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Twenty-two days.

It took more than three months for the United States to reach one million coronavirus cases after reporting its first confirmed infection, but less than a third of that time to notch the latest million-case leap.

On Sunday, the United States hit yet another milestone, with six million reported cases, according to a New York Times database.

But while the virus continues to spread relentlessly, raising tensions as states and school systems take ginger steps toward normalcy, the newest numbers provide evidence that the outbreak may be slowing.

It took 16 days, for example, for U.S. cases to climb to five million from four million. And new daily cases have been going down since the end of July.

Still, U.S. case numbers remain at the top of the global chart, accounting for almost a quarter of the 25 million cases.

And while daily death reports in the United States remain far below the peak they hit in the spring, the cumulative toll is closing in on 200,000. Daily death counts in August more than doubled the average for early July.

United States › On Aug. 30 14-day
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New cases 33,452 -18%
New deaths 374 -15%

Where cases are highest per capita

Credit…Chandan Khanna/Agence France-Presse — Getty Images

Dr. Stephen M. Hahn, the commissioner of the Food and Drug Administration, who has been under pressure from the White House to speed coronavirus treatments, said in a newspaper interview that his agency would be willing to approve a coronavirus vaccine before Phase 3 clinical trials were complete if the agency found it “appropriate” to do so.

Dr. Hahn told the newspaper that a vaccine developer could apply for approval before the end of Phase 3 clinical trials, which are the largest and most rigorous, but that the agency would make “a science, medicine, data decision” and might issue emergency authorization for use for particularly vulnerable groups rather than a blanket approval.

“This is not going to be a political decision,” he said.

Dr. Hahn’s comments, published online on Sunday by The Financial Times, were not his first indication that the agency could fast-track a vaccine under the right circumstances, which would not be out of line with the agency’s standard protocols. But the interview came at the end of a particularly turbulent week for the F.D.A.

Last weekend, after President Trump criticized the agency for moving too slowly to develop vaccines and treatments and accused it of being part of the “deep state,” Dr. Hahn appeared with Mr. Trump at a news conference where they made erroneous claims that overstated the benefits of plasma treatments for Covid-19, prompting a wave of scientific disbelief and criticism.

Dr. Hahn later corrected the misleading claims. On Thursday, the Department of Health and Human Services, the parent agency of the F.D.A., terminated the contract of a public relations consultant who had advised Dr. Hahn to issue the correction, and the F.D.A.’s chief spokeswoman, who had been on the job for just 11 days, was removed from her position.

Last week, The Times reported that, on July 30, Treasury Secretary Steven Mnuchin and the White House chief of staff, Mark Meadows, told Speaker Nancy Pelosi and Senator Chuck Schumer, the Democratic leader, that a vaccine would probably be given emergency approval before the end of Phase 3 clinical trials in the United States, perhaps as early as late September.

The account was based on information from two people briefed on the discussion, who said that Mr. Meadows indicated it would most likely be the one being developed by AstraZeneca and Oxford University, which is now undergoing Phase 2 and Phase 3 trials in Britain, Brazil and South Africa. However, senior administration officials disputed the account, saying Mr. Meadows and Mr. Mnuchin were either being misrepresented or had been misunderstood.

Last week, Dr. Anthony S. Fauci, the nation’s leading expert on infectious diseases, told The Times of London that three vaccine candidates at the heart of Operation Warp Speed, the White House’s effort to speed vaccine development, were lined up for testing and that getting results by November or December was “a safe bet.” He also said that it was “conceivable that we would get an answer before that.”

The former F.D.A. commissioner Dr. Scott Gottlieb said in an interview on the CBS program “Face the Nation” on Sunday that the agency leadership could not “obviate” the process of approval. But he also said that the trials could “read out early” if the data shows a particular vaccine to be “very effective” and such results might allow emergency authorization for vulnerable populations.

Some experts fear that rapid approval could have unintended consequences. In a letter to Dr. Hahn dated Aug. 26, the Infectious Disease Society of America, an association of infectious disease doctors, warned that approval before the completion of a Phase 3 trial “could significantly undermine Covid-19 vaccination efforts and seriously erode confidence in all vaccines in the current atmosphere of vaccine hesitancy.”

Dr. Deborah L. Birx, the White House coronavirus response coordinator, said on Sunday that she hoped Americans would want to receive a coronavirus vaccine once they saw data that proved it was safe and effective. In the meantime, she urged people to continue wearing masks and taking other precautions.

“Don’t wait for the vaccine to do the right thing,” she said in St. Paul, Minn., after meeting with Gov. Tim Walz.

“I’m hopeful for a vaccine, but I’m also very convinced right now that we can stop community spread by wearing masks, socially distancing and avoiding crowds,” she said.

Global roundup

Credit…Prakash Singh/Agence France-Presse — Getty Images

Five months after shutting down the subway in New Delhi, India is reopening the city’s underground rail network, even as the country continues to set global records for the greatest number of new daily confirmed cases.

India, a nation of 1.3 billion people, is loosening some restrictions in parts of the country while adding others aimed at thwarting the virus.

“This is good news,” said Anuradha Raman, a college student in New Delhi. “But people are also scared, because we don’t follow social distance guidelines here.”

India imposed one of the world’s most severe lockdowns in late March, but as an ailing economy started sharply contracting, officials lifted some of the restrictions.

Indian officials say the steep rise in confirmed infections is partly explained by an increase in testing. More than 64,000 Indians have died from Covid-19, according to a Times database, surpassing Mexico as the country with the third-highest number of deaths after the United States and Brazil.

Updated

Arvind Kejriwal, New Delhi’s chief minister, said he was glad the subway, which is used by 2.6 million commuters a day, was resuming service. But the capital also recorded more than 2,000 new cases on Sunday, its largest daily tally in 51 days.

It was not clear whether subways in other cities would also resume service.

While sports events and religious festivals have been allowed with restrictions on attendance, the country’s schools will remain closed until the end of September.

Other coronavirus developments around the world:

  • Global confirmed cases have surpassed 25 million, reaching 25,125,300, according to a Times database, and at least 845,000 people have died. The 10 countries reporting the highest per capita infections in the last week are largely clustered in the Caribbean (Aruba, Turks and Caicos, Sint Maarten) and in Central and South America (Peru, Argentina, Colombia, Panama). The Maldives, Bahrain and Israel are also in that category.

  • New Zealand reported nine new cases on Monday, including four imported cases and five community cases linked to a cluster in Auckland, New Zealand’s largest city, which came out of lockdown late Sunday after more than two weeks. Monday is also the first day it is mandatory to wear masks on public transportation nationwide.

  • Australia reported its highest daily death toll on Monday, most of them deaths from the past month that had not been recorded earlier. Of the 41 deaths — all of them in the state of Victoria, the center of Australia’s worst outbreak — eight were in the previous 24 hours, officials said. The rest occurred in nursing homes as early as late July but are being counted now because of a change in the way they are required to report coronavirus deaths. Australia has had almost 26,000 cases and 652 deaths, according to a Times database.

Credit…Al Drago for The New York Times

Almost 183,000 people in the United States have died of Covid-19, the illness caused by the coronavirus. But President Trump retweeted multiple messages overnight and Sunday morning by people embracing fringe conspiracy theories claiming the death toll has been grossly exaggerated.

The reposted messages, decidedly at odds with government and other tallies, assert that the virus’s real death toll is only around 9,000 because many of those who died also had other health issues and most were of an advanced age.

“So get this straight — based on the recommendation of doctors Fauci and Birx the US shut down the entire economy based on 9,000 American deaths to the China coronavirus,” said the summary of a story by the hard-line conservative website Gateway Pundit that was retweeted by the president, assailing his own health advisers, Dr. Anthony S. Fauci and Dr. Deborah L. Birx.

In fact, experts say, the official estimate of deaths may actually undercount mortality attributable to Covid-19. The more accurate figure may well exceed 200,000, according to an analysis by The Times earlier this month.

There were at least 370 new coronavirus deaths and 33,239 new cases reported in the United States on Sunday, according to a database maintained by the The Times.

Twitter deleted one of the tweets that Mr. Trump reposted advancing this claim, replacing it with a message: “This Tweet is no longer available because it violated the Twitter Rules.”

Mr. Trump also retweeted a message calling for New York’s governor, Andrew M. Cuomo, to be imprisoned because of the high death toll from the virus in nursing homes in the state. “#KillerCuomo should be in jail,” said the message by the actor James Woods, a strong supporter of the president.

Mr. Cuomo responded on his own Twitter feed a few hours later, pointing to the Trump administration’s failure to contain the pandemic. “The White House has learned nothing from COVID,” Mr. Cuomo wrote. “National threats require national leadership. It’s been 6 months without a national strategy on testing or mask mandate. Only the federal government has the power to go to war with COVID. They are failing and the nation suffers.”

Mr. Trump’s tweets were part of more than 80 presidential tweets and retweets, many of them inflammatory comments or assertions about violent clashes in Portland, Ore., where a man wearing the hat of a far-right, pro-Trump group was shot and killed Saturday after a large group of Mr. Trump’s supporters gathered in the streets.

Education Roundup

Take a look at the places where the coronavirus is spreading fastest in the U.S. relative to population, and you’ll see that many have something worrisome in common: Nearly half of the top 20 metropolitan areas where new cases per capita rose the most over the past two weeks are college towns, home to the reopened campuses of large public universities.

The trend has prompted municipal officials to reimpose restrictions on businesses, especially bars, to slow outbreaks that they attribute mostly to young adults.

The starkest so far has been Ames, Iowa, home to Iowa State University. The school found 104 cases on campus in the first week of fall classes and quarantined 204 more people. Officials also reported a 13.6 percent positivity rate for tests performed in the first week.

Iowa City is also on the list. The University of Iowa had 607 students test positive by last Friday, a week into the semester. The outbreaks at the two universities prompted Gov. Kim Reynolds to order bars closed through most of September in six Iowa counties.

In small cities with large schools, per capita rates can be somewhat exaggerated, if students are counted among the city’s virus cases but not in its overall population. Even so, the recent spikes in college towns pose significant dangers.

Other college towns with the greatest increases in cases relative to their populations include Oxford, Miss.; Lawrence, Kan.; Auburn, Ala.; Pullman, Wash.; Statesboro, Ga.; and Grand Forks, N.D.

In other education news:

  • In Philadelphia, Temple University announced on Sunday that it would suspend in-person classes for two weeks and shift to online learning after more than 100 students tested positive for the virus. The university said it had conducted more than 5,000 tests for the virus during the past two weeks and that there were 103 active cases, most of which were asymptomatic.

  • The University of Alabama has reported that more than 1,000 students at its main campus in Tuscaloosa have tested positive. Even before the latest count, the university’s president said in a message to faculty, students and staff members that “there is an unacceptable rise in positive Covid cases on our campus.” In his latest message to the community, on Wednesday, he wrote that “we all want to remain on campus throughout this fall, but we can only do so with your daily assistance.”

  • SUNY Oneonta, a public college in central New York, closed down in-person classes within a few days of reopening. The college took the step after learning of more than 100 coronavirus cases connected with the campus. Officials began testing 3,000 students and faculty members after “several large parties” and positive tests for 20 people on campus. Fall classes at the school began last week.

Credit…Laura Freeman

The U.S. Open is always a showcase for grace under pressure, but as tennis officials in New York prepare for it to get underway Monday, the stakes are a lot higher.

This year, the Open is not merely a tennis tournament but a grand experiment that may show what is possible for many international sports during the pandemic.

New York may be rooting especially hard for the Open to prove a success, since it is taking place as the local sports calendar heats up.

After the tennis tournament ends on Sept. 13, the world’s top golfers will arrive in the New York City area for their U.S. Open, which will be held at Winged Foot Golf Club in Westchester County.

In baseball, the Yankees may have a good shot at the playoffs in October.

And later in the year, the N.H.L. and the N.B.A., home to five teams in the region, want to start playing in their arenas again.

The United States Tennis Association realized months ago that this year’s U.S. Open would be unlike anything they had ever experienced — if they could stage it at all.

For one thing, it soon became clear that whatever happened at the cavernous stadiums of the Billie Jean King National Tennis Center in Flushing Meadows, Queens, fans would not be part of it.

Players, who began arriving in mid-August for a smaller tournament held before the U.S. Open, are mostly cloistered in a Long Island hotel, prohibited even from sharing an outdoor table with friends.

But already one player has withdrawn from the tournament after testing positive for the virus.

Credit…EcoHealth Alliance

A worldwide virus-hunting program allowed to expire last year by the Trump administration, just before the coronavirus pandemic broke out, will have a second life — whatever the outcome of the presidential election.

The Obama-era program, called Predict, searched for dangerous new animal viruses in bat caves, camel pens, wet markets and wildlife-smuggling routes around the globe.

USAID, the government agency that let Predict lapse last October, has quietly created a $100 million program with a similar purpose set to begin in October. It will be called Stop Spillover.

And Joseph R. Biden Jr. has promised that, if elected, he will restore Predict.

The program’s expiration came just weeks before the advent of the pandemic, and its termination prompted wide criticism among scientists, who noted that the coronavirus is exactly the sort of catastrophic animal virus the program was designed to head off.

In a speech on Thursday, ahead of the last night of the Republican National Convention, Kamala Harris, the Democratic vice-presidential candidate, briefly alluded to the controversy.

“Barack Obama and Joe Biden had a program, called Predict, that tracked emerging diseases in places like China,” she said. “Trump cut it.”

Dennis Carroll, Predict’s creator and director, retired from government service when the program shut down. In an interview on Friday, he said Predict was closed by “risk-averse bureaucrats who were trying to divine what the Trump administration did and didn’t want.”

Dr. Carroll is now a fellow at the Bush School of Government and Public Service at Texas A&M in College Station and an informal adviser on global health to the Biden campaign.

On Friday, a USAID spokeswoman, Pooja Jhunjhunwala, denied that Predict had been canceled and said it simply came to the end of its 10-year “life cycle.”

Ms. Jhunjhunwala said that Stop Spillover “is not a revival of Predict, nor a follow-on project,” but that it was designed to “implement the scientific gains of Predict to reduce the risk of viral spillover.”

Also, on Thursday, the National Institute of Allergy and Infectious Diseases announced that it would spend $82 million over five years to create 11 centers in which American and foreign scientists would collaborate to hunt emerging diseases.

“Yes, it’s like Predict, but it wasn’t the cancellation of Predict that inspired it,” said Dr. Anthony S. Fauci, director of the institute.

Credit…Karsten Moran for The New York Times

Over three days in late July, a three-bedroom house in East Orange, N.J., was listed for sale for $285,000, had 97 showings, received 24 offers and went under contract for 21 percent over that price. On Long Island, six people made offers on a house listed at $499,000 in Valley Stream without seeing it in person after it was shown on a Facebook Live video.

Since the pandemic began, the suburbs around New York City have experienced enormous demand for homes of all prices, a surge unlike any in recent memory, according to officials, real estate agents and residents.

In July, there was a 44 percent increase in home sales for the suburban counties surrounding the city compared with the previous year, according to Miller Samuel Real Estate Appraisers & Consultants. The increase was 112 percent in Westchester, just north of New York City, and 73 percent in Fairfield County, Conn., just over the state border.

“The people from New York are coming with a sense of urgency, and the thing they want is space,” said James Hughes, a real estate agent in New Jersey, who said that roughly 60 percent of potential buyers for his properties lived in the city. “The demand is insane.”

At the same time, the number of properties sold in Manhattan plummeted 56 percent, according to Miller Samuel.

The suburban demand, driven in part by New York City residents who are able to work remotely while offices are closed, raises unsettling questions about how fast the city will be able to recover from the pandemic.

Experts have predicted the city’s demise during past crises, including the terrorist attacks of Sept. 11, 2001, only to be proven wrong. In fact, even as office towers in Manhattan remain largely empty because of the outbreak, some businesses, including Amazon and Facebook, are expanding their footprints, betting that workers will eventually return to their desks.

Credit…Erin Baiano

For months, the internet has been the New York Philharmonic’s only venue for performing, with many of its offerings including videos of individual pieces stitched together in “Brady Bunch”-like tiles.

That changed a bit this weekend, when a trio took their instruments to the streets and staged pop-up concerts in Brooklyn.

“I feel suddenly energized,” said Yulia Ziskel, the trio’s violinist.

Cynthia Phelps, the orchestra’s principal violist, agreed. “It’s a charge,” she said.

That may have been because as the musicians performed in Downtown Brooklyn on Friday evening, dark storm clouds loomed; at one point, orchestra administrators had to unfurl umbrellas over the musicians as they performed.

But the electricity in the air came more from the prospect of a genuine ensemble performance.

“This is the thing, to groove off each other,” Ms. Phelps said. “It’s not the same when we’re at home doing things over the internet.”

The Philharmonic had not given a public performance since the pandemic forced it to close in March. Its return comes in the form of a new venture called the NY Phil Bandwagon.

Over the next eight weeks, the Philharmonic plans to perform at three unannounced locations around New York City each Friday, Saturday and Sunday.

For the first one, Ms. Ziskel, Ms. Phelps and the third member of the trio, the cellist Sumire Kudo, arrived in front of the Brooklyn Academy of Music wearing red shirts and black masks.

It did not take long for a crowd to form.

But playing in the streets is a far cry from playing at the Philharmonic’s usual home, and so the musicians are prepared to do what musicians do best: improvise.

Credit…Sarahbeth Maney for The New York Times

In the spring, teenagers started showing up at U.S. doctors’ offices with angry red and purple blisters on their fingers and toes — the latest unexpected feature of the coronavirus. Suddenly photographs of so-called Covid toes were everywhere on social media.

But almost all of the images depicted glossy pink lesions on white skin. Though people of color have been affected disproportionately by the pandemic, pictures of Covid toes on dark skin were curiously hard to find.

The problem isn’t unique to Covid toes or social media. Although progress has been made in recent years, most textbooks that serve as road maps for diagnosing skin disorders often don’t include images of skin conditions as they appear on people of color.

It’s a glaring omission that can lead to misdiagnoses and unnecessary suffering.

“Pattern recognition is central to dermatology, and a lot of the pattern recognition is training your eye to recognize certain colors that trigger you to think of certain diseases,” said Dr. Jenna Lester, the director of the skin of color program at the University of California, San Francisco.

As the coronavirus spread, dermatologists started an international registry to catalog examples of skin manifestations of Covid-19. It included more than 700 images, but only 34 of disorders in Hispanic patients and 13 in Black patients were submitted.

It wasn’t until July that Dr. Roxana Daneshjou and her colleagues at Stanford University published some of the first pictures of Covid toes in nonwhite patients, in the Journal of the American Academy of Dermatology.

“We know for certain that if dark skin images are not well represented, skin doctors — but also other doctors who are not skin experts — are at a disadvantage for making a proper diagnosis,” said Dr. Hao Feng, an assistant professor of dermatology at the University of Connecticut.

Credit…Matthias Hangst/Getty Images

The Times’s Jeré Longman talked to five elite athletes — a shot-putter, a long-distance runner, a swimmer, a discus thrower and a baseball outfielder — who have found ways to turn the limitations of the pandemic into benefits.

Ryan Crouser, the 2016 Olympic shot-put champion, had expected to defend his gold medal in Tokyo this summer. He did not expect to enter bass-fishing tournaments as a way to feed his competitive bend that was being stifled by a pandemic.

“Finished in the money three of the last four tournaments,” Mr. Crouser, 27, who lives in Fayetteville, Ark., said in a telephone interview.

Many Olympic sports lost their primary showcase with the postponement of this year’s Tokyo Games. The annual international circuit for dozens of sports were also disrupted. Some athletes, their motivation sagging, decided to throw in the towel and resume serious training in the fall.

But not everyone.

On July 18, after driving 10 hours to compete in one of the rare track meets held this summer, Mr. Crouser unleashed the best throw of his life — 75 feet 2 inches, or 22.91 meters — which tied for the fourth-best throw of all time.

He is one of many athletes who have performed as well as or better than ever despite the complications of the last several months. They say they feel refreshed by increased rest, less exhaustive travel, enhanced focus on training, healed injuries, creative improvisation and a less stressful perspective.

Claire Curzan, 16, an Olympic swimming hopeful from Raleigh, N.C., said it had been “almost a relief” when the Tokyo Games were postponed. After posting a top-20 time in the world last year in the 100-meter butterfly and reaching the medal podium at the world junior championships, she said she felt pressure to make the Olympic team “to make everyone proud.”

Yet when her club pool shut down in March, Ms. Curzan was forced to rethink her approach. She improvised her workouts, ran to maintain her stamina, and began focusing on improvement instead of international rankings. And perhaps most important, she slept at least nine hours per night instead of six or seven.

After resuming her usual workouts, Ms. Curzan posted four personal-best times at an intrasquad meet.

Credit…Mario Tama/Getty Images

California this weekend became the first state to pass 700,000 known coronavirus cases, according to a New York Times database, even as its infection rate continued a steep decline.

By far the most populous state in the country, California has not been among the most severely affected by the virus on a per-capita basis: It ranks 21st among the states in cases and 26th in deaths per 100,000 residents. But along with the Sun Belt states, it has been among the hardest hit in the virus’s summer resurgence.

On Friday, Gov. Gavin Newsom unveiled a new plan that would allow some counties, including San Diego and San Francisco, to reopen businesses like gyms and houses of worship indoors as early as Monday under limited circumstances. It will also permit indoor dining, though bars will remain closed in most of the state.

California has seesawed through the pandemic. It was the first state to issue a comprehensive stay-at-home order, on March 19, when it was reporting about 116 new cases a day. But after the state started to reopen two months later, its caseload surged.

Mr. Newsom allowed counties to reopen certain sectors such as gyms and indoor entertainment in May and June, but backtracked after an increase of cases in July. As the new school year has started across the state, most districts have stuck to online instruction.

Louisiana currently has the highest number of cases per 100,000 people in the United States, with over 3,100, while California has about 1,770. New Jersey, where the virus peaked months ago, has the highest death rate: 179 per 100,000 residents. California has 33 deaths per capita.

Credit…Erin Schaff/The New York Times

The $2.2 trillion rescue package that the government passed in March — the largest economic stimulus measure in U.S. history — was a crucial victory for President Trump, who was facing withering attacks over his response to the pandemic.

It also was a much-needed win for the program’s chief architect, Treasury Secretary Steven Mnuchin.

He didn’t have a lot of fans. The president ran hot and cold on him. Conservatives distrusted him as a Republican in Name Only. Liberals demonized him as a plutocrat. Even members of his immediate family distanced themselves.

When the pandemic hit, the task of saving the economy was an opportunity for Mr. Mnuchin, a former banker and film financier, to transform himself from an unremarkable Treasury secretary into a national hero.

After Mr. Mnuchin worked with Democrats to devise and pass the landmark stimulus bill, Mr. Trump hailed him as a “great” Treasury secretary and “fantastic guy.”

Yet the acclaim didn’t last. Republicans said Mr. Mnuchin had been outfoxed by Speaker Nancy Pelosi, the embodiment of free-spending liberals. And on a spring day in the Oval Office not long after the stimulus package was passed, the president was venting about it.

“I never should have signed it,” Mr. Trump bellowed, according to someone who was present. He pointed at his Treasury secretary and said, “You’re to blame.”

Yet Mr. Mnuchin insisted that he didn’t take the criticism personally.

“When people ask why have I succeeded in this job, one, I understand why the president is the president. I was there — I saw why he won,” he said in a mid-August interview.

After all, he said he was simply acting on behalf of Mr. Trump. “Anything that’s significant or material,” Mr. Mnuchin said, “I check with the president.”

Reporting was contributed by Peter Baker, Joshua Barone, Tess Felder, Matthew Futterman, Abby Goodnough, Matthew Haag, Thomas Kaplan, Sharon LaFraniere, Jeré Longman, Donald G. McNeil Jr., Eric Nagourney, Roni Caryn Rabin, Alan Rappeport, Matt Richtel, James B. Stewart, Lucy Tompkins, Neil Vigdor, Sameer Yasir and Mihir Zaveri.