Variations of the SIR model for COVID-19 evolution

Abstract: In this work, we discuss the SIR epidemiological model and different variations of it applied to the propagation of the COVID-19 pandemia; we employ the data of the state of Guanajuato and of Mexico. We present some considerations that can improve the predictions made by those models. We consider a time-dependent infection rate, which we adjust to the data. Starting from a linear regime where the populations are much smaller that the country or state population and the population of susceptible (S) can be approximated in convenient units to S approximately 1, we make fits of the parameters. We also consider the case when the susceptible starts departing from 1, for this case we adjust an effective contagion rate. We also explore the ratio of detected populations and the real ones, obtaining that -for the analyzed case it is of approximately 10%. We estimate the number of deaths by making a fit versus the recovered cases, this fit is in first approximation linear, but other powers can give a good agreement. By predictions to past data, we conclude that adaptations of the SIR model can be of great use in describing pandemia's propagation, specially in limited time periods.