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The Algebra of Condoms and Abstinence

Rothenberg, Richard MD*; Potterat, John J. BA; Koplan, Jeffrey P. MD*

Sexually Transmitted Diseases: April 2005 - Volume 32 - Issue 4 - p 252-254
doi: 10.1097/01.olq.0000158495.66446.44

From the *Emory University School of Medicine, Atlanta, GA; and †Independent Consultant, Colorado Springs, CO.

Correspondence: Richard Rothenberg, MD, Department of Medicine, Division of Infectious Disease, Emory University School of Medicine, 49 Jesse Hill Jr. Drive, Atlanta, GA 30303.

THE OBSERVED EFFECTIVENESS OF an intervention aimed at sexually transmitted diseases (STDs) may result, in part, from the mathematics related to the probability of infection. Using the Bernouilli approach,1–5 the shape of the effectiveness curve is determined in part by transmission parameters and in part by the exponential function itself.

Consider an individual who is infected and has n sexual encounters with an uninfected new partner. We wish to assess the effectiveness of that person's condom use. (For convenience, we conflated nonuse and condom failure into a single measure. Such a simplification is likely to have an effect only for high transmission probabilities, and even in such cases, the effect would be small.) With the standard Bernouilli approach, the probability of transmission to an uninfected partner (pi) is a function of the probability of transmission (pt), condom use effectiveness (pc), the number of sexual acts (here, n), and the probability that the individual is infected (pk, which we take to be 1.0).

In this example, we set n = 10, allow condom use effectiveness (pc) to vary from 0.0 to 1.0, and examine transmission probabilities (pt) for 3 different STDs: 0.01, which approximates the highest published estimate for penile-vaginal transmission of HIV3,4,6–10; 0.20, which is the approximate published transmission probability for chlamydia11,12; and 0.50, which is the approximate (high) published transmission for gonorrhea.12,13 Clearly, the Bernouilli equation is highly sensitive to the transmission probability overall (Fig. 1), but, more important, at low transmission probabilities even desultory condom use has a substantial protective effect. Using condoms effectively only half the time, the probability of transmitting HIV to a partner during 10 sexual encounters would be 0.05. At higher transmission probabilities, the curve is unforgiving, and a high level of condom use is required to prevent transmission: 50% condom use would result in a probability for transmitting chlamydia of 65% and a probability of 94% for transmitting gonorrhea. This may account, in part for the seemingly greater effectiveness of condoms for preventing HIV14 and the comparative lack of supporting evidence for effectiveness with bacterial STDs (study design notwithstanding). Human papilloma virus, which would appear to be highly infectious, in part because of transmission via perigenital skin (that is, areas not covered by a condom)15 would clearly fall on the upper curve or on one even higher.

Fig. 1

Fig. 1

The probability of transmission to an uninfected partner is also sensitive to the frequency of sexual contact (as expected), but this sensitivity differs for different transmission probabilities. As transmission probability varies from 0.001 (the usual estimate for penile-vaginal transmission of HIV) through 0.50 (high-end estimate for gonorrhea), it is clear that at very low transmission probabilities, frequent contact is required for transmission. As transmission probability rises, large numbers of sexual contacts virtually assure transmission at any level of condom use (assuming that 100% condom use effectiveness is a statistical, not a realistic, construct). It is perhaps accidental, but at least confirmatory, that studies of serodiscordant monogamous heterosexual couples in both Western nations and African countries estimate a yearly probability of infection of 8% to 12% in the negative partner.16 Most of these studies, particularly in Africa, assume the relative absence of condom use. In Figure 2, with condom effectiveness of 10%, the probability of transmission to an uninfected partner after 100 sexual episodes is 8.6%.

Fig. 2

Fig. 2

This “model” reduces a complex social configuration to a single, monogamous, infection-discordant couple. In fact, each of the parameters invoked (transmission probability, frequency of intercourse, probability of infection in one of the partners, and the use effectiveness of condoms) has a large distribution that is not always well defined. In particular, the probability of transmission may vary, and such variation will have significant impact on the propagation of disease.17 We do not wish to foster inappropriate simplicity in assessing transmission dynamics. The point here, however, is that the use-effectiveness of condoms—given that it could be established with some certainty—is in some measure determined by the mathematics of transmission.

This phenomenon may explain, in part, the differential impact of condoms on the transmission of STDs and may contribute to the observation that different organisms reach different endemic levels in the same population. The observation is obviously in keeping with the simple intuitive notion that if a disease is difficult to acquire, even relatively inefficient preventive measures will have a substantial impact.18 If a disease is readily transmitted, assiduous use of the preventive measure is required.

For the bacterial and many of the viral STDs, any programs that diminish condom use will increase transmission since such efforts will quickly put nonusers on the portion of the curve that indicates a high probability of transmission. This same reasoning applies to abstinence as a preventive measure. In an abstinence-only program to prevent bacterial and many of the viral STDs, deviation from complete abstinence will have a deleterious effect, but the impact would be greatest for the bacterial STDs and smallest for HIV.

Abstinence-only programs, which by definition abjure condom use, would assure increased transmission unless the diminution in condom use is offset by abstinence adherence. The data currently available on abstinence-only programs provide little reassurance.19–22 The data, though sparse, suggest that the effects of abstinence-only education are transient, and those who have received it are less likely to use condoms, should they have sexual intercourse, than those receiving more comprehensive advice. It would appear that abstinence-only programs are unlikely to compensate for the nonuse of condoms and would place persons on the riskier segment of the transmission curve.

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