OK, here's the thing:
Pokerus does not really work that way
Pokerus does not have fixed hours of stay, rather, if the Pokemon is in the party when the clock strikes 0:00, the disease will fade away.
So coming to the question, if the Caterpie you say has been transfered over to your game and the time in the DS clock is 0:00, it will go away. If not, Pokerus stays. It does not depend on how many hours it has stayed.
Source: Personal experience in both games and pokerus.
Hope I helped!