Numerical treatment for a novel crossover mathematical model of the COVID-19 epidemic

Fawaz K. Alalhareth; Seham M. Al-Mekhlafi; Ahmed Boudaoui; Noura Laksaci; Mohammed H. Alharbi; Fawaz K. Alalhareth; Seham M. Al-Mekhlafi; Ahmed Boudaoui; Noura Laksaci; Mohammed H. Alharbi

doi:10.3934/math.2024259

AIMS Mathematics

2024, Volume 9, Issue 3: 5376-5393. doi: 10.3934/math.2024259

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Numerical treatment for a novel crossover mathematical model of the COVID-19 epidemic

1.
Department of Mathematics, College of Arts & Sciences, Najran University, Najran, Saudi Arabia
2.
Department of Engineering Mathematics and Physics, Future University in Egypt, New Cairo 11835, Egypt
3.
Laboratory of Mathematics Modeling and Applications. University of Adrar, Adrar, Algeria
4.
Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia

Received: 24 November 2023 Revised: 07 January 2024 Accepted: 17 January 2024 Published: 26 January 2024
MSC : 26A33, 39A50, 65L05

This paper extends a novel piecewise mathematical model of the COVID-19 epidemic using fractional and variable-order differential equations and fractional stochastic derivatives in three intervals of time. The deterministic models are augmented with hybrid fractional order and variable order operators, while the stochastic differential equations incorporate fractional Brownian motion. To probe the behavior of the proposed models, we introduce two numerical techniques: the nonstandard modified Euler Maruyama method for the fractional stochastic model, and the Caputo proportional constant-Grünwald-Letnikov nonstandard finite difference method for the fractional and variable-order deterministic models. Several numerical experiments corroborate the theoretical assertions and demonstrate the efficacy of the proposed approaches.
Citation: Fawaz K. Alalhareth, Seham M. Al-Mekhlafi, Ahmed Boudaoui, Noura Laksaci, Mohammed H. Alharbi. Numerical treatment for a novel crossover mathematical model of the COVID-19 epidemic[J]. AIMS Mathematics, 2024, 9(3): 5376-5393. doi: 10.3934/math.2024259

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Abstract

This paper extends a novel piecewise mathematical model of the COVID-19 epidemic using fractional and variable-order differential equations and fractional stochastic derivatives in three intervals of time. The deterministic models are augmented with hybrid fractional order and variable order operators, while the stochastic differential equations incorporate fractional Brownian motion. To probe the behavior of the proposed models, we introduce two numerical techniques: the nonstandard modified Euler Maruyama method for the fractional stochastic model, and the Caputo proportional constant-Grünwald-Letnikov nonstandard finite difference method for the fractional and variable-order deterministic models. Several numerical experiments corroborate the theoretical assertions and demonstrate the efficacy of the proposed approaches.

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