In figure 6a , if F%0.61, R(N) is smaller on assortatively mixed networks. Contact tracing on assortatively mixed networks removes nodes of higher degree (figure 5b) than on disassortatively mixed networks. For small F values, the final epidemic size is still high and the population of highly connected nodes is depleted well before the epidemic ends, as shown by the crossover between the average degree of newly infected nodes on the two network types (figure 5b). Over the epidemic, susceptible nodes are on average of lower degree and are more difficult to reach. On disassortatively mixed networks, the depletion of highly connected nodes is less marked and epidemics persist, with disease spread alternating between highly and less well-connected nodes producing an average degree of newly infected nodes which is more even in time (figure 5b). In the latter stages of the epidemic, on disassortatively mixed networks, highly connected nodes are not completely depleted and can become infected. Thus, on the assortatively mixed networks, the epidemic ends earlier with a smaller final epidemic size. On assortatively mixed networks, when global depletion of susceptible nodes is important, contact tracing acts to enhance the early depletion of nodes of high degree (figure 5b). At higher tracing probability, the proportion of nodes removed through contact tracing (figure 6a) decreases with increasing tracing probability. This is indicative of effective control with a limited proportion of nodes becoming infectious and, hence, fewer targets for tracing. In the regime of more effective control (FR0.61), the epidemics die out early on and susceptible depletion becomes less important. This is illustrated in figure 7 , showing that the depletion of susceptibles is only found at low F values. This is also reflected in the very rapid reduction of R g (i.e. average reproduction ratio in generation g defined as the ratio between the number of nodes infected in consecutive generations) below 1 when F is high. This is a more general effect corroborated by examining contacttracing efficacy in a different parameter regime. In figure 6b , the scenario where tZ0.0528 on both networks is considered. For this value of t and in the absence of tracing, the final epidemic size is the same on both networks (R(N)z0.225). Here, the final epidemic size is similar to the point at which contact tracing starts to perform better on disassortatively mixed networks in figure 6a. In this case, for all F values, contact tracing always performs better on disassortatively mixed networks. The behaviour in this regime can be explained by interpreting contact tracing as a mechanism acting to reduce the effective transmission probability T p past the first generation of infection. Contact tracing achieves this by shortening the average infectious period of traced nodes. In figure 4 , lower transmission probabilities correspond to lower values of the transmission rate t. While we do not have exact analytic relationships between the implications of reducing the transmission probability through the different routes, the effect of contact tracing can be approximated by following the trend of the final epidemic size (figure 4) as the transmission probability decreases. The steeper curve of the final epidemic size on disassortatively mixed networks suggests that a small decrease in the transmission probability has a more marked effect on final epidemic size than on assortatively mixed networks. This effect is especially dominant since in the absence of tracing the same R(N) is observed on both networks. This supports the higher contact-tracing efficacy observed on disassortatively mixed networks.