Mathematical modeling of coronavirus disease COVID-19 dynamics using CF and ABC non-singular fractional derivatives

In this article, Coronavirus Disease COVID-19 transmission dynamics were studied to examine the util-ity 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 trajecto-ries 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 tau 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 tau value results of both approaches were identical. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This article studied the transmission dynamics of Coronavirus Disease COVID-19 using the SEIR compartmental model and two non-singular kernel fractional derivative operators, CF and ABC models. The models were used predictively to demonstrate long-term trajectories of COVID-19 and the basic reproduction number expression. Local stability of equilibrium points and the existence and uniqueness of solutions were also investigated in both models. Comparisons showed significant effects on epidemic dynamics for non-integer tau value using the ABC approach, while the CF approach demonstrated promise for mild cases. Identical results were found for integer tau values in both approaches.