Always learning here. This is our first experience with rats - a wood rat. The hawks and falcons have all been pushed out due to so much tree destruction from new housing developments so there are no natural predators for the rats. Haven't seen or heard a hawk in weeks or an owl for that matter.Please consider traps first. Maybe an electronic one that can catch multiple at once?
I don't worry about mice. They don't cause much damage and chickens will eat them. Rats are a bigger problem.

I'll check into the electronic traps - interesting concept since we have dogs. Thanks for the suggestion.