Moussa Yacine El Hadj, Boudaoui Ahmed, Ullah Saif, Bozkurt Fatma, Abdeljawad Thabet, Alqudah Manar A
Department of Probability and Statistics, University Djillali liabes, Algeria.
Laboratory of Mathematics Modeling and Applications, University of Adrar, Algeria.
Results Phys. 2021 Jul;26:104324. doi: 10.1016/j.rinp.2021.104324. Epub 2021 May 23.
The novel coronavirus infectious disease (or COVID-19) almost spread widely around the world and causes a huge panic in the human population. To explore the complex dynamics of this novel infection, several mathematical epidemic models have been adopted and simulated using the statistical data of COVID-19 in various regions. In this paper, we present a new nonlinear fractional order model in the Caputo sense to analyze and simulate the dynamics of this viral disease with a case study of Algeria. Initially, after the model formulation, we utilize the well-known least square approach to estimate the model parameters from the reported COVID-19 cases in Algeria for a selected period of time. We perform the existence and uniqueness of the model solution which are proved via the Picard-Lindelöf method. We further compute the basic reproduction numbers and equilibrium points, then we explore the local and global stability of both the disease-free equilibrium point and the endemic equilibrium point. Finally, numerical results and graphical simulation are given to demonstrate the impact of various model parameters and fractional order on the disease dynamics and control.
新型冠状病毒感染疾病（即COVID-19）几乎在全球广泛传播，在人群中引起了巨大恐慌。为了探究这种新型感染的复杂动态，人们采用了几种数学流行病模型，并利用各地区COVID-19的统计数据进行了模拟。在本文中，我们提出了一种新的Caputo意义下的非线性分数阶模型，以阿尔及利亚为例分析和模拟这种病毒性疾病的动态。最初，在模型建立之后，我们利用著名的最小二乘法从阿尔及利亚在选定时间段内报告的COVID-19病例中估计模型参数。我们通过皮卡德-林德洛夫方法证明了模型解的存在性和唯一性。我们进一步计算基本再生数和平衡点，然后探究无病平衡点和地方病平衡点的局部和全局稳定性。最后，给出了数值结果和图形模拟，以展示各种模型参数和分数阶对疾病动态和控制的影响。
