Dynamics of a delayed integro-differential HIV infection model with multiple target cells and nonlocal dispersal

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.

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

Discrete Dynamics in Nature and Society ◽

10.1155/2012/253703 ◽

2012 ◽

Vol 2012 ◽

pp. 1-13 ◽

Cited By ~ 12

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.

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

International Journal of Biomathematics ◽

10.1142/s1793524514500557 ◽

2014 ◽

Vol 07 (05) ◽

pp. 1450055 ◽

Cited By ~ 21

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

Discrete Dynamics in Nature and Society ◽

10.1155/2012/963864 ◽

2012 ◽

Vol 2012 ◽

pp. 1-20 ◽

Cited By ~ 5

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.

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Global Exponential Stability of a Delayed HIV Infection Model with a Nonlinear Incidence Rate

Discrete Dynamics in Nature and Society ◽

10.1155/2021/8886322 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Zhiwen Long

Keyword(s):

Stability Analysis ◽

Hiv Infection ◽

Exponential Stability ◽

Incidence Rate ◽

Infection Model ◽

Target Cells ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Virus Particles ◽

Hiv Infection Model

Under the assumption that there is a time delay between the time target cells are contacted by the virus particles and the time the contacted cells become actively infected, we investigate the exponential stability of the noninfected equilibrium for a delayed HIV infection model with a nonlinear incidence rate. Compared with the global asymptotic stability analysis based on basic reproduction number, exponential stability analysis reveals the change range of various cells in different time periods.

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Threshold dynamics and threshold analysis of HIV infection model with treatment

Advances in Difference Equations ◽

10.1186/s13662-020-03057-2 ◽

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

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127418501092 ◽

2018 ◽

Vol 28 (09) ◽

pp. 1850109 ◽

Cited By ~ 6

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.

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