On a simplistic level, medication should be taken for the prescribed duration and not less, irregardless of the fading of symptoms - many STIs are asymptomatic or have latent phases in their progression anyway. Lots of medication is given to reduce the effects of incurable STIs like HPV ,HBV or HIV (Viral). However antibiotics are given to bacterial infections like syphilis or chlamydia which can remove the pathogen, thusly the presenting symptoms. "Medication" is a broad term ,as is "STI", so unfortunately there isn't a neat, all-encompassing answer as there are too many variables . Play it safe and say, "No" as incorrectly taken medication is harmful not only for the patient but the wider population as it increases the risk of pathogen resistance.
