What the coronavirus reproduction number is, and why we should keep an eye on it

On average, how many people does one person with the novel coronavirus infect?

Reduced to its most basic level, the answer to the question can tell whether the virus’s spread is unmanageable, overwhelming hospitals or becoming a scary but manageable burden.

Epidemiologists call it the “R number,” or reproduction number, and want it to be as low as possible.

“The usefulness is basically for monitoring epidemic control,” says University of Toronto epidemiologist Ashleigh Tuite. “It provides, effectively, a snapshot of current transmission.”

Think about it this way:

If one person, on average, infects one other person, R is one.

If on average one person infects two, R is two.

An R of two is catastrophic, if the cycle keeps going, out of control: one person infects two, who infect four, who infect eight, who infect 16, who infect 32 and so forth. Each doubling would happen roughly every five days, and in theory the process only stops when the virus has infected the whole population, which in Canada’s case would happen at about the four-month point.

“If, on average, each old case has made more than one new case, we’re experiencing exponential growth, and that’s a bad sign,” Tuite explains.

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On the other hand, if for every two infected people, they only infect one other person between them, R is 0.5. That’s not exactly good news, if you’re the person that gets infected, but much better.

“When R falls below one, that’s a good thing and that’s what we want,” she says.

“That basically means that each case is, on average, making less than one new case, we’ve exited the exponential growth phase of the epidemic and we expect to be able to control the outbreak and, eventually, we hope that it would die out.”

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An R of 0.5 is more manageable: 128 people infect 64, who infect 32, who infect 16, who infect eight, four and two people as the cycle continues.

“If it’s one, so, on average, each case is making one new case, it means that we’re basically having a sustained growth,” Tuite says.

“Cases are going to continue to grumble along. We’re not growing, having epidemic growth any more, but we’re also not going to decline. We’re sustaining the disease in the population.”

According to data analyzed by Tuite and fellow epidemiologist David Fisman, Canada dipped below one in early May:

The line is very high in the earliest phases of the epidemic in Canada and starts to fall in mid-March as schools close and the economy starts to shut down.

On Wednesday, it was thought to be between 0.67 and 0.91, less than a third of what it was on March 15.

One way to think about what measures like physical distancing are trying to do is to bring the R number down as low as possible, which Canada is getting better at achieving.

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“That could be that you’ve reduced the number of contacts that you have because of physical distancing, it could be that you’re really good at identifying people who are infected and isolating them, so that they’re not able to transmit to other people … that would be another reason how you would reduce that reproductive number and keep it below one,” Tuite says.

However, Tuite says that one problem in calculating the R number correctly is that infection numbers aren’t broken out between group settings, like long-term care homes, and the mainstream community.

“What’s happening in the community is quite different from what’s happening in institutional settings,” she says.

“Being able to separate that out would be incredibly helpful for understanding the impact that public health measures are having, and as we start opening things up again, it’s really important for monitoring how things are going.”

The math that epidemiologists use to figure out what R is is complicated under the hood, but the most basic lesson is simple: