一类具有年龄结构和Beddington-DeAngelis功能反应的HIV感染模型的全局动态性质分析

Global Dynamics Analysis of An Age-Structured HIV Infection Model with Beddington-De Angelis Functional Response

研究了一类具有年龄结构和Beddington-De Angelis功能反应的HIV感染动力学模型.通过分析特征方程,证明了未感染稳态解和染病稳态解的局部稳定性.通过构造恰当的李雅普诺夫函数以及使用La Salle不变集原理,证明了当基本再生数小于1时,未感染稳态解是全局渐近稳定的;当基本再生数大于1时,染病稳态解是全局渐近稳定的.

An age-structured HIV infection model with Beddington-De Angelis functional response is investigated.By analyzing the characteristic equations,the local stability of an infection-free steady state and an infected steady state of the model are established. By using suitable Lyapunov functional and La Salle＇s invariance principle,it is proved that if the basic reproduction number is less than unity,the infection-free steady state is globally asymptotically stable; and if the basic reproduction number is greater than unity,the infected steady state is globally asymptotically stable.