Serengeti lions frequently experience viral outbreaks. In 1994, one-third of Serengeti lions died from canine distemper virus (CDV). Based on the limited epidemiological data available from this period, it has been unclear whether the 1994 outbreak was propagated by lion-to-lion transmission alone or involved multiple introductions from other sympatric carnivore species. More broadly, we do not know whether contacts between lions allow any pathogen with a relatively short infectious period to percolate through the population (i.e. reach epidemic proportions). We built one of the most realistic contact network models for a wildlife population to date, based on detailed behavioural and movement data from a long-term lion study population. The model allowed us to identify previously unrecognized biases in the sparse data from the 1994 outbreak and develop methods for judiciously inferring disease dynamics from typical wildlife samples. Our analysis of the model in light of the 1994 outbreak data strongly suggest that, although lions are sufficiently well connected to sustain epidemics of CDV-like diseases, the 1994 epidemic was fuelled by multiple spillovers from other carnivore species, such as jackals and hyenas.