit

7、，whichimpliestheexistenceoftwolimitcyclesandhomoeliniebifurcationsWehavealsofoundthatthemodeladmitsbistablesteadystatessuchthattheoutcomeofdiseaseevolutiondependsuponinitialpositionsInthesecondpartofthispaper。weconsider8