Abdulwasaa Mansour A, Abdo Mohammed S, Shah Kamal, Nofal Taher A, Panchal Satish K, Kawale Sunil V, Abdel-Aty Abdel-Haleem
Department of Statistics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, (M.S), India.
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, (M.S), India.
Results Phys. 2021 Jan;20:103702. doi: 10.1016/j.rinp.2020.103702. Epub 2020 Dec 15.
Fractional-order derivative-based modeling is very significant to describe real-world problems with forecasting and analyze the realistic situation of the proposed model. The aim of this work is to predict future trends in the behavior of the COVID-19 epidemic of confirmed cases and deaths in India for October 2020, using the expert modeler model and statistical analysis programs (SPSS version 23 & Eviews version 9). We also generalize a mathematical model based on a fractal fractional operator to investigate the existing outbreak of this disease. Our model describes the diverse transmission passages in the infection dynamics and affirms the role of the environmental reservoir in the transmission and outbreak of this disease. We give an itemized analysis of the proposed model including, the equilibrium points analysis, reproductive number , and the positiveness of the model solutions. Besides, the existence, uniqueness, and Ulam-Hyers stability results are investigated of the suggested model via some fixed point technique. The fractional Adams Bashforth method is applied to solve the fractal fractional model. Finally, a brief discussion of the graphical results using the numerical simulation (Matlab version 16) is shown.
基于分数阶导数的建模对于用预测来描述现实世界问题并分析所提模型的实际情况非常重要。这项工作的目的是使用专家建模者模型和统计分析程序（SPSS 23版和Eviews 9版）预测2020年10月印度新冠肺炎确诊病例和死亡病例疫情的未来趋势。我们还推广了一个基于分形分数算子的数学模型来研究这种疾病的现有疫情。我们的模型描述了感染动态中的多种传播途径，并肯定了环境宿主在这种疾病传播和爆发中的作用。我们对所提模型进行了详细分析，包括平衡点分析、繁殖数以及模型解的正性。此外，通过一些不动点技术研究了所提模型的存在性、唯一性和Ulam-Hyers稳定性结果。应用分数阶亚当斯-巴什福思方法来求解分形分数模型。最后，展示了使用数值模拟（Matlab 16版）得到的图形结果的简要讨论。
