When infected, a Pokémon's status screen will indicate it much as it does any other status condition (with icon being different for Generation III and IV, while Generation V has the same as Generation IV and Gen II having no icon at all). When another normal status condition, such as Sleep, affects the Pokémon, the Pokérus icon will be replaced. As long as the Pokémon is infected with Pokérus, it can spread the virus to the other Pokémon in the player's party. The infection may spread if the infected Pokémon is in the main party after a battle. An uninfected Pokémon must be next to a Pokémon infected with Pokérus in the main party for the virus to spread. If Pokémon that have already been infected and cured from Pokérus are in the main party and are on either side of a Pokémon currently with the disease, Pokérus will not spread after any amount of battles. Pokémon that are put into the PC will keep the status indefinitely.
Also Once a Pokémon's immune system has fought off the virus, they cannot spread it further, nor can it be spread to them by other Pokémon.