ANALYSIS OF THE DYNAMICS OF HIV AND THE IMMUNE SYSTEM UNDER THE EFFECT OF DRUGS THROUGH A FRACTIONAL FRAMEWORK

Rashid Jan, Normy Norfiza Abdul Razak, Mufda Alrawashdeh (), Asma Alharbi, Viet-Thanh Pham and Mohamed Mousa ()
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Rashid Jan: Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia†Department of Mathematics, Saveetha School of Engineering (SIMATS), Thandalam, Chennai 600124, Tamil Nadu, India
Normy Norfiza Abdul Razak: Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia
Mufda Alrawashdeh: Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Asma Alharbi: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Viet-Thanh Pham: Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam
Mohamed Mousa: Electrical Engineering Department, Future University in Egypt, Cairo, Egypt

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-17

Abstract: The multifaceted burden of HIV infection encompasses significant health, social, economic, and psychological challenges. Mitigating these impacts, improving the well-being of those affected, and eliminating the HIV epidemic are of paramount importance. In this research, a mathematical model is constructed to study the dynamics of immune response and HIV with the effects of antiretroviral drugs through the application of fractional derivatives. The foundational theory of fractional calculus is introduced for the analysis of the system. This research focuses on the qualitative and quantitative examination of the proposed system of HIV. The existence and uniqueness of solutions are examined using the fixed-point theorems of Banach and Schaefer. Furthermore, the solutions of the system are examined for Ulam–Hyers’ stability. The impact of different input parameters on the dynamics is investigated numerically. The system’s key parameters are identified to facilitate the control and effective management of the infection.

Keywords: HIV Infection; Fractional Derivatives; Nonlinear Eqautions; Stability Analysis; Solution Pathways; Public Health (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401486

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