Zombies must be real and permanent main threat in the game. It will solve all problems with PVP.
Like in the game Project Zomboid. There are plenty of zombies at all and to survive you must be very stealthy. Besides that there is an interesting script. When the player stays in one place, after some time there appears a sound of helicopter fly around and hordes of zombies begin throng to the player position. In that situation player has only two choices - run or make friends with any other players to build defences and fight off zombies.
Similar system is in the game State of Decay.
Zombie must be real and permanent main threat and any player will just has not time for PVP.
To be a real threat zombie must be faster than player, must be killed headshot only, must be very sensitive to sounds of shots and quickly gather to the shooter (doesn't matter it's a shooter in the city or sniper in the forest).
I don't know about the future but at the moment (0.59) I can gather horde of 20-30 zombies (it's hard enough, there are not so many even in Cherno and Electro) and bring them from Cherno to NWA.
I made it couple of times and I was killed on the airfield by other players not by zombies. I drived 20 zombies over all Chernarus's map and they were not a threat for me and players that joined to me on the way.
All my states is only IMHO.
But at the moment in the game there is PVP because player (who has hi loot and lay on the hill with sniper rifle) doesn't have to worry about his life every minutes.
He doesn't have to worry his shot can hear zombies (in the forest there are no zombies at all, but even through they are there, there are not many of them and they are not a problem even for one player).
Very strong, dangerous zombies is a real reason to play in a group.
IMHO
Sorry for my bad English.
P.S. About PVP skill. Doesn't matter how good you are in PVP.
One lucky noob with sniper rifle on the hill can kill you with one lucky shot when you just will go pass. Because he knows he can shoot with impunity and in the game zombies are not threat at all.
Hope, in the future there will be hundreds of zombies for one noisy player in the game.
And they'll be very fast and sensitive.