Brewer, Devon D. PhD*; Rothenberg, Richard B. MD, MPH†; Potterat, John J. BA‡; Muth, Stephen Q. BA§
To the Editor:
In 2004, we suggested that a major challenge to mathematical modelers was to “… construct a model that involves only penile–vaginal sex and that reproduces the epidemic curve seen in the 11 southern African nations that account for half of the disease on the African continent” (p. 786).1 French et al2 respond with a model that meets many of the specifications we detailed, and they also develop a model for HIV transmission through contaminated needles and syringes in healthcare settings. From their simulations, they conclude that an HIV epidemic based on sexual transmission was easy to start and sustain with estimates of transmission probabilities and partner change they deem “plausible.” In contrast, they argue that the transmission probabilities and number of injections with reused equipment required to generate an epidemic are “unfeasibly high.”
Although their modeling technique may be questioned, primarily for the limitations of compartment approaches, the most fundamental concern is their estimation of parameters. In their simulations, French and colleagues allow the per-contact heterosexual transmission probability to vary between 0.0025 to 0.015 (their Fig. 1). They cite an unpublished, privately communicated synthesis of transmission probabilities3 as the source for this range. However, the most rigorous estimate of the per-contact heterosexual transmission probability in sub-Saharan Africa is 0.0011 based on data from monogamous couples in Rakai, Uganda.4 This estimate is well below French and colleagues' lower bound and below the level at which any epidemic could be produced in their model even with very high partner change rates. Transmission probability estimates derived from studies of prostitutes or their clients in sub-Saharan Africa have many uncontrolled confounders yet include values nearly an order of magnitude less than French and colleagues' lower bound.5 Even the Rakai estimate of the sexual transmission probability may be exaggerated because sharing of syringes and razor blades (for making incisions to administer herbal medicines) within households is widespread in eastern and southern Africa.6–11 Such nonsexual blood exposures can act in concert with sexual exposures in married or cohabiting couples and have not been controlled for in published estimates of heterosexual transmission probabilities. Furthermore, estimated transmission probabilities based only on seroconversion in serodiscordant couples are biased upward, because 13% of couples in a Zambian cohort thought to have transmitted HIV within the partnership on similar grounds had genetically unrelated infections.12
French and colleagues also used estimates of sex partner change (1.5–4 new partners each year; their Fig. 1 and Table 1) much higher than observed in probability sample surveys of sub-Saharan Africans. The sources cited for their partner change estimates actually include no explicit basis for these estimates aside from “inspection” of unreferenced data13 and nonempiric values “to generate the scale of epidemic observed.”14 The number of sex partners in the prior year cannot be used to estimate annual sex partner change, because many partnerships, especially marriages, last longer than a year.
Publicly available data from the national probability sample household Demographic and Health Surveys (www.measuredhs.com) in 11 eastern and southern African countries indicate levels of partner change that are dramatically lower than the parameter estimates used by French and colleagues. A reasonable proxy measure of annual partner change is the number of nonmarital partners reported by men in the previous year (keeping in mind that sampled women consistently reported fewer partners than men). The mean for each survey is substantially below the lowest estimate examined by French and colleagues (Table 1). These surveys are current, but they concur with findings over the last 15 years.15,16
Some similar problems obtain for the model proposed by French and colleagues for medical injections. In this case, French and colleagues use transmission probabilities for medical injections that encompass the range of published estimates.17,18 The problem here, rather, is that the topic has been inadequately studied. The proportion of used needles in medical settings that have detectable HIV varies from 0% in needles that had been boiled at several Ethiopian clinics19 to 33% of needles previously used by HIV-infected Cameroonians for intravenous injections.20 Clearly, empiric experience is inadequate to understand where the true risk lies or to assess its heterogeneity or multiplicative effect on other modes of transmission. In addition, French and colleagues' allowing only one “spread” infection from a contaminated needle or syringe precludes the possibility of multiple infections arising from a single reused needle or syringe or from contaminated multidose medication vials and rinsing pans.17 Other types of blood exposures may also be involved with HIV transmission such as blood transfusion, dental procedures, circumcision, and induced abortion.
French and colleagues' model for heterosexual transmission is similar to prior modeling efforts for sub-Saharan Africa in which parameter estimates exceeded those in the empiric record.21–24 An important contribution of these efforts has been to demonstrate the level of sexual contact and sexual transmission that would actually be needed to “generate the scale of the epidemic observed.” The disjunction between those parameters and the ones observed is cause for reconsideration.
The real value of mathematical models is in raising questions about the phenomenon modeled and identifying gaps in empiric knowledge.25 Indeed, the modeling of HIV transmission in sub-Saharan Africa highlights important gaps in epidemiologic evidence. To determine modes of transmission with confidence, researchers should trace incident cases and uninfected controls' contacts about the full spectrum of time- and place-specific sexual and nonsexual exposures and sequence infected persons' HIV isolates.26 Such strategies are the most informative and are usually the first used for investigating emerging infections,27–30 including HIV in the United States in the early 1980s31,32 as well as other endemic infections such as tuberculosis.33–35 In parallel with more comprehensive empiric evaluations, modelers might consider a more comprehensive, multifactorial approach. Not only are multiple modes and their interactions important, but the much discussed presence of adjuvants such as sexually transmitted infections (especially herpes simplex virus type 2)36,37 or of variable transmission probabilities such as the those potentially associated with the high viral loads of acute HIV infection38,39 need to be considered. For example, Gray and colleagues40 constructed a model incorporating empirically based estimates of transmission probabilities and variable viral loads from their Rakai study4 to assess the impact of antiretroviral therapy and HIV vaccines on transmission.
Whatever questions may be raised, French and colleagues' simulations advance an important discussion and may serve as a stimulus to new investigations, both empiric and theoretical, that deal with an increasingly complex and recalcitrant problem.
1. Rothenberg RB, Potterat JJ, Brewer DD. The case against sexual transmission of HIV. Int J STD AIDS 2004; 14:784–786.
2. French K, Riley S, Garnett G. Simulations of the HIV epidemic in sub-Saharan Africa: Sexual transmission versus transmission through unsafe medical injections. Sex Transm Dis 2006; 33:127–134.
3. Baggaley R, Boily MC, White RG, et al. Systematic review of HIV-1 transmission probabilities in absence of antiretroviral therapy. London: Imperial College, 2004.
4. Gray RH, Wawer MJ, Brookmeyer R, et al. Probability of HIV-1 transmission per coital act in monogamous, heterosexual, HIV-1-discordant couples in Rakai, Uganda. Lancet 2001; 357:1149–1153.
5. Gilbert PB, McKeague IW, Eisen G, et al. Comparison of HIV-1 and HIV-2 infectivity from a prospective cohort study in Senegal. Stat Med 2003; 22:573–593.
6. Birungi H. Injections and self-help: risk and trust in Ugandan health care. Soc Sci Med 1998; 47:1455–1462.
7. Birungi H, Asiimwe D, Whyte SR. Injection Use and Practices in Uganda. Geneva: World Health Organization, 1994.
8. Jitta J, Reynolds Whyte S, et al. The availability of drugs: What does it mean in Ugandan primary care? Health Policy 2003; 65:167–179.
9. Plummer ML, Mshana G, Wamoyi J, et al. ‘The man who believed he had AIDS was cured': AIDS and sexually-transmitted infection treatment-seeking behaviour in rural Mwanza, Tanzania. AIDS Care 2006; 18:460–466.
10. Allen T. Upheaval, affliction, and health: A Uganda case study. In: Bernstein H, Crow B, Johnson H, eds. Rural Livelihoods: Crises and Responses. Oxford: Oxford University Press, 1992:217–248.
11. Marburg haemorrhagic fever, Angola. Wkly Epidemiol Rec 2005; 80:158–159.
12. Trask SA, Derdeyn CA, Fideli U, et al. Molecular epidemiology of human immunodeficiency virus type 1 transmission in a heterosexual cohort of discordant couples in Zambia. J Virol 2002; 76:397–405.
13. Garnett GP, Anderson RM. Factors controlling the spread of HIV in heterosexual communities in developing countries: Patterns of mixing between different age and sexual activity classes. Philos Trans R Soc Lond B Biol Sci 1993; 342:137–159.
14. Garnett GP, Gregson S. Monitoring the course of the HIV-1 epidemic: The influence of patterns of fertility on HIV-1 prevalence estimates. Math Pop Stud 2000; 8:251–277.
15. Carael M, Cleland J, Deheneffe JC, et al. Sexual behavior in developing countries: Implications for HIV control. AIDS 1995; 9:1171–1175.
16. Ferry B, Carael M, Buve A, et al. Comparison of key parameters of sexual behaviour in four African urban populations with different levels of HIV infection. AIDS 2001; 15(suppl 4):S41–50.
17. Gisselquist D, Upham G, Potterat JJ. Transmission efficiency of HIV through injections and other medical procedures: Evidence, estimates, and unfinished business. Infect Control Hosp Epidemiol 2006; 27:944–952.
18. Baggaley RF, Boily MC, White RG, et al. Risk of HIV-1 transmission for parenteral exposure and blood transfusion: A systematic review and meta-analysis. AIDS 2006; 20:805–812.
19. Priddy F, Tesfaye F, Mengistu Y, et al. Potential for medical transmission of HIV in Ethiopia. AIDS 2005; 19:348–350.
20. Apetrei C, Becker J, Metzger M, et al. Potential for HIV transmission through unsafe injections. AIDS 2006; 20:1074–1076.
21. Rothenberg R, Gisselquist D, Potterat J. A simulation to assess the conditions required for high level heterosexual transmission of HIV in Africa. Int J STD AIDS 2004; 15:529–532.
22. Bongaarts J. A model of the spread of HIV infection and the demographic impact of AIDS. Stat Med 1989; 8:103–120.
23. Anderson RM, May RM, Boily MC, et al. The spread of HIV-1 in Africa: Sexual contact patterns and the predicted demographic impact of AIDS. Nature 1991; 352:581–589.
24. Auvert B, Buonamico G, Lagarde E, et al. Sexual behavior, heterosexual transmission, and the spread of HIV in sub-Saharan Africa: A simulation study. Comput Biomed Res 2000; 33:84–96.
25. Rothenberg R. Model trains of thought. Sex Transm Dis 1997; 24:201–203.
26. Brewer DD, Hagan H, Sullivan DG, et al. Social structural and behavioral underpinnings of hyperendemic hepatitis C virus transmission in drug injectors. J Infect Dis 2006; 194:764–772.
27. Fisher-Hoch SP, Tomori O, Nasidi A, et al. Review of cases of nosocomial Lassa fever in Nigeria: The high price of poor medical practice. BMJ 1995; 311:857–859.
28. Francesconi P, Yoti Z, Declich S, et al. Ebola hemorrhagic fever transmission and risk factors of contacts, Uganda. Emerg Infect Dis 2003; 9:1430–1437.
29. Chow KY, Lee CE, Ling ML, et al. Outbreak of severe acute respiratory syndrome in a tertiary hospital in Singapore, linked to an index patient with atypical presentation: Epidemiological study. BMJ 2004; 328:195.
30. Ebola haemorrhagic fever in Zaire, 1976. Bull World Health Organ 1978; 56:271–293.
31. Auerbach DM, Darrow WW, Jaffe HW, et al. Cluster of cases of acquired immune deficiency syndrome. Am J Med 1984; 76:487–492.
32. Klovdahl AS. Social networks and the spread of infectious diseases: The AIDS example. Soc Sci Med 1985; 21:1203–1216.
33. Klovdahl AS, Graviss EA, Yaganehdoost A, et al. Networks and tuberculosis: An undetected community outbreak involving public places. Soc Sci Med 2001; 52:681–694.
34. McElroy PD, Rothenberg RB, Varghese R, et al. A network-informed approach to investigating a tuberculosis outbreak: Implications for enhancing contact investigations. Int J Tuberc Lung Dis 2003; 7:S486–493.
35. Fitzpatrick LK, Hardacker JA, Heirendt W, et al. A preventable outbreak of tuberculosis investigated through an intricate social network. Clin Infect Dis 2001; 33:1801–1806.
36. Cohen MS. Sexually transmitted diseases enhance HIV transmission: No longer a hypothesis. Lancet 1998; 351(suppl 3):5–7.
37. Wald A, Link K. Risk of human immunodeficiency virus infection in herpes simplex virus type 2-seropositive persons: A meta-analysis. J Infect Dis 2002; 185:45–52.
38. Pilcher CD, Fiscus SA, Nguyen TQ, et al. Detection of acute infections during HIV testing in North Carolina. N Engl J Med 2005; 352:1873–1883.
39. Pilcher CD, Tien HC, Eron JJ Jr, et al. Brief but efficient: Acute HIV infection and the sexual transmission of HIV. J Infect Dis 2004; 189:1785–1792.
40. Gray RH, Li X, Wawer MJ, et al. Stochastic simulation of the impact of antiretroviral therapy and HIV vaccines on HIV transmission; Rakai, Uganda. AIDS 2003; 17:1941–1951.