Eleven 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 Covid-19 had been diagnosed on Tuesday.
Bloomfield said the latest people diagnosed were a Wellington man in his 30s and his father, who had recently travelled back from the United States, and a Dunedin man in his 40s who had recently travelled back from Germany.
The Dunedin man's family - including a school student - are now being tested.
The Wellington patients travelled on a Los Angeles to Auckland flight, then travelling to Wellington on Air New Zealand NZ419 on the same day, he said. They sat on seats 1B and 1C.
"The public health unit and Healthline are contacting those close contacts," Bloomfield said.
Not all have been reached yet. Those close who were on the flights, and sat close to the cases, are asked to call Healthline. If you were sitting further away, there is no need to call Healthline, Bloomfield said.
The Wellington man in his 30s 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 father nor son require hospital care, he said, and are recovering at home.
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The Dunedin man began to develop symptoms five days after returning from Germany, Bloomfield said, so there was no risk to others on the plane.
Two of his family members are being tested, and have symptoms. One is a student of Logan Park School in Dunedin.
"Our advice to the school is that, if the test is positive, the school is closed over the next 48 hours as close contacts are traced" he said.
The school would be carefully cleaned before reopening.
"We are expecting more sporadic cases of Covid-19. All our cases to date are associated with international travel ... We would expect more travellers returning to New Zealand to present with symptoms," he said.
As at 8am on Tuesday, there were 11 confirmed tests, 2 probable cases in New Zealand, Bloomfield said. More than 500 tests were also under way on Tuesday, he said.
The World Health Organisation has encouraged further testing and isolating of coronavirus cases, he said.
"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.
There had been a spike in the number of people calling Healthline. Some calls had been dropped, he said. Calls were now being triaged, with calls for information were being referred to a Government helpline.
Testing would still be conducted when people had symptoms and a history of travel, or contact with a possible case of Covid-19.
"Our system is gearing up to cope with if we do get a wider outbreak in New Zealand," he said.
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 would have to be cancelled, he said.
Bloomfield said he was "pleased" to hear the Government had announced $500 million for health services to respond to coronavirus.
Starting from Tuesday, spot checks will now be carried out on some people 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.
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People who knew of travellers who weren't going to self-isolate should notify Customs or Healthline know, he said.
"I can understand why someone who might've planned a trip for a long time, two weeks in New Zealand, might be disappointed to find at the eleveneth hour that they can't travel around the country, " he said.
Schools may well have to be closed if community transmission begins, he said.
"It's very important this year that we vaccinate our most vulnerable [for influenza]," he said. "We're bringing forward the campaign, but we're also asking people that are not in those groups are deferring getting the vaccine," he said.
Bloomfield said the ministry was ramping up testing, from around a 100 a day to 500.
"We have the capacity to do up to 1500 tests a day, well actually we could do 750 to 1000 if we need to," he said. Scaling up the number required another shift of laboratory staff, and they were being careful not to run these staff into the ground, he said.
Bloomfield's update follows the Government's announcement that it would provide a $12.1 billion package as a response to the coronavirus pandemic.
The money will go towards infrastructure spending, wage support and health services.
The three new cases come on top of eight people who had already tested positive for the virus in New Zealand.
An Australian man who visited Wellington last weekend and was named as case number seven remained symptom-free. He has moved from the QT Wellington Hotel and was in self-isolation with family members. Wellington cafe Milk Crate confirmed the man visited on Saturday.
New Zealand's eighth case, a Danish woman in Queenstown, had been discharged from hospital and was recovering in self-isolation.
A passenger on the Golden Princess cruise ship, which arrived in Akaroa on Sunday morning, tested negative for coronavirus. The cruise ship has now left New Zealand waters.
On Monday, passengers aboard the Le Laperouse which docked in Wellington, disembarked as the remainder of their trip around New Zealand had been cancelled.
Prime minister Jacinda Ardern has announced that everyone entering New Zealand from anywhere in the world - excluding the Pacific - would have to self-isolate for 14 days.
According to the Ministry of Health website, those in self-isolation should avoid social gatherings, work, school, child care facilities, university, religious gatherings, aged care and health facilities, prisons, sports gatherings, restaurants, and all public gatherings.
The travel ban on China and Iran remained in place. Cruise ships were now banned from docking in New Zealand until at least June 30.
What you need to know
Covid-19 is a respiratory disease caused by a recently discovered coronavirus. It spreads via droplets from the nose or mouth expelled when a person with the disease coughs, sneezes or exhales. To avoid infection, people should stay at least a metre away from someone who has, or may have, the virus.
The viral incubation period, that is time between catching the virus and showing symptoms, ranges between 1-14 days.
The most common symptoms are fever, tiredness and dry cough. Some patients may have aches and pains, nasal congestion, runny nose, sore throat or diarrhoea. Some people become infected but don't develop symptoms or become unwell.
From what we know thus far, about four in five people recover without needing special treatment. About one in six become seriously ill and develop difficulty breathing. About one in 50 die.
The risk of catching Covid-19 from someone with no symptoms is very low, because the virus spreads via droplets expelled by coughing. However, it is possible to catch the disease from someone with very mild symptoms, including a cough.
To minimise the spread of infection, wash your hands thoroughly with an alcohol-based rub or soap and water, cover your mouth and nose when coughing and sneezing, and keep at least a metre away from other people coughing and sneezing.
People who have been in or transited through any country other than those in the Pacific islands or have been in close contact with someone with Covid-19, should self-isolate for 14 days from the date of departure or close contact. They should also register with Healthline (0800 358 5453).
People who display symptoms should phone Healthline in the first instance - don't head straight to your doctor or medical centre.