Analysis of existence and uniqueness of solutions of fractional-order Mathematical model of HIV/AIDS

In this study, the Atangana-Baleanu-Caputo (ABC) fractional derivative with the Mittag-Leffler kernel is applied to analyze the transmission dynamics of an HIV/AIDS model. The Picard-Lindelöfmethod is applied to establish the existence and uniqueness of the model’s solution. The findings showed that early detection, timely treatment, awareness campaigns, and stigma reduction play a crucial role in curbing the spread of HIV/AIDS within the population. Furthermore, the MATLAB fmincon algorithm is employed to simulate the model, providing realistic insights into the disease progression under different scenario. The simulation results showthat effective treatment of infected individuals, along with reduced contact rate through safe sex practices, can significantly decrease HIV/AIDS transmission. The incorporation of fractional calculus enhances the model’s accuracy, as non-integer order derivatives better capture memory effects compared to traditional models.