Fractal-Fractional Modeling of the Delayed Dynamics of Mpox Disease.

Fractal-fractional calculus has evolved into a powerful mathematical framework for modeling and analyzing complex processes in bioengineering and biomedical sciences. This study introduces a delayed fractal-fractional Mpox model aimed at exploring the biological effects of memory and behavioral response lags on disease progression. Theoretical analysis establishes the non-negativity, existence, and boundedness of solutions, ensuring biological viability of model. Furthermore, basic reproduction number and equilibrium points are derived analytically, followed by a detailed stability analysis. By fitting the model to Mpox data from the United States, its feasibility and applicability are further validated. Sensitivity analysis indicates that increasing vaccination interventions is the most effective strategy for mitigating Mpox transmission. Numerical results show that higher fractal-fractional orders and longer time delays reduces the infected population, indicating the effects of memory and temporal lag on lowering disease transmission. Sustained protective behaviors and transmission delaying interventions, such as booster vaccination and rapid detection with isolation, can significantly reduce disease spread. Policymakers should focus on the strategies that combine behavioral measures, booster vaccination, and rapid detection with isolation as an effort to mitigate Mpox transmission.