Qualitative results from simulations indicate that epidemics on networks, for some parameter values, show features that distinguish them from homogeneous models. The principal features are a very variable length slow-growth phase, followed by a rapid increase in the infection rate and a slower decline after the peak [180] . However, in quantitative terms, there is usually very limited information about the underlying network and parameters are often not identifiable. When the details of the network are unknown, but something is known or assumed about its formation, estimation of both the epidemic parameters and parameters for the network itself are in principle possible using MCMC techniques. All the stochastic models for generating networks described in Section 2.7 above realise a distribution over all or some of the 2 N(N−1)/2 possible networks. In most cases, this distribution is not tractable; MCMC techniques are in principle still possible but in practice would be too slow without careful design of algorithms.