One of Adelaide's most prestigious private colleges has confirmed one of its students has tested positive for COVID-19, as South Australia's total number of confirmed coronavirus cases has its biggest jump in one day.

Key points: Both campuses at the school will be bio-cleaned on Tuesday

Both campuses at the school will be bio-cleaned on Tuesday A Sacred Heart College student also tested positive for the virus last week

A Sacred Heart College student also tested positive for the virus last week The total number of confirmed cases in SA now sits at 29

Scotch College, which has two adjacent campuses in Torrens Park and Mitcham, in Adelaide's inner-south, will close both campuses for 24 to 48 hours.

It said both campuses would be bio-cleaned on Tuesday.

The student's movements on Friday have been identified, and the school is working closely with SA Health to get in touch with parents, students and staff who may have come into close proximity with the child.

It is the second confirmed case of a student testing positive for coronavirus, after a high school student from Sacred Heart College was confirmed as a case last week.

Later on Monday night, the Department of Education said Unley High School will close after a member of the school community tested positive for COVID-19.

The school's middle and senior campuses were closed today after the boy tested positive for the virus on Friday.

Health authorities issued a late update to the number of confirmed cases of coronavirus, jumping from 20 to 30.

A coronavirus clinic set up at the Royal Adelaide Hospital. ( ABC News: Dean Faulkner )

The new cases include the Scotch College student, as well as a man and woman in their 50s.

The woman recently returned from the Philippines and the man had contact with a confirmed case in the United States.

People should be 'bracing themselves for more cases'

Dr Michael Cusack said there was still no clear evidence of community transmission in the state.

"It's so important that we adopt the public health measures that we've been discussing in previous press conferences around social distancing, hand hygiene and so forth," he said.

"And if people become sick or develop symptoms, it is essential that they self-isolate and if they meet the criteria, then they should attend a COVID clinic and get tested."

SA Health Minster Stephen Wade said after another two confirmed cases, the advice for the public was clear.

"South Australians need to be bracing themselves for the fact that there will be more cases," he said.

"There's been a significant number of additional confirmed cases in Australia in the last week, it's very important that we step up, the people of SA need to be taking the message of public health officials very seriously."

Yesterday, Premier Steven Marshall declared a public health emergency for South Australia.

He said public health officers had been empowered "to take all the necessary actions to keep the people of South Australia as safe as we possibly can".

"We have declared a public health emergency," the Premier said.

"These are uncharted waters for our nation."

It is understood to be the first time such a step has been taken in South Australia.