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The reproduction number R has been a central metric of the COVID-19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations of R, the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulating R becomes increasingly complicated and inevitably model-dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Supplementary Material 1

The SARS-CoV-2 epidemic has impacted children’s education, with schools required to implement infection control measures that have led to periods of absence and classroom closures. We developed an agent-based epidemiological model of SARS-CoV-2 transmission in a school classroom that allows us to quantify projected infection patterns within primary school classrooms, and related uncertainties. Our approach is based on a contact model constructed using random networks, informed by structured expert judgement. The effectiveness of mitigation strategies in suppressing infection outbreaks and limiting pupil absence are considered. Covid-19 infections in primary schools in England in autumn 2020 were re-examined and the model then used to estimate infection levels in autumn 2021, as the Delta-variant was emerging and it was thought likely that school transmission would play a major role in an incipient new wave of the epidemic. Our results were in good agreement with available data. These findings indicate that testing-based surveillance is more effective than bubble quarantine, both for reducing transmission and avoiding pupil absence, even accounting for insensitivity of self-administered tests. Bubble quarantine entails large numbers of absences, with only modest impact on classroom infections. However, maintaining reduced contact rates within the classroom can have a major benefits for managing Covid-19 in school settings.

Supplementary materials accompanying Thomas et al.'Limits of lockdown: characterising essential contacts during strict physical distancing'. &nbsp

Executive Summary - Key Findings● Reductions in adherence to NPIs (including case and household isolation) will have more impact than any marginal benefits generated from a staggered return of students to university.●The emergence of more transmissible new variants results in impaired effectiveness of mass asymptomatic testing.●We observe evidence of spillover transmission between higher education and the wider

Supplemental material, sj-pdf-1-smm-10.1177_09622802211065159 for Meta-analysis of the severe acute respiratory syndrome coronavirus 2 serial intervals and the impact of parameter uncertainty on the coronavirus disease 2019 reproduction number by Robert Challen, Ellen Brooks-Pollock, Krasimira Tsaneva-Atanasova and Leon Danon in Statistical Methods in Medical Research

Supplemental material, sj-pdf-2-smm-10.1177_09622802211065159 for Meta-analysis of the severe acute respiratory syndrome coronavirus 2 serial intervals and the impact of parameter uncertainty on the coronavirus disease 2019 reproduction number by Robert Challen, Ellen Brooks-Pollock, Krasimira Tsaneva-Atanasova and Leon Danon in Statistical Methods in Medical Research

Additional file 1. This includes information on how the SimInf code was adapted, how the agricultural survey data and the movements data were reconciled, detail on parameter estimation, outbreak data per county in the model simulations and in the reported data and the posterior distributions from the SMC-ABC fitting.

These tables provide further detail to the data sources and processing applied, and more comprehensive set of numerical results from the reproduction number estimates made in mid July.