Why R is a key COVID-19 metric to watch
Reproduction number can help decision-makers adjust policies to keep pandemic in check
COVID-19 is highly contagious. Now that schools have reopened, restrictions on gatherings have been loosened and businesses from bars to fitness clubs have reopened across Canada, cases are again rising sharply in some provinces. On Sept. 28, Ontario reported a single-day record of 700 new cases as scientific modelling suggested the province would hit a peak of 1,000 cases a day by mid-October. Meanwhile, the same day, Quebec reported 750 new cases as officials announced new restrictions in three regions that ban visits to other people’s homes, along with places such as restaurants, bars, libraries and cinemas.
But how do researchers and officials predict the next peak? How do we know when we’ve reached it? When might restrictions to curb the spread of the disease need to be reimposed? And when can they be eased again?
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.
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.
COVID-19
R0 = 2.6
1 total infection
Influenza
(Spanish flu)
R0 = 1.8
1 total infection
Ebola
(high)
R0 = 2
1 total infection
Smallpox
(high)
R0 = 6
1 total infection
Measles
(high)
R0 = 15
1 total infection
Measles
(high)
R0 = 15
1 total infection
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, posted an interactive tool earlier this year 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).
We’re now all very aware that if you’re tracking cases, hospitalizations or deaths 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 adjust their policies to keep the pandemic in check?
In the spring, as governments weighed when to ease lockdown measures, it was “very important,” said 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.
More recently, epidemiologists and public health officials have been tracking R as cases rise sharply with the start of the fall season, especially in Ontario and Quebec.
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.
He added that if R went back above one, governments might need to reimpose measures that increase physical distancing.
Panovska-Griffiths noted that if R did climb back above one, that could lead to a second wave of infection.
“Historically speaking,” she said, “the second pandemic wave in all the existing epidemics today has been more severe than the first.”
As of Sept. 25, the Public Health Agency of Canada reported that nationally, R had risen to 1.4. That was two days after Prime Minister Justin Trudeau said there can be no doubt that four of the country's provinces — Alberta, B.C., Ontario and Quebec — are in the second wave of COVID-19.
And as Fisman predicted, the Quebec government imposed new restrictions on Sept. 28 to reduce contact between people that could help the virus spread in three regional hot spots: Montreal, Quebec City and Chaudière-Appalaches. That includes banning home visits, restricting the number of people in houses of worship and event venues, and closing restaurants, bars, casinos, libraries, museums, cinemas and theatres that had previously reopened. Ontario has closed strip clubs, reduced opening hours for bars and reduced the permitted size of private gatherings.
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.
Besides R, what else do governments need to keep an eye on?
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 added that even when the average rate of spread is low, “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.