具有免疫时滞的分数阶HBV感染模型稳定性分析

Stability Analysis of Fractional-Order Hepatitis B Virus Infection Model With Immune Delay

基于相关的病理知识,研究了具有免疫时滞和非线性发生率的分数阶HBV感染模型的稳定性问题.讨论了系统解的存在唯一性、正性和有界性.此外,利用泛函微分方程和Caputo分数阶导数的稳定性理论,通过分析模型在平衡点处超越特征方程根的分布情况,讨论了时滞对平衡点稳定性的影响.研究结果表明:时滞不影响无病平衡点的稳定性,但会诱发地方病平衡点的稳定性,并且在其附近产生小振幅的周期解.通过构造合适的Lyapunov函数,分析了无病平衡点的全局渐进稳定性.最后,利用分数阶时滞稳定性原理,设计相应线性控制器,对分数阶HBV感染模型进行有效控制.

In this paper,we study the stability of fractional-order HBV(Hepatitis B Virus)infection model with immune delay and nonlinear incidence.Initially,the existence,uniqueness,positivity and boundedness of the model solutions are discussed.In addition,with the stability theory of functional differential equation,combining some new lemmas about Caputo fractional derivatives and some theories about fractional dynamic system,we discuss the in?uence of time delay on the stability of equilibrium point by analyzing the distribution of the characteristic equation roots on the equilibrium point.The results show that time delay does not a?ect the stability of disease-free equilibrium,while induces the stability of endemic equilibrium and produces periodic solutions with small amplitude nearby.Meanwhile,global asymptotic stability of the disease-free equilibrium is investigated by constructing a suitable Lyapunov function.Finally,using the fractional order delay stability principle,the corresponding linear controller is designed to effectively control the fractional order HBV infection model.