There are 11 new cases of coronavirus in New Zealand, the Ministry of Health says.

Director-General of Health Ashley Bloomfield said that brought New Zealand's total to 39 positive cases.

"We are expecting more given the rapidly evolving situation overseas and the number of people who have travelled overseas into New Zealand, including returning Kiwis, in the last week or two," he said.

Of the new cases, five were in Auckland, two in the Waikato, one in the Hawke's Bay, two in Wellington and one in Canterbury.

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None of the new cases were in hospital and they were all at home self-isolating, Bloomfield said.

Focus Live: Auckland's art galleries, pools, recreational centres and libraries will be closed in response to Covid-19, Mayor Phil Goff says. The public facilities will be closed for two weeks.

The Ministry was investigating whether all were linked to overseas travel. Public health staff are interviewing every case so they can trace their movements and identify all close contacts and isolate them.

Countries visited include France, Spain the United States and England.

Of the eight cases confirmed yesterday, a man in his 60s had been hospitalised in Lakes District Hospital.

Two in Taranaki, a male and female, both aged in their 40s, had recently returned to New Zealand from Egypt.

Bloomfield said the ministry was keeping a close eye on any signs of community transmission in New Zealand.

Foodstuffs South Island chief executive Steve Anderson said supermarkets were under huge pressure right now.

"We don't have a supply issue, we have a demand issue."

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He said customers could expect limits on some products. He encouraged customers to shop normally.

"If we all purchase as usual, there will be no problems."

"We may all need to take a deep breath or two collectively."

Bloomfield said the ministry was doing enough testing for the coronavirus. There had been 1000 negative tests in the last day, he said.

No district health boards had reported a lack of supplies.

Bloomfield also reminded university students ahead of the weekend that the limit for indoor gatherings was 100.

He was encouraged by some students who had arranged to do deliveries or help people in isolation, and encouraged other students to follow suit.

There had been interest in how many people have fully recovered from coronavirus. Officials were looking at how they collect and report on the information.

Recovery was a lot like recovering from a flu: You should rest, recuperate, keep up your fluids and get lots of sleep.

Even when recovered, individuals will need to remain in strict isolation until cleared by your health provider.

The Ministry was looking at all of its options to increase the number of ventilators. Recently retired ventilators could still be used and will be brought back into service, Bloomfield said.

New Zealand borders closed at midnight last night to non-residents - only citizens and residents are being permitted entry.

The unprecedented move was made in an attempt to prevent widespread community transmission of the coronavirus. It was also influenced by the number of positive cases which had come from overseas travellers, and concerns about whether tourists were self-isolating after arrival.

Earlier today, Prime Minister Jacinda Ardern said New Zealand schools would close where there were positive tests to conduct contact tracing, but they would not be closed generally without a widespread community transmission.

This was the model that had been adopted in Singapore and Taiwan, where transmission of Covid-19 had been slowed.

Shutting schools prematurely could send students to their grandparents to be looked after, and elderly people were more susceptible to coronavirus, Ardern said. It would also take health workers out of the workforce.

PM Jacinda Ardern talks to Mike Hosking about the government's response to coronavirus.

The Government was looking for spikes in transmission, Ardern told Mike Hosking on Newstalk ZB.

"If you want to be ahead of outbreaks, everyone needs to be prepared to work from home. Be prepared to cancel non-essential trips. Be prepared to reduce down that social contact. Do that now."

• This morning, the Government stepped in protect Air New Zealand by making a $900 million available to keep essential flights going and domestic routes open.

• At midnight, New Zealand's borders closed to all foreign nationals - an unprecedented move designed to prevent widespread community transmission. It was also influenced by concern that some tourists were not following self-isolation rules. There are some exceptions to the border closure for key health workers and humanitarian arrivals.

• Social gatherings have been limited to 100 people at indoor venues, except for schools, universities and educational institutions. Gatherings of more than 500 people have banned.