Well, yeah... the civilopedia that you link in your sig. Like it says, you need to clear jungles and marsh within your city radii to stop disease from those sources. Flood plain disease, according to the same entry, should end with the discovery of Sanitation - I don't think you actually need to build a Hospital, though I've never really checked. Granaries don't do anything in any event, though they will at least make it easier for a city to regain population due to keeping half its food box.
Good point... sometimes the most obvious answers are hardest to see
here's what is says:
At the same time aqueducts reduced the chance of contracting water-borne diseases, by reducing the dependence on stagnant ponds and wells as water sources.
Hospitals are institutions that focus on the diagnosis and treatment of disease and trauma.
I always thought there is a chance your citizen will die from disease as it seems to happen randomly to me. Sometimes I can have one flood plain tile and have disease stirke me 4 times in 20 turns. Other times I will have a city with several flood plain tiles and won't be hampered by disease throughout the game.
So, I thought it makes sense that improvements (ie, hospitals and aqueducts) reduce that chance. I know that clearing jungle and marshes does too.
Also, I thought all of these factors along with which techs you have researched affect the disease % that you see when you hit F11.