Optimal Control Strategy for Fractional Model of Monkeypox Transmission Under Real Data

Abstract

Monkeypox (mpox) is a zoonotic infectious disease that has re-emerged as a global public health concern due to its increasing transmission in various regions. In this study, we propose a fractional-order epidemiological model to investigate the transmission dynamics of mpox involving human and rodent populations. The use of fractional-order derivatives allows the model to incorporate memory effects, which are relevant for capturing the long-term influence of past infections, immune responses, and exposure history. To evaluate effective intervention measures, an optimal control framework is developed by combining two time-dependent control strategies: human vaccination and rodent eradication. The optimal control problem is solved using Pontryagin's Principle of Minimum in conjunction with a forward-backward iterative algorithm, while the fractional-order system is numerically approximated using an Eulerian scheme. Model parameters are estimated using real mpox case data, and the performance of the fractional-order model is compared across different fractional-order values. Numerical simulations show that the combined control strategy significantly reduces the infected population and overall implementation costs compared to a single control intervention. Furthermore, the results show that higher fractional orders, approaching the integer order case, result in improved system performance and earlier separation between control strategies. These findings highlight the importance of memory effects in mpox transmission dynamics and provide insights for designing efficient and cost-effective intervention policies.