Modeling the early evolution of the COVID-19 in Brazil: results from a Susceptible-Infectious-Quarantined-Recovered (SIQR) model

The world evolution of the Severe acute respiratory syndrome coronavirus 2 (SARS-Cov2 or simply COVID-19) led the World Health Organization to declare it a pandemic. The disease appeared in China in December 2019, and it has spread fast around the world, specially in european countries like Italy and Spain. The first reported case in Brazil was recorded in February 26, and after that the number of cases growed fast. In order to slow down the initial growth of the disease through the country, confirmed positive cases were isolated to not transmit the disease. To better understand the early evolution of COVID-19 in Brazil, we apply a Susceptible-Infectious-Quarantined-Recovered (SIQR) model to the analysis of data from the Brazilian Department of Health, obtained from February 26, 2020 through March 25, 2020. Based on analyical and numerical results, as well on the data, the basic reproduction number is estimated to $R_{0}=5.25$. In addition, we estimate that the ratio unidentified infectious individuals and confirmed cases at the beginning of the epidemic is about $10$, in agreement with previous studies. We also estimated the epidemic doubling time to be $2.72$ days.