Australia’s most populous state has reported a record number of new coronavirus cases and a sharp jump in hospital numbers, while thousands of people isolate at home after contracting the virus or coming into contact with someone who has.

New South Wales reported 6,394 new infections on Sunday, up from 6,288 a day earlier. Case numbers in the state have surged over the past two weeks but hospitalisations have lagged behind new infections.

More than 70% of cases in some Australian states are the Omicron variant but New South Wales does not routinely carry out genome testing to identify the variant.

New South Wales health minister Brad Hazzard indicated on Sunday that Omicron is widespread.

“We would expect that pretty well everybody in New South Wales at some point will get Omicron,” he said.

“If we’re all going to get Omicron, the best way to face it is when we have full vaccinations including our booster.”

Health officials reported 458 active cases in hospitals across the state, up sharply from 388 the day before. There are 52 people in intensive care in New South Wales.

Meanwhile, a major laboratory in Sydney, which is in New South Wales, said on Sunday that 400 people who had been informed a day earlier that they had tested negative for Covid had in fact tested positive.

The lab’s medical director said those people are being contacted and informed of the error.

“An emergency response team is now investigating the cause of this mistake, which is believed to be due to human error,” he said. “We sincerely apologise.”

Doctors and pharmacists in New South Wales have said they are running short of vaccine doses amid a rush for shots spurred by concern over the Omicron variant.

Victoria, the country’s second most populous state, reported 1,608 new Covid cases and two deaths on Sunday, with 374 people in hospitals, including 77 in intensive care.

More than 30,000 people in Victoria spent Christmas isolating at home, unable to celebrate with family or friends. Of those, about half were reported to be active cases who contracted the virus in the days leading up to Christmas.