The new restrictions on people in Ireland travelling to the United States came into effect in the early hours of this morning.
It comes as European Commission proposed a ban on non-essential travel to the EU for a period of at least 30 days in an attempt to slow the spread of COVID-19.
France is beginning a 15-day lockdown and President Emmanuel Macron has warned violations of it would be punished.
In Australia, leaders are meeting to discuss tighter restrictions on movement.
However, in South Korea, the rate of infection has dropped again with the number of new diagnoses below 100 for the third day in a row.
In the UK, Prime Minister Boris Johnson said people need to avoid pubs, clubs, restaurants and theatres and to only make essential journeys in the "national fightback" against coronavirus.
Here, the Tánaiste said all non-essential travel from Ireland should be avoided until at least March 29th.
Speaking to Newstalk, Eoghan Corry of Travel Extra says people will have to decide what they consider "essential travel".
He said: "It isn't that significant in the context of the last two days but it was beforehand because it had implications for travel insurance.
"The way things are looking, essential travel would be self-defined and it's really people deciding to defy the risk and go ahead.
"The risks include, in some countries, being turned away at the border."
Mr Corry added that people should now think about how to change existing bookings.
He said: "Ryanair and Aer Lingus and different airlines and ferry companies have allowed date changes
"A lot of them are saying don't change to a date in April because this is going to take quite a while to sort out.
"Otherwise, you could run into trouble, you could lose money and you could be refused boarding.
Yesterday, Ryanair said it expects to see the majority of its European fleet grounded in the coming days.
In a statement, the airline said it expects to reduce its seat capacity by up to 80% within the next seven to 10 days and warned that it can’t rule out grounding the entire fleet.
Meanwhile, Aer Lingus owner IAG said it was reducing capacity by at least 75% for the next two months.