TORONTO -- COVID-19 is officially a pandemic, public health experts and politicians are warning that up to 70 per cent of people could be infected with the virus, and talk is ramping up about “flattening the curve.”

But what does that mean?

It means putting in place interventions and restrictions that will slow the spread of the virus so that a huge spike in infections in a short period of time doesn’t lead to swamped health systems. When hospitals can’t handle an influx of seriously sick people, as has happened in northern Italy, Iran and parts of China, it leads to a higher mortality rate.

Flattening the curve means keeping the number of infections manageable at any one time. The good news is that interventions worked in China, outside Hubei province, and in South Korea, says Toronto infectious diseases specialist Dr. Isaac Bogoch.

“We are relatively early on in Canada and so far we are doing well but the real test will come in the weeks and months ahead.”

Bogoch says he’s concerned that the U.S. has not been as proactive in rolling out surveillance and screening measures and that a number of states have now declared emergencies.

“We are so closely tied. If they are having a tough time, we will have a tough time.”

As Canada’s federal government released a $1-billion aid package Wednesday, Health Minister Patty Hajdu for the first time acknowledged that Canada faces a possible infection rate of 30 to 70 per cent of the population. Other world leaders, including German Chancellor Angela Merkel issued similar warnings.

So here’s a bit of math:

According to Stanford University-educated mathematician Grant Sanderson, who posts math explainers on his YouTube channel 3Blue1Brown, viruses are a “textbook case” illustrating exponential growth because existing cases cause new cases.

New cases are the result of multiplying the number of people with the virus by how many people each of them are exposed to, on average, on a given day, and multiplied again by the probability of each of those exposures becoming a new infection, Sanderson explained in a March 6 video that’s been viewed more than two million times.

He crunched the public data for COVID-19 cases outside China and found that it took 20 days, starting in late January, to go from 100 cases to 1,000 cases and then 13 days to go from 1,000 to 10,000.

“If the present trend continues, it would mean hitting a million cases in 30 days (April 5), hitting 10 million in 47 days (April 22), 100 million in 64 days (May 9) and 1 billion in 81 days (May 26).”

He said that the rate of new cases will slow down but the crucial question is when.

Growth rates of new cases fall when exposure rates decline and when people cut their risk by taking better precautions.

“If people are sufficiently worried, then there is a lot less to worry about. But if no one is worried, that’s when you should worry,” said Sanderson.

Imposing travel restrictions and quarantine requirements, cancelling large gatherings, closing schools and tourist spots, requiring people to work from home, and promoting social distancing and diligent hand-washing, are just some of the ways public and private organizations have responded around the world.

Ottawa-based online shopping platform Shopify announced Wednesday that it was instituting a work-from-home policy for its 5,000 workers around the world and closing its offices.

Sudbury’s Laurentian University suspended all classes and campus events as of noon Wednesday until further notice amid a local case of the virus. All instruction will move online.

A number of retailers, including Tim Hortons, Starbucks and McDonald’s, are suspending the use of reusable cups over concern of transmission of the virus.

Conferences, conventions, concerts and sporting events around the world have been cancelled or postponed.

The U.S. State Department is also shifting its upcoming ministerial meeting scheduled for Pittsburgh to a video teleconference.

Bogoch says it’s not always necessary to close institutions or cancel gatherings. He says a more nuanced approach, including spreading out the number of people in a building such as a school, or selling fewer event tickets, all while promoting hand-washing and social distancing practices, can also be effective.