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 \(R_{0} > 1\); a disease-free equilibrium \(E_{0}\) and a disease endemic equilibrium \(E_{1}\). The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number \(R_{0} <1\), we show that the endemic equilibrium state is locally asymptotically stable if \(R_{0} > 1\). 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.

本文研究了冠状病毒 19 疾病 (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 SIR 流行模型，其中在 Caputo 意义 (ABC) 中具有 Mittag-Leffler 核的导数算子。当基本再生数\(R_{0} > 1\)时，模型有两个平衡点；无病平衡\(E_{0}\)和疾病流行平衡\(E_{1}\)。当基本再生数\(R_{0} <1\) 时，无病平衡阶段是局部和全局渐近稳定的，我们证明，如果\(R_{0} > 1\)，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，因此对指数核导数给出了更好的精确结果，因此，它是指数核导数的一种推广形式。针对分数阶的各种值探索数值模拟。最后，仔细检查了 ABC 分数阶导数对疑似和感染个体的影响，并与真实数据进行了比较。