Humans and other group-living animals tend to distribute their social effort disproportionately. Individuals predominantly interact with a small number of close companions while maintaining weaker social bonds with less familiar group members. By incorporating this behaviour into a mathematical model we find that a single parameter, which we refer to as social fluidity, controls the rate of social mixing within the group. We compare the social fluidity of 13 species by applying the model to empirical human and animal social interaction data. To investigate how social behavior influences the likelihood of an epidemic outbreak we derive an analytical expression of the relationship between social fluidity and the basic reproductive number of an infectious disease. For highly fluid social behaviour disease transmission is revealed to be density-dependent. For species that form more stable social bonds, the model describes frequency-dependent transmission that is sensitive to changes in social fluidity.