考虑非溶解治愈和免疫损伤的乙肝病毒模型分析

发布时间：2018-04-02 11:05

本文选题：非溶解治愈　切入点：全局稳定性　出处：《西南大学》2012年硕士论文

【摘要】：本文建立并分析了考虑具有非溶解自愈,免疫损伤.免疫反应时滞等因素的乙型肝炎病毒感染模型.首先我们建立了一个三维模型,考虑了健康细胞、感染细胞以及CTL免疫细胞数量的动力学性态.然后建立了具有免疫反应时滞的模型及同时考虑抗体免疫和CTL免疫的数学模型.随后讨论了平衡点的局部和全局稳定性及相应的生物意义.全文共分四章. 第一章,简述了乙型肝炎的发病,传播原理及预防,治疗措施.进一步给出了传染病动力学.病毒动力学和微分方程稳定性理论和基础知识. 第二章,我们主要考虑一个具有免疫损伤和细胞因子介导的乙肝病毒感染模型.研究了平衡点的全局和局部稳定性,得到了只要无疾病平衡点和无免疫平衡点是局部稳定的.就一定是全局渐近稳定的.并得证明了若感染平衡点存在.则系统是一致持续生存的. 第三章,我们考虑了具有免疫反应时滞的乙肝病毒感染模型.通过对模型的分析,我们证明了免疫反应对无感染平衡点和无免疫平衡点的局部和全局稳定性均无影响.但是会影响感染平衡点的稳定性. 第四章,我们同时考虑了抗体免疫和CTL免疫反应并建立了一个五维模型.我们研究了平衡点的局部稳定性,并且分析了免疫损伤对乙肝病毒感染的影响. 第五章,我们对全文的结论进行总结和讨论.本文从数学的角度为乙型肝炎控制与治疗提供了一个优化合理的策略,为乙肝的治疗及预防提供了一定的理论参考.
[Abstract]:In this paper, a hepatitis B virus infection model with insoluble self-healing, immune damage, immune response delay and other factors was established and analyzed. The dynamic state of the number of infected cells and CTL immune cells is discussed. Then, a model with immune response delay and a mathematical model considering both antibody and CTL immunity are established. Then, the local and global stability of equilibrium point is discussed. Qualitative and corresponding biological significance. The full text is divided into four chapters. In the first chapter, the pathogenesis, transmission principle, prevention and treatment of hepatitis B are briefly introduced. Furthermore, the theory and basic knowledge of infectious disease dynamics, viral dynamics and differential equation stability are given. In the second chapter, we mainly consider a model with immune damage and cytokine mediated hepatitis B virus infection. We study the global and local stability of the equilibrium point. As long as the disease-free equilibrium point and the non-immune equilibrium point are locally stable, it must be globally asymptotically stable, and it is proved that the system is uniformly persistent if the infection equilibrium exists. In the third chapter, we consider the hepatitis B virus infection model with immune response delay. We prove that the immune response has no effect on the local and global stability of the non-infective equilibrium point and the non-immune equilibrium point, but it will affect the stability of the infective equilibrium point. In chapter 4, we consider both antibody immunity and CTL immune response and establish a five-dimensional model. We study the local stability of equilibrium point and analyze the effect of immune injury on hepatitis B virus infection. In the fifth chapter, we summarize and discuss the conclusions of this paper. This paper provides a reasonable strategy for the control and treatment of hepatitis B from the mathematical point of view, and provides a certain theoretical reference for the treatment and prevention of hepatitis B.
【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】：R311;O19

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