The differences in the initial epidemic growth rate and epidemic duration are likely to have consequences for the efficacy of contact tracing on the different networks. For example, on assortatively mixed networks with fast epidemic turnover, efficient contact tracing has to be comparably fast. The prevalence of traced nodes (dashed line) for assortatively and disassortatively mixed networks is illustrated in figure 5a . The average degree of newly infected (Barthélemy et al. 2004 ) and contact-traced nodes is plotted in figure 5b . While assortatively mixed networks sustain epidemics with fast turnover and quick initial growth rate, they also allow contact tracing to remove a larger number of highly connected nodes early on in the epidemic. In contrast, on disassortatively mixed networks, disease spread is slower, but contact tracing is also less efficient. Contact tracing can be viewed as an exploration of the local network structure (Cohen et al. 2003) , and thus we would expect its efficacy to depend on the mixing patterns of the network. This is investigated by varying 4, while keeping d fixed. For comparison purposes, we contrast the cases where R(N) is the same on both assortatively and disassortatively mixed networks, but possibly with differing transmission rates, later concentrating on the unique transmission rate that results in the same R(N) on both networks.