Optimal control of pandemic dynamics using a piecewise fractional order SVIR model

F. Gassem; Ashraf A. Qurtam; Mesfer H. Alqahtani; Mohammed Rabih; Khaled Aldwoah; Abdelaziz El-Sayed; S. O. Ali; F. Gassem; Ashraf A. Qurtam; Mesfer H. Alqahtani; Mohammed Rabih; Khaled Aldwoah; Abdelaziz El-Sayed; S. O. Ali

doi:10.3934/math.2025936

AIMS Mathematics

2025, Volume 10, Issue 9: 20947-20978. doi: 10.3934/math.2025936

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Optimal control of pandemic dynamics using a piecewise fractional order SVIR model

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia
2.
Biology Department, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia
4.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
6.
Biology Department, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia
7.
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia

Received: 27 July 2025 Revised: 25 August 2025 Accepted: 29 August 2025 Published: 12 September 2025
MSC : 26A33, 34A08, 34A12

Modeling the long-term dynamics of the COVID-19 pandemic is challenged by evolving public behavior and interventions. We propose a novel piecewise fractional-order (SVIR) model incorporating vaccination and education controls. The model uniquely employs a classical derivative for the initial, memoryless phase of the epidemic. It then transitions to a Caputo-Fabrizio fractional derivative to capture long-term collective memory effects on transmission. We establish the model's mathematical well-posedness and derive the basic reproduction number ($ R_{0} $). Under our baseline parameterization, the reproduction number is $ R _{0}\simeq 4.95 $. An optimal control problem is formulated to determine the ideal implementation of time-varying vaccination and education. Numerical simulations validate the distinct crossover dynamics produced by our piecewise approach. Results demonstrate that a synergistic strategy combining vaccination and education is highly effective, reducing the peak of infected individuals by over 90% compared to the uncontrolled scenario, and significantly outperforms isolated interventions. This study offers a flexible tool for understanding and controlling epidemics.
- COVID-19 model,
- piecewise Caputo-Fabrizio model,
- basic reproduction number,
- optimal control,
- stability,
- simulation
Citation: F. Gassem, Ashraf A. Qurtam, Mesfer H. Alqahtani, Mohammed Rabih, Khaled Aldwoah, Abdelaziz El-Sayed, S. O. Ali. Optimal control of pandemic dynamics using a piecewise fractional order SVIR model[J]. AIMS Mathematics, 2025, 10(9): 20947-20978. doi: 10.3934/math.2025936

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Abstract

Modeling the long-term dynamics of the COVID-19 pandemic is challenged by evolving public behavior and interventions. We propose a novel piecewise fractional-order (SVIR) model incorporating vaccination and education controls. The model uniquely employs a classical derivative for the initial, memoryless phase of the epidemic. It then transitions to a Caputo-Fabrizio fractional derivative to capture long-term collective memory effects on transmission. We establish the model's mathematical well-posedness and derive the basic reproduction number ($ R_{0} $). Under our baseline parameterization, the reproduction number is $ R _{0}\simeq 4.95 $. An optimal control problem is formulated to determine the ideal implementation of time-varying vaccination and education. Numerical simulations validate the distinct crossover dynamics produced by our piecewise approach. Results demonstrate that a synergistic strategy combining vaccination and education is highly effective, reducing the peak of infected individuals by over 90% compared to the uncontrolled scenario, and significantly outperforms isolated interventions. This study offers a flexible tool for understanding and controlling epidemics.

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