一类具有Beddington-DeAngelis功能性反应的时滞HIV模型全局性分析

研究了一类四维的HIV传染病动力学时滞模型,模型使用的是Beddington-DeAngelis功能性反应形式的非线性发生率.考虑了受感染细胞CD4-T细胞的潜伏特性,也就是说被感染后没有传染性,只有被激活后才产生病毒细胞.通过构建Lyapunov函数,利用LaSalle不变集原理,给出了疾病平衡点,包括无病平衡点和地方性平衡点的全局渐近稳定.证明了当基本再生数小于1,无病平衡点全局渐近稳定;当基本再生数大于1,地方性平衡点全局也是渐近稳定.还考虑了具有n阶潜伏阶段的模型,并给出了平衡点的全局渐近稳定.

Global Dynamics for an HIV-1 Infection Model with Beddington-DeAngelis Functional Response and with Time Delays

This paper investigates the global stability of an HIV dynamics model with discrete delays incorporating Beddington-DeAngelis functional response infection rate.An eclipse stage of infected cells(i.e.latently infected cells),not yet producing virus,is included in our model.We consider nonnegativity,boundedness of solutions and global asymptotic stability of the uninfected and infected equilibria(steady states)by constructing suitable Lyapunov functionals and using LaSalle invariance principle.It is proved that if the basic reproduction number R0 is less than unity,then the disease-free equilibrium is globally asymptotically stable,and if R0 is greater than unity,then the infected equilibrium is globally asymptotically stable.The results show that the global dynamics are completely determined by the basic reproduction number R0.That is,time delay has no effect on the global asymptotic stability of our model.What is more,we develop and analyze an n-stage-structured HIV model including Beddington-DeAngelis functional response.We also prove the global asymptotical stability of two equilibria by constructing suitable Lyapunov functionals.