The reproduction number (R) is the average number of secondary infections produced by 1 infected person.
An R number of 1 means that on average every person who is infected will infect 1 other person, meaning the total number of new infections is stable. If R is 2, on average, each infected person infects 2 more people. If R is 0.5 then on average for each 2 infected people, there will be only 1 new infection. If R is greater than 1 the epidemic is growing, if R is less than 1 the epidemic is shrinking.
R can change over time. For example, it falls when there is a reduction in the number of contacts between people, which reduces transmission.
What is a growth rate?
The growth rate reflects how quickly the number of infections are changing day by day It is an approximation of the change of number infections each day. If the growth rate is greater than zero (+ positive), then the disease will grow. If the growth rate is less than zero (- negative) then the disease will shrink.
The size of the growth rate indicates the speed of change. A growth rate of +5% will grow faster than one with a growth rate of +1%. Likewise, a disease with a growth rate of -4% will be shrinking faster than a disease with growth rate of -1%. Further technical information on growth rate can be found on Plus magazine.
How are growth rates different to R estimates?
R does not tell us how quickly an epidemic is changing. Different diseases with the same R can give epidemics that grow at very different speeds. For instance, a disease with R=2 with infection lasting years will grow much more slowly than a disease with R=2 with infection lasting days.
The growth rate provides us with information on the size and speed of change, whereas the R value only gives us information on the direction of change.
To calculate R, information on the time taken between each generation of infections is needed. That is how long it takes for one set of people in an infected group to infect a new set of people in the next group. This can depend on several different biological, social, and behavioural factors. The growth rate does not depend on the “generation time” and so requires fewer assumptions to estimate.
Neither one measure, R nor growth rate, is better than the other but each provide information that is useful in monitoring the spread of a disease.
The R estimate and growth rates are not the only important measures of the epidemic. Both should be considered alongside other measures of the spread of disease, such as the number of people currently infected. If R equals 1 with 100,000 people currently infected, it is a very different situation to R equals 1 with 1,000 people currently infected. The number of people currently infected with coronavirus (COVID-19) – and so able to pass it on – is therefore very important.
Estimates of the growth rates and R are currently updated on a weekly basis. However, as the numbers of cases decrease, these metrics will become less helpful indicators and other measures need to be considered. These include the number of new cases of the disease identified during a specified time period (incidence), and the proportion of the population with the disease at a given point in time (prevalence), and these will become more important to monitor.
How are R and growth rates estimated?
Individual modelling groups use a range of data to estimate growth rates and R values including:
- epidemiological data such as hospital admissions, ICU admissions and deaths – it generally takes 2 to 3 weeks for changes in the spread of disease to be reflected in the estimates due to the time delay between initial infection and the need for hospital care
- contact pattern surveys that gather information on behaviour – these can be quicker (with a lag of around a week) but can be open to bias as they often rely on self-reported behaviour and make assumptions about how the information collected relates to the spread of disease.
- household infection surveys where swabs are performed on individuals. These can provide estimates of how many people are infected. Longitudinal surveys (where samples are repeatedly taken from the same people) allow a more direct estimate of the growth in infection rates
Different modelling groups use different data sources to estimate these values using mathematical models that simulate the spread of infections. Some may even use all these sources of information to adjust their models to better reflect the real-world situation. There is uncertainty in all these data sources so estimates can vary between different models, so we do not rely on just one model; evidence from several models is considered, discussed, combined, and the growth rate and R are then presented as a range. The most likely true values are somewhere towards the middle of this range.
Who estimates the R and growth rates?
The growth rate and R are estimated by several independent modelling groups based in universities and Public Health England (PHE). The modelling groups discuss their individual R estimates at the Science Pandemic Influenza Modelling group (SPI-M) – a subgroup of SAGE. Attendees compare the different estimates of each and SPI-M collectively agrees a range for which the values are very likely to be within.
Limitations of R
R is an average value that can vary in different parts of the country, communities, and subsections of the population. It cannot be measured directly so there is always uncertainty around its exact value. This becomes even more of a problem when calculating R using small numbers of cases, either due to lower infection rates or smaller geographical areas. This uncertainty may be due to variability in the underlying data, leading to a wider range for R and more frequent changes in the estimates.
Even when the overall UK R estimate is below 1, some regions may have R estimates that include ranges that exceed 1, for example from 0.7 to 1.1; this does not necessarily mean the epidemic is increasing in that region, just that the uncertainty means it cannot be ruled out. It is also possible that an outbreak in one specific place could result in an R above 1 for the whole region.
Estimates of R for geographies smaller than regional level are less reliable and it is more appropriate to identify local hotspots through, for example, monitoring numbers of cases, hospitalisations, and deaths.
Limitations of growth rates
The growth rate is an average value that can vary. When case numbers are low, uncertainty increases. This could happen when only a very small proportion of people are infected, or the geographical area considered has a very small population. A smaller number of cases means that variability in the underlying data makes it difficult to estimate the growth rate; there will be a wider range given for growth rate and frequent changes in the estimates. This will happen for both R and the growth rate; however, the growth rate requires fewer assumptions about the disease when it is calculated than R.
Even when the overall UK growth rate estimate is negative (below 0), some regions may have growth rate estimates that include ranges that are positive (above 0), for example from -4% to +1%; this does not necessarily mean the epidemic is increasing in that region, just that the uncertainty means it cannot be ruled out. It is also possible that an outbreak in one specific place could result in a positive (above 0) growth rate for the whole region.