Health, to me, would be a lot of quality of life factors... mainly nutrition, medicine, and mental well being.
Nutrition would be determined not just by an adequate food supply, but a new series of "food luxuries". You would not need a lot of food luxuries to survive. Quite the contrary. Every civilization bases their existence around a specific grain unique to a region (wheat, corn, barley, oats, rice...). For all considerations the grains are basically equal, but collecting a greater variety of grains will give your civilization a health bonus more than just relying on one. There would also be various food luxuries, from beef to pork to chicken, from bananas to cabbage to milk. These would not provide the abundance of food that is provided by grain. (In fact, they would not even count as food that would prevent starvation. They would count as luxuries.) But these excesses will improve the health of an already well-fed nation. Once they've satisfied their basic hungers (grain), it's now a question of how lavish their lifestyle is (with fancy oils, exotic fruits, and succulent meats). While the variety would be great, the interface and goal would be simple -- diversify. You do this more by trading than expanding, with a few civilizations being lucky enough to have their own unique food luxury. (This would also have huge implications for the value of trade and cooperation.)
Medicine would be largely determined by technology. This is your aqueduct and hospital stuff. Rather than acting as "growth bonuses" like food luxuries, these are more "growth penalties" where if you lack them you cannot grow period. Pollution would be a tie-in here, with certain percentages tied into each city, leading to more and more severe growth penalties. Pollution is naturally cleaned up if you stop polluting. But I'd still like to play with other variables like plagues in mismanaged empires, or empires that choose to subsidize health care for all their citizens, making it a right instead of a privelege.
And mental well being, of course, is related mainly to stress. If you constantly overwork your citizens, that would be an imposition on health. War, aside from its physical casualties, would also lead to mental casualties -- people frightened of a draft or constantly upset because of the loss of their brothers and fathers and mothers and sisters.
It may sound like a lot, but much of it is automated and is an extension of how you behave (are you a tyrant or a philanthropist?), what you acquire (do you rely on a few basics, or are you depsperately trying to get pineapples to complete your assortment of fruit?), and what you build (do you pump out barracks or aqueducts?). These would determine whether your civilization is basically healthy, suffering, or booming. Its main impact would be on population, but small amounts on happiness and productivity.
A healthy society is a productive society! How productive is it to take advantage of your people and let them suffer?
