“We saw something we hoped wasn’t happening, but it’s there,” said Lei Zhang, lead researcher and director of the Maryland Transportation Institute at the University of Maryland. “It seems collectively we’re getting a little tired. It looks like people are loosening up on their own to travel more.”

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Zhang said he anticipates the number of people staying home will continue to drop as some states begin allowing businesses, beaches and other public facilities to reopen. That process began last week in South Carolina and Georgia.

Public health experts say any data showing widespread public resolve or cooperation beginning to wane is noteworthy. Because this is the first U.S. pandemic in 100 years, they don’t know how long people are willing to tolerate cabin fever for the greater good.

They say they’re not surprised, however, that a slide occurred in a week that saw the first highly publicized challenges to such orders by protesters and President Trump, who tweeted his support to “liberate” states from shutdowns. The White House also released federal guidelines that week for states seeking to reopen their economies. And a growing number of governors, including in Texas, Minnesota and Vermont, set dates for when they planned to gradually lift restrictions.

By April 17, the researchers found, the share of people presumed to have stayed home — meaning their phones didn’t move at least a mile that day — declined from a national average of 33 percent to 31 percent, compared with the previous Friday. That came after six weeks of the staying-home percentage increasing or holding steady.

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The number of work trips remained about the same. However, the average number of personal daily trips grew to 2.5 per person, up from 2.4 the previous Friday — a 4 percent increase. Trips between counties and states also increased.

Because the study’s sample size is so large — more than 100 million cellphones observed monthly — even slight changes are statistically significant, Zhang said.

Dr. Wilbur Chen, an associate professor at the University of Maryland School of Medicine, said it’s too soon to know whether the findings reveal a one-week blip or the start of a trend. Chen, a member of Maryland Gov. Larry Hogan’s (R) covid-19 task force, said he’s keeping a close eye on the data, but researchers won’t know for several weeks if more travel led to more coronavirus hospitalizations or deaths — the two most reliable measures of the virus’s spread.

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“But it all makes sense,” Chen said. “If people are out and about, there’s more risk of transmission, and when there’s transmission, you have more cases of hospitalizations and deaths.”

George Rutherford, an epidemiology professor at the University of California at San Francisco, said he’s concerned to hear that more people are venturing out while infections remain on the rise in much of the country.

“We’re going to have to do this carefully,” Rutherford said of states beginning to ease restrictions. “Letting people decide for themselves because they’re bored is not a good way to do it. . . . This is not the time to be letting up.”

Experts have theories about why the week of April 13, the most recent data available, became a tipping point. Many homebound Americans hit the mental milestone of the fifth week, technically entering a second month, with no clear end in sight. Even with the boom in video calls and virtual cocktail hours, they say, feelings of loneliness and isolation continue to mount. Balmy spring temperatures also probably drew people out, particularly in warmer regions where a hot, sticky summer will soon descend.

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It’s also no coincidence, they say, that resolve would begin to wane amid the Trump-supported protests, even as most Americans tell pollsters they support stay-at-home requirements.

Lorien Abroms, a public health professor at George Washington University, said it doesn’t help that the public has received “mixed messages,” including Trump’s “tacit support” of the protesters.

“I think the message is getting out that you can give in to your fatigue and say ‘It’s enough,’ ” Abroms said.

Some people also might have mistakenly believed they could safely start bending the stay-at-home rules, experts say, when some governors began to publicly announce how and when their economies would begin to reopen.

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“People can feel it’s coming, so they get more antsy,” said Susan Hassig, an associate professor of epidemiology at Tulane University. “It’s kind of like a kid before Christmas.”

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Governors in Georgia, South Carolina and Tennessee announced reopening dates Monday, after the latest cellphone data was analyzed. However, the percentages of people staying home in those states as of April 17 already were among the lowest in the country, between 23 percent and 26 percent.

Travis Gayles, the chief health officer in Montgomery County, Md., called the potential problem of residents losing patience “an important point that I think every jurisdiction across the country is grappling with in terms of making sure we reinforce our message related to shelter-in-place.”

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Gayles said he wasn’t familiar with the data, but questioned whether Montgomery residents might have ventured out more after the county began requiring shoppers to wear face coverings in stores, pharmacies and other retailers.

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Even so, Gayles said, “The message is very clear. We’re still encouraging folks to stay home and only come out when they need to,” such as to go to work or the grocery store.

The reversal first became apparent last week, when the Maryland researchers continued to analyze the movements of smartphones via location data from apps. The aggregated and anonymous data, while imperfect, is an easily obtainable and consistent way to measure how much people move about, Zhang said. He said researchers are sharing the mobility data with government officials and epidemiologists modeling the spread of covid-19.

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The nationwide drop in the researchers’ “social distancing index” started April 14. That was one day before thousands of protesters in Michigan received national attention for jamming roads around the state capitol, demanding that the restrictions be eased and people be allowed to return to work.

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The social distancing index reflects how much people stay home, as well as how much and how far they travel by plane, car, transit, bicycle and on foot, Zhang said. Phones that didn’t make any stops of 10 minutes or more, such as those on people out for a bike ride or walk with the dog, were counted as staying home, Zhang said.

In the Washington region, the District and its suburbs all saw an increase in travel and a 1 percent to 5 percent drop in people staying home by April 17. The biggest drop occurred in Arlington County, where 50 percent of residents stayed home, down from 55 percent the previous Friday. However, Arlington tied with the District for the highest percentage in the region.

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In Montgomery, the number of those staying home fell from 45 percent to 43 percent, while Prince George’s County fell from 37 percent to 34 percent. In Northern Virginia, Fairfax County dropped from 46 percent to 44 percent, while Prince William County ended the week with 34 percent and Loudoun County with 37 percent.

Of course, the data has its limits. Zhang said researchers are still trying to determine where people are going. If someone takes a round-trip drive to walk alone in the woods, for example, they would be counted as making two trips, even though they weren’t any more likely to spread or catch the virus.

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Hassig, of Tulane, said the data is interesting because the United States has such limited experience requiring residents to stay home for lengthy periods. Any quarantines typically are small enough that local health officers can check in daily to monitor people’s symptoms and encourage them to stay isolated. Moreover, she said, most last a maximum 14 to 21 days. “We can usually reduce the likelihood of substantial quarantine fatigue,” Hassig said. “. . . On this massive scale, the support and encouragement can get lost.”

The coronavirus stay-at-home orders are far less restrictive than quarantines, but public health experts say convincing people to stay in will become harder as the weeks pass. The more effectively such orders lower rates of infection, they say, the more some people will incorrectly assume they’re no longer necessary.

Most importantly, experts say, governments wanting to discourage people from venturing out need to better understand why they’re doing so. The response to restlessness, for example, might be to reopen larger parks or close more streets to traffic to allow people to get outdoors at safe distances. If some people are starting to drive for Uber or Lyft because they lost their retail job, the response might be more financial aid. For those feeling cut off, experts say, government messages of sympathy and compassion would help.