Leprechaun said...
These people ... choose to run vermin on their leases.
I don't think there's any choice in the matter. We had rats in the roof earlier this year when the neighbours decided to knock down their house. We didn't choose to have them and it was a PITA to get rid of them. Initially I thought we had mice because one found it's way into the kitchen. Put out some mice traps and twice one went off but no mouse and just a spot of blood. One night I was up late watching something on TV and snap! off goes the mouse trap. I went to have a look and it was a decent sized rat, but the mouse trap had obviously only stunned it. I quickly got together a plastic bag and scooped it up just as it was beginning to come back to life. Rat started squealing and squirming as I picked up his warm body so I was just in time. I took him outside and squashed his head in with a 6" x 2".
Anyway, I digress. The point is, you don't choose to run vermin, and controlling them is nigh on impossible. It would require an Australia-wide approach and would still fail. A bit like controlling cane toads.
The best idea would be to introduce lions. Once the lions eat all the goats, introduce polar bears. Once the polar bears eat all the lions global warming should kill them off.