Mandatory hotel quarantine is expected to be in effect by next week.
President Higgins has signed into law the legislation for a 14-day stay in a hotel for people arriving here from 33 countries.
They could get a fine or jail time if they don't stick to the rules.
Immunologist Trinity Professor Luke O'Neill, says our borders have to become tighter.
"We've got to tighten up the borders, especially when we open everything up.
"We go to a situation where the virus is very low in Ireland, the risk then is inward travel to Ireland, we've got to be extra zealous then with regards to inward travel for definite."
