A zombie outbreak would end in a few days by itself. In Africa, in a few hours.

In the winter, between the cold destroying nerves and incapacitating movement and corpses getting waterlogged by rain, which would accelerate rot, zombies wouldn't last long.

In the heat, zombies would be quickly turned into maggot meals by every fly available. Add bloating from the heat and the entire situation would sort itself out quick and dirty.

And let me just add another thought: our main advantage is our brains. Zombie crave for it but are not particularly known for using it. Any zombie trying to attack a wild animal would end up made in pieces. Bears would have a field day. Imagine the carnage by pigs and cows. A single wild boar would be capable of plowing through a horde. At some point, even dogs would turn feral and attack on sight any two legged figure.