This study examines the new time-fractional model for Mpox, utilizing Caputo fractional derivatives, specifically focusing on pregnant individuals. The fractional variational iteration method (FVIM) is used to compute a numerical solution for this model. The results of the convergence investigation indicate that the solution obtained exhibits positivity and possesses a well-defined limit. The study yielded significant insights into the intricate dynamics of Mpox viral transmission in pregnant women, affirming the dependability and strength of the Caputo fractional variational approach in forecasting the progression of the illness. The novelty lies in demonstrating how fractional derivatives can capture memory effects in the spread of disease; it provides a more enhanced understanding of the dynamics. Moreover, the suggested model incorporates the notion of optimal control inside different mathematical systems, such as the Fornberg-Whitham equation and the Newell-Whitehead-Segel equation. The convergence of the model described in this study offers empirical support that validates the dependability and suitability of the proposed methodology.

This research investigates a fractional-order mathematical model for analyzing the dynamics of Monkeypox (Mpox) disease using the Caputo-Fabrizio derivative. The model incorporates both human and rodent populations, aiming to elucidate the disease's transmission mechanics, which is demonstrated to be more effective than integer-order models in capturing the complex nature of disease spread. The study determines the fundamental reproduction number ($R_{0}$) while assessing the existence and uniqueness of the solutions. Numerical simulations are conducted to validate the model using Adams-Bashforth technique and illustrate the influence of different factors on the progression of the disease. The findings shed light on Mpox control and prevention, emphasizing the importance of fractional calculus in epidemiological modeling.