The HIV Paradox: A Tale of Two Males

[CallMeIshmael]

Meet two guys: Jordan and Jason.

Jordan: Jordan is a successful good looking guy, and has managed to find himself a great wife: Sarah. They've talked about their past sexual history. Sarah is not a virgin, but she isnt a whore either. But, she has never been tested. Jordan would consider her less likely to have HIV than a member of the US adult population picked at random (that number is 0.6% ( source)). He is willing to cut that number in half, to 0.3%. Sarah is on the pill, and when she and Jordan have sex, he doesnt wear a condom. He estimates they will have sex 15 times per month over the course of the next year. (180 times in total) He will never have sex with another female, nor is he an IV drug user.

Jason: Jason doesnt have a girlfriend. His sexual encounters over the next year will all be one night stands. He estimates he will have sex 20 times. These women are not overly 'clean', as Jason isnt of discriminating taste. He estimates that each women is twice as likely to have HIV than an average adult (1.2%). On top of that, he tends to visit a prostitute every two months, for a total of 6 for the year. It is estimated that 4% of prositutes in the LA area have HIV (source) Jason doesnt like the way condoms feel, and never wears them. He is also not an IV drug user.


We can calculate the probability of both Jordan and Jason contracting HIV over the course of the next year.

The probability of someone contracting HIV through unprotected sex with an HIV-postitve partner is 0.002 (This is the upper bound, taken from source)

Jordan: He is in an 'Either/Or' situation. If Sarah doesnt have HIV, then he will never contract HIV over that year. IF she is, however, the probability of him contracting HIV =

1 - (499/500)^180 = 0.3026

Since, Jordan estimates the probability of Sarah having HIV is 0.3%, his final chance of contracting is:

= 0.0907%


Jason: His equation looks like:

1 - P(Getting HIV)

= 1 -

(1 - (1.2/100*1/500))^20*(1-(4/100)*(1/500))^6

= 0.0959%


These two are about equally likely to contract HIV over the next year.


EDIT: Since this seems SO counterintuitive, there is a decent chance I messed up the math somewhere. Can anyone verify that I did the math right? It seems right.