It has long been recognised that the structure of social networks plays an important role in the dynamics of disease propagation. The spread of HIV usually results from a complex network of social interactions and other factors related to culture, sexual behaviour, demography, geography and disease characteristics, as well as the availability, accessibility and delivery of healthcare. The small world phenomenon has been used for representing social network interactions. It states that, given some random connections, the degrees of separation between any two individuals within a population can be very small. In this paper we present a discrete event simulation model which uses a variant of the small world network model to represent social interactions and the sexual transmission of HIV within a population. We use the model to demonstrate the importance of the choice of topology and initial distribution of infection, and capture the direct and non-linear relationship between the probability of a casual partnership (small world randomness parameter) and the spread of HIV.