In this paper, the authors use statistical models in two stages to estimate the total number of coronavirus (COVID-19) cases per day at the state and national level in Mexico until was March 17, 2020 (shortly after the first peak of the pandemic). Two types of models are proposed: first, a polynomial model of the growth for the first part of the outbreak until the inflection point of the pandemic curve and then a second nonlinear growth model is used to estimate the middle and the end of the outbreak. Model selection was performed using Vuong’s test. The proposed models show overall fit similar to predictive models (e.g. time series, and machine learning); however, the interpretation of parameters is less complex for decision-makers unfamiliar with epidemic modelling. Additionally, the autocorrelation of the measures is not an issue for the proposed models as the residuals follow the expected distribution.