The Blue Sickness inoculation is an inoculation against Blue Sickness. The inoculation was created by the Aschen for the People of Blue.
Blue Sickness is caused by too much exposure to the gas that is mined by the people of the moon called Blue. The Aschen helped the people of Blue with their mining operations and provided an inoculation against the sickness.
The inoculation isn't mandatory but it has become a prerequisite for working in the gas mines, which is the largest source of employment on Blue.
The People of Blue take the immunization, as they believe the sickness is the only thing stopping them from harvesting the full riches of the fuel. They also anticipate industrial leaps once they can ramp up their mining operation.
When Phoenix-1 visited Blue, the locals hadn't yet experienced any ill side effects and were lining up to receive the immunization. They didn't force Phoenix-1, (who had posed as travelers from a nearby town), to get it, but the locals did look askew when they declined. (RPG: "Core Rulebook")