The parameter estimation of epidemic data-driven models is a crucial task. In some cases, we can formulate a better model by describing uncertainty with appropriate noise terms. However, because of the limited extent and partial information, (in general) this kind of model leads to intractable likelihoods. Here, we illustrate how a stochastic extension of the SEIR model improves the uncertainty quantification of an overestimated MCMC scheme based on its deterministic model to count reported-confirmed COVID-19 cases in Mexico City. Using a particular mechanism to manage missing data, we developed MLE for some parameters of the stochastic model, which improves the description of variance of the actual data.