具有潜伏期和饱和CTL增长率的病毒感染模型的稳定性分析  

Dynamics Analysis of a Viral Infection Model with Latent Infection and Saturation CTL Proliferation Rate

作　　者：程贝贝[1] 胡志兴[1] 廖福成[1] 

机构地区：[1]北京科技大学数理学院,北京100083

出　　处：《中北大学学报（自然科学版）》2016年第4期335-339,349,共6页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61174209);北京科技大学冶金工程研究院基础研究基金资助项目(YJ2012-001)

摘　　要：健康细胞被病毒感染后先进入潜伏期,处于潜伏期的感染细胞能逃避CTL免疫作用,并且当CTL免疫细胞的浓度很高时,CTL增长率会达到饱和.据此建立了一个具有潜伏期和饱和CTL增长率的病毒感染动力学模型.利用适当的Lyapunov泛函和LaSalle不变原理证明了无病平衡点的全局渐近稳定性;讨论了染病平衡点局部渐近稳定的充分条件,并且研究了在染病平衡点处Hopf分支的存在性.利用数值模拟验证了以上结论.A state of latent infection can be established in cells and these latently infected cells are capable of abrogating CTL recognition.The CTL proliferation rate often saturates at high CTL concentration.Thus,a viral infection model with latent infection and saturation CTL proliferation rate is investigated.By suitable Lyapunov functional and the LaSalle＇s invariance principle,the global stability of the uninfected equilibrium is first proved.Then,the sufficient conditions to the local stability of the infected equilibrium are presented,and the existence of Hopf bifurcations at the infected equilibrium is also studied.Numerical simulations are carried out to support the obtained main results.

关 键 词：潜伏期 CTL免疫反应 时滞 稳定性 HOPF分支 

分 类 号：O175.13[理学—数学]