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.

“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.

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

The coronavirus pandemic has produced a somber Thursday ritual: the tally of unemployment claims across the United States.

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.

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.

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.

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.”

“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.

Officials said there were no known injuries or deaths tied to the floods.

As news of the disaster spread, Mr. Trump threatened on Twitter to withhold federal funds to Michigan if the state proceeded to expand vote-by-mail efforts. The president then followed up by saying that the Federal Emergency Management Agency and the military had been deployed to Michigan to assist with disaster response.

Global updates: China imposes a quarantine in its northeast.

The latest outbreak of coronavirus cases in China is concentrated in Jilin, a northeastern province of 27 million people that sits near the borders with Russia and North Korea. Jilin has reported only about 130 cases and two deaths, but experts there have warned of a potential “big explosion.”

Tips for biking as a family.

The humble bicycle is the surprise star of lockdown. With youth sports on hold, car traffic down 75 percent or more throughout the United States (according to the research firm StreetLightData), and cooped-up children doing parkour on the living room furniture, family bike rides have never sounded better. Here are some tips for a safe and successful trip.

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, Kaly Soto, Chris Stanford Alexandra Stevenson.

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