Dynamics Analysis for a Fractional-Order HIV Infection Model with Delay

We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.

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Stability Analysis for a Fractional HIV Infection Model with Nonlinear Incidence

Discrete Dynamics in Nature and Society ◽

10.1155/2015/563127 ◽

2015 ◽

Vol 2015 ◽

pp. 1-11 ◽

Cited By ~ 6

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.

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Global stability of a fractional order HIV infection model with cure of infected cells in eclipse stage

Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées ◽

10.46298/arima.4359 ◽

2019 ◽

Vol Volume 30 - 2019 - MADEV... ◽

Author(s):

Moussa Bachraoui ◽

Khalid Hattaf ◽

Noura Yousfi

Keyword(s):

Hiv Infection ◽

Global Stability ◽

Fractional Order ◽

Infection Model ◽

Proposed Model ◽

Immunodeficiency Virus ◽

Infected Cells ◽

Hiv Infection Model ◽

With Memory ◽

Theoretical Results

Modeling by fractional order differential equations has more advantages to describe the dynamics of phenomena with memory which exists in many biological systems. In this paper, we propose a fractional order model for human immunodeficiency virus (HIV) infection by including a class of infected cells that are not yet producing virus, i.e., cells in the eclipse stage. We first prove the positivity and bound-edness of solutions in order to ensure the well-posedness of the proposed model. By constructing appropriate Lyapunov functionals, the global stability of the disease-free equilibrium and the chronic infection equilibrium is established. Numerical simulations are presented in order to validate our theoretical results.

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Dynamics Analysis of a Delayed HIV Infection Model with CTL Immune Response and Antibody Immune Response

Acta Mathematica Scientia ◽

10.1007/s10473-021-0322-y ◽

2021 ◽

Vol 41 (3) ◽

pp. 991-1016

Author(s):

Junxian Yang ◽

Leihong Wang

Keyword(s):

Immune Response ◽

Hiv Infection ◽

Infection Model ◽

Dynamics Analysis ◽

Hiv Infection Model ◽

Ctl Immune Response

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

The European Physical Journal Plus ◽

10.1140/epjp/s13360-020-01049-5 ◽

2021 ◽

Vol 136 (1) ◽

Author(s):

Peng Wu

Keyword(s):

Hiv Infection ◽

Infection Model ◽

Target Cells ◽

Multiple Target ◽

Nonlocal Dispersal ◽

Hiv Infection Model

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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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