The human fight against diseases is as old as human history. From ancient Egypt to modern times, diseases have changed the course of battles and shaped major events. Sexually Transmitted Diseases (STDs), those infectious diseases whose main or sole mode of transmission involves sexual contact with infected partners, are mentioned in the Bible and ancient Chinese and Greek medical texts. Today they are known to be the source of many common health problems throughout the world. Although the most common STDs are easily diagnosable, treatable and curable, the Human Immunodeficiency Virus (HIV) which causes the Acquired Immune Deficiency Syndrome (AIDS) has no cure and by virtue of its lifelong infection and long incubation period, the virus can infect a large number of individuals before its carriers are aware of any symptoms. Since the first reported case in 1981, HIV has been transmitted to every corner of the world, infecting and killing people from all ethnic and social backgrounds. 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 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 recently 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 thesis 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.