Coronavirus: What is the R number and how is it calculated?

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There is a simple but crucial number at the heart of understanding the threat posed by the coronavirus. It is guiding governments around the world on the actions needed to save lives and to lift lockdown.

It is called the reproduction number, or simply the R value.

What is R?

The reproduction number is a way of rating a disease’s ability to spread.

It’s the number of people that one infected person will pass the virus on to, on average

Measles has one of the highest numbers in town with a reproduction number of 15 in populations without immunity. It can cause explosive outbreaks.

The new coronavirus, known officially as Sars-CoV-2, has a reproduction number of about three, but estimates vary.

How is R calculated?

You cannot capture the moment people are infected; instead scientists work backwards.

Using data – such as the number of people dying, admitted to hospital or testing positive for the virus – allows you to estimate how easily the virus is spreading.

Generally this gives a picture of what the R number was two to three weeks ago. Regular testing of households should soon give a more timely estimate.

Why is a number above one dangerous?

If the reproduction number is higher than one, 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 peter out, as not enough new people are being infected to sustain the outbreak.

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If the R-value is above one then the number of cumulative cases takes off, but if it is below one then eventually the outbreak stops. The further below one, the faster that happens.

Governments everywhere want to force the reproduction number down from about three (the R number if we took no action) to below one.

This is the reason you’ve not seen family, have had to work from home and the children have been off school – stopping people coming into contact with each other to cut the virus’s ability to spread.

What is the R number in the UK?

The reproduction number is not fixed. Instead, it changes as our behaviour changes, or as immunity develops.

Mathematical modellers at Imperial College London are attempting to track how the number has changed as isolation, social distancing and the full lockdown were introduced.

Before any measures came in, the number was well above one and the conditions were ripe for a large outbreak. Successive restrictions brought it down, but it was not until full lockdown that it was driven below one.

The R value in the UK has crept up recently and is now thought to be between 0.7 and 1.0.

Counter-intuitively, this increase is probably due to the success in slowing the virus in society as a whole. As cases collapse in the community, the R value is largely reflecting what is happening in care homes.

Does R vary across the UK?

The R number has come down across every part of the UK since the start of the epidemic.

But multiple research groups, including those at the University of Cambridge, show it has come down the most in London. It is proving far more stubborn in the north-east of England.

Those figures are more optimistic than other groups’ calculations. Similar work by the London School of Hygiene and Tropical Medicine puts the number for London at 0.6, and the south-west at 0.9.

It also showed the R-values were 0.8 in Wales, and 1 in both Scotland and Northern Ireland.

So how does this inform lifting lockdown?

As any country thinks about how to lift lockdown, the aim will be to keep the reproduction number below one.

Dr Adam Kucharski, of the London School of Hygiene and Tropical Medicine, told the BBC: “It’s a big challenge making sure you’re not loosening too much and increasing transmission.”

However it has taken a monumental effort, one that has caused damage to people’s lives, to get the number from three to 0.7.

“It doesn’t give you a lot of room to play with [to keep the number below one]”, Dr Kucharski added.

Which measures could be lifted?

Unfortunately, there is no confirmation of how much each intervention affects the virus’s spread, although there are estimates.

“Opening schools versus workplaces versus other gatherings – understanding how much they increase the reproduction number, is going to be the challenge,” said Dr Kucharski.

Another issue is that people’s behaviour changes over time, so the number can creep up even if lockdown policies remain unchanged.

What is likely to be needed are new ways of controlling the virus, such as more extensive testing and tracing or location-tracking apps.

These can suppress the reproduction number in a more targeted way, allowing some of the other measures to be lifted.

Is it the most important number?

The reproduction number is one of the big three.

Another is severity – if you have a very mild disease that does not cause many problems, then you can relax a bit. Coronavirus, and the disease it causes, Covid-19, can be severe and deadly, unfortunately.

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

What about a vaccine?

Having a vaccine is another way to bring down the reproduction number.

A coronavirus patient would naturally infect three others on average, but if a vaccine could protect two of them from infection, then the reproduction number would fall from three to one.

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