Pokerus means ur pokemon has ebola and it will go bye bye ?\_(ツ)_/?
Hah, on a more serious note though, Pokerus doesn't give double EXP, it gives double Effort Value's (EV's) every time you faint a wild/trainer's Pokemon, but yes, the rates are assumed to be more rarer than the shiny chances.
Basically to spread pokerus just take the infected pokemon with you and knock out a few wild pokemon, it doesn't spread every time but when it does spread it goes to the pokemon above and below it in the party so keeping it in the middle of your team is a good method to spread it fast.
Pokerus stops being contagious if you leave the infected pokemon out of the box overnight (midnight for your 3ds clock so if your time is off keep that in mind) and after that they can't catch it again but a little pink circle remains so you can easily spot a non-contagious pokerus carrier, I think the EV boost remains for those non-contagious carriers but I'd have to double check.
It's definitely not that rare nowadays, and it can only spread when placed in a party with non-infected Pokemon. The effects still remain after it goes away.
Battling wild pokemon and receiving pokerus is extremely rare indeed, and yes rarer than shiny pokemon. However since the invention of hacking and cheats, pokerus becomes a default application on many "created" pokemon as it makes EV training and such much easier. From here they are traded and it spreads all around.
So in summary, it isn't really that special anymore, unless you managed to get it from battling pokemon.