The difference between the scenarios arises due to the following reasons. Once the proportion of susceptibles in the community falls below 1/R 0 , the effective reproduction number drops below unity regardless of the degree of social distancing, and the epidemic is doomed to extinction. A freely flowing epidemic, however, overshoots a min because at this stage the largest number of infectives is active. In the optimal case, social distancing is used to minimize the number of infectives at this stage, so that there is no overshoot. The ultimate attack rate therefore depends on how many individuals are infected as R(t) crosses 1.