Before the latest coronavirus outbreak in Auckland, 60 per cent had never been tested, with many only having symptom checks.
The latest modelling found testing border staff weekly doubled the chance of detecting Covid before it could spread further.
If no surveillance was done there was only a 40 per cent chance of it being found before it got into the community, compared with a much more secure 80 per cent with weekly testing.
Researchers found the regime was most effective when done alongside symptom checks by a health professional.
Detecting a worker with Covid at the border could mean an outbreak of fewer than three people, but if it was first discovered in someone they had infected, the outbreak could be as high as 17 people.
And even if that second person was someone a border worker lives with, it could be enough to warrant a lockdown because other people were also likely to have caught it.
The research has also looked into the danger of community complacency.
Health workers have said they worried the country had become too relaxed at level 1, with people refusing testing and appearing to forget about the threat.
The modelling found if communities kept up a "high awareness" of Covid, it could half the size of a silent outbreak.
Researcher Nic Steyn said that was because people were more likely to get tested and self isolate if they felt sick.
"In the end what that means is if we can detect the outbreak earlier then we don't have to spend as long at higher alert levels when we do have these outbreaks," he said.
And it found if there was community complacency about Covid in the North Island, it could double or triple the risk of an outbreak there spreading to the South Island.
The researchers looked again at managed isolation and quarantine facilities, warning that any shared space greatly increased the chances of Covid getting out into the community.
That was because if someone caught the disease while in the hotel, they could still be infectious when they left.
