I have a few Pokemon with PKRS and I know that if you put a Pokemon with this virus with the rest of your Pokemon in your party, they will catch PKRS as well, though does it go away by a certain amount of time or steps taken?
On the DS games, it will last forever so long as the infected Pokémon isn't in your party when the clock turns midnight. The Pokémon will still have the added effects from Pokérus but they won't be able to pass it on. A Pokémon in the PC will keep it forever. If you're worried about losing it, catch a random Pokémon and infect it then put it in the PC and just take it out when you need to spread Pokérus around.