Abstract
This paper demonstrates how Bayesian stochastic filtering techniques can be used to detect changepoints in the transmission rate, as well as identify the rate itself, in the spread of disease using the susceptible-infectious-recovered (SIR) model. To better model real-world scenarios, a stochastic SIR model is considered where the transmission rate is unknown a priori, the number of people moving between compartments is perturbed by additional randomness, and the rate changes at unknown points in time. Changepoints can be used to model disruptions in disease spread, such as those caused by public health measures or new variants. We consider this problem in a Bayesian setting, where the unknown rate and changepoints are modelled as random variables with known prior distributions. This rate can be observed indirectly via the drift of a Brownian motion, before optimally filtering the transmission rate along with any changepoints using Bayesian stochastic filtering techniques. The methods are illustrated with an example using a real dataset from the COVID-19 pandemic, effectively detecting changepoints related to public health measures and the spread of the Omicron variant in the United Kingdom.