Health officials are calling for restraint and calm after an Auckland family in coronavirus isolation have been subjected to "sustained and abusive bullying" on social media.

It emerged on Wednesday that a Kiwi woman in her 30s had tested positive for the virus after taking an international flight, two domestic flights and visiting two medical centres after feeling unwell.

Her family is now in isolation and two Auckland high schools are on alert for the virus.

Yet they have become the focus of sustained and abusive bullying on social media and are being hounded by the media.

Auckland Regional Public Health Service director Dr William Rainger says the family has done everything right and has minimised the risk to others.

"The woman with the virus has gone straight into isolation with her family when she was told she was suspected of having COVID-19.

"Yet they have become the focus of sustained and abusive bullying on social media and are being hounded by the media.

"There is a high level of anxiety and concern in the school and wider communities, but it is not acceptable to attack people who have been caught up in this global outbreak.

"They have taken all the right actions to protect others."

Rainger said the public health service was worried that such attacks would lead people to hide any illness that might be COVID-19, and not seek medical attention.

"We will not be able to contain this spread of this illness, if the public response is so hostile towards cases and their families," he said.

"I want to say that this is a Kiwi family that has been affected by a virus that is part of a worldwide outbreak. What they need is support and understanding.

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"Our task is to ensure they have all the support and health care they need."

Health officials are piecing together the day-to-day movements of the Auckland woman and her partner since February 25, when they flew back from northern Italy.

The family, including two high school children who have not shown any symptoms, are now self-isolated in their home.

Their high schools - Westlake Boys and Westlake Girls - have been alerted but are not closed.

The woman's movements include flights from Auckland in and out of Palmerston North, and visits to two medical centres where she sought treatment after starting to feel unwell.

She flew into Auckland on Air NZ flight NZ0283 from Singapore on February 25, and on March 2 flew from Auckland to Palmerston North on Air NZ flight NZ5103, returning on the same day on Air NZ flight NZ 8114.

Passengers on the flights are now being contacted and any passengers who feel unwell are urged to call Healthline on 0800 358 5453.

Bloomfield said between 30 and 40 people might have been in close contact with her on her flights in and out of Palmerston North, if the plane was full.

Outside of close contacts, the chances of her having infected someone was "very low".