Some extensions to the endemic-epidemic model class for infectious disease surveillance counts

The endemic-epidemic class (Held et al 2005, DOI 10.1191=1471082X05st098oa) is a modelling framework for multivariate infectious disease surveillance counts closely related to INGARCH models. It allows to model counts stratified by e.g. disease type, geographical area or age group and is readily implemented in the R package surveillance. I will present some recent developments for this model class. In a first part I will talk about an extension to higher-order lags and some properties of the resulting model class, in particular their periodically stationary properties. These can be used for model assessment and to link retrospective modelling to prospective outbreak detection. In a second part I will talk about the problem of underreporting, which is very common in infectious disease epidemiology. I will show how inference for models with an additional reporting step can be done using an approximate maximum likelihood scheme. Moreover I will address some biases which can occur in naive analyses where underreporting is ignored. The different extensions are illustrated using various data examples.