Modeling Monkeypox dynamics with human–rodent interactions and waning vaccination

Turki D. Alharbi; Md Rifat Hasan; Turki D. Alharbi; Md Rifat Hasan

doi:10.3934/math.2025834

AIMS Mathematics

2025, Volume 10, Issue 8: 18660-18679. doi: 10.3934/math.2025834

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Modeling Monkeypox dynamics with human–rodent interactions and waning vaccination

Turki D. Alharbi ¹,
Md Rifat Hasan ^{2
,
,}

1.
Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca 24382, Saudi Arabia
2.
Department of Applied Mathematics, Faculty of Science, Noakhali Science and Technology University, Noakhali 3814, Bangladesh

Received: 28 June 2025 Revised: 07 August 2025 Accepted: 11 August 2025 Published: 18 August 2025
MSC : 34D08, 34D20, 34D23, 92D30, 93D05, 97M10, 97M60

The global outbreak of the monkeypox virus (Mpox) in 2022–2023, which affected over 100 countries, has underscored the urgent need for robust public health interventions and predictive modeling tools. In this study, we develop a novel mathematical model that captures the transmission dynamics of Mpox between human and rodent populations, incorporating both direct and environmental transmission pathways as well as the effects of vaccination. We prove the model's positivity and boundedness to ensure epidemiological feasibility. Using the next-generation matrix method, we derive the basic reproduction number and assess the local and global stability of both disease-free and endemic equilibria through Lyapunov-based techniques. Sensitivity analysis identifies critical parameters influencing Mpox spread and informs targeted intervention strategies. Numerical simulations illustrate how varying key parameters such as vaccination rates, recovery rates, and transmission pathways affect disease progression. The results emphasize that increasing vaccination coverage and enhancing recovery rates can significantly reduce disease burden. This model provides a comprehensive framework to support evidence-based public health decision-making for controlling future Mpox outbreaks.
- Monkeypox virus (Mpox),
- vaccination,
- Lyapunov,
- sensitivity,
- global stability
Citation: Turki D. Alharbi, Md Rifat Hasan. Modeling Monkeypox dynamics with human–rodent interactions and waning vaccination[J]. AIMS Mathematics, 2025, 10(8): 18660-18679. doi: 10.3934/math.2025834

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Abstract

The global outbreak of the monkeypox virus (Mpox) in 2022–2023, which affected over 100 countries, has underscored the urgent need for robust public health interventions and predictive modeling tools. In this study, we develop a novel mathematical model that captures the transmission dynamics of Mpox between human and rodent populations, incorporating both direct and environmental transmission pathways as well as the effects of vaccination. We prove the model's positivity and boundedness to ensure epidemiological feasibility. Using the next-generation matrix method, we derive the basic reproduction number and assess the local and global stability of both disease-free and endemic equilibria through Lyapunov-based techniques. Sensitivity analysis identifies critical parameters influencing Mpox spread and informs targeted intervention strategies. Numerical simulations illustrate how varying key parameters such as vaccination rates, recovery rates, and transmission pathways affect disease progression. The results emphasize that increasing vaccination coverage and enhancing recovery rates can significantly reduce disease burden. This model provides a comprehensive framework to support evidence-based public health decision-making for controlling future Mpox outbreaks.

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