I think we should find a permanent way to control invasive species, of course to understand how to control invasive species, we must know what invasive species are and what separates them from an introduced species . An introduced species may not automatically be an invasive species, for example the mustangs of North America are not invasive, they actually assist the environment by feeding on flammable grass and migrating from waterhole to waterhole which prevents water from being dried up. The only reason why they are considered "invasive" is because they compete with invasive cattle that overgraze and drink up waterholes.
Banteng in Australia are not considered an invasive species in the right that it doesn't negatively affect the ecosystem, but rather has adapted to living in it. Studies have shown that mutual relationships have developed involving the removal of ectoparasites residing on the bovid body by the Torresian crow. It is possible that grazing by banteng minimises potential dry grass build-up, thus limiting encroachment of seasonal fires (and hence post-fire grassland) into monsoonal forest areas and that this may be assisting the spread and germination of monsoonal forest seeds. However this possibility was not firmly concluded by the study.
Likewise, a few populations of feral landrace cattle and horses in mainland Europe aren't generally considered invasive, because they replace the extinct aurochs and tarpan in their ecological roles. However, with invasive species, we need to find a way to control them. One idea is to introduce their native predator to hunt them, because animals hunting other animals is cheaper than regularly culling through shooting and poisoning them.
Another idea, is neutering/spaying individuals and letting them go free. This is how we completely eradicated nutria from Maryland and it appears to be a working technique. Because when you remove completion from other individuals, it just leaves more space to thrive and reproduce.