Modeling rotavirus transmission with booster vaccination using fractal-fractional derivatives

Rabeb Sidaoui; Ashraf A. Qurtam; Arshad Ali; Muntasir Suhail; Khaled Aldwoah; Abdelaziz Elsayed; E. I. Hassan; Rabeb Sidaoui; Ashraf A. Qurtam; Arshad Ali; Muntasir Suhail; Khaled Aldwoah; Abdelaziz Elsayed; E. I. Hassan

doi:10.3934/math.2025895

AIMS Mathematics

2025, Volume 10, Issue 9: 20025-20049. doi: 10.3934/math.2025895

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Modeling rotavirus transmission with booster vaccination using fractal-fractional derivatives

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 of Malakand, Chakdara Dir(L), 18800, Khyber Pakhtunkhwa, Pakistan
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: 25 May 2025 Revised: 06 August 2025 Accepted: 20 August 2025 Published: 01 September 2025
MSC : 26A33, 34A08, 34A12

Rotavirus remains a leading cause of gastroenteritis in children under five in low- and middle-income countries due to waning immunity and incomplete vaccine coverage. To address this, we propose a mathematical model to analyze the transmission dynamics with primary and booster vaccination strategies. The model is formulated using the fractal-fractional derivative in the Caputo-Fabrizio sense, which allows for the incorporation of memory effects and hereditary properties in disease evolution. The population is structured into five compartments, including booster-immunized individuals. We derive the disease-free and endemic equilibrium points and analyze their local stability. The basic reproduction number is computed to determine the threshold conditions for disease persistence. We establish the existence and Hyers-Ulam (H-U) stability of the model, and validate the results through numerical simulations using the Adams-Bashforth method (ABM), confirmed by comparison with Runge-Kutta 4th Order (RK-4) solution plots to assess the booster vaccination impact. The results reveal that booster immunization plays a significant role in reducing the infection burden, thereby highlighting its relevance in public health planning.
- rotavirus transmission,
- booster vaccination,
- fractal-fractional calculus,
- equilibrium points,
- existence and stability analysis,
- numerical analysis
Citation: Rabeb Sidaoui, Ashraf A. Qurtam, Arshad Ali, Muntasir Suhail, Khaled Aldwoah, Abdelaziz Elsayed, E. I. Hassan. Modeling rotavirus transmission with booster vaccination using fractal-fractional derivatives[J]. AIMS Mathematics, 2025, 10(9): 20025-20049. doi: 10.3934/math.2025895

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Abstract

Rotavirus remains a leading cause of gastroenteritis in children under five in low- and middle-income countries due to waning immunity and incomplete vaccine coverage. To address this, we propose a mathematical model to analyze the transmission dynamics with primary and booster vaccination strategies. The model is formulated using the fractal-fractional derivative in the Caputo-Fabrizio sense, which allows for the incorporation of memory effects and hereditary properties in disease evolution. The population is structured into five compartments, including booster-immunized individuals. We derive the disease-free and endemic equilibrium points and analyze their local stability. The basic reproduction number is computed to determine the threshold conditions for disease persistence. We establish the existence and Hyers-Ulam (H-U) stability of the model, and validate the results through numerical simulations using the Adams-Bashforth method (ABM), confirmed by comparison with Runge-Kutta 4th Order (RK-4) solution plots to assess the booster vaccination impact. The results reveal that booster immunization plays a significant role in reducing the infection burden, thereby highlighting its relevance in public health planning.

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