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

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.