  We analyze the dynamics of the COVID-19 epidemic taking into account the role
of the unreported cases. After a first section in which we deal with a
framework of very slow test capacity, we turn to the model recently
introduced/implemented by Liu, Magal, Seydi and Webb. First, we prove some
basic structural results for the corresponding ODE, as for instance the
convergence of S(t) to a positive limit. These are similar to those of the
classical SIR model, although the maxima of the corresponding curves are not
necessarily unique. Finally, we implement the model -- but with a variable
transmission rate -- in the Chilean context. A key parameter adjustment
(namely, the fraction of unreported cases) is done via an argument using
mortality rates. We conclude with several conclusions and lines of future
research.
