Inference of epidemiological parameters from household stratified data

We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide a method for inferring the model parameters -- governing within-household transmission, recovery, and between-household transmission -- from data of the day upon which each individual became infectious and the household in which each infection occurred. This is achieved by calculating an approximation for the likelihood that is evaluated using a novel combination of numerical methods. This allows us to use Bayesian Markov chain Monte Carlo to calculate posterior distributions for all parameters and hence the household reproduction number and the early growth rate of the epidemic. Our methodology is motivated by the analysis of first few hundred study data.