  An epidemiological study of deaths is carried out in a dozen countries by
analyzing the first wave of the COVID-19 pandemic. These countries are among
those most affected by the first wave, i.e. where daily-death data series may
closely resemble a solution of the basic SIR equations. The SIR equations are
solved parametrically using the proper time as parameter. Some general
properties of the SIR solutions are studied such as time-scaling and asymmetry.
Additionally, we use approximations to the SIR solutions through Gumbel
functions, which present a very similar behavior. The parameters of the SIR
model and the Gumbel function are extracted from the data and compared for the
different countries. It is found that ten of the selected countries are very
well described by the solutions of the SIR model, with a basic reproduction
number between 3 and 8.
