Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel

Advances in Difference Equations

Fehaid Salem Alshammari¹  F. Talay Akyildiz¹ 

[1] Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad ibn Saud Islamic University (IMSIU);

关键词: Coronavirus-19 disease;    Complex fractional SIR model;    Atangana–Beleanu–Caputo (ABC) derivatives;    Fixed-point method;    Stability;   

DOI  :  10.1186/s13662-021-03470-1

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown