A generalized fractional HIV-1 infection model with humoral immunity and highly active antiretroviral therapy

Volume 32, Issue 2, pp 160--174 http://dx.doi.org/10.22436/jmcs.032.02.06

Publication Date: August 18, 2023 Submission Date: May 07, 2023 Revision Date: July 08, 2023 Accteptance Date: July 15, 2023

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Authors

Z. Hajhouji - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, P. O. Box 7955, Sidi Othman, Casablanca, Morocco. K. Hattaf - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, P. O. Box 7955, Sidi Othman, Casablanca, Morocco. - Equipe de Recherche en Modelisation et Enseignement des Mathematiques (ERMEM), Centre Regional des Metiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco. N. Yousfi - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, P. O. Box 7955, Sidi Othman, Casablanca, Morocco.

Abstract

Highly active antiretroviral therapy (HAART) is a treatment that uses a combination of three or more drugs to treat human immunodeficiency virus type 1 (HIV-1). On the other hand, immunological memory is an important characteristic of humoral immunity. In this paper, we propose a mathematical model that takes into account immunological memory to describe the dynamics of HIV-1 infection in the presence of such therapy. We first show that the developed model is mathematically and biologically well posed. Furthermore, we discuss the existence of equilibrium points and their stability. Both effects of HAART and memory on the dynamical behavior of our proposed model are rigorously investigated. In addition, numerical simulations are presented to illustrate our analytical findings.

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Keywords

• Therapy
• HIV-1 infection
• humoral immunity
• Hattaf fractional derivative
• global stability

MSC

•  26A33
•  34A08
•  65D05
•  92B05
•  93D30

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