A pandemic expert wants the government to look at extending its ban on visitors from China to include other Asian countries.
Since the government ramped up border restrictions last week more then 6000 New Zealanders have entered the country from China.
They're supposed to isolate themselves for two weeks, but only about 2000 have told Healthline they are doing so.
Earlier this week the Ministry of Health entered an agreement with Customs to get these people's personal information and now health officials are scrambling to follow up with them and re-emphasise the message they had received when re-entering New Zealand that they should quarantine themselves for two weeks].
Speaking at a University of Otago public event in Wellington last night pandemic researcher Professor Nick Wilson said having to go back and track them down now was a waste of time and resources.
"It would have been much more efficient to collect that information as they arrived," he said.
"When we re-look at this whole saga we'll actually learn some useful lessons about upping the anti at an earlier stage and putting lots more effort into how we deal with things at the border.
"I think we have, as a country, missed a bit of an opportunity to get this right from the start."
He said officials should have been collecting the details of all travellers from Asia at the border weeks ago.
Prof Wilson said health workers should then have been following up daily with any travellers who presented symptoms and put themselves under quarantine.
He said the government should even consider barring foreign travellers from countries other than China until more was known about the disease.
"There's some evidence [that there's] uncontrolled spread [of the virus] in places like Thailand, Malaysia, Singapore.
"We should be thinking about potential restrictions for those travellers as well as."
He said the government and health officials overall response to the outbreak has been slow.
"And [it's] a bit disappointing that you more effort and planning hadn't been done beforehand.
"New Zealand's got a pretty good influenza pandemic plan, but... when it was rated recently on an international scale it was... 35th in the world.
"We should should be able to do better than that as a relatively remote island nation."
Wellington doctor Sally Talbot also criticised the officials' reaction to the outbreak.
She said many community GPs were worried they did not have the right kind of PPE (protective gear) should a potential carrier of the virus turn up at their clinic.
"Adequate PPE should protect... the mucous membranes of your face - that's your eyes, nose and mouth - and perhaps a gown that fits your arms right to your gloves and maybe down to the ground.
"A lot of us just have the simple paper masks and glasses but not goggles."
But Professor Raina MacIntyre from the University of New South Wales said increased demand - especially from China which was a major producer of the products - has put the squeeze on supply.
"Governments everywhere are constrained by very limited supplies.
"There is a global shortage of PPE and the wiser strategy is to keep it in reserve until you really need it.
"At the moment, there are no cases [of coronavirus] documented in New Zealand."