The probable medical origin of the single serpent around a rod: In ancient times infection by parasitic worms was common. The filarial worm Dracunculus medinensis aka "the fiery serpent", aka "the dragon of Medina" aka "the guinea worm" crawled around the victim's body, just under the skin. Physicians treated this infection by cutting a slit in the patient's skin, just in front of the worm's path. As the worm crawled out the cut, the physician carefully wound the pest around a stick until the entire animal had been removed. It is believed that because this type of infection was so common, physicians advertised their services by displaying a sign with the worm on a stick.

http://drblayney.com/Asclepius.html#AIM

I thought David might find this interesting - researching symbols