Qualitative analysis of a COVID-19 model involving the ABC fractional derivative

Abstract

In this paper, we present a fractional-order COVID-19 model based on a mathematical framework using the ABC derivative. We first derive the equilibrium points and analyze their stability. Next, we establish the existence and uniqueness of a nonnegative solution for the system under study, employing Schauder's fixed-point theorem and the Banach contraction principle. Furthermore, we investigate global asymptotic stability using Ulam-Hyers (UH) stability analysis. The primary objective is to highlight the importance of non-classical derivative orders in capturing complex dynamical behaviors. For numerical simulations, we implement Adams' method, and our results demonstrate that the fractional-order model (particularly when adjusting the fractional parameter ? yields higher accuracy and stability than its integer-order counterpart. This framework provides a more realistic and robust representation of such phenomena.