非自治SEIRS傳染病模型和裂谷熱傳播模型的動力學行為研究.pdf

1、碩士研究生學位論文論文題目（中文）:論文題目（英文）:研究生姓名：學科專業(yè):學位類別：研究方向：導師姓名職稱:疆大學非自治SEIRS傳染病模型和裂谷熱傳播模型的動力學行為研究TheStudyontheDynamicalBehavisinNonautonomousSEIRSEpidemicModelRiftValleyFeverTransmissionModel劉文林數(shù)學理學碩士應用數(shù)學滕志東教授論文答辯日期年月日學位授予日期年月日Abs

2、tractAbstractInrecentyearsthestudyofnonautonomousepidemicmodelhasbeenwidelyconcernedbyanumberofscholars.Duetothechangesofseasonsthetransmissionofmanydiseaseoftenshowdifferentseasonalbehavisinrealisticlife.Therefethegener

3、alnonautonomousepidemicdynamicalmodelsareproposedwhicharemeclosertotherealenvironmentthanautonomousmodels.InthispaperwemakedetaileddiscussfaSEIRSepidemicmodelwiththedifferentdegreeofdiseaseaRiftValleyFevertransmissionmod

4、elwithperiodiccoefficientsbyusingthepersistencepermanencetheyofdynamicalsystemsinequalityanalysismethodproofsbycontradictionsoon.Wediscussthepermanenceextinctionofdiseaseobtainthesufficientconditionsonthepermanenceextinc

5、tionofdiseasefthemodel.Thispaperisdividedintofourparts.Itscontentscanbesummarizedasfollows:Thefirstpartisintroductionweintroducetheresearchbackgroundthepresentinvestigationofthenonautonomousepidemicmodel.wegivethemainres

6、earchcontentsofourpaper.InthesecondpartwewillmainlydiscussthedynamicbehavisofanonautonomousSEIRSepidemicmodelwithdifferentdegreeofdisease.Wewillestablishthepositivityboundednessofsolutionsofthemodel(2.1)byusingproofsbyco

7、ntradiction.WewillobtainthethresholdconditionsRiR[R2R2aboutthepermanenceextinctionofdiseasebyapplyingthepermanencetheyofdynamicalsystems.AtthesametimeweprovethatthediseaseisextinctifthethresholdvaluesRi0R20.Particularlyw

8、henthemodel(2.1)degeneratesintoperiodicalmostperiodicmodelsthethresholdconditionsofthepermanenceextinctionofdiseasearediscussed.Finallywegivesomenumericalsimulationindertofurtherverifythecrectnessofourtheeticalresults.In

9、thethirdpartwewilldiscussthedynamicbehavisofaRiftValleyFevervirustransmissionmodelwithperiodiccoefficients.Thepositivityboundednessofsolutionsofthemodel(3.2)areestablished.Byusingthenextgenerationmatrixapproachthepersist

10、encetheyofdynamicalsystemsthepropertiesofperiodiclinearsystemswecalculatebasicreproductionnumberRo.weestablishthatthediseasefreeperiodicsolutionisgloballyasymptoticstabilitywhenthebasicreproductionnumberRo1.Finallywechoo