Factors that I've already thought of include: accountability (whether or not you'll see the person again), likelihood of transmission (including whether or not you'll have sex with that person), seriousness of transmission (ex: herpes is pretty non-threatening, whereas HIV can kill), likelihood of transmission to other people (whether your partner is likely to sleep with other people or not), where you got the STI from (getting herpes as a kid/kissing/born with it/sex), what stigmas are associated with the STI, previous reactions to sharing the information, and so on...
Of course, this excludes the "I think it's the right thing to do" option. What other factors do you know of?
Anecdata and real data welcome!
On a different note, what's a better way of saying "not polyamorous and not in an open relationship"? Monogamous isn't exactly right.
Edited to clarify wording. Also edited to remove a typo.