In Figures 3(a) -3(e), continuous-time simulations have their temporal origin shifted so that they agree on the time at which a cumulative incidence of 200 is reached, and then confidence intervals in the mean prevalence of infection are achieved through bootstrapping. The 95% confidence interval is shown as a red shaded region (although typically, this is sufficiently narrow it resembles a line). Six different deterministic models are compared to simulations: HomPW is the pairwise model of Keeling [95] with zero clustering, HetPW is the heterogeneous pairwise model of Eames and Keeling [96] , ClustPW is the improved clustered pairwise closure of House and Keeling [133] , PGF is the model of Volz [129] , Pair-based is the model of Sharkey [139] , integrated using the supplementary code from Sharkey [143] , and Degree-based is the model of Pastor-Satorras and Vespignani [87] . Figure 3 (a) shows a heterogeneous network composed of two risk groups, constructed according to the configuration model [18] . In this case, models that incorporate heterogeneity like HetPW and PGF (which are numerically indistinguishable in this case and several others) are in very close agreement with simulation, while just taking the average degree as in HomPW is a poor choice. In Figure 3 (b), assortativity is added to the two group model following the approach of Newman [89] , and HetPW outperforms PGF. Figure 3 (d) the rate of making and breaking links is much faster than the epidemic process. Models like HomPW and PGF are therefore better for the former and degree-based models are better for the latter-in reality the ratio of the rate of network change to the rate of transmision may not be either large or small and so a more sophisticated method may be best [137, 138] . Figure 3 (e) shows a graph with four links per node where clustering has been introduced by the rewiring method of Bansal et al. [144] sometimes called the "big V" [133] . In this case, ClustPW performs better than HomPW and PGF, but clearly there is significant inaccuracy around the region of peak prevalence and so this model captures qualitatively the effects of clustering without appearing to be exact for this precise network. Finally, Figure 3 (f) considers the case of a one-dimensional next-nearest-neighbour lattice (so there are four links per node). This introduces long path lengths between nodes in addition to clustering, meaning that the system does not converge onto a period of asymptotic early growth and so realisations are shown as a density plot rather than a confidence interval. ClustPW accounts for clustering but not long path lengths and so is in poor agreement with simulation while the pair-based curve captures the qualitative behaviour of an epidemic on this lattice whilst being quantitatively a reasonable approximation.