Mathematical model of Mpox: assessing the impact of early therapeutic education on seasonal variation

Mohammed M Al-Shomrani; Abdullahi Yusuf; Mohammed M Al-Shomrani; Abdullahi Yusuf

doi:10.3934/math.2026167

AIMS Mathematics

2026, Volume 11, Issue 2: 4147-4199. doi: 10.3934/math.2026167

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Mathematical model of Mpox: assessing the impact of early therapeutic education on seasonal variation

Mohammed M Al-Shomrani ^{1
,
,},
Abdullahi Yusuf ^{2,3,4
,
,}

1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Firat University, Elazig, Turkiye
3.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India
4.
Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkiye

Received: 29 October 2025 Revised: 27 January 2026 Accepted: 29 January 2026 Published: 10 February 2026
MSC : 26A33, 34A08, 34A34, 65L20, 92D30

The 2022–2023 global monkeypox (Mpox) virus outbreak, which affected more than 100 nations, has highlighted the importance of effective public health measures and predictive modeling techniques. In this work, we formulated a mathematical model (MD) of Mpox to assess the impact of early therapeutic education on seasonal variation. To guarantee epidemiological viability, we demonstrated the boundedness and positivity of the model. The next-generation matrix method was employed to determine the basic reproduction number and evaluate the stability of the disease-free equilibrium at the local and global levels. We assessed the existence of an arbitrary equilibrium. The center manifold theorem was employed to assess the backward bifurcation, which shows that imperfect vaccination causes the backward bifurcation. An evaluation of the existence of an endemic equilibrium point was also conducted. The global stability of an endemic equilibrium point was established through the application of a nonlinear Lyapunov function of the Goh-Voltterra type. Data fitting was done to show the model's fitness and estimate the data's parameters. Sensitivity analysis was ascertained. Seasonal variation was assessed. In a numerical simulation, we assessed five controls, which indicated that early therapeutic education is the most effective way to control the re-emergence of Mpox disease in the human (HUM) population.
- mathematical model,
- monkeypox,
- parameter estimation,
- therapeutic,
- education,
- seasonal Variation
Citation: Mohammed M Al-Shomrani, Abdullahi Yusuf. Mathematical model of Mpox: assessing the impact of early therapeutic education on seasonal variation[J]. AIMS Mathematics, 2026, 11(2): 4147-4199. doi: 10.3934/math.2026167

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Abstract

The 2022–2023 global monkeypox (Mpox) virus outbreak, which affected more than 100 nations, has highlighted the importance of effective public health measures and predictive modeling techniques. In this work, we formulated a mathematical model (MD) of Mpox to assess the impact of early therapeutic education on seasonal variation. To guarantee epidemiological viability, we demonstrated the boundedness and positivity of the model. The next-generation matrix method was employed to determine the basic reproduction number and evaluate the stability of the disease-free equilibrium at the local and global levels. We assessed the existence of an arbitrary equilibrium. The center manifold theorem was employed to assess the backward bifurcation, which shows that imperfect vaccination causes the backward bifurcation. An evaluation of the existence of an endemic equilibrium point was also conducted. The global stability of an endemic equilibrium point was established through the application of a nonlinear Lyapunov function of the Goh-Voltterra type. Data fitting was done to show the model's fitness and estimate the data's parameters. Sensitivity analysis was ascertained. Seasonal variation was assessed. In a numerical simulation, we assessed five controls, which indicated that early therapeutic education is the most effective way to control the re-emergence of Mpox disease in the human (HUM) population.

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