New Zealand has eight new cases of coronavirus, bringing the total number of confirmed cases to 20.

There were four cases in Auckland, two in Waikato, one in Christchurch and one in Invercargill. All had returned from overseas travel; some returned more than a week prior to the Sunday night deadline for required self-isolation.

The Ministry of Health provided a partial list of the Covid-19 cases' travel history on Wednesday afternoon. The cases had flown from London, Europe, Australia, Canada, and the United States — and contact tracing for other people on the flights was underway.

Contact tracing had also identified 150 students from Dunedin's Logan Park High School who came into contact with a boy who had tested positive for Covid-19. All were in self-isolation and being tested for the virus.

BRADEN FASTIER/STUFF Patients are tested for coronavirus by medical staff outside Nelson Hospital on Wednesday.

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Ministry of Health's director-general of health Dr Ashley Bloomfield, speaking at a daily press conference, said all the recent arrivals with Covid-19 that he knew about had been in self-isolation.

"We expected more cases ... The clear link to recent overseas travel for these eight cases reinforces the border restrictions that were implemented this last weekend," he said.

"These restrictions are not retrospective, but I urge others who have arrived earlier from overseas to voluntarily self-isolate and, of course, be aware of what symptoms could be of Covid-19 and that they should ring Healthline or call ahead to their general practitioner for testing if they think that is warranted."

Bloomfield said Logan Park High School would be closed for the rest of the week, and reopen on Monday.

All 150 identified close contacts students will self-isolate for 14 days regardless of the test result, as they may be incubating the virus, he said.

​"All close contacts will be tested, and we won't have those tests all back until Friday.

"This is a unique situation and it is part of our precautionary approach that we have taken all along with our response to Covid-19."

Health officials ran 620 tests for Covid-19 on Tuesday, identifying the eight new cases. Bloomfield said there were 30,000 swabs for coronavirus tests being distributed across the country.

Hamish McNeilly/Stuff Logan Park High School in Dunedin has been closed for at least 48 hours.

Further testing measures — both community testing centres and "sentinel testing" run at certain GP clinics — were also being rolled out.

Bloomfield said there remained "no evidence at the moment of community outbreak" and our border restrictions are intended to keep that risk low".

He said all scientific modelling for the virus' showed that, if Covid-19 spread as a single wave, community transmission would begin early in April and peak before August.

More recent modelling showed that "flattening the peak" could still overwhelm a health system. Bloomfield said their approach was to instead have a series of "small peaks, over a long period of time".

"And you amplify up quite stringent controls to ensure that you don't exceed your health system capacity, and then as it goes down again you can ease those [controls] and be prepared to ramp them up again."

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Prime Minister Jacinda Ardern echoed Bloomfield during a later press conference, saying "if you arrived before those border restrictions, seeing out the balance of your 14 days of self-isolation is the sensible, safest and best thing you can do for the community".

The eight new cases on Wednesday comes in addition to 12 people who have already been tested positive for coronavirus in New Zealand. On Tuesday evening, a case was confirmed by Logan Park High School after a student contracted the virus from his father, who had travelled from Singapore to Dunedin on March 8.

Other people recently diagnosed include a Wellington man in his 30s and his father in his 70s, both who had recently travelled back to New Zealand from the United States.

HAGEN HOPKINS/GETTY Director-general of health for Ministry of Health Ashley Bloomfield confirmed confirmed the country now has 20 cases of the Coronavirus.

Ministry of Education secretary of education Iona Holsted said the ministry continued to plan for temporary school closures as needed, but had no intentions to close all schools.

The ministry was also working to ensure students in self-isolation could do distance learning not necessarily because of closures but with self-isolation instances, she said.

"We've planned of this, and will be able to respond," Holsted said.

On Tuesday, police officers visited and questioned 41 people who to make sure they were complying with the self-isolation order.

Latest Covid-19 cases

The Ministry of Health has provided the flight number of one of the latest eight Covid-19 cases, as of 4pm on Wednesday.

The new cases are:

- An Auckland man in his 50s, who travelled extensively through Europe.

- An Auckland women in her 40s, who arrived in Auckland on a flight from Europe on March 9.

- An Auckland man in his 60s, who arrived in Auckland on a flight from San Francisco on March 13. The flight number is NZ007.

- An Auckland man in his 60s, who arrived on a flight from Canada on March 12.

- An Invercargill man in his 40s, who arrived on a flight from the Gold Coast on March 5.

- A Canterbury women in her 40s, who arrived on a flight from London on March 16.

- A Waikato woman in her 20s, who arrived on a flight from Sydney on March 8.

- A Waikato man in his 70s, who arrived on a flight from Europe on March 15.