So, umm, how do you test this vaccine? Are the participants expected to have unprotected sex with HIV-positive people?
In the USA, estimated new HIV infections in 2019 35k. Assuming 350 million Americans, that gives a very rough estimate of 1 case out of 10,000 per year.
You can enrich this by shifting target population. You could do this in the USA by targetting high risk communities, or by moving the trial overseas.
An trial in the USA with 10k in each arm could very likely be constructed to generate at least 10 cases per year. Likely up to 50.
https://www.hiv.gov/hiv-basics/overview/data-and-trends/stat...
For a common cold, or other lower-impact disease, you could do a challenge trial.