非自治SEIRS傳染病模型和裂谷熱傳播模型的動(dòng)力學(xué)行為研究.pdf

1、碩士研究生學(xué)位論文論文題目（中文）:論文題目（英文）:研究生姓名：學(xué)科專(zhuān)業(yè):學(xué)位類(lèi)別：研究方向：導(dǎo)師姓名職稱(chēng):疆大學(xué)非自治SEIRS傳染病模型和裂谷熱傳播模型的動(dòng)力學(xué)行為研究TheStudyontheDynamicalBehavisinNonautonomousSEIRSEpidemicModelRiftValleyFeverTransmissionModel劉文林?jǐn)?shù)學(xué)理學(xué)碩士應(yīng)用數(shù)學(xué)滕志東教授論文答辯日期年月日學(xué)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