The dynamics of the HIV/AIDS infection in the framework of piecewise fractional differential equation

Abstract

We study the HIV/AIDS infection dynamics using the new concept of piecewise fractional differential equations in the sense of Atangana–Baleanu derivative. The cases of HIV/AIDS in Indonesia have been utilized to provide better fitting to the real data. We show that the piecewise modeling approach has the better fitting to the cases in the present work compared to the previous case of the model in the Caputo sense. We study that the model is locally asymptotically stable when R0<1. The fractional model is extended to the piecewise model and provided a numerical procedure for their graphical solution. We provide some graphical results for the model which indicates the usefulness of the piecewise modeling approach.

Keywords

• Atangana–Baleanu operator
• HIV/AIDS model
• Real cases
• Simulation results