I was playing on the community server "DayZed.gg | Chernarus" when I got sick from another player. I needed to leave(in real life) so I logged off for a few hours, when I logged back in, my sickness was gone. As I was playing, I got sick again, on the same character. I decided to log off just to see if I could recreate the bug; logged back in 30 minutes later and the sickness was gone again.

Currently trying to get sick on official to test it here as well.