Exponential growth is one of the latest COVID-19 terms to pop up in the media. It’s how COVID-19 grows, and it can be hard to absorb how it works and what it means to us.
It is the reason for the rapid expansion of stay-at-home orders around the country and in New Hampshire. The more an explanation can sink in the more we can see what’s at stake and why we need to take those orders seriously.
The orders are going to depend almost entirely on an honor system. No one is going to tightly supervise what we do. Each one of us makes the decision about why we have to leave our home. We decide how we maintain safe distances if we do. These are small and personal decisions, but they are serious ones and exponential growth explains why. Essentially, these orders are civil defense in a time of war.
Imagine COVID-19 as the perfect virus spreading with perfect transmission. If it were spread by the process of addition, it would look something like this starting on day one, using April 1 as that date. The first case appears on that day. Adding one new case each day leaves us with three cases on April 3, five cases on April 5 and 10 cases on April 10.
Everything changes with exponential growth because each case becomes two cases by the next day. That’s the core fact about exponential growth. Each case becomes two cases over some time period. The longer the time period, the slower the growth. The perfect unimpeded April 1 case becomes two cases by April 2 and each of those cases becomes two cases by April 3. We face four cases on April 3 instead of the three expected through addition. Exponential growth is already underway.
Each of those four cases becomes two cases so there are eight cases on April 4. Each of those eight cases become two cases, so April 5 has 16 total cases, April 6 has 32, and on it goes if nothing stops its spread. This unimpeded, daily exponential growth gets to 512 cases on April 10. In contrast, we’d only face 10 cases if COVID-19 grew by addition.
I think I understand COVID-19’s exponential growth when I look at those numbers, but I really don’t. When I realize how much the number increases each day, I get lost in the numbers. Each new day brings another doubling of the total number of cases. Impossibly big numbers quickly appear, but they don’t sink in. They lose their emotional power because of their sheer size.
This changed when I heard an analogy presented by Soren Wheeler on the Radiolab podcast episode from March 27, titled “Dispatch 1: Numbers.” You can fast forward about 7:30 minutes to get right to his portion. What follows is a version of his story in case the podcast is inaccessible.
Lots of people have something in their home about the size of an 8-by-10 rug, or a 5-by-8 bathroom with a tub. One of the rugs (or two of the bathrooms) covers 80 square feet. Imagine that I buy a rug on April 1, then another on the second day, and another on the third. I’ve got 4 rugs by April 4. At the end of a week of buying, I have 7 rugs, covering 560 square feet and taking over. On April 10, the 10 rugs would cover 800 square feet, but I could live with them.
Imagine, instead, that I innocently bought a rug that somehow becomes two rugs by the next day. On April 1 there is one rug and on April 2 there are two, apparently just like adding. But those two rugs became four rugs on April 3, and I’m back in Exponential Land. Each new rug becomes two by the next day so April 4 brings eight rugs.
If the rug keeps doubling its size unimpeded, there are 64 rugs on April 7, not the seven expected through addition. They cover 5,120 square feet, flow out of the house and take over the yard. On April 8, there are 128 rugs, almost covering my whole quarter-acre lot. With no brake on its growth, it almost carpets an acre by April 10, and abruptly it has covered six square miles by April 22.
That is already astonishing and the exponential growth is just getting starting. Each day the rug covers twice as much as the day before and 10 days later, by May 2, it has spread massively to more than 6,000 square miles of New Hampshire. The state has 9,350 square miles and the rug has taken over almost two-thirds of our land. Its daily spread accelerates so quickly over the next 10 days that it carpets the entire landmass of the continental United States by May 12.
The idea of that rug starting in my home and carpeting the entire country in just 42 days takes my breath away. Images of it get to me in a way that numbers never have. I hope another image will spring from the same approach if this one doesn’t grab you. We need to feel the power of that kind of growth without any brake. COVID-19 is capable of this kind of growth without any brake.
All the official preparations, all the risks that health care providers are taking and all that each of us is sacrificing right now is about braking that exponential growth. COVID-19 is in our future and we have to get through the worst of the cresting wave right now in order to learn about braking it in a more prepared way with vaccines and effective treatments. Everyone with a foot on the brake needs to keep pushing, and everyone who isn’t pushing needs to step on it.
(David Coursin of Northwood is a doctor and state representative in Rockingham District 1.)