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The doctor who led the federal agency involved in developing a coronavirus vaccine said on Wednesday that he was removed from his post after he pressed for rigorous vetting of hydroxychloroquine, an anti-malaria drug embraced by President Trump as a coronavirus treatment, and that the administration has put “politics and cronyism ahead of science.”

Dr. Rick Bright was abruptly dismissed this week as the director of the Department of Health and Human Services’ Biomedical Advanced Research and Development Authority, or BARDA, and removed as the deputy assistant secretary for preparedness and response. He was given a narrower job at the National Institutes of Health.

In a scorching statement, Dr. Bright assailed the leadership at the health department, saying he was pressured to direct money toward hydroxychloroquine, one of several “potentially dangerous drugs promoted by those with political connections” and repeatedly described by the president as a potential “game changer” in the fight against the virus.

“I believe this transfer was in response to my insistence that the government invest the billions of dollars allocated by Congress to address the Covid-19 pandemic into safe and scientifically vetted solutions, and not in drugs, vaccines and other technologies that lack scientific merit,” he said in his statement. “I am speaking out because to combat this deadly virus, science — not politics or cronyism — has to lead the way.”

Doubts about the use of hydroxychloroquine as a treatment for the coronavirus and the lack of evidence about the drug’s effectiveness — including some small studies that indicated patients could be harmed — appear to have dampened Mr. Trump’s enthusiasm for it.

But as the seriousness of the pandemic became clear in mid-March, the president seized on anecdotal reports about victims of the coronavirus who recovered quickly after using the drug. Desperate for good news as he watched the death toll climb and the stock market plummet, Mr. Trump could hardly contain his excitement.

In a post on Twitter on March 21, the president urged federal officials to quickly approve the use of hydroxychloroquine with an antibiotic called azithromycin — a combination that he believed could work on the coronavirus.

By then, Mr. Trump’s favorite Fox News hosts were echoing his optimism that hydroxychloroquine could be a magic bullet against the virus. A day after meeting in the Oval Office with Laura Ingraham and two doctors promoting the drug as a cure-all, Mr. Trump promoted it from the White House briefing room.

“I’ll say it again: What do you have to lose?” Mr. Trump said on April 4, carefully pronouncing the drug, hydroxychloroquine. His presidential prescription: “Take it.”

Trials, however, suggested the drug might not be as effective as the president hoped. In mid-April, a small trial in Brazil was halted after some patients developed irregular heart rates. Then a study this week of 368 Veterans Affairs patients, which has not been peer-reviewed, found that it did not help patients avoid the need for ventilators, and that the use of the drug alone was associated with an increased risk of death. And this week, a panel of the government’s own experts at the National Institute of Allergy and Infectious Diseases said there was “insufficient data” to recommend taking it to treat symptoms from the virus.

The president no longer talks much about hydroxychloroquine.

Asked at his daily briefing if Dr. Bright had been forced out because he challenged the president’s support for an unproven drug, Mr. Trump said, “Maybe he was and maybe he wasn’t; I don’t know who he is.”

President Trump signed an executive order on Wednesday temporarily blocking the issuance of green cards to those outside the United States, but the measure includes numerous exemptions, like for overseas spouses and young children of American citizens.

The order, which will be in place for at least 60 days, will affect thousands of parents, adult children and siblings of citizens seeking to immigrate to the United States. Under the measure, a diversity visa lottery that issues about 50,000 visas each year will be suspended, and green card holders in the United States will be prevented from reuniting with their spouses abroad.

But it does not apply to immigrants already in the United States, nor to those seeking temporary visas, including students or guest workers like farmers. Other exceptions include health care professionals and their families as well as people in the EB-5 program, who invest hundreds of thousands of dollars in programs that create jobs. Also exempt are members of the military and their children, as well as Iraqis and those from Afghanistan who obtain a visa by assisting military operations.

President Trump has made clear that he is impatient for businesses to reopen — and has even egged on protesters who were urging some states to ease restrictions — but he said Wednesday evening that he thought that Gov. Brian Kemp of Georgia had gone too far by allowing barbershops, nail salons and other businesses to open later this week.

“I think it’s too soon,” Mr. Trump said, adding that he had shared his disagreement with Mr. Kemp, a fellow Republican and a political ally.

In Georgia, Mr. Kemp’s call to let gyms, hair salons and tattoo parlors reopen Friday and restaurants and theaters reopen Monday has drawn rebukes from mayors and public health experts, who fear it will lead to more infections and death. On Wednesday, Mr. Trump added his voice to the mix.

“I love those people that use all of those things, the spas, the beauty parlors, barbershops, tattoo parlors, I love them,” Mr. Trump said. “But they can wait a little bit longer. Just a little bit, not much, because safety has to predominate.”

But Mr. Trump added that in most cases he would defer to governors: “At the same time, he must do what he thinks is right,” he said, referring to Mr. Kemp.

Mr. Kemp acknowledged speaking with Mr. Trump in a series of Twitter posts after the president’s briefing. And while he praised Mr. Trump for his “bold leadership and insight,” he gave no indication he was reconsidering his decision. “Our next measured step is driven by data and guided by state public health officials,” he wrote.

Mr. Trump has swerved from one message to another in the weeks since the coronavirus crisis consumed the United States: He first claimed he had total authority over the states, then said governors should “call your own shots” to determine when to reopen. At the same time, he openly encouraged right-wing protests of social distancing restrictions.

States around the nation have been trying to balance combating a public health crisis with the need to ameliorate a growing economic crisis. In some states, small protests — with the support of some conservative groups — have urged governors to ease restrictions. But polls have found that Americans are more fearful of easing restrictions too early than too late, and some business leaders have cautioned against moving too quickly to reopen. The tensions are playing out across the nation in different ways.

On Wednesday, the mayor of Las Vegas, Carolyn Goodman, called for the city’s casinos, restaurants and other businesses to immediately reopen but declined to provide any guidance on social distancing measures that might protect employees and customers. “They better figure it out,” she said in an interview with Anderson Cooper on CNN, during which she said she had offered the city “to be a control group” for relaxing restrictions.

The mayor, an independent, does not have the power to reopen the city’s economy, but Gov. Steve Sisolak of Nevada, a Democrat, and the largest union representing Las Vegas casino workers swiftly condemned her comments. “I will not allow the citizens of Nevada, our Nevadans, to be used as a control group,” Mr. Sisolak said.

California’s quest to retrace the early steps of the coronavirus entered a new phase Wednesday after officials linked the death of a 57-year-old woman in early February to the virus, placing it weeks before any other known death in the United States.

The death of the woman, Patricia Dowd, had piqued the interest of a local coroner in Santa Clara County. After further examination, local officials sent tissue samples to the Centers for Disease Control and Prevention for testing in mid-March, but the results, confirming a coronavirus diagnosis, did not come back until Tuesday.

Friends and family said Ms. Dowd had developed symptoms on Feb. 2 and died four days later, on Feb. 6, while working from home. She worked at a Silicon Valley semiconductor manufacturing company with offices worldwide, including in Wuhan, China, where the outbreak began. She had gone to Beijing in November, according to a longtime friend.

The case suggests that the virus was in California as early as January, even though officials, hampered by limited testing capacity, did not identify cases of community spread until late February.

Gov. Gavin Newsom of California said Wednesday that there could be “subsequent announcements” as investigations across California further examine the early origins of the virus. He said investigators were looking at coroner and autopsy reports going back to December in some counties.

Another previously unconnected death in Santa Clara County, on Feb. 17, has also now been linked to the coronavirus.

The revelation that a coronavirus death took place in the United States in early February shifts the understanding of its arrival and changes the picture of what the nation was contending with by the time government officials began taking action.

The first Covid-19 death in the United States had previously been believed to be on Feb. 26 in Seattle, one of the worst-hit cities in the country.

Dr. Sara Cody, the chief health officer of Santa Clara County, south of San Francisco, said the newly diagnosed cases underlined that the virus was spreading undetected for weeks in the country in January and February.

Dr. Cody led the effort to issue the nation’s first stay-at-home orders on March 16. But she said she would have issued the orders even earlier had she known about the February deaths.

“I think if we had had widespread testing earlier and if we had been able to document the level of transmission in the county, if we had understood then that people were already dying, we probably would have acted earlier than we did,” Dr. Cody said.

Could the United States face two epidemics at the same time next fall, flu and the coronavirus?

That frightening idea was raised by Dr. Robert Redfield, the director of the Centers for Disease Control and Prevention, in an interview Tuesday with The Washington Post. He suggested that a new surge in coronavirus cases could coincide with the next flu season, causing an even more difficult crisis than the one the nation is facing now.

At Wednesday’s White House briefing, President Trump contended that Dr. Redfield had been misquoted. But when pressed by reporters, Dr. Redfield said that The Post had reported his answers accurately, even as he tried to dial back the alarm his comments had provoked.

“I didn’t say that this was going to be worse,” he said. “I said that this was going to be more difficult.”

Taking the lectern, Mr. Trump said Dr. Redfield didn’t actually know if “the corona” would come back, and said “it might not come back at all.”

“If it does come back, and I’ve spoken to 10 different people, it’s not going to be like it was,” Mr. Trump added, without citing any evidence.

When pressed by reporters, Dr. Deborah Birx, the head of Mr. Trump’s coronavirus task force, did not directly support the president’s assertion. Dr. Anthony S. Fauci, the head of the National Institute of Allergy and Infectious Diseases, clashed with the president’s forecast more directly.

“We will have coronavirus in the fall,” he said. “I am convinced of that.”

The funding is part of about $12 billion allocated for colleges and universities under a $2 trillion coronavirus stabilization law that Congress passed last month. Half of those funds are supposed to go directly to students affected by campus closures. In the coming weeks, schools are expected to award emergency relief grants to students to pay for expenses like food, housing, child care and technology.

The stimulus law, titled the Coronavirus Aid, Relief and Economic Security Act, or CARES Act, did not explicitly define which students qualified for the funds. The Education Department defended its choice to do so. “The CARES Act makes clear that this taxpayer-funded relief fund should be targeted to U.S. citizens, which is consistently echoed throughout the law,” a spokeswoman said in statements to reporters.

The department’s guidance alarmed higher education advocates and policy experts, who said it ran counter to what Ms. DeVos told them when she announced the funding was coming.

Harvard announced Wednesday that it would not accept $8.6 million in taxpayer money that the university was set to receive as part of an emergency relief package for higher education, whose losses have been mounting during the pandemic.

The school’s decision came a day after President Trump criticized Harvard for receiving federal relief funds despite its large endowment, valued at $41 billion before the pandemic. “Harvard’s going to pay back the money,” he said.

Harvard said on Wednesday that there had been a lot of confusion surrounding the emergency fund, and that Harvard “did not apply for this support, nor has it requested, received or accessed these funds.” Mr. Trump had criticized the university in response to a reporter’s question about an entirely different relief fund meant for small businesses.

Harvard, which had previously said it would use all of the federal money to support students in need, opted not to take it after Mr. Trump and others, including several Republican congressmen, complained that it was unseemly for the country’s richest university to receive taxpayer money during a crisis that has left millions of Americans without jobs.

At least two other universities, Princeton and Stanford, also announced on Wednesday that they would not be taking the money allocated to them by Congress through a $14 billion federal aid package for some 5,000 American colleges, universities and trade schools.

Chief Jorge Colina of the Miami Police Department said violent crime had fallen sharply since the start of the coronavirus pandemic, including the city’s first six-week period without a homicide since 1956. He said that he worried, though, about underreported domestic violence and child abuse, and that the amount of car break-ins has started to creep up.

The chief has instructed officers to avoid giving tickets as much as possible.

“I literally told them, ‘I don’t care if we don’t issue a single ticket summons in the month of April,’” he said. “‘I don’t want you to unnecessarily interact with someone if you don’t have to, for your safety and theirs.’ And the amount of people who have been impacted financially is absolutely something that we should be mindful of.”

Chief Colina spoke from home as he recovers from the coronavirus. He fell ill a week ago and said he did not know how he got infected. He wore a mask at work. The department had been checking officers’ temperatures, and patrol cars are disinfected after each arrest.

Even so, 20 of the department’s nearly 1,400 officers are sick.

“A couple of days there I did not feel well at all,” Chief Colina said. “It was scary.”

Two Tennessee brothers who stockpiled 17,700 bottles of hand sanitizer have avoided prosecution and a fine, but they will not recoup the thousands of dollars they spent on the supplies under the terms of a price-gouging settlement that the state attorney general announced this week.

The brothers, Matt Colvin and Noah Colvin, donated the supplies last month to people in Tennessee and Kentucky, which the authorities said on Tuesday was acceptable as restitution and was a factor in the settlement terms in the highly publicized case.

The siblings, who live outside Chattanooga, were widely vilified after Matt Colvin, 36, told The New York Times last month that he and his brother, who is 21, had canvassed dollar stores and other retailers for hand sanitizer and antibacterial wipes during the early stages of the coronavirus pandemic.

Dr. Jerome Adams, the United States surgeon general, clarified on Wednesday the Trump administration’s current guidelines on whether Americans should wear masks in public.

They should, he said, though he acknowledged at the White House briefing that “I understand why the American public has been confused over time.”

As late as Feb. 29, Dr. Adams was telling Americans that healthy individuals did not need to wear masks when out in public, which he noted was the guidance from the World Health Organization and the Centers for Disease Control at the time. “Seriously people — STOP BUYING MASKS!”, he said in a tweet that day. “They are NOT effective in preventing general public from catching #Coronavirus.”

But by the end of March, the C.D.C. had reversed its recommendation, and so did Dr. Adams.

In remarks to reporters on Wednesday, after a question to Mr. Trump about whether Dr. Adams would be held “accountable” for his shifting guidance early in the pandemic, the surgeon general said he resented the implication that he had misled the American public.

“The recommendation changed because the information changed,” he said. “That’s what you want from your public health leaders.”

He added: “We are humble enough to say, ‘Look, if we don’t know, we are going to change.’”

He emphasized that N95 and medical masks, which offer the most protection and are heavily in demand, should be reserved for health care workers who are regularly exposed to infected patients.

To keep the general public supplied with face coverings, some clothing companies have turned to making masks. In North Carolina, one sock manufacturer is working to outfit an entire city with them.

Officials in Winston-Salem announced a new “Mask the City” campaign this week that aims to give all residents access to face masks made by Renfro Corporation, a local sock manufacturer. The city is collaborating with the company to distribute 300,000 masks, with about 60,000 to be sent for free to low-income and other at-risk residents.

Testing positive does not mean the cats have the same illness that people have, nor does it mean that the cats can pass the illness to people. And tests for pets are not the same as those for people, so no humans missed out on testing because of the cats.

Veterinarians tested both cats because they showed symptoms of a respiratory infection. One owner had tested positive for the virus. No human in the other cat’s household tested positive.

The federal government’s stimulus checks were meant to help people exactly like Krystle Phelps of Owasso, Okla.

She and her husband, Christopher, who have two children, recently lost their incomes after Oklahoma shut down the bars near Tulsa that she cleaned and that he supplied with vending machines. But when Ms. Phelps, 33, went to the I.R.S. website to check on the status of her family’s stimulus funds, she learned someone else had filed taxes on her husband’s behalf and used his identity to obtain their $3,400 payment.

“I cried all day,” said Ms. Phelps, who is about a month away from being unable to pay her mortgage and has cut out everything but the basics, canceling cable and eliminating snacks for the children. “It is a little relief, and then you find out it isn’t happening.”

In recent weeks, criminals have used people’s Social Security numbers, home addresses and other personal information — much of which was available online from past data breaches — to assume their identities and bilk them out of their stimulus checks and unemployment benefits.

Stocks rallied on Wednesday and oil prices reversed some of their tremendous losses as investors regrouped after two days of turmoil in financial markets.

The S&P 500 climbed more than 2 percent, and shares in Europe were also higher. The benchmark for American crude — which had been hammered out of concern that a glut in supply would soon overwhelm storage facilities — bounced back more than 20 percent.

Investors also rallied behind a handful of earnings updates that showed companies had not done as poorly in the first three months of the year as some had expected. After Snap, the owner of Snapchat, reported a surge in revenue and user growth, its shares rallied along with those of Twitter and Facebook.

Similarly, shares of some restaurant chains jumped after Chipotle Mexican Grill said on Tuesday that digital and delivery sales driven by the crisis soared. Executives at Chipotle also said the company was preparing to reopen stores, as states lift stay-at-home restrictions. Chipotle was the best performer in the S&P 500 on Wednesday, with a gain of 14 percent.

Lawmakers are making their way back to Washington ahead of an expected vote on Thursday to give final approval to a $484 billion package that would revive a loan program for distressed small businesses and provide additional aid for hospitals and testing.

The Senate approved the measure on Tuesday on a voice vote — a necessity since the chamber is on an extended recess amid the pandemic and most senators are outside of Washington. But that will not be possible in the House, where there is enough dissatisfaction in both parties about the bill that leaders have summoned lawmakers back to the Capitol for a vote. House Republicans have signaled that they would force a roll-call vote on the measure, while some of the most liberal Democrats are deeply opposed to a bill they argue provides far too little for the most urgent needs, omitting funding for struggling cities and localities.

“It is insulting to think that we can pass such a small amount of money — in the context of not knowing when Congress is even going to reconvene — pass such a small amount of money, pat ourselves on the back and leave town again,” Representative Alexandria Ocasio-Cortez, Democrat of New York, said on Monday. “I need legislation that is going to save people’s lives.”

The measure was the product of an intense round of negotiations between Democrats and the Trump administration that unfolded as the small-business loan program — created by the $2.2 trillion stimulus law — quickly ran out of funding, collapsing under a glut of applications from desperate companies struggling to stay afloat.

The measure would provide $320 billion to replenish the Paycheck Protection Program, $75 billion for hospitals, $25 billion for testing and a mandate that the Trump administration establish a national strategy to help states and localities, which are required to outline their own plans, deploy testing widely.

In that interview, Dr. Redfield warned that the fall and winter seasons would be taxing on Americans because influenza and the coronavirus would be circulating at the same time. “He was misquoted,” Mr. Trump said at the start of his daily news briefing on Wednesday. “His whole purpose in making the statement was to get a flu shot so that next fall we don’t have such a big season of flu.”

But when pressed by reporters, Dr. Redfield said that he had been accurately quoted. “There’s a possibility that the assault of the virus on our nation next winter will actually be even more difficult than the one we just went through,” Dr. Redfield said in that interview, published on Tuesday.

On Wednesday, directed by the president to take the stage, Dr. Redfield said, “When I commented yesterday that there was a possibility of next fall and winter, it could be more difficult, more complicated when we had two respiratory illnesses circulate at the same time.”

He added, “I didn’t say that this was going to be worse, I said that this was going to be more difficult.” Taking the lectern to quibble with reporters over the article, Mr. Trump said that Dr. Redfield didn’t actually know if “the corona” would come back.

Asked how he could repeatedly assert that the coronavirus would come back in pockets or not at all by the winter, Mr. Trump said multiple times that there was reason to believe it might not. Health experts — including Dr. Redfield — have stressed that Americans need to be prepared either way.

“If it does come back, and I’ve spoken to 10 different people, it’s not going to be like it was,” Mr. Trump said, citing improved containment and mitigation efforts.

Epidemiologists and infectious disease experts interviewed before the Wednesday briefing doubted that the virus would go away and did not rule out the prospect of a worse crisis in the fall if the two diseases struck at the same time.

“When flu season comes, there is the possibility that we will be dealing with two respiratory viruses at the same time — flu and Covid,” Dr. Thomas Frieden, the former head of the C.D.C. and now the president of Resolve to Save Lives, a nonprofit focused on disease prevention, said in an email. “This could be a double challenge for our health care systems.”

Tyson Foods said on Wednesday that it would close its largest pork processing facility, the latest in a string of plant closings that has put a strain on the nation’s meat supply.

The plant in Waterloo, Iowa, had been running at reduced levels in recent days because workers were staying home, the company said.

Over the last few weeks, meat plants have become major “hot spots” for the coronavirus pandemic, with some reporting widespread illnesses among workers, posing a serious challenge to meat production. Other major meatpackers like Smithfield, JBS and Hormel have also closed plants in recent days.

Tyson said it would invite the Waterloo plant’s 2,800 workers to be tested for the coronavirus at the facility this week.

“The closure has significant ramifications beyond our company, since the plant is part of a larger supply chain that includes hundreds of independent farmers, truckers, distributors and customers, including grocers,” the chief of Tyson’s fresh meats division, Steve Stouffer, said in a statement.

The company had closed another meat plant in Columbus Junction, Iowa, but it reopened the facility on Tuesday.

Public health officials in California are expanding testing to include some people who are asymptomatic, going beyond federal guidelines that have so far focused on testing people who were most at risk and showing symptoms.

The new guidelines in California prioritize screening and testing people who are living in communal living facilities, such as prisons and homeless shelters, as well as asymptomatic health care employees working in hospitals or nursing homes.

The expanded testing — which has already begun at a homeless shelter in the Los Angeles neighborhood of Skid Row — could offer an early glimpse of how widely the virus has infiltrated society, even among people who otherwise appear healthy. As many as 25 percent of people infected may not show symptoms, according to the Centers for Disease Control and Prevention.

More than 200 people have been tested so far at the homeless shelter, Union Rescue Mission, and at least 43 people had tested positive as of Tuesday afternoon, said Dr. Barbara Ferrer, the public health director in Los Angeles County. Of the 43 who tested positive, she said more than half had not been showing symptoms.

The results mirror findings of asymptomatic cases that have begun to emerge at other facilities in the United States, as officials ramp up aggressive testing.

In Ohio, where an outbreak at a prison has become the country’s largest-known source of infections, officials said that many of the people who tested positive did not appear sick. In Boston, where universal testing was conducted at a homeless shelter earlier this month, officials found that nearly everyone who tested positive had not been showing symptoms.

Dr. Jim O’Connell, president of the Boston Health Care for the Homeless Program, said he was “baffled” by how many people without symptoms had tested positive at the shelter.

“The lesson for this is there is so much we don’t know, and in this particular very poor and vulnerable population,” Mr. O’Connell said. “We suspect all around the country, this is probably going to be duplicated.”

He said on Wednesday that the former New York City mayor, Michael Bloomberg, had volunteered to help with the state’s effort to test and trace the virus.

In New York City, Mayor Bill de Blasio said that public housing residents would be a priority at six testing sites set to open in the coming days, and that three sites opening next week would be based in public housing.

The roots of social distancing go back to a request from former President George W. Bush some 14 years ago in the wake of the terror attacks in 2001, Hurricane Katrina in 2005 and a heightened need to prepare for future disasters, found Eric Lipton and Jennifer Steinhauer.

Inspired by a book he read about the spread of germs, Mr. Bush asked two federal government doctors to come up with a plan for the United States to respond to the next pandemic. The doctors, Richard Hatchett, a White House biodefense adviser, and Carter Mecher, a Veterans Affairs medical officer based in Georgia, took a deep dive into historical responses to contagious diseases dating back to the Middle Ages when there was not advanced medicine to treat such viruses.

When the doctors who presented their plan to other federal officials, they were laughed at and ridiculed. Much like today, social distancing was not a popular option because of the disruption it would cause to everyday life, especially the economy. But without a guarantee that a drug to treat the particular illness spreading around the globe would be available, keeping a safe distance from other people would have to work.

And in February 2007, social distancing became the plan if a drug was not available. It was reaffirmed in a 2017 Centers for Disease Control and Prevention guide to local communities. And it went live across the country in mid-March when the coronavirus was spreading faster than medical response could handle.

Democratic leaders on Wednesday backed away from a planned move to change the rules of the House of Representatives to allow lawmakers to cast votes remotely for the first time in history during the pandemic, scrapping a vote on the plan after Republicans registered sharp opposition.

Speaker Nancy Pelosi told Democrats during a conference call that the House would no longer vote on Thursday as planned on a proposal to allow members to designate another lawmaker to cast votes for them by proxy, according to two officials familiar with the private discussion who spoke on condition of anonymity. Instead, she said she and Representative Kevin McCarthy, Republican of California and the majority leader, will task a bipartisan group of lawmakers to consider remote voting and reopening Congress.

The debate over whether the House should resume business as usual or allow lawmakers to register their votes remotely has become bitterly partisan, mirroring those taking place in cities and states across the nation as elected officials struggle to balance the economic pain and disruption of social distancing and shelter-in-place orders with the public health imperative of slowing and mitigating the spread of the virus. House Republican leaders have opposed the plan to vote by proxy, and some Republicans argued lawmakers should return to Washington and get back to work.

Democrats, who hold the majority in the House, had planned to muscle through the change in the rules over Republican objections.

“Republicans were not included,” said Representative Rodney Davis of Illinois, the top Republican on the Administration Committee. “We are against this proposal because it hasn’t been put together in a bipartisan way.”

“It would throw out over 200 years of precedent,” he added, “without so much as a discussion with Republicans.”

But Santa Clara County officials said that autopsies of two people who died at their homes on Feb. 6 and Feb. 17 showed that the individuals were infected with the virus. The presence of Covid-19, the disease caused by the virus, was determined by tissue samples and was confirmed by the Centers for Disease Control and Prevention, county health officials said in a statement.

“Each one of those deaths is probably the tip of an iceberg of unknown size,” Dr. Sara Cody, the county’s chief medical officer, said in an interview. “It feels quite significant.”

Scientists around the world are also racing to use small genetic changes in the virus — biological markers that act as something like fingerprints for disease detectives — to map how the pathogen swept across the country and around the world.

Mike Baker and Sheri Fink report on how the high-tech detective work of the researchers in Seattle and their partners elsewhere have opened the first clear window into how and where the virus was spreading — and how difficult it will be to contain.

Both studies were performed in California: one among residents of Santa Clara County, south of San Francisco, and the other among residents of Los Angeles County. In both cases, the estimates of the number of people infected in those counties were far higher than the number of confirmed cases.

But in a reflection of how much remains unknown and how hard it is to draw sweeping conclusions, the studies, conducted by public health officials and scientists at Stanford University and the University of Southern California, have earned the ire of critics who questioned both the recruitment methods and the analyses.

New York State has registered more than 14,800 deaths because of the virus since the outbreak began in earnest in March, about 70 percent of them in New York City. Sandwiched between overflowing hospitals and backed up cemeteries, the city’s funeral homes have been functioning at maximum capacity. And the cases keep pouring in.

Of the 50 crematories across the state, only four are in the city, and they have struggled to keep up with demand. Slots are now booked weeks in advance.

Joe Neufeld Sr., a New York funeral home owner, did not know the professor, David Penepent, when he received his call, but he had heard of SUNY’s mortuary science program. Still, Mr. Neufeld said, he was initially “leery and unsure how this was going to work.”

Now, he says, he cannot imagine how he would have managed without him.

On Easter weekend, Mr. Penepent, 57, and his students moved about 70 bodies. Last week, using two vans, Mr. Penepent transported 150. This week they expected to take 300.

“It’s a godsend,” said Mr. Neufeld, the owner of the Gerard J. Neufeld Funeral Home in Queens, which is just blocks from Elmhurst Hospital Center in one of the hardest hit areas in the country. “He came out of nowhere to save us.”

Struggling to keep their businesses alive in the second month of compulsory closings, many owners of independent restaurants and bars across the country are starting to despair of getting the help they need to return.

The relief bills that have passed Congress don’t seem to be working for them, they say. Emergency loans made available in the first injection of funds into the Paycheck Protection Program, said one New York baker, went to “people who knew people, and things got pushed around.”

“It just seemed — corrupt is the word to use,” he said.

Many are doubtful that a fresh injection of aid — including a $484 billion plan expected to win approval later this week — will solve their problems, and other measures they favor seem to be going nowhere.

They are confused, they are angry and they all say they know a dozen other small-business owners just like them.

“Independent restaurants have never had a great voice in Washington,” said Andy Ricker, the chef and founder of several Thai restaurants in Portland, Ore. “The people who have a voice in Washington have the money to pay for it. I don’t have a spare $1,000 a month to pay for this stuff.”

Whether you are cooking meals from scratch, turning to your childhood comfort foods or don’t have much of an appetite, the lockdown has probably changed your eating habits. Here are some tips to ensure your diet is healthy and help you remember that moderation is key:

Track the progress of the pandemic and stay abreast of the latest developments with our team of international correspondents.

Reporting was contributed by Mike Baker, Karen Barrow, Alan Blinder, Michael Cooper, Monica Davey, Caitlin Dickerson, Catie Edmondson, Richard Fausset, Sheri Fink, Jacey Fortin, Thomas Fuller, James Gorman, Denise Grady, Erica L. Green, Maggie Haberman, Amy Harmon, Anemona Hartocollis, Nicole Hong, Tiffany Hsu, Shawn Hubler, Miriam Jordan, Zolan Kanno-Youngs, Gina Kolata, Lisa Lerer, Patricia Mazzei, Sarah Mervosh, Alexandra E. Petri, Nathaniel Popper, Alan Rappeport, Katie Rogers, Rick Rojas, Marc Santora, Michael D. Shear, Knvul Sheikh, Natasha Singer, Eileen Sullivan, Vanessa Swales, Jim Tankersley, Katie Thomas, Neil Vigdor, Kenneth P. Vogel and Pete Wells.