A discrete-time model for the statistical analysis of infectious disease incidence data

A discrete-time model is devised for the per-time-unit distribution of infectious disease cases in a sample of households. Using the time at which an individual is identified (e.g., when illness symptoms appear) as a marker for being infected, the probabilities of becoming infected from the community or from a single infectious household member are estimated for various risk factor levels. Maximum likelihood procedures for estimating the model parameters are given. An individual may be classified with regard to level of susceptibility and level of infectiousness. The model is fitted to a combination of symptom and viral culture data from a rhinovirus epidemic in Tecumseh, Michigan. In general, it is observed that decreasing risk of infection is associated with increasing age.