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The Ministry of Health reported in a statement this afternoon that the person tested positive. It said there was also one historical case.
Speaking more than an hour later, Ardern said the border worker cleaned planes which had come from places with Covid-19 and carrying people with the coronavirus.
"A very clear link at this stage to cases that are high risk," she said.
"The reason this person was part of our surveillance testing was because they were working in an area we consider to be high-risk. They are coming in contact with the planes that are carrying passengers from high risk countries and so that is a place where our workers, they are in the kinds of roles that means they need to be tested, they need to be vaccinated, but they also need to be thanked for the jobs that they do because of the risk that it carries."
They were fully vaccinated early on in the campaign and were last tested on 12 and 19 April, she said. Yesterday's test showed a positive result.
Ardern said people can still get Covid-19 after being vaccinated, but it would make them a lot less sick than otherwise. The Pfizer vaccine which is being used in New Zealand provides about 95 percent protection against the virus.
"So in this case it is working as intended. This is not a worker who is very unwell and yet they have Covid, so it is doing its job. It doesn't mean people won't get it."
They were fully vaccinated early in the vaccination roll-out, Ardern said. She reiterated people who are vaccinated can still get Covid-19 "but they won't get sick and they won't die".
"That's what the vaccine is for - it's to stop the pandemic becoming so dire that we see our hospitals full and people losing their lives. It means the symptom onset is greatly reduced."
Early data showed it also reduced the likelihood the virus could be passed on to others.
The new case came just one day into the start of a quarantine-free travel bubble for Australia and New Zealand.
Ardern said both countries had expected there would be cases of Covid-19 among border workers while the trans-Tasman bubble was open.
She had not spoken to Australian Prime Minister Scott Morrison yet, but said she would anticipate the border case would not alter the bubble arrangement.
The person was tested regularly because they worked in an area of high risk, Ardern said.
In a statement, the ministry said the usual protocol of isolating the case, interviewing them and tracing their contacts and movements was under way.
In its statement this afternoon, the Ministry of Health said the historical case was a recent returnee from Somalia via UAE who was tested on day 12 of their stay, but was considered recovered.
There are no new cases of Covid-19 in the community today, it said.
With 17 previous cases recovering, total active cases was 86. Total confirmed cases was 2241.
Since 1 January 2021, there have been 49 historical cases, out of a total of 425 cases.
On Monday, 3252 tests were processed for a seven-day rolling average of 4254.
Yesterday two new cases of Covid-19 in MIQ were reported - both in arrivals from India before travel from there was suspended.
One was part of a bubble with two previously reported cases and had been transferred to a quarantine facility on 4 April. The other had contact with a confirmed case while in transit and had been tranferred to a quarantine facility, the ministry said.