  The severe acute respiratory syndrome COVID-19 has been in the center of the
ongoing global health crisis in 2020. The high prevalence of mild cases
facilitates sub-notification outside hospital environments and the number of
those who are or have been infected remains largely unknown, leading to poor
estimates of the crude mortality rate of the disease. Here we use a simple
model to describe the number of accumulated deaths caused by COVID-19. The
close connection between the proposed model and an approximate solution of the
SIR model provides a system of equations whose solutions are robust estimates
of epidemiological parameters. We find that the crude mortality varies between
$10^{-4}$ and $10^{-3}$ depending on the severity of the outbreak which is
lower than previous estimates obtained from laboratory confirmed patients. We
also estimate quantities of practical interest such as the basic reproduction
number and the expected number of deaths in the asymptotic limit with and
without social distancing measures and lockdowns, which allow us to measure the
efficiency of these interventions.
