几娄具有非线性传染率的传染病模型的研究常红果.pdf

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w*o<).ITitle:ThestudyonepidemicmodelswithrecruitmentrateandnonlinearincidencerateMajor:AppliedMathematicsName:ChangHongguoSignature:Supervisor:ProfessorJiaJianwenSignature:AbstractInthispaper,wemainlystudythedynamicsofsomeclassesofepidemicalmodelwi

9、thanonlinearbirthinpopulation.Thearticleincludesthreechapters.Theprefaceisinchapter1,weintroducetheresearchbackgroundofthisarticle,themaintaskandsomeimportantpreliminaries.InChapter2,epidemicmodelsinvolvingaverticaltransmissionwarestudied.Therearetwopartinthischapte

10、r:Inthefirstpart,apulsevaccinationSEIQRepidemicmodelwithverticaltransmissionandnonlinearincidenceratewasstudied.Usingthediscretedynamicalsystemdeterminedbythestroboscopicmap,weobtainedtheexactdisease-freeperiodicsolution.WeobtainedtwothresholdvalueR1andR2.Weshowthatt

11、hedisease-freeperiodicsolutionofthissystemisgloballyattractivewhenR1<1bythetheoryofdelayeddifferentialequationsandthecomparisontheoremforimpulsivedifferentialequations.ThesystemispermanentunderR2>1.Inthesecondpart,ASEIQRepidemicmodelwithverticaltransmissionandnonlinea

12、rincidenceratewasstudied.WeobtainedthethresholdvalueR0todeterminethedynamicsqualitiesoftheepidemicmodelbydirectlyusingthenextgenerationmet