Twelve people have now tested positive for coronavirus in New Zealand.

The Ministry of Health's director-general of health Dr Ashley Bloomfield confirmed three new cases of coronavirus on Tuesday afternoon.

A fourth case was confirmed by Logan Park High School on Tuesday evening after a Dunedin high school student in self-isolation was tested.

The latest people diagnosed were a Dunedin man in his 40s who recently travelled back from Germany and his family member who attended Logan Park High School, as well as a Wellington man in his 30s and his father in his 70s, who had recently travelled back from the United States.

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The test results of another family member of the Dunedin man were still unknown as of Tuesday evening.

An email to parents from the Southern District Health Board (SDHB) on Tuesday evening said the boy had tested positive for coronavirus.

"Logan Park High School will close for at least 48 hours while close contacts are traced and put in self-isolation and casual contacts will be given advice about what to do if they become unwell.

"The school will be carefully cleaned before reopening. The school is working closely with Ministry of Education staff and Public Health staff. The family, including the father and student who have tested positive for Covid-19 are all in isolation."

The Dunedin man began to develop symptoms five days after returning from Germany so there were no risks to others on the plane, Bloomfield said.

MONIQUE FORD/STUFF The Ministry of Health's Director-General of Health Dr Ashley Bloomfield is delivering an update on coronavirus to the media on Tuesday (file photo).

Two other patients travelled on American Airlines flight AA83 from Los Angeles to Auckland and sat on seats 4A and 10H, arriving on Saturday March 14.

The pair then travelled to Wellington on Air New Zealand flight NZ419 the same day, he said. They sat on seats 1B and 1C.

People sitting within two seats of the pair - to the front, back, side and diagonally - would be contacted by the public health unit and Healthline.

HAMISH MCNEILLY/STUFF A student from Dunedin's Logan Park High School is being tested for coronavirus.

The Wellington man developed symptoms on the plane from the US to New Zealand, but Bloomfield did not know what the symptoms were or if any staff were notified during the journey.

The two had limited movement in the days before they were tested, he said. Neither required hospital care and they were recovering at home.

The Ministry of Health expected more sporadic cases of coronavirus.

"New Zealand has no barrier from cost to testing, including there be no cost to individuals ... nor is their a constraint on capacity ... However we also need to ensure that the right people are tested," he said.

GETTY IMAGES For coronavirus to spread, droplets with the viral particle need to enter through the eyes, nose or mouth.

This included people who had recently travelled overseas or had contact with probable cases and have symptoms linked to Covid-19.

Bloomfield said the ministry was ramping up testing, from about a 100 a day to 500.

"We have the capacity to do up to 1500 tests a day - well actually, we can do 750 to 1000 if we need to - but to go up to 1000, that just means doing an extra shift of laboratory staff. Again, we don't want to run our laboratory staff to the ground so what's most important is that we test the right people."

There had also been a spike in the number of people calling Healthline, which had answered more than 7000 calls in a day. Calls were now being triaged with calls for information being referred to a Government helpline.

There was a lot of interest in ICU capacity and the ability to ventilate people if they're unwell, he said. Capacity for ventilators could be surged by using post-surgery beds. This would be surgeries that would have to be cancelled, he said.

Starting from Tuesday, spot checks would now be carried out on some people, Bloomfield said.

There are now health staff at the border who are quizzing travellers about their plans for self-isolation while they're in the country.

People who knew of travellers who weren't going to self-isolate should notify Customs or Healthline, he said.

"Our system is gearing up to cope with if we do get a wider outbreak in New Zealand," he said.