Resolving outbreak dynamics using approximate Bayesian computation for stochastic birth-death models

Earlier research has suggested that approximate Bayesian computation (ABC) makes it possible to fit simulator-based intractable birth-death models to investigate communicable disease outbreak dynamics with accuracy comparable to that of exact Bayesian methods. However, recent findings have indicated that key parameters such as the reproductive number R may remain poorly identifiable with these models. Here we show that the identifiability issue can be resolved by taking into account disease-specific characteristics of the transmission process in closer detail. Using tuberculosis (TB) in the San Francisco Bay area as a case-study, we consider a model that generates genotype data from a mixture of three stochastic processes, each with their distinct dynamics and clear epidemiological interpretation.  We show that our model allows for accurate posterior inferences about outbreak dynamics from aggregated annual case data with genotype information.  As a by-product of the inference, the model provides an estimate of the infectious population size at the time the data was collected. The acquired estimate is approximately two orders of magnitude smaller compared to the assumptions made in the earlier related studies, and much better aligned with epidemiological knowledge about active TB prevalence. Similarly, the reproductive number R  related to the primary underlying transmission process is estimated to be nearly three-fold compared with the previous estimates, which has a substantial impact on the interpretation of the fitted outbreak model.