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Emerging evidence of Covid-19 clusters where the virus has unwittingly been passed through New Zealand communities before the nationwide lockdown shows that contact tracing measures are working, experts say.

While most of New Zealand's 368 coronavirus cases have been linked to overseas travel, Ministry of Health officials say there are now several suspected clusters of community transmission.

Marist College, the decile 7 Catholic girls' school with 759 students in Mt Albert, this afternoon confirmed it has 16 cases, with 10 teachers including its principal and six students.

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And it's feared that a "handful of students" from two other Auckland schools - Lynfield College and Mount Albert Grammar – could have been exposed to infectious Marist College students after that rode on the same school bus.

The other major cluster emanates from an international Hereford cattle conference in Queenstown, where 15 cases in New Zealand have now been linked.

The Southern District Health Board expects more cases to be confirmed in coming days as a result of exposure at the World Hereford Conference where attendees visited various spots across the South Island between March 9 and 18, with pre- and post-conference tours.

"Public health staff are working very hard at identifying close contacts of these cases and providing advice and thank everyone for their cooperation and assistance," Southern DHB says.

The Herald understands that members of a youth Hereford competition team have now tested positive for Covid-19. They have since returned home to their homes across the country.

But NZ Hereford today said they were "not privy to the identity of the confirmed cases".

Colin Corney, NZ Herefords president, says more than 300 people attended the conference from across North and South America, Europe, Scandinavia, UK and Ireland, Australia, South Africa and New Zealand.

"New Zealand had no travel warnings or restrictions in place before the conference," Corney says.

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"The situation did escalate globally during the event, but New Zealand restrictions were not put in place until after the conference closed."

All attendees were contacted by the Ministry of Health last week after the first positive test was notified and again on Saturday.

Other New Zealand cluster fears come from a wedding at Wellington's Ohariu Valley on March 14 where close contacts are being traced, a US trip by a group of Wellington friends, a rest home in Wellington, and when people on board the Ruby Princess cruise ship visited a Hawke's Bay winery. Four other possible community transmissions cases are linked to Auckland and Wairarapa.

The Ministry of Health says it will give more information on the clusters as it becomes available.

Covid19.govt.nz: The Government's official Covid-19 advisory website

Professor Shaun Hendy, director at Te Punaha Matatini at University of Auckland who has been doing modelling for the Government, says the community clusters show for the first time that not all cases can now necessarily be linked directly to overseas travel.

Aggressive and rapid contact tracing, testing and isolation measures are critical in fighting the virus' spread, he says.

"Where we're seeing some of those clusters that have essentially been contained, they're worrying, but they're a sign that things are working – we're actually finding these things," Hendy says.

"The concerning thing is, say that Hereford conference for example, is that it took place before we had a lot of the controls in place. If we were still holding those big events, that would be a major concern. We have to expect that, for a little while, we'll be picking up cases that might have spread from some of the big events before we started shutting them down."

The historic nationwide four-week coronavirus lockdown which came into force at midnight on Wednesday should fortify the country against community transmission, believes Mick Roberts, an infectious disease modeller and professor in mathematical biology at Massey University.

While there is still potential for the virus to spread, it should be limited to "a few cases instead of thousands" and the health service should cope, he says.

But he warns that contact tracing will never capture everyone who's been exposed in a cluster.

"They [Ministry of Health] are doing contact tracing but with a cluster you've got an awful lot of contacts and only a few days to trace them. You can't trace everybody and it's the ones that get away that you really worry about."