The Sickness is a disease that affects the Ribika, most commonly females, leaving them with a fever and missing body parts. It is said to consume the infected victim until death. Unlike normal diseases it just makes the infected body parts disappear, -not to rot or deteriorate- just like magic.
It is said by Konoe in the beginning of the game that the phenomenon of the Sickness started around his birth. Later in the story it is revealed that it was caused by Leaks' powers. It was one of his methods to take revenge from Shui, who he thought had betrayed him, thus the time of it's origin being close to the main character's birth.
In any good ending, the phenomenon is stopped due to Leak's defeat.