On Monday, Prime Minister Jacinda Ardern announced mass gatherings of 500 people or more would be banned, however other public places including schools can remain open.
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Professor Michael Baker, of Otago University's department of public health, told MediaWorks the Government needs to go even further with such measures and should look at school closures and public transport bans.
"We should probably be going even further at the moment with these measures. We need to look at school closures now and also even look at public transport."
However, leading microbiologist Dr Siouxsie Wiles told Newstalk ZB that, at this stage, schools do not need to be closed.
"What it would take would be some cases of community transmission. Once we know that it's happening, then we need to act really fast to 'stamp it out'."
Baker said he was pleased with the Government's new mass gathering ban and the travel restrictions put in place over the weekend.
Anyone travelling to New Zealand, apart from the Pacific Islands, has to self-isolate for 14 days.
Baker believes the entire health sector and many Kiwis most likely "breathed a huge sigh of relief" after those announcements were made.
"The alternative is a very different scenario for New Zealand, where we would at a certain point have a pandemic wash over the whole country and potentially infect quite a high proportion of people," Baker told The New Zealand Herald yesterday.
"Really this is new for all of us. No one alive today has experienced a pandemic on this scale, so we are just not used to it.
"Anyone looking ahead at what could happen, what we're trying to avoid, would appreciate that the Government is really doing everything it can to prevent that scenario."
The self-isolation rules related to the "keep it out" phase of pandemic management, but Baker hoped there would be further announcements regarding how to "stamp it out" shortly.
That included upping New Zealand's ability to test for the virus, identifying cases so they could be isolated, and very swift effective follow-ups of contacts so they could be quarantined.
"The world is splitting now into countries that have not contained this virus ... and a small group of countries that have successfully contained Covid-19."
That included Singapore and Taiwan and possibly South Korea and Japan.
"New Zealand really wants to be among those countries that have contained this pandemic," Baker said.
"It will require obvious huge national commitment and I'm really impressed that the Government is making these tough decisions now to contain this infection... Hopefully the whole nation will get behind that move."
With eight cases of coronavirus being confirmed in New Zealand so far, Baker told Newshub that people need to think again if they think the Government was overreacting.
"They need to get a basic lesson in mathematics. Every six day you double the number of cases - by the time you're aware of it, it may be very hard to contain it," he said.
A group of New Zealand entrepreneurs also called on the Government to introduce tougher measures to protect the nation against the impact of coronavirus.
The group, which has been communicating on social media, includes Zuru founder Nick Mowbray, founder of Sky TV Craig Heatley, Fantail Ventures founder Jonty Kelt, Valocity founder Carmen Vicelich, MindLab founder Frances Valintine, Smudge programme director Toby Vincent and entrepreneur Guy Horrocks.
They have made a unified call now for schools to be shut down as soon as possible, borders closed to all non-New Zealand citizens and residents, health screening at airports and a ban on all gatherings of more than 100 people.
"The most important thing we can do right now is educate the New Zealand public on the need for proactive social distancing," the group said.
