Dynamics of Fractional Order SIR Model with a Case Study of COVID-19 in Turkey

Abstract

The new coronavirus illness 2019 (COVID-19) poses a major danger to civilization today. Despite its simplicity, the susceptible-infectedrecovered/removed (SIR) model and its variations are frequently used to predict the spread of COVID 19 across the world. However, using the SIR model to obtain exact solutions is difficult, especially in the early stages of a pandemic when data is few and sometimes noisy. The goal of this study is to describe COVID-19 dynamics in Turkey. The classical model is fractionalized via Atangana-Baleanu fractional derivative. From the 30th of October to the 8th of November 2020, we examine the available infection cases and fit or estimate various parameters appropriately. The basic reproduction number has been obtained as 0 ??‚ ?‚»1.09457 . To analyse the model's dynamics and transmission, stability analysis is performed at disease free equilibrium DFE and endemic equilibrium EE. Finally, the numerical results of AB fractional model are obtained and the influence of different parameters like fractional parameter ??§ , contact rate ??­ , and recovery rate ??« on the model are shown by plotting graphs. We have forecasted the disease's spread for the next 800 days.