NSW has confirmed another day without locally acquired coronavirus cases, making it a week since it has had an infection outside hotel quarantine.

There were four more cases in returned Australians and permanent residents in hotel quarantine.

State Health Minister Brad Hazzard said it was “a very exciting day with no COVID transmission”.

“There are four new cases in our hotel quarantine system, which again just verifies the absolute need for the hotel quarantine system, when we look at the disaster that is going on in so many countries overseas,” he said.

“So many Australians coming back from those countries are landing here in NSW.”

The last COVID case in NSW that is thought to be locally acquired was confirmed last Thursday. She is a worker in a hotel quarantine hotel who is thought to have somehow picked up the virus from a visiting overseas air crew.

Confirmation of the woman’s infection sparked a raft of travel warnings for some of Sydney’s busiest public transport routes after it was revealed she had caught trains and the light rail from her home in Minto to work at Darling Harbour.

NSW Health is continuing to investigate the woman’s case. Her close contacts remain in isolation, although no further positives have been identified.

The public transport alerts are also still active.

• See all of NSW’s latest COVID locations and alerts here

State health authorities have also issued a renewed alert for residents of south-western Sydney after fragments of the virus that causes COVID-19 were detected at the Liverpool sewage treatment plant.

NSW Health said it was concerned there could be active cases in the local community in people who had not been tested.

Elsewhere, Victoria’s run of COVID-free days edged closer to the six-week mark on Thursday, with the state confirming its 41st consecutive day without a new case.

There are hundreds of returned Australians and permanent residents in hotel quarantine in Melbourne after Victoria resumed taking returned travellers this week. None has yet tested positive to the coronavirus.

But Victorian Premier Daniel Andrews said as international travel resumed, more virus cases were inevitable.

“We will finish up with infections,” he said on Wednesday.

“You can’t make it zero risk, but you can get that risk down very low, and then do everything you can to mitigate it.

Up to 1120 international arrivals are scheduled to land at Melbourne airport each week, with travellers sent to city hotels to quarantine for 14 days.

On Wednesday, Tasmania – which also started taking returning Australians this week – reported three virus infections in a returned mother and her young children. Her husband was also confirmed with the virus on Thursday, becoming the island state’s fourth COVID case in 120 days.

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Victoria will no longer require permits for people crossing into the state from South Australia from December 12.

Chief health officer Brett Sutton said his decision was based on COVID exposure dates from SA – which has not had a new virus infection for 11 days.

Professor Sutton said Victorian health authorities would conduct spot checks on flights arriving in Melbourne from South Australia.

“This is also in line with the removal of the border and voluntary testing at the road checks,” he said.

“To date, the voluntary testing scheme of travellers from SA has not received one positive result.”