BALL, F.G. and SIRL, D.J., 2012. An SIR epidemic model on a population with random network and household structure, and several types of individuals. Advances in Applied Probability, 44, pp.63-86.
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.