24 AUGUST 2020 Reproduction number (R) and growth rate (r) of the COVID-19 epidemic in the UK: methods of estimation, data sources, causes of heterogeneity, and use as a guide in policy formulation This rapid review of the science of the reproduction number and growth rate of COVID-19 from the Royal Society is provided to assist in the understanding of COVID-19. This paper is a pre-print and has been subject to formal peer-review. 1. Executive summary required in the UK (as a proportion of the population), that Purpose of the report must be effectively immunised to halt transmission and This paper examines how estimates of the reproduction protect the population when a vaccine becomes available. number R and the epidemic growth rate r are made, what data are used in their estimation, the models on which the There remains much uncertainty in estimates of key estimation methods are based, what other data sources and epidemiological parameters defining the growth and epidemiological parameters could be employed to assess the decay of the epidemic and, concomitantly, the impact of effectiveness of social distancing measures (‘lockdown’) and the relaxation or strengthening of control measures. This is to evaluate the impact of the relaxation of these measures. largely due to data availability and quality. This uncertainty must be factored into policy formulation. Throughout this report we refer to the reproduction number as R. This number reflects the infectious potential of a The responsibilities of SAGE with respect to COVID-19 disease. R0 represents the basic reproduction number, will eventually be taken over by the new Joint Biosecurity which is the number of secondary infections generated Centre (JBC) which is to be part of a new body called the from an initial case at the beginning of an epidemic, National Institute for Health Protection (NIHP) to replace in an entirely susceptible population. In contrast, Rt is Public Health England (PHE). This new body will also the reproduction number at time t since the start of the include existing Test and Trace activities. This JBC must epidemic. As more individuals are infected or immunised, seek independent scientific advice on epidemiology, and Rt captures the number of secondary infections generated mathematical plus statistical analyses of infectious disease from a population consisting of both naïve/susceptible and transmission and control. The UK university sector has world exposed/immune individuals and therefore it both changes renowned expertise in infectious disease epidemiology in value over time and will always be less than R0. and JBC, like SAGE before it, should make full use of this independent resource. Overall conclusions High quality data underpins the ongoing assessment of As the Government response to the COVID-19 pandemic key epidemiological parameters, such as the reproduction reaches the end of its first phase, there are opportunities to number, R, which defines the average number of secondary be taken and some important challenges to be met. Specific cases generated by one primary case, and the growth rate opportunities include greatly improving data collection and of the epidemic, r. The pristine value of R at the start of the management – and putting in place as quickly as possible epidemic, R0, gives wide insights into the epidemiology of an effective ‘Test and trace’ system for the UK. Both are of the virus, such as determining the level of herd immunity immediate and high priority. The challenges include the REPRODUCTION NUMBER (R) AND GROWTH RATE (r) OF THE COVID-19 EPIDEMIC IN THE UK • 24 AUGUST 2020 1 creation of a high level of research expertise within the new Science and research orientated conclusions body (JBC) in the many fields that are required to tackle A wide variety of models of COVID-19 transmission, data a novel epidemic. The new body should be an informed sources and methods of parameter estimation have been customer that distils knowledge for policy formulation, rather employed to advise SAGE through SPI-M on transmission than a creator of that knowledge. and control within the UK. This is a strength. Uneven data quality and slow access to information More comparative studies of model outcomes need to be on COVID-19 spread and impact collected by different conducted in the near future to examine the sensitivity of government organisations such as Pubic Health England, epidemiological predictions to model structure, the data Office for National Statistics (ONS) and NHS Trusts have source used and parameter uncertainty with the aim of been a major impediment to good epidemiological analysis improving analyses supporting policy formulation. of the state of the epidemic and predictions of future trends. Timely access through one portal, and ensuring that data With regards to reproduction numbers and rates, the two definition, accuracy and consistency over time are of the parameters, R and r, measure different facets of epidemic highest standards possible are essential. An authoritative pattern. Negative values for the growth rate in infections, body should both acquire timely and relevant data at scale r, clearly reveals a contracting epidemic, while if the across government bodies and distributing it openly through reproduction number of the virus, R, is less than unity a carefully curated portal. Careful thought should be given in value, onward transmission is insufficient to sustain to how a national data base is effectively fed by local public the infection in the population in the longer term and is health bodies, and how in return this national information therefore the desired outcome of control measures. portal feeds back to facilitate local action. The National The growth rate, r, is more easily measured than the Statistician has a key role here, as do societies such as the reproduction number R. The latter however, provides more Royal Society, the Academy of Medical Sciences, and the information about the impact of control measures given the Royal Statistical Society. very non-linear epidemic curve for COVID-19 which will have The most informative data on epidemic trends arise from a long right-hand tail, possibly with further peaks due to longitudinal (over time) cohort based (following the same resurgence, which complicates the interpretation of r. The individuals) studies of seroprevalence of past infection and magnitude of R at the start of the unmitigated epidemic (R0) the incidence of new infections, stratified by the appropriate also provides information on what level of herd immunity variables such as home and work locations, age, gender must be created by those recovered from infection and and ethnicity. The UK needs to greatly expand collection vaccination to halt transmission. of these data and to continue to review the sensitivity and Lock down measures and modifications in behaviour may specificity of the currently available diagnostic tests (both not totally eliminate the occurrence of local outbreaks of antibody to detect past infection and the polymerase chain infection that are patchy in nature across time and space. reaction (PCR) to detect current infection). These do not necessarily mark the beginning of the second Effective contact tracing at scale which relies on testing for wave, provided the average R value across the country active viral infection is an essential part of the ability to control (or a defined region) is less than unity in value. Targeted and limit chains of transmission, especially so-called ‘super- measures and good contact tracing are required to bring spreading’ events where a single individual is responsible for local outbreaks rapidly under control. transmitting infection to many other people. A high degree If patterns of human behaviour (eg mixing and movement) of competence in this area, notably before a summer or return to the pre-epidemic state, the pristine value of the autumn resurgence in incidence is essential. This information basic reproduction number, R , in the UK will be reduced is needed for the day to day management of the epidemic, it 0 somewhat by any herd immunity created by people who also feeds into making forward projections through models of have recovered from infection. This level is low at present trends that give advanced warning of resurgence. hence each new case of infection is likely on average to Given the importance of testing for active viral infection in generate two to three further cases and the epidemic will any expanded contact tracing system to improve control rapidly increase again with a doubling time of 3 – 5 days. measures, the provision of adequate testing facilities with a fast turn round time is an important requirement. REPRODUCTION NUMBER (R) AND GROWTH RATE (r) OF THE COVID-19 EPIDEMIC IN THE UK • 24 AUGUST 2020 2 COVID-19 research priorities must include reducing Uncertainty uncertainties about and heterogeneities in key The estimates of the epidemic growth rate r and epidemiological parameters, such as the level and duration reproduction number R are affected by many sources of infectiousness in infected people who never show of variability and these have not been clearly explained clear symptoms of infection, and the average duration of model by model. infectiousness prior to the appearance of symptoms in those who do show clear symptoms of COVID-19 infection. Uncertainty intervals so far reported on estimates of the The average values of these parameters have a very big reproduction number R are too narrow – much more impact on the epidemic pattern and the severity of control uncertainty exists in the estimates depending on many measures required for effective control. factors, including substantial variability between infected people on how many individuals they transmit the Specific longitudinal (over time) studies on the duration infection on to. of seropositivity to COVID-19 in both symptomatic and asymptomatic infected people are an urgent priority, as is If these estimates of R and r are based on deaths, then they understanding how seropositivity correlates with protective reflect transmission weeks before.