Oddly, I recently researched this issue, and placed such a case into suit. If you are suing for intentional transmission, it's one year, and if you are suing for negligent transmission, its 3 years. To be safe, you should sue from the date you contracted the illness, but if the statute has run with respect to the date of contact, you can argue that the appropriate date is the date the illness manifested itself. I'd be happy to discuss this with you. Keep in mind, most (almost all) insurance policies exclude coverage for transmission of STDs, so the cases tend to be viable only if the transmitter has assets.
I just settled a similar case for a woman who's boyfriend denied having an STD and then gave her herpes. The guy had money so I was able to negotiate a settlement. I seem to recall that my research showed that a one year statute of limitations applied. I would certainly want to sue within a year if possible to avoid issues later. Another issue for you will be whether or not the person has assets to go after as insurance will not cover this. I am a former federal and State prosecutor and now handle civil litigation so feel free to check out my web site and contact me if you wish to retain counsel.