The mixing function in the 2-sex model must also satisfy the requirement that the number of females in sexual activity class j that are partners of males in class i must be identically equal to the number of males in class i who are partners of females in sexual activity class j. What Anderson and colleagues have termed the class-specific “sum rule” is expressed by Eq. (3):
where apostrophes are used to denote the opposite sex, c(s,i) is the rate of partner change for a person sex s in sexual activity class i, and N(s,i) is the size of the sex- and class-specific group.
To maintain consistency in the heterosexual simulation model [i.e., to ensure that Eq. (3) is satisfied], the rates of partner change and the sexual mixing matrix are initially specified only for females. Sexual mixing probabilities for males are then calculated based on the distribution of females by sexual activity class and the matrix of mixing probabilities for females, subject to constraints (1) through (3).
Adding partner selection probabilities from the mixing matrix to the age preferences in the Palloni and Lamas model yields the age- and sexual activity class-specific probability of an individual entering a sexual relationship with an HIV-infected partner given by:
If s refers to females then IP(s,x,i,j) is the probability that a female age x in class i has a sexual relationship with an infected male partner in group j; H(s′,x,j) is the weighted proportion of males in class j and within the age preferences for a female in class i that are HIV-infected; c(s,i) is the rate of new partner acquisition for an individual in class i; and p(s,i,j) is the probability that a female in class i selects a male partner from class j. From Eq. (4), it is clear that the probability that an individual has sexual contact with an infected partner is wholly determined by the HIV prevalence among potential partners, the individual’s sexual behavior as defined by the number of new partners per year, and the sexual mixing matrix that describes the likelihood that an individual selects a partner from each of the sexual activity classes.
The probability that an individual will acquire HIV within a unit of time is closely related to the probability of entering a relationship with an infected partner, but is further determined by that individual’s frequency of coitus and the per coitus infectivity of HIV. Because HIV is most infectious in the period immediately following HIV seroconversion and in the time following the onset of symptoms of AIDS,18–21 the model imposes the assumption that HIV is trebly infectious in the year following seroconversion and after transitioning to symptomatic AIDS. T(s,x,i,j) is the probability that HIV is transmitted to a person sex s and age x in sexual activity class i through sex with a opposite-sex partner in class j and is given by:
where A(i) is the average number of coituses for an individual in class i with each sexual partner; βs is the per coitus transmission probability of an individual of sex s contracting HIV from an opposite sex partner; and H(s′,x,j), c(s,i) and p (s,i,j) are as defined in Eq. (4).
Rate of Partner Change.
To define the 2 rate of partner change scenarios to be simulated, data have been accessed from 2 sources. The first represents a high rate of sexual partner change and comes from a sexual behavior survey conducted among MSM in England and Wales during the period from February 1986 through January 1987 and were employed by Anderson et al. to describe the impact of sexual mixing patterns on the spread of HIV in their 1-sex simulation model.13 These data are selected for the present analyses so that the results may be easily compared with those presented by Anderson and colleagues in what was among the first and most important studies to illustrate the effect of sexual mixing patterns on the spread of HIV within a population.
The second rate of partner change scenario comes from the Chinese Health and Family Life Survey (CHFLS) (PIs: William Parish and Edward Laumann, University of Chicago), a sexual behavior survey of 3821 adults between the ages of 20 and 64 sampled from China’s general population in 1999 and 2000. Because the CHFLS included only a question on the number of partners in the past 12 months and did not specifically ask about the number of new partners in the past 12 months (a data point that is required in order to directly measure the rate of partner change), the rate of partner change is instead estimated based upon information collected on sexual partners in the lifetime.14,22 The total reported lifetime partners are divided by the years from reported sexual debut up to the survey date for each subject. The individual-level estimates are then averaged using survey weights to obtain an estimate of the average annual rate of partner change for the population.
Table 2 provides the population mean and annual rates of partner change for 6 sexual activity classes identified in the MSM data cited in Anderson et al.13 and from the CHFLS. These population distributions by sexual activity class and the sexual activity class-specific mean rates of partner change are utilized as inputs to the macrosimulation model. The overall mean rate of partner change in the MSM data to represent a high rate of partner change is 8.81 new partners per year and is substantially greater than the average 0.29 new partners per year obtained based on the CHFLS.
The proportions of the population that fall into each sexual activity class according to the MSM data are taken directly from the data table provided by Anderson et al.13) According to this source, 57% of MSM fall into sexual activity class 1 and have an average annual rate of partner change of 0.45 new partners per year. Fourteen percent of MSM are in class 2 with an average rate of partner change of 3.20 new partners per year. Classes 3 and 4 contain 10% and 8% of the MSM population studied with average rates of partner change of 7.02 and 13.84 new partners per year respectively. The 2 sexual activity classes with the highest rates of partner change according to the MSM data, classes 5 and 6, contain 7% and 4% of the population respectively. The average rate of partner change for those in class 5 is 43.60 new partners per year and for class 6 is 81.23 new partners per year.
To define the sexual activity classes based on the CHFLS data, the distribution of the simulated population by sexual activity class is constrained to be nearly identical to the distribution specified by Anderson et al.13 for the MSM data. This step ensures that any changes in the simulated spread of HIV associated with a shift in the rate of partner change scenario are wholly attributable to the rate of partner change and not to a shift in the population distribution by sexual activity class.
Under the low rate of partner change scenario defined using the CHFLS, class 1 has an average rate of partner change of 0.07 new partners per year, class 2 has 0.16, class 3 has 0.26, and class 4 has 0.41 new partners per year on average. The 2 sexual activity classes with the highest rates of partner change under the CHFLS scenario, classes 5 and 6, have, respectively, 0.96 and 2.51 new partners per year on average.
Sexual Mixing Patterns.
Empirical measurements of sexual mixing patterns are not widely available, but the need for data on this key determinant of the sexual spread of HIV is increasingly recognized and several surveys that aim to measure sexual mixing patterns have been recently fielded or are in the planning stages. In the absence of empirical data, the sexual mixing patterns utilized in the macrosimulation model represent a continuum of assortativeness ranging from nearly perfectly assortative, with 90% of partnerships formed within each sexual activity class, to highly disassortative with only 30% of partnerships formed within each sexual activity class. Also considered is the random mixing scenario in which partnerships are formed in proportion to the contribution of each sexual activity class to the overall number of partnerships.
A “restricted assortative” mixing concept is adopted to define the features of the sexual mixing matrix. In these scenarios the probability of selecting a partner within one’s own sexual activity class is constant across classes (p(s,i,j) = γ for all i = j). The remaining 1-γ proportion of each class’ partnerships is distributed across the remaining sexual activity classes with those classes that are closer to the reference class in terms of rate of partner change preferred to those classes that are more distant.14
To test the sensitivity of the effects of sexual partner change rates and mixing patterns on HIV spread to changes in the biologic parameters that impact HIV transmission, simulations are obtained while varying the heterosexual transmission probabilities. The macrosimulation model takes as inputs the per coitus infection probabilities. At the baseline these are set to 0.0009 per contact for female-to-male transmission and 0.0015 per contact for male-to-female transmission, which are consistent with estimates obtained from longitudinal studies of HIV serodiscordant couples.23 Annual coituses per partner are held constant across sexual activity classes according to the coital frequencies reported in the CHFLS, indicating an average of 76 coituses per partner per year. Holding coituses per partner constant across classes is equivalent to modeling per partnership HIV transmission probabilities, corresponding to 0.0061 for female-to-male transmission and 0.1078 for male-to-female transmission. These fall into the low end of the range of per partnership transmission probabilities estimated in longitudinal cohort studies.24
The presence of STD as comorbidities enhance the per coitus transmission probabilities by reducing immune function, increasing viral shedding in the HIV-infected partner, and providing an efficient path for the virus to enter the body in the susceptible partner.25 Simulations are run for a population in which 4% of adults are assumed to be currently infected with an STD, corresponding to the proportion of adults testing positive for gonorrhea, chlamydia, or trichomoniasis based on the urinalysis that accompanied the CHFLS. Those STD are modeled with an average per coitus infectivity enhancement factor of 4, consistent with the results of population-based studies of the effects of STD comorbidities on the sexual transmission of HIV.26 To test the impact of changes in the average HIV transmission probabilities experienced in a population, the simulation results obtained with 4% prevalence of comorbid STD are compared with those obtained assuming an arbitrary increase in the prevalence of STD to 20%.
A hypothetical population of 200,000 persons at the outset is simulated as they move through the 3 HIV-related states over a period of 50 years according to the annual transition rates determined by the biologic and behavioral input parameters. The initial population is defined using the age and sex distributions from China’s 1990 census. HIV is introduced in simulation year zero by assigning minimal HIV prevalence (0.001%) to the sexual activity class with the highest rate of partner change (class 6). The other 5 sexual activity classes are assigned zero prevalence at the outset and are thus exposed to HIV only through their sexual partnerships formed during the simulation period. Mixing between partners of varying ages is assigned according to the distribution of age differences between partners determined based on existing partnerships reported in the CHFLS, with males partnering with females who are 1.9 years younger on average (standard deviation = 2.6 years). Mixing by age does not vary across the simulated scenarios. Age-specific mortality from causes other than HIV corresponds to mortality rates from China’s 1990 census and HIV/AIDS related mortality is determined by the Weibull-distributed HIV incubation function built into the model.14 Population renewal (births) occurs according to the age-specific fertility rates in China’s 1990 census. Births are distributed into the 6 sexual activity classes according to the proportional distribution by class specified for each rate of partner change scenario.
Sexual Mixing and Rate of Partner Change
Figure 1 presents the annual adult (ages 15–49) HIV incidence in the simulated population under the 2 rate of partner change scenarios (high and low) and the 4 sexual mixing scenarios (90, 60, and 30% assortative mixing, and random mixing). In the high rate of change scenarios displayed in chart A of Figure 1, the simulation results confirm the pattern described in previous literature on the effect of sexual mixing patterns. The 90% assortative scenario is characterized by a multipeaked HIV incidence curve, a maximum annual HIV incidence just under 9000 new infections, and an incidence curve that flattens out to around 2300 new infections per year after ∼37 simulation years. Consistent with the results of previous simulation studies, decreasing the proportion of sexual partnerships formed assortatively from 90% to 60%, results in a change in the shape of the HIV incidence curve as well as a larger epidemic overall. The 60% assortative curve is marked by a maximum annual incidence of over 13,000 new HIV infections per year and an eventual flattening out of the curve at around 3000 new adult HIV cases per year. Further decreases in the proportion of partnerships that are formed assortatively continue to yield higher peak and endemic incidence, although the differences between the 60% and 30% adult HIV incidence curves are less pronounced than those between the 90% and 60% assortative curves. Adult HIV incidence simulated under random mixing and a high rate of partner change shows the highest peak incidence of the 4 mixing scenarios with more than 18,000 new infections and an endemic annual incidence similar to that that simulated for the 60% and 30% assortative mixing scenarios.
The varying toll of the simulated epidemic associated with each of the sexual mixing scenarios is reflected in the size of the population at the end of the simulation period. Each scenario begins with a total population of 200,000 people; 111,718 are adults between the ages of 15 and 49. Under the high rates of partner change, random mixing produces the largest epidemic and leaves an adult population of only 66,507 at the end of the 50-year simulation period. Because under high rates of partner change assortative mixing produces smaller epidemics and thus reduced mortality relative to disassortative and random mixing, the end adult population size is largest in the most assortative scenario. With 90% assortative mixing, the adult population in simulation year 50 is 38% larger than under random mixing at nearly 92,000.
Chart B of Figure 1 displays the results of simulations that are identical to those presented in chart A, with the sole exception that the class-specific rates of partner change are decreased to be consistent with those estimated from the CHFLS. The y axis on chart B is reduced by a factor of 10 relative to chart A so that the effect of changes in the sexual mixing pattern may be clearly detected even with the substantial decrease in annual incidence. The 90% assortative scenario with the low rate of partner change (chart B) shows a peak HIV incidence of approximately 950 new infections in simulation year nine, dropping to less than 400 new infections in simulation year 14 and then leveling to an annual incidence just under 500. Decreasing the proportion of partnerships that are formed assortatively about sexual activity class to 60% reveals a deviation from the relationship noted under high rates of sexual partner change. Similar to chart A, the 60% assortative mixing curve in the low rate of partner change scenario (chart B) continues to show a higher endemic annual adult HIV incidence relative to the 90% scenario. However, contrary to the association observed under the high rate of partner change, the 60% assortative scenario with a low rate of partner change is characterized by a slightly lower peak annual incidence relative to the 90% assortative mixing scenario. When the percent mixing assortatively is decreased to 30%, the pattern further deviates from what was observed under high rates of partner change. Under low rates of partner change, the 30% assortative mixing scenario reveals both a lower peak annual incidence and a lower endemic incidence relative to the 60% assortative mixing scenario. While the random mixing scenario was associated with the highest peak and endemic incidence levels in chart A, in chart B it produces by far the smallest epidemic, yielding no more than 100 new HIV infections during any single simulation year.
As one would expect given that assortative mixing is associated with greater HIV incidence in the low rate of partner change scenario, the final adult population size is smaller with assortative mixing compared to disassortative and random mixing. With random mixing, the low rate of partner change scenario yields an adult population size of more than 131,000 at the end of 50 simulation years, but with 90% assortative mixing, the simulated adult population in year 50 is closer to 127,000.
To assess the experience of each risk group in the simulated epidemics, Figure 2 illustrates the proportional contribution of the 6 sexual activity classes to the overall adult HIV incidence simulated in year 30, a point at which epidemics have matured and incidence has leveled to an endemic state. When the rate of partner change is high (chart D) and as mixing becomes less assortative, new HIV cases in sexual activity class one, the class with the lowest annual rate of partner change, make up a growing proportion of all incident cases, from less than 40% in the 90% assortative scenario to greater than 50% with 30% assortative mixing and nearly 60% of incident HIV cases under random mixing conditions. As mixing becomes less assortative, the proportional contribution of each of the sexual activity classes more closely approximates the proportional contribution of each class to the total population (Table 2), with sexual activity class 1 contributing the largest number of infections and sexual activity class 6, the class with the highest annual rate of partner change, contributing the fewest.
The sexual activity class composition of the adult HIV incidence pattern simulated for year 30 is strikingly different when the rate of partner change is low (chart E). In these scenarios, classes 5 and 6, the sexual activity classes with the highest respective annual rates of partner change, make up more than 50% of incident HIV cases in all 4 mixing scenarios, despite comprising only 10% of the total simulated population. While class 1 was the largest contributor to HIV incidence in the high rate of partner change scenarios in chart D, under low rates of partner change sexual activity class 1 contributes only a small fraction of incident cases ranging from a low of 5% of incident HIV infections from class 1 with 90% assortative mixing to a high of 19% of adult HIV incidence from class 1 with a random mixing pattern.
To assess the impact of changes in the underlying heterosexual transmission probabilities on the interaction effect described above, the proportion of the population assumed to be infected with STD comorbidities is increased to affect an enhancement of infectivity rates. Chart C in Figure 1 presents the results of simulations conducted under low rates of partner change and an assumed STD prevalence of 20% with an infectivity enhancement factor of 4. The resulting enhancement to the sexual transmission probabilities produces higher annual adult HIV incidence relative to that observed in chart B. The 90% assortative scenario shows multiple pronounced peaks with a maximum incidence of more than 1500 new adult HIV infections in simulation year 13 and a leveling off around 1100 new cases annually after simulation year 30.
Close examination of the relationship between assortativeness in sexual mixing patterns and the adult HIV incidence curve in chart C reveals a notable change in the interaction effect identified in the comparison of the high and low rate of partner change scenarios under baseline infectivity conditions. When the proportion of partnerships formed assortatively declines under enhanced infectivity conditions (chart C), the relationship between the degree of assortativeness in mixing and HIV incidence closely resembles that observed under the lower infectivity conditions but high average annual rates of partner change (chart A). Decreasing the proportion of partnerships formed assortatively to 60% and then to 30% yields both a higher peak incidence and endemic incidence relative to the 90% assortative mixing scenario. In contrast to what was observed under the low rate of partner change and baseline infectivity scenario when random mixing produced the smallest epidemic curve (chart B), random mixing with enhanced infectivity (chart C) yields the highest peak incidence at 2500 new adult HIV infections in simulation year 22, and a endemic state close to the level simulated in the 30% assortative mixing scenario. Thus the role of sexual mixing patterns in producing or suppressing the spread of HIV through heterosexual transmission is sensitive not only to the prevailing rates of sexual partner change, but also to the infectivity rates that determine the probability of HIV transmission during a sexual contact involving an infected and a susceptible partner.
An HIV epidemic is the product of the many biologic and behavioral factors that determine the rate of disease transmission in a population. A great deal of existing research on the behavioral parameters that influence HIV spread has focused on each of those determinants individually, omitting discussion of any interaction effect that may substantially alter the associations described. The analyses presented above systematically assess the interaction between 2 of the most important behavioral determinants of HIV spread: the rates of sexual partner change in the population and the prevailing patterns of sexual mixing between population subgroups defined by the rates of partner change. This interaction effect is powerful and has important implications for the population adult HIV incidence—both the magnitude and the shape of the epidemic curve—and the degree to which sexual activity classes (i.e., risk groups) are exposed to HIV infection.
Previous research has shown that larger epidemics are associated with disassortative or random mixing patterns and have done so by simulating the spread of HIV in high-risk populations characterized by high rates of sexual partner change. In assortative mixing scenarios, sexual contacts between groups are infrequent and infection remains concentrated in the highest sexual activity classes. As mixing becomes less assortative, partners in other sexual activity classes are exposed, accelerating the spread of disease in the population. The results presented above confirm this association in populations with high rates of partner change, but indicate that the direction of the association is not constant across all rates of partner change scenarios. When the rate of partner change is relatively low, as is estimated based on data obtained in the CHFLS, patterns of disassortative mixing yield smaller epidemics relative to those characterized by assortative mixing patterns. For an epidemic to be sustained in a population, the biologic and behavioral risk factors must come together to produce a reproductive rate of infection (the average number of secondary cases produced from a given infection) that is greater than 1 in the population.4 When the rate of partner change is sufficiently low and those with multiple partners do not mix among themselves (mixing is disassortative), the average individual’s probability of contact with an infected partner is low such that the epidemic fails to reproduce at a rate large enough to sustain itself.
These findings underscore the necessity of understanding both the rates of partner change in a population and the prevailing sexual mixing patterns in order to more precisely identify the groups most at risk for acquiring HIV. In the high rate of partner change example above, highly assortative mixing means that those with more rapid rates of partner change are most at risk of acquiring HIV infection. But diassortativeness in the sexual mixing pattern under precisely the same rates of partner change leads those with the lowest rates of partner change to constitute a major at-risk group. In contrast, under low average rates of partner change in a population, the epidemic is driven and sustained by the sexual partnerships of those with the highest rates of partner change, regardless of the sexual mixing pattern.
By assessing the potential for HIV spread in the context of both the rates of sexual partner change and the sexual mixing patterns between population subgroups, interventions may be developed and implemented that are expressly targeted to the epidemic dynamics at hand. In addition, one must consider the potential for changes in epidemic dynamics that may accompany any targeted intervention. For example, Anderson and colleagues imagine that a program initially aimed at reducing the average rates of sexual partner change may actually influence changes in the sexual mixing patterns as the supply and demand for partnerships shift in the population, with unintended consequences for rates of new infection.10
The conclusions drawn here are limited in that they focus primarily on a single interaction between only 2 behavioral determinants of HIV spread. Other characteristics of a population are important in the development and progression of an HIV epidemic and must also be considered when evaluating the respective roles of the rate of sexual partner acquisition and patterns of mixing between population subgroups. The analyses presented above reveal that the identified interaction effect is highly sensitive to changes in the underlying sexual transmission probabilities of HIV. The situation is considered where sexual transmission probabilities are enhanced by an increase in the prevalence of STD comorbidities. However, other factors not explicitly considered here also impact the average sexual transmission probabilities experienced in a population. For example, male circumcision is known to have a protective effect against female-to-male HIV transmission,27,28 and use of antiretroviral drug therapy lowers transmission probabilities by decreasing the viral load in the HIV-infected partner.29
Other behavioral patterns within a population may further alter the interaction effect observed between the rates of sexual partner change and patterns of sexual mixing in the spread of HIV. Concurrency in sexual relationships, for example, has been shown to accelerate HIV spread by increasing sexual contacts within the initial highly infectious stage of acute HIV disease.30,31 Assessments of the potential for the spread of HIV in specific contexts must also consider the prevalence of concurrent sexual relationships in that population.
Results of the analyses presented above demonstrate that some impression of prevailing sexual mixing patterns in addition to rates of partner change is necessary to accurately assess the HIV epidemic dynamics in a population. Unfortunately, despite continued calls for advanced data collection,30 a few surveys are designed to amass the data necessary to empirically estimate the sexual behavior determinants of HIV epidemics. Representative population-based surveys are needed to assess not simply the total number of sexual partners of respondents per unit time, but also the number that were newly acquired during that time so that the rate of new partner acquisition may be estimated. This can be accomplished by assessing the beginning and ending dates for each sexual partnership, which will additionally facilitate identification of concurrent relationships. Surveys are also needed to collect data on the sexual network that describes the formation of sexual partnerships and the degree of contact between population subgroups. The most resource intensive in this genre involves graphing the complete sexual network in a closed population. However, valuable gains may also be had from assessing the local network by simply asking respondents to report on the demographic, social, and sexual behavior characteristics of their partners when known. Such efforts will further our understanding of HIV epidemic dynamics in populations newly at risk for HIV infection and will inform the design of interventions targeting those most at risk for fueling the epidemic into the future.
1. Anderson R, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford, UK: Oxford University Press, 1991.
2. Bongaarts J. A model of the spread of HIV infection and the demographic impact of AIDS. Stat Med 1989; 8:103–120.
3. Hyman JM, Stanley EA. Using mathematical models to understand the AIDS epidemic. Math Biosci 1988; 90:415–473.
4. May RM, Anderson RM. The transmission dynamics of HIV infection. Nature 1987; 326:137–142.
5. Anderson R. Some aspects of sexual behavior and the potential demographic impact of AIDS in developing countries. Soc Sci Med 1992; 34:271–280.
6. Gupta S, Anderson RM, May RM. Networks of sexual contacts: Implications for the pattern of spread of HIV. AIDS 1989; 3:807–817.
7. 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.
8. Boily MC, Masse B. Mathematical models of disease transmission: A precious tool for the study of sexually transmitted diseases. Can J Public Health 1997; 88:255–265.
9. Kault DA. The impact of sexual mixing patterns on the spread of AIDS. Math Biosci 1995; 128:211–241.
10. Anderson R, 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.
11. Morris M. Data driven network models for the spread of infectious disease. In: Molison D, ed. Epidemic Models: Their Structure and Relation to Data. Cambridge, UK: Cambridge University Press, 1995:302–322.
12. Service S, Blower SM. HIV transmission in sexual networks: An empirical analysis. Proc R Soc Lond B Biol Sci 1995; 260:237–244.
13. Anderson R, Gupta S, Ng W. The significance of sexual partner contact networks for the transmission dynamics of HIV. J Acquir Immune Defic Syndr 1990; 3:417–429.
14. Merli MG, Hertog S, Wang B, et al. Modeling the spread of HIV/AIDS in China: The role of sexual transmission. Popul Stud 2006; 60:1–22.
15. Palloni A, Lamas L. The AIDS Epidemic and Its Demographic Consequences. New York: United Nations and Geneva: WHO, 1991:109–118.
16. Palloni A. Demography of HIV/AIDS. Popul Index 1996; 62:601–652.
17. Anderson RM, May RM, Ng TW, et al. Age-dependent choice of sexual partners and the transmission dynamics of HIV in sub-Saharan Africa. Philos Trans R Soc Lond B Biol Sci 1992; 336:135–155.
18. 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.
19. Royce RA, Seña A, Cates W, et al. Sexual transmission of HIV. N Engl J Med 1997; 336:1072–1078.
20. Klausner JD, Kent CK. HIV and sexually transmitted diseases: Latest views on synergy, treatment, and screening. Postgrad Med 2004; 115:79–84.
21. Ambroziak J, Levy JA. Epidemiology, natural history, and pathogenesis of HIV infection. In: Holmes KK, Mardh PA, Sparling PF, et al., eds. Sexually Transmitted Diseases. New York: McGraw-Hill, Health Professions Division, 1999:251–258.
22. Turner KME, Garnett GP, Ghani AC, et al. Investigating ethnic inequalities in the incidence of sexually transmitted infections: Mathematical modeling study. Sex Transm Infect 2004; 80: 379–385.
23. Downs AM, de Vincenzi I. Probability of heterosexual transmission of HIV: Relationship to the number of unprotected sexual contacts. J Acquir Immune Defic Syndr 1996; 11:388–395.
24. Mastro TD, de Vincenzi I. Probabilities of sexual HIV-1 transmission. AIDS 1996; 10 (Suppl A):S75–S82.
25. Fleming DT, Wasserheit JN. From epidemiological synergy to public health policy and practice: The contribution of other sexually transmitted diseases to sexual transmission of HIV infection. Sex Transm Infect 1999; 75:3–17.
26. Røttingen J-A, Cameron DW, Garnett GP. A systematic review of the epidemiologic interactions between classic sexually transmitted diseases and HIV. Sex Transm Dis 2001; 28:579–597.
27. Buve A, Carael M, Hayes RJ, et al., For the Study Group on Heterogeneity of HIV Epidemics in African Cities. Multicentre study on factors determining differences in rate of spread of HIV in sub-Saharan Africa: Methods and prevalence of HIV infection. AIDS 2001; 15 (Suppl 4):S5–S14.
28. Auvert B, Taljaard D, Lagarde E, et al. Randomized, controlled intervention trial of male circumcision for reduction of HIV infection risk: The ANRS 1265 trial. PLos Med 2005; 2:1–11.
29. Porco TC, Martin JN, Page-Shafer KA, et al. Decline in HIV infectivity following the introduction of highly active antiretroviral therapy. AIDS 2004; 18:81–88.
30. Morris M. Sexual networks and HIV. AIDS 1997; 11 (Suppl A):S209–S216.
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31. Morris M, Kretzschmar M. Concurrent partnerships and the spread of HIV. AIDS 1997; 11:109–134