An additional eight cases of coronavirus have been confirmed in NSW taking the state's total to 55.

The "new normal" of the global COVID-19 outbreak is starting to bite in Sydney, with schools bracing for temporary closures and fears of lasting economic damage.

The latest cases include a woman in her 20s who had contact with a previously confirmed case at Ryde Hospital, a woman in her 40s who recently returned from South Korea and a Victorian man in his 20s who recently returned from Hong Kong.

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NSW Health is separately working to establish how three others were infected: two women in their 30s and 40s and a man in his 70s.

Two other cases are related to the outbreak at the Dorothy Henderson Lodge nursing home in Macquarie Park.

Total now 55 cases of Covid 19 in NSW. Our community should be assured that this virus remains well managed in Australia. But everybody has a part to play. Most importantly follow good hygiene steps. Particularly wash hand regularly. ⁦@NSWHealth⁩ pic.twitter.com/9YMVGfRP7E — Brad Hazzard (@BradHazzard) March 9, 2020

Two year 10 students from St Patrick's Marist College in Dundas and a year 7 pupil from Willoughby Girls High School were on Monday confirmed to have coronavirus.

The fathers of the two St Patrick's students are both Defence staff and had previously tested positive for the infection.

NSW authorities are now investigating a coronavirus cluster centred around Ryde Hospital, the Australian Defence Force and Dorothy Henderson Lodge.

St Patrick's Marist College and Willoughby Girls High School will be closed on Tuesday as a precautionary measure.

NSW Premier Gladys Berejiklian told the nine Network on Tuesday that the state government was trying to keep the public informed and up to date.

"All of us are feeling a bit uncertain and a bit worried about what's going on ... we are taking an overcautious approach, we want to make sure we don't leave any stone unturned and public safety comes first," the Liberal leader said.

"It has been a tough couple of months for NSW but I'm confident that through the options we have before us that we will come out the other end."

School closures 'new norm'

Federal Education Minister Dan Tehan said rolling school closures "will become the new norm".

"School closures, I think, will become the norm as we go ahead, but we are doing everything we can to keep our children safe," Federal Education Minister Dan Tehan told Nine's Today program.

The minister was asked why schools were being closed for a day or two, while people with or suspected of having the virus are being told to self-isolate for two weeks.

"The schools have been closed for a day so they can be thoroughly cleaned," he replied.

"That is the best medical advice that we're being given at the moment. Now, if that changes and it says that schools need to close for longer, then schools will close for longer."

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Two residents at Dorothy Henderson Lodge have died from the virus, with the national death toll standing at three.

According to NSW Health, the health status of 618 people is still being assessed, but almost 8400 people have been tested and cleared of COVID-19.

The Qantas Group has announced further cuts to international passenger numbers, reducing capacity by almost a quarter for the next six months.