A simple and well known epidemiological deterministic model was selected to estimate the main results for the basic dynamics of the Covid-19 epidemic breakout in the city of S. Paulo, Brazil. The methodology employed the SEIR Model to characterize the epidemics outbreak and future outcomes. A time-dependent incidence weight on the SEIR reproductive basic number accounts for local Mitigation Policies (MP). The insights gained from analysis of these successful interventions were used to quantify shifts and reductions on active cases, casualties, and estimatives on required medical facilities (ITU). This knowledge can be applied to other Brazilian areas. The analysis was applied to forecast the consequences of releasing the MP over specific periods of time. Herd Immunity (HI) analysis allowed estimating how far we are from reaching the HI threshold value, and the price to be paid.