基于双时滞HTLV-I病毒模型的稳定性分析

Stability Analysis on a HTLV-I Virus Model with Two Time Delays

针对双时滞HTLV-I病毒感染模型,探讨其平衡点及稳定性理论.依据模型固有属性,研究解的正性和有界性;通过构造适当Lyapunov泛函和利用稳定性理论,获证未感染平衡点和免疫耗尽平衡点是全局渐近稳定的;借助Hopf分支理论,分析免疫激活平衡点处相应特征方程具有的性质,获得该平衡点的局部稳定性和发生Hopf分支的充分条件.最后,数值实验结果表明,将HLTV-I模型中引入双时滞是合理的,有助于解释HTLV-I病毒的传播现象.

This work investigates equilibrium points and their stability for the HTLV-I virus infection model with two time delays.First of all,combining with the intrinsic characteristics of such model,the positivity and boundedness of solutions are discussed.Secondly,the global asymptotic stability of the infection-free and immune-exhausted equilibrium points are proved by constructing appropriate Lyapunov functional,and then,with the help of Hopf bifurcation theory,some sufficient conditions of asymptotic stability and Hopf bifurcation for the immune activated equilibrium point are derived by analyzing the associated characteristic equation.Finally,numerical simulations are carried out to analyze and support the results.