You have to cook curative soup and have to feed him (You don't get the recipe until you start repairing the dam, then half way through they need johns help, so lucio gives you the recipe, then you make and give to john to help you finish repairing it, he takes over a hour to eat it mind).
So Believe it or not but John after you feed him the curative soup and he has that little pop up say something saying he feels better. The diseased marker will not go away and John will still be sick but the fiving of the dam can progress. It confused me for a bit until i just got fed up and went to try and fix the dam...and lo and behold the story progressed.
Good luck! ;)