Infectious zoonotic diseases are a threat to wildlife conservation and global health. They are especially a concern for wild apes, which are vulnerable to many human infectious diseases. As ecotourism, deforestation, and great ape field research increase, the threat of human-sourced infections to wild populations becomes more substantial and could result in devastating population declines. The endangered mountain gorillas (Gorilla beringei beringei) of the Virunga Massif in east-central Africa suffer periodic disease outbreaks and are exposed to infections from human-sourced pathogens. It is important to understand the possible risks of disease introduction and spread in this population and how human contact may facilitate disease transmission. Here we present and evaluate an individual-based, stochastic, discrete-time disease transmission model to predict epidemic outcomes and better understand health risks to the Virunga mountain gorilla population. To model disease transmission we have derived estimates for gorilla contact, interaction, and migration rates. The model shows that the social structure of gorilla populations plays a profound role in governing disease impacts with subdivided populations experiencing less than 25% of the outbreak levels of a single homogeneous population. It predicts that gorilla group dispersal and limited group interactions are strong factors in preventing widespread population-level outbreaks of infectious disease after such diseases have been introduced into the population. However, even a moderate amount of human contact increases disease spread and can lead to population-level outbreaks.