scholarly journals Stability and Hopf bifurcation of a HIV infection model with CTL-response delay

2011 ◽  
Vol 62 (8) ◽  
pp. 3091-3102 ◽  
Author(s):  
Huiyan Zhu ◽  
Yang Luo ◽  
Meiling Chen
Keyword(s):  
Hopf Bifurcation ◽  
Hiv Infection ◽  
Infection Model ◽  
Response Delay ◽  
Ctl Response ◽  
Hiv Infection Model

scholarly journals Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and Cell-to-Cell Transmissions

2018 ◽  
Vol 28 (09) ◽  
pp. 1850109 ◽  
Author(s):  
Xiangming Zhang ◽  
Zhihua Liu
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Hiv Infection ◽  
Bifurcation Analysis ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Positive Equilibrium ◽  
Semilinear Equations ◽  
Age Structured ◽  
Hiv Infection Model

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD[Formula: see text] T cells by a logistic function and the infected CD[Formula: see text] T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a nontrivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out.

scholarly journals Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Fuxiang Li ◽  
Wanbiao Ma ◽  
Zhichao Jiang ◽  
Dan Li
Keyword(s):  
Hiv Infection ◽  
Incidence Rate ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Ctl Response ◽  
General Incidence Rate ◽  
Immune Impairment ◽  
Hiv Infection Model ◽  
The Stability

We investigate the dynamical behavior of a delayed HIV infection model with general incidence rate and immune impairment. We derive two threshold parameters, the basic reproduction numberR0and the immune response reproduction numberR1. By using Lyapunov functional and LaSalle invariance principle, we prove the global stability of the infection-free equilibrium and the infected equilibrium without immunity. Furthermore, the existence of Hopf bifurcations at the infected equilibrium with CTL response is also studied. By theoretical analysis and numerical simulations, the effect of the immune impairment rate on the stability of the infected equilibrium with CTL response has been studied.

Stability and Hopf Bifurcation for a HIV Infection Model with Delayed Immune Response

2013 ◽  
Vol 641-642 ◽  
pp. 808-811
Author(s):  
Xiao Zhang ◽  
Dong Wei Huang ◽  
Yong Feng Guo
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Asymptotic Stability ◽  
Hiv Infection ◽  
Numerical Simulations ◽  
Global Asymptotic Stability ◽  
Infection Model ◽  
Immune State ◽  
Hiv Infection Model ◽  
The Stability

In this paper, a class of HIV infection model with delayed immune response has been studied. We analyze the global asymptotic stability of the viral free equilibrium, and the stability and Hopf bifurcation of the infected equilibrium have been studied. Numerical simulations are carried out to explain the results of the analysis, and the change of the immune response of CTLs infects stability of system. These results can explain the complexity of the immune state of AIDs.

scholarly journals Dynamics Analysis of an HIV Infection Model including Infected Cells in an Eclipse Stage

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Shengyu Zhou ◽  
Zhixing Hu ◽  
Wanbiao Ma ◽  
Fucheng Liao
Keyword(s):  
Hiv Infection ◽  
The Body ◽  
Infection Model ◽  
Hopf Bifurcations ◽  
Asymptotically Stable ◽  
Ode Model ◽  
Response Delay ◽  
Globally Asymptotically Stable ◽  
Infected Cells ◽  
Hiv Infection Model

In this paper, an HIV infection model including an eclipse stage of infected cells is considered. Some quicker cells in this stage become productively infected cells, a portion of these cells are reverted to the uninfected class, and others will be latent down in the body. We consider CTL-response delay in this model and analyze the effect of time delay on stability of equilibrium. It is shown that the uninfected equilibrium and CTL-absent infection equilibrium are globally asymptotically stable for both ODE and DDE model. And we get the global stability of the CTL-present equilibrium for ODE model. For DDE model, we have proved that the CTL-present equilibrium is locally asymptotically stable in a range of delays and also have studied the existence of Hopf bifurcations at the CTL-present equilibrium. Numerical simulations are carried out to support our main results.

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