Do you know what makes humans the top of the food chain? It's not our biology, we have no natural weapons, no real defenses against attacks, are natural and greater than normal animal endurance helps us out last our prey, but when attacked, it doesn't help much.
What makes us the top is our ability to think new ways of killing #%|+. We are the only species who have designed and implemented weaponry that not only protects us, but can murder faster and more efficiently than any other earth species. Not only that, our instincts of self preservation kick in at the slightest provocation.
No imagine what happens when you remove that. And slow us down. And remove our ability for self-preservation. And now watch as every single animal predator take us down.
But we have cities, where few animals would have that sort of presence. Ignoring the fact that you'd have several thousand stray dogs and carrion birds screaming, "BaconBaconBaconMobileMeatBag" as they chowed down. Cities are built for defense, allowing us to funnel our enemies into a killing field. Not to mention that Zombies, never use tactics. The police would clear them in a week.
Ah, but you bring up the movies laughably silly method of infection. Biting someone is one of the most ineffective method of spreading diseases. If it was as super effective in the movies, then all dogs would have been rabid within a month of the first case of rabies.
And then there's the fact that Zombies are... Well, ambulatory corpses. And do you know what corpses do? They deteriorate. Namely rot. And it gets better! Did you know we have bacteria in our bodies? Bacteria that our immune system keeps under control? And what happens whenever we die and our immune system also stops? Well, the little germs inside you don't stop. Worse they produce gas, which makes corpses bloat! And bloat, and blot until they literally cause their home to explode in a putrified mess. Such fun!
And it gets worse if the weather is North American, heat, humidity makes bodies rot faster! It's no better in hot and dry weather either. Maybe the won't putrify. No, they'll mummify instead! Dessicating until they can't move. Cold weather is worse, as freezer burn would set in. And that just doesn't freeze meat, it destroys it.
And that's excluding the fact that organizations like the CDC are trained to deal quickly and efficiently with a viral outbreak of any kind in the first place.
There will never be a Zombie Apocalypse unless we spontaneously discover "magic". Science as we know it is against it.