R number: the figure that will determine when lockdown lifts

The reproduction, or ‘R’ number, has become the most-watched indicator of governments’ success in suppressing coronavirus outbreaks and unlocking social distancing measures without allowing a “second wave” resurgence of cases. “Keeping the R down will be vital to our recovery and we can only do it with discipline and by working together,” Boris Johnson, UK prime minister, said in a televised press conference on Thursday evening. 

What is the R number?

Epidemiologists have used R for decades as a measure of a disease’s ability to spread between people. It is the average number of new cases generated by an infected individual.

If R is above 1, an outbreak expands exponentially — the higher the number the faster it grows. An R below 1 means the outbreak is contracting and, if it stays low, the disease will eventually die out. 

For Covid-19 the “basic reproduction number” in an uninfected population before any precautions are taken is between 2.5 and 3, epidemiologists believe. That makes it much less transmissible than measles, with R at 15 but more than seasonal flu at about 1.3.

Until an effective vaccine can be found and rolled out, social distancing will be the most effective way to lower the R, because keeping people apart prevents the virus from transmitting between them. In those European countries that put in place strict lockdown measures several weeks ago, declining numbers of cases — and, with a time delay, deaths — have brought the R down below 1. The average figure probably ranges between 0.6 and 0.9. 

How is R measured?

Politicians view R as a key indicator for lifting lockdowns enough for significant social and economic activity to resume, without allowing a resurgent coronavirus to rampage through the population — and a relatively simple number to convey success or otherwise to the public.

The reality, like so much about Covid-19, is more complicated. Jagjit Chadha, director of the UK National Institute of Economic and Social Research, said: “Not only is an aggregate measure of R incredibly difficult to measure, it is also potentially misleading because what people want to know is the R in their local area.” 

In theory, an accurate value of R could be calculated by a very good testing and contact-tracing system, which would show the proportion of infected people who pass the virus on to someone else.

Scientists have done this in China and South Korea, but most other countries with significant virus outbreaks do not have the capacity to do this. So epidemiologists are instead working out the R from mathematical models, based on numbers of new cases and deaths and/or simulations of how changing human behaviour will affect transmission. 

Can we trust the results? 

The uncertainties are illustrated by two modelling teams, at Imperial College London and the London School of Hygiene and Tropical Medicine, which have calculated the R number for Covid-19 in the UK. They give quite different results.

Imperial College’s chart shows R steady at just below 4 from February until March 12, then a slow and unsteady decline to 3.5 to March 23, followed by a precipitous fall over a few days to the present level of 0.7. In contrast, the London School of Hygiene modellers calculated a much longer and steadier fall from about 2.5 in late February, as people began to distance themselves ahead of any official advice to do so. Under their model, the R does not fall below 1 until April 8. 

“We have taken very different approaches,” said Sebastian Funk, an associate professor of London School of Hygiene’s Centre for the Mathematical Modelling of Infectious Diseases. “The truth probably lies somewhere between our results and theirs.”

He continued: “You have to be cautious about interpreting these curves. In Germany, there was a fair amount of consternation when the Robert Koch Institute [which is co-ordinating the county’s public health response to the pandemic] put out data showing R less than 1 before the lockdown started. The institute then had to do a lot of backtracking.” 

How will R numbers guide our future? 

Despite its imperfections, R is the best indicator available to show how the disease is spreading, so public health experts around the world will continue to monitor changes in the number very closely as lockdowns are lifted.

For example, Denmark’s Statens Serum Institut reported this week that R rose from 0.6 to 0.9 after the country reopened its primary schools and kindergartens in mid-April. That is still below 1 but it means that the Danish government will have to be cautious about other relaxations that could take R above 1 and risk rekindling the epidemic. 

Later on, if and when an effective Covid-19 vaccine becomes available, it could push R down hard. If we assume that R is 3 in the absence of other preventive measures and a vaccine protects two people out of three from infection, then vaccination alone could cut R to 1, said Adam Kucharski, an epidemiologist at the London School of Hygiene and Tropical Medicine. 

Additional reporting by Chris Giles 

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