The goal of this paper is to yield physical constrains on the nature and evolution of a seismic swarm by means of a quantitative stochastic modeling of earthquakes occurrence. With this purpose, we fit different stationary and nonstationary stochastic ETAS models to the Izu Islands seismic swarm occurred in 2000. We find that a nonstationary model with background activity and p-value varying through time describes the observations better than other simpler ETAS models. The coherent fluctuations of these parameters and of the spatio-temporal earthquake distribution are interpreted in terms of a magma/fluids source process that evolves through outbursts of activity superimposed to low frequency variations. The results obtained suggest that suitable nonstationary ETAS modeling can be very useful to characterize the nature of the swarm source, and it may provide the basis to build a quantitative tool for tracking in almost real-time the evolution of a magma/fluids source.