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This is scientific Americans.

60 second science.

I’m Steve Moresky.

Exponential Infection Increases Are Deadly Serious

Here in New York the coronavirus cases are exploding—we’re on the steep part of the curve. Now, you’ve probably heard about the basic reproduction number, R0, or R-naught. And that’s basically how many people an infected person goes on to infect themselves. The other night, I happened to see a tweet that showed just how big a difference there is over 10 cycles of transmission between a basic reproduction number of 1.3 and a basic reproduction number of 3. The different was astounding. The 1.3 after 10 cycles infected on average 14 other people total. The basic reproduction number of 3.0 led to 59,000.

Looking at those numbers was startling. So I got a calculator out. And I’m going to repeat this exercise that I did with the calculator. And you can do it, too. It’s even a little bit fun. And it’s kind of amazing. So I’ve got two calculators, because I’m going to do the two different basic reproduction numbers, the R-naughts, together.

Okay, so the calculator on my left—I’m going to assume 1.3 as the basic reproduction number. Each person infects 1.3 other people on average. The calculator on the right—I’m going to do 2.5—just to pick a number and because that looks like it may be fairly close to what the coronavirus number is.

So we’ll start with one person (1) on each side. We multiply by 1.3 on the left to get 1.3, obviously. We multiply by 2.5 on the right to get, not surprisingly, 2.5. For cycle two, we multiply the one on the left by 1.3 again, and we get 1.69. On the right, we take 2.5, and we multiply it by 2.5, and we get 6.25. So that’s two rounds.

Let’s do it again. On the left, for the third round, multiplying by 1.3, we now have 2.197. On the right, multiplying by 2.5, we’re up to 15.625.

So let’s do the fourth round here. On the left, we multiply by 1.3, and we’re up to 2.86 people. On the right, we multiply by 2.5—we’re up to 39.1.

On the left, 1.3 is our number—we’re up to 3.7. On the right, 2.5 is our number—we’re up to 97.7.

Another round: 1.3, we multiply by, and we get 4.8 on the left. When we multiply our number on the right by 2.5, we’re up to 244.

Let’s do it again. We’re going to multiply by 1.3, and we’re now up to 6.3 people on the left. We multiply our right figure of 244.1 by 2.5, and now we’re up to 610 people.

Let’s do another round. Multiply by 1.3 on the left—we now have 8.2 people infected. Multiply the right number, 610.4, times 2.5—we’re up to 1,525.9. But we’re not done; we’re going to go through this and take rounds.

One more on the left by 1.3—we’re up to 10.6 people. On the right, multiply by 2.5: 3,814.7.

Let’s do it again: 1.3 on the left—13.8. 2.5 on the right brings us up to 9,537.

That’s why it’s so important to cut the number of people each individual can infect with the policies of social distancing.