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In a statement the HRC said Professor Hunt returned from a business trip to London and Geneva arriving in Wellington on Sunday 15 March and immediately went into self-isolation.
- This story was first published by RNZ
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During the week he began experiencing symptoms and was tested for the virus on Friday, receiving a positive test result on Sunday.
Professor Hunt said he was reported on his health status because "there was nothing to hide".
"There is no stigma. I work from home and enjoy solitary walks. I feel solidarity with past, present and future patients.
"These are extremely dangerous times especially for the most vulnerable members of our communities, such as older people, disabled people, those with underlying health problems, and those living in poverty. History demonstrates the severe and unequal impact of introduced disease on tangata whenua.
Professor Hunt is recovering at home in Wellington.
Meanwhile, the New Zealand Film Commission has confirmed its chief executive Annabelle Sheehan has tested positive for Covid-19.
The commission said her symptoms are minor, and Sheehan is recovering in isolation at home in Wellington.
Sheehan worked in the Commission's Wellington office for three days while she was asymptomatic but infectious, a statement said.
The commission was trialling its virtual-meeting capability at the time, so there was reduced staff contact, no physical contact with people in the film industry or with other government officials, and none with Ministers or Parliamentary staff, it said.
Other professional and personal contacts have been informed.
Staff in close contact with Sheehan during the three-day period are contacting their professional and personal contacts.
The Film Commission's chief operating officer Mladen Ivancic is standing in as acting chief executive, while Ms Sheehan recovers.