Fractional-order mathematical model for Monkeypox transmission dynamics using the Atangana-Baleanu Caputo operator.

Monkeypox continues to be a major global health concern, marked by recurring outbreaks and complex transmission dynamics. Traditional models of Monkeypox often fail to account for reinfection and the benefits of fractional-order systems, limiting their ability to accurately represent real-world disease progression. This study addresses these gaps by applying the Atangana-Baleanu-Caputo fractional derivative with the Mittag-Leffler kernel to model the transmission dynamics of Monkeypox. The Picard-Lindelöf method is used to establish the existence and uniqueness of solutions, ensuring the model's mathematical soundness. Numerical simulations are carried out using the MATLAB ODE45 package to assess the long-term behavior of the disease, with a focus on the impact of secondary infection rates, as well as the effectiveness of treatment and quarantine interventions. Sensitivity analysis is performed to identify key parameters that influence disease spread, offering valuable insights for targeted control strategies. Our results show that combining quarantine and treatment measures with public health interventions, such as personal protective equipment, contact tracing, and vaccination, significantly reduces the spread of Monkeypox. Furthermore, the fractional-order model's memory effect provides a more accurate representation of disease dynamics compared to traditional integer-order models, capturing how past states influence current disease progression. The study concludes with recommendations for improving preparedness and strategies to mitigate the risk of future infectious disease outbreaks.