In short, there's no definitive answer to this question. The film's themes of psychology and chaotic treatment of time travel make it difficult to pin down a solid answer. Still...
The voice <PERSON> hears calling him <PERSON> is mostly unexplained, but the homeless man he and <PERSON> run into multiple times shares the voice. While it is unlikely that this man is the sole source of the voice (as <PERSON> hears it several times before when escaping the mental hospital, and at other points where it is incredibly unlikely the homeless man is around), the confusion and mental degradation caused by repeated time travel (or the medication in the mental hospital) throughout the film is hinted at as the source of the voice. Keep in mind that the first place <PERSON> hears it is while strapped down after his first return to the future. <PERSON> may simply be imagining it because he has started to go insane, an interesting contrast to the dramatic irony produced in the audience, who know that <PERSON> is sane about being from the future.
Nonetheless, the voice does seem to perform a <PERSON>-like role in driving <PERSON>'s actions as another personality only he can hear. 295
As <PERSON> can be thought of as the "monkey" (in reference to the monkey sent into the well to retrieve the kid, but instead taking the sandwich, much like <PERSON> is only back in time to find a sample of the virus, not stop it from spreading), there's a possibility he is being used as a test animal by the scientists. To support this piece of speculation, note that the virus first breaks out in the airport where young <PERSON> is. Odds are, if he weren't immune, he would have died, but even if he weren't (and built up an immunity after being exposed to the virus), he would have lived through the virus outbreak, and probably had it at one point. Unless the scientists had a way to rid a person of the virus (which would negate the need to send somebody back to begin with to get a sample), the sanitation procedures the scientists are putting on are all a show, and everyone still alive is infected, with an immune response keeping them unharmed.
If <PERSON> is a test animal, it is likely that it is for time travel itself, as the procedure seems unrefined (they send him to the wrong time frequently). Thus, he may very well be receiving brain damage from time travel (if not already from the stress of the events), and the voice may be a product of that fact. One other explanation is that somebody from the future is somehow observing and speaking to <PERSON> during his ordeal, which isn't out of the question either. Otherwise, it has a supernatural explanation. 494