Significant research has been conducted in identifying optimal recovery and adaptation decisions in disruptive scenarios using engineering models. In this context, an aspect that has been target of limited research is that of response times. Modelling is expected to grow progressively more complex as it becomes more accurate. Such complexity increases modelling efforts, and the promise of optimal adaptation and recovery may become hindered. The present work discusses the role of modelling fidelities in adaptation and recovery of systems, and in particular that of using a lower fidelity model that enables zero-time analyses of a system. A framework is proposed for using different fidelities in adaptation and recovery, considering system's decision time requirements. The relevance of this analysis is researched in two traffic networks and results show that multi-fidelity models should be expected to play a key role in increasing the efficiency of optimal adaptation and recovery decisions.