There is one disease that I know of, called psittacosis. You can read a little about it at
http://www.multiscope.com/hotspot/psittacosis.htm .
I suppose another might be a lung problem from breathing in the feather dust from a lot of birds. Most people will not get a lung problem from the dust & some birds have more dust than others.
I don't know if this is the information you are looking for or not.