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Meanwhile the Government is stepping up precautions, extending the current travel ban on foreigners arriving from China and Iran by another week - until March 10 - and cancelling Foreign Minister Winston Peters' trip to the Pacific, scheduled for later this month.
While the travel ban has not been imposed on northern Italy or Korea, people arriving from those places would have to self-isolate for 14 days.
People coming from those areas would need to register with Healthline to enable health officials to stay in contact and ensure they comply.
Prime Minister Jacinda Ardern said travelers from those regions planning to holiday in New Zealand may want to reconsider their plans, as they would have to be stationary for a fortnight.
"We know self-isolation works."
Measures are also being put in place to ensure every person arriving in New Zealand on an international flight will be given public health information.
Ardern also announced $4 million to bolster the Regional Business Partner network, which would help businesses with issues such as cash flow and the ability to pay taxes.
Ministry of Social Development teams were also helping affected workers transition into other jobs.
Ardern said as many as 300 individuals on the east coast have been affected by at least a reduction of work hours.
She and Finance Minister Grant Robertson were meeting with business representatives and the Council of Trade Unions this evening.
"In the meantime, public health remains our primary focus."
The patient who had tested positive was stable and improving, and Ardern said that the patient's previously reported mobility issues had nothing to do with Covid-19.
She said the 15 passengers - originally thought to be 18 people but since reduced - who were near the patient on the Emirates flight had been traced.
All but 10 people on the flight had been contacted, even those who were not in close proximity to the patient, as a precaution.
There are about 87,000 global cases of Covid-19. About 3000 deaths had been linked to the virus, while about 42,000 individuals are thought to have recovered from Covid-19.
Bloomfield said people who have traveled to countries that have cases of Covid-19 should ring Healthline - 0800 611 116.
The Ministry of Health was modelling how Covid-19 coronavirus might move around the country, but Bloomfield said it was "early days".
There were still six people from the Diamond Princess cruise ship in isolation at Whangaparaoa, he said.
Two being monitored in Nelson
Today Nelson-Marlborough Health confirmed that two people in the region are being monitored for signs of Covid-19 - these cases were not the same as the two suspected cases that Bloomfield spoke about.
A health board spokesperson said the two were passengers on the same Emirates flight - from Dubai to Auckland, via Bali - as the person who has tested positive for the virus.
The two people in the Nelson-Marlborough region were now in isolation and were being monitored daily by health services, but neither had been tested.
This morning Ardern told Newstalk ZB that the announcement to extend the travel ban to Iran came just before the first New Zealand case was confirmed.
"We did know we had a potential case, but at that point there were still negative tests coming through."
This morning Ardern said the public should follow basic hygiene practises, and the Government would be closely monitoring whether more specific measures were necessary.
The Government announced a travel ban on foreign nationals travelling from mainland China since February 2.
The first New Zealand Covid-19 case was announced on Friday, sparking a flurry of people buying emergency items at supermarkets with reported queues running out the door.
Travel restrictions
• Foreign nationals arriving in New Zealand from mainland China or Iran cannot enter New Zealand as a precautionary measure to protect against the spread of COVID-19.
People who are exempt from the temporary restrictions are:
New Zealand citizens (including those from the three Countries of the Realm: Tokelau, Niue and the Cook Islands), permanent residents and their immediate family,
Australian citizens and permanent residents whose primary place of established residence is New Zealand, air crews who have been using appropriate personal protective equipment.
People should self-isolate for 14 days after their return if they have been in mainland China or Iran, or exposed to a confirmed case of COVID-19.
• People who have been in or transitted through northern Italy or the Republic of Korea should self-isolate for 14 days after their return.
• There are still six people from the Diamond Princess cruise ship in isolation at Whangaparaoa.
• The 157 people who were evacuated from Wuhan - where the outbreak of the virus originated - are out of isolation. They stayed in quarantine at Whangaparaoa for 14 days.
