具有潜伏期和免疫应答的HIV感染模型的全局稳定性  

Global Stability of an HIV Infection Model with Latent Stage and Immune Responses

作　　者：李琳[1] 李益群[1] 李建全[1] 

机构地区：[1]空军工程大学理学院,陕西西安710051

出　　处：《应用数学》2017年第1期203-208,共6页Mathematica Applicata

基　　金：国家自然科学基金(11371369)

摘　　要：本文考虑具有CTL免疫应答和细胞内部潜伏阶段的HIV感染数学模型,得到其基本再生数,通过构造适用的Lyapunov函数,研究该模型的健康平衡点和感染平衡点的稳定性.当基本再生数不大于1时,健康平衡点在可行域上是全局稳定的,即HIV在个体体内最终灭绝;当基本再生数大于1时,模型存在惟一的感染平衡点在可行域上是全局稳定的,即HIV在个体体内呈现持续存在状态,且其浓度最终趋于一个常数.In this paper, an HIV infection model with latent stage and CTL immune response is considered, the basic reproduction number is obtained. The global stabilities of the healthy equilibrium and infection equilibrium of the model are studied by constructing the suitable Lyapunov functions. When the number is not greater than 1, the healthy equilibrium is globally stable on the feasible region, which implies that in-host HIV dies out eventually; when the number is greater than 1, the model has a unique infection equilibrium, which is globally stable in the feasible region, that is, HIV persists in the body of the infected individuals, and the concentration of in-host HIV tends to a positive number.

关 键 词：潜伏阶段 基本再生数 LYAPUNOV函数 全局稳定性 

分 类 号：O175.1[理学—数学]