tetano
Editor, Senior Moderator
Chaos Solitons Fractals
. 2021 Feb 4;110757.
doi: 10.1016/j.chaos.2021.110757. Online ahead of print.
Mathematical Modeling of Coronavirus Disease COVID-19 Dynamics using CF and ABC Non-Singular Fractional Derivatives
Virender Singh Panwar[SUP] 1 [/SUP], P S Sheik Uduman[SUP] 1 [/SUP], J F G?mez-Aguilar[SUP] 2 [/SUP]
Affiliations
Abstract
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 τ
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 τ
value results of both approaches were identical.
Keywords: Atangana–Baleanu fractional derivative in the Caputo sense; Caputo-Fabrizio (CF) derivative; Coronavirus COVID-19 model; Fractional differential equations; fixed-point theory; numerical simulation.
. 2021 Feb 4;110757.
doi: 10.1016/j.chaos.2021.110757. Online ahead of print.
Mathematical Modeling of Coronavirus Disease COVID-19 Dynamics using CF and ABC Non-Singular Fractional Derivatives
Virender Singh Panwar[SUP] 1 [/SUP], P S Sheik Uduman[SUP] 1 [/SUP], J F G?mez-Aguilar[SUP] 2 [/SUP]
Affiliations
- PMID: 33558794
- PMCID: PMC7859658
- DOI: 10.1016/j.chaos.2021.110757
Abstract
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 τ
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 τ
value results of both approaches were identical.
Keywords: Atangana–Baleanu fractional derivative in the Caputo sense; Caputo-Fabrizio (CF) derivative; Coronavirus COVID-19 model; Fractional differential equations; fixed-point theory; numerical simulation.