In a heterogeneous population, the behaviour of an epidemic within any particular locality is governed by the relationship between infected and susceptible individuals. For inference in the early stages of an epidemic, it is important to quantify the amount of uncertainty in the underlying contact networks as the early growth of the epidemic is known to be subexponential due to the depletion of the local susceptible population. This contrasts markedly to the exponential growth observed in a large homogeneously mixing population [10] . When the network is known and details of individual infections are available, contact tracing data may be used to infer the network; this data could also be used for inference on the epidemic parameters [116, 149] . Conversely, if the network is completely unknown, it would be useful if estimation of both the epidemic parameters and parameters specifying the structure of the network was possible. This is a difficult problem because the observed epidemic contains very limited information about the underlying network, as demonstrated by Britton and O'Neill [150] . However, with appropriate assumptions, some results can be obtained; the limited amount of existing work in this area is described in Section 5.3.1 below although clearly the problem is worthy of further study.