And one Covid-19 data modeller here says should either variant get past New Zealand's border, he expects an alert level 4 lockdown would be needed.
Of the 75 active cases in currently in managed isolation in New Zealand, at least 19 are linked to the UK variant, which is believed to be between 40 and 70 per cent more infectious than the original strain.
The Ministry of Health reported yesterday that the first case of the South African variant has now been detected at the border.
While less is known about this variant, ESR scientist Joep de Ligt said it seemed to be more transmissible than the original but less so than the UK variant.
"That's another one that we're monitoring very closely to see if that one's coming in and how it's behaving.
"We're also keeping tabs on anything that we see coming in that might not have been described globally because the UK is doing a really stellar job at sequencing samples and telling us about them, but we're also receiving travellers from regions where that is not happening, and we're still monitoring that as well."
Covid-19 data modelling expert Shaun Hendy warned a community outbreak of either variant in New Zealand would in all likelihood need a level 4 lockdown to bring it under control.
"If we do have a community outbreak that involves the South African or the UK variants of Covid then we're likely looking at needing to use level 4 to contain and then to eliminate that outbreak," he said.
"Level 3 was effective back in August ... but I think if you take into account the extra infectiousness of these new variants, level 3 is probably not strong enough."
Hendy said the country would continue to see more variant cases at the border and they might be a community case.
In Australia, authorities are scrambling to ensure the UK variant hasn't spread into the community after two people tested positive following their release from quarantine.
A hotel quarantine worker in Brisbane also tested positive for the strain having spent up to five days in the community while infectious.
That prompted a three-day lockdown for the city.
Due to concerns about the UK strain, new rules mean people travelling to and around Australia must now remain in quarantine for at least 14 days and be tested before they're let out.
Deakin University chair of epidemiology Catherine Bennett said they were taking the extra precautions should the variant prove to make people infectious for longer than the original strain.
"What we find as we follow up these cases and continue to track people in quarantine for a longer period will help us know how to handle these new variants; whether we need to adapt our quarantine methods because something's changed in terms of infectivity or length of the infectious period.
"At this stage, we don't know - we're just assuming it's possible and therefore we're being very, very careful in extending that quarantine and testing protocol."
Australian health authorities are now trying to identify contacts of anyone released from quarantine under the old rules having contracted the variant.
"If it's more infectious then there's a small risk that maybe other things have changed about this virus as well, including how long a person might be infectious," Bennett said.
"So we're just looking into that in this process and doing more testing and monitoring cases who are still positive will help us answer that question."
The World Health Organisation says that while the new variants appear to be more transmissible than the original form of Covid-19, neither seem to cause more severe illness.
