There are a handful of creatures, mostly animals, that have an attack with an additional chance to inflict the “Bleed” effect, sort of like how zombie attacks have a chance to be “really deep.” (It’s either that or a special move with a chance, I can’t remember which.)
A new bleed system would be complicated and kind of time-consuming to make, so editing what’s in place may be best. My suggested change would be to nerf bleed damage, draw out its length to have similar numbers by the end of its duration, and to compound it with the “deep wound” effect that zombies current give. A LOT of stuff can bite you, and the lore says that the zombification process is not due to virus or any such thing. It thus seems silly to me that infections are exclusively from zombies. If it’s just a bacterial infection from a festering bite, why not apply that to the animals that can currently bleed you? I have to assume that the wolves and coyotes are biting you when they inflict bleed. Give both bleed and possible infection at the same time.
Also, the additive pain either needs to go away, or be significantly reduced. One of the biggest and most frustrating early game hurdles is that, quite simply, animals will kill you even more often than zombies. Like, if an animal runs you down and bleeds you, you are simply dead. The damage is too huge, you have no way to stop it, and the debilitating penalties caused by pain rapidly strips the player of any feasible possibility of escaping. The huge dodge chances of animals also plays a part in this (Fucking fuck krecks; I don’t care what dimension you came from, fuck your dodge chance), but a lot of it is how damning bleed effects are right now. There’s just too much pain and you are dead well before the animal actually kills you. That’s not fun.
Bullets and bad cuts would also give you the bleed effect. While not guaranteed to get infected like bite wounds, regular bleeds can become infections on top of the regular bleeding, further compounding the problem because it was ignored or neglected. Odds are, though, the worst of the damage will be done by the bleed itself. Infection on top of that would just be from bad luck.