A Stochastic HIV Infection Model with Latent Infection and Antiretroviral Therapy

Recent studies have demonstrated that the latent infection is a major obstacle to the viral elimination in HIV infection process. In this paper, we formulate a stochastic HIV infection model to include both latent infection and combination drug therapies. We derive that the model solution is unique and positive, and the solution is global. By constructing appropriate stochastic Lyapunov functions, the existence of an ergodic stationary distribution is obtained when the critical condition is greater than one. Furthermore, through rigorous analysis and deduction, the extinction of the virus is established under certain conditions. Numerical simulations are performed to show that small intensity of white noises can maintain the existence of a stationary distribution, while large intensity of white noises is beneficial to the extinction of the virus.

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Effects of delay in immunological response of HIV infection

International Journal of Biomathematics ◽

10.1142/s1793524518500766 ◽

2018 ◽

Vol 11 (06) ◽

pp. 1850076

Author(s):

Saroj Kumar Sahani ◽

Yashi

Keyword(s):

Immune Response ◽

Steady State ◽

Immune Responses ◽

Hiv Infection ◽

Killer Cell ◽

Immunological Response ◽

Infection Model ◽

Combination Drug ◽

Hiv Infection Model

In this paper, a human immunodeficiency virus (HIV) infection model with both the types of immune responses, the antibody and the killer cell immune responses has been introduced. The model has been made more logical by including two delays in the activation of both the immune responses, along with the combination drug therapy. The inclusion of both the delayed immune responses provides a greater understanding of long-term dynamics of the disease. The dependence of the stability of the steady states of the model on the reproduction number [Formula: see text] has been explored through stability theory. Moreover, the global stability analysis of the infection-free steady state and the infected steady state has been proved with respect to [Formula: see text]. The bifurcation analysis of the infected steady state with respect to both delays has been performed. Numerical simulations have been carried out to justify the results proved. This model is capable of explaining the long-term dynamics of HIV infection to a greater extent than that of the existing model as it captures some basic parameters involved in the system such as immunological delay and immune response. Similarly, the model also explains the basic understanding of the disease dynamics as a result of activation of the immune response toward the virus.

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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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