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On the evening of May 21, 2020, Montrealers relax in Jeanne-Mance Park.

Kate Hutchinson/The Globe and Mail

How much more contact will be too much? As provinces across Canada lift physical distancing measures, each has a threshold. It’s the point where the increase in the average contact rate among individuals across the population is sufficient to spark a resurgence of COVID-19 cases and a potential return to stricter distancing measures.

As opportunities for people to interact increase, a new analysis conducted for The Globe and Mail offers some insights into what Canadians can expect in an uncertain situation – and of the challenges facing policy makers.

In Ontario, a rate of 20-per-cent more contact between individuals would likely lead to a modest increase in case counts. It means health agencies will be dealing with new cases at a steady pace but at rates that are similar to what the province is experiencing now. But that changes with 40 per cent or higher. Under those circumstances, the case count in Ontario would be expected to rise quickly beyond what has been seen thus far.

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In British Columbia neither a 20-per-cent nor a 40-per-cent increase causes problems. At the other end of the spectrum, the latest data suggest that Quebec, as a whole, may not yet be below the threshold that would permit a relaxing of measure without driving case counts higher. A more local breakdown would show differences between Montreal and other parts of the province coming out of lockdown.

Determining how much freedom to allow is a question bedevilling politicians and public health officials across the country. In Ontario, for example, Premier Doug Ford has repeatedly said he won’t hesitate to impose restrictions again if case numbers continue to go up in the province, but he hasn’t given specifics on when he would consider tightening the rules again.

Businesses in some provinces prepare to reopen as COVID-19 restrictions loosen

B.C. begins reopening plan as COVID-19 risk drops to lowest point since March

“I think of it 24/7,” he said on Friday. “And we’re seeing some peaks and valleys but hopefully we’re going to see the trend go down because I know in the last few days it’s gone up. And it’s concerning. These are things that you’re up all night thinking about. It’s tough.”

Indeed, a key take away from the Globe analysis is that small shifts in rates of contact can lead to vast differences in predicted new cases. And even if everyone across the country were to adopt identical precautions, the fallout from reopening will change depending on region – dramatically so, in some scenarios.

Projected COVID-19 cases in Ontario by change in social restrictions

90% likely

Likelihood of

falling within range

50% likely

No change in rate of contact

Daily reported cases

1,000

Projection

based on

reported cases

500

0

March

April

May

June

July

20% increase in rate of contact

1,000

500

0

March

April

May

June

July

40% increase in rate of contact

2,000

1,500

1,000

500

0

March

April

May

June

July

60% increase in rate of contact

2,000

1,500

1,000

500

0

March

April

May

June

July

MURAT YÜKSELIR / THE GLOBE AND MAIL, SOURCE: CAROLINE COLIJN, SIMON FRASER UNIVERSITY; SEAN ANDERSON, FISHERIES AND OCEANS CANADA

Projected COVID-19 cases in Ontario by change in social restrictions

90% likely

Likelihood of

falling within range

50% likely

No change in rate of contact

Daily reported cases

1,000

Projection

based on

reported cases

500

0

March

April

May

June

July

20% increase in rate of contact

1,000

500

0

March

April

May

June

July

40% increase in rate of contact

2,000

1,500

1,000

500

0

March

April

May

June

July

60% increase in rate of contact

2,000

1,500

1,000

500

0

March

April

May

June

July

MURAT YÜKSELIR / THE GLOBE AND MAIL, SOURCE: CAROLINE COLIJN, SIMON FRASER UNIVERSITY; SEAN ANDERSON, FISHERIES AND OCEANS CANADA

Projected COVID-19 cases in Ontario by change in social restrictions

90% likely

Likelihood of

falling within range

50% likely

20% increase in rate of contact

No change in rate of contact

1,000

Daily reported cases

1,000

Projection

based on

reported cases

500

500

0

0

March

April

May

June

July

March

April

May

June

July

40% increase in rate of contact

60% increase in rate of contact

2,000

2,000

1,500

1,500

1,000

1,000

500

500

0

0

March

April

May

June

July

March

April

May

June

July

MURAT YÜKSELIR / THE GLOBE AND MAIL, SOURCE: CAROLINE COLIJN, SIMON FRASER UNIVERSITY; SEAN ANDERSON, FISHERIES AND OCEANS CANADA

“Different populations are experiencing different COVID-19 epidemics, so the impacts of their reopening are not likely to be the same,” said Caroline Colijn, who holds the Canada 150 research chair in mathematics for evolution, infection and public health at Simon Fraser University in British Columbia.

This heterogeneity mean provinces have different amounts of leeway as they move forward, said Dr. Colijn, who worked with The Globe and Mail in March to generate trajectories for the pandemic under different levels of physical distancing. The exercise revealed the necessity of strong measures to slow the rate of new infections and avoid overwhelming hospitals with patients in need of critical care. It also showed that if measures were lifted too soon, and too abruptly, the pandemic returned in full force.

Now, Dr. Colijn has collaborated with additional colleagues, including Sean Anderson, an ecologist with Fisheries and Oceans Canada, to consider a different question: At what point would a loosening of restrictions on public contacts trigger a return to rising case counts?

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Because it is not possible to know or measure every factor in a particular region, the results should be taken as a guide to important differences between the four provinces that account for most of the cases in Canada – Ontario, Alberta, B.C. and Quebec – as well as a selection of U.S. states for comparison. But while they show what impact increasing contact may have, they cannot predict how much contact will actually occur as people begin to work and socialize in less restrictive conditions.

In contrast with Dr. Colijn’s first projection, the mathematics underlying these models can now be checked against two months of real experience with how the pandemic has played out in different parts of the country. These data, together with what is known about the characteristics of the virus and various estimates for increasing contact rates, is what goes into each forecast. The contact rates themselves consider the number of opportunities that the disease might have to spread between individuals in a given instance of time. They do not correlate to individual actions by a provincial government; how the projections will match up with steps that provinces are taking will only become clear after the fact.

Projected COVID-19 cases across selected states based on a 20 per cent increase in rate of contact

90% likely

Likelihood of

falling within range

50% likely

NEW YORK

20,000

Daily reported cases

Projection

based on

reported cases

15,000

10,000

5,000

0

March

April

May

June

July

MICHIGAN

1,500

1,000

500

0

March

April

May

June

July

CALIFORNIA

25,000

20,000

15,000

10,000

5,000

0

March

April

May

June

July

WASHINGTON

500

400

300

200

100

0

March

April

May

June

July

MURAT YÜKSELIR / THE GLOBE AND MAIL, SOURCE: CAROLINE COLIJN, SIMON FRASER UNIVERSITY; SEAN ANDERSON, FISHERIES AND OCEANS CANADA

Projected COVID-19 cases across selected states based on a 20 per cent increase in rate of contact

90% likely

Likelihood of

falling within range

50% likely

NEW YORK

20,000

Daily reported cases

Projection

based on

reported cases

15,000

10,000

5,000

0

March

April

May

June

July

MICHIGAN

1,500

1,000

500

0

March

April

May

June

July

CALIFORNIA

25,000

20,000

15,000

10,000

5,000

0

March

April

May

June

July

WASHINGTON

500

400

300

200

100

0

March

April

May

June

July

MURAT YÜKSELIR / THE GLOBE AND MAIL, SOURCE: CAROLINE COLIJN, SIMON FRASER UNIVERSITY; SEAN ANDERSON, FISHERIES AND OCEANS CANADA

Projected COVID-19 cases across selected provinces

based on a 20 per cent increase in rate of contact

90% likely

Likelihood of

falling within range

50% likely

BRITISH COLUMBIA

ALBERTA

120

400

Daily reported cases

Projection

based on

reported cases

90

300

60

200

30

100

0

0

March

April

May

June

July

March

April

May

June

July

ONTARIO

QUEBEC

1,000

4,000

750

3,000

500

2,000

250

1,000

0

0

March

April

May

June

July

March

April

May

June

July

MURAT YÜKSELIR / THE GLOBE AND MAIL, SOURCE: CAROLINE COLIJN, SIMON FRASER UNIVERSITY; SEAN ANDERSON, FISHERIES AND OCEANS CANADA

As provinces move to reopen there is more diversity in how measures are being lifted, as well as in the degree to which provincial guidelines are understood and adhered to. All of these factors together produce some increase in the average rate of contact between individuals in different locations. This average rate can be estimated and then used to run the model forward and see what happens next.

Both the existing data and Dr. Colijn’s projections appear to be in agreement with other studies, including one posted online on Tuesday by a U.S.-Canadian team that considers how public awareness of the pandemic is influencing rates of infection. Instead of infection curves rising and falling in a symmetrical fashion such models project a steep rise going in followed by a long shoulder or plateau going out.

“The message is don’t be overconfident. Don’t assume that because you’ve reached the peak you have a lot of momentum to go back down,” said Jonathan Dushoff, a biologist at McMaster University in Hamilton who has been studying the pandemic and was a co-author on the study.

That’s the message from public health officials as well. Dr. Horacio Arruda, Quebec’s public health director warned residents on Friday against letting their guard down as the province detailed plans to lift restrictions on museums, libraries and drive-in movie theatres. Warmer weather, he said, might tempt people to ignore the rules.

“You know being away from other people is not natural for humans – especially when there’s good weather, we are outside, we go back to our own reflexes,” Dr. Arruda said.

Dr. Arruda said that’s the reason behind the province’s gradual approach to reopening, allowing limited outdoor gatherings of up to 10 people from three households beginning Friday. If the rules aren’t followed, the number of COVID-19 cases could increase quickly, forcing the province to shutter again, he warned.

“And all that we’ve done to get to this point could [turn around] very fast,” Dr. Arruda said.

The models can also be applied to U.S. states that could be likely sources of interaction once the international border reopens. While case numbers and death rates vary, the models suggest that Ontario and Quebec are more similar to counterpart regions New York and Michigan than B.C. is to nearby Washington state or California. That means B.C. would be more likely to have its case numbers driven upward when cross-border traffic resumes.

Projected COVID-19 cases across selected provinces based on a 20 per cent increase in rate of contact

90% likely

Likelihood of

falling within range

50% likely

BRITISH COLUMBIA

120

Daily reported cases

Projection

based on

reported cases

90

60

30

0

March

April

May

June

July

ALBERTA

400

300

200

100

0

March

April

May

June

July

ONTARIO

1,000

750

500

250

0

March

April

May

June

July

QUEBEC

4,000

3,000

2,000

1,000

0

March

April

May

June

July

MURAT YÜKSELIR / THE GLOBE AND MAIL, SOURCE: CAROLINE COLIJN, SIMON FRASER UNIVERSITY; SEAN ANDERSON, FISHERIES AND OCEANS CANADA

Projected COVID-19 cases across selected provinces based on a 20 per cent increase in rate of contact

90% likely

Likelihood of

falling within range

50% likely

BRITISH COLUMBIA

120

Daily reported cases

Projection

based on

reported cases

90

60

30

0

March

April

May

June

July

ALBERTA

400

300

200

100

0

March

April

May

June

July

ONTARIO

1,000

750

500

250

0

March

April

May

June

July

QUEBEC

4,000

3,000

2,000

1,000

0

March

April

May

June

July

MURAT YÜKSELIR / THE GLOBE AND MAIL, SOURCE: CAROLINE COLIJN, SIMON FRASER UNIVERSITY; SEAN ANDERSON, FISHERIES AND OCEANS CANADA

Projected COVID-19 cases across selected states

based on a 20 per cent increase in rate of contact

90% likely

Likelihood of

falling within range

50% likely

WASHINGTON

CALIFORNIA

500

25,000

Projection

based on

reported cases

400

20,000

300

15,000

200

10,000

100

5,000

Daily reported cases

0

0

March

April

May

June

July

March

April

May

June

July

MICHIGAN

NEW YORK

1,500

20,000

15,000

1,000

10,000

500

5,000

0

0

March

April

May

June

July

March

April

May

June

July

MURAT YÜKSELIR / THE GLOBE AND MAIL, SOURCE: CAROLINE COLIJN, SIMON FRASER UNIVERSITY; SEAN ANDERSON, FISHERIES AND OCEANS CANADA

“It puts the lower risk places at higher risk and that’s something to be concerned about,” Dr. Colijn said.

Another modelling study specific to Ontario was published this week in the journal Biology. Jianhong Wu, a mathematician and infectious disease specialist at York University in Toronto, led the study. Its findings showed that efforts to reduce spread through reduced contact rates must go hand in hand with other public health strategies including mask wearing, increased testing, contact tracing and isolation of new cases, to be effective.

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Without such a concerted and organized effort the likely outcome is a return to distancing measures, with even less enthusiasm from the public.

“I don’t think the public can tolerate a second lock down. That’s why we have to be very cautious,” Dr. Wu said.

What all the models underscore is the fact that while the virus is transmitted between individuals, it is the sum total of actions taken by everyone – combined with effective public health strategies – that will determine if the breathing room purchased by a two-month shutdown can be made to last.

In essence, COVID-19 has made freedom a shared resource – and a finite one – that should be used carefully.

For Françoise Baylis, a philosopher who specializes in bioethics at Dalhousie University, this puts the focus where it should be: on public health rather than on trying to engineer individual escape hatches such as immunity passports that would, in theory, allow some individuals to return to life as normal while others remain in complete isolation. In comments published this week in the journal Nature, Dr. Baylis and a co-author based at Harvard University lay out a host of reasons, both ethical and practical, why such a scheme is unworkable.

“The real issue here is that we’re all in this together and if we all want to come out of it we have to look after each other,” Dr. Baylis said.

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