ON ASSESSING THE POTENTIAL SEVERITY OF AN OUTBREAK OF A RARE INFECTIOUS DISEASE: A BAYESIAN APPROACH

In this paper an infective population, during the early stages of the outbreak of a disease, is approximated by a Galton-Watson process. Attention is focused on the threshold theorem which assesses an epidemic as major if the associated Galton-Watson process is supercritical (i.e. the mean μ of the offspring distribution is greater than one). A Bayesian formulation is adopted together with the assumption of a power series offspring distribution and an approximate form is found for P(μ >1) computed from the posterior distribution of μ. Exact results are given for the case of a Poisson offspring distribution. The results are illustrated with applications to three sets of data on smallpox outbreaks. The Bayesian approach has a number of advantages over classical methods and in particular allows the cases μ < 1, μ > 1 to be treated without distinction.