With 14 days before the lockdown period is - for now - set to end, big questions remain about how the country is going to be able to stamp out flareups of Covid-19.
Experts agree rapid mass tracing of all a sick person's close contacts is the most vital weapon against the virus - and that tracing is far easier when under lockdown.
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Epidemiologist Sir David Skegg spoke to the Epidemic Response Committee on Tuesday about New Zealand's tracing system compared to overseas.
"Singapore, for example, after the first 100 cases, they published an analysis: how many days it took on average to reach the contacts ... they were getting to people within three or four days."
National Party health spokesman Michael Woodhouse said he was hearing otherwise in New Zealand.
"I've heard an anecdote of up to 18 days from exposure to the virus, to somebody being notified that they could have been in close contact," he said.
Health Ministry records seen by RNZ show about a third of close contacts - nearly 3000 people - have not been hunted down at all.
The ministry said numbers changed daily, but Woodhouse remained unconvinced.
The ministry's reports also do not show the average time it takes to track a contact down.
Its public statements claim it can trace 700 close contacts a day, a tenth of what some epidemiologists say is good enough.
Health Minister David Clark told the Epidemic Response Committee on Tuesday the manual tracing system relied on phone calling, and had to be augmented by technology because the country has been "too far behind for too long".
A source who RNZ agreed not to name said tracing without advanced technology would miss 20 to 30 per cent of the contacts of sick people.
Prime Minister Jacinda Ardern and the Health Ministry both said the government was looking at technology options.
Woodhouse said the government had told the response committee about what technology it may be considering.
"And indeed, there seems to me to be an ambivalence about that, given that we're starting to get on top of the virus. The reality is we're going to need to continue to do surveillance and contact tracing for months, if not a year and a half before a vaccine is developed.
"They don't seem to understand this is going to be a long-term solution. They need to have a system that is much nimbler and more automated than the manual process they've got right now and I'm not sure they're even thinking about that."
The Prime Minister's chief science advisor Juliet Gerrard said a ministry team had been monitoring Covid-19 for 11 weeks, and had also been looking at tracing technology for weeks.
"Weeks ago we were looking around what was successful overseas, but there's no off-the-shelf solution that you can just buy and bring into New Zealand - you have to adapt it to New Zealand situations," she told RNZ's Nine to Noon yesterday.
"I understand the group is hoping to have something before the end of lockdown. [Director-General of Health Ashley Bloomfield] would be able to give you more details on that."
She repeated the Prime Minister's statements that any technology would be opt-in.
Bloomfield did not respond to RNZ's questions on the matter but told the committee on Tuesday that many local tech firms were offering help, and should send ideas to a portal called good ideas at police.com.
Police yesterday told RNZ they had been advised there was no such portal, but ideas were being sourced from businesses.
Woodhouse was nonplussed.
"What the committee would like to know, what I would like to know, is whether there has been a single acceptance of any offers of support, whether it's for equipment, for testing or for tracing, that has been taken up by the Ministry of Health that they didn't already have."
The ministry in recent days added four university epidemiologists to a sub-group looking at what information is needed and when, to help decide whether to extend the lockdown.
The subgroup has met twice, but did not respond to RNZ's requests for comment.
Skegg had called for an audit of New Zealand's tracing. Starting today, it will be led by epidemiologist Aeysha Verrall, who has been outspoken in her demand that contact tracing be stepped up.
By last night she said she had received no terms of reference from the ministry yet, so could not say if the audit would cover technological options.
A London company that monitors Covid-19 digital tracking technology said it would be a hard choice for New Zealand to make.
"If they're using GPS location data, that's only accurate to about 16 feet, which when you're talking about the spread of coronavirus isn't accurate enough," said Samuel Woodhams of Top-10-VPN who has assessed systems in 20 countries.
"It's also not great for people if they're indoors.
"I think Bluetooth is going to be the most accurate but it depends on whether it's reliant on users uploading their own information or if that's done by the state."
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Only 16 per cent of Singaporeans installed Bluetooth-using TraceTogether on their phones.
The city-state went into a lockdown on Tuesday this week, with a similar number of Covid-19 cases per capita to New Zealand, though arising over a much longer time period.