well in our area the cats eat the mice..but they would also eat the
chickens and hens that we might try to raise..esp my big boy cat, he is a monster.
however, you might also try attracting wild birds..i have lived in a high deer area for 39 years and have never had a tick on me..ever.
people complain about deer ticks..but i
feed the deer and don't get ticks.
i do put flea and tick collars on my cats though, to protect them mostly from fleas..but maybe they are killing off the ticks too?