An Application of the Caputo Fractional Domain in the Analysis of a COVID-19 Mathematical Model

Abstract

Vaccination programs aimed at preventing the spread of the coronavirus appear to have a significant global impact. In this research, we have investigated a mathematical model projecting COVID-19 disease spread by considering five groups of individuals viz. vulnerable, exposed, infected, unreported, recovered, and vaccinated. Looking at the current abnormal pattern of the virus spread in the projected model, we have implemented the fractional derivative in the Mittag-Leffler context. Using the existing theory of the fractional derivative, we have examined the theoretical aspects such as the existence and uniqueness of the solutions, the existence and stability of the disease-free and endemic equilibrium points, and the global stability of the disease-free equilibrium point. In computing the basic reproduction number, we have analyzed that the existence and stability of points of equilibrium are dependent on this number. The sensitivity of the basic reproduction number is also examined. The importance of the vaccination drive is highlighted by relating it to the basic reproduction number. Finally, we have presented the simulation of the numerical results by capturing the profile of each group under the influence of the fractional derivative and investigated the impact of vaccination rate and contact rate in controlling the disease by applying the Adams-Bashforth-Moultan (ABM) method. The present research study demonstrates the importance of the vaccination campaign and the curb on individual contact by featuring a novel fractional operator in the projected model and capturing the corresponding consequence.