Shah Kamal, Arfan Muhammad, Mahariq Ibrahim, Ahmadian Ali, Salahshour Soheil, Ferrara Massimiliano
Department of Mathematics, University of Malakand, Dir(L) 18800, Pakistan.
College of Engineering and Technology, American University of the Middle East, Kuwait.
Results Phys. 2020 Dec;19:103560. doi: 10.1016/j.rinp.2020.103560. Epub 2020 Nov 12.
This work is the consideration of a fractal fractional mathematical model on the transmission and control of corona virus (COVID-19), in which the total population of an infected area is divided into susceptible, infected and recovered classes. We consider a fractal-fractional order type model for investigation of Covid-19. To realize the transmission and control of corona virus in a much better way, first we study the stability of the corresponding deterministic model using next generation matrix along with basic reproduction number. After this, we study the qualitative analysis using "fixed point theory" approach. Next, we use fractional Adams-Bashforth approach for investigation of approximate solution to the considered model. At the end numerical simulation are been given by matlab to provide the validity of mathematical system having the arbitrary order and fractal dimension.
这项工作是对冠状病毒（COVID-19）传播与控制的分形分数阶数学模型的研究，其中感染区域的总人口分为易感、感染和康复三类。我们考虑用分形分数阶模型来研究新冠病毒。为了更好地实现冠状病毒的传播与控制，首先我们使用下一代矩阵和基本再生数来研究相应确定性模型的稳定性。在此之后，我们使用“不动点理论”方法进行定性分析。接下来，我们使用分数阶亚当斯-巴什福斯方法来研究所考虑模型的近似解。最后，通过Matlab进行数值模拟，以验证具有任意阶和分形维数的数学系统的有效性。
