Ten residents of mandatory quarantine hotels have tested positive for COVID-19 since the system was introduced.
Since late last month, arrivals from dozens of countries have had to quarantine in a hotel for two weeks after they arrive in Ireland.
The Government is currently looking at adding a number of EU states - like Germany, Italy and France - to the list of high-risk countries.
HSE National Lead for Testing and Tracing Niamh O'Beirne says all residents and staff are regularly swabbed.
She said: "To date, 413 people have been swabbed who've come through as residents.
"To date, there have been ten detected cases in the quarantine residents."
Meanwhile, the HSE also says public health teams aren't concerned about supermarkets and petrol stations being possible sources of COVID-19 spreading,
It has been looking at almost 800 cases of community transmission in the last week as part of an enhanced contact tracing system.
Over half of people said shopping in the likes of supermarkets is somewhere they may have contracted the virus.
Ms O'Beirne explained the other potential sources of infection noted so far.
She said: "The second place was workplace at about 15%, then the top six would have been school, transport, travel and social gatherings outdoor.
"There were other areas mentioned, but to a much lower volume - birthday parties, weddings funerals, personal care appointments, and cafés indoors and outdoors."