You may want to try going in to the "Paint" work space and using the paint brush tool. In the paint work space there are several brushes with soft boundaries and you adjust the settings from there.
Window/Workspace/Paint to change the work space.
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I would first draw a shape layer using the pen tool with a stroke only. Then I would animate the stroke path to show the changing border. Then I would duplicate the shape layer, change the path to a fill, delete the stroke on the top copy and set it as a track matte. To facilitate further editing I would add an expression to the animated path and drag the pickwhip from the track matte copy to the bottom copy. The last step would be to add Gaussian blur to the stroke layer, adjust the width and the blur to get the look I want. You could also experiment with the blend mode of the stroke layer to compliment the map and improve the look. Something like this:
To be perfectly honest I would use a very similar technique to create this kind of illustration in Photoshop. Use a path layer for the outline, duplicate and set to fill, set as a clipping matte, then add a blur to the stroke and experiment with blend modes. Much faster than brushing.
If your outline does not move it would be faster to create it in Illustrator using a gradient filled stroke with opacity in the gradient.