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1、StabilityanalysisofanSIRSmodelwithtime-delayonScale-FreeNetworkAbstractItiseasyforthestudyofthepropagationprocessofmanyinfectiousdiseasestoobtainconclusionsbytheanalysisofcomplexdynamicnetworks.ManySI,SISandSIRmodelsonScale-FreeNetworksareanalyzedaccurately.Duetoth
2、espeedofinformationtransferormemory,delayoftenoccursinmanycomplexnetworks.Inthispaper,SIRSmodelwithdelayonScale-FreeNetworksisresearched.Inchapterone,weintroducethestudysignificanceofthepaper,andthedevelopmentofmodelsonScale-FreeNetwork.Inchaptertwo,weintroducecomm
3、onknowlegeofinfectiousdiseases,forexample,thedynamicsofhomogeneityinfectiousdiseases,thebasicreproducenumber;then,weexplainsimpleknowlegeaboutcomplexnetwork,suchas,degreeanddegreedistribution,Scale-FreeNetwork,andmodellingofinfectiousdiseasesonnetwork;finally,wepre
4、sentsimplelytherelevanttheoreticalknowledgethatneedtouse,forexample,thetheoryofpersistence.Inchapterthree,weinvestigateanSIRSmodelwithtimedelayontheuncorrelatedScale-FreeNetworks,andanalyzethedynamicalbehaviorofthemodel.Wegivetheexpressionofthebasicreproductionnumb
5、erbyconsideringtheexistenceoftheendemicequilibrium.ByconstructingJocabimatrixandLyapunovfunction,theglobalstabilityofthedisease-freeequilibriumisproved.Finally,thepersistenceofendemicequilibriumisobtained.Inchapterfour,basedonthemodelofchapertthree,wepresentanSIRSm
6、odelwithtimedelayandsaturatedlinkontheuncorrelatedScale-FreeNetworks.Thebasicreproductionnumberandtheuniqueendemicequilibriumofthismodelareobtained.ByconstructingJocabimatrixandLyapunovfunction,theglobalstabilityofthedisease-freeequilibriumisproved.Keywords：Scale-F
7、reeNetwork,time-delay,thebasicreproductionnumber,globalstability,permanence第一章引言1.1研究背景及意义11.2国内外研究现状21.3本文的主要内容4第二章预备知识2.1均勻混合传染病动力学基本概念62.2基本再生数72.3度与度分布82.4无标度网络92.5网络传染病动力学的建模102.6持续性理论11第三章无标度网络上带有时滞的SIRS模型的稳定性分析3.1模型的构造133.2地方病平衡点的存在及基本再生数153.3无病平衡点的稳定性分析173.
8、4地方病平衡点的持续性分析20第四章无标度网络上具有饱和链接的带有时滞的SIRS模型4丄模型的构造224.2地方病平衡点的存在及基本再生数244.3无病平衡点的稳定性26第五章结束语5丄本文的工作与总结295.2存在的问题以及以后的工作30参考文献攻读硕士学位期间研究成果致谢第一章引言1.
