Modeling adenovirus transmission dynamics using a SEVAIR framework with asymptomatic and vaccinated classes

Mohamed S. Algolam; Ashraf A. Qurtam; Arshad Ali; Khaled Aldwoah; Amer Alsulami; Mohammed Rabih; Mahmoud M. Abdelwahab; Mohamed S. Algolam; Ashraf A. Qurtam; Arshad Ali; Khaled Aldwoah; Amer Alsulami; Mohammed Rabih; Mahmoud M. Abdelwahab

doi:10.3934/math.20251031

AIMS Mathematics

2025, Volume 10, Issue 10: 23235-23260. doi: 10.3934/math.20251031

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Modeling adenovirus transmission dynamics using a SEVAIR framework with asymptomatic and vaccinated classes

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, 11623, Saudi Arabia
3.
Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa 18800, Pakistan
4.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
5.
Department of Mathematics, Turabah University College, Taif University, Taif, Saudi Arabia
6.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
7.
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia

Received: 17 June 2025 Revised: 18 September 2025 Accepted: 24 September 2025 Published: 14 October 2025
MSC : 26A33, 34A08, 34A12

In this work, we extended the classical Susceptible–Exposed–Vaccinated–Infected–Recovered (SEVIR) framework by incorporating an asymptomatic class, leading to the formulation of a new Susceptible–Exposed–Vaccinated–Asymptomatic–Infected–Recovered (SEVAIR) model that more accurately reflects the transmission characteristics of adenovirus. To account for memory effects and capture complex temporal behavior, the model was developed using the fractal-fractional Caputo-Fabrizio derivative with a power-law kernel. Existence and stability of solutions based on fixed point theory and Hyers-Ulam stability criteria were derived. Both the disease-free and endemic equilibrium states were derived, and their local stability properties were examined. Additionally, the basic reproduction number was computed to understand the disease's spread threshold. The theoretical results were supported by numerical simulations, which were performed using a modified Adams-Bashforth approach tailored for the fractional framework.
- SEVAIR epidemic model,
- adenovirus dynamics,
- asymptomatic transmission,
- disease-free and endemic equilibrium analysis,
- solution stability,
- Adams-Bashforth scheme,
- simulations
Citation: Mohamed S. Algolam, Ashraf A. Qurtam, Arshad Ali, Khaled Aldwoah, Amer Alsulami, Mohammed Rabih, Mahmoud M. Abdelwahab. Modeling adenovirus transmission dynamics using a SEVAIR framework with asymptomatic and vaccinated classes[J]. AIMS Mathematics, 2025, 10(10): 23235-23260. doi: 10.3934/math.20251031

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Abstract

In this work, we extended the classical Susceptible–Exposed–Vaccinated–Infected–Recovered (SEVIR) framework by incorporating an asymptomatic class, leading to the formulation of a new Susceptible–Exposed–Vaccinated–Asymptomatic–Infected–Recovered (SEVAIR) model that more accurately reflects the transmission characteristics of adenovirus. To account for memory effects and capture complex temporal behavior, the model was developed using the fractal-fractional Caputo-Fabrizio derivative with a power-law kernel. Existence and stability of solutions based on fixed point theory and Hyers-Ulam stability criteria were derived. Both the disease-free and endemic equilibrium states were derived, and their local stability properties were examined. Additionally, the basic reproduction number was computed to understand the disease's spread threshold. The theoretical results were supported by numerical simulations, which were performed using a modified Adams-Bashforth approach tailored for the fractional framework.

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