Mathematical Analysis of the Monkeypox Epidemic With Infective Immigrants Using Real Data From Nigeria

The recent resurgence of monkeypox highlights the urgent need for a deeper understanding of its transmission dynamics and effective intervention strategies. This study develops a nonlinear SEIR-type model that integrates vaccination, treatment, and the impact of infective immigrants to assess monkeypox spread, especially under conditions of regional mobility. Real epidemiological data from Nigeria (2022–2023) are used to calibrate the model, which is shown to be mathematically well-posed with positive, unique, and bounded solutions. Analytical results demonstrate that the disease-free equilibrium is locally and globally stable when the basic reproduction number R0 1. Sensitivity analysis identifies key parameters influencing transmission, notably contact rate, vaccine efficacy, and immigration. The model further incorporates time-dependent control strategies for vaccination and treatment. Simulations using the Forward-Backward Sweep Algorithm and fourth-order Runge–Kutta method reveal that combining high vaccine coverage with timely treatment substantially reduces infection levels and shortens the duration of outbreaks. A cost-effectiveness analysis based on the Incremental cost-effectiveness ratio (ICER) confirms that implementing both vaccination and treatment is the most efficient and impactful strategy. These findings provide critical insights to guide public health policy, emphasizing the importance of proactive vaccination campaigns, efficient treatment protocols, and transboundary surveillance to curb monkeypox transmission.MSC2020 Classification: 92D30, 37N25, 34D20, 92B05, 92D25