  The COVID-19 disease has forced countries to make a considerable
collaborative effort between scientists and governments to provide indicators
to suitable follow-up the pandemic's consequences. Mathematical modeling plays
a crucial role in quantifying indicators describing diverse aspects of the
pandemic. Consequently, this work aims to develop a clear, efficient, and
reproducible methodology for parameter optimization, whose implementation is
illustrated using data from three representative regions from Chile and a
suitable generalized SIR model together with a fitted positivity rate. Our
results reproduce the general trend of the infected's curve, distinguishing the
reported and real cases. Finally, our methodology is robust, and it allows us
to forecast a second outbreak of COVID-19 and the infection fatality rate of
COVID-19 qualitatively according to the reported dead cases.
