A RANDOM-EFFECTS MODEL FOR ANALYSIS OF INFECTIOUS-DISEASE FINAL-STATEDATA

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 tr ansform 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 likeli hood function. We extend the model in several ways, including an exten sion to allow for random-effects heterogeneity in disease transmission rate between individuals. We give an algorithm for the efficient nume rical computation of maximum likelihood estimators of the transmission rates, and describe the assessment of goodness of model fit. The meth odology is illustrated with recent survey data on outbreaks of Shigell a sonnei in 102 households in Manchester, UK. The results are consiste nt with previous anecdotal evidence of the infectiousness and suscepti bility of individuals within households as a function of age and sex.