Transient redshifted events monitored in the spectrum of β Pictoris have been interpreted as resulting from the evaporation of numerous comet-like bodies in the vicinity of this star. The dynamical origin for this phenomenon is attributed to mean-motion resonances (4:1 and 3:1) with a Jovian-like planet. Numerical simulations of this phenomenon are able to correctly reproduce the dynamical characteristics of the star-grazers observed. The numerical study allows to estimate the density of the planetesimal disk from which the bodies are supposed to originate, i.e. ∼ a few 108 bodies per AU. A key issue with this model is the refilling of the resonances, as without refilling they should be cleared within a few 105 yr and the observed phenomenon should stop. Collisions among planetesimals are a plausible mechanism. Collisional simulations show that collisions are able to sustain the observed phenomenon over much more than 106 yr, provided the population of the disk is high enough. The mass density of this population is estimated to a few tens of Earth masses per AU, which is only marginally realistic. However, the mass estimate is very poorly constrained.