If this isn't good for you let me know and I'll stop posting. The main culling method is a poison developed from an Australian native plant that doesn't harm Australian wildlife but kills cats and foxes. Any sort of catch and care method would cost vastly more, and while kinder to the cats, is a) almost impossible to get through the australian government and B) would result in more animal deaths in the long run as creatures are killed to feed the cats being cared for.

WHY ARE FERAL CATS SUCH A BIG PROBLEM?

The peer reviewed science (for example, the Action Plan for Australian Mammals, published in 2014) tells us feral cats are the single biggestthreat to Australia’s native mammals. The threat of feral cats to Australian mammals is almost double that of foxes,which is the next highest threat, and substantially greater than habitat loss.Feral cats have already directly contributed to extinctions of more than 20of our Australian mammals, like the rusty numbat, the desert bandicoot, the broad-faced potoroo and the crescent nailtailwallaby. We will never see these remarkable animals again. And they are implicated in another eight mammal extinctions. Feral cats put direct pressure on at least 124 Australian species endangered with extinction. Feral cats hunt, kill and eat bilbies, numbats, quokkas, quolls, bandicoots, parrots, lizards, frogs and many other endangered animals.Indigenous rangers in South Australia found an endangered black-footed rock-wallaby in the stomach of a 6.5kg feral cat. Many Australian animals simply cannot survive where there is predation by feral cats. Feral cats also threaten 19 migratory birds listed under international conventions.