Several Sydney private schools have banned students who have recently visited China from returning to school without medical certificates, as concerns grow about the spread of coronavirus.

Pymble Ladies College in Sydney’s north has told parents in a text message they should not send their daughters to school for at least 14 days after returning to Australia from an affected area of China, or after contact with someone who had visited an affected area.

Other private schools, including Scots College, Ravenswood School for Girls, Kambala School and Newington College, have told parents that students who have visited affected regions in China must provide medical clearance from a doctor, the ABC reported.

In Victoria, Wesley College has told parents it “strongly recommend[s]” keeping students away from school until they have been in Australia and symptom-free for two weeks. If students return to the boarding school without meeting this requirement, they will be “isolated and appropriate health advice sought”.

Other Victorian schools that have contacted parents include Firbank Grammar, Scotch College, Haileybury, Caulfield Grammar, Waverley Christian College, Methodist Ladies College and Balwyn High School, the Age reported.

The New South Wales’ chief medical officer, Kerry Chant, said on Monday that children returning from Hubei province with symptoms should seek immediate medical advice, and that anyone who had been in contact with a confirmed case should not attend school for 14 days.

The Commonwealth’s chief medical officer, Brendan Murphy, said there was still no evidence of sustained human-to-human transmission outside Hubei province.

“We don’t think there’s any reason to cancel public gatherings. There’s no evidence of human-to-human transmission in Australia. Were there evidence, that’s a very different matter,” he said.

A spokesperson for the NSW education department said it was not advising that students should be kept at home unless they had a confirmed case of the virus or had been in close contact with someone who had.

“Children and staff who have recently returned from overseas and are well, and are not close contacts of a confirmed case, are able attend school as normal,” the department said in a statement.

A spokesperson for the Victorian department of education and training said it is advising schools regarding “precautionary measures” they can take to avoid the spread of the virus.

Most NSW and Victorian public school students are due to return to classes from Wednesday.

On Monday a 21-year-old woman in NSW was confirmed to have the virus, taking the number of cases in Australia to five. She was identified as a student at the University of NSW, and was being treated in Sydney’s Westmead hospital.

The university said in a message to staff and students that the infected student had stayed on her own in campus accommodation “with no close contact before she was admitted to hospital”.

“NSW Health has advised that the student adhered to their advice and precautions since arriving from Wuhan on 22 January,” the university said. “NSW Health has stated the student was not infectious on the plane.”

The woman arrived in Sydney on Thursday on the last flight to Australia from Wuhan before Beijing banned all out-bound travel.

“Pleasingly that patient was met at the airport and acted on the advice provided to her,” Chant told reporters in Sydney.

“So for that patient, there are actually no close contacts [with others], there are just a couple of low-level contacts that we are tracing.”

At least 80 people are confirmed to have died from the virus in China, and 2,744 people have contracted the illness, which has its origins in the city of Wuhan.

Chinese authorities last week imposed a mass ban on travel outside the city in a bid to stop the spread of the virus. It has since expanded the ban to 10 cities.

A petition on change.org calling for NSW school students to be kept home for two weeks after returning from China has received more than 12,000 signatures in 24 hours.

Concern has also been raised about university students arriving from affected areas.

The University of NSW has advised students in an email that “some members of our community who have travelled through the affected areas have reported feeling unwell” and “have been taken to hospital for monitoring”.

The University of Sydney, which has about 17,000 Chinese nationals among its student body, said it was “contacting all students from Wuhan, both current and commencing, asking them to provide us with an update on their circumstances and offering support”.

“Students still in China are asked to follow the advice of the Chinese Government and to avoid travel if they are ill,” a spokesperson said. The university said it would offer students different enrolment options if the travel ban prevented them starting the first semester of 2020.

The president of the National Union of Students, Molly Willmott, said it was important that anyone who had been in affected areas should follow advice from the department of health, but it was important not to “scapegoat” Chinese students.

“Universities need to be taking the lead and offering better triage and psychological services to students affected by the virus,” she said.

Wing Kuang, an international student at the University of Melbourne, said she and many of her friends were worried about their families, and others stuck in China were worried about their studies and getting back to Australia.NSW Health has advised people that the primary symptom of coronavirus is fever, but people should also look out for “cough, sore throat and shortness of breath”.

Exactly how long it takes for the virus to incubate is unknown, but it is thought to take from two to 14 days.

There are currently no vaccines that protect against coronavirus.