Authorities have confirmed a fourth case of coronavirus in Western Australia after a woman who travelled from Cuba via London tested positive to the virus after returning home to Perth.

Key points: The woman attended a West Australian Symphony Orchestra event on Saturday night

The woman attended a West Australian Symphony Orchestra event on Saturday night It is not known if her GP had asked her to self-isolate after she was tested on Friday

It is not known if her GP had asked her to self-isolate after she was tested on Friday A woman who spent six days in Perth recently has also tested positive in Victoria

The woman, aged in her 70s, also attended a West Australian Symphony Orchestra (WASO) event on Saturday night and efforts are underway to contact those who sat near to her.

The event at the Perth Concert Hall was advertised as Absolute Beethoven, with the Australian String Quartet.

She arrived in Perth on Qantas flight QF10 on Thursday and was tested on Friday after falling ill. The test returned a positive result late on Saturday night.

The Health Department has been contacting those who were seated near her on the flight.

The woman has now been isolated in her home in Perth's western suburbs with one other family member.

WA's chief health officer Andrew Robertson said the woman was not showing any symptoms on her flight.

"She originated in Cuba, then she flew to London, had six days in London then flew directly from London back to Perth … became unwell the following day, got in contact with her GP, was tested on the Friday and we got the result late last night," Dr Robertson said.

"She was not symptomatic on the plane, she was fine when she arrived and then became symptomatic the following day when she woke up."

Dr Robertson said the woman's physician would be asked whether she was directed to self-isolate while awaiting the test result.

Visitor spent time in Perth before diagnosis

In another case of concern to WA authorities, a woman in her 50s, who spent six days in Perth last week, has tested positive to the virus in Melbourne.

She arrived in WA from Jakarta aboard a Garuda flight on February 27 and she developed symptoms two days later.

She then flew to Melbourne on Virgin Australia flight VA682 on March 2.

She saw a GP in Victoria, who ordered a COVID-19 test, which returned a positive result on March 7.

People onboard the Garuda flight with the woman are not considered at risk as she did not become unwell until two days later.

The Victorian Health Department is contacting people who sat near her on the Virgin Airlines flight she took to Melbourne.

The woman is in a stable condition.

Health authorities have been tracing her movements while in Perth.

The cases come after a woman in her 30s, who had been in Europe and travelled through Dubai before returning to Perth, tested positive earlier this week.

Woman released from hospital after husband's death

Meanwhile, 79-year-old Perth woman Theresa Kwan has recovered from COVID-19 and is now resting at home after she was infected aboard the Diamond Princess cruise ship and evacuated from Japan.

Mrs Kwan's husband, 78-year-old James Kwan, also had coronavirus but died from the illness a week ago.

There has as yet been no local transmission of coronavirus in WA.

WA Health Minister Roger Cook gives the media an update on the coronavirus while Premier Mark McGowan and the state's chief health officer Andrew Robertson stand behind him. ( ABC News: James Carmody )

WA's Health Minister Roger Cook said the latest cases underscored how important community effort was when dealing with coronavirus.

"We need people to really listen to the advice of their health professionals, use common sense, and above all do their best to make sure that they don't spread the virus in the event that they are positive," he said.

"It's really important that people understand that if they are being tested for the coronavirus that they need to exercise some common sense and precaution."

His comments were backed by Dr Robertson

"If people become unwell, can we strongly ask them not to go to public events or restaurants," Dr Robertson said.

"If you are unwell, particularly if you have just come back from overseas, this is the time to stay home, get in contact with your GP and get the testing.

"And if you have had the testing, obviously do not go out while you're awaiting the results, it's really important that people do stay home and self-isolate, because they do place other people at risk if they don't."

About 300 coronavirus tests are now being conducted daily in WA, and on Tuesday three specialised fever clinics will open at major hospitals.