Sickness can occur to anyone in the shelter that came back from an expedition without a Gas Mask (If the fallout outside is highly radiated), didn't get at least 1 soup serving every 5 days, or by certain events. People that are sick will eventually die/run away after 15/20 days. It can be cured by using a medkit or when the affected person is well fed or with the shower event.
Gallery
A sick and tired Ted
A sick and tired Timmy
Ted Sick
