The two cases are a child from the original family at the centre of the Parafield cluster and a man in his 30s believed to have contracted the virus while attending an English language school adjacent to Flinders University.
The child was already in quarantine and poses no risk to the public, chief public health officer Nicola Spurrier says.
The other case and his family were also in quarantine before they tested positive.
Spurrier says the man’s infection validates the decision to ask some casual contacts to self-isolate.
“The information I’m giving you today shows how contagious this virus is,” she told reporters on Saturday.
“This person was considered a casual contact rather than a close contact and again it absolutely backs up the information we were already giving to people.
“We’re seeing people that have got infected through fairly brief contacts.”
The diagnoses bring the Parafield cluster number to 33 people but Prof Spurrier said she worried that unidentified cases were be circulating.
Her concern is heightened by the fact only 3840 tests were conducted in the previous 24 hours.
“In terms of testing, it has been quite a drop and I was a little bit disappointed when I saw this number this morning,” she said.
The one person who had been in hospital with COVID-19 was discharged overnight.
The state’s business sector is calling for compensation amid ongoing restrictions leading up to Christmas.
As health officials continue to grapple with the outbreak, the state government will implement a two-week, step-down strategy in easing measures imposed at the start of the outbreak.
That will include opening the borders to Victorians from December 1 and scrapping limits on pub, restaurant and cafe patrons.
But a general work from home advisory remains along with a one person per four square metres rule for all indoor venues.
Business SA chief executive Martin Haese says that means most businesses will be operating at 25 per cent capacity, which is not financially viable.
He says the continued measures will have a significant impact on hospitality, retail and events and leisure during their busiest time of the year.
“Business SA also has grave concerns for the city with work from home advice all but cancelling Christmas for city traders, who will wear the brunt of this as they have all year,” Haese said.
He’s called on the government to regularly review progress with the Parafield cluster to consider if all restrictions can be lifted earlier.
And he’s reaffirmed calls to relax eligibility criteria for $10,000 emergency grants to help businesses get through Christmas
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