Dynamics in the absence of tracing Figure 2 shows the comparison of stochastic simulation on networks of the type we have been considering with both mean-field SIS, standard pairwise, improved pairwise, and also the triplewise model of [29] . This demonstrates good agreement between simulation and network ODE models, but poor agreement with the mean-field model. The inclusion of the triplewise model shows that disagreements between pairwise models and simulation in the clustered network are largely due to higher order structure, however these effects are nowhere near as large as the differences between mean-field and pairwise models. Since triplewise models involve a massive increase in computational burden, we do not consider that in this case their use is justified.