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R, a key metric to watch as COVID-19 restrictions are lifted

COVID-19 is highly contagious. Government restrictions to impose physical distancing such as business and school closures have curbed its contagion and new cases are down from their peak across the country.

Provinces across Canada have started easing those restrictions, although each in its own way and its own pace. Some have also already said restrictions may need to be reimposed if the outbreak worsens.

But when is it really safe to ease those restrictions? How does that relate to the “peak” of the epidemic? And when might restrictions need to be reimposed?

Tracking the disease’s changing contagion is a key, researchers say. Here’s how it’s done and what that means.

What is the reproduction number?

The contagiousness of diseases is represented by a seemingly simple number: the number of other people a single infected person infects. This is known as the reproduction number, commonly abbreviated with the letter “R.”

The basic reproduction number, R0, pronounced “R-naught,” where “naught” means “subscript zero,” is the fundamental infectiousness of a new disease, when no one has any immunity and no interventions have been imposed to curb its spread.

What R0 means

This diagram illustrates a disease with an R0 of two as it spreads from an initial infection through four “generations.” Each dot represents an infected person.

What R0 meansGeneration 2Generation 1Generation 3Generation 4

How contagious is COVID-19?

For COVID-19, the R0 averages around 2.6 to 2.7 based on data from China and South Korea, researchers from the Centre for Evidence-Based Medicine at the University of Oxford report. That means in the absence of interventions, the average infected person gave the disease to between two and three people. That makes COVID-19 about twice as contagious as the flu, more contagious than Ebola, only half as contagious as smallpox and a lot less contagious than measles.

R0 and contagiousness

These diagrams show how quickly each of five viruses spreads over four generations, depending on its R0, which represents how contagious it is.



1 total infection


(Spanish flu)


1 total infection




1 total infection




1 total infection




1 total infection

R0 and contagiousness for smallpox




1 total infection

R0 and contagiousness for measles

What can R0 tell us?

David Fisman, a professor of epidemiology at the University of Toronto, says R0 tells us four things:

  • Whether the disease has epidemic potential. It does if R is bigger than one — in that case, without intervention, it will grow exponentially.

  • The approximate fraction of the population that needs to be immune for “herd immunity,” where the disease doesn’t have enough potential hosts to spread. For COVID-19, if R0 is 2.6, 62 per cent of the population would need to be immune to have herd immunity.

  • How steep the slope of the epidemic will be when it takes off, which can have implications like the strain on the health-care system.

  • How big the epidemic can be expected to become (without intervention).

How herd immunity works

The diagram shows that if R0=two, then once half the population is immune, there aren’t enough susceptible people left for the infection to increase in the population.

How do interventions fit into the equation?

R depends on the:

  • Infectiousness of the organism that causes the disease.

  • Contact rate between people.

  • Rate at which infections are removed by recovery or death.

So any intervention that changes any of those things can change R — a vaccine or increased immunity in the population, a therapy that speeds recovery or measures such as physical distancing that reduce the contact rate between people. Fisman and his colleague Ashleigh Tuite, also an epidemiology professor at the University of Toronto, have posted an interactive tool that shows how that works.

Beyond the initial pandemic, R is referred to as the effective reproduction number, Re or Rt (where t represents a point in time).

By now, we’ve heard that if you’re tracking cases, hospitalizations or deaths during an epidemic, they roughly follow a bell-shaped curve. The more people infected by a single person, the steeper the curve will climb. If each person infects more than one person — even just 1.1 people — the epidemic will keep growing exponentially.

At the point where new cases stop increasing, R is one — each infected person infects only one other person. If R remains one, we get a plateau.

But if R falls below one, the curve will start to go downhill and eventually reach zero.

When R is below or above 1

These diagrams show what happens if R is less than one, equal to one or more than one — respectively, the number of new cases declines exponentially, stays the same or increases exponentially.

How important is R as governments ease restrictions?

“Very important,” say both Fisman and Jasmina Panovska-Griffiths, a senior research fellow at University College London and lecturer at Oxford University who specializes in mathematical modelling of diseases.

If R is below one, Fisman said, “the disease is at a slow burn without epidemic spread.”

That suggests it may be safe for governments to ease restrictions.

However, because R fluctuates and is based on case and hospitalization data that may not be accurate, it’s a “good guide” but isn’t very precise, Panovska-Griffiths said.

For example, in the U.K., during the first week of May, it was estimated to be between 0.6 and 0.9. “That’s a big difference,” Panovska-Griffiths said. It also may not take into account “hot spots” of infection somewhere in the system.

Because of that, she recommends easing measures slowly and keeping an eye on R, along with related indicators such as hospitalizations and deaths — in conjunction with widespread testing and contact tracing.

Fisman recommends waiting until R remains below one for a couple of weeks before loosening things up.

“In the context of reopening, we are going to hopefully keep Re at or below one because then we don’t have exponential epidemic growth,” he said.

He added that if R goes back above one after easing restrictions, governments may need to reimpose measures that increase physical distancing.

”I think it’s almost inevitable that we will need to go through the winter,” he said during an interview on CBC’s Metro Morning in late May.

He warned that while Ontario’s R was previously below one, as of May 25, it was 1.1. That means the disease’s spread has, at least temporarily, returned to growing exponentially — if slowly — and that could represent a setback.

Panovska-Griffiths notes that if R does climb above one, that could lead to a second wave of infection (although that’s not what’s happening right now, as the World Health Organization says the first wave isn’t yet over).

“Historically speaking,” she said, “the second pandemic wave in all the existing epidemics today has been more severe than the first.”

How fast the epidemic declines

The rate of decline depends on R. The further below one it is, the more quickly the number of new cases declines.

How fast the epidemic declines

How fast the epidemic declines

Besides R, what else do governments need to keep an eye on as they ease restrictions?

Panovska-Griffiths emphasized that because of the uncertainties in R, it’s important to track other metrics such as hospitalizations and deaths and compare them.

She said that government physical distancing measures need to be lifted slowly, but even then, “we could be getting social bubbles where we have infections.”

Because of that, she said another important component is widespread testing and making sure contacts of those who test positive are quickly traced and isolated to prevent further spread of the epidemic.

“It’s only once we have an effective contact tracing and isolation strategy in combination with easing the lockdown [that] you can possibly get to the end,” said Panovska-Griffiths.

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