I just thought
Since there doesn't seem to be many NPC's as of yet, and the teacher doesn't really know much of what's happening.. as well as the fact that the game rewards you for exploring, how about this:
You can find notes spread out across the different levels that will shed some light as to what is happening in this world, how the infection happened.. or just simply experiences from people that got infected, and their development as the infection spreads through their body, as an example: "A damn dog just bit me in the arm, fuck it hurts.. but that's not all, I feel.. weird, was that dog infected too?" and things of the sort. It would add a lot of immersion to the game, to know that these people were once human.. and that via an unexpected event (which would later be discovered) they transformed into the zombies they are now.. their bodies mutating, developing body parts that weren't there before (for the futanari enemies, for example)
For this to work though, we would need an inventory system.
Not only would the inventory work with things like medkits and such, since as someone pointed out before, if you're max health and you happen to come across a medkit, you can't really store it somewhere.. but it would also help with keeping mementos of people, or these story bits, which you can later read when you are at a safe zone.
It would also add some flavor if the player character could react to those story bits, saying something like: "These.. these monsters were once human? B-but how? Who would do such a thing to them?"