Complete maximum likelihood estimation for SEIR epidemic models: theoretical development

TL;DR

This paper develops a comprehensive maximum likelihood estimation framework for SEIR epidemic models, incorporating various population dynamics and disease progression scenarios, validated through numerical simulations.

Contribution

It introduces a unified approach for parameter estimation in complex SEIR models with stochastic population changes and disease periods.

Findings

Validated the models with numerical simulations

Provided detailed maximum likelihood estimation procedures

Characterized special types of SEIR Markov chain models

Abstract

We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions between states of the population. The SEIR models consist of random dynamical equations for each state (S, E, I and R) involving driving events for the process. We characterize some special types of SEIR Markov chain models in the class including: (1) when birth and death are zero or non-zero, and (2) when the incubation and infectious periods are constant or random. A detailed parameter estimation applying the maximum likelihood estimation technique and expectation maximization algorithm are presented for this study. Numerical simulation results are given to validate the epidemic models.