As the government in Hong Kong struggles to contain the city’s worst Covid outbreak ever, some residents have panicked. They have emptied supermarket shelves of vegetables and meat. They have raided drugstores for pain and fever medication. Those who could afford it have jumped on flights out of the city.

Tens of thousands of new Omicron cases are being reported each day, and deaths have surged. The anxiety gripping Hong Kong is not just about the explosion of infections, but also about what the government will do next. Mixed messages from officials have left residents wondering: Will there be a lockdown? Will we be sent into isolation facilities? Will our children be taken from us if they test positive?

Under pressure from Beijing to eliminate infections, Hong Kong officials have vowed to test all 7.4 million residents. Such an operation would require restricting people’s movements, but the government has been ambiguous about whether it would impose a lockdown, and if so, when. Just the possibility of one, however, set off the run on groceries and other supplies.

“I’ve been here most of my life, through everything, and it’s never come to something like the panic I’ve seen by the public,” said Allan Zeman, 72, a property developer and an adviser to Hong Kong’s leader, Carrie Lam

The city’s fatality rate from the virus is currently among the world’s highest, at three per 100,000 residents, largely because many older Hong Kongers are unvaccinated. (Since the pandemic started, though, Covid has killed Americans at far higher rates than people in other wealthy nations, as well as in Hong Kong.)

Hong Kong is one of the last places in the world that is still trying to eradicate the coronavirus, rather than live with it. It has doubled down on a strategy of isolating every case found, regardless of severity and symptoms, and imposing quarantine orders on people deemed close contacts, despite a shortage of facilities and workers. Rising infections, as well as the government’s measures, have already overwhelmed hospitals, morgues, ambulance services and quarantine facilities, and forced understaffed post offices, banks and even prisons to cut back on services.

Residents have been particularly alarmed by the government’s approach to children who test positive for the coronavirus. The city erupted in an outcry two weeks ago after health workers took an infected 11-month-old girl from her parents and isolated her in a hospital. One parent is typically allowed to accompany a child, but the hospitals are too crowded, with hundreds of children stuck in Covid isolation wards. Officials later said they would organize video chats to allow hospitalized children to stay in touch with their family members

Kaylah Tong, a 35-year-old pastor, said that she sent her 2-year-old son to a hospital last month after he had tested positive, with a high fever and convulsions. He stayed alone in an isolation ward for two days.

A doctor had initially warned her that her son could be kept in isolation for weeks because of the hospital’s Covid-19 protocols, which include requiring patients to test negative before being discharged. That made Ms. Tong worry about her son’s mental health.

“How could children be kept there so long without the parents at their side, just because of quarantine measures? I cannot accept that,” she sai.

By the third day, though, the hospital let Ms. Tong take her son home to recover; his condition had improved and his hospital bed was needed. The government later said it would temporarily loosen its policy so that only children with severe coronavirus symptoms would need to hospitalized.

Foreign governments have also responded to Hong Kong’s pandemic measures with concern. Citing the risk of familial separation, the United States Consulate last week warned Americans not to travel to Hong Kong. The French consul general acknowledged that the latest measures would “profoundly affect everyone’s life, with a price to pay that has been steadily increasing for two years, especially for families with children.”

Consular officials have worked to help expatriates find travel arrangements to leave Hong Kong, which has banned flights from nine countries, including the United States, Canada, Britain and Australia. The Swiss Consulate arranged one flight for citizens. The Irish Consulate said it had “never experienced this level of demand for consular service for those wishing to leave.”

Hong Kong, a place once known as “Asia’s World City,” now has some of the strictest travel restrictions, isolating it from the rest of the world. The new uncertainty has driven the largest exodus of residents since the early days of the pandemic in 2020, with more than 70,000 net departures last month, according to data from the Immigration Department.

Weeks earlier, Cordula Kotanko, a German management consultant, and her husband had been thinking about leaving Hong Kong because their three daughters had been struggling with remote learning during much of the pandemic. They were also worried about the prospect of being caught in a citywide lockdown.

Then, late last month, the government said it would bring forward the summer holiday to start in March and April, around four months earlier than usual. Officials said they planned to use schools to conduct mass testing and isolation of the sick. That prompted Ms. Kotanko and her husband to pack their family up and fly to Singapore.