Sequential Monte Carlo Squared for online inference in stochastic epidemic models

Effective epidemic modeling and surveillance require computationally efficient methods that can continuously update parameter estimates as new data becomes available. This paper explores the application of an online variant of Sequential Monte Carlo Squared (O-SMC²) to the stochastic Susceptible-Exposed-Infectious-Removed (SEIR) model for real-time epidemic tracking. The advantage of O-SMC² lies in its ability to update parameter estimates using a particle Metropolis-Hastings kernel by only utilizing a fixed window of recent observations. This feature enables timely parameter updates and significantly enhances computational efficiency compared to standard SMC², which requires processing all past observations. First, we demonstrate the efficiency of O-SMC² on simulated epidemic data, where both the true parameter values and the observation process are known. We then make an application to a real-world COVID-19 dataset from Ireland, successfully tracking the epidemic and estimating a time-dependent reproduction number of the disease. Our results show that O-SMC² provides accurate online estimates of both static and dynamic epidemiological parameters while substantially reducing computational cost. These findings highlight the potential of O-SMC² for real-time epidemic monitoring and supporting adaptive public health interventions.