South Australia has recorded two new coronavirus cases, one a woman in her 20s who was at a school while likely infectious.
The new cases were revealed on Sunday as the state warned of the potential for tougher protection measures.
The woman was a close contact of a known COVID-19 case and had been placed in hotel quarantine, SA Chief Public Health Officer Nicola Spurrier said.
Health representatives are contacting staff and students at Thebarton Senior College and Roma Mitchell Secondary College where the woman attended while infectious.
The second case is a teenage girl who flew into the state from Victoria on July 26.
"The chances of her being infectious in South Australia are very low," Prof Spurrier said.
Authorities have found seven close contacts of the girl, who had symptoms 11 days before arriving in SA and tested positive on Saturday.
More broadly, police will step up efforts to combat complacency about restrictions, with the state considering tougher protections.
Premier Steven Marshall on Sunday said his government was poised to quickly impose stricter rules if needed, to separate SA from the growing threat of eastern states.
"We're very concerned about the unfolding situation in Victoria and we're very supportive of further restrictions being put in place in that state," he told reporters.
"We here in South Australia have been on high alert for weeks ... with what has been happening in Victoria. We don't rule out further restrictions should they become necessary."
The state's "transition committee", established to manage SA's response, is due to meet on Tuesday but Mr Marshall said restriction changes could be implemented beforehand.
The premier appealed to aged care workers to be particularly vigilant, to help protect the state's most vulnerable.
A 25-year-old man and 20-year-old woman remained in custody awaiting a court appearance in Adelaide on Monday after sneaking into SA despite having earlier been turned away at the NSW border.
Meanwhile, a man has copped a whopping fine after going to the gym instead of self-quarantining.
The 25-year-old, from Woodside, returned to Adelaide by air on July 20 after holidaying in NSW, and was directed to quarantine for 14 days.
An investigation was launched after SA Police were told he was disobeying the order.
The man later allegedly admitted attending a gym and was issued six fines totalling $6360.