Inference for epidemic models with time-varying infection rates: Tracking the dynamics of oak processionary moth in the UK

Invasive pests pose a great threat to forest, woodland, and urban tree ecosystems. The oak processionary moth (OPM) is a destructive pest of oak trees, first reported in the UK in 2006. Despite great efforts to contain the outbreak within the original infested area of South-East England, OPM continues to spread.Here, we analyze data consisting of the numbers of OPM nests removed each year from two parks in London between 2013 and 2020. Using a state-of-the-art Bayesian inference scheme, we estimate the parameters for a stochastic compartmental SIR (susceptible, infested, and removed) model with a time-varying infestation rate to describe the spread of OPM.We find that the infestation rate and subsequent basic reproduction number have remained constant since 2013 (with $R_0$ between one and two). This shows further controls must be taken to reduce $R_0$ below one and stop the advance of OPM into other areas of England. Synthesis. Our findings demonstrate the applicability of the SIR model to describing OPM spread and show that further controls are needed to reduce the infestation rate. The proposed statistical methodology is a powerful tool to explore the nature of a time-varying infestation rate, applicable to other partially observed time series epidemic data.