Advanced Mathematical Models & Applications

This study develops and analyzes a fractional-order mathematical model for the transmission dynamics of monkeypox (mpox) virus in Nigeria using the Caputo fractional derivative. Unlike classical integer-order epidemic models, fractional calculus enables incorporation of memory and hereditary properties in disease dynamics, thereby capturing long-range temporal correlations that are inherent in real-world epidemic processes. We extended a previously established integer-order compartmental model of mpox by reformulating it in the Caputo sense and applied a corrected fractional Adams-Bashforth–Moulton predictor–corrector integrator to obtain numerical solutions. Weekly confirmed case data from Nigeria, spanning May 29, 2022 to May 21, 2023, were employed for model calibration and parameter estimation. Using nonlinear least squares fitting, we simultaneously estimated the effective transmission rate, reporting factor, and the fractional order of differentiation. The results yielded an optimal fractional order of α*≈0.215, indicating strong memory effects in mpox spread. The fractional model showed superior agreement with the observed epidemic trajectory compared to the classical model. Sensitivity analysis further demonstrated the influence of vaccination and quarantine rates on the basic reproduction number R₀ and its components. Our findings highlight the importance of fractional-order modeling in accurately capturing epidemic persistence and provide a framework for improved forecasting and control strategies against mpox and similar emerging diseases.