A New Zealand mother diagnosed with coronavirus says her family has experienced bullying and misinformation.

She said her husband has also tested positive for the illness - which would make him the fourth person in the country confirmed to have coronavirus.

But the Ministry of Health would not confirm on Thursday that there had been a fourth coronavirus diagnosis in New Zealand.

"People assume we are these monsters that have all these symptoms out in public infecting people. We've had very, very, very few symptoms," the Auckland mother told Stuff on Thursday.

The mother was confirmed as being the second New Zealander with coronavirus on Tuesday night, after having travelled to Italy. She is the first New Zealander with the virus to speak out publicly.

She said she was confident she'd done the right thing since arriving home, happy with public health providers, and alarmed at ignorant harassment directed at her family.

"Can you imagine my children going back to school at this point? There are already people pulling their kids out of school when they've been told really clearly that there is absolutely zero threat to their children," she said.

On Wednesday, Auckland Regional Public Health Service director Dr William Rainger said despite the family doing "everything right" and minimising the risk to others by coming forward, they had become the focus of "sustained and abusive bullying on social media".

The Auckland mother said that before travelling to Italy, she had been diagnosed with a sinus infection.

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She returned to New Zealand with her husband on Wednesday February 26, and felt slightly unwell, and tired - but the couple put it down to having just stepped off a long flight.

"I didn't think much of it. However, I stayed home. I stayed home all day on Thursday."

She said in days that followed, she had visited private healthcare providers. "I told them my symptoms. I told them where I'd travelled."

She said she had travelled to Palmerston North after having being told she did not have coronavirus. Once there, she started to feel unwell, so "I changed my flight and came back to Auckland."

She sought medical advice again at home in Auckland, and eventually was tested for coronavirus.

"From there I had no contact with anybody," she said.

When the test returned as positive, she had to call everyone she'd had contact with since her return to New Zealand.

The mother said it had been embarrassing and difficult, but friends and colleagues had been supportive.

She and her husband were staying on their property in isolation, but had almost no symptoms, she said. Their children were also isolated.

Her husband had experienced some tiredness, consistent with jetlag, she said, and a very minor cough. She had taken paracetamol.

"People need to be aware that you don't need to be sick to have this virus," she said.

Earlier this week, Ministry of Health's director-general of health Dr Ashley Bloomfield said the number of people the woman had been in contact with was small.

"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," Bloomfield added.

New Zealand's first coronavirus case was confirmed last week.

That patient, in their 60s, was a citizen of New Zealand who had been to Iran and flown back to New Zealand via Bali.

The third case was confirmed on Thursday as a New Zealand resident who had contracted Covid-19 after family members returned home to Auckland from a trip to Iran.

The man in his 40s was not connected to either the first or second confirmed cases, suggesting he likely contracted the virus from a family member, in what was the first transmission within New Zealand.

CORONAVIRUS HEALTH ADVICE

​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 transitted through China, Iran, northern Italy or the Republic of Korea, or have been in close contact with someone with Covid-19, are now advised to self-isolate for 14 days from the date of departure or close contact. They should also register with Healthline.

People showing symptoms who have recently been to mainland China, Iran, or have been in close contact with someone confirmed to have Covid-19, should phone Healthline on 0800 358 5453.