There has been considerable recent interest in expanding traditional mass action models for disease transmission to include selectivity and clustering in the contact process. One approach has been to stratify the population according to one or more population characteristics and then to model the effect of these characteristics on contact patterns. The contact rate between two members with known attributes is described by a mixing matrix or kernel function. The usual approach is to consider a parameterized family of mixing matrices and ask how important epidemiological outcomes are affected by these parameters.

In contrast, we have taken the contact network as the primary unit of observation. Networks are modeled as weighted graphs (static and undirected in the studies reported here). Because a complete description of a network entails a very large amount of information, our goal was find summary statistics that were effective predictors of the speed at which a disease would propagate through the network. The approach was to generate random networks, compute summary statistics, simulate a disease spreading through the network, and then examine the relationship between the statistics and epidemiologically significant outcomes. These simulation studies are preliminary, indicating the direction of ongoing research, and ask more questions than they answer.

Networks were generated using two different probability models, producing clustering by different mechanisms. The first model assumes that spatial proximity is a major consideration in network formation. Each individual in the population is assigned a random location in a square region and is assigned a circular territory of radius r in which it seeks contacts.