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[–] DrShitlord 0 points 19 points (+19|-0) ago  (edited ago)

Quite simple. The transmissibility of HIV in untreated individuals through anal intercourse is at about 4% per intercourse, so after 50 ejaculations which are reasonably possible within 10 days, the likelihood of infection is at 95.5%, which is close enough to 100% regarding our infection model. The virus rapidly enters the system and is heavily replicated throughout the course of two to six weeks, so let's take an average of four weeks, or 28 days. Plus the 10 days necessary to catch it in the first place gives us 38 days. We have to multiply that by seven (the last one in line is already infected) and then substract 28 days from the first one in line (because we don't care about him showing symptoms or even viral replication, all that matters is infection).

(38 days * 7) - 28 days = 238 days

Or quite precisely two thirds of a year.

After that, the pool is closed due to AIDS.

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[–] Workingsteel 0 points 6 points (+6|-0) ago 

Thanks Doc.