具有非线性发生率和时滞的HIV感染模型分析

Dynamics Analysis of an HIV Infection Model with Nonlinear Incidence Rate and Delay

研究了一类具有Beddington-DeAngelis发生率和免疫反应时滞的艾滋病传染模型.首先通过构造适当的Lyapunov泛函并利用LaSalle不变原理证明了无病平衡点以及染病无免疫平衡点的全局渐近稳定性;其次讨论了感染免疫平衡点局部渐近稳定的充分条件,CTL免疫反应时滞可以改变感染免疫平衡点的稳定性并产生Hopf分支现象;最后利用数值模拟验证了以上结论.

An HIV infection model with Beddington-DeAngelis incidence rate and CTL-response delay is investigated.First,with suitable Lyapunov functional and the LaSalle’s invariance principle,the global stabilities of the uninfected equilibrium and the infected equilibrium without immunity are proved.Then the sufficient conditions to the local stability of the infected equilibrium with immunity are dicussed.The time delay can change the stability of the infected equilibrium with immunity and lead to the existence of Hopf bifurcations.Finally,numerical simulations are carried out to support the main results.