  The study of social networks, and in particular the spread of disease on
networks, has attracted considerable recent attention in the physics community.
In this paper, we show that a large class of standard epidemiological models,
the so-called susceptible/infective/removed models, and many of their
generalizations, can be solved exactly on a wide variety of networks. Solutions
are possible for cases with heterogeneous or correlated probabilities of
transmission, cases incorporating vaccination, and cases in which the network
has complex structure of various kinds. We confirm the correctness of our
solutions by comparison with computer simulations of epidemics propagating on
the corresponding networks.
