Denmark does by no means impose restrictions on the travel of HIV positive persons to the country. All tourists are welcome and Denmark is generally a very gay friendly place.

Still, there are special restrictions regarding the sexual actions of people with HIV.

If you are HIV positive you can be prosecuted for having unprotected sex with an HIV negative partner, if you have not informed that person of your HIV status.

If you have safe sex you are not required to disclose your status.