I'm kind of surprised that being an island would help, actually. Is international travel into prosperous islands really less than into equally prosperous contintental countries? Most long-distance travel is by air anyway.
NZ doesn’t rely on cross border lorry drivers either, and is far enough away that any boats are quarantined
So islands will ship everything already, whereas most land-countries move a lot of goods with trucking, and spread the disease that way, even when land-borders are closed.
International travel can be closed off with little repercussion.
You can't land just anywhere on an island, but you can take lots of roads into large countries on a continent. Islands have much more control over arrivals than landlocked countries with lots of neighbors and very integrated road & train networks.