The number of weekly coronavirus outbreaks recorded in schools doubled again last week, according to the latest data from the Health Protection Surveillance Centre (HPSC).
The figure of 46 outbreaks - two or more confirmed cases - compared with 25 the previous week and 12, 13, 11 and 12 in each of the preceding four weeks.
It brings the total since term began to 119, out of 4,000 primary and post-primary schools.
Although the number is relatively low and schools are not seen as hubs for transmission of the disease, the figure reflects how the increasing level of infection in the community is seeping into education settings.
The spread has added to pressures on principals, teachers and other school staff, compounded by delays in contact tracing and testing because the system was overwhelmed.
The strain on schools was evident earlier this week when some took a decision to close because they couldn't get updated information from public health officials.
Where an outbreak happens in a school, the HPSC says transmission of Covid-19 within the school has not necessarily been established.
Health chiefs say it is more likely pupils or staff bring in the infection.
Confirmation of Covid-19 infection in an educational setting triggers a public health risk assessment, which determines what action - such as contact tracing - is required.
Post-primary schools are much more likely to experience a case of Covid-19 than primary schools, according to information provided to Aontú party leader and TD Peadar Tóibín.
Data released by the HSE in response to a parliamentary question shows that, up to October 14, mass testing had been undertaken at 102 post-primary schools out of about 730. It compares with 184 primary schools, out of about 3,100 mainstream primary schools.
Testing had also been conducted at 84 childcare facilities and 14 special education settings over the same period.
Some 56pc of the settings were in the east - classified by Public Health department - with 8pc each in the midlands and north-east, 7pc each in the west and mid-west, 6pc each in the north west and south and 3pc in the south east.
Up to that date, the mass testing detected 125 additional cases, across 47 schools - 20 individuals are over 18 and the remaining 105 were under 18.
Meath TD Mr Tóibín criticised delays in testing that have been experienced.
"Constituents are telling me they were waiting up to five days or a week for their child to be tested after being told to self-isolate," he said.
"Delays in testing have a knock-on effect on others. A child waiting a week for a test means he or she will fall behind in their studies.
"It means that if they are positive, the virus has had plenty of time to spread to others who haven't been told to self-isolate.
"It also means that a parent or family member has to take time off work to care for the child.
"If we are to keep schools open then we need intense testing and tracing, and we cannot afford delays," he added.