I doubt they would be as affected since they have total control of everyone's movement. Their medical system would be able to handle a small number of cases pretty easily, and it would be easy for them to plug the leak and quarantine an affected area considering there aren't many ways into the country and no one is allowed to move around the country as they want. And they'd probably just execute the infected and burn them before it can spread.

...but if they remove everyone's teeth and move their entire population underground, that's when we should worry...