I would love this, myself.
Here's an idea of how it could be realistic in terms of infection and spread:
Instead of being thrust into a swarm of zombies, a player starts in a location of his choice in a rather large city, and he's basically having a normal day, and there's a few (less than 10) zombies that spawn in random places in the map and infect people who turn at a rather fast rate, making a greater total of zombies as time goes on.
The beautiful thing would be having the possibility to kill those 10 zombies BEFORE they can infect others, thus ending the infection on the first day.
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