U.S. states struggle with a shifting pandemic as federal guidance falls silent.

The federal government’s leadership in the coronavirus pandemic has so waned that state and local health officials have been left to figure out on their own how to handle rising infections and navigate conflicting signals from the White House.

Covid-19 is still taking hundreds of American lives a day — a pace that, if sustained over the next few months, would yield about 200,000 total dead by the end of September. Arizona, Florida, Nevada, Oregon and Texas all reported their largest one-day increases in new cases this week.

On Wednesday, Oklahoma recorded 259 new cases, a single-day record for the second day in a row, and three days before President Trump is scheduled to hold an indoor campaign rally in Tulsa in defiance of his administration’s guidelines for “phased reopening.”

That rally is not the only confusing signal from Washington. The Trump re-election campaign is requiring rally-goers to sign a statement waiving their right to sue the campaign if they get sick.

In an interview with Sean Hannity on Wednesday, Mr. Trump said the virus was “fading away.”

While the president refuses to wear a mask, Surgeon General Jerome M. Adams has spent this week doing a round of television interviews to implore Americans to do so.

Vice President Mike Pence said in a Wall Street Journal opinion column this week that panic over a second wave was “overblown.” But Dr. Anthony S. Fauci, the government’s top epidemiologist, said the United States was not in a second wave because it was still in the first one.

The governors of at least six states — Michigan, Maine, Minnesota, Missouri, South Carolina and Vermont — have recently extended their state of emergency orders, even as cases in some of the states have been declining. Along with control over travel restrictions and business closures, the emergency declarations provide a direct line to federal funding for disaster relief.

Stocks on Wall Street fall as the weekly tally of U.S. jobless claims again exceeds a million.

Stocks on Wall Street fell on Thursday, adding to a modest decline from the day before, as investors considered new data on unemployment claims and the latest reports on fresh outbreaks. The S&P 500 dropped about half a percent. European stocks were about 1 percent lower.

For the 13th straight week, more than a million Americans have applied for state unemployment benefits. The Labor Department said on Thursday that 1.5 million people had claimed state benefits last week. Until the coronavirus pandemic, the most new claims in a single week was 695,000, in 1982.

Applications for an emergency federal program for self-employed workers, independent contractors and others ineligible for standard benefits added another 760,000 claims on top of the states number.

Not all the unemployment claims reported on Thursday necessarily reflect new layoffs. Some states are still working through backlogs of claims filed earlier in the pandemic, and in other cases people filing under multiple programs may be counted twice.

Yet there is little doubt that layoffs remain elevated, and economists say that job losses could worsen if government support that has helped prop up the economy is allowed to lapse too soon.

Stocks have been unsteady for the past week, as investors weighed concerns about a rise in new cases around the world against the prospects for an economic recovery. It’s a pullback that many analysts have described as long overdue, after the S&P 500 posted a string of gains from late March to early June.

Antibodies may last only two months, especially in people who didn’t show symptoms, a new study finds.

Antibodies to the new coronavirus may last only two to three months in the body, especially in people who never showed symptoms while they were infected, according to a study published on Thursday.

The new study, published in Nature Medicine, looked at only 37 people who did not show symptoms when infected, but it is the first to offer a characterization of the immune response in such people.

It suggests that asymptomatic people mount a weaker response to the virus than people who develop symptoms. And within weeks, antibody levels fall to undetectable levels in 40 percent of asymptomatic people and 13 percent of symptomatic people.

“That is a concern, but I’d point out that these are pretty small group sizes,” said Angela Rasmussen, a virologist at Columbia University in New York who was not involved in the work. She also noted that immune cells would continue to offer protection even in the absence of antibodies.

“Most people are generally not aware of T cell immunity and so much of the conversation has focused on antibody levels,” she said.

Still, the results offer a strong note of caution against the idea of “immunity certificates” for people who have recovered from the illness. If levels of immunity decrease so soon after illness, the authors suggest, people who have had the infection once might fall ill a second time.

Antibodies to other coronaviruses, including those that cause SARS and MERS, are thought to last about a year. Scientists had hoped that antibodies to the new virus might last at least as long.

Global Roundup

Beijing’s outbreak prompts a backlash against salmon.

When a new outbreak emerged last week in Beijing, residents were jolted by reports that traces of the virus had been found on a cutting board used for imported salmon.

The backlash was swift. Within a few days, salmon was removed from the shelves of Beijing’s major supermarkets, reserves of the fish were dumped, and diners rushed to cancel reservations at local Japanese restaurants whose menus feature the fish.

“We were packed on Friday and now dead ever since,” said Alan Wong, the owner of a chain of Japanese restaurants in Beijing and Shanghai. “Totally empty.”

Chinese officials later said that imported salmon was not responsible for spreading the virus, but the damage to its reputation had already been done.

For months, China has waged a campaign to highlight its successes in taming the outbreak and deflect blame for the pandemic to outsiders. Officials have cast foreigners as public health risks, sowed doubt about the virus’s origins and even pushed an unfounded conspiracy theory that the U.S. military had deliberately brought the virus to China.

In that climate, salmon, which is mostly imported from Norway and Chile, was an easy target. Drew Thompson, a former director for China in the Pentagon, called the recent backlash a form of “‘xenopescophobia’ — the fear of foreign fish.”

Other news from around the world:

• Amid a partial lockdown in Beijing, the government said Thursday that the number of coronavirus cases in the recent outbreak had risen to 158, after an additional 21 cases were reported. Wu Zunyou, the chief epidemiologist of China’s Center for Disease Control and Prevention, said the city had brought the outbreak under control.

• Prime Minister Boris Johnson of Britain has praised the country’s efforts to track down people who are exposed to the virus as a “world-beating” operation. But as with much of the government’s response, the results have been inconsistent and fallen short of the promises.

• Prime Minister Scott Morrison of Australia called the economic blow from lockdowns “devastating,” as data showed that the country’s unemployment rate had surged to a 19-year high.

• New Zealand recorded its third new case of the week, days after declaring itself among the first countries to be free of the virus.

• In Germany, schools and day care centers in the northwestern district of Gütersloh remained closed on Thursday after more than 650 workers in a meatpacking plant tested positive. Separately, a chicken processing plant in Wales was shut down for two weeks after several employees tested positive for the virus.

• The World Health Organization said it was halting its major trial of hydroxychloroquine, the malaria drug hailed by President Trump as a possible treatment for Covid-19. It said there was no evidence that the drug was effective against Covid-19.

U.S. Roundup

Reversing course, Arizona and Texas allow some local governments to require masks.

Arizona did not record its first 20,000 coronavirus cases until June 1, but it took less than three weeks for the state to record 20,000 more. So on Wednesday, its governor, Doug Ducey, said he would switch gears and allow mayors to require mask wearing if they see the need.

“The trend is headed in the wrong direction,” he said at a news conference.

In Texas, which also had record case increases this week, similar tensions have arisen between local officials and the governor, whose statewide reopening orders take precedence. The mayors of nine cities sent a letter to Gov. Greg Abbott urging him to give them the authority to require masks.

Although Mr. Abbott has strongly urged people to wear face masks, the state’s policies do not require their use, and the governor has resisted calls to do so, saying that he believes in “individual responsibility” and not “government mandates.”

But at least one Texas county got permission to proceed with a limited mask requirement.

Bexar County, which includes San Antonio, is ordering businesses to require employees and customers to wear face masks when they are unable to observe social distancing. County Judge Nelson Wolff issued the order on Wednesday, a day after the county confirmed 436 new cases, its biggest single-day increase.

Other news from around the United States:

• An Arizona sheriff who was scheduled to meet with President Trump tested positive ahead of his trip to the White House. Sheriff Mark Lamb of Pinal County, who had called enforcement of the state’s stay-at-home order unconstitutional, said that he did not have symptoms and would self-isolate.

• Four college football games involving historically black colleges and universities have been canceled because of the pandemic, the first cancellations of major college football leading up to a season that appears tenuous just over two months before its scheduled kickoff.

The virus hits Florida’s farmworkers hard, just as many get ready to travel north for harvest season.

Each year, thousands of migrant workers make their way from southern Florida up the East Coast and into the Midwest, following the ripening of fruits and vegetables. This year, many will undoubtedly bring the coronavirus with them.

Florida’s agricultural communities have become cradles of infection, fueling a disturbing spike in the state’s daily toll of new infections, which has hit records in recent days. The implications go far beyond Florida: As case numbers in places there are swelling, many farmworkers are migrating north.

As in other agricultural communities around the country, Florida’s farming regions have a high degree of built-in risk. Fruit and vegetable pickers toil close to each other in fields, ride buses shoulder-to-shoulder and sleep in cramped apartments or in trailers with other laborers or several generations of their families.

While many of them are guest workers on temporary visas, others are undocumented, with little access to routine health care and an ingrained fear of the authorities.

Gov. Ron DeSantis, a Republican, has called the contagion in agricultural communities Florida’s “No. 1 outbreak.” (He has also repeated the Trump administration’s misleading claim that the rising case numbers in the state should be attributed primarily to more widespread testing and not to the economic reopening.)

Farmworkers tend to be younger and fitter than the rest of the population and may not suffer as severely from the virus. Some of them joke, in gallows humor, that if the tomato fertilizer has not killed them yet, maybe the virus will not.

‘We can’t stay inside forever’: Here’s how New Yorkers are stretching the rules.

New Yorkers who once ducked for cover at the sound of a cough a block away are stretching both their comfort levels and the rules, venturing out to lay claim to the parts of their lives they haven’t known since March.

And they are met by bars and businesses starved for income and doing their own feats of stretching — of their necks, as they look the other way as customers gather at uncomfortably close quarters. As the city began reopening earlier this month, a kind of informal outdoor dining took place, with large groups eating and drinking on streets outside businesses.

New York City, the center of the U.S. outbreak in its earliest weeks, is being observed as a barometer of recovery around the country, its slow-and-steady approach helping bring the number of daily deaths to just 29 reported on Thursday from a high of 799 on April 8.

On Thursday, Mayor Bill de Blasio confirmed that the city will ease more restrictions on Monday. As many as 300,000 workers are expected to get back to work as outdoor dining, in-store shopping and office work resumes, with limits, he said at his daily briefing. It came a day after Gov. Andrew M. Cuomo announced the city was on track to move to the next phase then, if current trends held.

The mayor said that restaurants, many who do not have available outdoor space but have been open for takeout, would be able to place seating on curbs and sidewalks adjacent to their restaurants, even if they had never had seating before. He also announced that in July, the city would allow restaurant seating on 43 miles of streets closed to vehicle traffic. The mayor predicted that the expanded outdoor dining plan would save 5,000 of the city’s restaurants and 45,000 jobs.

Mr. Cuomo said Thursday that he is signing an executive order allowing the state to immediately suspend the liquor license of a business or shut it down if they’re not complying with reopening guidelines. He said he was also signing another order that gives bars the responsibility to limit the number of people gathered outside their establishments.

New surges of the virus in states like Florida, Arizona and Texas, which reopened more, quickly suggest the perils of letting down the collective guard. Mr. Cuomo said Thursday that he was considering requiring travelers coming into New York from other states with higher infection rates, such as Florida, to quarantine for 14 days. “I have experts who have advised me to do that,” he said. “I’m considering it now.”

In that way, too, New York City has become a barometer, of a nation of pent-up souls eager for a change no matter what their governors or mayors think.

It is as if the city is rebuilding itself, not with scaffolding and steel, but with cheeseburgers eaten at outside tables and fathers hoisting toddlers over the locked gates of closed playgrounds. It is a city built on festive, furtive and sometimes troubling pushing of boundaries. A lot more social, a lot less distancing.

In Williamsburg, Brooklyn, Heather Sumner, 32, repeated a phrase commonly heard these days: “We can’t stay inside forever.”

Here’s what else is going on in New York:

• The mayor again repeated concerns that the virus might have spread as massive protests over systemic racism and police brutality recently filled city streets. Still, he said that city and state officials had been encouraged by “the trend line” of test results and hospitalizations, which have stayed flat in recent weeks, and decided to allow the reopening to go forward.

• The mayor said that the city’s playgrounds, which have been shut since March, would also reopen on Monday. But team sports, like basketball, soccer and softball, will not be permitted in city parks.

• The New York City panel that sets rents for the roughly 2.3 million residents of rent-regulated apartments froze those rents for a year, delivering a slight reprieve to tenants struggling in the worst economy in decades.

‘In Harm’s Way’: The Times is collecting stories from health care workers fighting the pandemic.

Since the killing of George Floyd, some of these health care workers have joined the fight against another crisis: racism. While acknowledging the risk of infection posed by protests, they say this movement is too important to sit out.

Tawana Coates, OB-GYN in Louisville, Ky.

A lot of the demonstrations took place around the hospital. I went back to work a couple of days after the death of George Floyd. You feel heartbroken. I was an African-American going back to work as a minority, not knowing if the majority is feeling the same way. The last place you want to be is at work. The first conversations I had with everyone were: “What can we do as white Americans? How can I help the black community? What can I do to help reduce my own implicit bias?” It was uncomfortable, but a lot of people were willing and open to have those conversations.

Talking to a lot of my patients, women who look like Breonna Taylor and who also look like me, and having conversations throughout clinic, you could tell how the city was fired up wanting justice for Breonna Taylor.

Knowing that we serve a majority African-American population and knowing black social injustices are happening around the country, I felt it was really important for us physicians to take a stand to show the community that we support them. That’s why I helped organize the White Coats for Black Lives demonstration.

As I told everyone, this was just a beginning.

Are you a health care worker? Submit your story here.

Small businesses face special challenges in reopening.

The percentage of American small businesses that were open in early June was nearly 16 points higher than it was in mid-April, according to Opportunity Insights, an economic tracker developed by researchers at Harvard using anonymized data from credit card processors, payroll firms and others.

But with a patchwork of rules and guidelines being issued at the city, county, state and federal levels, many smaller employers find themselves wondering when it will be safe to open and how to make that choice.

Slow rollouts are happening even in places that have not been Covid-19 hot spots. In Montana, which has the fewest cases in the nation, some owners are taking a wait-and-see approach.

Gov. Steve Bullock allowed bars and restaurants to reopen in early May with 50 percent capacity limits and layout restrictions, but Brett Evje held out until the end of the month before bringing customers back into Plonk, the restaurant he co-owns. It has locations in Bozeman and Missoula.

He used the downtime to refresh the Bozeman location, doing all of the projects he said could never complete with a restaurant open 365 days a year.

“Everybody wants to return back to normal, but from my standpoint you’re already closed, so you might as well wait and see what the reaction is going to be,” Mr. Evje said. “There’s nothing as hard as remobilizing and bringing everyone back and then having to close down again.”

Australian universities hope to fly in some international students.

Australia’s international borders could see their first major reopening next month, as two universities make plans to fly in some international students who have nearly completed their degrees.

The proposal is one of several plans being presented to Australia’s government by universities and states seeking travel exemptions that aim to be a model for others.

Under the plan, two Canberra universities would ask around 350 students to fly to a hub destination like Singapore and then connect to a charter flight. Upon arrival in Australia, the students would be quarantined for 14 days and would be tested for Covid-19 at the beginning and end of their stay.

Students with practical requirements or ongoing research projects would initially be given priority, and university officials said the goal was to create a process that could be broadened over time.

“We need a trial for Australia to build that confidence,” Paddy Nixon, the vice chancellor at the University of Canberra, told Australia’s main public broadcaster.

The state of South Australia also plans to bring up to 800 international students to Adelaide’s universities.

Prime Minister Scott Morrison has emphasized that state borders will have to fully reopen before international students can return, and that has yet to happen.

China’s government has advised students to reconsider studying in Australia, citing “racist incidents targeting Asians,” but university officials say their students will not be deterred.

“Our students in China want to get back to campus as much as any of our students do,” said Brian Schmidt, the vice chancellor of Australian National University.

An audience in Madrid isn’t completely human.

When one of Madrid’s main public theaters reopened on Wednesday, the audience was limited to a third of the theater’s capacity because of virus-related restrictions.

The rest of the auditorium was filled with dummies.

Madrid is Spain’s last major city to be kept under a stricter version of a nationwide lockdown, ahead of the June 21 lifting of a state of emergency that was declared in mid-March.

Before the show, spectators lined up outside the Canal theater complex under the supervision of theater workers, in order to maintain social distancing and have their temperatures checked at the entrance.

A dance performance by Israel Galván, one of Spain’s most famous flamenco choreographers, lasted less than an hour. What took longer than usual, however, was leaving, as an employee used the sound system to tell each section of the auditorium exactly when to stand up.

Check out these tips for wearing a mask while exercising.

Gyms are slowly reopening, outdoor fitness classes are starting up, and many people are hoping to get back to their typical workout routines. But wearing a mask while working out can be challenging. Here are some ways to make it more tolerable.

Reporting was contributed by Alan Blinder, Jane Bradley, John Branch, Chris Buckley, Ben Casselman, Damien Cave, Melissa Eddy, Luis Ferré-Sadurní, Michael Gold, Matthew Haag, Amy Haimerl, Tiffany Hsu, Apoorva Mandavilli, Patricia Mazzei, Sarah Mervosh, Raphael Minder, Benjamin Mueller, Elian Peltier, Amy Qin, David E. Sanger, Matt Stevens, Sheryl Gay Stolberg, Eileen Sullivan, Noah Weiland, Michael Wilson, Billy Witz, Will Wright, Mihir Zaveri and Karen Zraick.