Pokérus - spreading to newly hatched Pokemon?

[Iron]

Microorganisms that can be "inherited" are called "endogenous" and there are many of them in real life. Some do nothing, like the ones latent within human DNA. Some few viruses are beneficial, and lots of useful bacterial cultures are passed along even in the womb. Some are horrible, like HIV.

But that's the real world. What about Pokemon?

Infection
When a Pokémon is infected with Pokérus, their status screen will display an icon indicating this special "status" the same way status conditions would be noted. If the Pokémon becomes affected by a status condition such as Sleep, the Pokérus icon will be temporarily replaced until the status condition is cured. As long as the Pokémon is infected with Pokérus, it can spread the virus to other Pokémon in the player's party.

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.

So it is not inherited from the mother, but passed through the eggshell membrane from other infected party members.
And you don't have to participate in a battle to gain it, but your party needs to battle for you.