The number of new coronavirus cases confirmed in the U.S. has steadily declined in recent days. In New York, the figure has dropped over the past month. The numbers have also plunged in hard-hit Massachusetts and Rhode Island, and some states, including Vermont, Hawaii and Alaska, are reporting few new cases at all.

But that progress is tenuous and uncertain.

The nation has reached a perilous moment, embracing signs of hope and beginning to reopen businesses and ease the very measures that slowed the virus, despite the risk of a resurgence. With more than two-thirds of states significantly relaxing restrictions on how Americans can move about over the last few weeks, an uptick in cases is widely predicted.

Months after the virus began spreading, only about 3% of the population has been tested for it, leaving its true scale and path unknown even as it continues to sicken and kill people at alarming rates. More than 20,000 new cases are identified on most days. And almost every day this past week, more than 1,000 Americans died from the virus.

“We’re seeing a decline; undoubtedly, that is something good to see,” Jeffrey Shaman, an epidemiologist at Columbia University, said. “But what we are also seeing is a lot of places right on the edge of controlling the disease.”

The slowing of new cases is a stark change from two weeks ago, when coronavirus cases were stuck on a stubborn plateau nationally and case numbers were rising in many states. As of Friday, new cases were decreasing in 19 states and increasing in three, while staying mostly the same in the rest, according to a database maintained by the New York Times.

Encouraging signs have emerged in some of the hardest-hit places.

In New Orleans, where hundreds of new cases were being identified each day in early April, fewer than 50 have been announced daily in the last three weeks. In the Detroit area, which saw exponential case growth beginning in late March, numbers have fallen sharply. And in Cass County, Ind., where a meatpacking outbreak sickened at least 900 people, only a handful of cases have been reported most days this past week.

Even as many large cities saw their cases drop, increasing infections continue to be reported in parts of rural America. Some communities that have been fighting to get outbreaks under control finally appear to have succeeded, but have little idea how long it will last.

In Sioux Falls, S.D., where the virus sickened more than 1,000 people at a Smithfield pork processing plant, the outbreak appears to be slowing, Mayor Paul TenHaken said. More than 4,000 Smithfield employees, along with their family members and close contacts, were recently tested.

Yet the mayor fears that his city’s progress could be temporary. On Monday, the plant will begin slaughtering hogs again. Hundreds of employees will be back together at work.

“I’ll be honest, it makes me nervous,” TenHaken said. “We’ve seen how a zero-case facility can become a 1,000-case facility.”

Epidemiologists pointed to one overarching reason for the decline in new cases: the success of social distancing.

Americans began to change their behavior in March, and it has undoubtedly helped control the spread of the coronavirus. Between mid-March, when public officials began to close schools and some workplaces, and late April, when the restrictions were lifted or eased in many states, 43.8% of the nation’s residents stayed home, according to cellphone data analyzed by the Times.

The major clusters of cases that have arisen have been almost exclusively in three settings without effective social distancing: nursing homes, correctional facilities and food-processing plants.

But in settings where distancing took place, the results have been overwhelming, researchers say. More than 70% of the U.S. population lives in counties where coronavirus cases were reduced as a result of less time spent outside the home, according to one estimate by a research team led by Yale economists. Without government orders to stay at home, 10 million more people in the U.S. would have been infected with the virus by the end of April, suggested a paper published this past week in the journal Health Affairs.

Why things got better

“There’s this disconnect of why it got better,” said Rockford, Ill., Mayor Thomas McNamara, who has repeatedly stressed to his constituents that it is not yet time to relax the measures that contributed: “Social distancing, stay at home, wear your face covering.”

The challenge has been convincing impatient Americans to continue taking precautions to continue to slow the spread of the virus while a cure or vaccine remains far out of reach.

“I just received an e-mail from someone yesterday who said, ‘I don’t think people in our community are taking it seriously,’ ” said Kelly Chandler, public health division manager for Minnesota’s Itasca County, which has 42 cases and six deaths.

Influxes of new cases are already turning up in some places that had seemed to tamp down earlier outbreaks.

In Arizona, which began reopening its economy without seeing a sustained drop in cases, infection numbers have continued to rise. More than 13,100 cases had been identified as of Friday. In Alabama, case numbers have grown since the state began to reopen its economy.

Along with cases, the number of deaths has slowed nationally.

Case and death reports vary greatly by day of the week, with spikes around midweek and steep drops on weekends. But on eight of the past nine days, there have been fewer deaths announced than there were seven days prior, an indication that the virus’ toll seems to be easing. More than half of the 24 counties that have recorded the most coronavirus deaths, including Oakland County, Mich., and Hartford County, Conn., are seeing sustained declines.

Deaths are a lagging sign of the virus’ progression because people who die of COVID-19 were typically infected three weeks earlier. But because death counts are not distorted by uneven testing practices, they are “a very clearly observed indicator,” said Nicholas Reich, a biostatistician at the University of Massachusetts, Amherst, who has begun to synthesize the projections of deaths produced by several modeling teams on a weekly basis. The “ensemble” model released last Tuesday sees the number drifting down from about 10,000 this week to about 7,000 in the first week of June.

Still, even with the slowing growth in new cases and deaths, the cumulative death toll in the U.S. is projected to reach about 113,000 by June 6, according to Reich’s latest ensemble model.

The effects of relaxing of restrictions on how Americans move about remain ahead. As more states lifted limits on businesses and movement, about 25 million more people ventured outside their homes on an average day last week than during the preceding six weeks, the analysis of cellphone data found.

But the lag after states reopen, combined with insufficient testing, may mask a rebound until it is underway for several weeks.

“At this point, there is uncertainty,” said Alessandro Vespignani, director of the Network Science Institute at Northeastern University, who has been modeling the path of the virus. “Probably the next week will be one of the crucial ones because if we see more decrease of cases we are still on a ‘good’ trajectory — if not, it really might be more problematic for the future.”