Objective to estimate the transmission rate, the epidemiological peak, and the number of deaths by the new coronavirus. Method a mathematical and epidemiological model of susceptible, infected, and recovered cases was applied to the nine Brazilian capitals with the highest number of cases of the infection. The number of cases for the 80 days following the first case was estimated by solving the differential equations. The results were logarithmized and compared with the actual values to observe the model fit. In all scenarios, it was considered that no preventive measures had been taken. Results the nine metropolises studied showed an upward curve of confirmed cases of COVID-19. The prediction data point to the peak of the infection between late April and early May. Fortaleza and Manaus had the highest transmission rates (≥2·0 and ≥1·8, respectively). Rio de Janeiro may have the largest number of infected people (692,957) and Florianópolis the smallest (24,750). Conclusion the estimates of the transmission rate, epidemiological peak, and number of deaths from coronavirus in Brazilian metropolises presented expressive and important numbers the Brazilian Ministry of Health needs to consider. The results confirm the rapid spread of the virus and its high mortality in the country.(AU)