HBV传染病模型的稳定性和持久性

The stability and permanence of HBV epidemical model

分析HBV传染病模型的稳定性和持久性,其中易感染者的增长方式是Logistic型,已感染者对易感染者的作用是非线性的,这样使得模型更具有生物学意义。研究解的正性和最终有界性,当基本再生数满足一定条件时,利用比较原理和Lyapunov-LaSalle不变集定理,证明无病平衡点的全局吸引性以及系统的持久性。

Stability and permanence for HBV epidemical model, in which susceptible population growth is subject to Logistic growth and the effect of infected person for susceptible person is nonlinear, are analyzed. Thus the model has more biological significance. Firstly, we study the positivity and ultimate boundedness of the solution for epi- demical model. On the basis, when the basic reproductive number satisfies certain conditions, the global attractivity of the disease-free equilibrium is proven by comparison principle and Lyapunov-LaSalle＇s invariance principle. Finally, the permanence of the model is demonstrated.