Estimating the time-varying reproduction number of SARS-CoV-2 using national and subnational case counts

Abstract

Background: Assessing temporal variations in transmission in different countries is essential for monitoring the epidemic, evaluating the effectiveness of public health interventions and estimating the impact of changes in policy. Methods: We use case and death notification data to generate daily estimates of the time-varying reproduction number globally, regionally, nationally, and subnationally over a 12-week rolling window. Our modelling framework, based on open source tooling, accounts for uncertainty in reporting delays, so that the reproduction number is estimated based on underlying latent infections. Results: Estimates of the reproduction number, trajectories of infections, and forecasts are displayed on a dedicated website as both maps and time series, and made available to download in tabular form. Conclusions: This decision-support tool can be used to assess changes in virus transmission both globally, regionally, nationally, and subnationally. This allows public health officials and policymakers to track the progress of the outbreak in near real-time using an epidemiologically valid measure. As well as providing regular updates on our website, we also provide an open source tool-set so that our approach can be used directly by researchers and policymakers on confidential data-sets. We hope that our tool will be used to support decisions in countries worldwide throughout the ongoing COVID-19 pandemic.

Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England

“…We calculated the weekly proportion of positive tests that were S-gene negative out of all positive tests that tested for the S-gene by English upper-tier local authority. We used reproduction number estimates obtained using the method described in (37) and (39) and implemented in the EpiNow2 R package (40), downloaded from https://github.com/epiforecasts/covid-rt-estimates/blob/ master/subnational/united-kingdomlocal/cases/summary/rt.csv. We then built a separate model of the expected reproduction number in UTLA i during week t starting in the week beginning the 5 October 2020 as a function of local restrictions, mobility indicators, residual temporal variation, and proportion of positive tests with S gene target failure.…”

Estimating epidemiologic dynamics from cross-sectional viral load distributions

“…To demonstrate the performance of these Ct-based methods, we simulate outbreaks under a variety of testing schemes using SEIR-based simulations and sample Ct values from the outbreaks (Materials and Methods: Simulated Testing Schemes). We compare the performance of Rt estimation using reported case counts (based on the testing scheme) via the R package EpiNow2 (32,33), where reporting depends on testing capacity and the symptom status of infected individuals, to the performance of our methods when one, two, or three surveillance samples are available with observed Ct values, with a total of about 0.3% of the population sampled (3000 tests spread among the samples).…”

Assessing Interventions against Coronavirus Disease 2019 (COVID-19) in Osaka, Japan: A Modeling Study

“…This 5-day period was specifically chosen because it is in the range of published estimates of the serial interval for COVID-19 [17,18,20,24]. Maximum likelihood estimates of R(t) were obtained by minimizing the negative logarithm of Equation (5). To quantify the confidence intervals (CIs) of R(t), we implemented parametric bootstrapping using the Hessian matrix H. We obtained 1000 resamples of parameters from the normal distribution with mean θ 0 and standard deviation σ, equal to the square root of diagonal elements of the inverse Hessian matrix (σ 2 = diag(H −1 (θ 0 ))).…”

“…However, the structure is in principle comparable to the commonly used renewal equation, as well as Equation 2. Using Equations (5) and 7, two different sets of R(t) estimates were obtained and overlaid with epidemic curves to assess their responsiveness to the implemented PHSM. We even included broad announcements by the governor of Osaka as PHSM, because they could have substantially reduced numbers of high-risk contacts.…”

“…As part of the evaluation of PHSM, the effective reproduction number (R(t), the actual average number of secondary cases per primary case at calendar time t), has been frequently employed [3][4][5][6][7][8][9][10]. Because R(t) reflects the frequency of transmission over time, it has been recognized as epidemiologically useful in assessing transmission dynamics in populations with varying susceptibility levels and experiencing various public health interventions.…”