A Dunedin school will close for at least 48 hours after a student tested positive for coronavirus.

Ministry of Health director-general of health Dr Ashley Bloomfield confirmed on Tuesday another three cases, from the existing eight. A fourth has now been confirmed by Logan Park High School in a message to parents.

A Dunedin man, in his 40s, began to develop symptoms five days after returning from Europe, so there was no risk to others on the plane, Bloomfield said. He is now recovering at home in self isolation.

His child, a student at Logan Park, also had symptoms, along with another family member.

An email to parents from the Southern District Health Board (SDHB) on Tuesday evening said the student 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.

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"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."

SDHB had already started contact tracing to identify individuals who may have come into close contact with the parent and would be working with the school and family to identify close contacts of the student over the next 24 to 48 hours.

Close contacts will be contacted by SDHB staff from Wednesday and asked to go into self-isolation for 14 days. 

Dunedin Mayor Aaron Hawkins said while it was a worrying time, he urged people to stay calm.

The health authorities were leading the response and the Dunedin City Council would provide support, he said.

"This is a fast-changing situation and we are ready to step up our response if and when required.

"It's more important than ever that we continue to look out for each other and check in on friends and family."

SDHB chief executive Chris Fleming added that the health board had been preparing for the arrival of the disease.

It was "unlikely to be the last case" of Covid-19 in Otago and Southland and he urged anyone who was unwell to stay away from work.

A Wellington man in his 30s and his father, aged in his 70s, have also tested positive after recently returning from the United States.

The man in his 30s became unwell on the flight and his father became unwell the day after they arrived.

Neither of the men required hospital care and both are recovering at home. Both travelled on American Airlines flight AA83 from Los Angeles to Auckland on seats 4a and 10h. They arrived on Saturday then travelled to Wellington on Air New Zealand flight NZ419 on seats 1b and 1c the same day.

The Ministry of Health said contact tracing on flights covered the two seats in all directions: front, back, both sides and diagonal.

"Healthline knows the seat numbers and will be able to advise anyone on the flight, whether they are considered a close contact," the ministry said.

The ministry expected more sporadic cases given the increase in cases globally.

"We want to find cases so we can trace and isolate close contacts and prevent community spread."

* A gender in the 12th case has not been confirmed and earlier mentions of son have been changed to student.