Seasonal influenza is a worldwide public health concern. Forecasting its dynamics can improve the management of public health regulations, resources and infrastructure, and eventually reduce mortality and the costs induced by influenza-related absenteism. In Belgium, a network of Sentinel General Practitioners (SGPs) is in place for the early detection of the seasonal influenza epidemic. This surveillance network reports the weekly incidence of influenza-like illness (ILI) cases, which makes it possible to detect the epidemic onset, as well as other characteristics of the epidemic season. In this paper, we present an approach for predicting the weekly ILI incidence in real-time by resorting to a dynamically calibrated compartmental model, which furthermore takes into account the dynamics of other influenza seasons. In order to validate the proposed approach, we used data collected by the Belgian SGPs for the influenza seasons 2010-2016. In spite of the great variability among different epidemic seasons, providing weekly predictions makes it possible to capture variations in the ILI incidence. The confidence region becomes more representative of the epidemic behavior as ILI data from more seasons become available. Since the SIR model is then calibrated dynamically every week, the predicted ILI curve gets rapidly tuned to the dynamics of the ongoing season. The results show that the proposed method can be used to characterize the overall behavior of an epidemic.