Pokérus

Description
Pokérus is a microscopic life-form that can attach to Pokémon. Your Kanto Starter Pokémon will automatically be infected with Pokérus upon clearing the Distortion World Dungeon in Sinnoh for the first time. Pokérus is a beneficial virus to any Pokémon that catches it. Once a Pokémon is infected by the Pokérus, it may gain Effort Values (EVs), which multiplicatively increase the attack of that Pokémon via the EV Damage Multiplier.

Spreading Pokérus
Spreading Pokérus can only occur in the Pokémon Day Care. Currently, only a Pokémon that fulfill the below conditions are capable of spreading the virus: Spreader Requirements
 * 1) infected with Pokérus, state is Contagious or Resistant (see Pokérus States)
 * 2) Not ready to hatch
 * 3) Being bred manually (ie: a hatchery helper is not assisting with its egg)

Only Pokémon that fulfill the below conditions are capable of contracting the virus: Contraction Requirements
 * 1) Not ready to hatch
 * 2) Share at least one type with a Pokémon that fulfills the "Spreader Requisites"
 * 3) Being bred manually (ie: a hatchery helper is not assisting with its egg)

If all of the above conditions are met, an uninfected Pokémon will automatically catch Pokérus upon gaining any number of egg steps. Pokémon in the Hatchery Queue will not catch Pokérus.

Pokérus States
There are 4 states of Pokérus as described below.

Effort Values (EVs)
EVs are a damage multiplying stat for each individual Pokémon that can be seen in the Pokédex page for that Pokémon and by using the Display Value setting in the Hatchery. EVs for a Pokémon can currently only be increased by obtaining that Pokémon again after it has caught the Pokérus. You can gain EVs for a Pokémon by: catching it on a Route or a Dungeon, obtaining it as a Wandering Pokemon, or by evolving it using Evolution Items. Breeding a Pokémon does not count towards gaining EVs. EV gain is further affected by the Rowap Berry Aura. See Farming Setups for an optimized EV gain farm setup.

Gaining EVs (Methods)
Different methods of catching a Pokémon will yield different amounts of EVs. If the Slow EVs Challenge Mode is activated, you will gain EVs at a 10x slower rate (You gain the same amount of EVs, but require 10x as many EVs to yield the same bonus. In some instances, the yield of EVs is further modified by an external factor (see below tables for specific information).

Examples
Example 1: Catching a Shiny Dungeon Pokémon with a Repeatball yields: $$0.1 * 3 * 5 * 5 = 7.5 EVs$$ Example 2: Catching a Shiny Roaming Pokémon yields: $$0.1 * 5 * 50 = 25 EVs$$ Example 3: Catching a Shiny Roaming Pokémon with a Repeatball yields: $$0.1 * 5 * 5 * 50 = 125 EVs$$

EV Damage Multiplier
EVs increase the amount of damage that a Pokémon does. EVs multiply the damage done by a Pokémon. If your Pokémon has fewer than 50 EVs, a Pokémon's EV Damage Multiplier increases by 0.01 per EV, and consequently a Pokémon gains 1% extra damage per EV for the first 50 EVs. Pokemon that have: contracted Pokérus, have left the hatchery after contracting Pokérus (ie: not Infected), and have gained less than 50 EVs are considered Contagious. However, Pokémon that fulfill all the above conditions but have gained 50 or more EVs are considered Resistant. See Pokérus States for more information on Pokérus States. Beyond 50 EVs, Pokémon will still gain EVs at the same rate, but will see diminishing returns with respect to the EV Damage Multiplier bonus gained per EV gained. There is no limit to this multiplier.

EV Formulas
When a Pokémon has fewer than 50 EVs: $$\colorbox{White}{$ \text{EV Damage Multiplier} = 1 + (\text{EV} / 100)$}$$ When a Pokémon has greater than 50 EVs: $$\colorbox{White}{$ \text{EV Damage Multiplier} = \text{EV}^{\left(\frac{\log\left(1.5\right)}{\log\left(50\right)}\right)}$}$$