On the fractional-order mathematical model of COVID-19 with the effects of multiple non-pharmaceutical interventions

Ihtisham Ul Haq; Nigar Ali; Hijaz Ahmad; Taher A. Nofal; Ihtisham Ul Haq; Nigar Ali; Hijaz Ahmad; Taher A. Nofal

doi:10.3934/math.2022877

AIMS Mathematics

2022, Volume 7, Issue 9: 16017-16036. doi: 10.3934/math.2022877

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On the fractional-order mathematical model of COVID-19 with the effects of multiple non-pharmaceutical interventions

1.
Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
2.
Section of Mathematics, international Telematic, University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, Roma 00186, Italy
3.
Department of Mathematics, College of Science, Taif University, Taif 21944, Saudi Arabia

Received: 30 April 2022 Revised: 04 June 2022 Accepted: 07 June 2022 Published: 30 June 2022
MSC : 92B05, 92C10

In this article, the Caputo fractional derivative operator of different orders $ 0 < \alpha\leq1 $ is applied to formulate the fractional-order model of the COVID-19 pandemic. The existence and boundedness of the solutions of the model are investigated by using the Gronwall-Bellman inequality. Further, the uniqueness of the model solutions is established by using the fixed-point theory. The Laplace Adomian decomposition method is used to obtain an approximate solution of the nonlinear system of fractional-order differential equations of the model with a different fractional-order $ \alpha $ for every compartment in the model. Finally, graphical presentations are presented to show the effects of other fractional parameters $ \alpha $ on the obtained approximate solutions.
- Adomian decomposition method,
- COVID-19,
- Uniqueness of the solutions,
- Arzelá-Ascoli theorem,
- Schauder's fixed-point theorem
Citation: Ihtisham Ul Haq, Nigar Ali, Hijaz Ahmad, Taher A. Nofal. On the fractional-order mathematical model of COVID-19 with the effects of multiple non-pharmaceutical interventions[J]. AIMS Mathematics, 2022, 7(9): 16017-16036. doi: 10.3934/math.2022877

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Abstract

In this article, the Caputo fractional derivative operator of different orders $ 0 < \alpha\leq1 $ is applied to formulate the fractional-order model of the COVID-19 pandemic. The existence and boundedness of the solutions of the model are investigated by using the Gronwall-Bellman inequality. Further, the uniqueness of the model solutions is established by using the fixed-point theory. The Laplace Adomian decomposition method is used to obtain an approximate solution of the nonlinear system of fractional-order differential equations of the model with a different fractional-order $ \alpha $ for every compartment in the model. Finally, graphical presentations are presented to show the effects of other fractional parameters $ \alpha $ on the obtained approximate solutions.

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