A Generalized Stochastic Model for the Analysis of Infectious Disease Final Size Data

A stochastic infectious disease model was developed by Ball (1986, Advances in Applied Probability 18, 289-310) in which the distribution of the length of the infectious period is allowed to have any distribution that can be described by its Laplace transform. We extend this model such that the infection can be transmitted within the population or from an unspecified source outside the population. Also, discrete heterogeneity in the population can be modeled to incorporate variable susceptibility, variable infectivity, and/or mixing behaviors. The model is fitted to serologic data from two influenza epidemics in Tecumseh, Michigan, using maximum likelihood estimation procedures. The estimates show a clustering pattern by age groups.