To calculate confidence intervals for the reproductive number we use an approximation of the parametric bootstrap percentile interval method [21] . To obtain proper parametric bootstrap intervals would involve generating infection times and trees according to the underlying epidemic model, which we do not wish to specify completely. Instead, the following two-step approximation is used, which we propose will be a good approximation for large N . These two steps approximate generating realisations from the underlying epidemic process. First, we take bootstrap samples of parameter values from the conventional approximation to the sampling distribution of the ML estimator,