There isn't really a chasing arc. It more so emphasises the fact that the experimental drugs that he uses to suppress his ruts, and him suppressing his ruts in the first place, is making him crazy. He's also really paranoid because I think his brother gaslighted him into believing that he slept with a dog during his first rut. The only chasing that I really saw in the novel, was that Chase overhears Josh talking with someone, during which Josh talks about Pete and Pete's mum (Pete doesn't have a mum, but he lies to most people who know that he has a child), and then Chase misunderstands and assumes that Josh has a wife, and begs and cries for Josh to choose him. Pretty ironic that his name is Chase and he doesn't do much chasing haha.
For those who have read the novel, may I ask which volume is the chasing arc? I know there are 3 volumes of the novel and one for the side stories but I haven't read anything.