一类病毒动力学模型的全局渐近稳定性分析

Global Properties of Virus Dynamics Models

建立和研究了具有潜伏细胞年龄结构,染病细胞年龄结构及分布时滞的病毒动力学模型。得到了每个模型的基本再生数,对3个模型通过建立适当的Lyapunov函数,证明了当基本再生数小于1时,无病平衡点全局渐近稳定,疾病消除。当基本再生数大于1时,正平衡点全局渐近稳定,疾病持续。

Virus dynamics models with age-of-infection,age-of-expose and distributed intracellular delay were discussed.The basic reproduction number was obtained.By constructing Lyapunov functions,it was proved that the disease-free equilibrium was globally and asymptotically stable for three models.If the basic reproduction number was less than one,the disease was cleared.The endemic equilibrium was globally and asymptotically stable for three models,if the basic reproduction number was larger than one,and the disease persists.