The reproduction number R for COVID-19 in England: Why hasn′t ″lockdown″ been more effective?


The reproduction number R, the average number of people that a single individual with a contagious disease infects, is central to understanding the dynamics of the COVID-19 epidemic. Values greater than one correspond to increasing rates of infection, and values less than one indicate that control measures are being effective. Here, we summarise how changes in the behaviour of individuals alter the value of R. We also use matrix models that correctly recreate distributions of times that individuals spend incubating the disease and being infective to demonstrate the accuracy of a simple approximation to estimate R directly from time series of case numbers, hospital admissions or deaths. The largest uncertainty is that the generation time of the infection is not precisely known, but this challenge also affects most of the more complex methods of calculating R. We use this approximation to examine changes in R in response to the introduction of lockdown restrictions in England. This suggests that there was a substantial reduction in R before large scale compulsory restrictions on economic and social activity were imposed on 23rd March 2020. From mid-April to mid-June decline of the epidemic at national and regional level has been relatively slow, despite these restrictions (R values clustered around 0.81). However, these estimates of R are consistent with the relatively high average numbers of close contacts reported by confirmed cases combined with directly measured attack rates via close interactions. This implies that a significant portion of transmission is occurring in workplaces; overcrowded housing or through close contacts that are not currently lawful, routes on which nationwide lockdown will have limited impact.

Competing Interest Statement

The authors have declared no competing interest.

Funding Statement

No external funding was received for this work

Author Declarations

I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.


The details of the IRB/oversight body that provided approval or exemption for the research described are given below:

Study consists of modelling and analysis of public data

All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.


I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).


I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.


Data Availability

All data are from public databases, available at locations cited in the paper

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