Li Xiao-Ping, Alrihieli Haifaa F, Algehyne Ebrahem A, Khan Muhammad Altaf, Alshahrani Mohammad Y, Alraey Yasser, Riaz Muhammad Bilal
School of Mathematics and Information Science, Xiangnan University, Chenzhou, 423000, Hunan, PR China.
Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia.
Results Phys. 2022 Aug;39:105685. doi: 10.1016/j.rinp.2022.105685. Epub 2022 Jun 4.
We proposed a new mathematical model to study the COVID-19 infection in piecewise fractional differential equations. The model was initially designed using the classical differential equations and later we extend it to the fractional case. We consider the infected cases generated at health care and formulate the model first in integer order. We extend the model into Caputo fractional differential equation and study its background mathematical results. We show that the fractional model is locally asymptotically stable when at the disease-free case. For , we show the global asymptotical stability of the model. We consider the infected cases in Saudi Arabia and determine the parameters of the model. We show that for the real cases, the basic reproduction is . We further extend the Caputo model into piecewise stochastic fractional differential equations and discuss the procedure for its numerical simulation. Numerical simulations for the Caputo case and piecewise models are shown in detail.
我们提出了一个新的数学模型，用于研究分段分数阶微分方程中的新冠病毒感染情况。该模型最初是使用经典微分方程设计的，后来我们将其扩展到分数阶情形。我们考虑在医疗保健机构产生的感染病例，并首先以整数阶形式构建模型。我们将该模型扩展为Caputo分数阶微分方程，并研究其相关的数学背景结果。我们表明，在无病情况下，分数阶模型是局部渐近稳定的。对于[具体条件]，我们证明了该模型的全局渐近稳定性。我们考虑沙特阿拉伯的感染病例，并确定模型的参数。我们表明，对于实际病例，基本再生数为[具体数值]。我们进一步将Caputo模型扩展为分段随机分数阶微分方程，并讨论其数值模拟过程。详细展示了Caputo情形和分段模型的数值模拟结果。
