Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel - F. Talay Akyildiz; Fehaid Salem Alshammari (Advances in Difference Equations, 2021)
Abstract This paper investigates a new model on coronavirus-19 disease (COVID-19), that is complex fractional SIR epidemic model with a nonstandard nonlinear incidence rate and a recovery, where derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The model has two equilibrium points when the basic reproduction number R 0 > 1 $R_{0} > 1$ ; a disease-free equilibrium E 0 $E_{0}$ and a disease endemic equilibrium E 1 $E_{1}$ . The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number R 0 < 1 $R_{0} <1$ , we show that the endemic equilibrium state is locally asymptotically stable if R 0 > 1 $R_{0} > 1$ . We also prove the existence and uniqueness of the solution for the Atangana–Baleanu SIR model by using a fixed-point method. Since the Atangana–Baleanu fractional derivative gives better precise results to the derivative with exponential kernel because of having fractional order, hence, it is a generalized form of the derivative with exponential kernel. The numerical simulations are explored for various values of the fractional order. Finally, the effect of the ABC fractional-order derivative on suspected and infected individuals carefully is examined and compared with the real data.