There was also one death following eight on Monday, a record-breaking day for coronavirus cases and fatalities in NSW.

"I make it very clear that we are assuming that case numbers will go up," Gladys Berejiklian said on Tuesday.

"Now, I say that only as a realist because when you have cumulative days of high case numbers, there is a tipping point where case numbers go up."

But the premier maintains that once the 70 and 80 per cent vaccination targets are met life will look "much freer than what it is today".

At least 54 people were circulating in the community for all or part of their infectious period in the 24 hours to 8pm on Monday, while 297 cases remain under investigation.

An unvaccinated woman in her 70s from western Sydney died in Westmead Hospital.

Southwest and western Sydney continue to be the epicentre of the outbreak and 70 per cent of cases in NSW are people under 40.

"And that's why those extra jabs we receive from the Commonwealth will be put straight into the arms of 16-to-39-year-olds in the local government areas of concern," Ms Berejiklian told reporters.

The entire state is now locked down and a 21-day police blitz came into effect on Monday to enforce new regulations with almost 18,000 police officers supported by 800 members of the Australian Defence Force.

NSW police issued nearly 600 infringement notices to people flouting tough new health orders.

Deputy Police Commissioner Gary Worboys said "the time was over for cautions and warnings".

Police also conducted 3800 welfare checks to see if people were following stay-at-home orders.

One COVID positive man from the hotspot of Fairfield in Sydney's southwest wasn't home when police arrived and was later unable to provide an excuse for his actions.

Non-compliance fines of up to $5000 are now in place with people confined to within five kilometres of their homes.

People flouting the two-person outdoor exercise rule or travelling into regional NSW without a travel permit could be fined $3000.

Meanwhile, Sydney hospitals are dealing with staff shortages as COVID clusters send workers into isolation at Nepean and St George Hospitals.

Health Minister Brad Hazzard said there was no question the hospital system was under enormous pressure.

He said the case of a long-term cancer patient who contracted COVID-19 at St George Hospital had snowballed into 80 health staff out of action for their mandatory 14-day quarantine.

Four patients and two staff members have tested positive at that hospital while 21 patients in the ward remain in isolation following their test, NSW Health's Jeremy McAnulty said.

There are now 116 cases in western NSW, including two in Bourke as well as one person confirmed overnight in far western Broken Hill.

"The person has been infectious for some days and has been in Broken Hill and Wilcannia," he said on Tuesday," Dr McAnulty said.

Four COVID-positive inmates are also being housed at the remand centre of Silverwater Jail, including two cases uncovered over the weekend. Their source of infection is being investigated.

Several schools are shut because of COVID cases including Jamisontown Public School and the Meadows Public School at Schofields in Sydney's west as well as Blacktown North Public School in southwest Sydney.

Australian Associated Press