考虑“细胞—细胞”传播的病毒动力学模型分析

发布时间：2018-01-21 19:15

本文关键词： “细胞-细胞”传播一般发生率双稳态离散时滞全局稳定性　出处：《西南大学》2015年硕士论文　论文类型：学位论文

【摘要】：近年来,实验研究显示病毒(如HTLV/HCV/HIV)能通过病毒性突触进行直接的“细胞-细胞”传播,且这种传播方式能抵制中和抗体.从而导致病毒持续.本文建立了考虑“细胞-细胞”传播方式的病毒动力学模型.分别研究了考虑体液免疫和离散时滞的“细胞-细胞”传播方式的数学模型,讨论了两个模型的数学及生物意义.本文第一章简要介绍了传统病毒动力学研究进展、病毒“细胞-细胞”传播的背景知识及本文运用的理论基础.本文第二章建立了包括一般发生率的自由病毒传播和“细胞-细胞”传播的一类病毒动力学模型.因为“细胞-细胞”传播方式能逃避抗体,因此模型同时考虑免疫损害.通过Lyapunov函数方法,我们知道：如果基本再生数R01,系统无感染平衡点是全局渐近稳定的；如果R01病毒持续生存；当系统只存在一个正平衡点时.抗体持续；如果感染细胞大于一个阈值,系统有两个平衡点,双稳态存在且抗体持续或消失取决于初始状态.文本第三章建立了一个具有离散时滞的“细胞-细胞”传播方式的病毒动力学模型.证明了解的正性和有界性,得到了基本再生数R0.当R01,始终存在无感染平衡点；当R01时,地方性平衡点存在.通过构造Lyapunov泛函,得到了该模型无感染平衡点的全局稳定性及地方性平衡点的全局稳定性.本文第四章简要回顾了前面的结论,着重介绍了本文研究内容的生物和实际意义.最后分析了本文的一些不足和需要进一步研究的问题和工作.
[Abstract]:In recent years, experimental studies have shown that viruses, such as HTLV- / HCV / HIV-1, can transmit directly through viral synapses "cell-cell". And this transmission method can resist neutralizing antibody, which leads to the persistence of virus. In this paper, a viral kinetic model considering "cell-cell" transmission mode is established. The humoral immunity and discrete time delay are studied respectively. Mathematical model of cell-to-cell transmission. The mathematical and biological significance of the two models were discussed. In the first chapter, the research progress of traditional virus dynamics was briefly introduced. The background of virus "cell-cell" transmission and the theoretical basis used in this paper. Chapter II of this paper establishes the free virus transmission and "cell-cell" including the general incidence of virus transmission. A viral kinetic model of transmission. Because "cell-cell" modes of transmission can escape antibodies. So the immune damage is considered in the model at the same time. By the Lyapunov function method, we know that if the basic reproduction number is R01, the system is globally asymptotically stable; If the R01 virus continues to survive; When there is only one positive equilibrium point in the system, the antibody continues; If the infected cell is greater than a threshold, the system has two equilibrium points. The existence of bistability and the persistence or disappearance of antibodies depend on the initial state. In Chapter 3, a viral kinetic model with discrete time-delay "cell-cell" transmission mode is established. The positive and boundedness of the solution are proved. The basic regeneration number R0. When R01, there is always no infection equilibrium point. When R01, the local equilibrium exists. The Lyapunov functional is constructed. The global stability of the non-infective equilibrium point and the global stability of the local equilibrium point are obtained. The previous conclusions are briefly reviewed in Chapter 4th of this paper. The biological and practical significance of this paper is emphatically introduced. Finally, some shortcomings of this paper and the problems and work that need to be further studied are analyzed.
【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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