Optimising Renewal Models for Real-Time Epidemic Prediction and Estimation

Abstract

The effective reproduction number, Rt, is an important prognostic for infectious disease epidemics. Significant changes in Rt can forewarn about new transmissions or predict the efficacy of interventions. The renewal model infers Rt from incidence data and has been applied to Ebola virus disease and pandemic influenza outbreaks, among others. This model estimates Rt using a sliding window of length k. While this facilitates real-time detection of statistically significant Rt fluctuations, inference is highly k -sensitive. Models with too large or small k might ignore meaningful changes or over-interpret noise-induced ones. No principled k -selection scheme exists. We develop a practical yet rigorous scheme using the accumulated prediction error (APE) metric from information theory. We derive exact incidence prediction distributions and integrate these within an APE framework to identify the k best supported by available data. We find that this k optimises short-term prediction accuracy and expose how common, heuristic k -choices, which seem sensible, could be misleading.