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

As recently as Aug. 16, the state’s seven-day average of new cases was at 9,323, and heading into Saturday, the average was 5,485. The state hit 600,000 cases on Aug. 13.

By far the most populous state in the country, California has not been among the most severely affected states by the virus on a per capita basis: It ranks 21st among the states in cases and 26th in deaths per 100,000 residents, according to the Times database. Along with the Sun Belt states, California has been among the hardest hit in the summer resurgence of the virus.

On Friday, Gov. Gavin Newsom unveiled a new plan for reopening, which would allow some counties, including San Diego and San Francisco, to reopen many businesses indoors as early as Monday under limited circumstances, such as gyms and houses of worship, as well as permit indoor dining. Bars will remain closed in most of the state.

The new plan was based on new daily case numbers per 100,000 residents, as well as positivity rates.

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, as severe outbreaks of the coronavirus shifted from the Northeast to the South and the West.

Mr. Newsom allowed counties to reopen certain sectors such as gyms and indoor entertainment in May and June, but backtracked after a surge of cases in July when he ordered statewide closures of many indoor activities, including places of worship and salons.

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.

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Berlin Police Disband Protest Against Virus Measures

Thousands marching against virus restrictions put in place by the German government were dispersed by the police for violating social-distancing rules.

[clapping, cheering] [sirens] [yelling, booing]

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Thousands marching against virus restrictions put in place by the German government were dispersed by the police for violating social-distancing rules.CreditCredit…John Macdougall/Agence France-Presse — Getty Images

In France, President Emmanuel Macron warned on Friday that the authorities were doing “everything to avoid a new lockdown.” A day later, the country reported over 7,300 new virus cases, its highest daily tally since March 31 and a number that sent its seven-day average to a new record of 4,668, according to a New York Times database.

As Germany faces its own more modest resurgence — its seven-day average for new cases has now risen to over 1,300, the database shows — Chancellor Angela Merkel said this week that managing the pandemic would become more challenging in the fall and winter, as the colder weather drives people back indoors. “We will have to live with this virus for a long time to come,” she said.

The sobering comments from Ms. Merkel and Mr. Macron come as European countries brace for — or even appear to be entering — a second wave of infections.

Nowhere on the continent is the threat more alarming than in Spain, where the Times database shows that the seven-day average has passed 7,600. The country reported nearly 9,800 new cases on Saturday, its highest number for a single day to date.

The mayor of Madrid has asked residents of the city’s southern neighborhoods to stay at home, and more than 2,000 members of its armed forces may soon be deployed to track local outbreaks, the authorities announced this week.

In Berlin, thousands of people took to the streets on Saturday to demand an end to government measures that they argue violate their constitutional rights. The rally was stopped by a police injunction because many were not respecting social distancing measures, The Associated Press reported.

Although Germany has been lauded for mostly minimizing the pandemic’s toll healthwise, many who have found themselves out of work are angry and afraid that they would not survive a second lockdown.

About 1,000 anti-mask protesters also gathered in the Swiss city of Zurich, and a similar number demonstrated in London at Trafalgar Square, according to The Associated Press.

While Mr. Macron has not ruled out another nationwide lockdown, the Tour de France, the prestigious cycling race, nonetheless departed from the southern city of Nice on Saturday, amid concerns that the peloton could carry infections as it rides across the country until Sept. 20. Teams will face possible exclusion if two of their riders test positive for the virus within a seven-day period during the race.

  • India reported 78,761 new coronavirus infections on Sunday, setting a global record for the third time in recent days. Until this past week, the U.S. had held the record for a single-day increase in cases, 75,682 on July 16, according to a Times database. India’s steep rise in infections — which officials say is partly explained by an increase in testing — comes as more state governments, desperate to stimulate an ailing economy, are loosening lockdown restrictions.

  • Prime Minister Jacinda Ardern of New Zealand thanked residents of Auckland, the country’s largest city, as they prepared to come out of lockdown at 11:59 p.m. on Sunday. But she encouraged residents to wear masks in public and remain vigilant. “Our system is only as good as our people, and our people are amazing,” she said. The city has been on lockdown since Aug. 12 as it tries to contain a cluster that has grown to 135 cases, including two reported on Sunday.

United States › On Aug. 29 14-day
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New cases 44,258 -20%
New deaths 870 -15%

Where cases are highest per capita

Colleges across the country are handing down suspensions and mandated quarantines as outbreaks at fraternity and sororities jeopardize fall reopening plans.

Health officials in Riley County, Kan., announced on Friday that 22 students affiliated with four sororities at Kansas State University had tested positive, and recommended that all members of the affected houses begin a two-week quarantine.

In Idaho, Boise State University revealed in a statement on Friday that three fraternities and a handful of students had been placed on interim suspensions in connection to “large gatherings that violated university policies.”

Outside Chicago, Northwestern University announced on Friday that its sorority and fraternity housing would be closed for the fall term. Also, first- and second-year students will, for the most part, be limited to remote learning, while undergraduate tuition will be reduced by 10 percent.

And Indiana University said on Thursday that it was requiring all Greek houses at its Bloomington campus to suspend “in-person organizational activities” after an alarming rise in new cases. The university also directed members of eight Greek organizations to quarantine.

The New York Times has tracked more than 26,000 cases of the virus linked to students returning to colleges, and the latest outbreaks underscore the challenges universities face in trying to regulate student behavior.

Credit…Erin Schaff/The New York Times

The most widely used diagnostic test for the virus, called a PCR test, provides a simple yes-no answer to the question of whether a patient is infected. But the results sent to doctors and patients do not include something else the tests reveal: an indication of the amount of virus in the patient’s body, which is a signal of how contagious the person may be.

That means many more people than necessary are being required to isolate and submit to contact tracing, and that the true picture of the state of the virus is skewed, according to reporting by Apoorva Mandavilli of The Times. The findings suggest that shifting to faster, less sensitive tests may help communities get a better handle on the virus.

“We’ve been using one type of data for everything, and that is just plus or minus — that’s all,” said Dr. Michael Mina, an epidemiologist at the Harvard T.H. Chan School of Public Health. “We’re using that for clinical diagnostics, for public health, for policy decision-making.”

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The PCR test amplifies genetic matter from the virus in cycles. Large viral loads take fewer cycles to register, while even small amounts of virus — or inactive virus fragments — will register if enough cycles are run. (Dr. Mina thinks the cutoff in cycles should be no more than 30, to limit positives for samples with very little virus.)

The number of cycles at which the virus registers is called the cycle threshold, or C.T. The Centers for Disease Control and Prevention said that it was examining the use of C.T. measures “for policy decisions,” and that it would need to collaborate with the Food and Drug Administration and device manufacturers to ensure the measures “can be used properly and with assurance that we know what they mean.”

In three sets of testing data that did include C.T. values, compiled by officials in Massachusetts, New York and Nevada, up to 90 percent of positive samples barely carried any virus, a review by The Times found. If that rate applied nationwide, then only about 4,500 of the 45,604 new U.S. cases reported on Thursday would actually require isolation and contact tracing.

“It’s just kind of mind-blowing to me that people are not recording the C.T. values from all these tests — that they’re just returning a positive or a negative,” said Angela Rasmussen, a virologist at Columbia University in New York.

Credit…Brittany Greeson for The New York Times

People around the world who have lost loved ones to the virus have been unable to hold funerals or memorial services. But in Detroit, the 1,500 city residents who died of Covid-19 will be honored with a motorcade funeral procession on Monday, Mayor Mike Duggan said in a news release.

“This is how we begin the healing process,” Mayor Duggan said.

Bells will ring across the city as the families of those who died drive around Belle Isle, a park in the Detroit River, in 15 processions led by hearses. A local radio station, WRCJ-FM (90.9), will play gospel, classical and jazz music as the vehicles pass 900 photographs, each 4 by 4 feet, of the deceased that will be scattered around the park, according to the news release.

“These are the funeral processions that many of these folks didn’t get to have,” said Rochelle Riley, the director of arts and culture for Detroit and the coordinator of the memorial. “We need to see hearses. We need to see the mourning, so that everyone will understand that this is a pandemic that is stealing people away from us.”

Mourners will remain in their cars to ensure the event abides by guidelines against large gatherings and the park will be closed to other traffic for the day. The photos will stay in the park until Wednesday.

In addition to helping the families through their losses, Ms. Riley said she hoped the memorial would emphasize the threat of the virus to those who haven’t taken it seriously. The memorial can be viewed on the city’s Facebook page and YouTube channel, she said.

Credit…Grace Pritchett/Rapid City Journal, via Associated Press

The number of new coronavirus cases in most of the United States is declining, but some states, including North and South Dakota, are announcing high numbers of new infections. Both states announced single-day records on Saturday: more than 370 in North Dakota and more than 420 in South Dakota.

Cases in Grand Forks County, N.D., spiked in the last week, a surge that health experts believe could be linked to college students returning to class at the University of North Dakota, the state’s largest university, with an enrollment of more than 13,000 students.

On Saturday, the county added 147 new cases, a single-day record, and in the past week recorded more cases than in any other seven-day stretch, according to a New York Times database.

The university currently has more than 300 positive cases among students, and almost 700 students and staff members quarantined, according to its online dashboard.

Molly Howell, the deputy state epidemiologist in North Dakota, said in an interview that the bulk of the new cases had appeared in people between the ages of 20 and 29. She noted that the health department had seen a rise in the number of residents defying quarantine rules.

“We’re finding some contacts aren’t necessarily staying home or even answering their phone or calling us back,” Ms. Howell said.

She said that as of Saturday, 28 coronavirus cases in North Dakota had been linked to the two-week motorcycle rally in the city of Sturgis that ended on Aug. 16.

In South Dakota, 88 cases have been associated with the rally, health department officials said at a briefing. Meade County, where Sturgis is located, reported 68 new cases on Thursday for a single-day record, and added a record 127 over the past week.

Minnesota, Wisconsin, Nebraska, Montana, Wyoming and Washington have also reported cases linked to the rally, according to The Associated Press.

Credit…Lauren Lancaster for The New York Times

As schools closed and students stayed home this year to comply with lockdown orders, the owners of companies that bus millions of students to and from schools idled their fleets and braced for financial losses.

But as the pandemic has stretched on, many privately owned bus companies are facing an existential threat. With most summer school programs canceled and many schools planning to operate online for the fall, they fear they may not survive.

“We’ve been in business for over 60 years,” said Glenn Every, who runs a school bus company that works with schools in the Hudson Valley of New York. “But this may be the end of the line for us.”

About 60 percent of school buses are owned and operated by school districts; privately owned bus companies account for the remainder, carrying nearly 10 million children to school a year.

If they fail, experts say, many schools districts may find few alternatives. Parents and students, particularly those who live far from their school of choice, will most likely be left to improvise transportation options.

The tens of billions of dollars Congress has earmarked for the flagging transportation industry is focused on airlines, public transit and Amtrak. Privately operated buses were largely left out, industry experts said. Another $13.5 billion in aid was set aside for school districts, but lawmakers left it up to district administrators whether to use any of that money to pay private contractors — and some are not.

In school districts that are adopting remote learning, bus companies worry about getting any income at all. In places that are returning fully to in-person instruction or a hybrid model, companies project that cleaning costs will rise and operational outlays will skyrocket because of the need to run more buses to ensure students remain socially distanced.

In addition, bus drivers who were laid off have flocked to industries like trucking and package delivery, making it difficult for companies that need to drive students in the fall to recruit the staff members they now need.

“Once it falls apart,” said Kyle DeVivo, a bus advocate and an assistant vice president of DATTCO Inc., a bus company in Connecticut, “good luck putting it back together.”

Credit…Fabio Bucciarelli for The New York Times

Sicily’s president, Nello Musumeci, ordered all migrant centers on the island closed last weekend, saying it was impossible to prevent the spread of the illness in them. A court blocked the order, but his effort underlined the challenges Italy faces as right-wing politicians seek to rekindle a polarizing debate about immigration in a country hit hard by the pandemic, and now seeing its cases surge.

In the last two weeks, Italy’s seven-day average of new cases has more than doubled, from 476 on Aug. 15 to 1,192 on Friday, according to a New York Times database.

Franco Locatelli, the president of Italy’s Superior Health Council, a government advisory body, said migrants’ role in bringing the virus to Italy was “minimal.”

In the first half of August, around 25 percent of the country’s new infections arrived from abroad, according to Italy’s National Health Institute. Italians who had traveled accounted for more than half, and many other cases were among foreign residents returning to the country. Less than 5 percent were among new immigrants, the Health Ministry said.

About 11,700 migrants have reached Sicily since June, and 3 percent either tested positive upon arrival or during a quarantine period imposed at shelters.

Last weekend, a ship carrying hundreds of migrants from Africa and the Middle East, about 20 of whom had tested positive, was turned away by mayor after mayor in Sicily, before eventually docking in Augusta, in the southeast.

“Outlaw state,” Matteo Salvini, the leader of the anti-immigrant League party and a former interior minister, said on Twitter. “An invasion of illegal migrants, a boom of infections, Sicily is collapsing.”

Pozzallo, in southern Sicily, has the highest rate of infections among arriving migrants: 73 tested positive out of about 200 quarantined there in one week this month. Roberto Ammatuna, the center-left mayor, has found himself trying to balance public fear with ethical obligations.

“Our citizens need to feel safe and protected, because we are here in the front lines of Europe,” he said in an interview.

“No one wants migrants who are sick with Covid,” he said, but “we can’t stop rescuing people at sea.”

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Marilyn Cortez, a retired cafeteria worker in Houston who has no health insurance, spent much of July in the hospital with Covid-19. When she finally returned home, she received a $36,000 bill that compounded the stress of her illness.

Then someone from the hospital, Houston Methodist, called and told her not to worry — President Trump had paid it.

But then another bill arrived, for twice as much.

Ms. Cortez’s care is supposed to be covered under a program that Mr. Trump announced this spring as the pandemic was taking hold — a time when millions of people were losing their health insurance and the administration was doubling down on trying to dismantle the Affordable Care Act, the law that had expanded coverage to more than 20 million people.

“This should alleviate any concern uninsured Americans may have about seeking the coronavirus treatment,” Mr. Trump said in April about the program, which is supposed to cover testing and treatment for uninsured people with Covid-19, using money from the federal stimulus package.

The program has drawn little attention since, but a review by The New York Times of payments made through it, as well as interviews with hospital executives, patients and health policy researchers who have examined the payments, suggests that the quickly concocted plan has not lived up to its promise.

It has caused confusion at participating hospitals, which in some cases have mistakenly billed patients who should be covered by it. Few patients seem to know the program exists, so they don’t question the charges. And some hospitals and other medical providers have chosen not to participate.

Large numbers of patients have also been disqualified because Covid-19 has to be the primary diagnosis for a case to be covered (unless the patient is pregnant).

“This is not the way you deal with uninsured people during a public health emergency,” said Sara Rosenbaum, a professor of health law and policy at George Washington University.

Credit…Ben Solomon for The New York Times

One of the U.S. Open’s most indelible moments featured one of the game’s greatest tennis players sitting on a flower box by the side of the court. On that day in 2016, his 39th birthday, Jimmy Connors was staging a riveting comeback against Aaron Krickstein. Sneaking a quick rest before the fifth-set tiebreaker, he looked into the camera and boasted, “This is what they paid for — this is what they want.”

“They” were the stomping, clapping, screaming, delirious fans whose rabid enthusiasm helped give Connors the energy and psychological edge to topple his younger opponent.

The U.S. Open is known for its passionate and raucous fans, so their absence this year will definitively change the tenor of the tournament, which begins Monday in New York.

“Playing in an empty stadium will be quite a change from what we’re used to, especially in New York,” said the 14th-ranked Petra Martic.

The most striking change might be in the Louis Armstrong and Arthur Ashe Stadiums, which feel cavernous and where struck balls sound different when the stands are empty.

Jamie Reynolds, ESPN’s vice president of production, said that without fans making noise between points, players might be able to hear the commentators.

“They can even listen to the analysis and change their tactics,” Reynolds said.

Yet in Ashe and Armstrong, players will hear recorded cheers from the moment they enter the stadium. And Lew Sherr, the U.S. Tennis Association’s chief revenue officer, promised that piped-in sounds of the game would be as accurate as possible.

If Serena Williams earns a break point with a winner in the first set during a second-round day session, for example, the computer system will seek a crowd reaction from a similar moment.

Credit…Sarah Stacke for The New York Times

A recent $84 million budget cut to New York City’s sprawling parks system, forced by the dire economic challenges the city faces because of the pandemic, comes as the city’s green spaces are hosting gatherings that once took place in bars, reception halls and living rooms.

In typical times, such heavy use would be a challenge for the parks system. But this summer, with maintenance crews shrinking, skipped lawn trims and infrequent trash pickup, some parklands have been left unsightly and dirty at a time when New Yorkers say they need the city’s 1,700 green oases more than ever.

Some New Yorkers fear that the disheveled parks are a portent of something far worse than litter: a city spiraling toward decline.

“It’s kind of depressing,” said 19-year-old Elizabeth Soto, as a squirrel licked a fruit snack wrapper nearby. “We’re stuck in the house, and then we come out of the house and we have to do extra cleaning.”

what we learned this week

As the Republican National Convention neared its end this week, President Trump vowed that a vaccine against the coronavirus would be produced before the end of the year “or maybe even sooner.”

The pledge is a tall order by any measure: Patients must be willing to take the vaccine, and there must be enough doses to be distributed.

The longer that vaccines are tested before being released, the likelier they are to be safe and effective. But the White House’s search for a silver bullet has prompted fears among government researchers that the president — who has spent his time in office undermining science and the expertise of the federal bureaucracy — may push the Food and Drug Administration to overlook insufficient data and give at least limited emergency approval to a vaccine.

Seven months into the pandemic, more than 30 vaccines are rapidly advancing through clinical trials. At least 88 vaccine candidates are under active preclinical investigation in laboratories across the world, with 67 of them due to begin clinical trials before the end of next year.

Other highlights in coronavirus news from the week:

Reporting was contributed by Ed Augustin, Melissa Eddy, Marie Fazio, Tess Felder, Abby Goodnough, Taylor Lorenz, Zach Montague, Sarah Maslin Nir, Apoorva Mandavilli, Stuart Miller, Elian Peltier, Christopher F. Schuetze, Pranshu Verma and Lauren Wolfe.