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Restaurants, gyms and coffee shops rank high among locations where the coronavirus is most likely to spread outside the home. That’s according to a newly published report based on data from millions of Americans, tracked by their phones as they went about daily life during the pandemic’s first wave.

The study provides statistical support for a strategy built around limiting capacity at indoor venues — such as capping crowds at 20 percent — while allowing those locations to remain open. The researchers contend that such a strategy can make a huge dent in the infection rate while causing a far more modest drop in the total number of visits to those venues.

Starting with a “very simple” epidemiological model, the researchers superimposed the cellphone mobility data and pressed play on a simulation of viral spread, said Northwestern University epidemiologist Jaline L. Gerardin.

The predicted infections largely matched actual coronavirus caseloads in the studied regions, as tallied by the New York Times.

“Based on the data, the main result is that mobility data can be useful for predicting the spread of covid-19. This is extremely helpful to policymakers,” said Solomon Hsiang, director of the Global Policy Laboratory at the University of California at Berkeley, who has modeled the effects of several nations’ pandemic policies and was not involved with this work.

There are a few caveats. The researchers’ model cannot say with certainty where exposure occurred. Nor was it able to capture information about nursing homes or schools, largely because that phone-based location data was unavailable. And it does not account for environmental factors such as ventilation, or the protective behaviors that have become more widespread since the outbreak began.

“It is important to emphasize that many behaviors, such as wearing masks, washing hands and providing services outdoors, reduce transmission,” Hsiang said.

Tuesday’s report in the journal Nature, by Gerardin and her colleagues at Northwestern and Stanford universities, used anonymized data from 98 million Americans living in Chicago, Washington, New York City and seven other metro areas. The scientists focused on movement within 57,000 census block groups — the small geographical units that make up census tracts — from March to May 2.

In those regions, the scientists traced visits to 550,000 cafes, hotels and other venues. Geospatial data, which the company SafeGraph provided to the scientists, showed how long people remained in locations, how frequently they visited and how crowded those places were.

Certain venues — places of worship, full-service restaurants and gyms — disproportionately contributed to infections. In Chicago, for instance, 10 percent of sites accounted for 85 percent of predicted infections.

The study discerned another pattern: Lower-income people, many of them essential workers, were less able to reduce their mobility during shutdowns and more likely to be exposed to crowded venues. Within low-income neighborhoods, with higher percentages of residents who are people of color, more people would be infected, which mirrors real-life patterns of transmission.

“They have to get to work; they are in occupations that are deemed vital,” said Northwestern sociologist Beth Redbird, a study co-author. Public-facing jobs may put people at higher risk of exposure — one recent study found 20 percent of workers at a Boston grocery store had the coronavirus in May.

This study suggested a grocery store would be twice as dangerous for a person in a low-income neighborhood as a person in a high-income one. The authors hypothesized that this was because those stores had nearly 60 percent more visitors per square foot per hour, and they shopped there longer on average.

Earlier models indicated that timing of shutdown orders was vital. One estimated that 36,000 lives would have been saved if social distancing rules in mid-March had begun a week sooner. This model indicates that setting caps on crowds is powerful, too.

“Reducing occupancy is very effective — even more effective than the timing of the intervention,” Redbird said.

John Carlo, a Dallas physician who specializes in public health, applauded the new study for highlighting the importance of the density of crowds in indoor venues such as grocery stores.

“It’s not just the activity itself; it’s the density of that activity. It’s one thing to go to a supermarket, and it’s another thing to go to a crowded supermarket,” Carlo said. He said if he shops at 7 a.m., there may be no one in the store, but “if I go Sunday afternoons, just before the Cowboys game, it’s jam-packed.”

Jeffrey Shaman, a Columbia University epidemiologist who also has worked on models of how the virus spreads, praised the new study but cautioned that it does not answer precisely where the virus is being spread.

“We can’t say, ‘This is a prescription to say you gotta shut down your pizza joints and your banks as opposed to your grocery stores,’ or whatever. This paper takes us a little closer to that, but I don’t know if we’re ever going to achieve it,” Shaman said.

Nor is he convinced that, with daily new infections topping 100,000, a nuanced approach to controlling the pandemic is going to work as the country endures a massive autumn surge and rising hospitalizations from covid-19, the disease caused by the virus.

“I’m not so sure that trying to go at it with a scalpel is going to be effective. We may need the sledgehammer approach. I struggle with that,” Shaman said.

More than nine months into the pandemic, there remains a great deal of uncertainty about the risks posed by different activities in different venues, and how to mitigate the risks in the most efficient manner.

In June, the Texas Medical Association surveyed 14 Texas physicians, including Carlo, asking them to rate activities based on risk levels. That resulted in a chart listing different activities on a 1-to-10 risk level, with opening the mail being the least risky (1) and going to a bar, a sports stadium, a music concert or a religious service with more than 500 participants the most risky (9).

That was not a scientific study but, rather, an aggregation of wisdom from some doctors. But the chart was distributed globally and translated into many languages — a sign of how much people wanted to know about how they might be able to safely coexist with the virus.

Meanwhile, governors and mayors and their health department officials struggled to decide how to impose restrictions and for how long. Guidance offered by the Centers for Disease Control and Prevention had no regulatory power and was sometimes disregarded by local and state governments eager to reopen.

Brute-force shutdowns — closing nonessential businesses, banning sporting events, imposing curfews, removing the rims and nets from basketball backboards — were employed in many states in March and April during the first desperate weeks of the pandemic, when infections were spreading exponentially in the Northeast and some large cities. Hospitals feared they would soon have to ration care.

Those shutdowns reversed the course of the crisis in the United States while also crashing the economy. Many states reopened while still having large numbers of new infections, a premature move that health experts blame for the subsequent national spikes in cases in the summer and now again in the fall.

Shutdowns remain unpopular with public officials and with many scientists and doctors who see the collateral effects on people who are economically vulnerable or need steady medical care or emergency treatment for health issues not related to covid-19. And so officials have hoped to find nuanced approaches to rising case numbers — something short of shutdowns but still effective at reversing the dangerous trends.

Redbird said she plans to use mobility data to observe how the pandemic has warped our culture. “What I’m going to watch for: How long does it take for the pattern of human interaction to return to normal — or, even, if it does,” she said.

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