A random-effects model for analysis of infectious disease final-state data

Ball (1986, Advances in Applied Probability 18, 289-310) presented an extension to the "General Epidemic Model" in which an individual's (random) infectious period could have any distribution whose Laplace transform could be specified. This paper describes the fitting of Ball's model to data on the final state of infection within households, and gives an intuitive mathematical derivation of the corresponding likelihood function. We extend the model in several ways, including an extension to allow for random-effects heterogeneity in disease transmission rate between individuals. We give an algorithm for the efficient numerical computation of maximum likelihood estimators of the transmission rates, and describe the assessment of goodness of model fit. The methodology is illustrated with recent survey data on outbreaks of Shigella sonnei in 102 households in Manchester, UK. The results are consistent with previous anecdotal evidence of the infectiousness and susceptibility of individuals within households as a function of age and sex.