We study the spreading of SARS-CoV-2 in Brazil based on official data available since March 22, 2020. The calculations are based on an adaptive susceptible-infected-removed (SIR) model featuring dynamical recuperation and propagation rates and can reproduce the number of confirmed cases over time with less than $5\%$ error. Furthermore, it is possible to predict the epidemic progression in the near future and we go on to estimate the time required to stabilize the virus propagation. The model is also proved to be accurate for analyzing the epidemic dynamics in other countries.