Infectious disease specialist Professor Sam McConkey has said the final step in eliminating community transmission of the coronavirus is actually the hardest.
It comes as there were 40 new cases of the virus confirmed here on Tuesday.
Some 75% of them were under 45 years of age, with a median age of 33 years.
While at least half were known close contacts of other confirmed cases.
Prof McConkey is head of the Department of International Health and Tropical Medicine at the Royal College of Surgeons in Ireland (RCSI).
He told Newstalk Breakfast: "I think we can't relax, and I think some of us feel it's very few deaths now and our numbers are down a lot from March and April, so lets just relax.
"I think that's very much the wrong message.
"I would say that in any process like this, getting the last one or two percent of control - the last little bit is actually the hardest.
"The easiest bit comes first and it happens quickly, but these last one or two percent of cases transmission we've really struggled to get this down - where I would like to see this - is zero cases of unexplained community transmission.
"We may still have some cases coming in from abroad because we're open to let people come in in certain circumstances - but I'd like to see no cases of unexplained community transmission.
"And we're not there yet, we're still seeing this.
"And unfortunately as long as we've got unexplained community transmission on the island, then there will still be a risk of it going into a big explosion like we had in February and March - and that means we've to keep all our social distancing measures.
"Whereas if we get down to zero and control it coming back into our country, then we could really be like New Zealand - have open soccer and rugby pitches and stadia full of people again and get back more to normal".
"There is, in my view, a very precious thing there that we'd like to aim for".
He said the best way to tackle the transmission is really quick testing.
"So it's when people get sick, rather than waiting three or four days... to call the GP, call them on the first day.
"Irish men are particularly notoriously bad at that - we're half sick before we do anything.
"But now in this new world, I think it's really right to call the GP on the telephone - the GPs don't mind - GP will organise a test if they feel it's appropriate, go for the test, get the test done quickly, and stay in self-isolation until you've got the result so you're not spreading it around.
"And then it's the speedy contact tracing - I'm hoping this new app we have is going to speed up some of the contact tracing, but also getting those phone calls to the contacts done within three, six or 12 hours - so that people aren't going to work the next day after their contact was found to be positive".
On rising infections in younger people, he said: "This is again very similar to what we had in February and March before we'd large numbers of elderly people getting it who sadly passed away from it.
"This is the sort of grumbling of a virus among young healthy people, who are often minimally symptomatic, which the risk is that then inevitably they meet with their parents and grandparents and older people - and then in two or four weeks time, it all goes wild in older people.
"The young people are unlikely to die from it, as we know, but they're likely to spread it around.
"So it's a matter really of our whole population keeping together, keeping on message, keeping social distancing, masks and so on".