I think it would add a whole new level of awareness to some people, to know that there is the chance of getting a disease or illness of sorts by doing a certain something, whether it's eating an animal, or drinking water from the ocean.
A few examples are listed below.
Rotten meat - If you've had cooked meat for too long in your inventory or if meat is left on the carcass of an animal, it will eventually turn rotten. If anyone were to eat it, there would be a high chance of maybe stomach pains and vomiting. Which could increase your hunger and thirst rate, maybe even lower your stamina.
Ocean/pond water - It's not always safe to drink from the ocean waters or ponds around the land, so unless you have antibiotics or water clearing pills, you have a chance of getting the same effects as rotten meat would.
Corpse diseases - Maybe we can adapt some sort of illness from dead carcass. There is always bodies littering the airfields and military compounds, as well as mass graves. What if there was some disease you could contract if you spend too much time around the area? Maybe diseases that could affect your blood levels, or vision. Say, since the zombie outbreak, Ebola has developed a new strain. It could case random hemorrhaging, affecting your blood levels. While Ebola would kill you in real life by now, maybe we could have some sort of newly developed medicine that either completely cures this, or only does so temporarily (it would at least have to last for 20-40 hours, otherwise players would get annoyed). That would also mean that players have to scavenge for more medicine if they hope to survive. Or they could simply avoid airfields and military compounds. Also assuming that everyone isn't immune to this zombie virus.
Medicine overdose - It doesn't happen often, but some players tend to get into trouble every minute, making them have to inject themselves with morphine, epi-pens and take painkillers constantly. Maybe there could be a side-effect to this? Perhaps affect their vision or aim, because I think normally, you've would've died from eating so many painkillers, but that would be too sudden for players.