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DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH ctl immune response AND ANTIBODY immune response

Acta Mathematica Scientia 2021年第3期41卷 991-1016页

作者： Junxian YANG Leihong WANG School of Science Anhui Agricultural UniversityHefei 230036China School of Forestry and Landscape Architecture Anhui Agricultural UniversityHefei 230036China

In this paper,dynamics analysis of a delayed HIV infection model with ctl immune response and antibody immune response is *** model involves the concentrations of uninfected cells,infected cells,free virus,ctl response cells,and antibody antibody response *** are three delays in the model:the intracellular delay,virus replication delay and the antibody *** basic reproductive number of viral infection,the antibody immune reproductive number,the ctl immune reproductive number,the ctl immune competitive reproductive number and the antibody immune competitive reproductive number are *** means of Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions for the stability of each equilibrium is *** results show that the intracellular delay and virus replication delay do not impact upon the stability of each equilibrium,but when the antibody delay is positive,Hopf bifurcation at the antibody response and the interior equilibrium will exist by using the antibody delay as a bifurcation *** simulations are carried out to justify the analytical results.

关键词： Beddington-DeAngelis incidence ctl immune response antibody immune response delay

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GLOBAL ASYMPTOTICAL PROPERTIES FOR A DIFFUSED HBV INFECTION MODEL WITH ctl immune response AND NONLINEAR INCIDENCE

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Acta Mathematica Scientia 2011年第5期31卷 1959-1967页

作者：王绍利冯新龙何银年 Faculty of Science Xi'an Jiaotong University College of Mathematics and Systems Science Xinjiang University

This article proposes a diffused hepatitis B virus （HBV） model with ctl immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.

关键词： HBV infection diffusion ctl immune response nonlinear incidence global asymptotical stability

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Stability and Hopf Bifurcation of a Virus Infection Model with a Delayed ctl immune response

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Chinese Quarterly Journal of Mathematics 2014年第3期29卷 426-437页

作者： LI Xiao-tong TIAN Xiao-hong XU Rui College of Science China University of Petroleum Beijing 102249 China Institute of AppliedMathematics Shijiazhuang Mechanical Engineering College Shijiazhuang 050003 China

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.

关键词： virus infection ctl immune response time delay Hopf bifurcation LaSalle’s invariance principle global stability

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