Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 402
A framework for the statistical analysis of counts from infectious disease surveillance database 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.
Branching Process with Immigration Infectious Disease Surveillance Maximum Likelihood Multivariate Time Series of Counts Observation-driven Parameter-driven Space-Time-Models