Hi and welcome,
Sex definitely is the highest risk factor for STD's and HIV, the risk of JC virus is low in the first year on Tysabri and increase in the second.
"An opportunistic infection is defined as an infection due to an organism that
generally does not cause disease, or causes only mild or self-limited disease in
people with normally functioning immune systems, but causes more significant
disease in people with impaired immunity. Examples include PML, oesophageal
candidiasis, systemic fungal infections, Pneumocystis jiroveci pneumonia,
mycobacterial infections (including atypical mycobacteria and tuberculosis),
chronic intestinal cryptosporidiosis, disseminated viral infections (such as
disseminated herpes or cytomegalovirus infections), toxoplasmosis and
Cryptosporidium infections.
2.2 Opportunistic infections associated with TYSABRI
A case of Cryptosporidium diarrhoea was reported in multiple sclerosis (MS)
clinical trials. In clinical trials in Crohn’s disease, cases of additional
opportunistic infections have been reported, some of which were fatal. In these
studies, concomitant use of other agents including immunosuppressants (IS)
was common. Occasional reports of other opportunistic infections have been
reported with marketed use of TYSABRI.
Version 16: 24 June 2016 6
2.3 Herpes infections
TYSABRI increases the risk of developing encephalitis and meningitis caused by
herpes simplex and varicella zoster viruses. In post-marketing experience, serious,
life-threatening, and sometimes fatal cases have been reported in MS patients
receiving TYSABRI."
https://www.hpra.ie/docs/default-source/3rd-party-documents/tysabri-physician-information-and-management-guidelines-(version-15-27th-april-2016).pdf?sfvrsn=2
I'm sorry but i too couldn't find anything that specifically links Tysabri and sexually transmitted disease, hopefully the guidelines information will help answer your question.
Hope that helps.....JJ