Towards Uncertainty Quantification and Inference in the stochastic SIR Epidemic Model

TL;DR

This paper presents a new method for uncertainty quantification and inference in stochastic epidemic models, specifically applying it to the SIR model using moment approximations and Bayesian inference, achieving accurate estimations in synthetic and real data.

Contribution

Introduces a novel inference approach for continuous-time Markov models applied to the stochastic SIR epidemic, utilizing moment matching and Bayesian methods.

Findings

Accurate epidemic parameter estimation in synthetic data.

Effective predictions in Dengue fever case studies.

Valid likelihood approximation for various data counts.

Abstract

In this paper we introduce a novel method to conduct inference with models defined through a continuous-time Markov process, and we apply these results to a classical stochastic SIR model as a case study. Using the inverse-size expansion of van Kampen we obtain approximations for first and second moments for the state variables. These approximate moments are in turn matched to the moments of an inputed generic discrete distribution aimed at generating an approximate likelihood that is valid both for low count or high count data. We conduct a full Bayesian inference to estimate epidemic parameters using informative priors. Excellent estimations and predictions are obtained both in a synthetic data scenario and in two Dengue fever case studies.