Bayesian estimation of the offspring mean in branching processes: Application to infectious disease data

A single-type Bienaymé–Galton–Watson branching process (BGWBP) with a generalized power series offspring distribution is considered as a model of the spread of an infectious disease in a population. Our main goal is to estimate the basic reproduction number R0R0, which is represented by the offspring mean of the BGWBP, applying a Bayesian approach. The only data assumed to be available are the initial number of infected individuals and the total number of infected individuals. We are using the Metropolis–Hastings algorithm to simulate the posterior distribution. The usefulness of the described method is demonstrated on some real data on the number of reported cases of mumps in Bulgaria during the period 2005–2008.