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.

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.

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."

Health Minister Brad Hazzard on Monday said rolling school closures was "likely to be the new norm".

"If a child or a staff member or any other person within a school is found to have the COVID-19 virus, then effectively a breather will be taken and a day out will be the immediate requirement," he told reporters.

NSW Treasury chief economist Stephen Walters has said while a state recession isn't inevitable, there is a risk of two quarters of negative gross state product growth.

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.

Australian Associated Press