A statistical framework for the analysis of multivariate infectious disease surveillance data

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.