Role of the Delta isobar in the reaction NN to NNπ near threshold

A model calculation for pion production in nucleon-nucleon collisions is presented. Direct production, pion rescattering and contributions from pair diagrams are taken into account. The amplitudes for the elementary processes are based on well established microscopic models of nucleon-nucleon and pion-nucleon scattering. The $\Delta (1232)$ is included explicitly and is found to play an important role even at energies close to production threshold. A good overall agreement with existing data from the pion production threshold up to the Delta resonance region is achieved.