People have been warned that any marginal increase in close contacts is likely to lead to a "significant" fourth wave of Covid-19 in Ireland.
Professor Philip Nolan said if people increased their contacts, the further surge in the disease could result in a rise in cases similar to that experienced in January of this year.
He made the comments during a National Public Health Emergency Team (Nphet) briefing where he outlined the advice the group provided to Government to help inform Tuesday's announcement on the phased easing of public health measures.
The chairman of Nphet's epidemiological modelling advisory group described the current Covid-19 situation as "very static", but that it remained "precarious".
Today a further 411 cases of Covid-19 were confirmed by the Department of Health, as well as six more deaths linked to the virus.
The rate of transmission is now estimated to be between 1 and 1.3.
Prof Nolan said the reason why the easing of Covid-19 restrictions were so conservative was because the risks of increasing social contacts were "enormous".
He projected that if there was a very marginal increase in social contact it would result in 1,000 cases per day by the end of June, and an additional 200,000 cases between April 5 and the end of September.
A medium level increase in close social contact would result in a "very significant surge" of disease, he estimated, somewhere in the region of half a million cases by the end of September.
"There is a critical window over the next eight weeks where any significant increase in social contact is likely to lead to a significant additional wave somewhere between what we saw in October and what we saw in January," Prof Nolan said.
Deputy chief medical officer Dr Ronan Glynn said the country was in a "much better position" than it was this time last year and it could be possible to "virtually eliminate" another spike of the virus, despite the concerning figures.
"We've so many more reasons for hope and to be optimistic of summer ahead," Dr Glynn said.
"I know that the modelling presented is concerning and it shows that we're in a precarious position and that things can go wrong, quickly and easily.
"But there is a very hopeful message within that modelling, which is that if we can stick with this for another four to eight weeks, we can dramatically reduce the number of cases that we have to deal with, and we can virtually eliminate another surge in terms of admissions to hospital and admissions critical care."
Dr Glynn joined Prof Nolan in urging people not to increase their social contacts in the coming weeks.
He said he was aware that some people were visiting households contrary to the public health restrictions and appealed to them not to meet, but added if they were going to do so to meet outside.
Dr Glynn said: "We can't afford to have intergenerational international mixing and especially not inside.
"Our advice is to please not meet up. But being pragmatic if you are going to meet up. Please meet up outside.
"And if you're going to meet up outside and somewhere that's going to be crowded please wear a mask. If you can't keep social distance please wear a mask, and don't meet up with someone if you've got symptoms."
He added that it would be a "shame" over the coming days for families to meet up and for older or more vulnerable people to get infected with the virus before the ramping up of the vaccination programme.