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

S. Manikandan, T. Gunasekar*, A. Kouidere*, K. A. Venkatesan, Kamal Shah, Thabet Abdeljawad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number149
JournalQualitative Theory of Dynamical Systems
Volume23
Issue number4
DOIs
Publication statusPublished - Jan 2024
Externally publishedYes

Keywords

  • CF-fractional derivative
  • Existence and uniqueness
  • Fixed point
  • HIV/AIDS
  • Non-singularity
  • Virus detection and treatment

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