More than 700 close contacts are being traced every day, the Ministry of Health says.
But there is still no sign of the use of bluetooth technology, which researchers have said is vital because manual contact-tracing cannot keep pace with how rapidly Covid-19 spreads.
The contact-tracing ability of public health units has been under scrutiny, with expert epidemiologist including Sir David Skegg and Professor Michael Baker saying repeatedly that New Zealand's contact-tracing capacity needs to be ramped up.
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Last month $40m of the Government's initial $500m to health resources dedicated to doubling the contact-tracing capacity of public health units around the country.
This included standing up a new contact-tracing workforce, the National Close Contact Service (NCCS), based at the Ministry of Health in Wellington.
"As of Saturday, 4909 close contacts had been traced by the NCCS since it was stood up on March 24, with 702 contacts traced in a single day on Thursday," Director of Public Health Dr Caroline McElnay said in a statement.
"Originally it was making 760 calls a day - now that's more than 2000."
The NCCS has about 100 people a day in its national call centre, who are split across two shifts operating from 8am until 830pm. They are being led by qualified nurses.
But while using location tracking via text message to monitor overseas arrivals in self-isolation, there is no indication yet whether the public health units are using bluetooth for contact-tracing, which has been used successfully in other countries, including Singapore.
Researchers at Oxford Universitypublished a paperlast week that looked at why such technology was urgently needed.
They analysed key parameters of the epidemic spread, concluding that it was simply too fast to be contained by manual contact-tracing.
"Our analysis suggests that about half of transmissions occur in the early phase of the infection, before you show any symptoms of infection," said Professor Christophe Fraser, of Oxford's Big Data Institute.
"Our mathematical models also highlight that traditional public health contact-tracing approaches provide incomplete data and cannot keep up with the pace of this pandemic."
They proposed a contact-tracing app which built a memory of proximity contacts and immediately notified contacts of positive cases – something which could achieve epidemic control, if used by enough people.
Dr Andrew Chen, a research fellow at the university's new think tank, Koi Tū: The Centre for Informed Futures, has praised the use of TraceTogether in Singapore.
People installed it on their phones with Bluetooth enabled, and when they were physically close to someone else with the app, the phones exchanged Bluetooth signals and any encounters were logged in the app.
It took just several seconds for the exchange – short enough to capture most interactions but long enough to ignore spurious connections.
Anonymous IDs were used so that phone numbers weren't exposed.
As Bluetooth worked at relatively short-distance, it provided a good proxy for physical proximity and was more accurate than GPS or cellphone-signal methods.
It could also help distinguish between people who had been "close contacts", as opposed to those who were "casual contacts".
Location wasn't necessary, because contact tracing relied mostly on connections between people.
The data was stored in encrypted form, and could only be sent to the Ministry of Health with the user's consent.
Chen said this methodology was promising because it took an opt-in approach: users chose to use the app and knowingly took part in contact tracing.
"More than 600,000 Singaporeans enrolled in a few days with the app seen as a way to protect themselves and to help protect those around them."
Germany now planned to launch such an app within weeks.