Alkahtani Badr Saad T, Jain Sonal
Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia.
Department of Humanity and Sciences, Rizvi College of Engineering, Bandra West, Mumbai, Maharashtra 400050, India.
Results Phys. 2021 Jan;20:103673. doi: 10.1016/j.rinp.2020.103673. Epub 2020 Dec 10.
This work has considered a mathematical model describing the spread of COVID-19 in a given population. The model comprised 5 systems of equations that take into account different classes describing the impact of COVID-19 in a given population. The time differential operator was replaced with three different types of nonlocal operators. These operators are defined as the convolution of variable order fractal differential operators with different kernels including power law, exponential decay law, and Mittag-Leffler functions. We presented the well-poseness of the models for different differential operators that were presented in detail. A novel numerical scheme was used to solve numerically the system and numerical simulations were provided.
这项工作考虑了一个描述新冠病毒在特定人群中传播的数学模型。该模型由5个方程组组成，这些方程组考虑了描述新冠病毒在特定人群中影响的不同类别。时间微分算子被三种不同类型的非局部算子所取代。这些算子被定义为具有不同核（包括幂律、指数衰减律和米塔格-莱夫勒函数）的变阶分形微分算子的卷积。我们详细阐述了针对不同微分算子的模型的适定性。使用了一种新颖的数值格式对该系统进行数值求解，并提供了数值模拟结果。
