Her backstory's an bit hard to understand because there are multiple versions of them, but here's one of them. Sorry if it's confusing.
Chiyoku is one of the last remaining humans on earth. Almost every human has become zombies due to an chemical accident. Her parents died in a car accident, but Chiyoku was at her friend's house, so she wasn't involved.
Chiyoku has been schizophrenic all her life, and as a result she finds it hard to find the difference between reality or delusion.
The knife that she's holding was used to kill an 'monster' that blocked her path. That as not an monster. It was an ordinary schoolgirl.
When Chiyoku found that out, she went mad and began killing more 'monsters'
When the zombie apocalypse struck, she was at school, hence her school uniform that's she's wearing in her design