26172.受環(huán)境和傳播路徑影響的幾種傳染病模型的研究

1、分類號(hào)：密級(jí)：無(wú)UDC:單位代碼：1011850!■山西師范大學(xué)研究生碩士學(xué)位論文受環(huán)境和傳播路徑影響的幾種傳染病模型的研究閏咪咪指導(dǎo)教師姓名石瑞青副教授學(xué)院山西師范大學(xué)數(shù)學(xué)與計(jì)算機(jī)科學(xué)學(xué)院申請(qǐng)學(xué)位級(jí)別理學(xué)碩士專業(yè)名稱應(yīng)用數(shù)學(xué)論文提交日期2014年3月20日論文答辯日期2014年5月20曰學(xué)位授予單位山西師范大學(xué)學(xué)位授予日期2014年月曰答辯委員會(huì)主席張勤海教授評(píng)閱人唐三教授肖燕妮教授2014年3月28日Title:Thestudyof

2、influenceofenvironmenttransmissionroutefsomeclassesofepidemicmodelsMaj:AppliedMathematicsName:YanMimiSupervis:ProfessShiRuiqingSignatureSignatureAbstractInthispapersomemathematicalmodelsareinvesticaled.(1)Amathematicalmo

3、delforcouplingwithinhostandbetweenhost(2)theeffectoftransmissionrouteonplantvirusepidemicdevelopmentanddiseasecontrol.Wediscussthedynamicbehavioursofthemodels.Thearticleincludethreechapters.Inchapter1weintroducetheresear

4、chbackgroundofthisarticlethemaintaskandsomeimportantpreliminaries.InChapter2wediscussamathematicalmodelforcouplingwithinhostandbetweenhost.Inthefirstsectionweanalyzeamathematicalmodelwithnonlinearincidenceratewhichinanen

5、vironmentallydriveninfectiousdisease.WedefineanewreproductivenumberRvoforthefastsystemsitiseasytoshowthatinfectionfreeequilibriumUqislocallyasymptoticallystableifRvO1usingtheRouthHurwitzstabilitycriterionweobtainthelocal

6、stabilityofJJ(E)undertheconditionthatthefastsystemhasthestableinteriorequilibriumIJ(E)wedynamiclinkageforthefastandslowsystemsisthroughtheenvironmentalcontaminationvariableEweobtaintheconditionthattheexistenceandstabilit

7、yofaninteriorequilibriumofthefullsystem.Atlastanumericalanalysisisgiventoshowtheeffectivenessofthemainresults.Inthesecondsectionanenvironmentallydriveninfectiousdiseasemodelwithabilinearincidencerateisstudied.Wegetthesuf

8、ficientconditionsfortheexistenceandstabilityoftheequilibriaofthefullsystem.Anumericalanalysisisgiventoshowtheeffectivenessofthemainresults.InChapter3weanalyzetheeffectoftransmissionrouteonplantvirusepidemicdevelopmentand

9、diseasecontrol.ByconstructionasuitableLyapunovfunctionaltheinfectionfreeequilibriumUqisgloballyasymptoticallystableifRq1.Weanalysethemodeltodeterminetheeffectofdirecttransmissiononplantdiseasecontroldirectedagainstindire

10、cttransmission.Intheendnumericalsimulationsarecarriedouttoexplainthemathematicalconclusions.【KeyWords】EpidemicmodelRouthHurwitzcriterionNonlinearincidencerateEquilibriumThebasicreproductionnumber【TypeofThesis】Application