Basic Reproduction Number

The basic reproduction number (R0), also called the basic reproduction ratio or rate or the basic reproductive rate, is an epidemiologic metric used to describe the contagiousness or transmissibility of infectious agents. R0 is affected by numerous biological, sociobehavioral, and environmental factors that govern pathogen transmission and, therefore, is usually estimated with various types of complex mathematical models, which make R0 easily misrepresented, misinterpreted, and misapplied. R0 is not a biological constant for a pathogen, a rate over time, or a measure of disease severity, and R0 cannot be modified through vaccination campaigns. R0 is rarely measured directly, and modeled R0 values are dependent on model structures and assumptions. Some R0 values reported in the scientific literature are likely obsolete. R0 must be estimated, reported, and applied with great caution because this basic metric is far from simple.

BackgroundTo mitigate and slow the spread of COVID-19, many countries have adopted unprecedented physical distancing policies, including the UK. We evaluate whether these measures might be sufficient to control the epidemic by estimating their impact on the reproduction number (R0, the average number of secondary cases generated per case).MethodsWe asked a representative sample of UK adults about their contact patterns on the previous day. The questionnaire was conducted online via email recruitment and documents the age and location of contacts and a measure of their intimacy (whether physical contact was made or not). In addition, we asked about adherence to different physical distancing measures. The first surveys were sent on Tuesday, 24 March, 1 day after a "lockdown" was implemented across the UK. We compared measured contact patterns during the "lockdown" to patterns of social contact made during a non-epidemic period. By comparing these, we estimated the change in reproduction number as a consequence of the physical distancing measures imposed. We used a meta-analysis of published estimates to inform our estimates of the reproduction number before interventions were put in place.ResultsWe found a 74% reduction in the average daily number of contacts observed per participant (from 10.8 to 2.8). This would be sufficient to reduce R0 from 2.6 prior to lockdown to 0.62 (95% confidence interval [CI] 0.37-0.89) after the lockdown, based on all types of contact and 0.37 (95% CI = 0.22-0.53) for physical (skin to skin) contacts only.ConclusionsThe physical distancing measures adopted by the UK public have substantially reduced contact levels and will likely lead to a substantial impact and a decline in cases in the coming weeks. However, this projected decline in incidence will not occur immediately as there are significant delays between infection, the onset of symptomatic disease, and hospitalisation, as well as further delays to these events being reported. Tracking behavioural change can give a more rapid assessment of the impact of physical distancing measures than routine epidemiological surveillance.

Estimation of the effective reproductive number Rt is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from 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 of Rt, we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, 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 resulting Rt estimates 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 in Rt estimation.

Extra-intestinal pathogenic Escherichia coli ubiquitously colonize the human gut and represent clinically the most significant bacterial species causing urinary tract infections and bacteremia. During the last two decades clades of the ST131 lineage have spread globally, but it remains unknown how their transmission dynamics compare to the basic reproduction numbers (R0) for viral pandemics. We develop a compartmental model for asymptomatic gut colonization and onward transmission coupled with an epidemiological observation model and fit it on the major ST131 clades. Our results indicate that the ST131-A transmission potential (R0 = 1.47) can be comparable to pandemic influenza viruses, while the significantly lower transmissibility of ST131-C1 (R0 = 1.18) and ST131-C2 (R0 = 1.13) suggests that their dissemination has been aided by antibiotic selection pressure and healthcare facilities. Our results provide an advance in understanding the relative transmissibility of these opportunistic pathogens.