@article{Gassem2025, 
author = {F. Gassem and Ashraf A. Qurtam and Mesfer H. Alqahtani and Mohammed Rabih and Khaled Aldwoah and Abdelaziz El-Sayed and S. O. Ali},
title = {Optimal control of pandemic dynamics using a piecewise fractional order SVIR model},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20947-20978},
keywords = {COVID-19 model, piecewise Caputo-Fabrizio model, basic reproduction number, optimal control, stability, simulation},
url = {https://www.sciopen.com/article/10.3934/math.2025936},
doi = {10.3934/math.2025936},
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        ≃  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.}
}