If you have unintelligent agents (zombies, animals) they have no reason to stick to roads but they are easier to stop. The roads might be tried by refugees in vehicles. It is so easy to make a road impassable (e.g. jersey barriers) that people in vehicles will go off-road also.
So how to rapidly encircle your area with a barrier?
It looks to me like this wire was laid down at about 1 mile/hour. On a vendor website I found they state it can be deployed at 20 meters/minute which is about the same. I estimate your quarantine area to have a circumference of 18 miles. You can figure out how long it would take to lay down an 18 mile circle of this stuff based on how many trucks you deploy. Not long.
It occurs to me that all concertina wire available has blades. Sentient things want to avoid being cut. Getting tangled in the wire happens also. If the blades were barbed it might sacrifice some cutting / injuring power but gain some tangling power which would be better against zombies.
Then you set out robot sentries. These paintball robot sentries are cheap and terrifying. You can find many videos posted by people who have built their own.
The area covered by a sentry depends on the range of its weapon and its sensor. One could have the sentry broadcast a message twice before it shoots to ward off intelligent refugees. You could set out many of these, with weapons appropriate for what you expect to try the wire.
The other reason for the robot sentries is that if one got triggered, it could turn on a camera and broadcast what it saw. So if you see your wire and sentries overwhelmed by a wave of zombies, or me in my fortified truck charging the wire, you could deploy an armed helicopter to the area.
I am thinking of a scene where the heroes are going to cross the fence. They have seen what happens to the infected who try it and seen what happens to me in my fortified truck. So they approach the wire very, very slowly, carrying large pieces of weighted plywood that they set across the wire very, very slowly.