The ability to relax assumptions further has been predominately due to use of Markov chain Monte Carlo (MCMC) methods as first considered by O'Neill et al. [162] for household models following earlier studies of Gibson and Renshaw [164] and O'Neill and Roberts [165] who focused on single, large outbreaks. This methodology has been used to in combination with simulation and data augmentation approaches to tailor inference methods for specific data sets of interest; for example, Neal and Roberts [166] consider a model with a spatial component of distance between households and data containing details of dates of symptoms and appearance of rash and has also resulted in a growing number of novel methods for inference, for example Clancy and O'Neill [167] consider a rejection sampling procedure and Cauchemez et al. [168] introduce a constrained simulation approach. Even greater realism can be captured within household models by considering the different compositions of households and, therefore, the weighted nature of contacts within households. For example, Cauchemez et al. [169] considered household data from the Epigrippe study of influenza in France 1999-2000 and showed that children play a key role in the transmission of influenza and the risk of bringing infection into the household.