The only way you can be sure you haven't killed anyone with
HIV (assuming you are positive) is to test every one of your
sexual contacts over the course of their life. If they get sick
or die, then it is still possible, with the best of current technology,
to determine if they died from a strain of the virus they got from
you. So, unless you've done this level and intensity of testing,
then you can't say for certain if anyone has died or gotten
sick after having sex with you.

What probably happens, in reality, is that uninfected people
have sex with a number of infected people and get the virus
from one or more of them. So it then becomes possible for
any one HIV+ person to say, with some belief, that they did
not pass HIV on to a given person--so responsibility is lost
in the crowd. There is the possibility for each infected person
to say some other person didn't get the virus from them. This
is nature's way of saying that having sex is more important
than being responsible.

Unless a complete fix is found for HIV, then you can look
forward to the epidemic continuing largely unabated.