Optimal drug control in a four‐dimensional HIV infection model

2019 ◽  
Vol 41 (2) ◽  
pp. 469-486 ◽  
Author(s):  
Elham Shamsara ◽  
Zahra Afsharnezhad ◽  
Sohrab Effati
Keyword(s):  
Hiv Infection ◽  
Drug Control ◽  
Infection Model ◽  
Optimal Drug ◽  
Hiv Infection Model

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 .

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.

Time-varying pharmacodynamics in a simple non-integer HIV infection model

2019 ◽  
Vol 307 ◽  
pp. 1-12 ◽  
Author(s):  
Carla M.A. Pinto ◽  
Ana R.M. Carvalho ◽  
João N. Tavares
Keyword(s):  
Hiv Infection ◽  
Infection Model ◽  
Time Varying ◽  
Hiv Infection Model

Quasilinearization-Lagrangian method to solve the HIV infection model of CD4 $$^+$$ + T cells

SeMA Journal ◽  
2017 ◽  
Vol 75 (2) ◽  
pp. 271-283 ◽  
Author(s):  
Kourosh Parand ◽  
Zahra Kalantari ◽  
Mehdi Delkhosh
Keyword(s):  
T Cells ◽  
Hiv Infection ◽  
Cd4 T Cells ◽  
Lagrangian Method ◽  
Infection Model ◽  
Hiv Infection Model
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