Testing rates are nowhere near the figure cited by Professor Murphy, with about 10,000 tests a day around the country. The ACT has done only about 100 tests a day in the past week but the states and territories are trying to ramp up testing, urging everyone with cold or flu symptoms to get tested.

Professor Murphy revealed new modelling, which excludes overseas-acquired coronavirus cases. Looking only at domestic cases, it shows a slight uptick in the number of people being infected by each person with the virus. But Professor Murphy said the "reproduction number" was still around and just below one in most states.

A reproduction number of one means each person infects just one other person, not the 2.5 people that coronavirus infects without restrictions, setting off exponential growth in cases.

"We are close to one, we've got to keep it below one, and we have to not be complacent," Professor Murphy said, warning that local outbreaks had the potential to significantly increase case numbers and overwhelm health systems without measures to control the spread.

"We want to be testing 40,000, 50,000 Australians a day if necessary, so that we can be absolutely sure."

Cases continue to dwindle, with the ACT and the Northern Territory now having too few even for the modelling.

By Friday morning, there had been 6667 virus cases, with just 13 new cases in the previous 24 hours. Just 48 cases have been reported since Monday around the country. Seventy-nine people have died as of Friday afternoon, a death rate of 1 per cent.

The government believes that Australia is detecting 93 per cent of all symptomatic cases - the highest detection rate in the world.

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"No Australian wants to see hundreds of people dying a day from coronavirus. We are not prepared to see that, and that's why we are being so cautious and we are putting in these extraordinary surveillance measures," Professor Murphy said, referring to other countries where "tens of thousands of people probably had it" before it was picked up.

"We have never been in that situation and we have no intention of being in that situation. I can't be 100 per cent sure. We don't know everything about this virus. But I can tell you we're going to be as prepared as we can to prevent that happening."

Australian National University infectious diseases expert Sanjaya Senanayake said more testing must accompany any lifting of restrictions.

"We need to see if there's a surge in cases and we need to identify it early and we need to clamp down on any outbreak if it happens otherwise we'll undo all the good work we have done."

While people could not be forced to get testing, people without symptoms should be tested in areas where there had been outbreaks and Australia should move also to antibody testing, to check how many people might already have been infected.

"The one great uncertainty here has been the asymptomatic cases. What proportion have been asymptomatic and can they transmit to other people?"

Health authorities have tackled three outbreaks in recent days - with more than 100 infected in an outbreak linked to a hospital in northwest Tasmania, more than 40 infected at the Newmarch aged care home in Sydney and 14 infected at a Melbourne psychiatric facility.

Grattan Institute health program director Dr Stephen Duckett said with some "hiccups", such as in NSW and Tasmania, the number was continuing to trend down, and within the next week or so Australia could start to make decisions about which restrictions it could lift.

"We should have enough data by then to be confident about the direction we should pursue," he said.

Dr Duckett supported more testing, but said even among people with symptoms, only one in every 100 tests was positive, so it was highly unlikely that wider testing of people with no symptoms would show significant disease.

The key was contact tracing and with a low take-up expected of the government app, that would come down to legwork and phone calls. Coronavirus had a long incubation period and a long period between when people become infectious and symptomatic, which meant it was crucial to swing into action as soon as someone developed symptoms, he said.

The national cabinet also released a set of principles covering coronavirus in the workplace as firms prepare for people to return. Businesses must ensure they have social distancing and "exemplary hygiene measures" in place and must "actively control" against the virus, the principle says. Businesses and workers must also prepare for cases and be ready to respond "immediately, appropriately, effectively and efficiently".

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