In this paper, we analyze phenomena related to user clumps and hot spots occurring in mobile networks at the occasion of large urban mass gatherings in large cities. Our analysis is based on observations made on mobility traces of GSM users in several large cities. Classical mobility models, such as the random waypoint, do not allow one to represent the observed dynamics of clumps in a proper manner. This motivates the introduction and the mathematical analysis of a new interaction based mobility model, which is the main contribution of the present paper. This model is shown to allow one to describe the dynamics of clumps and in particular to predict key phenomena such as the building of hot spots and the scattering between hot spots, which play a key role in the engineering of wireless networks during such events. We show how to obtain the main parameters of this model from simple communication activity measurements and we illustrate this calibration process on real cases.