Zhou Jian-Cun, Salahshour Soheil, Ahmadian Ali, Senu Norazak
College of Information and Electronic Engineering, Hunan City University, Yiyang 413000, PR China.
School of Computer Science and Engineering, Central South University, Changsha 410083, PR China.
Results Phys. 2022 Feb;33:105103. doi: 10.1016/j.rinp.2021.105103. Epub 2021 Dec 30.
This research study consists of a newly proposed Atangana-Baleanu derivative for transmission dynamics of the coronavirus (COVID-19) epidemic. Taking the advantage of non-local Atangana-Baleanu fractional-derivative approach, the dynamics of the well-known COVID-19 have been examined and analyzed with the induction of various infection phases and multiple routes of transmissions. For this purpose, an attempt is made to present a novel approach that initially formulates the proposed model using classical integer-order differential equations, followed by application of the fractal fractional derivative for obtaining the fractional COVID-19 model having arbitrary order and the fractal dimension . With this motive, some basic properties of the model that include equilibria and reproduction number are presented as well. Then, the stability of the equilibrium points is examined. Furthermore, a novel numerical method is introduced based on Adams-Bashforth fractal-fractional approach for the derivation of an iterative scheme of the fractal-fractional ABC model. This in turns, has helped us to obtained detailed graphical representation for several values of fractional and fractal orders and , respectively. In the end, graphical results and numerical simulation are presented for comprehending the impacts of the different model parameters and fractional order on the disease dynamics and the control. The outcomes of this research would provide strong theoretical insights for understanding mechanism of the infectious diseases and help the worldwide practitioners in adopting controlling strategies.
本研究包含一种新提出的用于冠状病毒（COVID - 19）疫情传播动力学的阿坦加纳 - 巴莱亚努导数。利用非局部阿坦加纳 - 巴莱亚努分数阶导数方法，对著名的COVID - 19动力学进行了研究和分析，并引入了各种感染阶段和多种传播途径。为此，尝试提出一种新颖的方法，该方法首先使用经典整数阶微分方程来构建所提出的模型，然后应用分形分数阶导数来获得具有任意阶数 和分形维数 的分数阶COVID - 19模型。出于这个目的，还给出了该模型的一些基本性质，包括平衡点和再生数。然后，研究了平衡点的稳定性。此外，基于亚当斯 - 巴什福斯分形分数阶方法引入了一种新颖的数值方法，用于推导分形分数阶ABC模型的迭代格式。这反过来帮助我们分别获得了分数阶 和分形维数 几个值的详细图形表示。最后，给出了图形结果和数值模拟，以理解不同模型参数和分数阶对疾病动力学和控制的影响。本研究的结果将为理解传染病机制提供强有力的理论见解，并帮助全球从业者采用控制策略。
