PokéBase - Pokémon Q&A
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Pokérus has a 3 in 65,536 or approximately a 1 in 21,845 chance of being generated on a Pokémon, either wild or bred, effectively making this rarer than a shiny Pokémon, which have a 3 in 24,576, or around 1 in 8,192 chance to be found wild or hatched. Through battling or capturing this wild Pokémon, players could get this helpful virus onto their own Pokémon, and subsequently spread it around. Due to the overwhelmingly low chance of encountering the virus (about 1/3 of the chance to encounter a Shiny Pokémon), and the fact that most would not even recognize a Pokémon with the virus and may flee from it, many players don't have a Pokémon with the virus.
Pokérus may spread if an infected Pokémon is in the player's party after a battle. Pokérus may only spread to a Pokémon directly adjacent to an already infected Pokémon and only if they have never had Pokérus before. From Generation III onward, Eggs may catch Pokérus like any other Pokémon.

To infect your Pokemon with Pokerus, you must either battle or capture a wild Pokemon that is infected with Pokerus or spread Pokerus to another Pokemon using a Pokemon that is already infected with Pokerus. After you get a Pokemon with Pokerus, it is pretty easy to spread it to other Pokemon. All you need to do is have a Pokemon infected with Pokerus in your party with the Pokemon that you want to infect with Pokerus and enter a battle. As said above, when the battle ends, any Pokemon that are left, right, above, or below the Pokemon infected in your party have a chance of getting Pokerus.