Stability and Hopf Bifurcation of a Virus Infection Model with a Delayed CTL Immune Response  

作　　者：LI Xiao-tong TIAN Xiao-hong XU Rui 

机构地区：[1]College of Science, China University of Petroleum, Beijing 102249, China [2]Institute of AppliedMathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

出　　处：《Chinese Quarterly Journal of Mathematics》2014年第3期426-437,共12页数学季刊（英文版）

基　　金：Supported by the NNSF of China(11371368,11071254);Supported by the NSF of Hebei Province(A2014506015);Supported by the NSF for Young Scientists of Hebei Province(A2013506012)

摘　　要：In this paper, a virus infection model with standard incidence rate and delayed CTL immune response is investigated. By analyzing corresponding characteristic equations,the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the CTL-activated infection equilibrium are established, respectively. By means of comparison arguments, it is verified that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio is less than unity. By using suitable Lyapunov functional and LaSalle's invariance principle, it is shown that the CTL-inactivated infection equilibrium of the system is globally asymptotically stable if the immune response reproduction ratio is less than unity and the basic reproduction ratio is greater than unity. Numerical simulations are carried out to illustrate the theoretical result.In this paper, a virus infection model with standard incidence rate and delayed CTL immune response is investigated. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the CTL-activated infection equilibrium are established, respectively. By means of comparison arguments, it is verified that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio is less than unity. By using suitable Lyapunov functional and LaSalle＇s invariance principle, it is shown that the CTL-inactivated infection equilibrium of the system is globally asymptotically stable if tile immune response reproduction ratio is less than unity and the basic reproduction ratio is greater than unity. Numerical simulations are carried out to illustrate the theoretical result.

关 键 词：virus infection CTL immune response time delay Hopf bifurcation LaSalle’s invariance principle global stability 

分 类 号：O175.1[理学—数学]