In Fig \ref{948197}, we report the effect of various network structures on three summary statistics of pathogen prevalence (and levels of immunity) using five common network ensembles. Depending on the system being explored, empirical network structures might have elements in common with one or more of these ensembles, for instance, many social networks are considered to be "small-world" in structure like Watts-Strogatz random graphs, while ecological networks are often commented on for their formation of "modules" or clusters of more densely interacting species as in stochastic block random graphs. Networks were parametrized to have approximately equal connectance and size in order to reduce uninformative variation (see Section \ref{930618}). This is because metapopulation size and connectance have known effects on pathogen persistence, independent of further network structure \cite{ganesh2005effect,Salathé2010,Keeling_2005}