Colin Dang

## What is The R Number?

We’ve all heard it mentioned in the news in the briefings by the government and their scientific advisors, but what actually is the reproduction (R) number? Well, quite simply, it’s the average number of secondary infections produced by a single 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 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. The higher R is above 1, the more people 1 infected person infects and so the faster the epidemic grows.

Quite a simple equation to understand even for those of us without great maths results!

R can change over time. For example, it falls when there is a reduction in the number of contacts between people, which reduces transmission, hence the drop in infection rates during lockdown. The third lockdown we’re in at the moment has seen the R number fall too; however, due to the highly infectious nature of the new variant, the decline is much slower than previous lockdowns. R increases when the numbers of contacts between people rise, leading to a rise in viral transmission.

Measles has one of the highest numbers with an R number of 15 in populations without immunity. That means, on average, one person will spread measles to 15 others.

## Why is a number above 1 dangerous?

If the R Numner is higher than 1, then the number of cases increases exponentially- It snowballs like debt on an unpaid credit card!. But if the number is lower the disease will eventually stop spreading, as not enough new people are being infected to sustain the outbreak.

## Is 1 the most important number?

The R number is one of the big three. Another is severity - some people have a very mild disease that does not cause many problems. But coronavirus and the disease it causes, Covid-19, can be severe and deadly.

The last is the number of cases, which is important for deciding when the authorities need to act. If you have a high number, but ease restrictions so the reproduction number is about 1, then you will continue to have a high number of cases.

## Limitations of R

R 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 can be an issue when trying to calculate R when using a small number of cases linked to the lower infection rate or a smaller geographical area.

## 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 percentage change in the number infections each day. If the growth rate is greater than 0 (+ positive), then the epidemic is growing. If the growth rate is less than 0 (- negative) then the epidemic is shrinking.

## How are growth rates different to R estimates?

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 and the actions required by the authorities to implement restrictions - or lift them.

## 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.

## Limitations of growth rates

The growth rate is an average value that can also vary. 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, estimation of the growth rate requires fewer assumptions about the disease than R.

Estimates of growth rate 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.

We hope you found this blog useful. Please share if you did and stay safe!

The Coda Team