SYDNEY (BLOOMBERG) - Australia's New South Wales state has recorded its first new case of the coronavirus in 25 days after a woman working at a quarantine hotel in Sydney tested positive.

Authorities are investigating whether she became infected in the community or through work at the facility, the state health department said in a statement Thursday (Dec 3). The woman's five family members were tested overnight and all returned a negative result for the virus.

Australia has largely controlled the spread of community transmission, but health experts say there is no room for complacency due to an ongoing risk of the virus entering the community from returned overseas travellers - despite a mandatory system of hotel quarantine. More than 30,000 Australians, many living in Europe and the United States where the virus is rampant, are waiting to return home.

"This is a good warning for all of us that we have to maintain our vigilance," NSW Premier Gladys Berejiklian told reporters.

"When you are welcoming 3,000 Australians back every single week, and when we know the rate of infection is increasing in all parts of the world, we have to remain ever vigilant."

Bungled security at quarantine hotels in Victoria, which reportedly included guards sleeping with guests, saw the virus escape into the community - leading to a three-month lockdown in Melbourne.

Meanwhile, in neighbouring South Australia, authorities are investigating how two security guards, a cleaner and two returned travellers contracted the virus while in hotel quarantine - seeding a cluster of infections in the state capital Adelaide.