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We consider the SIR epidemiological model applied to the evolution ofCOVID-19 with two approaches. In the first place we fit a global SIR model,with time delay, and constant parameters throughout the outbreak, including thecontagion rate. The contention measures are reflected on an effective reducedsusceptible population $N_{eff}$. In the second approach we consider atime-dependent contagion rate that reflects the contention measures eitherthrough a step by step fitting process or by following an exponential decay. Inthis last model the population is considered the one of the country $N$. In thelinear region of the differential equations, when the total population $N$ islarge the predictions are independent of $N$. We apply these methodologies tostudy the spread of the pandemic in Argentina, Brazil, Colombia, Mexico, andSouth Africa for which the infection peaks are yet to be reached. In all ofthese cases we provide estimates for the reproduction and recovery rates. Thescenario for a time varying contagion rate is optimistic, considering thatreasonable measures are taken such that the reproduction factor $R_0$ decreasesexponentially. The measured values for the recovery rate $\gamma$ are reportedfinding a universality of this parameter over various countries. We discuss thecorrespondence between the global SIR with effective population $N_{eff}$ andthe evolution of the time local SIR.

Time-dependent and time-independent SIR models applied to the COVID-19 outbreak in Argentina, Brazil, Colombia, Mexico and South Africa