Maximum likelihood estimation for a stochastic SEIR system for COVID-19

TL;DR

This paper develops a maximum likelihood estimation approach for a stochastic SEIR model to better quantify uncertainty in COVID-19 case data, addressing intractable likelihoods with a novel data management mechanism.

Contribution

It introduces a stochastic extension of the SEIR model and a new MLE method to improve parameter estimation and uncertainty quantification for COVID-19 data.

Findings

Enhanced variance description of COVID-19 case data

Improved parameter estimation accuracy

Better uncertainty quantification in epidemic modeling

Abstract

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.