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

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.