Queensland’s Premier has declared it is “all systems go” in her state, despite four more local coronavirus cases on Monday.

All are linked to existing outbreaks in the state.

One case was reported on Sunday, in a close contact of a worker at a Greek community centre in Brisbane.

The second is the child of that case and the third is the partner of a 29-year-old man who tested positive after travelling to the Noosa area last week.

The fourth case is a colleague of the 29-year-old man.

Premier Annastacia Palaszczuk said contact tracers had linked almost all active cases of COVID-19 in the state.

“All of these are the Alpha strains, so another piece of good news is that we do not believe that the Delta variant is circulating in our community which is excellent news, and it’s now two weeks since the Portuguese restaurant outbreak,” she said on Monday.

“At this stage, it’s all systems go, we’re feeling pretty, pretty good at where we are at the moment.”

“We just need everyone to keep doing the right thing, like I said: it’s really important that everyone continues to wear their masks, they check-in, using that QR code wherever they go outside.”

Queensland also had three new overseas-acquired infections on Monday. The state has one patient, a 69-year-old man, on a ventilator.

Additionally, health authorities have linked all of the most recent community infections to the Zeus Street Greek kitchen at Westfield Chermside. Chief health officer Jeannette Young said that was being treated as the site of transmission for the latest cases.

They are also narrowing down the links in other recent cases, including an infected DFO worker and the link between the Greek community centre at the Portuguese family restaurant, which now has 23 linked cases.

“That means this cluster of the Alpha variant is all coming together and we’re finding out where all the issues are,” Dr Young said.

“We need a bit longer to work through this, to manage all of the cases and I expect we will see a few more still come through.”

Ms Palaszczuk urged people across south-east Queensland to keep wearing masks and check-in whenever they went into shops, cafes and restaurants.

“We have got a week and a half to go of the mandatory mask-wearing but it just goes to show that those short, sharp lockdowns do work,” she said.

“They actually give our contact tracers that vital time that they need to get on top of things, and fingers-crossed that we will continue to go quite well.”

She said more than 92,000 Queenslanders had been vaccinated in state-run clinics in the past week, while nearly 140,000 have registered to receive the Pfizer shot. Bookings for those people are likely to be later in the year, as supply of the vaccine ramps up.

“The bulk of the supply is due in October. We are asking people to be patient,” Ms Palaszczuk said.

“We’re waiting on the Commonwealth supply so we can make sure that you get your dosage.”