Three family members in the Victorian border city of Albury have tested positive for COVID-19 as NSW remains on high alert for “seeding” of the deadly virus from its southern neighbour.

Two of the Albury cases were among 13 new COVID infections in NSW on Thursday. The others are in returned travellers in hotel quarantine.

The other Albury case is not included in Thursday’s numbers, but NSW chief health officer Kerry Chant confirmed the infection on Thursday morning.

One of the Albury people who has the virus recently visited Melbourne, where it’s believed they picked it up.

“There’s been an extensive turnout for testing in the community and I would continue to ask all the border communities to be vigilant and to ensure that they present for testing whenever they have the mildest symptoms,” Dr Chant said.

Premier Gladys Berejiklian said authorities were on high alert as Victoria’s infection numbers continued to surge.

“What we need to do is to make sure there hadn’t been any seeding prior to the rate of community transmission becoming apparent in Melbourne,” she said.

“We won’t know for sure for a couple of weeks, so we are monitoring the situation daily.”

Ms Berejiklian warned tightened measures were likely if community transmission of the coronavirus increased in NSW.

“What’s occurred in Victoria is a wake-up call for all of us about how contagious the virus is,” she said.

“That’s the state we’re in.”

Ms Berejiklian said there would be no immediate changes to restrictions, but community transmission remained authorities’ main focus.

Earlier, there were warnings that NSW might be approaching a “magic number” of infections that could become a tipping point.

Mary-Louise McLaws, an epidemiologist and World Health Organisation adviser, said active cases could quickly reach a point where authorities were so overwhelmed they could no longer do effective contact tracing.

“If it gets to about 100 cases across two incubation periods – about 14 days each – in very quick succession it doubles and then after that, it can double and triple each period,” she said.

On Wednesday, health authorities in NSW were scrambling to contain two major breaches of its tough new border restrictions, after plane passengers from Melbourne left Sydney Airport without screening and a Victorian child tested positive for the virus while holidaying on the NSW South Coast.

A sign displays COVID-19 restrictions in the NSW-Victoria border town of Albury.

Professor McLaws said infected travellers crossing the NSW border could mean the virus spread rapidly.

“A few cases coming over the border from Victoria [can] tip that magic number into outbreaks that are going to be very hard to control,” she told the ABC.

In the ACT, three new cases of coronavirus were also traced back to the outbreak in Victoria, more than a month since the last known positive case in the territory.

NSW has progressively eased restrictions, including reopening public spaces such as the State Library of NSW.

Fiona Stanaway, a clinical epidemiologist from the University of Sydney, said it was highly likely carriers of the virus from Melbourne were already in NSW.

“If there’s been some transmission from people coming back from Melbourne, and people having contact with those people, we won’t really see that until another couple of weeks or so,” Dr Stanaway told the ABC.

“That really emphasises the importance of people getting tested.”

Professor McLaws said up to 18 per cent of COVID-19 cases were asymptomatic, but those people were still capable of spreading the virus.

Both experts said bringing back tighter social-distancing restrictions – something the Ms Berejiklian has repeatedly said she wants to avoid – was a possibility.

Anyone who comes from Victoria to NSW must self-isolate for 14 days. The state government has said it is considering forcing them into hotel quarantine.

Ms Berejiklian also said creating a second set of checkpoints around Albury was a possibility, which would make it more difficult for travellers to get deep into NSW.

Dr Stanaway said she had noticed people in NSW become more complacent about social-distancing.

“I think it’s really still important for people to try to social distance as much as they can,” Dr Stanaway said.

“It’s hard because I think we’re all quite exhausted by the whole thing and because we’ve had things open up, people have felt that it’s quite safe to go back to what was a much more normal life.

“This shouldn’t just be thought of as Melbourne’s problem and we really need to realise that this can happen anywhere and can happen again.”

-with agencies