How do you get rid of Foxes in australia and manage the problem?

Given that foxes are an introduced species (within the past 200 years, relatively young) and the ecosystem has not yet adapted to their presence and in adapting more native species may be lost, it is a difficult problem to address.

Widescale extermination campaigns might seem the practical if unpopular solution, but they come with problems (bait and traps may snare native species, causing harm to native species and not just the fox) and are not necessarily effective against an adaptive and nocturnal species like the fox.

The dingo is also an introduced species (descended from domestic dogs), but the Australian ecosystem has had time to adapt to the dingo's presence; after thousands of years, the Dingo is essentially part of the Australian ecosystem now and could have a vital role in controlling the invasive fox as a competing predator. Protecting the Dingo and other native, wild Australian predators competitive with the fox may be the best overall solution. Extermination programs against these native competitors should be curtailed, including in cases of cattle depredation and alternative, non-lethal measures should be taken instead of shoot-to-kill against the native predators (and dingoes) such as robust fences, so that the native predators can survive to keep the fox in check. They would probably not be able to completely kill off the invasive fox, but may keep the population in constant check (so long as the populations of native predators are healthy).

In terms of individuals trying to protect their ranches, chicken coops, etc., the best defense really is a strong defense: robust fencing protected against being dug under or chewed through and protective guard animals such as dogs (which should be well-contained and not let run loose in the wilderness, as that would exacerbate invasive species problems).