Apr 6, 2020

Quick Reads: Virginians and the Mathematics of Contagion

How social distancing today will pay public health dividends tomorrow
Robert Graboyes Senior Research Fellow

On Friday, April 3, at 11:53 pm, I lay in bed, and my cellphone buzzed. A treasured friend from elementary school had a question on the dynamics of a pandemic. The question warranted some deep thought, so I stared at the darkened ceiling for a while, searching for a suitable answer. Her question was sparked by some comments from my Mercatus colleague, Chuck Blahous, that I had posted on Facebook. Chuck had noted that the US COVID-19 mortality rate was inexplicably low compared with many other countries: 2.95 percent, as opposed to 12.75 percent for Italy, 9.75 percent for Spain, and 9.93 percent for the Netherlands.

Chuck said, “it’s clear that there are many other countries whose healthcare systems lack the adaptability, supplies, and resources to handle a crisis.” He hedged his observation with, “obviously the data are fragmentary and highly changeable given the inadequacy of testing to date. When this is all over, we should have a clear-eyed assessment of what went wrong, but also what went right.”

Anyway, A.W. my childhood friend, was intrigued, but curious why the epidemic’s peak was forecast to be six or eight weeks in the future. Her (lightly edited) question was this:

“I read your post with great interest, and I am heartened by it. I have a question: I completely understand that our cases have not yet peaked in Virginia, because the incubation period can be 14 days or maybe even a little above. So clearly, the cases we are seeing now are those that were exposed about two weeks ago. However, if we are doing a better job of social distancing, I don’t understand why they say Virginia’s peak will be late May. I would think that if we started social distancing very seriously a few days ago, our peak would be in two or three weeks. What am I missing here?”

A great question. As happens with me, my response formed in my mind during waking moments through the night. Here’s a lightly edited version of how I responded:

I’m not an epidemiologist, but here’s the best answer I can give. Suppose we went to 100 percent social distancing—every Virginian went to a private place and stayed away from everyone else. And no one touched a bottle or refrigerator handle or anything else that anyone else had touched recently. Then, yes, your supposition would be correct. The epidemic would likely peak in the next two weeks or so and then drop off quickly.

But social distancing isn’t 100 percent perfect. Some people ignore the warnings and have poker parties. Delivery people drop goods off at your house, and there will be some transmission when someone picks up a package delivered by a sick delivery person. An asymptomatic plumber might spread the illness to customers with burst water pipes or clogged sinks. Some unlucky people shopping for groceries will touch infected surfaces at the stores. Some infected people will enter Virginia and spread it here when they stop at stores or visit friends. And, of course, medical professionals are exposed to COVID-19 and then carry it home and elsewhere.

So once less-than-perfect social distancing begins, there will still be some transmission. The social distancing slows the avalanche but doesn’t stop it immediately. And the two-week delay from infection to symptoms makes this all the worse.

Social distancing is like slamming on the brakes of your car. Hitting the brakes begins the process of slowing down. It doesn’t end it. You can also think of those times when you realize that a pot is boiling over on the stove. You rush over and turn off the gas. But even after you do, the soup keeps rising in the pot and then spills over the sides. Like hitting the brakes of a car, turning off the gas begins, but does not end, the process.

The best explanation I’ve seen is in this Washington Post article, which includes some mesmerizing animations of pandemic. The first animation shows an epidemic spreading wildly in the case of no action. The next shows how China’s forced quarantine slows it, but holes in the quarantine allow the pandemic to leak out into the larger population—and to the rest of the world. Next, you see what happens when 75 percent of a population begins social distancing—the preferred solution in America. Once the distancing begins, cases still rise for a while and only begin declining much later. The final animation shows what happens when you increase compliance to 87.5 percent. But to reiterate, in all these animations, the public health solution—quarantine or social distancing—is already in place when those graphic simulations begin.”

There’s a curious and hopeful end to this little lesson in the mathematics of contagion. As of today, Monday, April 6, the latest projections for Virginia show the epidemic peaking around April 18—two weeks and a day after my friend A.W. asked me her late-night question—not the six to eight weeks forecast at the time. A.W. was always bright, and perhaps she understands the behavior of Virginians better than epidemiologists do.

Photo by ALEX EDELMAN/AFP via Getty Images

If you are interested in speaking with Robert Graboyes about his research, please reach out to media@mercatus.org.

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