Fractional HIV infection model described by the Caputo derivative with real data

Abstract

The goal of this research is to explore the HIV infection model through Caputo derivative in considerable detail. We employ a non-local fractional derivative having singular kernel to thoroughly evaluate the dynamics of the HIV infection model. Also, we present some important theoretical results and main features of the fractional disease model addressed. The dynamic behavior of the HIV infection is investigated by a suitable numerical scheme based on the Caputo fractional operator. Furthermore, the non-linear least-squares curve fitting procedure is utilized for estimating the parameters of the proposed model with real-world data. On the other hand, it is worth noting that during the fractionalization process, we take into account dimensional consistency.