  We formulate models for the spread of infection on networks that are amenable
to analysis in the large population limit. We distinguish three different
levels: (1) binding sites, (2) individuals, and (3) the population. In the
tradition of Physiologically Structured Population Models, the formulation
starts on the individual level. Influences from the `outside world' on an
individual are captured by environmental variables. These environmental
variables are population level quantities. A key characteristic of the network
models is that individuals can be decomposed into a number of conditionally
independent components: each individual has a fixed number of `binding sites'
for partners. The Markov chain dynamics of binding sites are described by only
a few equations. In particular, individual-level probabilities are obtained
from binding-site-level probabilities by combinatorics while population-level
quantities are obtained by averaging over individuals in the population. Thus
we are able to characterize population-level epidemiological quantities, such
as $R_0$, $r$, the final size, and the endemic equilibrium, in terms of the
corresponding variables.
