NSW’s local coronavirus cases spiked to 38 on Thursday – including 20 people who were active in the community for at least part of their infectious period.

It is the highest daily tally yet for the state since the Bondi outbreak began in mid-June.

The outbreak has risen to 395 cases.

“Those numbers are too high. We need to get those numbers down,” a clearly worried Premier Gladys Berejiklian said.

“I want to say in the most strongest possible terms, please, please avoid contact with households with other households, please avoid visiting family and friends – because you are not allowed to.”

Of the new cases, nine people were in isolation for part of their infectious period while 11 spent “a number of days in the community” before being diagnosed.

Ms Berejiklian said the virus was largely being spread to household contacts and by people continuing to be active in the community with symptoms.

“The strongest message is do not visit people outside your household in indoor settings,” she said.

“Secondly, please, please make sure if you have the mildest of symptoms, you are not going out of your house to a workplace or to visit a loved one who needs care out or for any other reason. If you have [even] the mildest of symptoms, the only reason you should be leaving your home is to get a COVID test.”

Tweet from @NSWHealth

NSW is treating 40 COVID patients in hospital. That includes 11 in intensive care, three of them on ventilators. The ICU patients are aged from their 30s to their 70s.

NSW Health also confirmed that a fifth aged-care worker at SummitCare Baulkham Hills has come down with the virus, but was already isolating. Six residents to date have caught COVID-19.

Chief health officer Kerry Chant said 26 of Thursday’s cases were linked to existing outbreaks – 13 close contacts and 13 household contacts.

“When we find a case in the family, we find that everyone in that household has the disease,” she said.

“What we are asking people to do is to redefine the sense of family. The family unit is the household. The people you live with.”

She urged people – especially in the Fairfield, Canterbury-Bankstown and Liverpool local government areas, where the virus’s spread is now centred  – to restrict compassionate visits to only one person and to restrict shopping or shop online where possible.

“If you are leaving your home, ask yourself you really need to leave your home,” she said.

“If you are going shopping, think about what you absolutely need, do the list, get in and out. This is not the time for browsing.”

Ms Berejiklian refused to be drawn on Wednesday’s comments by Health Minister Brad Hazzard that NSW might have to give up the fight to halt the spread of the Delta strain and “accept that the virus has a life which will continue in the community”. She said the Delta strain was a “game-changer”.

“You can’t live with the Delta variance unless you have a certain proportion of job population vaccinated. That’s the bottom line,” she said.

“If you could have done that, NSW would have found a way – and in previous outbreaks that we have had, we have managed not to go into lockdown.”

She said NSW had “had a sense of urgency” about COVID vaccinations from the beginning, and again pushed for anyone eligible to get their shots.

She also wouldn’t predict the likely end to the lockdown of greater Sydney and surrounding area, now planned for July 16.

“All the experts have said if every single person does the right thing, that we can get to where we need to go at the end of the three-week period,” she said.

“That is a big ask because we know that unfortunately, unintentionally at times, people don’t do the right thing.”

NSW Police are continuing to fine people for breaching virus rules. That included one man who recently travelled from Sydney to Mudgee to meet someone – he was fined and sent back to Sydney.

However, police say most Sydneysiders – including those in the three south-west local government areas – are abiding by restrictions.

Meanwhile, NSW teachers and senior students in Greater Sydney and surrounds will be required to wear masks when they return to school next term.

Masks will be mandatory for all staff in all school settings, as well as students from Year 7 upwards when on-site learning resumes on July 19.

Education Minister Sarah Mitchell said the new COVID-safe rules would apply to schools inside areas covered by the stay-at-home orders – greater Sydney, the Blue Mountains, Central Coast, Wollongong and Shellharbour.

In regional areas, masks will be recommended for all staff in all school settings as well as high school students.