If a pokemon has the Pokerus "virus" it doesn't spread when it's in the PC at all. The pokemon doesn't lose the Pokerus though, as long as it's in the PC.
To spread it to other pokemon you need to have it on your party, walk around a bit and battle a few times, then the rest of your party will catch it.
Pokerus will usually stay on your pokemon for a few days. It disappears at midnight after those few days so if you need to keep PKRS put the pokemon in the PC overnight.