摘要
考虑到HIV-1感染过程中免疫反应和非线性感染函数,建立了一类具有三个分布时滞的HIV-1感染动力学模型.得到了关于病毒感染的基本再生数R0和CTLs免疫反应的基本再生数R1<R0.通过构造Lyapunov泛函证明了系统具有阈值动力学性质,即当R0≤1时,系统存在全局渐近稳定的无感染平衡点;当R1≤1<R0时,系统出现一个全局渐近稳定的无免疫应答感染平衡点;当R1>1时,系统出现一个全局渐近稳定的免疫应答感染平衡点.
Based on immune response and nonlinear infection function in HV-1 infection,an HIV-1 infection model with three distributed delays was established. The basic reproduction number R0 for viral infection and R1 〈R0 for CTLs response were obtained. By constructing Lyapunov functions, it is shown that the model exhibits a threshold dynamics., the uninfected equilibrium exists and is globally asymptotically stable if Ro ≤1 ;the infected equilibrium without immune response exists and is globally asymptotically stable if R1 ≤1≤Ro ; the infected equilibrium with immune response is globally asymptotically stable if R1 〉1.
出处
《经济数学》
北大核心
2011年第4期1-5,共5页
Journal of Quantitative Economics
基金
广西自然科学基金(2010GXNSFC013012)
