The 40-year-old woman, who returned to South Australia from Iran on Sunday, tested positive on Wednesday morning.

Both her and the eight-month-old baby are in a stable condition in the Flinders Medical Centre.

The second new confirmed case is a 58-year-old-man who arrived in Adelaide from Taiwan on Tuesday.

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He had recently travelled to Adelaide via Brisbane.

The two new cases are the sixth and seventh to be confirmed in South Australia.

The 40-year-old woman travelled to Australia from Iran via Kuala Lumpur on Malaysia Airlines flight MH139.

Yesterday, the state's chief public health officer Nicola Spurrier confirmed the fifth case in the state was a 24-year-old who was also admitted to the Royal Adelaide Hospital on Wednesday night.

"[She] also has a travel history and she's from a regional part of South Australia," Dr Spurrier said.

"I've been told she's in a stable condition … we have a team that is also doing the contact tracing for this person."

The 24-year-old recently travelled around Europe, including Italy, SA Health said.

SA Health is today opening a dedicated clinic for coronavirus patients at the Royal Adelaide Hospital and said it was currently waiting test results for 14 people.

Mother's result was 'strongly positive'

Dr Spurrier yesterday said the 40-year-old mother had been tested on Tuesday and the "strongly positive" result was flagged on Wednesday.

She said the woman was being interviewed by health authorities, but would not comment on whether her neighbours had been told, nor which suburb the woman lived in.

"We will be making every effort possible to contact all of the potential close contacts of this person," she said.

"We are not providing anything which might break private confidentiality or privacy."

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