By considering the number of secondary cliques infected by a clique with one initial infected individual, a threshold called R * can be defined. (For the configuration-model of households where each household is of the same size and each individual has the same number of random connections outside the household, the threshold R * is given later as (20) ; however, the methodology is far more general). The calculation of the invasion threshold for the recently defined triangular configuration model [118, 119] involves calculating both the expected number of secondary infectious individuals and triangles rather than just working at the individual level. Trapman [120] deals with how these sort of results can be related to more general networks through bounding. A general feature of clustered networks for which exact thresholds have been derived so far is that there is a local-global distinction in transmission routes, with a general theory of this given by Ball and Neal [121] , where an "overlapping groups" and "great circle" model are also analysed. Nevertheless, care still has to be taken in which threshold parameters are mathematically well behaved and easily calculated (e.g [122] ).