Fractional‐Order Modeling of Monkeypox Dynamics: Insights From Optimal Control

This study develops a fractional‐order (FO) Susceptible–Exposed–Quarantined–Vaccinated–Infected–Treated–Recovered model for monkeypox that incorporates Caputo fractional derivatives to capture memory effects in disease transmission. The model includes vaccination, quarantine, and treatment as time‐dependent controls within a fractional optimal control framework, combined with a cost‐effectiveness analysis. We calibrate the model to 2022‐2023 Nigerian surveillance data using Bayesian Markov Chain Monte Carlo methods, achieving high predictive accuracy with R 2 values ranging from 0.94 to 0.98. The FO system is numerically solved using the Adams–Bashforth–Moulton predictor‐corrector method, which is convergent and stable for the chosen time step ( h = 0.01) and well suited for memory‐dependent epidemiological dynamics. Sensitivity analysis shows that transmission rate and recruitment rate have the highest positive influence on the basic reproduction number, while disease‐induced death rates have the largest negative effect. Simulation results indicate that combined vaccination, quarantine, and treatment strategies significantly reduce infection prevalence and are cost‐effective under memory effects. This work fills a gap in the monkeypox modeling literature by jointly incorporating fractional dynamics, multiple optimal controls, and Bayesian calibration, providing a robust and adaptable tool for public health planning.