I'm not sure how "HIV+ positive people must be tracked" follows from "HIV+ people can make mistakes".
By that logic, everyone's movements and personal details should be tracked by the police/government/some third-party because there's a risk, someday, of someone sexually assaulting (or committing any other crime against) someone else.
Brand everyone with QR codes that can be scanned to show a quick list of things like HIV, mental health issues, wrong political beliefs.
I'm pretty sure there's ways to design QR codes, so we could come up with a way to embed a brand of a few of the "worst" traits so you can see before you scan.
I honestly have no idea what do drunk people do, that leads to random intercourses. It is an "educated guess", that in many if not the most cases the participants know each other.
And looking people up on the Internet is a common thing nowadays.
Maybe it would be a good idea for you to actually understand the problem domain you're inventing solutions for before you start thinking up far-reaching methods to mitigate a problem using a method that is unlikely to be used the way you intend it to. Especially if said methods have the potential to impact actual people's lives in a very negative way.