Questions and postings pertaining to the usage of ImageMagick regardless of the interface. This includes the command-line utilities, as well as the C and C++ APIs. Usage questions are like "How do I use ImageMagick to create drop shadows?".
I have renamed your input map as "mapRedPath.png".
The following Windows BAT command make a copy. For that copy, it turns red into white and everything else black. It thickens the white line. Then it makes black transparent, and turns white into red. The result is composited over the map.
convert ^
mapRedPath.png ^
( +clone ^
-fill Black +opaque Red ^
-fill White -opaque Red ^
-morphology dilate disk:1 ^
-transparent black ^
-fill Red -opaque White ^
) ^
-compose Over -composite ^
m.png
This works with any colour of path. As "red" uses a single channel, it could probably be optimised.