The fact that AIDS is mainly a sexually transmitted disease has brought human sexual behaviour into the focus of attention and with it the underlying social structure of the population. The problem of how to incorporate the determinants of the sexual contact structure into a mathematical model of disease transmission has been one of the central questions in AIDS-modelling in recent years. While most of this work up to now has been based on the methodology of differential equations, lately there has been some interest in so-called network models. The basic idea of the network approach is that a population and its sexual contact structure can be described by a graph, where the vertices represent individuals and the edges existing sexual relations.

A simulation model based on the network approach has been developed in Kretzschmar et al. (1990,1994). The model describes a stochastic pair formation and dissolution process in a heterosexual population. Infection can be transmitted in contacts between an infected and a susceptible individual. A major problem in analyzing results from network simulations is the question of what are the appropriate quantities to measure and compare. I have chosen, amongst others, to look at the degree distribution of the ‘cumulative’ network over a given time of observation, because this can be determined with a certain accuracy in sociological surveys. One can then study how the number of infected individuals in the course of the epidemic depends on the mean and variance of this degree distribution.