Emory University School of Medicine, Atlanta, Georgia
Correspondence: Richard B. Rothenberg, MD, Department of Family and Preventive Medicine, Emory University School of Medicine, 69 Butler St., SE, Atlanta, GA 30333. E-mail: firstname.lastname@example.org
Received for publication April 24, 2002 and accepted May 10, 2002.
THE ESTEEMED BRITISH VENEREOLOGIST, R. R. Willcox, wrote a series of articles in the 1960s 1–5 in which he explained the role of “feed back” in gonorrhea control. Simply put, he defined gonorrhea control “in terms of the number of men infected per promiscuous female (male:female source ratio) and the percentage of infected men who restore infections to the female promiscuous pool (‘feed back’)”5 (p. 65). He provided extensive arithmetic calculations to demonstrate the relationship of these factors and the relatively small changes needed to affect the balance of gonorrhea endemicity. His ideas are the intellectual primordia of many of the phenomena (compartments, core groups, networks, concurrency) that are now of interest in the exploration of sexually transmitted disease (STD) transmission dynamics.
Professor Willcox's treatise, and his tables of calculations, were not taken very seriously at the time. In fact, his work had been largely forgotten when, 15 to 20 years later, his concepts of gonorrhea homeostasis—similar to concepts from population ecology 6,7 —were applied to the epidemiology of STDs and HIV. But antecedents are important because they reinforce an underlying tenet: simple ideas recur (as does the observation that they recur 8,9).
The simple idea here is that a person who interleaves his or her sexual contacts is at greater risk for either transmitting or contracting a sexual infection. In network terms, such a relationship is denoted by three nodes connected by two lines: o—o—o. Such a structure is called, perhaps perversely, a “2-plex, n = 3,” or a nontransitive triad. Alhough the jargon is opaque, it serves a purpose: the symbology was developed to describe configurations that do not lend themselves easily to geometric nomenclature, and there has to be a short way of saying “one person is connected to two other people but those two other people are not connected to each other.” Whatever the name, o—o—o is the next step beyond a simple dyad. As investigators 10–14 have begun to explore this simple structure using tools not available to Professor Willcox, a second underlying tenet has emerged: when you think hard about them, simple ideas become complex. After Watts and May examined the role of concurrency in a simple random mixing model, 14 Kretzschmar and Morris 10 used a graphed theoretical interpretation to demonstrate how concurrency in a network could be represented simply as a function of the mean and variance of the distribution of numbers of partners in a network. They showed, with simulation models, that the intensity, variability and final size of an epidemic increase dramatically as concurrency increases. 13 Lagarde and colleagues 11 introduced another measure (an individual indicator of concurrency, or iic) that reflects the probability that an individual will keep or dissolve a relationship before beginning a new one. It is almost assured that this line of investigation will be vigorously pursued, with the introduction of new measures; with the use of such measures in mathematical simulations; and with the expansion of concurrency to the examination of more complex structures, or “cycles,” that may play a role in the dynamics of transmission.
The real complexity of concurrency may not lie in the mathematics, however. Concurrency is often casually defined as having sex with more than one person at the same time. Nominally, that definition would refer to group sex, but clearly “same time” is not meant to specify simultaneity. Rather, investigators characterize concurrency as overlapping durations of sexual activity, so that an organism can be conveyed from one partner to another, and possibly even back again. 15 Another surrogate is simply to determine that a person had more than one sexual partners in a given time interval (the traditional contact tracing approach). A further removed stand-in for concurrency—one often used by the mathematical models—is to consider a network degree of two or greater to be representative of concurrency in an instantaneous sexual network.
The mathematical complexity may thus be ignoring the more daunting complexity found in the variety of social and sexual arrangements that can influence transmission. In the current issue of Sexually Transmitted Diseases, two articles begin to explore how such arrangements may have an effect on the importance of concurrency in transmission. Gorbach and colleagues 16 conducted semistructured interviews in 108 persons with STD infections and with 120 from high prevalence and randomly selected neighborhoods. They established an initial typology by whether a primary partner was present. Those with a primary partner experienced concurrency as separational (seeking other partners when the primary one is not available);transitional (other partners at the start or end of a new relationship;reactive (other partners are sought in response to similar behavior by the primary partner);reciprocal (both agree that their partner will have other contacts); or compensatory (other partners are sought because of perceived deficiencies in the primary partner). In addition, those with or without a primary partner may be “coparents” and continue a sexual relationship when the social one has changed, or may practice “survival sex.” Finally, they define as experimental the type of concurrency that occurs with “dating” in the absence of a primary partner. It is apparent just from the list (and explicated in detail in the article) that each of these categories poses somewhat different potential for transmission: compare, for example, separational and experimental concurrency.
In the companion paper, Voeten et al 17 provide a broad ethnographic description of the types of relationships established between female commercial sex workers and their clients. They gathered this information by focusing on venues (places of social aggregation) and by interviewing the clients directly, rather than the sex workers. The picture that emerged was one of substantial diversity with patterns of long-term and short-term concurrent sexual relationships that are treated differently from each other in terms of frequency of sex contact and use of barrier prophylaxis. The authors point out that these clients are not simply “bridges” to wives and noncommercial girlfriends, but constitute a group that can support the active propagation of disease. It is not a leap to recognize that the specifics of concurrency can affect the dynamics of transmission, and that models of both concurrency and intervention might take heed.
In their discussion, Gorbach et al 16 point to the need for such studies in other sociogeographic settings and allude to the varieties of concurrency that may be available but not yet identified. The two articles illustrate the admonition. Both are careful not to generalize from their own observations, but rather to stress the need for better explication of the specifics of relationships in understanding transmission. Both have a richness of observation that exemplify their underlying messages. Please read the articles.
1. Willcox RR. The essence of gonorrhoea control. I. The importance of “feed back.” Acta Derm Venereol 1965; 45: 302–8.
2. Willcox RR. The essence of gonorrhoea control II. The delineation of “feed back.” Acta Derm Venereol 1966; 46: 95–100.
3. Willcox RR. The essence of gonorrhoea control III. The delineation of the male: female source ratio. Acta Derm Venereol 1966; 46: 250–256.
4. Willcox RR. The essence of gonorrhoea control IV. The promiscuous female pool. Acta Derm Venereol 1966; 46: 460–465.
5. Willcox RR. The essence of gonorrhoea control. V. The influence of promiscuity. Acta Derm Venereol 1967; 47: 65–69.
6. Yorke JA, Hethcote WHJ, Nold A. Dynamics and control of the transmission of gonorrhea. Sex Transm Dis 1978; 5: 51–56.
7. Anderson RM. The Population Dynamics of Infectious Diseases: Theory and Application. London: Chapman and Hall, 1982.
8. Garnett GP, Johnson AM. Coining a new term in epidemiology: concurrency and HIV. AIDS 1997; 11: 681–683.
9. Morris M. Concurrent partnerships and syphilis persistence. New thoughts on an old puzzle. Sex Transm Dis 2001; 29: 504–507.
10. Kretzschmar M, Morris M. Measures of concurrency in networks and the spread of infectious disease. Math Biosci 1996; 133: 165–195.
11. Lagarde L, Auvert B, Carael M, et al. Concurrent sexual partnerships and HIV prevalence in five urban communities of sub-Saharan Africa. AIDS 2001; 15: 884.
12. Morris M, Kretzschmar M. Concurrent partnerships and transmission dynamics in networks. Soc Networks 1995; 17: 299–318.
13. Morris M, Kretzschmar M. Concurrent partnerships and the spread of HIV. AIDS 1997; 11: 641–648.
14. Watts CH, May RM. The influence of concurrent partnerships on the dynamics of HIV/AIDS. Math Biosci 1992; 108: 89–104.
15. Potterat J, Zimmerman HP, Muth SQ, et al. Chlamydial transmission: concurrency, reproduction number and the epidemic trajectory. Am J Epidemiol 1999; 115: 1331–1339.
16. Gorbach PM, Stoner BP, Aral SO, Whittington WLH, Holmes KK. “It takes a village”: understanding concurrent sexual partnerships in Seattle, WA. Sex Transm Dis 2002; 29: 453–462.
17. Voeten HACM, Egesah OB, Ondiege MY, Varkevisser CM, Habbema JDF. Clients of female sex workers in Nyanza province, Kenya: a core-group in STD/HIV transmission. Sex Transm Dis 2002; 29: 444–452.