A new fractional SICA model and numerical method for the transmission of HIV/AIDS

Abstract

In this research, a new SICA model is proposed in a fractional framework for the HIV/AIDS transmission dynamics. The new model involves a Caputo-type fractional derivative with a Mittag-Leffler function as its nonsingular kernel. In addition, the resultant fractional equations avoid dimensional mismatching by using an auxiliary parameter. Furthermore, the nonnegativity of the solution, the equilibrium points, and their stability are studied. Additionally, we implement the model by a powerful approximation scheme based on the product-integration rule. Comparative results with the real experimental observations, happened in Cape Verde Islands from 1987 to 2014, verify that the new fractional model is more efficient than the pre-existent classical model with ordinary time derivatives. More to the point, the fractional order itself provides a degree of flexibility affecting the performance of the model, which is helpful to exhibit the hidden features of the disease transmission in an accurate, appropriate manner.