COVID-19 spreading in Rio de Janeiro, Brazil: do the policies of social isolation really work?

The recent Coronavirus (COVID-19) has been spreading through all the world fastly. In this work we focus on the evolution of the COVID-19 in one of the most populous Brazilian states, namely the Rio de Janeiro state. The first case was reported in March 5, 2020, thus we have a considerable amount of available data to make a good analysis. First we study the early evolution of the disease, considering a Susceptible-Infectious-Quarantined-Recovered (SIQR) model. This initial phase shows the usual exponential growth of the number of confirmed cases. In this case, we estimate the parameters of the model based on the data, as well as the epidemic doubling time. After, we analyze all the available data, from March 5, 2020 through April 26, 2020. In this case, we observe a distinct behavior: a sub-exponential growth. In order to capture this change in the behavior of the evolution of the confirmed cases, we consider the implementation of isolation policies. The modified model agrees well with data. Finally, we consider the relaxation of such policies, and discuss about the ideal period of time to release people to return to their activities.