New model of HIV-AIDS dynamics based on the Caputo–Fabrizio derivative: Optimal strategies for controlling the spread

The goal of this study is to introduce a new model to better understand the spread of HIV/AIDS, with a particular focus on individuals who are unaware of their infection status. We propose and analyze a new Caputo–Fabrizio fractional model, examining its local stability around the equilibrium point using the abdicate method tailored for Caputo–Fabrizio derivatives. To assess global stability, we employ linear matrix inequalities (LMI). Furthermore, we formulate a fractional optimal control problem to identify effective strategies for controlling the disease. Numerical simulations are conducted to confirm the stability of the equilibrium and to demonstrate the behavior of the proposed solutions.