For the case of a clustered network in Pane B, the agreement between pairwise models and simulation becomes slightly worse than for the unclustered network results of Pane A, with the improved pairwise model providing a closer fit. Most importantly, the improved pairwise model is in qualitative disagreement with simulation-while both mean-field and standard pairwise models predict a peak in infection before reaching the endemic state, which is not seen in either the improved pairwise model or simulation. We therefore use the results of Panes A and B to rule out the use of mean-field and standard pairwise models. This leaves the improved pairwise model, which we systematically compare to simulation in Panes C and D. Since both the improved pairwise model and simulation depend on underlying parameters in the same way, they form a complementary pair of approaches to the study of contact tracing in clustered populations. The only exception to this is the case of low prevalence of infection, where stochastic effects become important and the stochastic model predicts extinction at higher transmission rates than the pairwise model. 