scholarly journals Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays

2017 ◽  
Vol 22 (6) ◽  
pp. 2365-2387 ◽  
Author(s):  
Hui Miao ◽  
◽  
Zhidong Teng ◽  
Chengjun Kang ◽  
Keyword(s):  
Hopf Bifurcation ◽  
Hiv Infection ◽  
Infection Model ◽  
Two Delays ◽  
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.

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 Threshold dynamics and threshold analysis of HIV infection model with treatment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zhimin Chen ◽  
Xiuxiang Liu ◽  
Liling Zeng
Keyword(s):  
Hiv Infection ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Immunodeficiency Virus ◽  
Hiv Infection Model

Abstract In this paper, a human immunodeficiency virus (HIV) infection model that includes a protease inhibitor (PI), two intracellular delays, and a general incidence function is derived from biologically natural assumptions. The global dynamical behavior of the model in terms of the basic reproduction number $\mathcal{R}_{0}$ R 0 is investigated by the methods of Lyapunov functional and limiting system. The infection-free equilibrium is globally asymptotically stable if $\mathcal{R}_{0}\leq 1$ R 0 ≤ 1 . If $\mathcal{R}_{0}>1$ R 0 > 1 , then the positive equilibrium is globally asymptotically stable. Finally, numerical simulations are performed to illustrate the main results and to analyze thre effects of time delays and the efficacy of the PI on $\mathcal{R}_{0}$ R 0 .

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