Mathematical and numerical analysis of a SEVIR-S model for adenovirus with immunity waning and reinfection effects

Rabeb Sidaoui; W. Eltayeb Ahmed; Arshad Ali; Mohammed Rabih; Amer Alsulami; Khaled Aldwoah; E. I. Hassan; Rabeb Sidaoui; W. Eltayeb Ahmed; Arshad Ali; Mohammed Rabih; Amer Alsulami; Khaled Aldwoah; E. I. Hassan

doi:10.3934/math.2025728

AIMS Mathematics

2025, Volume 10, Issue 7: 16291-16316. doi: 10.3934/math.2025728

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Research article

Mathematical and numerical analysis of a SEVIR-S model for adenovirus with immunity waning and reinfection effects

1.
Department of Mathematics, College of Science, University of Ha'il, 55473 Ha'il, Saudi Arabia
2.
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
3.
Department of Mathematics, University of Malakand, Lower Dir, Chakdara 18000, Khyber Pakhtunkhwa, Pakistan
4.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
5.
Department of Mathematics, Turabah University College, Taif University, Taif, Saudi Arabia
6.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia

Received: 17 April 2025 Revised: 03 July 2025 Accepted: 04 July 2025 Published: 18 July 2025
MSC : 26A33, 34A08, 34A12

In this study, we proposed a modified SEVIR-S (susceptible, exposed, vaccinated, infected, recovered) model for the transmission dynamics of adenovirus by incorporating the effects of immunity waning and reinfection. Unlike the classical SEVIR framework, the extended model accounted for the possibility that recovered individuals may lose immunity over time and become susceptible again — a critical feature for accurately modeling diseases like adenovirus. To better capture the disease's memory effects and temporal dynamics, the model used the fractal-fractional Caputo-Fabrizio derivative with a power-law kernel. The paper analyzed the model's existence and stability using fixed point theory and Hyers-Ulam (H-U) stability. Furthermore, both the disease-free and endemic equilibrium points and their stability were analyzed. Also, the basic reproduction number was provided. The findings were validated through numerical simulations using an extended Adams-Bashforth method.
- SEVIR-S model,
- adenovirus transmission,
- immunity waning and reinfection,
- disease-free and endemic equilibria,
- model existence and stability,
- approximate solution,
- simulations
Citation: Rabeb Sidaoui, W. Eltayeb Ahmed, Arshad Ali, Mohammed Rabih, Amer Alsulami, Khaled Aldwoah, E. I. Hassan. Mathematical and numerical analysis of a SEVIR-S model for adenovirus with immunity waning and reinfection effects[J]. AIMS Mathematics, 2025, 10(7): 16291-16316. doi: 10.3934/math.2025728

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Abstract

In this study, we proposed a modified SEVIR-S (susceptible, exposed, vaccinated, infected, recovered) model for the transmission dynamics of adenovirus by incorporating the effects of immunity waning and reinfection. Unlike the classical SEVIR framework, the extended model accounted for the possibility that recovered individuals may lose immunity over time and become susceptible again — a critical feature for accurately modeling diseases like adenovirus. To better capture the disease's memory effects and temporal dynamics, the model used the fractal-fractional Caputo-Fabrizio derivative with a power-law kernel. The paper analyzed the model's existence and stability using fixed point theory and Hyers-Ulam (H-U) stability. Furthermore, both the disease-free and endemic equilibrium points and their stability were analyzed. Also, the basic reproduction number was provided. The findings were validated through numerical simulations using an extended Adams-Bashforth method.

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