具有两类靶细胞的病毒感染模型的全局稳定性

研究了具有两类靶细胞和CTL免疫应答与抗体免疫反应的时滞病毒感染模型的动力学行为.模型描述了病毒和两类细胞的相互作用：CD4＋T淋巴细胞与巨噬细胞.通过构造适当的Lyapunov泛函,使用LaSalle不变性原理,证明了CD4＋T淋巴细胞和巨噬细胞的基本再生总数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和抗体免疫竞争再生数R4决定了模型的全局性态.若R0≤1,病毒在体内清除.若R0〉1,正解在R1≤1,R2≤1时趋于无免疫平衡点,在R1〉1≥R4时趋于CTL主导平衡点,在R2〉1≥R3时趋于抗体主导平衡点,在R3〉1且R4〉1时趋于正平衡点,获得了无病平衡点、无免疫平衡点、CTL主导平衡点、抗体主导平衡点和正平衡点全局渐近稳定的充分条件.

Global Stability for Delayed Viral Infection Model with Two Class Target Cells

The dynamical behaviors of the delayed viral infection model with two class target cells and CTL immune response and antibody immune response are studied. The model describes the interaction of viral and target cells： CD4＋T cells and macrophages. By constructing suitable Lyapunov function,using the LaSalle invariance principle,we have shown that CD4＋T cells and macrophages basic reproductive amounts R0,CTL immune response reproductive number R1,antibody immune response reproductive number R2,CTL immune response competition reproductive number R3 and antibody immune response competition reproductive number R4 determine the global properties of the model. If R0≤1,the virus is cleared. For R0 1,positive solutions approach to an immune-free equilibrium if R1≤1,R2≤1,to a CTL dominant equilibrium if R1〉 1 ≥R4,to a antibody dominant equilibrium if R2 1≥R3,and to an endemic equilibrium if R3〉1,R4〉1,the sufficient conditions of the global stability of the infection-free equilibrium,the immune-free equilibrium,the CTL dominant equilibrium,the antibody dominant equilibrium and the positive equilibrium are obtained.