考虑免疫反应的病毒动力学模型的全局性态

发布时间：2018-01-15 08:12

本文关键词：考虑免疫反应的病毒动力学模型的全局性态　出处：《西南大学》2006年硕士论文　论文类型：学位论文

【摘要】：本文主要研究了考虑免疫反应的病毒动力学模型的全局性态。第一章研究了考虑抗体免疫反应的病毒动力学模型的全局性态。我们证明了当基本再生数R_0≤1,病毒在体内清除;而R_01时,病毒在体内持续生存,并且模型的正解当抗体免疫再生数R_1≤1时趋于无免疫平衡点,R_11时趋于正平衡点。第二章研究了两个考虑CTL免疫反应的病毒动力学模型性态。当考虑宿主体内健康细胞增长函数为线性时,我们证明了当基本再生数R_0≤1,病毒在体内清除;而R_01时,病毒在体内持续生存,并且模型的正解当抗体免疫再生数R_1≤1时趋于无免疫平衡点,R_11时趋于正平衡点。而假设健康细胞增长函数为logistic型时,我们发现当基本再生数R_0≤1,病毒在体内被清除;而R_01时,病毒在体内持续生存。在无免疫平衡点和正平衡点存在的条件下,我们得到了它们渐近稳定的充分条件。在这些条件不满足时,数值模拟分析出在一定参数条件下,系统会产生Hopf分支或者复杂的动力学性态。第三章我们综合考虑了抗体免疫反应和CTL免疫反应,研究了一个五维ODE模型的全局性态。我们证明了基本再生数R_0,CTL免疫再生数R_1,抗体免疫再生数R_2,CTL免疫竞争再生数R_3,抗体免疫竞争再生数R_4决定了模型的全局性态。若R_0≤1,病毒在体内清除。若R_01,正解在R_1≤1且R_2≤1时趋于无免疫平衡点,在R_11且R_4≤1时趋于CTL主导平衡点,在R_21且R3≤1时趋于抗体主导平衡点,在R_31且R_41时,趋于正平衡点。第四章我们研究了在免疫反应损害情况下的细胞-细胞病毒动力学模型的确定稳定性和随机稳定性。证明了当基本再生数R_0≤1,病毒在体内清除;而R_01时,病毒在体内持续生存,并且模型的正平衡点在随机扰动下也是稳定的。
[Abstract]:This paper mainly studies the global properties of virus dynamics model with immune response. The first chapter studies the virus dynamics model with immune response to the global state. We prove that when the basic reproduction number R_0 is less than 1, the virus clearance in vivo; R_01, viral persistence in vivo survival, and the model is solution when the antibody reproduction number is less than or equal to 1 when R_1 tends to have no immune balance, steady R_11.
The second chapter studies two virus dynamics with CTL immune response model. When considering the health of the host cells in vivo growth function is linear, we prove that when the basic reproduction number R_0 is less than 1, the virus clearance in vivo; R_01, virus persistence, and the model of positive solution of the immune antibody the number of R_1 is less than 1 when the regeneration tends to have no immune balance, steady R_11. And the hypothesis of healthy cells growth of logistic type, we found that when the basic reproduction number R_0 is less than 1, the virus in the body; and R_01, virus persistence. In the presence of immune free equilibrium and positive equilibrium conditions, we obtain sufficient conditions for their asymptotic stability. In these conditions is not satisfied, the numerical simulation analysis under certain parameter conditions, the system produces Hopf bifurcation or complex dynamics.
The third chapter, we consider the immune response and immune response to CTL, the global state of a five dimensional ODE model. We show that the basic reproduction number R_0 CTL number R_1 antibody immune regeneration, regeneration R_2, CTL immune antibody competitive reproduction number R_3, competition R_4 determines the overall number of students state model. If R_0 is less than 1, the virus clearance in vivo. If the R_01 is in R_1 less than or equal to 1 and less than or equal to 1 when R_2 tends to have no immune balance in R_11 and R_4 < 1 CTL leading tends to equilibrium, in R_21 and R3 less than 1 is to dominate equilibrium in the R_31 antibody, and R_41 when tends to an equilibrium point.
The fourth chapter, we study the immune response in the absence of cell damage cell virus dynamics model to determine the stability and stochastic stability. It is proved that if the basic reproduction number R_0 is less than 1, the virus clearance in vivo; R_01, virus persistence, the positive equilibrium point and the model is stable under random perturbation.

【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2006
【分类号】：R392

【相似文献】