Undirected networks with different mixing patterns (assortative and disassortative) are generated using a method proposed by Newman (2003a) . The mixing pattern here is based on node degree (i.e. the number of links of each node). The level of mixing is given by the correlation coefficient of the 'excess' degrees (see below) calculated on all pairs of connected nodes. The generation of networks with different mixing properties is based on a Monte Carlo sampling scheme with repeated link switching at a probability determined by the values of the connectivity matrix EZe ij . Here, e ij is the probability that a randomly chosen link connects a node with i connections to a node with j connections where the link under consideration is itself not counted. Defining the distribution of the 'excess' degree (i.e. degree minus one) of vertices at the end of links as q k Z P j e jk , the level of mixing by vertex S T R I Figure 1 . Transitions among the four disease progression states. Contact tracing is represented by either the I/T transition (multi-step, dashed) or the I/R transition (singlestep, dotted), both with rate 4. Tracing occurs through either multi-step or single-step tracing. degree is given by