A mathematical analysis of Mpox transmission with integrated control strategies in public health

Mpox is a zoonotic disease transmitted between humans and animals, posing a serious threat to public health. This study develops and analyzes a mathematical model describing the dynamics of Mpox transmission while incorporating multiple optimal control strategies. A theoretical analysis was conducted to ensure the well-posedness of the model by examining the existence, positivity, and uniqueness of solutions. The model admits two biologically meaningful equilibrium states: Mpox-free and endemic equilibrium. The local stability of the Mpox-free was established in terms of the basic reproduction number, while the global stability of the endemic equilibrium was investigated using a Lyapunov function approach. To control disease transmission, vaccination, treatment, quarantine, and educational campaigns were introduced as time-dependent control variables within the framework of Pontryagin’s minimum principle. Numerical simulations demonstrated that the full-control scenario, integrating all four interventions, achieved the greatest reduction in the total number of infected individuals among all simulated scenarios, successfully decreasing infections by approximately 97.85%, compared to the without control condition. Cost-effectiveness analysis, based on iteratively calculated ICER values, indicated that the full-control strategy is the most efficient intervention. This conclusion is supported by the control profiles, showing that quarantine and educational campaigns are applied intensively at the early stage of the outbreak, while vaccination and treatment are implemented from the beginning with lower intensity, leading to a more cost-efficient intervention strategy. Accordingly, the adoption of the full-control strategy is recommended as the most effective and cost-efficient approach to mitigating Mpox transmission.