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

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. 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.

An exact method for quantifying the reliability of end-of-epidemic declarations in real time

“…Panel (d) plots these R s profiles (top) and the serial interval distributions for each disease (bottom). Generally, we find that t µ is a good approximation to , with some error naturally emerging from the difficulty of estimating R s in conditions where data are necessarily scarce [33]. Our prior distribution over R τ ( j ) is Gam(1, 5), which is both uninformative and has a large mean of 5.…”

“…We found that our method generated sensible and reasonably accurate estimates, given the fundamental difficulties of inferring R s at low incidence. Integrating our method with newly developing approaches that improve on R s estimates in these low data conditions [33], should further enhance performance and forms part of our future work. we have ∆t * 95 ).…”

“…Knowing when to relax non-pharmaceutical interventions, such as social distancing or lockdowns, can be essential to effectively managing and mitigating the financial and social disruption caused by an outbreak as well as to safeguarding populations from the risk of future waves of the disease [1, 2]. The ongoing COVID-19 pandemic for instance, which in some countries such as New Zealand entered a prolonged period of near-elimination before resurgence occurred [33], provides a current and important example where this question might soon become urgent.…”

“…While these factors could limit the accuracy of our predicted declaration times, many can be accommodated as future extensions. We can incorporate heterogeneity by using negative binomial renewal models [1], improve on low incidence estimates by capitalising on specialised methods [33] and extend the models in Fig. 1 to examine mixed noise types.…”

Deciphering early-warning signals of SARS-CoV-2 elimination and resurgence from limited data at multiple scales

“…Vertical lines provide key policy change-times and alert levels in response to these caseloads. The bottom panel presents effective reproduction number ( R ) estimates from EpiFilter 4 (red with 95% confidence bands – these rigorously extract more information from incidence curves than several standard approaches 3 ) and corresponding probabilities (in %) of epidemic elimination ( Z ) – defined as the probability of no future local cases (blue). Both analytics account for the difference between local and imported cases.…”