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.