The Math
The following equation calculates the probability P of a man transmitting a virus with a transmission frequency of f to N
number of women as a result of having n number of vaginal sex contacts per each transmission:
P = [1 - (1 - f) n ] N
f = 1/1,000 = 0.001 (Odds of a healthy woman becoming HIV positive following a single act of unprotected vaginal
intercourse with an HIV-positive man.)
N = 10 (Number of Williams' female sex partners who have tested positive so far.)
n = 500/10 = 50 (Let's assume that Williams had 500 sex contacts during his sex spree, which lasted a maximum of
two years, the time between incarceration for murder, which ended when he was 19, and his current incarceration at
the age of 21 for peddling crack. That comes out to five contacts a week for two years, or ten contacts a week for one
year. So far, ten women that he had sex with during this time have tested HIV-positive. That comes out to 50 contacts
per positive partner.)
P = [ 1 - (1 - 0.001) 50 ] 10 = [1 - (0.999) 50 ] 10 = [1 - 0.951] 10 = [0.0488] 10
= 7.65 x 10-14 = 0.0000000000000765 (7.65 per 100 trillion)
This analysis applies to an HIV-positive man who engages in 500 acts of unprotected vaginal intercourse distributed
among a large number of women, with all parties declaring themselves free of AIDS symptoms, anal intercourse,
traditional venereal diseases, and injected drugs.
HIV-pos Rates Among Various Populations
Nushawn Williams' female sex partners [1]: 10% (10/100 = 0.10)
Injection drug free American females [2]: 0.01% (1/10,000 = 0.0001)
Female drug injectors in New York City [3]: 38.6%
Gay men in San Francisco [4]: 54%
(1) Ten positive tests from approximately 100 partners; various media sources.
(2) 1993 data for first time female blood donors; CDC, National HIV Serosurveillance Summary Update for Vol. 3,
Results Through 1993, p. 7, Figure 17.
(3) Females reporting to drug treatment facilities; CDC, National HIV Serosurveillance Summary 3, Results Through
1992, p. 20, Table 3.
(4) Random selection of gay men; Ascher MS, Nature 362:103-104, March 11, 1993.