Sequential Monte Carlo Squared for online inference in stochastic epidemic models

TL;DR

This paper introduces an online Sequential Monte Carlo Squared (O-SMC$^2$) method for real-time inference in stochastic epidemic models, enabling efficient and accurate updating of parameters during ongoing outbreaks.

Contribution

The paper presents the novel O-SMC$^2$ algorithm that updates epidemic model parameters using a fixed window of recent data, improving computational efficiency over traditional methods.

Findings

O-SMC$^2$ accurately tracks epidemic parameters in simulated data.

The method effectively estimates the time-varying reproduction number for COVID-19.

O-SMC$^2$ significantly reduces computational costs compared to standard approaches.

Abstract

Effective epidemic modeling and surveillance require computationally efficient methods that can continuously update estimates as new data becomes available. This paper explores the application of an online variant of Sequential Monte Carlo Squared (O-SMC$^2$) to the stochastic Susceptible-Exposed-Infectious-Removed (SEIR) model for real-time epidemic tracking. The particularity of O-SMC$^2$ lies in its ability to update the parameters using a particle Metropolis-Hastings kernel, ensuring that the target distribution remains invariant while only utilizing a fixed window of recent observations. This feature enables timely parameter updates and significantly enhances computational efficiency compared to the standard SMC$^2$, which processes the entire dataset. First, we demonstrate the efficiency of O-SMC$^2$ on simulated data, where both the parameters and the observation process are known. We then apply the method to a real-world COVID-19 dataset from Ireland, successfully tracking the epidemic trajectory and estimating the time-dependent reproduction number of the disease. Our results show that O-SMC$^2$ provides highly accurate online estimates of both static and dynamic epidemiological parameters while substantially reducing computational costs. These findings highlight the potential of O-SMC$^2$ for real-time epidemic monitoring and supporting adaptive public health interventions.