The problem of fitting parameters of a dynamical system appears to be relevant in many areas of knowledge, like weather forecasting, system biology, epidemiology, and financial markets. In this paper, we analyze the Susceptible-Infected-Recovered (SIR) epidemiological model. We first derive an alternative representation of the SIR model, reducing it to one differential equation that models the cumulative number of infected cases in function of time. Then we present a differential evolution approach to estimate the parameters of this dynamical model from data. We illustrate the proposed approach with COVID-19 data from Santiago, Chile. The goodness of fit, obtained by the differential evolution algorithm outperformed ten times the results obtained by a random search strategy used in previous works.