一类具有分布时滞和饱和发生率的海洛因传染病模型的全局动力学性态

Global dynamics of a class of heroin epidemic models with distributed delay and saturated incidence rate

研究一个具有分布时滞和饱和发生率的海洛因传染病模型。计算得到疾病的基本再生数;分析相应特征方程根的分布,研究系统可行平衡点的局部渐近稳定性;构造适当的Lyapunov泛函和应用La Salle不变性原理,证明当基本再生数小于1时,系统的无病平衡点全局渐近稳定;当基本再生数大于1时,系统的地方病平衡点全局渐近稳定。

Consider a heroin epidemic model with distributed delay and saturated incidence rate. The basic reproduction number is obtained by computing. The locally stability of feasible equilibrium is stud- ied by analyzing the distribution of characteristic roots of the model. By constructing suitable Lyapunov functional and applying LaSalle invariable principle, it is shown that the disease-free equilibrium is global asymptotically stable if the basic reproduction number is less than unity ; and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity.