Active COVID-19 case numbers could be as high as half a million, or one in 10 New Zealanders, with many unreported positive results and others asymptomatic, according to new modelling.

The country set another record in daily cases today - 23,183 - the figure could be four times as high, or close to 100,000.

Figures from COVID Modelling Aotearoa expect actual infections to be about four times the number of reported cases.

There have been 146,779 confirmed active cases in the past 21 days. Some of these would have recovered. If the modelling is correct, that confirmed case number would indicate there have been around half a million actual COVID-19 infections in the country in the last three weeks.

That is one in every 10 people. The higher rate in Auckland means it would be about one in five people.

Director-General of Health Dr Ashley Bloomfield did expect actual COVID-19 case numbers to be higher than their official numbers showed.

"Well, it's very hard for us to know [the actual numbers]. My sense is that if people are motivated enough to go out and pick up a rapid antigen test, then they'll generally be motivated to record that result."

Surveillance swabbing at hospitals and hospitalisation numbers gave them a pretty good idea of how widespread COVID-19 actually was, Dr Bloomfield said.

'I don't know anybody who's reported a case'

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A tradie in Auckland says he knows about 25 people with COVID-19, none of whom have officially recorded their cases with the Ministry of Health.

The tradesman, who did not want to be named, had seven or eight staff out at the moment - about half his workforce.

"I asked the guys if they're going to report their tests, and they're actually just sick, they just want to go to bed. They don't want to sit online trying to work out how to log a case. It's just more admin."

They could track most of the company's cases to two construction sites.

"One particular construction site that a few of my guys were on is now just a ghost town. There's normally 60 or 70 people working there, and at the moment there's, like, five."

Even people he knew in a personal capacity were not reporting tests. Knowing they had COVID-19 and what to do about it - isolate and have paracetamol on hand - seemed to be enough for them, he said.

"I don't know anybody who's reported a case, and I probably know 25 people who have it. I think it's far more prevalent than the what is out there in the [Ministry of Health] case numbers."

The man said all the cases he knew were isolating and following the rules, just not officially notifying their positive results.

The Ministry of Health has also made it easier for people to access rapid antigen tests. Over 20 million have arrived into the country in the last two weeks.

There's now a website for household contacts and symptomatic people to order free RATs for pick up at collection centres around the country.

"More than 65,000 orders have been placed online already. You can think of that as a click-and-collect," Bloomfield said.

Rather than lining up at community testing centres, many of the sites are solely for collecting RATs.