  The COVID-19 pandemic (SARS-CoV-2 virus) is the defying global health crisis
of our time. The absence of mass testing and the relevant presence of
asymptomatic individuals causes the available data of the COVID-19 pandemic in
Brazil to be largely under-reported regarding the number of infected
individuals and deaths. We propose an adapted Susceptible-Infected-Recovered
(SIR) model which explicitly incorporates the under-reporting and the response
of the population to public policies (such as confinement measures, widespread
use of masks, etc) to cast short-term and long-term predictions. Large amounts
of uncertainty could provide misleading models and predictions. In this paper,
we discuss the role of uncertainty in these prediction, which is illustrated
regarding three key aspects. First, assuming that the number of infected
individuals is under-reported, we demonstrate an anticipation regarding the
peak of infection. Furthermore, while a model with a single class of infected
individuals yields forecasts with increased peaks, a model that considers both
symptomatic and asymptomatic infected individuals suggests a decrease of the
peak of symptomatic. Second, considering that the actual amount of deaths is
larger than what is being register, then demonstrate the increase of the
mortality rates. Third, when consider generally under-reported data, we
demonstrate how the transmission and recovery rate model parameters change
qualitatively and quantitatively. We also investigate the effect of the
"COVID-19 under-reporting tripod", i.e. the under-reporting in terms of
infected individuals, of deaths and the true mortality rate. If two of these
factors are known, the remainder can be inferred, as long as proportions are
kept constant. The proposed approach allows one to determine the margins of
uncertainty by assessments on the observed and true mortality rates.
