Fewer than six in 10 people arriving to the country are answering calls to check they are self-isolating.
Passengers are required to fill out a form to say where they will be staying during their mandatory 14-day quarantine.
Over 45,500 Passenger Locator Forms were filled out between May 28 and June 30.
Some people were exempt from follow up calls because they were travelling on to Northern Ireland or staying in the state for less than two days.
In Dublin Airport alone, 21,455 calls to check people were self-isolating were made two days after they arrived.
Just 13,192 people or 61% answered the phone.
When a second call was made 12 days after arrival, just over half answered.
CEO of Irish Tourism Industry Confederation Eoghan O'Mara Walsh thinks testing and tracing could be more effective ways of controlling the virus.
"The kind of quarantine rule is ineffective and I think there is other ways of ensuring that public health concerns are addressed in terms of testing and tracing and so on.
"That could be deployed more effectively and that would allow full tourism to resume which is particularly important for the tourism industry here in Ireland which is hugely dependent on overseas visitors to the country."
In Cork Airport, 1,007 forms were filled out, resulting in 857 follow up calls.
Of these calls, 48% of passengers picked up.
Less than half of people arriving into the country through Dublin Port answered the check up call.
The response was better in Rosslare Port, where 54% of people took the call.