HBV传染病模型的稳定性与Hopf分支分析  

Stability and Hopf Bifurcation Analysis for HBV Epidemical Model

作　　者：杨洪[1] 魏俊杰 

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)理学院,威海264209

出　　处：《应用数学学报》2014年第4期696-705,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金重点项目(11031002);黑龙江省教育厅科学技术基金(12541593)资助项目

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型以及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.针对该HBV传染病模型所对应的二阶超越特征方程根的分布进行分析,进而得到平凡平衡点的不稳定性.特别地,应用Beretta和Kuang的方法,给出在正平衡点处该模型Hopf分支的存在性条件.然后,基于Hassard的中心流形定理和规范型方法,推导出几个确定Hopf分支性质的计算公式.We analyze permanence and stability 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.Thus the model has more biological significance.In view of analyzing the distribution of root relating to the second degree transcendental Characteristic equation of the HBV epidemical model,and obtain the unstability of the trivial equilibrium.Particularly,we give the existence condition at an interior equihbrium of a Hopf bifurcation by approach of Beretta and Kuang.Moreover,we deduce several calculation formulas to determine the properties of Hopf bifurcation in the help of Hassard's center manifold theorem and normal form theory.

关 键 词：传染病模型 非线性接触率 稳定性 超越方程 HOPF分支 

分 类 号：O[理学]