DP and I have these conversations regularly (I am a big fan of the walking dead and zombie films , no idea why,i don't really watch much else....DP thinks i have mildly aggressive tendencies and zombies would be a legitimate way for me to become an aggressive ass kicker
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So we have come up with this.
As above even if you are eaten you are still a zombie until your brain is eaten , you just can't move . Many examples of half eaten zombies wandering around with bits missing.
The moving thing is basically two canons....fast and slow. 28 days later v the walking dead. We decided it was just different forms of the virus and length of infection. Older zombies (since being zombies no relation to biological age ...keep losing bits so harder to move)
Need to bite is more about incpnciois virus spread. A primal impetus like an instinct rather than a conscious need. No conscious need at all.. because zombie. Definition of instinct driven behaviour.
We also regularly discuss that there are two worlds. One where people have zombie films an done where they don't. On the grounds that many start with a shuffling , blood covered , growling , ill looking attacker and the victim is all confused and thinks they are on drugs or whatever. When in reality anyone who has seen the walking dead would instantly think " Bloody hell it's a zombie" run like hell ,change into suitable leather and canvas apocalyptic clothing and start arming the DC.
So some must be set in a world where they have never seen a zombie film to be confused as to what this clearly zombie like individual who is trying to bite them is.
We may or may not have over discussed this in 2020 