A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

Abstract

SARS-CoV-2 and its variants have been investigated using a variety of mathematical models. In contrast to multi-strain models, SARS-CoV-2 models exhibit a memory effect that is often overlooked and more realistic. Atangana-Baleanu’s fractional-order operator is discussed in this manuscript for the analysis of the transmission dynamics of SARS-CoV-2. We investigated the transmission mechanism of the SARS-CoV-2 virus using the non-local Atangana-Baleanu fractional-order approach taking into account the different phases of infection and transmission routes. Using conventional ordinary derivative operators, our first step will be to develop a model for the proposed study. As part of the extension, we will incorporate fractional order derivatives into the model where the used operator is the fractional order operator of order Ψ1. Additionally, some basic aspects of the proposed model are examined in addition to calculating the reproduction number and determining the possible equilibrium. Stability analysis of the model is conducted to determine the necessary equilibrium conditions as they are also required in developing a numerical setup. Utilizing the theory of nonlinear functional analysis, for the model, Ulam-Hyers’ stability is established. We present a numerical scheme based on Newton’s polynomial in order to set up an iterative algorithm for the proposed ABC system. The application of this scheme to a variety of values of Φ1 indicates that there is a relationship between infection dynamics and the derivative’s order. We present further simulations which demonstrate the importance and cruciality of different parameters, as well as their effect on the dynamics and administer the disease. Furthermore, this study will provide a better understanding of the mechanisms underlying contagious diseases, thus supporting the development of policies to control them.