【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.更多还原

【Abstract】 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.更多还原