The Elegant Mathematics of Social Distancing

My cousin had to cancel his bar mitzvah, which was planned for Saturday in Washington, DC. Some 100 people were scheduled to be there, but like many houses of worship this week, the synagogue suspended its services to help prevent the spread of the coronavirus. For my cousin, it means postponing the payoff from years of study, and a celebration with friends and family.

Many other Americans are in similar situations during the outbreak of Covid-19, which has sickened more than 1,700 Americans and killed more than 40, according to an online tally being kept by Johns Hopkins University. Schools, religious institutions, and sports and concert venues have closed. Those who can work from home have been urged to do so. The White House reportedly overruled a proposal from the Centers for Disease Control that would have urged anyone over 60 to avoid airplane travel.

In states and cities around the country, gatherings of 500, 250, or sometimes even 75 people have been forbidden. The term “social distancing”—that is, public health measures to reduce the spread of a highly contagious disease—has become one of those particular pieces of field-specific esoterica that’s vaulted into the American vernacular, like “obstruction of justice” or “security theater.”

But people have lives: weddings to attend, kids’ birthday parties to endure, commutes to make, bonkers grocery store lines to stand in. What is safe right now? What isn’t?

The answer isn’t clear, given what researchers know—and don’t know—about the disease. And even experts aren’t united in their responses.

“This is not black and white,” says Ben Lopman, an infectious disease epidemiologist at Emory University’s Rollins School of Public Health. “We’re trying right now to increase social distancing to slow down transmission of this infection. But that doesn’t mean no human contact for the foreseeable future. It means us all taking sensible steps and doing our part to reduce the amount of interactions we have.”

Go to the grocery store, Lopman says, but maybe take one big trip rather than three smaller ones. Other experts suggest staying about six feet away from other people, if you can. If the person in front of you keeps coughing, maybe choose another line.

To some degree, the sorts of things you should be doing right now depend on who you are. Are you someone at higher risk, like over age 60, or someone with a chronic medical condition like heart disease, diabetes or lung disease? Do you often come into contact with someone with those conditions? Are you exhibiting any Covid-19 symptoms, like fever, cough, or shortness of breath? Have you been in contact with anyone who has? Check any of those boxes, and you might want to be more careful about where you go and who you interact with.

But “if you feel pretty sure that those answers to those questions are ‘no,’ you can get together [with others with similar answers] and play board games,” says Katie Colborn, a biostatistician and assistant professor at the University of Colorado at Denver.

Illustrated woman, speech bubble, virus cell

What Is the Coronavirus?

Plus: How can I avoid catching it? Is Covid-19 more deadly than the flu? Our in-house Know-It-Alls answer your questions.

“We all have to make contacts with people while we live our lives, what we should aim to do is to limit them, and certainly not to add more,” says William Hanage, an associate professor of epidemiology at Harvard’s Chan School of Public Health. “This may seem silly if your community is not yet reporting infections, but it is best to get used to thinking this way.”

From a mathematical perspective, determining how big a crowd is safe depends on a couple of key questions: How many people in a given area are infected with the disease? And how big is the event? If you know those things, you can estimate the probability of someone getting infected at the event. An elegant “Covid-19 Event Risk Assessment Planner” by the Georgia Tech quantitative biologist Joshua Weitz makes the following calculation: If, say, 20,000 cases of infection are actively circulating the US (far more than are known so far), and you host a dinner party for 10 folks, there’s a 0.061 percent chance that an attendee will be infected. But if you attend a 10,000-person hockey match, there’s a 45 percent chance. Hence the suspension of the NHL season, along with the NBA, March Madness, and Major League Baseball.



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