  The COVID-19 pandemic has had worldwide devastating effects on human lives,
highlighting the need for tools to predict its development. Dynamics of such
public-health threats can often be efficiently analysed through simple models
that help to make quantitative timely policy decisions. We benchmark a minimal
version of a Susceptible-Infected-Removed model for infectious diseases (SIR)
coupled with a simple least-squares Statistical Heuristic Regression (SHR)
based on a lognormal distribution. We derived the three free parameters for
both models in several cases and tested them against the amount of data needed
to bring accuracy in predictions. The SHR model is approximately +/- 2%
accurate about 20 days past the second inflexion point in the daily curve of
cases, while the SIR model reaches a similar accuracy a fortnight before. All
the analyzed cases assert the utility of SHR and SIR approximants as a useful
tool to forecast the evolution of the disease. Finally, we have studied
simulated stochastic individual-based SIR dynamics, which yields a detailed
spatial and temporal view of the disease that cannot be given by SIR or SHR
methods.
