A secondary teachers union say the COVID-19 situation in schools is "quite worrying".
The HSE estimates that up to 12,000 children are restricting their movements due to being a close contact of someone with the virus - meaning they're not able to attend school.
That's based on around 700 primary schools and 500 secondary schools reporting a COVID-19 case since the start of the new school year.
At primary school level, each case has an average of 15 close contacts, while it's around four in secondary schools.
Kieran Christie, General Secretary of the Association of Secondary Teachers in Ireland (ASTI), told The Pat Kenny Show it is a concerning situation.
He said: “It is something to some extent had been predicted - we all knew transmission within society was widespread prior to schools reopening, and we’re being advised we’re getting the backwash of that.”
He said the mitigation measures in place and assurances they've been given are being “seriously tested”.
However, he said they'll know more about the situation in 8-10 days, once more time has passed since the start of the new school year.
More students in secondary school will also receive their second dose of a COVID-19 vaccine in the coming weeks.
Mr Christie also suggested there seems to be a "reticence across society" - including in schools - around the use of rapid antigen testing.
He said: "[There's reticence to] even proper piloting, to see what role it could play.
"We’ve been pressing for that, but without success."
Monaghan-based GP Dr Illona Duffy, meanwhile, says the number of cases and close contacts "was an inevitable consequence of going back to school".
She observed: “We knew that when gathering people together - which means gathering kids in a classroom - inevitably there would be some teenagers and children who would already be positive, and - without knowing - bring that into the school.
“We have known this was going to happen - this is part of the step-by-step opening up. We have to prepare at each stage that there’ll be a rise in cases."
Dr Duffy said the challenge with reopening is to prevent a surge in hospital and ICU admissions.
She suggested that’s "really all going to be down to vaccinations".
Dr Duffy has previously said the reopening of schools would "definitely" lead to a surge in COVID-19 cases.