We present a model based on two-order integer-valued autoregressive time series to analyze the number of hospital emergency service arrivals caused by diseases that present seasonal behavior. We also introduce a method to describe this seasonality, on the basis of Poisson innovations with monthly means. We show parameter estimation by maximum likelihood and model validation and show several methods for forecasting, on the basis of long-time means and short-time and long-time prediction regions. We analyze an application to model the number of hospital admissions per week caused by influenza. Copyright © 2011 John Wiley & Sons, Ltd.