New COVID-19 modelling shows more than 5500 tests are needed every day to catch a breach at the border before it becomes a widespread outbreak.
That's significantly more than is being done at present, with a seven-day rolling average of just 5034 in the past week.
The study, published in the New Zealand Medical Journal on Friday, simulated what it would take to catch at least 95 percent of all infections within five weeks of the virus getting through.
If there were at least 5580 tests being done each day, the study found the outbreak would likely be detected 17 days after the border was breached, when just five people were infected.
There would be a 95 percent chance of picking up the outbreak in the first five weeks.
Nick Wilson of the University of Otago's Department of Public Health, who led the research, told Newshub it shows the importance of getting tested if you feel sick.
"It would be possible to detect such outbreaks at a reasonably early stage - within five weeks - before the numbers got too high."
There are a number of assumptions built into the modelling, such as the virus' reproduction number and how many people seek medical attention when they feel ill with the kinds of symptoms common to both the flu and COVID-19. Usually that's around 39.5 percent - if three-quarters of people sought medical attention, the modelling shows the outbreak would likely be detected after just 12 days, and almost certainly - 95 percent - by the 26th day.
Dr Wilson says there's room for improvement in the current system, such as more testing in cities with border control facilities - Auckland, Hamilton, Rotorua, Wellington and Christchurch - and wherever cargo ships dock.
And though it wasn't the focus of the research, he says any new outbreak could possibly be detected earlier by monitoring wastewater for the virus.
"It allows you potentially to detect cases in the city from the sewerage system at an even earlier stage - that has worked in Sydney, for example."
There are currently 70 active cases of COVID-19 in New Zealand - 66 of them picked up in managed isolation and quarantine facilities.