Abstract
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. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.
Highlights
During an unfolding epidemic, one of the most commonly available and useful types of surveillance data is the daily number of newly reported cases
R measures the average number of secondary cases caused by a primary case and has provided insight into many diseases including COVID-19
One of the most commonly available and useful types of surveillance data is the daily number of newly reported cases. This time-series of case counts, known as the incidence curve, measures the epidemic size and burden, and provides information about trends or changes in its transmissibility [1, 2]
Summary
One of the most commonly available and useful types of surveillance data is the daily (or weekly) number of newly reported cases. This time-series of case counts, known as the incidence curve, measures the epidemic size and burden, and provides information about trends or changes in its transmissibility [1, 2]. Such estimates have proven valuable throughout the COVID-19 pandemic, providing updating synopses of global transmission [8] and evidencing the impact of past control actions (e.g., lockdowns and social distancing) [9] or the likelihood of a resurgence in infections when those controls are relaxed [10]
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