An SIR epidemic model on a population with random network and household structure, and several types of individuals

We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious indi- viduals can make infectious contacts on two levels, within their own ‘household’ and with their neighbours in a random graph represent- ing additional social contacts. This random graph is an extension of the well-known configuration model to allow for several types of in- dividuals. We give a strong approximation theorem which leads to a threshold theorem for the epidemic model and a method for calcu- lating the probability of a major outbreak given few initial infectives. A multitype analogue of a theorem of Ball et al. (2009) heuristically motivates a method for calculating the expected size of such a major outbreak. We also consider vaccination and give some short numerical illustrations of our results.