Be stars are main-sequence massive stars with emission features in their spectrum, which originates in circumstellar gaseous discs. Even though the viscous decretion disc (VDD) model can satisfactorily explain most observations, two important physical ingredients, namely the magnitude of the viscosity (α) and the disk mass injection rate, remain poorly constrained. The light curves of Be stars that undergo events of disc formation and dissipation offer an opportunity to constrain these quantities. A pipeline was developed to model these events that uses a grid of synthetic light curves, computed from coupled hydrodynamic and radiative transfer calculations. A sample of 54 Be stars from the OGLE survey of the Small Magellanic Cloud (SMC) was selected for this study. Because of the way our sample was selected (bright stars with clear disc events), it likely represents the densest discs in the SMC. Like their siblings in the Galaxy, the mass of the disc in the SMC increases with the stellar mass. The typical mass and angular momentum loss rates associated with the disk events are of the order of ∼10 −10 M yr −1 and ∼5 × 10 36 g cm 2 s −2 , respectively. The values of α found in this work are typically of a few tenths, consistent with recent results in the literature and with the ones found in dwarf novae, but larger than current theory predicts. Considering the sample as a whole, the viscosity parameter is roughly two times larger at build-up ( α bu = 0.63) than at dissipation ( α d = 0.26). Further work is necessary to verify whether this trend is real or a result of some of the model assumptions.