Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. This combination of maximising information and minimising assumptions, makes EpiFilter more statistically robust in periods of low incidence, where existing methods can struggle. As a result, we find EpiFilter to be particularly suited for assessing the risk of second waves of infection, in real time.