Government publicity and communications about the latest Covid-19 outbreak will be reviewed by Covid-19 Response Minister Chris Hipkins, to see if they were effective.

There were no new Covid cases in the community on Sunday.

Hipkins says he's feeling positive this outbreak had been contained, but says Auckland is not out of the woods yet.

"I've learned never to get too optimistic, but I'm feeling reasonably optimistic about this one, at this point."

Extensive testing and vigorous tracking down of people who needed testing had helped to manage and contain the potential spread, he says.

There's just one close contact remaining who the police are still trying to track down for testing.

Hipkins says there will be a nervous wait over the next week to feel sure that there has been no community transmission, but he says that if there had been, authorities would have expected to have seen more cases by now.

The next step will be reviewing whether the close contact and casual-plus contact categories were effective, after some had claimed it was confusing, he says.

However, Hipkins warns that changing part of the system could cause more communication challenges, so any changes must be made in such a way it would remain robust.

• If you have symptoms of the coronavirus, call the NZ Covid-19 Healthline on 0800 358 5453 (+64 9 358 5453 for international SIMs) or call your GP - don't show up at a medical centre