【作者】 闫银翠；

【导师】 王稳地；

【作者基本信息】 西南大学 ， 应用数学， 2011， 硕士

【摘要】 本文主要从数学上研究具有免疫作用和细胞内时滞的细胞动力学行为.通过构造Lyapunov函数和Lyapunov泛函将模型的动力学性态进行完整的分析.首先,研究了两个考虑CTL免疫反应的细胞动力学模型的全局性态.两个模型都可得出当基本再生数R0≤1时,无病毒感染的平衡点是全局渐近稳定的.当R0>1时,平凡平衡点失去稳定性,第一个模型的感染平衡点是全局渐近稳定的,第二个模型是一致持续的.其次,我们考虑含细胞内时滞和体液免疫反应的细胞动力学模型的全局性态.得出模型的动力学行为完全由基本再生数R0和体液免疫基本再生数R1决定,且R1<R0.当R0≤1时,无病毒感染的平衡点是全局渐近稳定的；当R1≤1<R0时,无体液免疫感染平衡点是全局渐近稳定的；当1<R1<R0时,体液免疫感染平衡点是全局渐近稳定的.最后,我们研究了含细胞内时滞和免疫反应(CTL免疫反应和体液免疫反应)的细胞动力学模型的全局性态.得出模型的动力学行为完全由病毒感染基本再生数R0,CTL免疫再生数R1,抗体免疫再生数R2,CTL免疫竞争再生数R3和抗体免疫再生数R4决定.当R0≤1时,无病毒感染平衡点是全局渐近稳定的；当R0>1,R1≤1和R2≤1时,无免疫感染平衡点是全局渐近稳定的；当R1>1和R4≤1时,CTL免疫介导的感染平衡点是全局渐近稳定的；当R2>1和R3≤1时,抗体免疫介导的感染平衡点是全局渐近稳定的；当R3>1和R4>1时,CTL免疫反应和抗体免疫反应共同介导的感染平衡点是全局渐近稳定的.更多还原

【Abstract】 In this paper, the virus dynamics with immune responses and intracellular delay are mainly studied in mathematics. We analyse the global dynamics of these models completely by con-structing Lyapunov function and Lyapunov functional.First, the properties of two virus dynamic models with CTL immune responses are studied. The two models imply that when the basic reproductive number R0< 1, the infection-free steady state is globally asymptotically stable. when R0>1, the trivial equilibriums lose stability, for the first model the infection steady state is globally asymptotically stable, and the second model is uniformly persistent.Second, the global properties of a virus dynamic model with intracellular delay and hu-moral immune responses are studied. We obtain that the dynamics of this model is completely determined by the basic reproductive number R0 and the humoral immune basic reproductive number R1, with R1<R0. When R0≤1, the infection-free steady state is globally asymptoti-cally stable; when R1≤1<R0, the immune-free infected equilibrium is globally asymptotically stable; when 1< R1< R0, the humoral immune infected equilibrium is globally asymptotically stable.In the end, the global properties of a virus dynamic model with intracellular delay and im-mune responses (CTL and humoral immune responses) are studied. We obtain that the global dynamics of this model is completely determined by the reproductive number for viral infection R0, for CTL immune response R1, for antibody immune response R2, for CTL immune competi-tion R3 and for antibody immune competition R4. when R0≤1, the infection-free steady state is globally asymptotically stable; when R0>1, R1≤1 and R2≤1, the immune-free infected equi-librium is globally asymptotically stable; when R1>1 and R4≤1, the CTL immune infected equilibrium is globally asymptotically stable; when R2>1 and R3≤1, the antibody immune infected equilibrium is globally asymptotically stable; when R3>1 and R4>1, the CTL and the antibody immune infected equilibrium is globally asymptotically stable.更多还原