where N is the number of nodes in the network, and n is the number of links per node. For SIR dynamics, improvements of this scheme are possible that have a factor of n{1 in the numerator of (2) in the place of n, representing the fact that after the first infection, each infected individual in an unclustered network will have one fewer link due to the individual they were infected by. For clustered networks, SIS dynamics and contact tracing, all of which we are considering here, it is not clear that a similar argument can be used and so we keep the factor of n. Pairwise models. In pairwise models, rather than using assumptions like (2), equations for the pair-level variables that appear on the right-hand side of (1) are written down, leading to triple-level variables that are then closed in terms of pairs.