This paper describes a model-based approach to analyse multivariate time series data on counts of infectious diseases. It extends a method previously described in the literature to deal with possible dependence between disease counts from different pathogens. In a spatio-temporal context it is proposed to include additional information on global dispersal of the pathogen in the model. Two examples are given: the first describes an analysis of weekly influenza and meningococcal disease counts from Germany. The second gives an analysis of the spatio-temporal spread of influenza in the U.S.A., 1996-2006, using air traffic information. Maximum likelihood estimates in this non-standard model class are obtained using general optimization routines, which are integrated in the R package surveillance. Copyright (c) 2008 John Wiley & Sons, Ltd.