SYDNEY — Australia is regularly hailed as one of the best places to be during the coronavirus pandemic, with low case numbers, comparatively few deaths and a strict quarantine system for returning citizens and residents.

But authorities say parts of the country are entering the most worrisome phase of the virus fight, just as vaccinated Americans are ditching masks and Europe is lifting bans on travelers.

Gladys Berejiklian, the premier of New South Wales, home to Sydney, on Thursday said an outbreak of the highly infectious delta variant in the city meant it was facing “perhaps the scariest period” of the entire pandemic.

The cluster began last week with an airport limousine driver and has grown to 36 cases, including 11 announced Thursday.

The outbreak is minuscule by global standards, but a big deal in a country that has pursued a strategy of zero transmission. The low tolerance for even single-digit daily cases has left Australians frequently caught in cycles of new restrictions every time a cluster emerges.

A slow vaccination rate is exacerbating the struggle, so that well over a year into the pandemic, Sydney, Australia’s most populous city, is grappling with reinstated limits on gatherings and movements this week just as restrictions are easing in the United States and Europe.

The New South Wales state parliament was shut down Thursday after a lawmaker tested positive for the virus. On Wednesday, passengers had to weigh midflight whether to enter quarantine or return to Sydney after other Australian states snapped their borders shut.

Officials and scientists are especially troubled by the apparent ease with which the delta variant, first detected in India, passes from person to person.

Video footage shows the limo driver infecting strangers at a shopping mall and in a cafe through only fleeting contact, which scientists say proves it is possible to catch the virus simply from sharing the same airspace as an infected person.

“That makes this variant extremely dangerous because of the way cases can grow exponentially,” said Michael Plank, a data-modeling expert at the University of Canterbury in New Zealand. “After just three chains of transmission, there would be eight times as many cases on average. So, where the original variant might have caused 10 cases, the delta variant could cause 80 cases in the same time, which would quickly make it impossible to control without a lockdown.”

Melbourne, in Victoria state, was locked down last month after the delta variant was detected there. So far, authorities in Sydney have stopped short of imposing a lockdown, although police said they would ensure people were complying with rules such as mask-wearing on public transportation and a ban on people from parts of Sydney from traveling outside the metro area.

“In a pandemic, complacency has no place,” Berejiklian told reporters. “I am appealing to every single citizen … all of us must conform to the health advice to the letter of the law.”

The state government on Wednesday introduced a limit of five visitors to homes in Sydney, more stringent social distancing rules, and mask-wearing at indoor venues, including workplaces.

New Zealand is on alert, too, after a Sydney man flew to the capital, Wellington, while infectious, and spent a weekend visiting sites such as restaurants and a museum. On Thursday, New Zealand extended a pause on a quarantine-free travel bubble with New South Wales for another 12 days.

Authorities limited gatherings in the Wellington region to fewer than 100 people on Wednesday, and masks were made compulsory on public transit.

Right now, Plank said, vaccination coverage is too low to make much of a difference in controlling any outbreak. “So, we need to take the threat of this variant very seriously, and take the measures needed to stamp it out as quickly as possible.”

Tony Blakely, an epidemiologist at the University of Melbourne, said Sydney had about a 50-50 chance of beating the outbreak without a lockdown.

“Each day you delay means that if you need a lockdown, which I think is more than likely now, it will be longer and harder,” he told the Australian Broadcasting Corp.

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