In emergency call centers (for police, firemen, ambulances, rescue teams) a single event can sometimes trigger many incoming calls to the center in a short period of time. Several people may call to report the same fire or the same accident, for example. Such a sudden burst of incoming traffic can have a significant impact on the responsiveness of the call center for other events in the same period of time. We examine data from the SOS Alarm center in Sweden, related to this type of situation. We also build a stochastic model for the bursts. We show how to estimate the model parameters for each burst by maximum likelihood, how to model the multivariate distribution of those parameters using copulas, and how to simulate the burst process from this model. In our model, certain events trigger an arrival process of incoming calls with a random time-varying rate over a finite period of time of random length. The time period can be short and the arrival rate over that period can be quite large.