Akyildiz F Talay, Alshammari Fehaid Salem
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
Adv Differ Equ. 2021;2021(1):319. doi: 10.1186/s13662-021-03470-1. Epub 2021 Jul 3.
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 ; a disease-free equilibrium and a disease endemic equilibrium . The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number , we show that the endemic equilibrium state is locally asymptotically stable if . 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.
本文研究了一种关于冠状病毒病（COVID-19）的新模型，即具有非标准非线性发病率和恢复率的复杂分数阶SIR流行病模型，其中导数算子是Caputo意义下具有Mittag-Leffler核的（ABC）。当基本再生数 时，该模型有两个平衡点；一个无病平衡点 和一个地方病平衡点 。当基本再生数 时，无病平衡阶段是局部和全局渐近稳定的，我们表明当 时，地方病平衡状态是局部渐近稳定的。我们还通过使用不动点方法证明了Atangana-Baleanu SIR模型解的存在性和唯一性。由于Atangana-Baleanu分数阶导数具有分数阶，因此对具有指数核的导数给出了更好的精确结果，因此它是具有指数核的导数的广义形式。针对分数阶的各种值进行了数值模拟。最后，仔细研究了ABC分数阶导数对疑似和感染个体的影响，并与实际数据进行了比较。
