Patients waited in line March 25 for a covid-19 test at Elmhurst Hospital Center in New York. (John Minchillo/AP)

With roughly 85,000 confirmed cases of the novel coronavirus in the United States as of Friday morning, it’s seemingly impossible to follow the updates without hearing of the pandemic’s “exponential spread.” Covid-19 has been spreading across Western Europe and is now showing up in every U.S. state and the District of Columbia.

March began with about 100 confirmed cases throughout the country, and could end with close to a quarter of a million, based on statistics from Johns Hopkins University.

At this rate of spread, a simple run of the numbers suggests close to 100,000 U.S. cases by the end of Friday, with a quarter of a million cases by April 1. Unless the curve at which covid-19 is spreading flattens soon, the country is likely to hit the millionth case mark by April 11.

This is exponential growth at its worst — but what does that mean?

Growth types

Let’s say you spend $10 a day commuting to and from work by public transportation (or at least you did before social distancing). How much might you shell out over time? Neglecting weekends, that’s a simple system to model because the total spent goes up by the same amount each day. We call that a linear function, or linear growth.

Now let’s imagine that while riding to work you happen upon one of those viral challenges circulating around social media, like the wildly popular Ice Bucket Challenge from a few years ago.

You decide to complete a task, then tag and challenge three of your friends. The next day, they do it, too. But if each of them tags three friends, suddenly nine people have completed the challenge … then 27 … and then 81, then 243, and so on each day — all from something that started with you. It’s sort of like paying it forward. We call this exponential growth.

An exponential growth curve means that with each unit of time, a quantity — in the case of the virus, it’s the number of infected individuals — increases in proportion to the running total. In most cases, it takes a while to get going, but before long it’s like a runaway train.

Exponential growth of coronavirus


Deaths from coronavirus in the U.S. (Tim Meko)

For coronavirus infections, the doubling time in the United States has been about 2½ days. That means that, on average, the number of reported covid-19 cases doubles every 2½ days. (Part of the reason for the increase in cases is because of expanded testing, whereas the death count from covid-19, which also exhibits some aspects of exponential growth, more closely captures the spread and impacts of the virus itself.)

According to U.N. Secretary General António Guterres, it took about three months to tally the first 100,000 cases of coronavirus. The next 100,000 occurred in 12 days. Then four days, and then a day and a half. Data from John Hopkins supports this, showing how difficult it is to slow down exponential growth once it is underway.

Thus far, covid-19 cases in the United States have spread with considerable predictability. The rate of increase in the United States appears faster than in most other countries around the world.

Because we know that coronavirus spreads exponentially, we can reformat and “linearize” graphs to make them easier to read. Rather than plotting a skyward-screaming curve, one can simply tweak the vertical axis to increase exponentially at roughly the same rate as the virus’s spread. That leaves behind a line, making prediction somewhat straightforward.

Understanding exponential growth offers clues about what may lie ahead

Extension of that line reveals some sobering numbers that put into focus just how dire the coronavirus pandemic is. Using data from Worldometer from between Feb. 15 and March 25, it’s possible to model how, at its current pace, the number of domestic coronavirus cases could increase.

Extending the numbers called for about 81,000 cases by Thursday afternoon. The observed number was around 82,000 — in close agreement.

Following the trend, nearly 100,000 cases in the United States are suggested for Saturday, with a quarter of a million by the start of April. And at that rate, more than a million could be infected by April 10 or 11.

And that’s not using any fancy modeling software. Instead, it’s a straightforward math problem that has thus far yielded accurate results.

However, there’s a major caveat with this. These numbers will likely slow down if social distancing proves effective. That’s what scientists mean when they use the phrase “flatten the curve.”

Why exponential growth makes the perfect case for social distancing

Modeling the number of coronavirus deaths through exponential growth is also possible, but it’s a lot more complex since it involves the vulnerability and demographics of infected individuals, as well as less predictable variables tied to the health-care system. The death rate could spike if hospitals are overwhelmed, for example.

It’s an unfortunate reality of an epidemic, but exponential growth can work both ways — and we can harness its power to our advantage. That’s where social distancing comes in.

Understanding exponential growth illustrates why social distancing is vitally important. If you can cut out even one transmission of the virus out of the equation early on, that can have cascading impacts down the road in reducing the number of overall transmissions.

Read more:

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Why outbreaks like coronavirus spread exponentially, and how to “flatten the curve”

What you need to know about coronavirus