The positivity rate in testing for COVID-19 has declined over the past eight days
Head of the HSE, Paul Reid says the number of close contacts has also reduced to an average of three.
He says that while it is still very early, the numbers are good news.
It comes as the latest figures show 295 people are being treated in hospital for the virus, a decrease of 20 since yesterday afternoon.
37 people are in ICUs.
The HSE boss also said that the majority of contacts are being traced to households rather than social interactions.
He said: "What we're seeing in terms of positivity rates in the testing that we're doing, we have seen it continuously reduce over the past eight days.
"It still has a very high level of over 5.5%, but we can take good positivity out of that because it has come down from 8.9%.
"The average of close contacts of those two tested positive for the virus is gone down to 3, and that had been 4.5.
"The second thing that's good is we're now seeing the majority of close contacts are generally household family contacts, more than social."
The positivity rate in testing has now come down over the past 8 days. The number of close contacts is now down to an avg. of 3. Most close contacts are household. Still very early but good. We're all be part of the solution. Let's keep this going. @HSELive #COVID19
— Paul Reid (@paulreiddublin) October 25, 2020
He emphasised the importance of people restricting their movements and isolating if they come in contact with a positive case.