Pokemon infected with Pokerus have the purple "Pokerus" symbol on their status screen. When Pokemon are in this phase, they gain double EVs in battle, and can spread Pokerus to Pokemon adjacent to them in the party.
A Pokemon cured of Pokerus will have a smiley face on their status screen. In this phase, Pokemon still gain double EVs in battle, but cannot spread Pokerus to Pokemon at all.
Once a Pokemon is cured of Pokerus, it will never gain it again.