Cost-effectiveness analysis of Mpox control policies: A hybrid rough set-machine learning approach

Mpox remains a major global public health challenge, with ongoing human-to-human transmission and increased severity from emerging viral clades, despite vaccine availability. We introduce a non-autonomous deterministic mathematical model to examine effective and economical Mpox policy across all 31 possible intervention combinations. The Mpox model incorporates five time-dependent interventions: vaccination, awareness, isolation, hospitalization, and booster dose vaccination, linked to transmission reduction and policy evaluation. We estimate the model parameters from Mpox outbreak data and determine the basic reproduction number. Sensitivity analysis identifies human transmission rate, vaccination rate, and vaccine failure rate as the most influential parameters affecting transmission. We establish the existence of optimal controls and derive the corresponding optimality conditions. We numerically evaluate 31 intervention policies using the forward-backwards sweep method over 90 days. Implementing all five controls yields the highest effectiveness, with an efficiency index of 99.37%, while awareness alone achieves 94.30%. The average cost-effectiveness ratio (ACER) analysis demonstrates that awareness alone is the most cost-effective policy. However, ACER only ranks policies and does not show policymakers under which budget and impact conditions a policy remains cost-effective. To address this gap, we combine rough set theory (RST) with machine learning methods. The RST identifies intervention cost as the core attribute and generates IF-THEN decision rules linking budget level and expected infections averted to cost-effectiveness class, helping policymakers select interventions under economic constraints. The hybrid RST-neural network model achieves the highest classification accuracy (approximately 93%), confirming the consistency of the extracted rules. These results provide a transparent, data-driven framework to help public health authorities develop effective Mpox prevention and control policies.