A Novel Study for the Spread of COVID-19 via Fractional Derivative: A New Perspective of Hybrid Stochastic Approach

Abstract

In the present research, we address a hybrid technique that combines the Caputo and Atangana-Baleanu formulations for a stochastic fractional differential equation applied to a chaotic framework. We primarily demonstrate the existence and uniqueness of solutions before presenting a new numerical scheme for the Caputo and Atangana-Baleanu derivatives. Our quantitative study is centered on a stochastic model of COVID-19 transmission and prevention, which classifies the population of an involved region into susceptible, exposed, infected (symptomatic and asymptomatic), treated, and recovered groups. Considering the natural unpredictability of illness progression, the number of symptomatic patients, fatalities, and recoveries is represented as stochastic processes. Therefore, the governing equations have to incorporate stochasticity. We construct stochastic differential and integral equations from the fundamental nonlinear systems and analytically analyze their existence and uniqueness. For various fractional orders, numerical simulations are conducted, and the outcomes for the Caputo and Atangana-Baleanu situations are thoroughly examined. We also provide numerical calculations with projected parameters for different fractional orders of the Caputo derivative. The understanding of disease behavior under stochastic and fractional
frameworks is improved by the fractional-order analysis, which is reinforced by simulation data and offers insightful information about the dynamics of COVID-19.