Roosters really hate rats, we let our flock roam fifty years ago, they pecked through the horse and cattle dung happily. We let them in to our grain bins hallways and they roamed in the barns, the roosters were kept busy tearing any rats to pieces.
We had very few rats and mice. We had about fifty Rhode Island reds and about that many Leghorns.
The only problem was collecting the eggs, they could be anywhere. But as there were five generations in that big old farmhouse, we were about a dozen or so kids, cousins all.
Egg collecting was one of our chores. We never bought feed for them, they did just fine on their own. There were two creeks on the 35 acres, they drank from them. Sometimes in August we would pump up one or two buckets of well water for them.The reds would sit and hatch their own chicks, we butcherd the males at 3lbs or so. I remember grandma breaking up the rooster fights with her homemade corn brooms. The reds were in constant turnover, we let them molt twice before butchering as roasters. The leghorns were butcherd during first molt and grandpa had another batch ready to lay at that time.The leghorns were not so good as an eating bird, kinda skimpy. But we loved the chicken soup.
Keep one rooster for each twenty to twentyfive hens.