Epidemiology and Social Networks:

The spread of a disease through human populations can be significantly altered by patterned networks of social contact. Largely in response to AIDS, the way in which social networks channel disease has recently become the focus of a sustained modeling effort in epidemiology. The challenge has been to develop a general framework capable of representing both simple and arbitrarily complicated mixing structures, and of solving the matching problem in a non-equilibrium multi-group population. This work is reviewed here. A recent contribution from network analysis links log-linear models of contact structure to diffusion equations for transmission. This framework is described in detail, and some applications to the spread of AIDS are described. The results show that careful analysis of structured mixing can reveal significant features of an epidemic that would otherwise be missed.