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

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  • Panwar, Virender Singh
  • Sheik Uduman, P.S.
  • Gómez-Aguilar, J.F.

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.

Suggested Citation

  • Panwar, Virender Singh & Sheik Uduman, P.S. & Gómez-Aguilar, J.F., 2021. "Mathematical modeling of coronavirus disease COVID-19 dynamics using CF and ABC non-singular fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001107
    DOI: 10.1016/j.chaos.2021.110757
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    References listed on IDEAS

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    1. Alkahtani, B.S.T. & Atangana, A., 2016. "Controlling the wave movement on the surface of shallow water with the Caputo–Fabrizio derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 539-546.
    2. Srivastava, H.M. & Saad, Khaled M. & Khader, M.M., 2020. "An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    Cited by:

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    7. Li, Tingting & Guo, Youming, 2022. "Modeling and optimal control of mutated COVID-19 (Delta strain) with imperfect vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Kumar, Sunil & Chauhan, R.P. & Momani, Shaher & Hadid, Samir, 2021. "A study of fractional TB model due to mycobacterium tuberculosis bacteria," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    9. Samad Noeiaghdam & Sanda Micula & Juan J. Nieto, 2021. "A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library," Mathematics, MDPI, vol. 9(12), pages 1-26, June.
    10. Khan, Hasib & Ibrahim, Muhammad & Abdel-Aty, Abdel-Haleem & Khashan, M. Motawi & Khan, Farhat Ali & Khan, Aziz, 2021. "A fractional order Covid-19 epidemic model with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    11. Baba, Isa Abdullahi & Rihan, Fathalla A., 2022. "A fractional–order model with different strains of COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).

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