Predicting the impact of disease epidemics on wildlife populations is one of the twenty-first century's main conservation challenges. The long-term demographic responses of wildlife populations to epidemics and the life history and social traits modulating these responses are generally unknown, particularly for K-selected social species. Here we develop a stage-structured matrix population model to provide a long-term projection of demographic responses by a keystone social predator, the spotted hyena, to a virulent epidemic of canine distemper virus (CDV) in the Serengeti ecosystem in 1993/1994 and predict the recovery time for the population following the epidemic. Using two decades of longitudinal data from 625 known hyenas, we demonstrate that although the reduction in population size was moderate, i.e., the population showed high ecological 'resistance' to the novel CDV genotype present, recovery was slow. Interestingly, high-ranking females accelerated the population's recovery, thereby lessening the impact of the epidemic on the population.