@Misadventure All Flesh Must Be Eaten has a very brutal firearms combat system, but guns are scary and I somewhat approve of it. One thing that I do love about it, is that it allows you to design your zombies. Is it "one bite equals dead", or "one bite and there's a chance" or "multiple bites and there's still a chance"?
That's one method. When I ran it, tabletop, I would pretty much always have a zombie grab in one turn, then try to bite the next, which usually left ample time for other players - even the player who was grabbed - to wrestle free or save the others before a bite was attempted, and even then, there were save rolls made against the zombie infection.
In the end, after someone was bitten, he/she was kept under observation, and the stamina rolls were made in private to leave the players with a sense of drama until signs of sickness did, or didn't, settle in.
I made ammunition and gas supplies that needed to be tracked. I incorporated conflict resolution when coming across certain bands of other survivors, and other groups of survivors were antagonists. There. Would. Be. Risks. The risks weren't insurmountable, though. Social/leadership skills could be used to sway the opinions of even the worst raiders. It wasn't "they're bad guys, so you're screwed". Everyone has a price, wants, needs, etc. Negotiation was a thing.
I presented certain options with degrees of difficulty and let the players determine whether or not it was worth the risk. If they decided not to run into the zombie-infested Wal-Mart, I gave other opportunities to find food and supplies with lesser difficulty, but those lesser options yielded less bountiful gains.
Most importantly, I kept introducing problems. Sure, they could wall up an area and try to make things comfortable, but just like TWD, I'd keep throwing things that would require them to exit their comfort zone. INSULIN IS LOW. Strangers come by. Zombies approach. Food is needed. The crops aren't growing. Someone comes by begging for help.
If I got the idea that the players were just content to go "No thanks, I'm gonna stay back behind this wall where everything is safe, where I've got a small farm and plenty of security." Then, eventually, storms would come, or a long winter, or and npc would hide a killing bite, and throw a monkey wrench into the whole goddamned thing.
Survival games are about an inability to secure lasting, meaningful resources, and just like TWD, the likelihood of the majority of the starting cast making it to the end of the show is low.
To ensure that the proper sense of risk/reward matched the setting, I would require the use of dice. Sometimes you cannot convince people. Sometime you can't shoot a zombie through the eye from a hundred meters out with a compound bow to save your girlfriend.
The bitch of the survival setting is that you must place yourself at risk to place yourself in a state of well-being, but that state of well-being isn't going to always last forever, so the job of the GM is to keep the genre relevant. Give them survival. Make them fight to survive.
(Sorry about the potential tl;dr)