People are still picking up the Covid-19 virus and have no idea where they were infected - signalling it is still spreading in the community.
In the two weeks up to July 1, well over a quarter - some 30 of the 109 newly diagnosed people with the virus - could not account for where they contracted it.
This is among the most worrying forms of transmission of the virus because it can be next to impossible to trace the source and the risk is that it could lead to a wider spread of the virus.
It comes as another 18 people were confirmed with the virus yesterday, bringing the total infected so far to 25,527.
There were no new fatalities, with the toll remaining at 1,741.
It emerged that testing of some passengers who arrive in Irish airports and ports is to get under way. The "green list" of the countries with low levels of the virus which would remove the need for tourists to quarantine has been postponed until July 20 amid fears there will be a surge in cases from abroad.
It means that all people coming into the country, including people returning from trips abroad, must continue to self-quarantine for two weeks after their arrival.
The testing of passengers is expected to be carried out on a random basis but airport testing remains controversial because it may mean people who are infectious will be missed because the virus will not be detected.
Newly released minutes of meetings of the National Public Health Emergency Team (Nphet) in June show it reiterated its advice that self-quarantine for new arrivals here from abroad should be mandatory for two weeks and they should be offered a designated facility during that time.
The Government has already indicated it will remain voluntary.
The Nphet expressed ongoing concern about the potential for cases of the virus to be brought back here.
The meeting also heard about a proposal to develop a national plan to secure supplies of a Covid-19 vaccine if one is developed.
The plan would set out funding, implementation and monitoring of the immunisation programme should a successful vaccine be made.
Meanwhile, new modelling analysis suggests that eliminating Covid-19 from Ireland over the course of the summer is possible and would require only a modest amount of additional effort.
The work by Prof Gerry Killeen, the AXA research chair in applied pathogen ecology at University College Cork, states that repeatedly imposing, lifting and re-imposing restrictions to merely suppress the epidemic until it hopefully burns itself may prove a dangerous gamble.
Commenting on the study published in the journals 'Infectious Disease Modelling' and the 'European Journal of Epidemiology', he said: "The quiet tail of a fading epidemic may be just as dangerous as the silent onset."
Prof Killeen added that Ireland should look to countries with ambitious national strategies to crush the curve of their epidemics, such as China, South Korea, Japan and Australia.
"With their approaches to eliminating the virus with sustained and uninterrupted restrictions, their timelines to that exit point are about three months and New Zealand is already there.
"Countries like Ireland, France, Spain, Italy and the United Kingdom, where daily incidence rates have been slowly falling, may well have achieved 80pc suppression of transmission.
"Their epidemics could slowly fizzle away if current measures were maintained, so why would these countries not build upon their successes by pushing even just a little further past this crucial tipping point?
"Faster progress towards elimination would obviously be better and these timelines could be shortened if we were to push ahead now with even more stringent and effective restrictions," he said.