Infectious disease data from surveillance systems are typically available as multivariate times series of disease counts in specific administrative geographical regions. Such databases are useful resources to infer temporal and spatiotemporal transmission parameters to better understand and predict disease spread. However, seasonal variation in disease notification is a common feature of surveillance data and needs to be taken into account appropriately. In this paper, we extend a time series model for spatiotemporal surveillance counts to incorporate seasonal variation in three distinct components. A simulation study confirms that the different types of seasonality are identifiable and that a predictive approach suggested for model selection performs well. Application to surveillance data on influenza in Southern Germany reveals a better model fit and improved one-step-ahead predictions if all three components allow for seasonal variation.