That's a great idea, I would love that game. I had a hospital game many moons ago, I don't remember the name of it, but the hospital kept expanding as it got more sophisticated.
To answer the question about how you would keep track of patients: It wasn't personal in the game I played, they didn't even have names, just a bunch if people coming in and out. I think it should be the staff with names and shifts but not the many patients and visitors.