In this work, a mathematical model consisting of a compartmentalized coupled nonlinear system of fractional order differential equations describing the transmission dynamics of COVID-19 is studied. The fractional derivative is taken in the Atangana-Baleanu-Caputo sense. The basic dynamic properties of the fractional model such as invariant region, existence of equilibrium points as well as basic reproduction number are briefly discussed. Qualitative results on the existence and uniqueness of solutions via a fixed point argument as well as stability of the model solutions in the sense of Ulam-Hyers are furnished. Furthermore, the model is fitted to the COVID-19 data circulated by Nigeria Centre for Disease Control and the two-step Adams-Bashforth method incorporating the noninteger order parameter is used to obtain an iterative scheme from which numerical results for the model can be generated. Numerical simulations for the proposed model using Adams-Bashforth iterative scheme are presented to describe the behaviors at distinct values of the fractional index parameter for of each of the system state variables. It was shown numerically that the value of fractional index parameter has a significant effect on the transmission behavior of the disease however, the infected population (the exposed, the asymptomatic infectious, the symptomatic infectious) shrinks with time when the basic reproduction number is less than one irrespective of the value of fractional index parameter.

在这项工作中，研究了一个数学模型，该模型由分数阶微分方程的分区耦合非线性系统组成，描述了 COVID-19 的传输动力学。在 Atangana-Baleanu-Caputo 意义上采用分数阶导数。简要讨论了分数阶模型的基本动力学性质，如不变区域、平衡点的存在性以及基本再生数。通过不动点论证以及 Ulam-Hyers 意义上的模型解的稳定性，提供了解的存在性和唯一性的定性结果。此外，该模型适用于尼日利亚疾病控制中心传播的 COVID-19 数据，并使用包含非整数阶参数的两步 Adams-Bashforth 方法获得迭代方案，从中可以生成模型的数值结果。使用 Adams-Bashforth 迭代方案对所提出的模型进行数值模拟，以描述每个系统状态变量的分数指数参数的不同值下的行为。数值表明分数指数参数的取值对疾病的传播行为有显着影响，但感染人群（暴露者、无症状感染者、