Mass vaccination programmes aim to maintain the effective reproduction number R of an infection below unity. We describe methods for monitoring the value of R using surveillance data. The models are based on branching processes in which R is identified with the offspring mean. We derive unconditional likelihoods for the offspring mean using data on outbreak size and outbreak duration. We also discuss Bayesian methods, implemented by Metropolis–Hastings sampling. We investigate by simulation the validity of the models with respect to depletion of susceptibles and under‐ascertainment of cases. The methods are illustrated using surveillance data on measles in the USA.