In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data range of more than one complete year. We propose a Atangana–Baleanu type fractional-order model and simulate it by using predictor–corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper.

在这项研究中，我们的目的是探索阿根廷 COVID-19 或 2019-nCOV 的动态，考虑基于该病毒从 2020 年 3 月 3 日至3月的真实数据的参数值 2021 年 2 月 29 日，这是一个超过一整年的数据范围。我们提出了一个 Atangana-Baleanu 类型的分数阶模型，并使用预测器 - 校正器 (PC) 方法对其进行了模拟。首先，我们以理论的方式介绍这种病毒的生物学特性，然后建立一个数学模型来定义它的动力学。我们使用基于著名的信任区域反射（TRR）方法的著名有效优化方案来执行模型校准。我们绘制了 COVID-19 的真实病例，并将我们的整数阶模型与模拟数据以及基本再生数的计算进行了比较。关于分数阶模拟，首先我们证明解的存在性和唯一性，然后将解连同给定 PC 方法的稳定性一起写出来。