Panwar Virender Singh, Sheik Uduman P S, Gómez-Aguilar J F
Department of Mathematics and Actuarial Science B.S. Abdur Rahman Crescent Institute of Science and Technology, 600048, India.
CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México.
Chaos Solitons Fractals. 2021 Apr;145:110757. doi: 10.1016/j.chaos.2021.110757. Epub 2021 Feb 4.
In this article, Coronavirus Disease COVID-19 transmission dynamics were studied to examine the utility of the SEIR compartmental model, using two non-singular kernel fractional derivative operators. This method was used to evaluate the complete memory effects within the model. The Caputo-Fabrizio (CF) and Atangana-Baleanu models were used predicatively, to demonstrate the possible long-term trajectories of COVID-19. Thus, the expression of the basic reproduction number using the next generating matrix was derived. We also investigated the local stability of the equilibrium points. Additionally, we examined the existence and uniqueness of the solution for both extensions of these models. Comparisons of these two epidemic modeling approaches (i.e. CF and ABC fractional derivative) illustrated that, for non-integer value. The ABC approach had a significant effect on the dynamics of the epidemic and provided new perspective for its utilization as a tool to advance research in disease transmission dynamics for critical COVID-19 cases. Concurrently, the CF approach demonstrated promise for use in mild cases. Furthermore, the integer value results of both approaches were identical.
在本文中，利用两个非奇异核分数阶导数算子研究了新型冠状病毒肺炎（COVID-19）的传播动力学，以检验SEIR compartmental模型的效用。该方法用于评估模型中的完全记忆效应。Caputo-Fabrizio（CF）模型和Atangana-Baleanu模型被用于预测，以展示COVID-19可能的长期轨迹。因此，推导了使用下一代生成矩阵的基本再生数表达式。我们还研究了平衡点的局部稳定性。此外，我们研究了这两种模型扩展的解的存在性和唯一性。这两种流行病建模方法（即CF和ABC分数阶导数）的比较表明，对于非整数值，ABC方法对疫情动态有显著影响，并为其作为推进COVID-19重症病例疾病传播动力学研究的工具提供了新视角。同时，CF方法在轻症病例中显示出应用前景。此外，两种方法的整数值结果相同。
