Here, we use square brackets to represent the prevalence of different species within the network. We also use some nonstandard notation to present several diverse approaches in a unified framework: generalised indices κ, λ represent any property of a node (such as its degree), while arrows represent the direction of infection (and so for a directed network, the necessity that an edge in the appropriate direction be present), see Table 1 . Clearly, the system (21) is not closed as it relies on the number of connected triples, and so some form of approximate closure must be introduced to relate the triples to pairs and nodes, which will depend on underlying properties of the network. Most commonly, these closure assumptions deal with heterogeneity in node degree, assortativity, and clustering at the level of triangles. Examples include Keeling [95] and Eames and Keeling [96] , where the generalised variables κ, λ above stand for node degrees (k, l), the triple closure is symmetric with respect to the direction of infection, and the network is assumed to be static and nondirected. A general way to write the closure assumption is