Can door rust be stopped?

I have a 2001 F250 with a 7.3. Body is in excellent condition, except
for rust in the corner of the front driver and front passanger doors mostly in the corner furtherest from the hinge and along the bottom of the door till about the midway point (inside only, cannot be seen from outside).

Anyone know the path the water is taking to cause this rust? Any ideas on how to stop it from causing further damage?