Statisticians and others have called for random testing of the community, but the government says that is not on the agenda.

In the first week of May, 159,000 tests were done nationwide, averaging 22,700 a day (by Saturday, it was higher again, to a seven-day average of 26,300). In the week to April 16, the average was 7100 tests a day.

As the states and territories reopen businesses and increase activity this week, no target figure has been released for the number of tests that should be done, other than Professor Murphy's reference to 40,000 or 50,000 tests a day "if necessary", and Prime Minister Scott Morrison's April 26 suggestion that tests were being ramped up to that number (it was about 12,000 a day then).

No one has thrown light on the 40,000 to 50,000 figure, nor suggested an ideal number. A Health Department spokesperson said Professor Murphy's figure was "considered in the context of the epidemiology of COVID-19 in Australia and to ensure alignment of testing capacity with any agreed surveillance strategy".

The World Health Organisation wants countries to test at a rate where fewer than 10 per cent are positive, describing one positive in 10 tests as "a general benchmark of a system that's doing enough testing to pick up all cases".

On this measure, Australia is well ahead. In Australia, about 1 per cent of total tests have been positive, 10 times fewer than the WHO benchmark. And the current rate of positives is orders of magnitude below that, with fewer than 30 positives from more than 25,000 tests a day.

All states have ramped up testing since mid-April as testing kits become more freely available and in anticipation of a return to work and business, although to different degrees.

Nationally, the testing rate more than tripled. In the ACT it more than doubled from 117 a day in mid April to 258 a day in the first week of May (and a seven-day average of 290 by Saturday).

On Friday the ACT finished what it described as a two-week testing blitz. In the fortnight, it averaged 252 tests a day, more than double the fortnight before.

When calculated as a proportion of the population, the ACT's testing rate is well below the national average, which is driven by high testing rates in NSW, Tasmania and Victoria, all of which have been hit by outbreaks. The ACT has remained free of outbreaks and has diagnosed just five cases in the past month. It has a testing rate on par with South Australia. The Northern Territory and Queensland are well behind.

Nationally, an average of 89 tests for every 100,000 people was done each day around the country in the first week of May, with NSW at 91. In the ACT, the testing rate was 60 per 100,000 population. Victoria and Tasmania are testing at much higher rates.

Experts are calling for more widespread random testing.

Professor in biostatistics at the University of Sydney Ian Marschner said with a low prevalence of infection, a very high number of tests was important to capture the extent of disease.

He has called for testing beyond people with symptoms and targeted groups.

"At the moment we're targeting people with suspected infection, people with symptoms and people in contact and clusters," he said.

"Targeted testing is useful for control so you identify the infected people and you take them out of the system ... What targeted testing doesn't do is help you understand the progress of the epidemic throughout the community. The way to do that is random testing."

Random testing overseas showed the disease prevalence was unexpectedly high - and the same could be true here, or random testing could confirm no hidden spread, he said.

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Visiting professor of statistics at the University of Sydney Nicholas Fisher also wants random testing of the entire community to build an accurate picture.

He suggests an initial random sample of 20,000 people, chosen by the Australian Bureau of Statistics, followed by weekly testing of smaller groups.

That would provide hard data about questions such as how many people might have the disease without showing symptoms and infection rates and re-infection rates in different age groups or parts of the country, he said.

"Governments all over the world have been flying blind when it comes to the level and nature of undetected COVID-19 in the community," Professor Fisher said. "These data are essential in enabling Governments to gain a better understanding of what is driving community transmission and the possibility of a second wave, which is their main current concern."

Professor Fisher said widespread testing of people with symptoms and sentinel testing of groups at risk of catching the virus were important, but the missing link was randomly surveying the entire population. Such a survey could also be tailored to give accurate information on risk factors. Without that, estimates of infection rates and estimates of at-risk groups or areas were guesswork.

Australian National University infectious disease specialist Sanjaya Senanayake said Australia was "doing fine" on testing against international measures and World Health Organisation recommendations.

But he warned that restrictions on work, business and social mixing must be lifted "very very slowly".

"We have to be very wary. We've seen what's happened in Singapore," Associate Professor Senanayake said. "There is this sense of euphoria coming from being in that state of attrition where we've been at home for the last few weeks and I'm concerned people might go the other way. I don't want all our good work to be undone by that."

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