In recent years, there has been growing interest in exponential random graph models (ERGMs) for social networks, also called the p * class of models. ERGMs were first introduced in the early 1980s by Holland and Leinhardt [79] based on the work of Besag [80] . More recently, Frank and Strauss studied a subset of those that have the simple property that the probability of connection between two nodes is independent of the connection between any other pair of distinct nodes. [81] . This allows the likelihood of any nodes being connected to be calculated conditional on the graph having certain network properties. Techniques such as Markov Chain Monte Carlo can then be used to create a range of plausible networks that agree with a wide variety of information collected on network structures even if the complete network is unknown [82, 83] . Due to their simplicity, ERGMs are widely used by statisticians and social network analysts [84] . Despite significant advances in recent years (e.g., [85] ), ERGMs still suffer from problems of degeneracy and computational intractability for large network sizes, which has limited their use in epidemic modelling.