South Australia may be able to eradicate the new coronavirus within a month, local health authorities say, as the state records no new COVID-19 cases for the second day in a row.

SA Health Minister Stephen Wade says he is cautiously optimistic that the highly contagious infection is under control in the state, but warned it was too early to abandon social distancing measures.

"This is the third week where we have zero or single digit cases each day, but that should not be a seed for complacency – that should spur us on for even further efforts," the minister said this afternoon.

South Australian Health Minister Stephen Wade speaks to the media in Adelaide. He says he is cautiously optimistic that the state is on track to eradicate COVID-19 in the next month. (AAP Image/David Mariuz) (AAP)

"We've got to this point through social distancing and border control. There is the chance that people will get slack. Over the next two to four weeks, I would very much encourage the public to hold the course.

"We will all stand to benefit at the end of this."

The promising figures come despite a massive increase in community testing as part of a two-week blitz of anyone with flu-like symptoms.

Over 5000 residents have been tested in the past two days alone.

South Australia has now conducted more than 40,000 tests, encompassing over two per cent of its population – the highest number per capita of any Australian state.

State authorities have credited a strict state border closure and widespread rapid testing for their success in reigning in the pandemic.

In a new measure to streamline the state's extensive testing regime, starting from tomorrow those who test negative will be able to receive their results via text message.

The new scheme will initially be rolled out for those who get tested at drive-through clinics, but is expected to be available to everyone by the middle of next week.

Hospital staff test people for COVID-19 outside the Tanunda War Memorial Hospital, a dedicated coronavirus testing clinic. South Australia has the most extensive COVID-19 testing in the country. (AAP Image/David Mariuz) (AAP)

Mr Wade urged young people in their 20s, who have so far been under-represented in the testing program, to come forward if they are feeling at all unwell.

"Young people are less likely to have severe symptoms, but I would urge younger South Australians to just be a bit more cautious," he said.

Testing across all demographics was vital to ensuring an accurate snapshot of COVID-19 in the community, which in turn would inform any rollback of social distancing restrictions, the minister said.

Two more international flights will land in Adelaide tomorrow and Tuesday, bringing home Australians stranded due to international lockdowns.