In the limit where n L → (n − 1) and m → ∞-such that there are infinitely many communities of equal size and each community forms a fully interconnected clique-"selfconsistent" equations such as in Ghoshal et al. [128] and House and Keeling [70] are exact. These equations evolve the proportion of cliques with x susceptibles and y infecteds, P x,y , as well as the proportion of infecteds in the population, I, as follows: