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 Stability Analysis for a Fractional HIV Infection Model with Nonlinear Incidence

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Linli Zhang ◽  
Gang Huang ◽  
Anping Liu ◽  
Ruili Fan
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Hiv Infection ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Nonnegative Solution ◽  
Infection Model ◽  
Nonlinear Incidence ◽  
Hiv Infection Model ◽  
The Stability

We introduce the fractional-order derivatives into an HIV infection model with nonlinear incidence and show that the established model in this paper possesses nonnegative solution, as desired in any population dynamics. We also deal with the stability of the infection-free equilibrium, the immune-absence equilibrium, and the immune-presence equilibrium. Numerical simulations are carried out to illustrate the results.

scholarly journals Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Mehdi Maziane ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Immune Response ◽  
Time Delay ◽  
Hiv Infection ◽  
Chronic Infection ◽  
Reproduction Number ◽  
Infection Model ◽  
Proposed Model ◽  
Hiv Infection Model ◽  
The Stability ◽  
Response Activation

We propose and analyse an human immunodeficiency virus (HIV) infection model with spatial diffusion and delay in the immune response activation. In the proposed model, the immune response is presented by the cytotoxic T lymphocytes (CTL) cells. We first prove that the model is well-posed by showing the global existence, positivity, and boundedness of solutions. The model has three equilibria, namely, the free-infection equilibrium, the immune-free infection equilibrium, and the chronic infection equilibrium. The global stability of the first two equilibria is fully characterized by two threshold parameters that are the basic reproduction number R0 and the CTL immune response reproduction number R1. The stability of the last equilibrium depends on R0 and R1 as well as time delay τ in the CTL activation. We prove that the chronic infection equilibrium is locally asymptotically stable when the time delay is sufficiently small, while it loses its stability and a Hopf bifurcation occurs when τ passes through a certain critical value.

scholarly journals On the Stability Property of the Infection-Free Equilibrium of a Viral Infection Model

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaoying Chen ◽  
Fengde Chen ◽  
Qianqian Su ◽  
Na Zhang
Keyword(s):  
Immune Response ◽  
Asymptotic Stability ◽  
Viral Infection ◽  
Linear Systems ◽  
Global Asymptotic Stability ◽  
Stability Property ◽  
Exponential Dichotomy ◽  
Infection Model ◽  
The Stability ◽  
Viral Infection Model

The dynamics of a viral infection model with nonautonomous lytic immune response is studied from the perspective of dying out of the disease. With the help of the theory of exponential dichotomy of linear systems, we give a new proof about the global asymptotic stability of the infection-free equilibrium for the caseR0=1. The result improves and complements one of the results of Wang et al. (2006).

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.

Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays

2014 ◽  
Vol 07 (05) ◽  
pp. 1450055 ◽  
Author(s):  
A. M. Elaiw ◽  
R. M. Abukwaik ◽  
E. O. Alzahrani
Keyword(s):  
Immune Response ◽  
Steady State ◽  
Hiv Infection ◽  
Infection Model ◽  
Target Cells ◽  
Cell Mediated Immunity ◽  
Globally Asymptotically Stable ◽  
Global Properties ◽  
Hiv Infection Model ◽  
Ctl Immune Response

In this paper, we study the global properties of a human immunodeficiency virus (HIV) infection model with cytotoxic T lymphocytes (CTL) immune response. The model is a six-dimensional that describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. The infection rate is given by saturation functional response. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic infection reproduction number R0 and the immune response activation number [Formula: see text]. We have proven that if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if [Formula: see text], then the infected steady state without CTL immune response is GAS, and if [Formula: see text], then the infected steady state with CTL immune response is GAS.

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