Our analysis seeks best social distancing strategies optimally balancing the direct costs of a threatening outbreak with its societal-level costs by investigating the effects of different levels of restrictions' intensity and of the continued importation of infective travellers, while controlling for the key dimensions of the response, such as early action, adherence and the relative weight of societal costs. We identify two primary degrees of freedom in epidemic control, namely the maximum intensity of control measures and their duration. In the absence of travellers, a lower (higher) maximum intensity requires a longer (shorter) duration to achieve similar control outcomes. However, uncontrollable external factors, like the importation of undetected infectives, significantly constrain these degrees of freedom so that the optimal strategy results to be one with low/moderate intensity but prolonged in time. These findings underscore the necessity for resilient health systems and coordinated global responses in preparedness plans.