You would want to prevent any animals that may carry the disease from entering the country without scrutiny to make sure they are not infected. This could be done in a number of ways.
Work Step by Step
Rabies-free countries typically require quarantine, careful vet records of vaccination over regulated intervals, or both in order to import animals that may carry rabies into the country. This is simpler for islands, where animals are only intentionally brought in through air and sea ports which are heavily regulated. You can propose a specific model for your own answer using just one or a combination of measures. Keep in mind that with current technology, a rabies test requires the death of the animal, so incoming animals cannot simply be tested for its presence.