Estimating parameters of continuous-time multi-chain hidden Markov models for infectious diseases

TL;DR

This paper develops a method to estimate key epidemiological parameters of infectious disease models using hidden multi-chain Markov models and the Baum-Welch algorithm, validated on synthetic data.

Contribution

It introduces a novel adaptation of the Baum-Welch algorithm for multi-chain Markov models in epidemiology and provides a framework for parameter estimation from case count data.

Findings

Accurate estimation of transmission and incubation rates from synthetic data.

Model selection insights when using simplified compartment models.

Validation of the approach through Monte Carlo simulations.

Abstract

This study aims to estimate the parameters of a stochastic exposed-infected epidemiological model for the transmission dynamics of notifiable infectious diseases, based on observations related to isolated cases counts only. We use the setting of hidden multi-chain Markov models and adapt the Baum-Welch algorithm to the special structure of the multi-chain. From the estimated transition matrix, we retrieve the parameters of interest (contamination rates, incubation rate, and isolation rate) from analytical expressions of the moments and Monte Carlo simulations. The performance of this approach is investigated on synthetic data, together with an analysis of the impact of using a model with one less compartment to fit the data in order to help for model selection.