On HIV Model with Adaptive Immune Response, Two Saturated Rates and Therapy

Allali, Karam; Tabit, Youssef; Harroudi, Sanaa

doi:10.1051/mmnp/201712501

Cited by 13 publications

(5 citation statements)

References 17 publications

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“…There is a group of treatment forms recommended by World Health Organization, it depends on the patient's age and also his health situation [2]. Many mathematical models take into consideration the treatment or quarantine to describe the dynamics of some diseases [39][40][41]. In this work, we suggest the following HCV fractional model with two modes of transmission virus-to-cell and cell-to-cell in which we take into account the treatment of HCV:…”

Section: Introductionmentioning

confidence: 99%

Fractional HCV infection model with adaptive immunity and treatment

Yaagoub,

Allali

2023

Math. Model. Comput.

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Fractional HCV infection model with adaptive immunity and treatment is suggested and studied in this paper. The adaptive immunity includes the CTL response and antibodies. This model contains five ordinary differential equations. We will start our study by proving the existence, uniqueness, and boundedness of the positive solutions. The model has free-equilibrium points and other endemic equilibria. By using Lyapunov functional and LaSalle's invariance principle, we have shown the global stability of these equilibrium points. Finally, some numerical simulations will be given to validate our theoretical results and show the effect of the fractional derivative order parameter and the other treatment parameters.

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Section: Introductionmentioning

confidence: 99%

Fractional HCV infection model with adaptive immunity and treatment

Yaagoub,

Allali

2023

Math. Model. Comput.

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“…The protease inhibitors (PIs) prevents the production of viruses from the actively infected CD4 + T cells. Some general models and their analysis have been established for the dynamics of HIV infection include [5,6,7,8,9,10,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of an Hiv Infection Model With the CTL Response and Two Saturated Rates

Lahmidani¹,

Baiz²,

Tabit³

et al. 2022

Int. J. of Appl. Math.

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In this paper, we study a mathematical model that describes the Human Immunodeficiency Virus (HIV) pathogenesis with Cytotoxic T Lymphocytes (CTL) response. This model includes the cure of infected cells, two saturated rates describing viral infection, CTL proliferation and two treatments. These latter represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. First, we derive the positivity and boundedness of solutions for nonnegative initial data, which is consistent with the biological studies. Furthermore, we prove the existence of the optimal control pair, and its characterization is obtained by using the Pontryagin's maximum principle. Finally, the optimality system is derived and illustrated by a numerical example. The obtained results show that the optimal treatment strategies reduce the viral load and then increase the uninfected CD4 + T cells as well as cytotoxic T-lymphocyte immune response, this improves the patient life quality.

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“…Individuals infected with HIV who are under treatment maintain their viral load below the detection limit [3,4]. Currently, there exist two main kinds of antiretroviral drugs; Reverse Transcriptase Inhibitors (RTIs) and Protease Inhibitors (PIs) [5]. Many mathematical models have proved their usefulness for describing and understanding the dynamics of HIV infection 1074 SANAA HARRO UDI, JAOUAD DANANE, AND KARAM ALLALI [6,5,7,8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Analysis and optimal control of an HIV model with logistic growth and infected cells in eclipse phase

Harroudi¹,

Danane²,

Allali³

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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A mathematical model of the human immunode…ciency virus infection with logistic growth, infected cells in eclipse phase and therapy is investigated. The model includes four nonlinear di¤erential equations describing the evolution of uninfected CD4 + T cells, infected CD4 + T cells in latent stage, productively infected CD4 + T cells and free virus. Two types of treatments are incorporated into the model; the purpose of the …rst one consists to block the viral proliferation while the role of the second is to prevent new infections. The positivity and boundedness of solutions are established. The local stability of the disease free steady state and the infection steady states are studied. An optimal control problem is proposed and investigated. Numerical simulations are performed, con…rming stability of the free and endemic equilibria and illustrating the e¤ectiveness of the two incorporated treatments via an e¢ cient optimal control.

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On HIV Model with Adaptive Immune Response, Two Saturated Rates and Therapy

Cited by 13 publications

References 17 publications

Fractional HCV infection model with adaptive immunity and treatment

Fractional HCV infection model with adaptive immunity and treatment

Optimal Control of an Hiv Infection Model With the CTL Response and Two Saturated Rates

Analysis and optimal control of an HIV model with logistic growth and infected cells in eclipse phase

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