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Held, Leonhard and Höhle, Michael and Hofmann, M. (2004): A statistical framework for the analysis of multivariate infectious disease surveillance data. Collaborative Research Center 386, Discussion Paper 402




A framework for the statistical analysis of counts from infectious disease surveillance databases is proposed. In its simplest form, the model can be seen as a Poisson branching process model with immigration. Extensions to include seasonal effects, time trends and overdispersion are outlined. The model is shown to provide an adequate fit and reliable one-step-ahead prediction intervals for a typical infectious disease surveillance time series. Furthermore, a multivariate formulation is proposed, which is well suited to capture space-time interactions caused by the spatial spread of a disease over time. Analyses of uni- and multivariate times series on several infectious diseases are described. All analyses have been done using general optimization routines where ML estimates and corresponding standard errors are readily available.