A Detailed Study of ABC-Type Fractal–Fractional Dynamical Model of HIV/AIDS

Abstract

This paper is aimed at studying the dynamics of community transmission of HIV by constructing a fractal fractional mathematical model whose kernel is a generalized Mittag–Leffler type. First, we collect and analyze statistical data for epidemiological surveillance of HIV/AIDS prevalence in Yemen from 2000 to 2022. Then, we employ the statistical analysis software EViews and apply ARIMA models to predict the number of HIV/AIDS cases from 2023 to 2024. The results of the selected model, free of standard problems, predicted a future increase in HIV/AIDS cases in Yemen. Next, relying on the well-known fixed-point theorem and a set of other associated results, we prove the existence and uniqueness results of the fractional model. Moreover, we use the Adams–Bashforth method to approximate the solutions of this system numerically. Finally, we plot, tabulate, and simulate our results using the Mathematica software and compare them to the results obtained from the statistical model.