Like I said, it all depends of the zombies, which ultimately are relatively easy unless it's the Return of the Living Dead zombies, which wont happen because those zombies are so impossible to exist (impossible to kill without incineration, control of severed limbs, able to think/speak/plan, hunger for only brains, still can keep normal motion and look like a human perfectly). A part of one of these (outside the impossible to kill without incineration or the control of severed limbs) could happen, but not combined. If it were them though, humanity is fucked and the only safe-haven, Nukes, would still lead to continual outbreak, though luckily these zombies are impossible to exist for numerous reasons.
If it's the Quarantine "zombies" or the 28 Days Later infected, it's then not so easy as you'll not only have to kill former humans but animals as well, but as long as you Quarantine the area, block water supply, kill any flying wildlife and send numerous small but heavily armed groups to rescue any survivors with air support. Then, when it seems pointless to continue rescue efforts, nuke.
It's relatively easy with Romero's zombies (even the runners) because the infection (I believe it to be but it really is up to interpretation) stays to just humans and is only passed on through bites or contact with blood on wounds. Quaratine the area, send in armored vehicles with troops around them and take on the swarm as you rescue victims. Then, Nuke.
This is all very dependent of course to the level of the outbreak (and I'm considering Level 2 to Early Level 3 Outbreaks), but as long as it's not in the middle to later stages of a level 3 outbreak, it should be ok. If it reaches the Middle to Later stages of a Level 3 outbreak, or worst, a Level 4, it depends on the lucky government that not infected's access to Nuclear weaponry and how far along the outbreak is on a global level. Like said, if it's the Return of the Living Dead's Zombies, humanity is basically fucked, but otherwise, it just goes to the area infected and the nuclear capabilities of those un-infected.