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.
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%.
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.
1. Allard R. A mathematical model to describe the risk of infection from sharing injection equipment. J Acquir Immun Defic Syndr 1990; 3:1010–1016.
2. Allard R. A family of mathematical models to describe the risk of infection by a sexually transmitted agent. Epidemiology 1990; 1:30–33.
3. Bell DC, Trevino RA. Modeling HIV risk. J Acquir Immun Defic Syndr 1999; 22:280–287.
4. Downs AM, De Vincenzi I, Isabell De Vincenzi, for the European Study Group in Heterosexual Transmission of HIV. Probability of heterosexual transmission of HIV: relationship to the number of unprotected sexual contacts. J Acquir Immun Defic Syndr 1996; 11:388–395.
5. Rothenberg RB. How a net works. Sex Transm Dis 2001; 28:63–68.
6. Mastro TD, Satten GA, Nopkesorn T, et al. Probability of female-to-male transmission of HIV-1 in Thailand. Lancet 1994; 343:204–207.
7. Royce RA, Sena A, Cates W, et al. Sexual transmission of HIV. N Engl J Med 1997; 336:1072–1078.
8. Chakraborty H, Sen PK, Helms RW, et al. Viral burden in genital secretions determines male-to-female sexual transmission of HIV-1: a probabilistic empiric model. AIDS 2001; 15:621–627.
9. Leynaert B, Downs AM, de Vencenzi I. Heterosexual transmission of human immunodeficiency virus: variability of infectivity throughout the course of infection: European Study Group on Heterosexual Transmission of HIV. Am J Epidemiol 1998; 148:88–96.
10. Satten GA, Mastro TD, Longini IM Jr. Modelling the female-to-male per-act HIV transmission probability in an emerging epidemic in Asia. Stat Med 1994; 13:2097–2106.
11. Quinn TC, Gaydos C, Shepherd M, et al. Epidemiologic and microbiologic correlates of Chlamydia trachomatis
infection in sexual partnerships. JAMA 1996; 276:1737–1742.
12. Brunham RC, Plummer FA. A general model of sexually transmitted disease epidemiology and its implications for control. Med Clin North Am 1990; 90:1339–1352.
13. Brunham RC, Nagelkerke NJ, Plummer FA, et al. Estimating the basic reproductive rates of Neisseria gonorrhoea
e and Chlamydia trachomatis
: the implications of acquired immunity. Sex Transm Dis 1994; 21:353–356.
14. National Institute of Allergy and Infectious Diseases, National Institutes of Health. Scientific evidence on condom effectiveness for sexually transmitted disease (STD) prevention. 2001. Available at: www.niaid.nih.gov/dmid/stds/condomreport.pdf
15. Winer RL, Lee SK, Hughes JP, et al. Genital human papillomavirus infection: incidence and risk factors in a cohort of female university students. Am J Epidemiol 2003; 157:218–226.
16. Gisselquist D, Rothenberg R, Potterat J, et al. HIV infections in sub-Saharan Africa not explained by sexual or vertical transmission. Int J STD AIDS 2002; 13:657–666.
17. Rottingen JA, Garnett GP. The epidemiological and control implications of HIV transmission probabilities within partnerships. Sex Transm Dis 2002; 29:818–827.
18. Potterat JJ. “Socio-geographic space” and focal condom use. In: Cates W, Campbell AA, eds. Behavioral Research on the Role of Condoms in Reproductive Health
. Washington, DC: NICHD, NIH; 1993:27–29.
19. Witkin A, Rotheram-Borus MJ, Milburn N. Comprehensive versus abstinence-only sex education: what works? Focus Guide AIDS Res 2003; 18:1–5.
20. Silva M. The effectiveness of school-based sex education programs in the promotion of abstinent behavior: a meta-analysis. Health Educ Res 2002; 17:471–481.
21. DiCenso A, Guyatt G, Willan A, et al. Interventions to reduce unintended pregnancies among adolescents: systematic review of randomised controlled trials. BMJ 2002; 324:1426–1430.
22. Thomas MH. Abstinence-based programs for prevention of adolescent pregnancies: a review. J Adolesc Health 2000; 26:5–17.