两类具有C-M发生率和免疫反应的HIV模型分析

发布时间：2018-10-29 11:06

【摘要】：本文依据HIV病毒进入宿主细胞感的感染过程及HIV病毒感染的动力学研究基础,建立了两类具有C-M发生率和免疫反应的HIV传染病模型，并对其动力学性质展开分析.第一章,介绍了HIV传染病的研究背景和进展、HIV病毒感染的过程、CTL免疫反应以及文章所需的相关理论知识.第二章,建立了具有C-M发生率及潜伏期的HIV传染病模型.为了能更好的描述免疫反应对感染的影响,模型中采用更为一般的免疫产生率.接下来得到基本再生数及免疫再生数.分析了无病平衡点，，无免疫平衡点及免疫平衡点的存在性及唯一性.通过构造Lyapunov函数和LaSalle不变集原理.得到无病平衡点,无免疫平衡点及免疫平衡点的全局稳定性.最后讨论了潜伏期感染细胞恢复率对模型结果的影响.第三章,通过引入CTL免疫细胞从识别到作用HIV病毒的滞后时间，建立了一个具有C-M发生率和CTL免疫时滞的HIV传染病模型.通过构造Lyapunov乏函及利用LaSalle不变集原理.得到了无病平衡点和无免疫平衡点的全局稳定性并证明了Hopf分支的存在性.当无时滞且免疫再生数大于1时.免疫平衡点局部渐近稳定.当时滞τ大于某一正数、免疫再生数大于1时.则会出现Hopf分支.第四章,简要回顾文章建立模型的思路及得到的相关结论.着重介绍了模型的实际意义.最后讨论文章的不足并提出值得进一步研究的问题.
[Abstract]:Based on the infection process of HIV virus into host cells and the dynamics of HIV virus infection, two kinds of HIV infectious disease models with C-M incidence and immune response were established, and their kinetic properties were analyzed. The first chapter introduces the research background and progress of HIV infection, the process of HIV infection, the immune response of CTL, and the relevant theoretical knowledge needed in this paper. In chapter 2, a HIV infectious disease model with C-M incidence and incubation period was established. In order to better describe the effect of immune response on infection, a more general immune production rate is used in the model. Then the basic number of regeneration and the number of immune regeneration were obtained. The existence and uniqueness of disease-free equilibrium point, non-immune equilibrium point and immune equilibrium point are analyzed. By constructing Lyapunov function and LaSalle invariant set principle. The global stability of disease-free equilibrium, immune equilibrium and immune equilibrium is obtained. Finally, the effect of the recovery rate of latent infection cells on the model results was discussed. In chapter 3, by introducing the lag time of CTL immune cells from recognizing to acting on HIV virus, a HIV infectious disease model with C-M incidence and CTL immune delay is established. By constructing Lyapunov function and using LaSalle invariant set principle. The global stability of disease-free equilibrium and non-immune equilibrium is obtained and the existence of Hopf bifurcation is proved. When there is no delay and the number of immune regeneration is greater than 1. The immune equilibrium point is locally asymptotically stable. At that time, the hysteresis 蟿 is greater than a positive number, and the immune regeneration number is more than 1. The Hopf branch appears. In chapter 4, we briefly review the ideas and conclusions of this paper. The practical significance of the model is emphatically introduced. Finally, it discusses the deficiency of the article and puts forward some problems worthy of further study.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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