Dreams utilize other characters to portray aspects of the individual - so dreaming of a Zombie can portray how you are recognizing a 'lifeless' yet active part of you that needs to be understsood and integrated. Like any stalker dream, the Zombie that pursues us embodies the Shadow archetype. We dream of what we are not facing and the zombie can represent a lifeless approach that is uninspired or without vision. While we may feel victimized by events - it can be our 'negativism' that undermines our success. Zombies can also suggest materialism over passion, or vampirism where one side of the self succeeds at the expense of another.
The Zombie Apocalpyse dream shows the movement of the psyche toward rebirth after overcoming what may have felt like a negative period. In most myths, or the inspiration of the collective unconscious ie: archetypes, the apocalypse is usually followed by a rebirth for civilization. The landscape in a dream shows the current climate of the inner landscape. If the 'world' is ending then an old way of thinking may be passing. If it is ending with a theme of Zombies, the message can be that a rebirth will lead to optimism and a more fulfilling way of interacting with life. Nightmares are a positive sign that something is shifting or coming into consciousness for examination and release.