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Supplementary material from "A renewal-equation approach to estimating $R_t$ and infectious disease case counts in the presence of reporting delays"

Posted on 2025-02-04 - 13:35
During infectious disease outbreaks delays in case reporting mean that the time series of cases is unreliable, particularly for those cases occurring most recently. This means that real-time estimates of the time-varying reproduction number, $R_t$, are often made using a time series of cases only up until a time-period sufficiently far in the past that there is confidence in the case counts. This means that the most recent $R_t$ estimates are usually out of date, inducing lags in the response of public health authorities. Here, we introduce an $R_t$ estimation method which simultaneously estimates the reporting delays, true historical case counts and $R_t$ in a single Bayesian framework, allowing the uncertainty in each of these quantities to be accounted for. We apply our method to both simulated and real outbreak data which shows that the method substantially improves upon naive estimates of $R_t$ which do not account for reporting delays. Our method is available in an open-source fully tested \textsf{R} package, \textit{incidenceinflation}. Our research highlights the value of keeping historical time series of cases since changes to these data can help to characterise nuisance processes, like reporting delays, which allow these to be accounted for when estimating key epidemic quantities

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