Mathematical Modelling of HIV/AIDS Treatment Using Caputo–Fabrizio Fractional Differential Systems

• S. Manikandan ^[1] ; T. Gunasekar ^[2] ; A. Kouidere ^[3] ; K. A. Venkatesan ^[1] ; Kamal Shah ^[4] ; Thabet Abdeljawad ^[5]
  1. [1] Institute of Science and Technology
  2. [2] Indian Institute of Technology (IIT), Institute of Science and Technology
  3. [3] Hassan II University
  4. [4] Prince Sultan University, University of Malakand
  5. [5] Sefako Makgatho Health Sciences University, Kyung Hee University, Prince Sultan University, China Medical University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
• Idioma: inglés
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• Resumen

  • The focus of this study lies in developing and evaluating a Caputo–Fabrizio fractional derivative model that encapsulates the dynamics of the worldwide HIV/AIDS epidemic while integrating an antiretroviral therapy component. The methodology involves employing iterative techniques alongside the fixed-point theorem to establish the existence and uniqueness solutions of the model. In particular, the model identifies equilibrium points corresponding to disease outbreaks and disease-free scenarios.

    Additionally, it showcases the local asymptotic stability of the disease-free equilibrium point and outlines the criteria for the presence of the endemic equilibrium point.

    The findings verify that as the fractional order decreases, the disease-free equilibrium point becomes more stable. To demonstrate the impact of altering the fractional order and to bolster the theoretical finding, numerical simulations are conducted over the fractional order range.