Measles persists as a major public-health challenge in Ethiopia, where recurrent outbreaks are driven by suboptimal routine immunization and high susceptibility among children. To characterize these dynamics more accurately, this study investigates a fractional-order measles model using the Caputo derivative, enabling the incorporation of memory and hereditary effects that are not captured by classical integer-order formulations. Model parameters, including the fractional order, are calibrated using weekly Ethiopian measles incidence data. The best-fit model corresponds to \(\alpha = 0.86\) and yields a \(3.4\%\) reduction in Root Mean Square Error together with lower Akaike Information Criterion and Bayesian Information Criterion values compared to the integer-order model. Within this framework, a fractional optimal control problem is developed by introducing time-dependent vaccination and treatment controls. The optimality conditions derived via Pontryagin’s Maximum Principle are solved numerically to evaluate alternative intervention strategies. Quantitatively, the combined vaccination–treatment strategy reduces the final number of infections by \(94\%\) relative to the uncontrolled scenario at \(\alpha = 0.86\) and achieves a \(60\%\) reduction compared with its integer-order counterpart; it also lowers the total control cost by approximately \(28\%\) under fractional dynamics. Overall, the fractional model provides a more flexible representation of measles transmission by accounting for delayed response and long-range temporal effects inherent in real epidemics. The findings demonstrate that optimally timed, memory-aware vaccination strategies can significantly reduce both disease burden and implementation cost in settings such as Ethiopia, where gaps in routine immunization continue to sustain measles circulation.
