I love it. I watched Highschool of the Dead in a single day just a few days ago and this is really similar to that (probably because zombie apocalypse >.<); was it influenced by HOTD? Either way, I really like it - your detail of the weapons, and the story gets off to a nice start here.
The infection 'had' spread, it is, though. It's all supposed to be in the past tense in stories, unless the thing is current. For example, 'he discovered that zombies eat brains,' is all right because they always do, but 'two days later, the zombies had eaten his brain.'