Mathematical analysis of Mpox transmission using SAIR-SI model with optimal control strategies

Articles in Press

Document Type : Research Article

Authors

Tuhfatul Janan ¹

Fatmawati Fatmawati ¹

Agus Hasan ²

¹ Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia

² Department of ICT and Natural Sciences, Norwegian University of Science and Technology, Alesund, Norway

10.22067/ijnao.2026.100294.1934

Abstract

This study presents a SAIR-SI (susceptible - asymptomatic - symptomatic - recovered - susceptible - infected) mathematical model of Mpox transmission using real data in the United States. First, the well-posedness, boundedness, and non-negativity of the solutions are analyzed. Then, it is shown that the model allows three equilibria: disease-free, human-endemic, and endemic. The local stability of the disease-free equilibrium is analyzed based on the Jacobian matrix, while the global stability of all equilibria is examined by defining distinct Lyapunov functions. Sensitivity analysis highlights transmission strength and progression rate as major determinants of epidemic behavior. Numerical simulations demonstrate that higher transmission accelerates spread, while slower progression from asymptomatic to symptomatic stages prolongs infectiousness and increases disease burden. Furthermore, two control measures, namely vaccination and rodenticide usage, are considered, in which the optimal control problem is formulated based on Pontryagin’s principle. Numerical simulations incorporating control measures demonstrate that the strategy combining both controls is the most effective approach for reducing the asymptomatic human, symptomatic human, and infected rodent subpopulations. The cost-effectiveness analysis also confirms that the combined implementation of vaccination and rodenticide usage is the most efficient strategy.

Keywords

Mpox disease: Asymptomatic humans

SAIR-SI model

Stability analysis

Optimal control

Subjects

• Modeling and Simulation

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