具有离散时滞和Crowley-Martin功能性反应的HIV动力学模型稳定性研究

A Note on Global Dynamics for an Hiv-1 Infection Model with Crowley-Martin Functional Response and Discrete Intracellular Delays

本文研究了一类具有三个离散时滞四维HIV传染病动力学模型，模型使用的是著名的Crowley—Martin功能性反应形式的非线性发生率，还考虑了受感染细胞CD4-T细胞的潜伏特性，也就是说被感染后没有立即具有传染性，只有被外界物质激活或者本身免疫失效后才具有传染性．首先我们求出了系统的基本再生数，通过构建Lyapunov泛函，利用LaSalle不变集原理，得出了无病平衡点和染病平衡点的全局渐近稳定．证明了当基本再生数小于1，对于任意的时滞，无病平衡点都是全局渐近稳定的，当基本再生数大于1，对于任意的时滞，染病平衡点也是全局渐近稳定的．最后用Matlab软件对模型平衡点的稳定性进行了数值模拟．

This paper investigates the global stability of an HIV dynamics model with discrete delays incorporating Crowley-Martin flmctional 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. We have proved that if tile basic reproduction munber R0 is less than unite, then tile disease-free equilibrium is globally asymptotically stable, and if R0 is greater than unite, then tile infected equilibrium is globally asymptotically stable. Numerical simulations have been presented to illustrate the asymptotical stability of equilibrium points by using Matlab.