Disease modelers find that tens of thousands of U.S. deaths could have been prevented with earlier lockdowns.

If the United States had begun imposing social-distancing measures one week earlier in March, about 36,000 fewer people would have died in the pandemic, according to new estimates from Columbia University disease modelers.

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.

On March 16, President Trump urged Americans to limit travel, avoid groups and stay home from school. Mayor Bill de Blasio of New York City closed schools on March 15, and Gov. Andrew M. Cuomo of New York issued a stay-at-home order that took effect on March 22.

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.

In Connecticut, flags that had been lowered to half-staff during the somber peak of the pandemic were raised high again to signal the state’s return to business.

In Kentucky, gift shops opened their doors. South Carolina will let mini-golf, water parks, amusement parks and other attractions reopen for Memorial Day weekend, Gov. Henry McMaster said on Wednesday.

And across Alaska, restaurants, bars and gyms, which have already been seeing customers for weeks, were getting ready to rev back up to full capacity. “It will all be open,” Gov. Mike Dunleavy said, “just like it was prior to the virus.”

As of Wednesday, all 50 states had begun to reopen to some degree, two months after the outbreak thrust the country into lockdown. But vast variations remain in how states are deciding to open up, with some forging far ahead of others. Many began to reopen despite not meeting White House guidelines for progress against the virus, and newly reported cases have been increasing in some states, including Minnesota and Texas, that are moving to ease restrictions. Public health officials warn that moving too fast could risk more outbreaks.

The dynamic has left many business owners and customers to decide for themselves what they think is safe.

“It is still a little scary, considering we don’t exactly know what this is,” said Ipakoi Grigoriadis, whose family owns Pop’s Family Restaurant in Milford, Conn., a diner that reopened its outdoor seating on Wednesday morning.

“It is quite exciting to see our customers we haven’t seen in a while,” she said. But it was not business as usual: Pop’s, like other Connecticut restaurants, now offers only outdoor seating and plans to gradually ramp up to 50 percent capacity. Servers are gloved and masked, and patrons are expected to wear masks as well, except when they are eating and drinking.

In New Jersey and many parts of New York State, the reopening has been more limited, with only curbside pickup at retail stores and allowances for certain industries.

Governors are increasingly facing intense pressure to reopen, as millions of Americans have lost their jobs and the unemployment rate reached a staggering 14.7 percent. But reopening in Texas, where businesses have been allowed to operate at 25 percent capacity for weeks, looks far different than it does in Illinois, where stores are still limited to curbside pickup.

In a medical research project nearly unrivaled in its ambition and scope, volunteers around the world are rolling up their sleeves to receive experimental vaccines against the coronavirus only months after it was discovered.

Companies like Inovio and Pfizer have begun early tests of candidates in people to determine whether the vaccines are safe. Researchers at the University of Oxford in Britain say they could have a vaccine ready for emergency use as soon as September.

Moderna Therapeutics on Monday announced encouraging results of a safety trial of its vaccine in eight volunteers. There were no published data, but the news alone sent hopes — and the company’s stock — soaring.

In labs around the world, there is now cautious optimism that a vaccine, and perhaps more than one, will be ready sometime next year. With many states and nations anxious to ease restrictions and reopen their economies despite the risk of further outbreaks, the race to create and manufacture a vaccine is more urgent than ever.

Scientists are exploring at least four approaches to creating a vaccine. The urgency is so great that they are combining trial phases and shortening a process that usually takes years.

“What people don’t realize is that normally vaccine development takes many years, sometimes decades,” said Dr. Dan Barouch, a virologist at Beth Israel Deaconess Medical Center in Boston. “And so trying to compress the whole vaccine process into 12 to 18 months is really unheard-of.”

“If that happens,” he added, “it will be the fastest vaccine development program ever in history.”

Even if scientists develop a vaccine that proves to be safe and effective, hurdles will remain. With nearly all of humanity vulnerable to the virus, officials will have to figure out how to speed the mass production of vaccines.

But signs of progress continue to appear. Researchers reported Wednesday that a prototype vaccine had protected monkeys from the virus, a finding that offered new hope for effective human vaccines.

“To me, this is convincing that a vaccine is possible,” said Dr. Nelson Michael, the director of the Center for Infectious Diseases Research at Walter Reed Army Institute of Research.

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 a torrent of 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. Evacuees, wearing face masks, arrived at schools repurposed as emergency shelters. Some slept in their cars because of worries about the coronavirus.

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.

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.

Prisons and jails across the country have been hot spots for the spread of the virus. In April, Attorney General William P. Barr ordered the prisons bureau, which is part of the Justice Department, to determine which federal inmates could be safely released to home confinement. As of May 13, more than 2,500 inmates had been, according to bureau data.

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.

Churches say they will defy Minnesota’s governor and resume in-person services.

Some Catholic and Lutheran churches in Minnesota plan to resume in-person worship services later this month in defiance of the governor’s orders, becoming the latest religious organizations applying pressure on political leaders to allow large religious gatherings.

Archbishop Bernard A. Hebda, the top Catholic official in the Minnesota diocese that includes St. Paul and Minneapolis, said in a letter to Gov. Tim Walz that he was concerned that the state had allowed stores and other businesses to reopen, with limitations, but had limited religious gatherings to no more than 10 people.

“We have concluded that many of our parishes are ready to safely resume Mass, albeit in a limited way, next week,” Archbishop Hebda wrote. The presidents of Minnesota’s two districts of the Lutheran Church-Missouri Synod wrote a similar letter to the governor, saying they were allowing Lutheran churches to reopen next Tuesday and to worship next Sunday, May 31.

Becket, a religious liberty group whose lawyers are among those representing the Minnesota churches, said in a statement that Minnesotans needed church services.

“If malls, casinos, liquor stores, bars and restaurants are reopening, why can’t Minnesota churches?” Eric Rassbach, a vice president and senior lawyer at Becket.

A spokesman for Mr. Walz, a Democrat, said the governor would be meeting with the Archdiocese this week and that he “understands the toll this pandemic is taking on the spiritual health of Minnesotans.”

“As the Governor has said, this is a challenging situation for him personally and a challenging situation for him as a public official charged with protecting the health and safety of Minnesotans,” Teddy Tschann, the spokesman, said in a statement.

The Minnesota churches joined opponents to restrictions on religious gatherings in several states, including in North Carolina, where a federal judge last weekend sided with churches who had sued over Gov. Roy Cooper’s efforts to restrict religious gatherings to 10 people. Mr. Cooper, a Democrat, said he would not appeal the ruling.

New York loosened its restrictions on religious gatherings on Wednesday, with Gov. Andrew M. Cuomo, a Democrat, saying that religious gatherings of up to 10 people could resume on Thursday if attendees wear masks and socially distance. The figure is particularly significant for Jewish congregations, where a minyan, defined as 10 people over the age of 13, is required for a worship service.

“I think that even at this time of stress and when people are so anxious and so confused, I think those religious ceremonies can be very comforting,” Mr. Cuomo said. “But we need to find out how to do it, and do it safely and do it smartly.”

And five lawyers with the Justice Department said in a letter to California on Tuesday that the state’s restrictions to combat the virus discriminated against religious institutions. The lawyers, which included all four U.S. attorneys assigned to California, objected to the state’s reopening plan, which seemed to allow restaurants and shopping malls to reopen before religious institutions could hold in-person services. They also objected to the state’s current policy limiting how members of the clergy could be classified as essential workers.

New health risks could be waiting when office buildings reopen.

Closed office buildings that were once in constant use may have been accumulating health risks during the pandemic.

As lockdowns are lifted, bacteria that built up internally in stagnant water, especially in the plumbing, may cause health problems for returning workers if the issue is not properly addressed by facilities managers. Employees and guests at hotels, gyms and other kinds of buildings may also be at risk.

A single small outbreak can sicken many people. The deaths of 12 people from Legionnaires’ disease were linked to the water crisis that started in Flint, Mich., in 2014 after the city changed its water source and officials failed to inform the public of quality problems.

Most worrying, Legionnaires’ disease tends to affect people with compromised immune systems. “Covid patients and survivors could be more vulnerable to this, so when they go back to work we might be concerned about another infection,” said Caitlin Proctor, a postdoctoral fellow at Purdue University.

It was unclear how closely the guidelines would be followed. The C.D.C. said that restaurants “may consider” a number of strategies to maintain healthy environments, including: “Avoid offering any self-serve food or drink options, such as buffets, salad bars and drink stations.”

When Vice President Mike Pence visited Beth’s Burger Bar in Orlando, Fla., on Wednesday with Gov. Ron DeSantis to call attention to restaurants reopening, he was filmed filling his own cup at a self-serve soda fountain. Mr. Pence — who leads the White House’s coronavirus task force and whose press secretary, Katie Miller, tested positive for the virus this month — was not wearing a mask.

Here are some key elements from the C.D.C. guidance:

If a person in a school building tests positive, schools should evaluate the risk and consider a brief dismissal of about two to five days, to clean and disinfect the building, coordinate with local health officials and contact trace. The C.D.C. offers different measures based on the level of community spread.

As restrictions across the country on restaurants and bars ease, the C.D.C. recommends owners give workers at a higher risk of getting sick a job that limits the person’s interaction with customers. The agency also suggests opening initially with limited seating to allow for social distancing. Once fully reopened, the C.D.C. recommends having a clear policy about when employees should stay home if sick and rules on hygiene, including at times wearing face coverings.

When mass transit resumes its full service, the agency recommends being prepared to adjust routes based on the different levels of virus spread and to coordinate with local health officials about prevention strategies, such as wearing a face covering.

For businesses that provide child care during the pandemic, the C.D.C. recommends having plans in place, for example, to have substitute workers if staff members are sick, and requiring staff and children older than 2 to wear face coverings.

The guidance describes the balance of slowing the virus’s spread with the economic threat of shuttering most businesses, and largely mirrors a draft version that was previously shelved by the White House, but with some changes.

The document omits a section on “communities of faith” that had troubled Trump administration officials and also tones down the guidance in several instances. For example, language that initially directed schools to “ensure social distancing” became “promote social distancing,” and the phrase “if possible” was added in several sentences.

While many roads and highways across the United States have become ghost towns during the pandemic, new data shows that the people still driving on them are dying more frequently.

There was a 14 percent increase in fatality rates per miles driven in March compared with the year before, according to preliminary data reports released by the National Safety Council.

There were 8 percent fewer roadway deaths over all, and the number of miles driven fell 18.6 percent.

It is possible that speeding and reckless driving on emptier roads — as people follow stay-at-home orders — have led to a disproportionate number of deaths.

“Disturbingly, we have open lanes of traffic and an apparent open season on reckless driving,” Lorraine M. Martin, the council’s chief executive, said in a statement on Wednesday. She added that law enforcement and health care workers “are rightly focused on coronavirus patients and should not be overwhelmed by preventable car crashes.”

Less than a week after lawmakers approved a major rule change, Speaker Nancy Pelosi on Wednesday formally initiated the remote work period for the House, jump-starting a 45-day period when remote voting can be used in the chamber.

With the move, the House will now be able to use proxy voting, which allows lawmakers to give specific instructions on each vote to a colleague authorized to vote on their behalf. Votes are expected in the chamber next week, and several lawmakers had previously expressed frustration with the need to travel to Washington during the pandemic.

The announcement came after the sergeant-at-arms, in consultation with Dr. Brian P. Monahan, the Capitol physician, sent Ms. Pelosi a letter formally notifying her of “an ongoing public health emergency.”

In direct contrast, however, Senator Mitch McConnell of Kentucky on Wednesday highlighted the Senate’s ongoing presence in Washington, outlining how “over here in the United States Senate, the lights are on, the doors are open, and we are working for the American people.”

Mr. McConnell, the majority leader, thanked Dr. Monahan — a Navy doctor whose office is responsible for the care of both chambers and the Supreme Court — for his continued guidance, saying that it had allowed the Senate to operate “smartly and safely” during the pandemic.

“Now that our Country is ‘Transitioning back to Greatness’, I am considering rescheduling the G-7, on the same or similar date, in Washington, D.C., at the legendary Camp David,” Mr. Trump wrote on Twitter. “The other members are also beginning their COMEBACK. It would be a great sign to all – normalization!”

It is unclear whether Mr. Trump has discussed the idea with other Group of 7 leaders and how willing they would be to travel abroad with the large staff and security entourages they require.

The French government said that President Emmanuel Macron was “prepared to go to Camp David, health conditions permitting,” given the importance of the group in the pandemic response.

After the virus struck, the Group of 7 agreed to hold the gathering by video for the first time. It is scheduled for June 10-12. The group is made up of the United States, Britain, Canada, France, Germany, Italy and Japan.

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Reporting was contributed by Reed Abelson, Mike Baker, Karen Barrow, Katie Benner, Alan Blinder, Nicholas Bogel-Burroughs, Julie Bosman, Ben Casselman, Emily Cochrane, Michael Cooper, Nick Corasaniti, Michael Crowley, Elizabeth Dias, Caitlin Dickerson, Reid J. Epstein, Sheri Fink, Neil Genzlinger, Thomas Gibbons-Neff, James Glanz, Michael Gold, Kathleen Gray, Max Horberry, Anemona Hartocollis, Shawn Hubler, Annie Karni, Dan Levin, Sarah Mervosh, Andy Newman, Sarah Maslin Nir, Jan Ransom, Campbell Robertson, Anna Schaverien, Knvul Sheikh, Kaly Soto, Chris Stanford, Sheryl Gay Stolberg, Eileen Sullivan, Vanessa Swales, Hiroko Tabuchi, Jim Tankersley, Daniel Victor, David Waldstein, Noah Weiland and Carl Zimmer.

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