Epidemic indicators do not determine intervention performance

Epidemic growth rates, reproduction numbers and counts of new infections are universally used to guide public health intervention decisions. It is widely and reasonably believed that larger values of these indicators evidence the need for more urgent or stringent control. Here we show that this intuition can fail dramatically. We construct pairs of epidemics with indistinguishable growth rates, reproduction numbers and infection curves but fundamentally divergent responses to identical interventions, with one epidemic subsiding while the other grows exponentially. Conversely, we identify pairs in which one epidemic exhibits larger indicators and causes three times as many infections, yet both become suppressed with equal effectiveness under the same intervention. These paradoxical outcomes arise from structural uncertainties in transmission, which are invisible to standard outbreak indicators but become decisive under feedback control. Because structural uncertainty is unavoidable when representing real outbreaks, epidemic controllability and intervention performance cannot be reliably inferred without explicitly modelling this feedback between transmission and intervention.