Fewer than 6 in 10 people arriving to the country are answering calls to check they're self-isolating.
The figures relate to both Dublin and Cork Airports and Dublin and Rosslare Ports for the month of June.
Passengers are asked to fill out a form to say where they will be staying during their mandatory 14-day quarantine.
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CEO of Irish Tourism Industry Confederation Eoghan O'Mara Walsh thinks testing and tracing could be more effective ways of controlling the virus.