If the consensus on Jenny Curran's death in Forrest Gump is HIV or Hep C, wouldn't both Forrest and little Forrest have it also? It doesn't seem feasible to me that she could have had either one of these viruses without passing it to her son, and possibly Forrest.
Without treatment, the chance of passing HIV on to a baby is 25% (source). Seems absurdly low to me but I am not a doctor. As far as I remember, Jenny and Forrest senior only had one sexual encounter, so it is possible he didn't contract the virus either.
We are not explicitely told, so it's up to the spectators. In my mind I let the Forrests live a happy, disease free life.
What Jenny died of is not clear and can not have a definitive answer. Therefore, it's almost impossible to have a irrefutable proof of Forrest and little Forrest being infected. What we can speculate about are the chances of getting infected by either HIV (2%) or Hepatitis (4%).
Therefore, unprotected sex with an HIV-positive person who has acute HIV infection could carry a transmission risk of up to 2% (the equivalent of 1 transmission per 50 exposures) for receptive vaginal sex and over 20% (equivalent to 1 transmission per 5 exposures) for receptive anal sex. (from Stanford Medicine). "Transmitting from woman to man is even probably less than 1 of 1,000 exposures according to The Department of Veterans Affairs".
Results: The risk factors of HCV infection were as follows: transfusion of blood or blood products 34.4%, intravenous drug abuse 20.6%, heterosexual contact 3.8%, occupational risk 1.9% and tattoo 0.6%. (from National Library of Medicine)
In the book / movie
Forrest Gump writer Eric Roth confirmed Jenny dies after becoming HIV-positive - but Jenny's illness being AIDs isn't made clear in the movie. The confusion surrounding these questions is due to the fact that the movie provides only clues about Jenny's death and did not adapt how Jenny dies in the book. Screenrant
There's confusion because the illness Jenny dies from in the books is different from how screenwriter Eric Roth has spoken about it, and Forrest Gump author Winston Groom has given conflicting comments over the years. That said, what's clear is that Jenny dies of Hepatitis C in the second book, while she dies of AIDS in the movies, even though it was only implied.
Notably, Hepatitis C was discovered in 1989, which is why the doctors could do little for Jenny in the '80s. Moreover, Hepatitis C - especially during the '80s - was transferred through blood contact with shared needles, which is also consistent with Jenny's character in Forrest Gump.