Ameen Ismail Gad, Ali Hegagi Mohamed, Alharthi M R, Abdel-Aty Abdel-Haleem, Elshehabey Hillal M
Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt.
Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypt.
Results Phys. 2021 Apr;23:103976. doi: 10.1016/j.rinp.2021.103976. Epub 2021 Feb 19.
One of the greatest challenges facing the humankind nowadays is to confront that emerging virus, which is the Coronavirus (COVID-19), and therefore all organizations have to unite in order to tackle that the transmission risk of this virus. From this standpoint, the scientific researchers have to find good mathematical models that do describe the transmission of such virus and contribute to reducing it in one way or another, where the study of COVID-19 transmission dynamics by mathematical models is very important for analyzing and controlling this disease propagation. Thus, in the current work, we present a new fractional-order mathematical model that describes the dynamics of COVID-19. In the proposed model, the total population is divided into eight classes, in addition to three compartments used to estimate the parameters and initial values. The effective reproduction number ( ) is derived by next generation matrix (NGM) method and all possible equilibrium points and their stability are investigated in details. We used the reported data (from January 23, 2020, to November 21, 2020) from the National Health Commission (NHC) of China to estimate the parameters and initial conditions (ICs) which suggested for our model. Simulation outcomes demonstrate that the fractional order model (FOM) represents behaviors that follow the real data more accurately than the integer-order model. The current work enhances the recent reported results of Zu et al. published in THE LANCET (doi:10.2139/ssrn.3539669).
当今人类面临的最大挑战之一是应对这种新出现的病毒，即冠状病毒（COVID-19），因此所有组织必须团结起来，以应对这种病毒的传播风险。从这个角度来看，科研人员必须找到能够描述这种病毒传播情况并以某种方式有助于减少传播的良好数学模型，其中通过数学模型研究COVID-19传播动力学对于分析和控制这种疾病的传播非常重要。因此，在当前的工作中，我们提出了一个描述COVID-19动力学的新的分数阶数学模型。在所提出的模型中，总人口被分为八个类别，此外还有三个用于估计参数和初始值的隔室。通过下一代矩阵（NGM）方法推导有效再生数（ ），并详细研究所有可能的平衡点及其稳定性。我们使用了中国国家卫生健康委员会（NHC）报告的数据（从2020年1月23日至2020年11月21日）来估计我们模型所需的参数和初始条件（ICs）。模拟结果表明，分数阶模型（FOM）比整数阶模型更准确地反映了实际数据的行为。当前的工作改进了Zu等人发表在《柳叶刀》（doi:10.2139/ssrn.3539669）上的最新报道结果。
