HBV传染病模型的稳定性和持久性  

The stability and permanence of HBV epidemical model

作　　者：杨洪[1,2] 魏俊杰[2] 郭英[1] 

机构地区：[1]黑龙江八一农垦大学理学院,大庆163319 [2]哈尔滨工业大学(威海)数学系,威海264209

出　　处：《黑龙江大学自然科学学报》2013年第6期742-747,共6页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金重点资助项目(11031002)

摘　　要：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.

关 键 词：传染病模型 Logistic型增长 稳定性 持久性 

分 类 号：O175.13[理学—数学]