  A social (sexual) network is modeled by an extension of the configuration
model to the situation where edges have weights, e.g. reflecting the number of
sex-contacts between the individuals. An epidemic model is defined on the
network such that individuals are heterogeneous in terms of how susceptible and
infectious they are. The basic reproduction number R_0 is derived and studied
for various examples, but also the size and probability of a major outbreak.
The qualitative conclusion is that R_0 gets larger as the community becomes
more heterogeneous but that different heterogeneities (degree distribution,
weight, susceptibility and infectivity) can sometimes have the cumulative
effect of homogenizing the community, thus making $R_0$ smaller. The effect on
the probability and final size of an outbreak is more complicated.
