具有CTL免疫反应的乙肝病毒模型的全局动力学

发布时间：2018-07-09 09:15

本文选题：病毒动力学 + 非溶解治愈　；参考：《西南大学》2012年硕士论文

【摘要】：本论文研究了具有CTL免疫反应的乙肝模型动力系统.首先研究了人体在感染了乙肝病毒后机体中的健康细胞、感染肝细胞以及免疫细胞数量的变化,建立了相应的乙肝病毒感染的数学模型.另外还考虑了具有CTL反应时滞的乙型病毒模型,研究时滞对系统平衡点稳定性的影响. 第一章中介绍了乙肝的相关病原学和传染病学,宿主内HBV病毒动力学模型的的研究进展和本文的相关工作. 第二章考虑具有溶解和非溶解免疫反应的乙肝病毒模型的全局动力学.证明了基本再生数小于一时无病平衡点是全局稳定的；当基本再生数大于一时系统是一致持续的.并通过几何方法的应用,得到了正平衡点全局稳定的一个充分条件. 第三章基于一些重要的生物意义,建立了一个具有时滞和CTL免疫的乙肝病毒模型.得到当基本再生数小于等于一时无病平衡点的全局稳定性；当基本再生数大于一时系统是一致持续的.并分析了感染平衡点的Hopf分支的存在性.研究CTL时滞对模型的影响. 通过本文从数学的角度进一步研究了乙肝病毒感染过程中CTL免疫的作用,这为我们更好的了解疾病发展和各种各样的药物治疗策略提供了依据.
[Abstract]:In this paper , we studied the dynamic system of hepatitis B model with CTL immune response . First , we studied the changes of healthy cells , infected liver cells and immune cells in the body infected with hepatitis B virus , established the corresponding mathematical model of hepatitis B virus infection , and also considered the effect of time lag on the stability of the system equilibrium point .

In the first chapter , the research progress of hepatitis B virus dynamics model and related work are introduced in this paper .

The second chapter considers the global dynamics of the hepatitis B virus model with dissolved and non - dissolved immune responses .
A sufficient condition for global stability of positive equilibrium point is obtained when the basic number of regeneration is greater than that of a system .

In chapter 3 , a model of hepatitis B virus with time lag and CTL immunity is established based on some important biological significance .
The existence of Hopf bifurcation of infection equilibrium point is analyzed . The effect of time delay on the model is studied .

In this paper , the effect of CTL immunity in the course of HBV infection is further studied from the point of view of mathematics , which provides a basis for us to understand the development of disease and various strategies for drug treatment .
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：R318.01;O19

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