Australia had just eight new coronavirus cases on Monday, from three states, signalling major progress in flattening the curve of new infections.

The latest numbers come as the Victorian government released modelling data showing thousands of people would have died had social distancing not been introduced.

On Monday, the state’s chief health officer, Professor Brett Sutton, said 36,000 Victorians could have died – an average of 70 every day and up to 650 deaths in a day at the peak, which would have been in week 24.

He said the restrictions were more successful than authorities had imagined they would be and reinforced that the government was never going to let this be an “unmitigated pandemic”.

Victoria recorded just one new coronavirus case overnight, NSW had six and the ACT one case. In the 24 hours from 6am Sunday to 6am Monday, there were been 26 new cases across Australia.

Later in the afternoon, South Australian confirmed its third day on end with no new coronavirus patients. Western Australia also had no new cases, after reporting just one on the weekend.

Queensland had no new cases on Monday, while the Northern Territory has had none for a fortnight.

Deputy chief medical officer Dr Nick Coatsworth told a media briefing on Monday afternoon 71 Australians had due because of COVID-19 with more than 2.4 million cases recorded worldwide.

“We have conducted over 424,000 tests for COVID-19 to date,” he said.

“Most importantly, in the past 24 hours, we have seen a further 26 cases, representing a continued ongoing low level of reporting of cases, which demonstrates that the physical distancing measures that we have asked of Australians – and that Australians have really embraced – are still paying dividends for us and still keeping our numbers of COVID-19 very low indeed.”

However, with a sense that restrictions might be eased in coming weeks if the trend of low numbers continues, state premiers continued to urge people to “stay the course”.

Victorian Premier Daniel Andrews said the reason for the success in “suppressing the virus” was that the majority of people were doing the right thing.

“Frustrating, very difficult, no one is enjoying it, but people are following the rules and it is working, making a big difference. That gives us options down the track that would not be available to us without this, the very low case numbers,” he said on Monday.

Victoria’s lone confirmed case came after about 7000 tests were conducted over the weekend.

It brought Victoria’s infection tally to 1329, with the death of a man in his 80s taking the state’s death toll to 15.

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But Mr Andrews doesn’t anticipate an early end to social distancing laws and partial lockdown.

He said there might be an important opportunity in four weeks to ease restrictions where there is a low risk of transmission but classrooms would remain closed for the majority of children.

NSW focuses on nursing home cluster

The total number of COVID-19 cases across the state rose slightly to 2963, with 22 people in intensive care. A total of 30 people have died.

NSW Health on Monday confirmed that a second person at the Newmarch House nursing home in Caddens, a 94-year-old man, had died.

NSW chief health officer Dr Kerry Chant said extensive testing had been done at the facility and the focus was on stopping the spread of the virus.

“We are aware that in those settings we see an amplification and spread of COVID-19 and we want to interrupt spread in those settings at the earliest possible time.”

Meanwhile, nine more crew members of the Ruby Princess cruise ship have tested positive to COVID-19. That takes the total number of crew infected to 171.

The ship remains docked at Port Kembla, where it will stay until at least Thursday.

Queensland’s ‘tremendous effort’

It is the first time in 81 days that there have been no new cases of COVID-19, leaving the state’s total at 1019.

“This is an absolutely tremendous effort,” Premier Annastacia Palaszczuk said on Monday.

“If we can keep this up over the coming weeks, I’m sure that that’s going to mean we will be able to make some changes and ease some of those restrictions on the population.”

The Premier said she was overjoyed at the result, but urged Queenslanders to continue to distance themselves socially and wash their hands.

Just 20 people are in hospital, with seven in intensive care on ventilators in the state’s south-east. Of those who have tested positive, 738 patients have recovered, while six Queenslanders have died.

“We’ve seen in other countries, reductions to near zero levels of cases and then a second wave of infection so we need to be very cautious, we need to keep up our current approach,” Health Minister Steven Miles said.

“But if we can sustain this, then the end is in sight.”

Modelling shows numbers without social distancing

Professor Sutton said collaborative government and university data showed “what might have occurred had we only had a case isolation and contact process many place without social distancing measures”.

• Related: Victorian government modelling data

“Using the assumptions that were in the modelling originally, there would be five unknown cases out in the community and an introduction of two new cases every week.

“We would have gotten to 58,000 infections per day at the peak. So literally, hundreds of thousands infected if we had just had isolation and quarantine in place.

“This is what would have been needed, had we not taken the actions we did: 10,000 intensive care beds required and 7000 of those ventilated.

“It would have peaked at 650 deaths per day, so not dissimilar to what’s being seen across Europe in a number of countries. You can see that Victoria has take an different trajectory. We did, along with all the states and territories of Australia, take an early robust measure with the physical distancing restrictions in place.

“It has pushed our curve on a very different pathway than other countries,” he said.