The novel Coronavirus infection disease is becoming more complex for the humans society by giving death and infected cases throughout the world. Due to this infection, many countries of the world suffers from great economic loss. The researchers around the world are very active to make a plan and policy for its early eradication. The government officials have taken full action for the eradication of this virus using different possible control strategies. It is the first priority of the researchers to develop safe vaccine against this deadly disease to minimize the infection. Different approaches have been made in this regards for its elimination. In this study, we formulate a mathematical epidemic model to analyze the dynamical behavior and transmission patterns of this new pandemic. We consider the environmental viral concentration in the model to better study the disease incidence in a community. Initially, the model is constructed with the derivative of integer-order. The classical epidemic model is then reconstructed with the fractional order operator in the form of Atangana–Baleanu derivative with the nonsingular and nonlocal kernel in order to analyze the dynamics of Coronavirus infection in a better way. A well-known estimation approach is used to estimate model parameters from the COVID-19 cases reported in Saudi Arabia from March 1 till August 20, 2020. After the procedure of parameters estimation, we explore some basic mathematical analysis of the fractional model. The stability results are provided for the disease free case using fractional stability concepts. Further, the uniqueness and existence results will be shown using the Picard–Lendelof approach. Moreover, an efficient numerical scheme has been proposed to obtain the solution of the model numerically. Finally, using the real fitted parameters, we depict many simulation results in order to demonstrate the importance of various model parameters and the memory index on disease dynamics and possible eradication.

通过给全世界带来死亡和感染病例，新型冠状病毒感染疾病对人类社会而言变得越来越复杂。由于这种感染，世界上许多国家遭受了巨大的经济损失。世界各地的研究人员都非常积极地制定计划和政策以早日根除该疾病。政府官员已采取各种可能的控制策略，为消除这种病毒采取了全面行动。开发针对这种致命疾病的安全疫苗以最大程度地减少感染是研究人员的首要任务。在这方面已经采取了不同的方法来消除它。在这项研究中，我们建立了数学流行病模型，以分析这种新流行病的动力学行为和传播方式。我们考虑模型中的环境病毒浓度，以更好地研究社区中的疾病发病率。最初，使用整数阶导数构造模型。然后使用分数阶算子以具有非奇异和非局部核的Atangana–Baleanu衍生物的形式重构分数阶算子，以便更好地分析冠状病毒感染的动态。2020年3月1日至2020年8月20日，沙特阿拉伯报告的COVID-19案例使用了一种著名的估计方法来估计模型参数。在参数估计过程之后，我们探索了分数模型的一些基本数学分析。使用分数稳定性概念为无病病例提供了稳定性结果。更多，将使用Picard-Lendelof方法显示唯一性和存在性结果。此外，已经提出了一种有效的数值方案来数值地获得模型的解。最后，使用真实的拟合参数，我们描绘了许多模拟结果，以证明各种模型参数的重要性以及记忆指数对疾病动态和可能消灭的重要性。