AbstractBackgroundLocal estimates of the time-varying effective reproduction number (Rt) of COVID-19 in England became increasingly heterogeneous during April and May 2021. This may have been attributable to the spread of the Delta SARS-CoV-2 variant. This paper documents real-time analysis that aimed to investigate the association between changes in the proportion of positive cases that were S-gene positive, an indicator of the Delta variant against a background of the previously predominant Alpha variant, and the estimated time-varying Rt at the level of upper-tier local authorities (UTLA).MethodWe explored the relationship between the proportion of samples that were S-gene positive and the Rt of test-positive cases over time from the 23 February 2021 to the 25 May 2021. Effective reproduction numbers were estimated using the EpiNow2 R package independently for each local authority using two different estimates of the generation time. We then fit a range of regression models to estimate a multiplicative relationship between S-gene positivity and weekly mean Rt estimate.ResultsWe found evidence of an association between increased mean Rt estimates and the proportion of S-gene positives across all models evaluated with the magnitude of the effect increasing as model flexibility was decreased. Models that adjusted for either national level or NHS region level time-varying residuals were found to fit the data better, suggesting potential unexplained confounding.ConclusionsOur results indicated that even after adjusting for time-varying residuals between NHS regions, S-gene positivity was associated with an increase in the effective reproduction number of COVID-19. These findings were robust across a range of models and generation time assumptions, though the specific effect size was variable depending on the assumptions used. The lower bound of the estimated effect indicated that the reproduction number of Delta was above 1 in almost all local authorities throughout the period of investigation.

Estimation of the effective reproductive numberRtis important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are usingRtto assess the effectiveness of interventions and to inform policy. However, estimation ofRtfrom available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation ofRt, we recommend the approach of Cori and colleagues, which uses data from before timetand empirical estimates of the distribution of time between infections. Methods that require data from after timet, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resultingRtestimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems inRtestimation.

Estimate Realtime Case Counts and Time-varying Epidemiological Parameters

Estimates the time-varying reproduction number, rate of spread, and doubling time using a range of open-source tools (Abbott et al. (2020) ), and current best practices (Gostic et al. (2020) ). It aims to help users avoid some of the limitations of naive implementations in a framework that is informed by community feedback and is actively supported.