We propose a Caputo-based fractional compartmental model for the dynamics of the novel COVID-19 pandemic. The newly proposed nonlinear fractional order model is an extension of a recently formulated integer-order COVID-19 mathematical model. Using basic concepts such as continuity and Banach fixed-point theorem, existence and uniqueness of the solution to the proposed model were shown. Furthermore, we analyze the stability of the model in the context of Ulam-Hyers and generalized Ulam-Hyers stability criteria. The concept of next-generation matrix was used to compute the basic reproduction number $R_0$, a number that determines the spread or otherwise of the disease into the general population. We also investigated the local asymptotic stability for the derived disease-free equilibrium point. Numerical simulation of the constructed epidemic model was carried out using the fractional Adam-Bashforth-Moulton method to validate the obtained theoretical results.

我们为新型 COVID-19 大流行的动态提出了一个基于 Caputo 的分数区室模型。新提出的非线性分数阶模型是最近制定的整数阶 COVID-19 数学模型的扩展。使用连续性和巴拿赫不动点定理等基本概念，展示了所提出模型的解的存在性和唯一性。此外，我们在 Ulam-Hyers 和广义 Ulam-Hyers 稳定性标准的背景下分析了模型的稳定性。使用下一代矩阵的概念来计算基本再生数${\mathrm{电阻}}_0$，一个确定疾病在普通人群中传播或以其他方式传播的数字。我们还研究了派生的无病平衡点的局部渐近稳定性。使用分数阶 Adam-Bashforth-Moulton 方法对构建的流行病模型进行数值模拟，以验证所获得的理论结果。