两类宿主体内基孔肯雅病毒的动力学模型

发布时间：2018-06-27 18:10

  本文选题：宿主体内模型 + 基孔肯雅病毒感染　； 参考：《西南大学》2016年硕士论文

【摘要】：本文根据基孔肯雅病毒在宿主体内的发病机制和免疫机制,在病毒动力学基本模型的基础上,建立并分析了考虑体液免疫和免疫时滞的基孔肯雅病毒动力学模型,以及具有饱和感染率的离散时滞动力学模型.探究了两个模型的动力学性态及生物意义.第一章首先介绍了有关基孔肯雅病毒的背景知识、该病毒动力学模型研究进展及本文用到的主要理论.第二章建立了双时滞的基孔肯雅病毒在宿主体内的动力学模型.计算了模型基本再生数R0.若R01,无感染平衡点全局渐近稳定且疾病消失.若Ro1,没有免疫时滞时,唯一的感染平衡点E1全局稳定,而免疫时滞可以改变E1的稳定性,导致Hop盼支的存在.而且,通过Hopf分支的方向的计算公式得到了分支周期解的稳定性.最后,给出了一些数值模拟来验证结论.第三章建立并分析了考虑基孔肯雅病毒在宿主体内的离散时滞动力学模型.首先,证明了解的正性和有界性,并计算出基本再生数Ro.其次,讨论了模型平衡点的存在性,无感染平衡点始终存在,而当Ro1时,存在唯一的感染平衡点.最后,通过构造Lyapunov泛函,得到了无感染平衡点的全局稳定性及感染平衡点的全局稳定性.第四章简要回顾了本文的结论,着重介绍了本文研究内容的生物和实际意义.最后讨论了本文的一些不足和需要进一步研究的问题.
[Abstract]:Based on the basic model of the virus dynamics, based on the basic model of the virus dynamics, based on the basic model of the virus dynamics, the dynamic model of the base hole Kenya virus, which consider the humoral immunity and the immune time delay, and the discrete time delay dynamic model with the saturated infection rate are established and analyzed. The dynamics of the two models are explored. The first chapter introduces the background knowledge about the base hole Kenya virus, the research progress of the virus dynamic model and the main theory used in this paper. In the second chapter, the dynamic model of the double time-delay base hole Kenya virus in the host is set up. The number of regenerative number R0. of the model, if R01, is calculated, the overall situation of the non infection equilibrium point is calculated. The asymptotically stable and disappearing of the disease. If Ro1 has no immune delay, the only infection equilibrium point E1 is globally stable, and the immune delay can change the stability of the E1 and lead to the existence of the Hop branch. Furthermore, the stability of the bifurcation periodic solution is obtained by the formula of the direction of the Hopf branch. Finally, some numerical simulations are given to verify the conclusion. The third chapter establishes and analyzes the discrete time-delay dynamics model of the base hole Kenya virus in the host. First, it proves the positive and boundedness of the knowledge, and calculates the basic regeneration number Ro. next, and discusses the existence of the equilibrium point of the model, and there is always the existence of the non infection equilibrium point. When Ro1, there is a unique equilibrium point of infection. The global stability of the non infectious equilibrium point and the global stability of the equilibrium point of infection are obtained by constructing the Lyapunov functional. The fourth chapter briefly reviews the conclusions of this paper, and focuses on the biological and practical significance of this study. Finally, some shortcomings of this paper and the problems to be further studied are discussed.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175
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本文编号：2074780