Integrated Optimal Control and Cost‐Effectiveness Analysis of Mpox Transmission With Imperfect Vaccination and Waning Immunity

The monkeypox virus (MPoxV) remains a significant public health concern, particularly in regions with limited vaccine availability and inadequate disease surveillance systems. In this study, a deterministic mathematical model is developed to describe Mpox transmission dynamics by incorporating imperfect vaccination, waning immunity following recovery, and time‐dependent optimal control interventions. The model is shown to be mathematically and epidemiologically well‐posed through the establishment of solution non‐negativity and boundedness. Using the next‐generation matrix approach, the control reproduction number, , is derived, and stability analysis demonstrates that the disease‐free equilibrium (DFE) is locally and globally asymptotically stable when , while the endemic equilibrium (EE) is globally asymptotically stable when . A global sensitivity analysis using Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCCs) identifies the key parameters influencing Mpox transmission dynamics. The model is further extended to evaluate time‐dependent control strategies, including vaccination, vaccine efficacy improvement, quarantine of exposed individuals, and treatment of infectious individuals using optimal control theory. Numerical simulations based on the forward‐backward sweep method demonstrate that combined intervention strategies substantially reduce exposed and infectious populations compared with the uncontrolled scenario. Although vaccination remains an essential component of Mpox prevention, its effectiveness is influenced by waning immunity, limited vaccine coverage, and viral evolution, highlighting the need for integrated intervention approaches. A comprehensive cost‐effectiveness analysis is conducted using average cost‐effectiveness ratio (ACER), incremental cost‐effectiveness ratio (ICER), and dominance analysis. The results show that the all‐controls strategy, combining vaccination, enhanced vaccine efficacy, quarantine, and treatment, provides the highest epidemiological benefit while achieving the lowest cost per human infection averted (ACER = 1.8956). Following dominance elimination, the final cost‐effectiveness frontier retained only treatment, vaccination combined with vaccine efficacy improvement and treatment, and all‐control strategies, with the all‐controls strategy emerging as the most economically efficient intervention. These findings demonstrate that integrated optimal control strategies provide superior epidemiological and economic outcomes and offer quantitative evidence for designing effective and sustainable Mpox control programs.