EB病毒感染模型的稳定性分析

发布时间：2018-06-19 20:08

本文选题：EBV感染 + Lyapunov泛函　；参考：《西南大学》2017年硕士论文

【摘要】：本文基于Epstein-Barr病毒(EBV)的发病原理,在潜伏期的特点及其传播机制,建立了两个动力学模型,分析并讨论了其性态和生物意义.本文第一章简要介绍了 EBV的研究背景、动力学模型的研究进展、宿主抗EBV免疫反应和本文所涉及到的一些理论基础知识.本文第二章建立了具有双线性感染函数并且带有潜伏期时滞的动力学模型.首先,证明了模型解的唯一性、非负性、有界性,求出无病平衡点和地方性平衡点,并计算出模型基本再生数R0.其次,我们通过构造恰当的Lyapunov函数,结合LaSalle不变原理证明两个平衡点的全局稳定性,并讨论了参数对EBV感染的影响.本文第三章建立了考虑细胞细胞感染的动力学模型.首先,证明了模型解的唯一性、非负性、有界性,并给出基本再生数R2.其次,我们讨论了模型平衡点的存在性,通过构造恰当的Lyapunov泛函,结合LaSalle不变原理分析了无病平衡点及正平衡点的全局稳定性.本文第四章简要回顾了前面的主要工作和主要结论,着重介绍了本文动力学模型的生物意义与实际意义,并对本文工作的不足之处及进一步的研究问题和工作进行了讨论.
[Abstract]:Based on the pathogenesis of Epstein-Barr virus (EBV), the characteristics of latent period and its transmission mechanism, two kinetic models were established, and their sexual state and biological significance were analyzed and discussed. In the first chapter, the research background of EBV, the research progress of kinetic model, the host versus EBV immune response and some basic theoretical knowledge involved in this paper are briefly introduced. In chapter 2, a dynamic model with bilinear infection function with latency delay is established. Firstly, the uniqueness, nonnegativity and boundedness of the model solution are proved, and the disease-free equilibrium points and local equilibrium points are obtained, and the basic reproducing number R _ 0 of the model is calculated. Secondly, by constructing appropriate Lyapunov function and combining LaSalle invariant principle, we prove the global stability of the two equilibrium points, and discuss the influence of parameters on EBV infection. In the third chapter, a dynamic model considering cell infection was established. Firstly, the uniqueness, nonnegativity and boundedness of the solution of the model are proved, and the basic reproducing number R _ 2 is given. Secondly, we discuss the existence of the equilibrium point of the model and analyze the global stability of the disease-free equilibrium point and the positive equilibrium point by constructing the appropriate Lyapunov functional and combining the LaSalle invariant principle. In the fourth chapter, the main work and conclusions are reviewed briefly, the biological significance and practical significance of the kinetic model are emphatically introduced, and the shortcomings of this work and the further research problems and work 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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