Thank you for your inquiry. From what we gather from the question, you were asking about the possibility of HIV transmission through a cut possibly coming into contact with blood from another individual who was bleeding. From the information given, this scenario is determined to be Negligible Risk (there is no evidence or no documented cases of transmission, however, there is a theoretical possibility of transmission under certain extenuating circumstances).
From the HIV Transmission Equation (see below), HIV transmission requires HIV particles in a bodily fluid (e.g. blood) to have direct access to the bloodstream through a High, Low, or Negligible Risk activity.
In this situation, you mentioned that although you had a fresh cut from a knife, you were not bleeding, so I am assuming this was a superficial cut. A superficial cut is a small cut that "does not involve fat or muscle tissue" (i.e., leaves the deeper skin layers intact) and is not bleeding heavily (1). Thus, this would not satisfy the HIV Transmission Equation as there would not be a 'pathway' to your bloodstream. However a higher risk assessment for HIV transmission would be applicable in this scenario if you had a large, gaping wound instead that would permit blood from the other individual to enter your bloodstream.
Recommendation: There is no evidence or no documented cases of transmission. Refer to a healthcare professional for more personalized answers.All the best,
AIDS Vancouver Online/Helpline, Shirley
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(1) Lacerations (Cuts) Without Stitches