Physical distancing – based on the harsh realities of math – is a vital step to fighting the coronavirus pandemic

As the coronavirus cases grow exponentially, what may seem like extreme measures are not. Colorado now has a statewide "stay-at-home" order. Without our immediate cooperation, sick people will easily overwhelm hospitals.
March 25, 2020
Crowd of people as a way to demonstrate that coronavirus math shows how fast coronavirus is spreading.
The coronavirus math is stunning. “It took three months to reach 100,000 coronavirus cases worldwide. The second 100,000 only took 12 days.” Photo: Getty Images.

We in Colorado and many around the country are now taking extraordinary measures to try stem the tide of the coronavirus pandemic sweeping across Colorado, the US and the globe.

Gov. Jared Polis has issued a statewide “stay-at-home” order. Our schools and most offices are closed. We have no sports, no events, no conferences, no skiing and no restaurants (besides take-out here and there).

To some, these extraordinary measures may seem like overkill, but make no mistake: all our efforts now to slow the spread of the coronavirus will make an enormous difference in how we come out of the coronavirus pandemic on the other side.

One of UCHealth’s top doctors now is admonishing Coloradoans to immediately do all they can to slow the spread of the virus that causes COVID-19.

Dr. Richard Zane.
Dr. Richard Zane has put out an urgent call for people to practice physical distancing.

“Lives are on the line. Please everyone. Get more serious,” said Dr. Richard Zane, UCHealth’s chief innovation officer and chair of the University of Colorado School of Medicine’s Department of Emergency Medicine on the Anschutz Medical Campus.

“There is no longer any debate. All medical experts agree that the spread of coronavirus is now on pace to overwhelm the U.S. health care system by this summer,” Zane said. “The most powerful, and really only, tool we have left to change this alarming projection is social distancing. Yet far too many people are falling short of what’s needed.”

You might ask why Zane is speaking out in such a direct way. After all, the number of COVID-19 cases that we know about and deaths thus far remain relatively small, adjusted for population.

For updated numbers in Colorado, please click here; to view the numbers globally, please see the tracker that Johns Hopkins University is updating in real time.

In a country of 327 million people, the current number of cases as of midday on Wednesday, March 25, translates into about one per roughly 5,400 people (these numbers are changing hourly). Now, given the challenges with testing, the late start, and other factors contributing to undercount, let’s say the actual number of cases is 10 times higher – no one knows for sure. That’s still only one case for every 540 people – about two tenths of one percent. As it happens, Colorado’s ratios track about the same as the national numbers right now. So the question: why all the fuss – and in particular, why is physical distancing, also known as social distancing, so important – in the face of perhaps 1-in-500 odds?

The essential exponential function for COVID-19

Because the coronavirus pandemic is progressing as an exponential function, and if we as a society don’t catch it early, we risk that we will have too many patients and too few hospital beds, ventilators, and health care providers all over the country – and yes, in Colorado, too – much sooner than makes intuitive sense.

There’s a reason for this – one often cited by the late Al Bartlett, the University of Colorado Boulder physics professor who emphasized during 1,742 talks he gave prior to his death in 2013: “The greatest shortcoming of the human race is our inability to understand the exponential function.”

Please don’t glaze over with the terms “exponential” and “function.” For most of us, they evoke grinding through math homework years or decades ago. But in practice, exponential functions are everywhere, and at some level, we can intuit them. The old phone tree is an exponential function: you call two people, they call two people, they call two people and you’ve just spread the word to 14 people. The “network effect” that has made Facebook CEO Mark Zuckerberg a billionaire many times over is an exponential function.

There are, though, exponential functions that seem outlandish. Put one grain of rice on the first square of a chess board and double the quantity on each of the next 63 squares (the second square has two rice grains, the third four, the fourth eight, and so on), you have, on that last square, a number grains about 100 million times greater than the number of stars in the Milky Way galaxy. And here’s one from a recent Washington Post headline: “It took three months to reach 100,000 coronavirus cases worldwide. The second 100,000 only took 12 days.”

The epidemiology of the coronavirus pandemic boils down to exponential math. With exponents, numbers seem to creep up early and then explode when they hit a certain threshold – an inflection point. With coronavirus, keeping people away from each other to avoid transmission is the very best tool we have right now to avoid reaching that inflection point and the enormous problems doing so will cause.

Colorado Gov. Jared Polis’ orders to shut down Colorado’s ski areas and nearly all non-essential businesses here, along with sweeping actions by his peers in California, New York, Illinois, New Jersey and Ohio are all based on math and the urgent need to take truly drastic measures to avoiding a runaway exponential function in human illness.

Among others who have investigated coronavirus’s exponential math in depth – and advocated powerfully for physical distancing and other measures to thwart that math – include a team at Imperial College London and the analyst and entrepreneur Tomas Pueyo.

“When you’re on an exponential curve every moment is dangerous,” Francis Collins, the director of the National Institutes of Health, told the USA Today. “This is a particularly critical moment for us to try to bring all the resources and determination of government and the American people to try to get off of it.”

The coronavirus math doesn’t lie

Getting off that curve means physical distancing, vastly expanded coronavirus testing, case-tracking, and other measures that contribute to the now-famous nugget “flattening the curve.” (Pueyo covers these measures in great depth here).

Despite all of this, there has been skepticism in some corners. Yes, one might argue, but most people don’t get that sick, right? True enough: about 80% of patients have mild to moderate symptoms – these include high fevers, nasty coughs, stomach problems, and “mild to moderate” breathing difficulties. And young people, listen up: you’re not immune. Nearly 40% of patients sick enough to be hospitalized in the United States have been age 20 to 54.

Either way, 10% or so of COVID-19 patients end up “severely ill” and hospitalized, and perhaps 4% of the overall total become critical in intensive care units. The math here is simpler. And math, it turns out, is important.

The American Hospital Association counts 6,146 U.S. hospitals with 924,2017 beds. That includes about 70,000 ICU beds once you subtract neonatal and pediatric ICUs. There will be some surge capacity in terms of adding ICU beds, as we’ve seen in Italy and, in particular, China.

A person walking alone. In order to change the coronavirus math, we must practice physical distancing.
Practicing physical distancing so we don’t infect others is critical now to change the coronavirus math. Photo: Getty Images.

There will be limits on critical care beds as well as on the number of available ventilators and extracorporeal membrane oxygenation (ECMO) machines that people with serious COVID-19 cases may need to survive as their bodies clear virus. Also, there are only so many doctors, nurses, and staff trained in emergency medicine and critical-care, and some will inevitably become ill and have to take time off. Maybe even as many as 20% for two weeks at a time.

Estimates vary, but without the curve-flattening that physical distancing, case quarantining, and other steps require, the numbers of very sick – while small in percentage terms – are expected to far exceed the health care system’s ability to care for everyone who needs care. Also important, there is the impact of not being able to care for “regular” illness like heart attacks, stroke and other emergencies which do not slow down.  Abiding by the requests in the near term to keep our distance from one another and to stay home if we are sick, however, can sap the exponent’s power. If we abide by orders to change our behavior drastically, we will also buy valuable time to develop therapies and vaccines, build medical-system capacity, and train and retrain medical staff.

For all updates and to read more articles about the new coronavirus, please visit

That’s “us” because we’re all in this together, and the better we understand the exponential nature of coronavirus, the more conviction we will have in playing our part in what’s shaping up to be a monumental battle against a stubborn microscopic foe. Our success will enhance our odds of following the paths of Korea, Japan, Singapore, and, of late, China, in keeping caseloads below capacity and saving many lives along the way.

Dr. Zane called on all of us to make sacrifices now so we can save lives in the months ahead.

“There is no question that consistently practicing physical distancing will require personal sacrifice and at times may be painful, but lives depend on it and that life may be your loved one or mine,” he said.

“The United States, Colorado, your friends and family need you to do this and you need everyone else to as well.”

About the author

Todd Neff has written hundreds of stories for University of Colorado Hospital and UCHealth. He covered science and the environment for the Daily Camera in Boulder, Colorado, and has taught narrative nonfiction at the University of Colorado, where he was a Ted Scripps Fellowship recipient in Environmental Journalism. He is author of “A Beard Cut Short,” a biography of a remarkable professor; “The Laser That’s Changing the World,” a history of lidar; and “From Jars to the Stars,” a history of Ball Aerospace.