said last year in a video promoting the country’s alert system, called Corona-Warn-App.

But the apps never received the large-scale efficacy testing typically done before governments introduce public health interventions like vaccines. And the software’s privacy features — which prevent government agencies from identifying app users — have made it difficult for researchers to determine whether the notifications helped hinder virus transmission, said Michael T. Osterholm, the director of the Center for Infectious Disease Research and Policy at the University of Minnesota.

“The apps played virtually no role at all in our being able to investigate outbreaks that occurred here,” Dr. Osterholm said.

Some limitations emerged even before the apps were released. For one thing, some researchers note, exposure notification software inherently excludes certain vulnerable populations, such as elderly people who cannot afford smartphones. For another thing, they say, the apps may send out false alarms because the system is not set up to incorporate mitigation factors like whether users are vaccinated, wearing masks or sitting outside.

Proximity detection in virus alert apps can also be inconsistent. Last year, a study on Google’s system for Android phones conducted on a light-rail tram in Dublin reported that the metal walls, flooring and ceilings distorted Bluetooth signal strength to such a degree that the chance of accurate proximity detection would be “similar to that of triggering notifications by randomly selecting” passengers.

Kimbley Craig, the mayor of Salinas, Calif. Last December, when virus rates there were spiking, she said, she downloaded the state’s exposure notification app on her Android phone and soon after tested positive for Covid-19. But after she entered the verification code, she said, the system failed to send an alert to her partner, whom she lives with and who had also downloaded the app.

“If it doesn’t pick up a person in the same household, I don’t know what to tell you,” Mayor Craig said.

In a statement, Steph Hannon, Google’s senior director of product management for exposure notifications, said that there were “known challenges with using Bluetooth technology to approximate the precise distance between devices” and that the company was continuously working to improve accuracy.

The companies’ policies have also influenced usage trends. In certain U.S. states, for instance, iPhone users can activate the exposure notifications with one click — by simply turning on a feature on their settings — but Android users must download a separate app. As a result, about 9.6 million iPhone users in California had turned on the notifications as of May 10, the state said, far outstripping the 900,000 app downloads on Android phones.

Google said it had built its system for states to work on the widest range of devices and be deployed as quickly as possible.

Some public health experts acknowledged that the exposure alert system was an experiment in which they, and the tech giants, were learning and incorporating improvements as they went along.

One issue they discovered early on: To hinder false alarms, states verify positive test results before a person can send out exposure notifications. But local labs can sometimes take days to send test results to health agencies, limiting the ability of app users to quickly alert others.

In Alabama, for instance, the state’s GuideSafe virus alert app has been downloaded about 250,000 times, according to Sensor Tower. But state health officials said they had been able to confirm the positive test results of only 1,300 app users. That is a much lower number than health officials would have expected, they said, given that more than 10 percent of Alabamians have tested positive for the coronavirus.

“The app would be a lot more efficient if those processes were less manual and more automated,” said Dr. Scott Harris, who oversees the Alabama Department of Public Health.

Colorado, which automatically issues the verification codes to people who test positive, has reported higher usage rates. And in California, UC San Diego Health has set up a dedicated help line that app users can call if they did not receive their verification codes.

Dr. Longhurst, the medical center’s chief information officer, said the California app had proved useful as part of a larger statewide public health push that also involved mask-wearing and virus testing.

“It’s not a panacea,” he said. But “it can be an effective part of a pandemic response.”

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India Suffers a Coronavirus Second Wave, With Global Impact

NEW DELHI — When the coronavirus first struck India last year, the country enforced one of the world’s strictest national lockdowns. The warning was clear: A fast spread in a population of 1.3 billion would be devastating.

Though damaging and ultimately flawed, the lockdown and other efforts appeared to work. Infections dropped and deaths remained low. Officials and the public dropped their guard. Experts warned fruitlessly that the government’s haphazard approach would bring a crisis when a new wave appeared.

Now the crisis is here.

India on Friday reported a daily record of 131,878 new infections as Covid-19 races out of control. Deaths, while still relatively low, are rising. Vaccinations, a mammoth task in such a large nation, are dangerously behind schedule. Hospital beds are running short.

Parts of the country are reinforcing lockdowns. Scientists are rushing to track new strains, including the more hazardous variants found in Britain and South Africa, that may be hastening the spread. But the authorities have declared contact tracing in some places to be simply impossible.

now behind the United States and Brazil.) The economic blowback of the resulting lockdown was devastating.

But the numbers at the time actually understated the first wave, scientists now say, and deaths in India never matched levels of the United States or Britain. Leaders began acting as if the problem had been solved.

Serum Institute of India, one of the world’s largest vaccine makers, boasted of a major stockpile of the Oxford-AstraZeneca vaccine, which makes up the bulk of the country’s drive. The government even launched a “vaccine diplomacy” campaign that sent doses to other countries.

But the initial rollout within India was slowed by complacency and plagued with public skepticism, including questions about the Oxford-AstraZeneca vaccine and lack of disclosure about an Indian-developed dose. Now the vaccination program is not matching the spread. The Serum Institute has said that practically all of its daily production of about two million doses will over the next two months go to the government, delaying commitments to other countries.

Several Indian states now worry that their vaccines stocks will run out. Mumbai, India’s largest city, had shut more than half of its vaccination centers, local media reported on Friday. The central government’s health minister lashed out at the states, reassuring that there would be no shortage and that more supplies were in the pipeline.

hit the campaign trail for state elections. Prime Minister Modi has addressed more than 20 rallies, each with thousands of often-unmasked people.

On Wednesday, Delhi officials said that even a solo car driver would be punished for not wearing a mask properly. The same day, Amit Shah, the country’s de facto No. 2 leader, drove through a campaign crowd in the state of West Bengal, waving without a mask and throwing rose petals.

The government also gave the go ahead for a long Hindu religious festival called Kumbh Mela, which runs through the end of April. Between one million to five million people attend the festival each day in the city of Hardiwar, on the banks of the river Ganges in the state of Uttarakhand.

no one would face restrictions as “the faith in God will overcome the fear of Covid-19.” Days later, Mr. Rawat tested positive for Covid.

The positivity rate of random tests is rising at the festival, and more than 300 participants have tested positive, said Dr. Arjun Singh Senger, a health officer at the festival.

The sheer speed of new infections has surprised health officials, who wonder whether variants might be a factor. Answering that question will be difficult. India has put only about 1 percent of its cases through genome sequencing tests, according to Dr. Reddy, of the Public Health Foundation of India, but researchers require a minimum of 5 percent to determine what is circulating.

So far, the government has found variants from the U.K. and South Africa as well as a local mutation. Limited information suggests that more infectious variants are circulating in India, as well, Dr. Reddy said.

Even if the variants have not yet been a major part of the new wave of infections, they have cast a shadow over India’s crucial vaccination drive. The AstraZeneca vaccine has been rejected by South Africa ineffective against that variant.

“This time, the speed is much faster than the last time,” said Dr. Vinod K. Paul, the head of India’s Covid response task force. “The next four weeks are very, very crucial for us.”

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Hong Kong’s Virus Rules Keep Cases Low but Stoke Complaints

HONG KONG — A pandemic illness had struck Hong Kong, and the Worley family had gamely followed the rules. They wore masks. They socially distanced. They skipped traveling overseas with their newborn baby to visit his grandparents.

Then the coronavirus came to the playgroup of their 15-month-old son. Now the three of them are stuck in a spartan government quarantine center for 10 days.

“We’ve done everything that was asked of us,” said Kylie Davies-Worley, the mother, who is Australian. “We’ve complied with every regulation, we’ve stayed home when we needed to, yet we feel like we’ve been treated like second-class citizens. It’s not humane.”

Hong Kong’s targeted approach to fighting the virus entails temporarily restricting the freedoms of a few for the benefit of the many. The Chinese territory has avoided full lockdown largely by moving aggressively to stamp out the virus wherever it may appear, whether among taxi drivers and restaurant workers, in densely crowded, low-income neighborhoods, or at dance halls popular with older women.

told CNN.

a separate statement the same day, the government specified the amenities available to children in quarantine centers and said that “each and every decision has been made in the interests of the children and their families.”

Quarantine is nothing new in Hong Kong, which has one of the strictest policies in the world. People who test positive for the virus are isolated in hospitals for monitoring and treatment, regardless of whether they have symptoms, while their close contacts are quarantined for up to 14 days, even if they test negative. More than 42,000 people have passed through government quarantine facilities during the pandemic.

a New York Times database.

“One of the lessons from SARS is that targeted approaches like contact tracing and quarantine are a useful way to limit transmission of an infection, and that has been applied with great success with the Covid pandemic in Hong Kong,” said Ben Cowling, an epidemiologist and biostatistician at the University of Hong Kong School of Public Health, referring to the 2003 epidemic that killed 299 people in the Chinese territory. (Hong Kong has recorded 203 deaths from Covid-19.)

stop the protests from resuming.

That distrust is reflected in lower-than-expected participation in a citywide vaccination campaign, with residents especially skeptical of the Chinese-made Sinovac vaccine. On Monday, the government said it was expanding eligibility to everyone 30 and older to accelerate vaccination efforts.

Confusion, distrust and misinformation on social media have contributed to accusations of unequal treatment in quarantine decisions. Parents asked why some children were allowed to quarantine at home or in hotels instead of in government facilities; health officials say it depends on their degree of exposure to the virus.

The case of a couple working at the U.S. Consulate who tested positive for the virus but were allowed to bring their two children with them to the hospital caused further consternation and complaints of exceptional treatment. Mrs. Lam said the decision had been made based on the couple’s family circumstances and not their status as consular employees.

“Everybody is treated equal before the law and in terms of our epidemic control measures, regardless of their race, their status, their identity, whether they are more resourceful or less resourceful,” she said on Tuesday. “This is a fundamental principle in Hong Kong and we will abide by that principle.”

Though officials did relent on quarantine for some children, no such reversal came for members of the playgroup used by the Worley family. One of them, Jennifer Choi, is spending seven nights in a government center with her 13-month-old daughter.

Like the Worleys, Ms. Choi, who is from South Korea, said she had been careful to follow social-distancing rules. Her daughter often wears a face shield even though Hong Kong does not require masks for children under the age of 2.

So it was frustrating for her and other parents when officials cited the presence of maskless babies in the group as one reason all eight of them and their caregivers were being sent to government quarantine.

“What kind of logic is that?” Ms. Choi said.

Tiffany May contributed reporting.

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