The Edges are very very safe, mostly. Not only are there wonderful defenses, monsters in general simply stay towards the Center of the continent! It is thought that the ambient Magica there is denser and more comfortable for them to exist in. Demons of course can pop up in any location, but thanks to the continued work by Humanity, demon sightings have dropped to record low levels, so you mostly have nothing to worry about.
If you do think you've seen a monster, or a demon, be sure to go to the nearest public phone and alert the local authorities! Remember, "Better to cry wolf, than to be silenced forever!"
-Part of a speech on public safety given to Students.