The National Public Health Emergency Team (NPHET) has said the growth rate for COVID-19 for the population at large is "at zero".
Modelling data shows that the reproduction number remains below 1.0.
Professor Philip Nolan, chair of the Epidemiological Modelling Advisory Group, said this means transmission of the virus is effectively suppressed.
Speaking on Thursday he said: "Our R number is between 0.5 and 0.8. This success emphasises how vital it is to remain vigilant in our behaviours.
"If the R number moves above one, we are no longer in control of the disease."
Ireland's Chief Medical Officer Dr Tony Holohan said great progress has been made.
But he said this must continue.
"We have achieved great progress through the action of staying apart.
“In order to continue protecting ourselves, our vulnerable groups and our healthcare workers, we must continue to practice physical distancing, respiratory etiquette and regular hand washing.
"These basic steps, if done by all, will save many lives."
It comes as 28 people diagnosed with COVID-19 in Ireland died on Thursday, bringing the total number of deaths to 794.
There were also 936 new confirmed cases of the virus here.
There is now a total of 17,607 confirmed cases of COVID-19 in Ireland.
Data from the HPSC, as of midnight on Tuesday, reveals:
- 56% are women and 43% are men
- The median age of confirmed cases is 48 years
- 2,424 cases (15%) have been hospitalised
- Of those hospitalised, 331 cases have been admitted to ICU
- 4,545 cases are associated with healthcare workers
Dublin has the highest number of cases at 8,216 (50% of all cases) - followed by Cork with 1,087 cases (7%).
Of those for whom transmission status is known community transmission accounts for 52%, close contact is 44% and travel abroad accounts for 4%.
Meanwhile research conducted on behalf of the Department of Health shows that for the first time since this tracking began, only 19% of people expect restrictions to end in May.
One in four expect them to end in August/September.
The nationally representative online survey of 1,270 adults also reveals 52% feel the worst of the pandemic is happening now, however 29% of people feel the worst is ahead of us.
People's main sources of worry are the health of family and friends and the economy.
These both ranked 3.8 on a scale of one to five, where five is very worried.
Adherence to safe behaviours remains high - 95% are washing their hands more often,
Some 89% are social distancing in queues and 78% are coughing into their elbow.
