具有胞胞感染的HIV-1病毒动力学模型分析

发布时间：2018-03-15 00:07

本文选题：胞胞感染　切入点：一般疾病发生率　出处：《西南大学》2016年硕士论文　论文类型：学位论文

【摘要】：本文依据HIV-1病毒对体内宿主细胞的感染过程及HIV-1病毒动力学特征,提出了一种新的疾病发生率形式,以之为基础构建了两个动力学模型对其性态加以分析.第一章,介绍了HIV-1的背景、动力学模型研究进展、宿主抗HIV免疫应答及本文所涉及到的一些理论基础和符号说明.第二章,建立了同时考虑病毒感染和胞胞感染并且带有一般疾病发生率的动力学模型.首先,证明了模型解的正性和有界性,计算出模型基本再生数R0.其次,讨论了模型平衡点的存在性及稳定性.第三章,建立了同时考虑病毒感染和胞胞感染并且带有一般疾病发生率的连续时滞动力学模型.首先,证明了模型解的正性和有界性,并给出基本再生数Ro.其次,讨论了模型平衡点的存在性.并通过构造恰当的Lyapunov泛函分析了无病平衡点及正平衡点的全局稳定性.第四章,简要回顾了本文的主要工作,着重介绍了模型的实际意义,并对本文工作的不足之处及进一步研究方向进行了讨论.
[Abstract]:According to the infection process of HIV-1 virus to host cells in vivo and the dynamics of HIV-1 virus, a new form of disease incidence is proposed in this paper. Based on it, two kinetic models are constructed to analyze the behavior of HIV-1 virus. This paper introduces the background of HIV-1, the research progress of kinetic model, the host versus HIV immune response, and some theoretical bases and symbolic descriptions involved in this paper. A kinetic model considering both viral and cellular infections with general disease incidence was established. Firstly, the positive and bounded solutions of the model were proved, and the basic regeneration number R0 was calculated. The existence and stability of the equilibrium point of the model are discussed. In chapter 3, a continuous time-delay dynamic model is established, which considers both virus infection and cellular infection and has a general incidence of disease. Firstly, the positive and boundedness of the solution of the model are proved. Then, the existence of equilibrium point of the model is discussed, and the global stability of disease-free equilibrium and positive equilibrium is analyzed by constructing appropriate Lyapunov functional. Chapter 4th, the main work of this paper is briefly reviewed. The practical significance of the model is introduced, and the shortcomings of this work and the direction of further research are discussed.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175

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