scholarly journals Global Dynamics of an HIV Infection Model with Two Classes of Target Cells and Distributed Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. M. Elaiw
Keyword(s):  
T Cells ◽  
Steady State ◽  
Hiv Infection ◽  
Infection Model ◽  
Target Cells ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Hiv Infection Model ◽  
Nonlinear Delay

We investigate the global dynamics of an HIV infection model with two classes of target cells and multiple distributed intracellular delays. The model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4+T cells and macrophages. The incidence rate of infection is given by saturation functional response. The model has two types of distributed time delays describing time needed for infection of target cell and virus replication. This model can be seen as a generalization of several models given in the literature describing the interaction of the HIV with one class of target cells, CD4+T cells. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of the model. We have proven that if the basic reproduction numberR0is less than unity then the uninfected steady state is globally asymptotically stable, and ifR0>1then the infected steady state exists and it is globally asymptotically stable.

scholarly journals Global Dynamics of HIV Infection of CD4+T Cells and Macrophages

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
A. M. Elaiw ◽  
A. S. Alsheri
Keyword(s):  
T Cells ◽  
Steady State ◽  
Hiv Infection ◽  
Reproduction Number ◽  
Infection Model ◽  
Global Dynamics ◽  
Globally Asymptotically Stable ◽  
Virus Particles ◽  
Hiv Infection Model ◽  
Invariant Principle

We study the global dynamics of an HIV infection model describing the interaction of the HIV with CD4+T cells and macrophages. The incidence rate of virus infection and the growth rate of the uninfected CD4+T cells and macrophages are given by general functions. We have incorporated two types of distributed delays into the model to account for the time delay between the time the uninfected cells are contacted by the virus particle and the time for the emission of infectious (matures) virus particles. We have established a set of conditions which are sufficient for the global stability of the steady states of the model. Using Lyapunov functionals and LaSalle's invariant principle, we have proven that if the basic reproduction numberR0is less than or equal to unity, then the uninfected steady state is globally asymptotically stable (GAS), and if the infected steady state exists, then it is GAS.

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.

scholarly journals Global Stability of HIV Infection of CD4+T Cells and Macrophages with CTL Immune Response and Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
A. M. Elaiw ◽  
R. M. Abukwaik ◽  
E. O. Alzahrani
Keyword(s):  
Immune Response ◽  
T Cells ◽  
Steady State ◽  
Hiv Infection ◽  
Global Stability ◽  
Reproduction Number ◽  
Infection Model ◽  
Target Cells ◽  
Globally Asymptotically Stable ◽  
Ctl Immune Response

We study the global stability of a human immunodeficiency virus (HIV) infection model with Cytotoxic T Lymphocytes (CTL) immune response. The model describes the interaction of the HIV with two classes of target cells, CD4+T cells and macrophages. 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 reproduction numberR0and the immune response reproduction numberR0∗. We have proven that, ifR0≤1, then the uninfected steady state is globally asymptotically stable (GAS), ifR0*≤1<R0, then the infected steady state without CTL immune response is GAS, and, ifR0*>1, then the infected steady state with CTL immune response is GAS.

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 .

Asymptotic Analysis of an Age-Structured HIV Infection Model with Logistic Target-Cell Growth and Two Infecting Routes

2020 ◽  
Vol 30 (04) ◽  
pp. 2050059
Author(s):  
Dongxue Yan ◽  
Xianlong Fu
Keyword(s):  
Steady State ◽  
Hiv Infection ◽  
Logistic Growth ◽  
Infection Model ◽  
Target Cells ◽  
Cell Infection ◽  
Numerical Examples ◽  
Distribution Of Eigenvalues ◽  
Age Structured ◽  
Hiv Infection Model

This paper deals with an age-structured HIV infection model with logistic growth for target cells and both virus-to-cell and cell-to-cell infection routes. Based on the existence of the infection-free and infection equilibria and some rigorous analyses for the considered model, we study the asymptotic stability of these equilibria via determining the distribution of eigenvalues. We also address the persistence of the solution semi-flow by proving the existence of a global attractor. Furthermore, Hopf bifurcation occurring at the positive steady state is exploited. At last, some numerical examples are provided to illustrate the obtained results.

Global Dynamics of a HIV Infection Model with Delayed CTL Response and Cure Rate

2013 ◽  
Vol 791-793 ◽  
pp. 1322-1327
Author(s):  
Yan Yan Yang ◽  
Hui Wang ◽  
Zhi Xing Hu ◽  
Wan Biao Ma
Keyword(s):  
Infection Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Cure Rate ◽  
Globally Asymptotically Stable ◽  
Ctl Response ◽  
Stable Periodic ◽  
Hiv Infection Model ◽  
The Stability ◽  
Viral Infection Model

In this paper, we have considered a viral infection model with delayed CTL response and cure rate. For this model, we have researched the stability of these three equilibriums depend on two threshold parameters and , that is, if , the infected-free equilibrium is locally asymptotically stable; if , the infected equilibrium without CTL response is globally asymptotically stable; and if , the infected equilibrium exists, at he same time, we have found that the time delay can lead to Hopf bifurcations and stable periodic solutions when the is unstable.

scholarly journals Stability and Feedback Stabilization of HIV Infection Model with Two Classes of Target Cells

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
A. M. Elaiw ◽  
A. M. Shehata
Keyword(s):  
Control System ◽  
Steady State ◽  
Hiv Infection ◽  
Highly Active Antiretroviral Therapy ◽  
Feedback Stabilization ◽  
Infection Model ◽  
Target Cells ◽  
Control Input ◽  
Time Model ◽  
Hiv Infection Model

We study the stability and feedback stabilization of the uninfected steady state of a human immunodeficiency virus (HIV) infection model. The model is a 6-dimensional nonlinear ODEs that describes the interaction of the HIV with two classes of target cells, CD4+T cells and macrophages, and takes into account the Cytotoxic T Lymphocytes (CTLs) immune response. Lyapunov function is constructed to establish the global asymptotic stability of the uninfected steady state of the model. In a control system framework, the HIV infection model incorporating the effect of Highly Active AntiRetroviral Therapy (HAART) is considered as a nonlinear control system with drug dose as control input. We developed treatment schedules for HIV-infected patients by using Model Predictive Control (MPC-)based method. The MPC is constructed on the basis of an approximate discrete-time model of the HIV infection model. The MPC is applied to the stabilization of the uninfected steady state of the HIV infection model. Besides model inaccuracies that HIV infection model suffers from, some disturbances/uncertainties from different sources may arise in the modelling. In this work the disturbances are modelled in the HIV infection model as additive bounded disturbances. The robustness of the MPC against small model uncertainties or disturbances is also shown.

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.

scholarly journals Dynamics Analysis and Simulation of a Modified HIV Infection Model with a Saturated Infection Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Qilin Sun ◽  
Lequan Min
Keyword(s):  
Drug Resistance ◽  
Antiretroviral Therapy ◽  
Hiv Infection ◽  
Equilibrium Point ◽  
Infection Rate ◽  
Reproductive Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Hiv Rna

This paper studies a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. It is proved that if the basic virus reproductive numberR0of the model is less than one, then the infection-free equilibrium point of the model is globally asymptotically stable; ifR0of the model is more than one, then the endemic infection equilibrium point of the model is globally asymptotically stable. Based on the clinical data from HIV drug resistance database of Stanford University, using the proposed model simulates the dynamics of the two groups of patients’ anti-HIV infection treatment. The numerical simulation results are in agreement with the evolutions of the patients’ HIV RNA levels. It can be assumed that if an HIV infected individual’s basic virus reproductive numberR0<1then this person will recover automatically; if an antiretroviral therapy makes an HIV infected individual’sR0<1, this person will be cured eventually; if an antiretroviral therapy fails to suppress an HIV infected individual’s HIV RNA load to be of unpredictable level, the time that the patient’s HIV RNA level has achieved the minimum value may be the starting time that drug resistance has appeared.

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