Exponential growth may explain why Omicron cases are skyrocketing in parts of the US

Exponential growth may explain why Omicron cases are skyrocketing in parts of the US
·4 min read
Women with red hair and red nail varnish in a black coat and gold hoops puts COVID-19 test swab into right nostril.
A woman uses a swab to take a sample from her nostril at an NHS Test and Trace Covid-19 testing unit.ADRIAN DENNIS/AFP/Getty Images
  • In pandemic terms, "exponential growth" means infections accelerate over time.

  • In New York City, the percentage of people testing positive for COVID-19 doubled over three days.

  • Exponential growth causes huge outbreaks in short time periods. But we know how to stop the virus from spreading.

As COVID-19 infections explode in the Northeast and Dr. Anthony Fauci warns Americans of a "really dark time ahead" come mid-January, a math concept known as "exponential growth" is relevant yet again.

Understanding how exponential growth works is key, experts say, because it sheds light on why they're so worried about the latest wave of cases sweeping parts of the United States. The easiest way to grasp the concept is to look at a graph, according to Zoe McLaren, an associate professor at the University of Maryland, Baltimore County, who studies policies to combat infectious disease epidemics.

"It's kind of been rising slowly, then that pace picks up — and then shoots off," McLaren said of plotting exponential growth.

Take New York City, for example, where the percentage of people testing positive for COVID-19 doubled over three days, according to Dr. Jay Varma, a professor at the Weill Cornell Medical School and a senior health adviser to New York Mayor Bill de Blasio, who posted the data on Twitter Thursday.

The trajectory of those infections — nearly straight upward — is both instructive and impossible to ignore.

Seven-day average of confirmed and probable COVID-19 cases in New York City, through December 13, 2021
Seven-day average of confirmed and probable COVID-19 cases in New York City, through December 13, 2021New York City Department of Health and Mental Hygiene

In the simplest terms, exponential growth means that numbers — in this case, coronavirus infections — accelerate over time. Instead of rising by the same number of cases each day, they double over a set period.

For example: Imagine doubling a single COVID-19 case each day. After one day, there would two cases. Two days, four cases. Three days, eight cases. Fourteen days later, there would be 16,384 cases.

That doubling phenomenon leads to extraordinarily high numbers of cases much more quickly than most people can conceptualize, McLaren explained. And the bigger the number you start with, the bigger explosion of infections you have each day.

"The pace of increases over time, because of the doubling," she said, adding, "When you're doubling very small numbers of cases, that's still resulting in a small number of cases. When you're doubling large numbers of cases, that's when we get these huge spikes. The spikes happened very quickly, before people realize, because doubling is happening over a period of days."

That breakneck change can be difficult for people to understand.

"The thing about exponential growth is that it's not it's not intuitive," McLaren said. "Cases shoot off and get quite out of control a lot more quickly than people realize."

While New York City officials aren't certain whether the highly infectious Omicron variant is fueling the city's rapid rise in cases, it could potentially be one piece of the puzzle. Centers for Disease Control and Infection data suggest that in the wider region, which includes New York and New Jersey, Omicron is gaining ground. An estimated 13.1% of samples analyzed between December 5 and 11 were Omicron variant, compared to just 2% of samples a week prior.

COVID-19 has been with us for 2 years. We know how to stop transmission.

People wearing masks queue in Austria
People waiting for a mass Covid-19 testing in Vienna, Austria.AP Photo/Ronald Zak

While watching COVID-19 cases skyrocket in a place like New York City is undoubtedly scary because of the risk it poses to hospitals, health care facilities, vulnerable people, the upside of being more than two years into a pandemic is that we know how to slow the virus' spread.

In addition to vaccines and booster shots, lockdowns, high-quality masks, and avoiding indoor public spaces all work to reduce infections, McLaren explained.

As was true of Delta, and will likely hold true for Omicron, "people realize there's a spike and that motivates them to change their behavior," McLaren said, adding,"people who don't want to get COVID are still willing to take precautions, especially when transmissions ramp at the top of the spike."

In New York, dozens of restaurants preemptively closed their doors Friday, some announcing that those closures would extend through the end of the year. Universities, including Cornell University, New York University, and Princeton University canceled in-person events or announced plans for remote exams.

If people change their behavior, cases can fall as quickly as they ballooned.

"I often say that the optimal reaction to exponential growth looks like an overreaction," McLaren said. "If you understand the trajectory, you realize you need to take some pretty big measures," she added.

"If you're reacting to the case rates you see right now, you're going to be underreacting to what's going to be there tomorrow. You need to be thinking about where things are going."

CORRECTION: The original version of this story stated that after 14 days of doubling there would be 1,584,323 COVID-19 cases. The actual number of cases after 14 days of doubling would be 16,384.

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