Read in the last year, probably not more than a few years old. Its either a GameLit novel, (Hero fights the monsters and levels up, and gets new stats and skills) Or a Fan Fiction story published on a story site.
Guy wakes up in about the 100th floor of an apartment tower and finds he has a Hud telling him he has to kill x zombies to complete level 1, and has xx minutes before they break down his door and he has to fight them.
Killing them yields XP (and on higher level zombies, monster cores, which he has to collect from the bodies)
Using random junk in his apartment he is able to kill the zombies when they break down the door. In addition to the kill xx zombies on each floor quests, he is given "rescue" quests. His first is to save a woman in a neighboring apartment. (xx minutes to save her before the zombies break in her door) Also "daily" quests such as exercise. (do 100 pushups, sit-ups, run 1 mile etc.)
One "cheat" he discovers, is when he sees lots of zombies clustered around the base of the tower, he starts dropping appliances, furniture, tools, flower pots, anything heavy to crush the zombies on the ground. This gives him a BIG boost to his XP gain.
There is a "Store" in his HUD where he can choose his new skills. One that he is able to get early is Time manipulation. (Slow time for fighting, and speed up time for himself, so he regains energy quickly, or sleeps 8 hours in a few minutes)
By absorbing the monster cores he is able to boost his stats and abilities. Also everyone (else?) is slowly being zombified (xx days) and will eventually turn into a mindless zombie like the ones he is killing. BUT if he gets other people (that he rescued) to absorb the cores, they become zombified in another fashion, and are immune to becoming mindless. (IIRC, the girl gets much stronger and tougher skin) and as those companions level up from kills, he can level their skills and stats.
By the time they get to about the 20th floor? He has rescued about 50 people? But has only made 3-4 companions by having them absorb cores. He is by now (from droppings things from windows and balconies) about 10x stronger/faster/tougher than his companions, and 100x stronger/faster/tougher than a normal person.
At about the 20th floor the normal people have built a barriers in the stairwells and want to hole up and eat what food they have collected and hope for rescue. So he bypasses the barrier and starts soloing the remaining floors a few at a time while everyone else sleeps.
The zombies are ranked like your typical GameLit ranking. Starting with E rank weaklings, D rank speedsters, C rank who can eat other zombies and level themselves up, to A rank in the bottom floors of the tower.
Pretty sure the story ends when he reaches the ground floor, and has to decide to proceed to another tower and continue fighting, or enter the basement and fight something very powerful that is down there.
