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ID:32263609
大小:1.41 MB
页数:47页
时间:2019-02-02
《具有脉冲、阶段结构与食饵染病传染病模型研究》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、中北大学学41《7:论文摘要近些年来,高度发达的经济、医药用品种类的增多和使用,方便的交通、频繁的经济往来,在促进社会发展、提高人类生存质量的同时,也为传染病病原体的变异、传染病的传播和蔓延提供了非常便利的条件,因此建立传染病模型时要考虑这样一些因素,比如疾病在多种群间传播、种群的阶段结构、疾病在斑块间扩散以及控制传染病所要采取的一些策略等等。本文就上述问题建立了一些传染病模型,主要内容如下:第二章首先研究了一类具有非线性发生率A[pSq且食饵染病的捕食与被捕食模型,得到了该系统的边界平衡点和正平衡点,讨论了系统的稳定性。有时为了对传染病进行控制,常常在固定的时间点对有疾病的种群直接进行捕杀
2、,以降低种群的密度,因此建立了一类具有脉冲效应且食饵有病的捕食与被捕食模型,该模型通过对食饵进行脉冲剔除对其进行疾病控制。利用比较原理得到了系统的有界性,并利用重合度理论得到了系统在脉冲条件下正周期解的存在性。第三章建立了含有两个年龄阶段结构和具有终身免疫性的传染病的数学模型。接着对模型进行了定性分析,通过利用比较定理、线性化方法和构造适当的Lyapunov函数,分析了模型平衡点的渐近稳定性,得到了在适当条件下,模型的渐近性质和其平衡点的局部渐近稳定性,并且得到了疾病最终消除的条件。第四章中利用动力系统和脉冲微分方程基本理论,首先分析了具有垂直传染且具有脉冲常量预防接种的SIR模型,获得了阈
3、值凰,当凰4、elopmentispromotedandthehuman’Ssurvivalqualityisimproved.Atthesametime,theyalsoprovidetheextremelyconvenientconditionstothevariationofinfectiouspathogenandthedisseminationandspreadoftheinfectious.Whentheinfectionmodelsareconstructed,weoftenconsidersomefa.ctors,suchasthedisseminationofthediseasebetw5、eenmulti—populations,population’sstagedstructure,thediffusionofdiseasesbetweenthepatches,somestrategytocontroltheinfectiousdiseasesandSOon.Aimingtothesefactorsmentionedabove,someinfectionsdiseasemodelsaredevelopedinthisarticle.Theprimarycoverageisasfollows.Inchapter2,aprey-predatormodelwiththepreyi6、nfectedandthenonlinearincidencerateAS。Ivisfirstlystudied.Inthispart,theboundaryequilibriumpointandpositiveequi—libriumpointaregot,andthestabilityofthissystemisdiscussed.Inordertocontrolsomeinfections,theinfectedpopulationaresometimeskilledatthestationarytimetoreducethedensityofpopulation.Consequent7、ly,aprey-predatormodelwithimpulsiveeffectandthepreyinfectedisestablished.Inthismodel,thediseaseiscontrolledbytheimpulsivecullingtotheprey.Byusingimpulsivedifferentialinequality,theboundednessofthesystemispr
4、elopmentispromotedandthehuman’Ssurvivalqualityisimproved.Atthesametime,theyalsoprovidetheextremelyconvenientconditionstothevariationofinfectiouspathogenandthedisseminationandspreadoftheinfectious.Whentheinfectionmodelsareconstructed,weoftenconsidersomefa.ctors,suchasthedisseminationofthediseasebetw
5、eenmulti—populations,population’sstagedstructure,thediffusionofdiseasesbetweenthepatches,somestrategytocontroltheinfectiousdiseasesandSOon.Aimingtothesefactorsmentionedabove,someinfectionsdiseasemodelsaredevelopedinthisarticle.Theprimarycoverageisasfollows.Inchapter2,aprey-predatormodelwiththepreyi
6、nfectedandthenonlinearincidencerateAS。Ivisfirstlystudied.Inthispart,theboundaryequilibriumpointandpositiveequi—libriumpointaregot,andthestabilityofthissystemisdiscussed.Inordertocontrolsomeinfections,theinfectedpopulationaresometimeskilledatthestationarytimetoreducethedensityofpopulation.Consequent
7、ly,aprey-predatormodelwithimpulsiveeffectandthepreyinfectedisestablished.Inthismodel,thediseaseiscontrolledbytheimpulsivecullingtotheprey.Byusingimpulsivedifferentialinequality,theboundednessofthesystemispr
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