That really sucks. I would hate to get sick on vacation. It seems like a stomach virus to me then if different people getting sick on different days. Unless they have a very large batch of whatever is making people sick. The problem with viruses is that you are most contagious when you have very little symptoms so you are passing it onto the next person before you even know you are sick.
Stomach viruses are spread by contaminated surfaces or hands to mouth. Apparantly the areas on and around airplane seats (trays, armrests etc) are one of the worst places. Best advice is to wash, wash, wash! Be sure to bring some gravol and immodium with you too!