After completing Lana's challenge in Pokémon Sun, I went to the Pokécenter to heal my team. That's where the nurse told me that one of my Pokémon had Pokérus. Apparently, my Dartrix had somehow caught it. Since Pokérus is actually beneficial and quite rare (1/3 the chance of encountering a shiny Pokémon), I decided to spread it among all my Pokémon.
Apparently, Pokérus only spreads from one Pokémon in my team to whichever is positioned next to it. In other words, I only need two infected Pokémon in my team to infect the entire team. One in the upper right position (2nd), and one in the lower left (5th). Therefore, I can infect 4 Pokémon in between two Pokécenter visits at most.
However, it seems that the rate of spreading is not consistent. Sometimes, I can infect the entire team by beating a single wild Pokémon, and sometimes it can take dozens of such encounters.
I was wondering if there was a faster way to spread Pokérus among my team. For instance: Do I even need to battle at all? Can I just flee instead of fighting? Do I need to battle stronger Pokémon, or are weak ones good enough? Should I find trainers instead of going for the wild ones?
While I'm personally more interested in Sun & Moon, answers concerning other generations are welcome as well.