More than 100 health workers at two Sydney hospitals are waiting to see if they have COVID-19, after a colleague caught the virus while wearing a mask.

NSW had four new cases of coronavirus to report on Monday – three in healthcare workers at two Sydney hospitals and one a returned overseas traveller in hotel quarantine.

NSW Health said the four new cases were diagnosed in the 24 hours to 8pm on Sunday, bringing the total number of cases in NSW to 3929.

There were 10,129 tests reported in the 24-hour reporting period, compared with 38,526 in the previous 24 hours – but the latter number includes 18,956 tests conducted by a private laboratory between August 10 and September 2, not previously reported to NSW Health.

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The three healthcare workers were diagnosed during investigations into an emergency department doctor reported on Saturday who worked at Sydney’s Concord Repatriation General Hospital and Liverpool Hospital while infectious.

Another case, a visitor to a hospital emergency department where the doctor worked or sought treatment, will be included in Tuesday’s numbers, taking the cluster to five.

Patients considered close contacts and all staff at Concord and Liverpool EDs at the same times as the positive cases are being isolated and tested.

Authorities are concerned by the likelihood at least one of the new cases caught the virus while both parties were wearing masks.

“For some of the cases there isn’t that clear-cut direct contact without a surgical mask,” NSW chief health officer Kerry Chant said on Monday.

Her team is investigating whether the new cases caught the virus by touching a contaminated object.

“We are exploring avenues of whether there could be fomite transmission,” Dr Chant said.

“What that means in lay terms is if your hands are contaminated, and then you’re touching computer screens or touching pens and pencils pieces of paper, can you actually transmit the virus?”

Premier Gladys Berejiklian said masks were important but remained only one piece in the line of defence against the deadly virus.

“Whilst the number of cases is low and declining in NSW, I think what cases like this remind us is just how contagious the disease is,” she said.

“We always need to be on our guard because this disease is like none other that we’ve experienced – extremely contagious, and even if you’re wearing a mask, you can still get it.”

The three newly reported health workers reported having no symptoms while at work and also wore personal protective equipment while caring for patients.

Dr Chant said NSW hospitals were still operating safely and effectively, and it was important NSW residents don’t delay urgent care.

Meanwhile, two Sydney schools are closed after students tested positive while the number of cases linked to a CBD gym has grown to 64.

Kincoppal-Rose Bay School in Sydney’s east is closed for on-site learning on Monday after two year 7 students were among the 10 new cases reported in NSW on Sunday.

Lidcombe Public School in western Sydney is also closed after a new case was linked to the school.

Despite a number of outbreaks in schools in recent months, Premier Gladys Berejiklian on Monday confirmed school formals and graduations would be allowed to go ahead in term four.

Health authorities are working with the education sector to come up with appropriate COVID-safe plans, but Dr Chant has hinted she may allow dancing, despite the activity being banned at weddings.

NSW Health is treating 83 COVID-19 cases, including seven in intensive care, four of whom are being ventilated.

-with AAP