Student or Learner
"Nowadays an HIV positive person can live their almost full life by taking precautions and medicines. They can live their full life and won't die early because of this disease."
We say that someone leads "a full life" to mean that the accomplish many things during their lifetime. If you mean that they will live to the same age they would have without being HIV-positive, then I would say they will live out their natural lifespan or something similar. I might even just stick with your "They won't die early".