宿主体内结核分枝杆菌的动力学模型分析

发布时间：2018-07-09 16:31

  本文选题：结核分枝杆菌 + 后向分支　； 参考：《西南大学》2017年硕士论文

【摘要】：本文根据结核分枝杆菌在体内的感染过程免疫机制,分别建立了一般发生率下包含结核分枝杆菌两种增殖方式的体内结核分枝杆菌动力学模型,及宿主体内包含离散时滞的结核分枝杆菌动力学模型,并讨论了两个模型的动力学性态和生物意义.第一章,介绍了结核病的疫情、结核分枝杆菌的背景知识、国内外结核分枝杆菌动力学模型的研究进展及本文所需的基本理论知识.第二章,建立了一个一般发生率下包含结核分枝杆菌两种增殖方式的宿主体内结核分枝杆菌动力学模型.首先,给出了结核分枝杆菌的基本再生数R0和免疫基本再生数R1;其次,借助基本再生数探究了无免疫平衡点的存在性及稳定性,并得到在无病平衡点处出现后向分支的充要条件,同时研究了该条件和发生率函数及胞内增殖所产生的裂解释放量的关系;最后,给出了 一些数值模拟以验证结论.第三章,建立了一个包含离散时滞与CTL饱和免疫发生率的宿主体内结核分枝杆菌动力学模型,并对其进行了分析.首先,证明了模型解的非负性和有界性,并计算出结核分枝杆菌的基本再生数R0和免疫基本再生数R1;其次,分析了平衡点的存在性和局部稳定性;最后,通过构造合适的Lyapunov泛函,得到了无病平衡点、无免疫平衡点和正平衡点的全局稳定的条件.第四章,对本文的主要工作进行了简要总结,着重介绍了模型的生物意义和实际价值,并讨论了本文的一些不足和需要进一步研究的问题.
[Abstract]:According to the immune mechanism of the infection process of Mycobacterium tuberculosis in vivo, a dynamic model of Mycobacterium tuberculosis in vivo containing two modes of mycobacterium tuberculosis proliferation was established in this paper. And the dynamic model of Mycobacterium tuberculosis with discrete time delay in the host is discussed. The dynamic behavior and biological significance of the two models are discussed. The first chapter introduces the epidemic situation of tuberculosis, the background knowledge of Mycobacterium tuberculosis, the research progress of dynamics model of Mycobacterium tuberculosis at home and abroad and the basic theoretical knowledge needed in this paper. In chapter 2, a dynamic model of Mycobacterium tuberculosis in host is established, which contains two modes of mycobacterium tuberculosis proliferation. Firstly, the basic regeneration number R _ 0 and the immune basic regeneration number R _ 1 of Mycobacterium tuberculosis are given. Secondly, the existence and stability of the non-immune equilibrium point are explored with the help of the basic regeneration number. The necessary and sufficient conditions for backward bifurcation at the disease-free equilibrium point are obtained, and the relationship between the condition and the incidence function and the amount of cracking release produced by intracellular proliferation is studied. Finally, some numerical simulations are given to verify the conclusions. In chapter 3, a dynamic model of Mycobacterium tuberculosis in host with discrete delay and CTL saturation immunity is established and analyzed. Firstly, the nonnegative and boundedness of the model solution are proved, and the basic regeneration number R0 and the immune basic regeneration number R1 of Mycobacterium tuberculosis are calculated. Secondly, the existence and local stability of the equilibrium point are analyzed. By constructing appropriate Lyapunov functional, the conditions for global stability of disease-free equilibrium, non-immune equilibrium and positive equilibrium are obtained. In the fourth chapter, the main work of this paper is briefly summarized, the biological significance and practical value of the model are introduced, and some shortcomings and problems need further study are discussed.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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本文编号：2109955