  Epidemiological models contain a set of parameters that must be adjusted
based on available observations. Once a model has been calibrated, it can be
used as a forecasting tool to make predictions and to evaluate contingency
plans. It is customary to employ only point estimators for such predictions.
However, some models may fit the same data reasonably well for a broad range of
parameter values, and this flexibility means that predictions stemming from
such models will vary widely, depending on the particular parameter values
employed within the range that give a good fit. When data are poor or
incomplete, model uncertainty widens further. A way to circumvent this problem
is to use Bayesian statistics to incorporate observations and use the full
range of parameter estimates contained in the posterior distribution to adjust
for uncertainties in model predictions. Specifically, given the epidemiological
model and a probability distribution for observations, we use the posterior
distribution of model parameters to generate all possible epidemiological
curves via the posterior predictive distribution. From the envelope of all
curves one can extract the worst-case scenario and study the impact of
implementing contingency plans according to this assessment. We apply this
approach to the potential evolution of COVID-19 in Mexico City and assess
whether contingency plans are being successful and whether the epidemiological
curve has flattened.
