Optimising Renewal Models for Real-Time Epidemic Prediction and Estimation

The effective reproduction number, R t , is an important prognostic for infectious disease epidemics. Significant changes in R t can forewarn about new transmissions or predict the efficacy of interventions. The renewal model infers R t from incidence data and has been applied to Ebola virus disease and pandemic influenza outbreaks, among others. This model estimates R t using a sliding window of length k . While this facilitates real-time detection of statistically significant R t 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.