Stochastic HIV Infection Model with CTLs Immune Response Driven by Lévy Jumps

This paper mainly investigates the effect of the lévy jumps on the stochastic HIV infection model with cytotoxic T lymphocytes (CTLs) immune response. First, we prove that there is a unique global positive solution in any population dynamics, then we find sufficient conditions for the extinction of the disease. For proofing the persistence in mean, a special Lyapunov function be established, we obtain that if the infected CD4+ T-cells and virus particles will persistence in mean. Finally, numerical simulations are carried out to illustrate the theoretical results.

GLOBAL ASYMPTOTICAL PROPERTIES FOR A DIFFUSED HBV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND NONLINEAR INCIDENCE

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.

DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND ANTIBODY IMMUNE RESPONSE

In this paper,dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated.The model involves the concentrations of uninfected cells,infected cells,free virus,CTL response cells,and antibody antibody response cells.There are three delays in the model:the intracellular delay,virus replication delay and the antibody delay.The 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 derived.By means of Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions for the stability of each equilibrium is established.The 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 parameter.Numerical simulations are carried out to justify the analytical results.

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

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.

Global Stability and Hopf Bifurcation for a Virus Dynamics Model with General Incidence Rate and Delayed CTL Immune Response

In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium E*0, CTL-inactivated infection equilibrium E*1 and CTL-activated infection equilibrium E*2. We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters R0 and R1, if R0 ≤ 1, E*0 is globally asymptotically stable, if R1 ≤ 1 < R0, E*1 is globally asymptotically stable and if R1 >1, E*2 is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at E*2 changes completely, although R1 > 1, a Hopf bifurcation at E*2 is established. In the end, we present some numerical simulations.

Stability of HIV-1 infection with saturated virus-target and infected-target incidences and CTL immune response

This paper studies the dynamical behavior of an HIV-1 infection model with satu- rated virus-target and infected-target incidences with Cytotoxic T Lymphocyte （CTL） immune response. The model is incorporated by two types of intracellular distributed time delays. The model generalizes all the existing HIV-1 infection models with cell-to- cell transmission presented in the literature by considering saturated incidence rate and the effect of CTL immune response. The existence and global stability of all steady states of the model are determined by two parameters, the basic reproduction number （R0） and the CTL immune response activation number （R1）. By using suitable Lyapunov functionals, we show that if R0≤1, then the infection-free steady state So is globally asymptotically stable; if R1≤1〈R0, then the CTL-inactivated infection steady state S1 is globally asymptotically stable; if R1〉1, then the CTL-activated infection steady state S2 is globally asymptotically stable. Using MATLAB we conduct some numerical simulations to confirm our results. The effect of the saturated incidence of the HIV-1 dynamics is shown.