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After many tries I managed to finish it finally.

But for me it's a bit too much out of the control with that delay, especially jumping parts. Maybe decreasing it  to make it 0.5 seconds will make it a bit easier to navigate.

And also one thing which came to my mind when I was dying tens of times. When zombie bites you, you end up in the begin of the level anyway, and when you die 3 times, it's game over. But when you restart game, you still start from beginning.

So maybe you were planning to make few levels, but the time restrictions knocked in or didn't have time to just maybe make animation, where the zombie bites, but your character pushes it off and kills or something and your health value decreases. But you can still keep going as long as you're alive.  Or instead of health system, just display game over when zombie touches it.  

Just giving these tips in case if you maybe want to keep working on it past jam or something.