your math assumes that all encounters are with someone who is hiv positive.
On Apr 8, 2005 7:41 AM, Horace Heffner <[EMAIL PROTECTED]> wrote: > I take it then that no one here actually knows the failure rate of condoms > with regard to protection from aids. Yet there are such fervent beliefs > expressed regarding promoting condom use as "safe sex". I can not see why > this posture is not utterly reckless. > > If you can not understand my point regarding the nominal effect of > reduction in the probability of infection per encounter upon the *final > outcome* predicted by the exponential growth curve for infections, then > maybe you can understand my point from an individual perspective. > > Surviving a string of sexual encounters without infection makes that string > a set of dependent events. If q_i is the probability of surviving event i, > then the probability of surviving n events is > > [product over all i] q_i > > If the probability of infection from a single encounter is p, then the > probability of survival is q=(1-p), and the probability P(n) of surviving n > events is: > > P(n) = (1-p)^n > > Since p is a number between 0 and 1, so is q = 1-p. Here is the important > fact: > > [lim n -> inf] q^n = 0, when 0<q<1 > > This is the essence of Murphy's law (though not the many humerous but bogus > correlaries.) As n goes to infinity, q^n approches zero surprisingly > rapidly, even if p is small and q is close to 1. From this, given p, we > can figure out how many encounters before the probability of survival is > less than any given probability. Suppose we want to know how many > encounters are required before the probability of infection is 90 percent. > We then have: > > P(n) = 0.1 = (1-p)^n > > ln(0.1) = n * ln(1-p) > > n = ln(0.1)/ln(1-p) > > So, for example, suppose the probabilty p of infection from an encounter is > 0.05. We then have > > n = ln(.1)/ln(0.95) = 45 > > At an encounter rate of 2 per week this means 90 percent probability of > infection after 23 weeks. If p = 0.01, then this increases to 115 weeks, > and so on. If the probability of infection in an encounter is 1/1000, then > the amount of time before a 50/50 chance of infection, > (ln(.5)/ln(0.999))/104, is less than 7 years. > > Reducing the probability of infection merely changes the amount of time > before infection, not the outcome. From an aggreagate point of view, it > merely changes the amount of time before some percentage of the vulnerable > population is infected. > > Making statements that might move people from a protected group (chaste or > monogamous) into an exposed group, when the probability p is not known, or > if the resultant p is larger than 1/1000, is reckless and deadly. Implying > the use of condoms makes for "safe sex" is such a statement. > > Form an aggregate point of view, condom use will have no effect on the > final outcome unless a cure or vaccine is developed. It does slow the rate > of progression though. It is important that the manner in which condom use > is advocated does not tend to move people from a protected group into the > exposed population. Barring a miracle of modern medicine, the exposed > group are mostly goners. > > Regards, > > Horace Heffner > > -- "Monsieur l'abb�, I detest what you write, but I would give my life to make it possible for you to continue to write" Voltaire
