具免疫时滞的HIV感染模型动力学性质分析

讨论了一类具免疫时滞的HIV感染模型.分析了未感染平衡点的全局渐近稳定性,给出了感染无免疫平衡点及感染免疫平衡点局部渐近稳定的充分条件.数值模拟结果表明,当易感细胞生成率的取值使得基本再生数满足平衡存在的条件且低于某一临界值时,时滞对平衡点的稳定性没有影响;若大于该临界值,随着时滞增大,稳定性开关发生,平衡点不稳定,出现一系列Hopf分支,最终表现为周期波动模式.

Dynamics of a HIV Infection Model with Delay in Immune Response

In this paper,a model for HIV infection with delay in immune response is considered. The global stability of the infection-free equilibrium is analyzed,and the sufficient conditions of local stability of the CTL-absent infection equilibrium and CTL-present infection equilibrium are obtained.Numerical results show that if production rate of uninfected cells is large so that when the basic reproductive ratio satisfies the existing condition of CTL-present infection equilibrium and it is below a certain threshold,the delay have no effect to the stability of the equilibrium; but if the basic reproductive ratio is greater than the certain threshold,and delay in immune response increase.the stability switches occur and equilibrium is unstable,moreover,a series of Hopf bifurcations and periodic solutions are observed.