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And if the country had begun locking down cities and limiting social contact on March 1, two weeks earlier than when most people started staying home, a vast majority of the nation’s deaths — about 83 percent — would have been avoided, the researchers estimated.

The enormous cost of waiting to take action reflects the unforgiving dynamics of the outbreak that swept through American cities in early March. Even small differences in timing would have prevented the worst exponential growth, which by April had subsumed New York City, New Orleans and other major cities, the researchers found.

“It’s a big, big difference,” said Jeffrey Shaman, an epidemiologist at Columbia and the leader of the research team. “That small moment in time, catching it in that growth phase, is incredibly critical in reducing the number of deaths.”

The findings are based on infectious-disease modeling that gauges how reduced contact between people starting in mid-March slowed transmission of the virus.

But in cities like New York, where the virus arrived early and spread quickly, those actions were too late to avoid a calamity. Dr. Shaman’s team modeled what would have happened if those same changes had taken place one or two weeks earlier and estimated the spread of infections and deaths until May 3.

The results show that as states reopen — all 50 states had eased restrictions somewhat as of Wednesday — outbreaks can easily get out of control unless officials closely monitor infections and immediately clamp down on new flare-ups.

And they show that each day that officials waited to impose restrictions in early March came at a great cost.

The Labor Department said Thursday that 2.4 million unemployment claims were filed last week. That means new claims are leveling off, but not declining, and brings the nine-week total to about 38 million.

A recent household survey from the Census Bureau suggests that the pain is widespread: 47 percent of adults said they or a member of their household had lost employment income since mid-March. Nearly 40 percent expected the loss to continue over the next four weeks.

And there is increasing concern that many jobs are not coming back, even for those who consider themselves laid off temporarily.

Nicholas Bloom, a Stanford University economist who is a co-author of an analysis of the pandemic’s effects on the labor market, estimates that 42 percent of recent layoffs will result in permanent job losses. “I hate to say it, but this is going to take longer and look grimmer than we thought,” he said of the path to recovery.

The coronavirus pandemic has devastated nursing homes in the United States, contributing to at least 20 percent of the nation’s Covid-19 death toll. The impact has been felt in cities and suburbs, in large facilities and small, in poorly rated homes and in those with stellar marks.

A collaboration by reporters at The New York Times, The Baltimore Sun, KPCC/LAist and The Southern Illinoisan illustrates the toll.

More than 60 percent of nursing homes where at least a quarter of the residents are black or Latino have reported at least one coronavirus case, a New York Times analysis shows. That is double the rate of homes where black and Latino people make up less than 5 percent of the population.

In the suburbs of Baltimore, for example, workers at one nursing home said they were given rain ponchos to protect from infection. Twenty-five employees at the facility, where most residents are African-American, tested positive for the coronavirus.

In East Los Angeles, a staff member at a predominantly Latino nursing home where an outbreak emerged said she was given swimming goggles before professional gear could be obtained. She said she later tested positive for the virus.

The scientist, Moncef Slaoui, is a venture capitalist and a former longtime executive at GlaxoSmithKline. Most recently, he sat on the board of Moderna, a Cambridge, Mass., biotechnology firm with a $30 billion valuation that is pursuing a coronavirus vaccine. He resigned when President Trump named him to the new post as chief adviser for Operation Warp Speed, the federal drive for coronavirus vaccines and treatments.

Just days into his job, the extent of Dr. Slaoui’s financial interests in drug companies has begun to emerge: The value of his stock holdings in Moderna jumped nearly $2.4 million, to $12.4 million when the company released preliminary, partial data from an early phase of its candidate vaccine trial that helped send the markets soaring on Monday.

Dr. Slaoui sold his shares on Tuesday, and the administration said he would donate the increased value to cancer research.

But the Moderna stock is just one piece of his pharmaceutical portfolio, much of which is not public. And some ethics and financial securities experts have voiced concerns about the arrangement Dr. Slaoui struck with the administration.

In agreeing to accept the position, Dr. Slaoui did not come on board as a government employee. Instead, he is on a contract, receiving $1 for his service. That leaves him exempt from federal disclosure rules that would require him to list his outside positions, stock holdings and other potential conflicts. And the contract position is not subject to the same conflict-of-interest laws and regulations that executive branch employees must follow.

States and cities around the country have begun with varying degrees of success to ramp up efforts to put contact tracing in place on a large scale. Last week, Gov. Philip D. Murphy of New Jersey said that his state would hire up to several thousand contact tracers to assist the 800 now working for local and county health departments.

Twenty miles to the west of New York City, Paterson, a poor, largely nonwhite city of about 150,000, has been tracing the virus at a level that could be the envy of larger cities. The team has been able to successfully investigate and trace about 90 percent of the more than 5,900 positive Covid-19 cases in Paterson, said the city’s top health officer, Dr. Paul Persaud.

As of Saturday, 306 Paterson residents have died, giving the city a Covid-19 death rate of 5.1 percent among those who have tested positive for the disease, compared to 7 percent statewide.

Perry N. Halkitis, the dean of the Rutgers School of Public Health, said that it was impossible to know how much contact tracing has helped control the spread of the virus. But contact tracing, he noted, “is one of the few tools that we actually have in the absence of a vaccine.”

Michigan, one of the states hardest hit by the pandemic, was confronted by a new emergency on Wednesday after days of torrential rainfall breached two dams the night before. Thousands of residents were forced to flee their homes, and much of Midland, the home of Dow Chemical and some of its plants, was submerged.

Gov. Gretchen Whitmer, a Democrat who has clashed with Republicans over the state’s response to the coronavirus, found herself in an ever more complicated position: urging residents to flee their homes while maintaining social distancing to avoid the spreading virus. Midland County has had 76 known cases, a relatively small number in a battered state.

“It’s hard to believe that we’re in the middle of a 100-year crisis, a global pandemic, and we’re also dealing with a flooding event that looks to be the worst in 500 years,” Ms. Whitmer said.

For years, federal regulators had warned that a dam in nearby Edenville Township could rupture and had chided its corporate owner, Boyce Hydro Power, for failing to make required structural changes. On Tuesday night, the dam gave way, sending water gushing into streets and threatening Dow Chemical, the producer of plastics that sits along the Tittabawassee River. Ten miles south of the Edenville dam, water was spilling over a second dam, a structure feared to be on the verge of collapse on Wednesday.

By then, floodwaters had crept high enough that red stop signs were barely peeking out in downtown Midland, a city of 42,000 residents about 130 miles northwest of Detroit.

Michael D. Cohen, President Trump’s former personal lawyer and fixer, will be released from a federal prison on Thursday on furlough, a Bureau of Prisons spokeswoman said on Wednesday. He had asked to be released over health concerns tied to the coronavirus.

Mr. Cohen’s release came a week after Paul Manafort, Mr. Trump’s onetime campaign chairman, was released into home confinement in Northern Virginia because of underlying health conditions and concerns about the virus. He had been serving a federal prison sentence of seven and a half years.

In many states, the beaches are open or opening for Memorial Day weekend. Exciting news, but no activity is going to be risk-free in a pandemic. Here are some things to remember when planning a beach day: know the rules, consider your beach’s geography, stay moving or far away, use your own gear and check out the restroom facilities when you arrive.

Reporting was contributed by Karen Barrow, Julie Bosman, Patricia Cohen, Andrew Das, James Glanz, Matthew Goldstein, Abby Goodnough, Kathleen Gray, Maggie Haberman, Sheila Kaplan, Sharon Otterman, Campbell Robertson, Anna Schaverien, Lauren Sloss, Kaly Soto, Chris Stanford and Alexandra Stevenson.