It appears that the mentality is to allow them to live so they reproduce and over-populate & wipe out the food sources faster so their population crashes due to starvation & disease?
I kill every one I see, and when one takes it's place I'll kill it as well. There has to be a limited number reached somewhere, but I assure you there's no limit to how many I'm willing to kill.
I do like the parvo-puppy idea....
I had a vet tell me the parvo puppy deal works. Gets carried back to the den and gets in the soil. It's the gift that keeps on giving.