One new COVID-19 case in South Australia

South Australia has reported another COVID-19 case linked to a miner who recently returned from the Northern Territory.

Premier Steven Marshall says a fourth child in the man's family has now tested positive for the virus.

All six family members, who all have the infection, have been transferred to Adelaide's dedicated facility for positive cases and are not considered a risk to the wider community.

But Mr Marshall says South Australia will not reduce its current COVID-19 restrictions given the level of community transmission around the country, including the extra 31 cases in NSW announced on Friday.

Those measures include a reduced density requirement for most venues, mandatory mask-wearing in high-risk settings and a limit of 10 people at family gatherings.

The crowd at this weekend's AFL game between the Adelaide Crows and the Brisbane Lions will also be limited to 50 per cent of the usual Adelaide Oval capacity.

The premier says those restrictions are now likely to stay in place until at least early next week.

At the same time, SA has hard border closures in place with Western Australia, NSW, Queensland and the ACT.

Chief Public Health Officer Nicola Spurrier said she was "feeling very comfortable this morning" about the situation in SA.

She said close and casual contacts of the miner, who flew back into Adelaide last week, had been tested and all returned negative results, including a group of his fellow workers.

The miner's young baby is considered "clinically well" but the man, in his 30s is regarded as "very unwell" and may be sent to hospital for an assessment because of a deterioration in his condition.

He and his family had self-isolated almost immediately on his return though there were some concerns for people he may have had contact with on the flight from Alice Springs, in the airport, and at a takeaway food outlet.

Mr Marshall said his thoughts were with the family at the moment.

"We reiterate our grateful thanks to this family for the great work that they have done," he said.

"The actions that they have taken have been precisely what have kept our state safe."

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