Controlling invasive species

Australia has a problem with an invasive species, the camel. There are, according to an AP article, one million of them in Australia and their population doubles every nine years. The solution may be to shoot them from helicopters, which is how wolves are controlled in Alaska. Some people have suggested birth controlling them, which may be how feral horses will be controlled in the U.S. Is there any problem for which birth control is not the solution for some people?