This is an economics problem and this teacher should work with their Econ department to change the rules for course auditing and increase reputational costs to disincentive this behavior. A few options: 1) Make auditing those classes more expensive by limiting the total number of courses a student can audit, or capping the number of students that can audit those courses. 2) Make auditing a remote-only class option. 3) Give lectures on how to spot this behavior which will make the perpetrators obvious and undesirable. 4)Have a no-dating policy between students within the same class under penalty of failure. 5) Couple course participation with a mandatory internship at a STEM company (something a serious student would want but a time-suck for a fake student).

The economics department might enjoy testing these policy changes and could get some papers out of them.

(I wish I could have posted on the original site but I need some sort of karma to do that)