Complex Systems Research Center, Shanxi University, Taiyuan 030006, China.
Math Biosci Eng. 2023 Jan;20(2):2544-2565. doi: 10.3934/mbe.2023119. Epub 2022 Nov 24.
In this study, we propose a Caputo-based fractional compartmental model for the dynamics of the novel COVID-19. The dynamical attitude and numerical simulations of the proposed fractional model are observed. We find the basic reproduction number using the next-generation matrix. The existence and uniqueness of the solutions of the model are investigated. Furthermore, we analyze the stability of the model in the context of Ulam-Hyers stability criteria. The effective numerical scheme called the fractional Euler method has been employed to analyze the approximate solution and dynamical behavior of the model under consideration. Finally, numerical simulations show that we obtain an effective combination of theoretical and numerical results. The numerical results indicate that the infected curve predicted by this model is in good agreement with the real data of COVID-19 cases.
在这项研究中，我们提出了一个基于 Caputo 导数的新型 COVID-19 分数 compartmental 模型。观察了所提出的分数模型的动态特征和数值模拟。我们使用下一代矩阵找到了基本再生数。研究了模型解的存在性和唯一性。此外，我们还在 Ulam-Hyers 稳定性准则的背景下分析了模型的稳定性。采用有效的数值方法——分数阶欧拉方法，分析了所考虑模型的近似解和动力学行为。最后，数值模拟表明，我们得到了理论和数值结果的有效结合。数值结果表明，该模型预测的感染曲线与 COVID-19 病例的真实数据吻合较好。
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