For the STDs included, the model predicted that the introduction of improved syndromic management was followed by substantial reductions in prevalence. These predictions are difficult to compare with data from Mwanza. After 2 years, the prevalence of infectious syphilis in the model was reduced by 59% and that of all stages of syphilis by 13%. The empirical data showed a significant reduction in the prevalence of syphilis in the intervention compared with the comparison arm . The reduction in active syphilis [Treponema pallidum haemagglutination assay (TPHA)+, rapid plasma reagin (RPR) ≥ 1 : 8] was 29% (95% CI, 7–46), but this was observed after treatment of all RPR + cohort members for syphilis at baseline of the trial for ethical reasons. The observed reduction in new cases of active syphilis, which are more likely to represent cases of infectious syphilis , was 38% (95% CI, −2 to 62). These observations seem broadly consistent with the predicted prevalence reduction.
The prevalences of chlamydia and gonorrhoea were in the model reduced by 20 and 43% after 2 years. In comparison, among a subset of men in the trial, the prevalence of gonorrhoea and/or chlamydia was reduced by only 4% (95% CI, −85 to 50), but the prevalence of symptomatic urethritis was reduced by 49% (95% CI, −3 to 75) . Among female antenatal clinic attenders, the reduction in the prevalence of gonorrhea and/or chlamydia was 7% (95% CI, −75 to 51). These data were, however, based on small numbers, available for only subsets of the trial population, and there were limitations in the sensitivity and specificity of the diagnostic tests. The model predicted an 81% reduction in the prevalence of chancroid; in the trial it was not possible to determine the prevalence of chancroid.
The projected single-round mass treatment cured 1119 STD episodes in the total population of 19 080. By reducing STD incidence, the intervention reduced the number of symptomatic episodes cured by clinical treatment in the years thereafter, for example, over the first 2 years from 121 to 67.
Mass treatment resulted in an immediate and steep reduction in all STDs, and prevalences 1 year later were 50–80% lower than without intervention (Fig. 2). Thereafter, without further intervention, prevalences increased over time and approached the levels observed in the absence of intervention within 5 to 10 years. The recurrence was comparatively slow for chancroid.
The reduction in the prevalence of syphilis was due mainly to a marked decrease in latent syphilis (Fig. 4). The prevalence of infectious syphilis showed a much smaller reduction, and returned to and exceeded its previous level within a short time. The incidence of syphilis also showed an initial reduction, but thereafter increased rapidly, exceeding initial levels by around 50% within 3 years (Fig. 3a). The size of these effects depended critically on the assumed period of non-susceptibility to re-infection following cure. The longer the period of non-susceptibility, the greater was the initial fall in incidence, and the slower and less marked the subsequent increase above baseline levels. However, a `rebound' effect was observed even assuming a 5-year period of non-susceptibility, albeit delayed.
Mass treatment reduced HIV incidence by up to 50% for the first 6 months after the intervention (Fig. 3b;Table 2). Thereafter incidence increased over time, but 10 years later it was still lower than without intervention. The short-term effect of mass treatment on HIV incidence was slightly greater assuming a period of non-susceptibility following cure of latent syphilis (Fig. 3b). When alternative regimens of mass treatment were considered, the reduction in HIV incidence was in the longer term comparable if treatment for syphilis was excluded or if infectious syphilis cases were treated while latent cases were not (Table 2).
The projected combined intervention achieved cure of 1119 STD infections by mass treatment in mid-1992; the sustained improvement of syndromic treatment resulted in a further 513 episodes cured over the first 2 years, compared with 121 effective clinical treatments for the scenario without intervention.
Under this combined intervention, HIV incidence was reduced steeply within the first year and continued to decrease thereafter (Fig. 5;Table 2). The reduction in cumulative HIV incidence over 2 years (57%) was much larger than the impact of either mass treatment (36%) or syndromic treatment (30%) in isolation. In the long run, incidence levels achieved under either the combined intervention or syndromic treatment alone converged. However, the cumulative reduction in HIV incidence over 10 years achieved with the combined intervention (70%) was larger than that of syndromic treatment alone (62%), because of a greater number of infections prevented over the first few years.
As an indication of the robustness of the results, we assessed the sensitivity of the predicted impact of treatment strategies to variations in STD parameter assumptions (Table 1), some of which were based on limited data. Table 3 shows prevalences of HIV and STDs by mid-1992 and the impact of the treatment strategies on HIV incidence over the first 2 years, for several alternative scenarios.
Decreasing all cofactor magnitudes in the same direction markedly decreased the projected impact on HIV of all interventions in comparison with the default scenario. At cofactor values above the default, however, impact hardly increased, indicating a saturation effect. These variations did not affect the ranking of impact between the three treatment strategies.
The impact of mass treatment was insensitive to the relative cofactor strengths of gonorrhoea and chlamydia (inflammatory STDs) as compared to syphilis and chancroid (ulcerative STDs). The impact of syndromic treatment, in contrast, would be larger (40% reduction over 2 years) if the cofactor effect of inflammatory STDs was decreased (from 10 to 2.5 times) and the cofactor effect of ulcerative STDs was, at the same time, increased (from 100 to 250 times). If inflammatory and ulcerative STDs had equal cofactor effects (25 times), the impact of syndromic treatment was much less (14% over 2 years) than in the default scenario.
Increasing or decreasing STD transmission probabilities caused an increase or decrease in the prevalence of the respective STD of a much larger magnitude, reflecting the non-linearity in STD transmission dynamics [29,80]. The resulting prevalence levels of gonorrhoea, chlamydia and syphilis, differed markedly from those observed in Mwanza. For chlamydia, the higher the transmission probability and, consequently, its prevalence, the more favourable the impact on HIV incidence of mass treatment would be compared with syndromic treatment. In contrast, for chancroid, the higher the transmission probability and prevalence, the less favourable the impact of mass treatment would be relative to syndromic treatment. These opposite effects reflect the low proportion of chlamydia episodes that are symptomatic (Table 1) and, hence susceptible to syndromic treatment, and the high proportion symptomatic for chancroid. For gonorrhea, the relative impact on HIV incidence of the different STD interventions was insensitive to variations in the transmission probability and prevalence. Assuming a higher transmission probability for syphilis, the impact of mass treatment was markedly less than in the default scenario, and less than that of syndromic treatment even in the first year of intervention. This reflects the critical influence of the rate of re-infection with syphilis on the impact of STD mass treatment.
The relative impact over time of the different treatment strategies on HIV was independent of whether HIV infectivity was assumed to be constant (the default scenario) or to vary over the course of infection, with peaks during primary infection and AIDS (Table 3).
In all scenarios except those varying the transmission probability of syphilis and the relative cofactor effects of inflammatory and ulcerative STD, single-round mass treatment reduced cumulative HIV incidence over the first 2 years as much as or slightly more than sustained syndromic treatment. In all scenarios, the combined intervention had about twice the impact of syndromic treatment alone over this period. Time patterns in HIV incidence under the respective interventions were comparable between all scenarios. In all scenarios except that equalling the cofactor effects of inflammatory and ulcerative STD, the instantaneous HIV incidence rate under conditions of syndromic treatment fell below that for mass treatment within 2 years (results not shown).
The projections indicate that single-round mass treatment may substantially reduce the prevalence of gonorrhoea, chlamydia and chancroid. Lacking regular repetition, however, the impact of mass treatment on the transmission dynamics of STDs is only temporary, so that prevalences will finally return to their equilibrium levels. The rate at which this occurs depends on the case reproduction rate of each STD, the coverage achieved, and the rate of re-introduction of STDs due to sexual contact with infected individuals from outside the study population. In these projections, chancroid, the STD with the lowest assumed transmission probability, re-emerged slowest.
The model showed that effects on syphilis are complex. In a population with poor treatment services, most prevalent cases have a latent infection and are therefore immune to new episodes of syphilitic ulceration [75,81]. Relatively few have ulcers or are in the infectious secondary stage, but mass treatment reaches both the infectious and the latent cases. As cured patients become susceptible again and are re-infected, syphilis incidence increases steeply, resulting in rates higher than before intervention. This effect is enhanced by heterogeneity in sexual behaviour. For example, in the simulation, the baseline syphilis prevalence in women engaging in one-off contacts was 38% compared with 7% in all women. Thus, although the overall pool of susceptible individuals increased only marginally as a result of mass treatment (from 93 to 98%), the number of those susceptible, among persons at high risk, and consequently of potential new source infections, increased substantially.
The extent and timing of any increase in syphilis incidence depends on the duration of non-susceptibility to re-infection following cure (Fig. 3a). Unfortunately empirical data on the duration and extent of non-susceptibility are sparse [74,76], and both may depend on the stage of infection when treatment is given. Epidemiological evidence for or against resurgence of syphilis at a population level following mass treatment is also scarce. Mass treatment campaigns against endemic syphilis and yaws were generally successful, although in some cases resurgence was noted [22,82–84]. However, the majority of these campaigns were uncontrolled, accompanied by general improvements of health services and living conditions, which may themselves have led to reductions in endemicity, and followed by regular re-treatment rounds. Furthermore, comparability with STD mass treatment is limited by differences between the endemic treponematoses and venereal syphilis in their mode of transmission (and consequently in the role of population heterogeneity in sexual behaviour), and in baseline prevalences. Prospective studies involving long-term follow-up of patients treated for venereal syphilis at different stages are needed to address this question.
Model simulations were based on cofactor effects by which STDs enhance the transmission of HIV. The results of cohort studies and intervention trials strongly argue for the existence of these effects [2–4,11,85], and biological studies have provided evidence for underlying mechanisms [6,7,68]. However, the magnitudes of these cofactor effects are not yet known. Odds ratios from observational studies are likely to considerably underestimate them, since they usually refer to extended periods of exposure during only some of which an STD would have been present . Data from cohort studies in Nairobi [2,3] have been estimated to be consistent with a 10- to 50-fold increase in the probability of male-to-female HIV transmission per single sexual exposure, and a 50- to 300-fold increase for female-to-male transmission, in the presence of genital ulcers . In simulations of a rural population cohort in Uganda, the assumption most consistent with empirical data was that the probability of HIV transmission per sexual contact was enhanced 100-fold during episodes of ulcerative STDs, and five-fold during episodes of non-ulcerative STDs . Assuming similar cofactor effects in our study, we obtained a satisfactory fit to HIV prevalence and incidence rates observed in the comparison arm of the Mwanza trial cohort, and to the impact of syndromic treatment. Assuming weaker or stronger cofactor effects, the predicted impact of both mass treatment and syndromic treatment would be smaller or larger, respectively (Table 3). Some conditions with potentially sizeable cofactor effects, such as Herpes simplex virus type-2 (HSV-2) infection and bacterial vaginosis [86,87], cannot be effectively treated. At present such infections are not included in STDSIM. If incurable STDs are prevalent and their cofactor effects are substantial, we may have overestimated the cofactor magnitudes for curable STDs and, consequently, the impact on HIV incidence of any STD treatment strategy.
The projected impact of mass treatment on HIV incidence was determined by the beneficial effect of comparatively long-lasting decreases in the prevalence of gonorrhoea, chlamydia and chancroid, and the adverse effect on the incidence and prevalence of infectious syphilis occurring soon after mass treatment. In these simulations, including the scenario assuming immediate susceptibility to re-infection after treatment in the latent phase (Fig. 3b;Table 2), the net effect was positive. Yet this may differ according to epidemiological conditions, depending for example on the relative prevalences of syphilis and other curable STDs in a population.
In the investigation of alternative regimens of mass treatment of syphilis the model predicted a similar long-term impact on HIV incidence if syphilis treatment was excluded from the mass treatment regimen altogether, or if infectious stages of syphilis were covered but latent syphilis remained untreated (Table 2). The first of these scenarios might be achieved if mass treatment consisted of a combination of single-dose oral antibiotics including azithromycin and ciprofloxacin, which would cover all four target STDs except syphilis. Azithromycin may have some effect on active infections with Treponema pallidum, but is unlikely to be curative unless given over a longer period . The second scenario would be achieved if single-dose benzathine penicillin injections were given only to individuals presenting with the symptoms or signs of a genital ulcer or condylomata lata (a common and highly infectious form of secondary syphilis). This regimen would combine features of mass treatment and syndromic treatment. Its disadvantages would be that genital examination would be required to detect unrecognized ulcers, which is unlikely to be feasible in mass treatment campaigns, and that patients with non-syphilitic ulcers would be treated unnecessarily, including some with latent syphilis. It is of note that the treatment strategy most effective in reducing HIV incidence may not be the best strategy for reducing the disease burden of syphilis at the individual level. Untreated latent syphilis may lead to serious late complications, and in women to perinatal infection and adverse birth outcomes. The design of STD interventions clearly needs to take such ethical considerations into account.
In our projections for the Mwanza population, the impact of a single round of mass treatment on HIV incidence was in the long run much smaller than that of sustained syndromic treatment (Fig. 5, Table 2). However, mass treatment achieved a much steeper initial decline in HIV incidence. From an epidemiological perspective, the effectiveness of mass treatment relative to syndromic treatment depends on the relative contribution to HIV transmission of commonly asymptomatic curable STD, like gonorrhoea and chlamydia, in compared with commonly symptomatic curable STD, like chancroid. This in turn depends on the relative prevalences of these infections and on their cofactor effects (Table 3). Other influential factors are the frequency of occurrence and the relative cofactor effects of a symptomatic relative to an asymptomatic course of an episode with a certain STD. Cofactor effects may be stronger for symptomatic than for asymptomatic STD, as suggested by a study of HIV-infected men with urethritis in which viral shedding correlated with the degree of inflammation . In our model, identical cofactor effects were assumed for symptomatic and asymptomatic episodes. Thus our projections may underestimate the impact of syndromic treatment, provided that a significant proportion of symptomatic patients would recognize their symptoms and act upon them. This latter effect could however not be explored with the present STDSIM, in which the cofactor effect of each STD is assumed to be the same regardless of symptomatology. If both treatment strategies were combined, the short-term decrease in HIV incidence resulting from mass treatment was sustained over time, because individuals experiencing new STD infections could thereafter access syndromic treatment services. This advantage would be particularly strong if syphilis incidence were to increase following mass treatment, as our projections suggest.
A number of comparisons were made between model projections and trial outcomes. The reduction in HIV incidence observed in Mwanza over the 2 years of follow-up was 38% (95% CI, 15–55) after adjustment for potential confounding variables . In the simulations, a reduction of 30% was achieved over the first 2 years (Table 2), which is well within the confidence interval of the trial.
In addition to random error, several factors may have contributed to the simulated impact being slightly lower than the point estimate from the trial:
(i) Some reproductive tract infections treated in the Mwanza intervention such as trichomoniasis, candidiasis, bacterial vaginosis and non-specific urethritis were not incorporated in the model;
(ii) Syndromic management in Mwanza covered not only the symptomatic infection presented by the patient but also concurrent, possibly asymptomatic, STDs, but this was not the case in the model;
(iii) The time between infection and cure may in reality have been shorter than assumed, reflecting an improvement in treatment-seeking behaviour in the intervention arm;
(iv) In the simulations, patients were assumed immediately susceptible to re-infection for all STDs considered, and re-infection may therefore have occurred earlier than in reality in some cases;
(v) The model assumed identical cofactor effects for asymptomatic and symptomatic STDs.
On the other hand, omission from the model of untreated STD such as HSV-2, and of immigration and mobility, which re-introduce STD from outside the study population, may have worked in the opposite direction, leading to overestimation of impact on HIV in Mwanza.
In the Rakai trial, periodic mass treatment resulted in only a small and non-significant reduction in HIV incidence (relative risk, 0.97; 95% CI, 0.81–1.16) over the first two rounds , which is much smaller than the reduction in our simulation (36% over 2 years). A number of factors may explain this apparent discrepancy:
(i) Our model fitted the demographic and epidemiological situation in Mwanza rather than Rakai, and the two situations are different. In particular, the HIV epidemic in Rakai has reached maturity, with an HIV prevalence and incidence of 16% and 1.5/100 person–years, compared with 4% and 1/100 person–years in Mwanza. In the later stages of an HIV epidemic, transmission may depend to a lesser extent on the enhancing effect of STDs ;
(ii) Incurable STDs, such as HSV-2, and genital tract infections only temporarily cured by single-dose mass treatment, such as bacterial vaginosis, may have played a substantial role in ongoing HIV transmission in Rakai. More than 40% of genital ulcers in Rakai were due to HSV-2 , and bacterial vaginosis is highly prevalent . Neither of these infections was incorporated in STDSIM;
(iii) In the model, mass treatment was given throughout the population at a single point in time. In Rakai, mass treatment of a cluster of villages took several weeks, as it was delivered at household level in order to achieve high coverage . In a situation of extended sexual networks, the time taken to deliver mass treatment may influence the re-infection rate;
(iv) The model ignored inward migration and may have underestimated the rate of re-introduction of infection from outside the study population. Mobility may reduce the long-term impact of STD mass treatment on HIV incidence by increasing STD re-infection rates . In a mass treatment trial for the control of trachoma in The Gambia, ocular chlamydial infection was re-introduced rapidly by returning residents, visitors and migrants, in spite of high coverage and the use of effective antimicrobials .
Finally, considering the many uncertainties in its determinants, no firm conclusions can yet be drawn on the effectiveness of STD mass treatment for HIV prevention. Our simulations predicted that in a rural African setting in which syndromic STD treatment can reduce HIV incidence, single-round mass treatment may also be effective in the short term. Mass treatment followed by sustained syndromic treatment would be particularly effective, both in the short and long term. The impact of mass treatment on syphilis is complex and requires further investigation.
As we have shown, the impact of mass treatment relative to syndromic treatment depends on the relative prevalence and cofactor effects of symptomatic and asymptomatic curable STD. However, the effectiveness and cost-effectiveness of different STD treatment strategies are also affected by many other epidemiological and non-epidemiological determinants which were beyond the scope of this study. Simulation modelling of alternative STD control strategies in different settings may help to identify those determinants, estimate their relative importance, and identify needs for further empirical research. We will use the STDSIM model to address these issues using the population-based longitudinal data of the trials of STD control for HIV prevention in Mwanza, Rakai and Masaka. The results may have major implications for the design of effective STD and HIV control strategies in populations in Africa, Asia and Latin America exposed to high STD prevalences.
We thank Maria Wawer, Ron Gray, Sake de Vlas, Liesbeth Meester, Roel Bakker and the anonymous reviewers for their useful comments on the manuscript.
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Demography and sexual behaviour in STDSIM: model structure and parameter values used in the simulation of rural Mwanza
The microsimulation model STDSIM simulates the spread and control of HIV and four bacterial STDs (gonorrhoea, chlamydia, syphilis and chancroid) over time in a population consisting of hypothetical individuals in a computer program [40,41]. Each individual is represented by a number of characteristics, of which some remain constant during simulated life (e.g. sex and date of birth), whereas others change (e.g. number of sexual partners and infection status). Changes in personal characteristics result from events such as the start and end of sexual relationships, or the acquisition of infection. These events are stochastic: if and when an event occurs is determined by Monte-Carlo sampling from probability distributions. Model outcomes for a simulated population are generated by aggregating the characteristics of the simulated individuals.
STDSIM is event-driven: all events are listed and performed in chronological order. At the occurrence of an event, the characteristics of the individual and/or relationship to which the event pertains are updated. In addition, events can generate new events, which occur either immediately, for example, the death of an individual terminates all relationships of this individual; or later in the simulation, for example, acquisition of HIV infection advances a person's earlier scheduled moment of death.
Aspects affecting the transmission and control of STDs are grouped into six modules. The modules: Transmission, Natural history, Health care and Interventions are described in Methods, subsections `Biomedical parameters' and `Coverage and effectiveness of STD treatment'. Below, we describe the structure and parameter quantification for the modules Demography and Sexual behaviour. For all parameter specifications, the distribution functions, numbers and borders of age groups and values listed are those used to represent rural Mwanza in this study. The modeller can however change these in an input file, for example to base assumptions on differently structured data-sets, or to do projections for populations with other endemic conditions.
Fertility is simulated by attributing pregnancies to sexually active females on the basis of user-specified fertility rates. The duration till each subsequent pregnancy in a certain age group a is sampled from an exponential distribution with mean ba ×Fa (t), where:ba is the user-specified birth rate for age group a and Fa (t) is the number of females in age group a at time t.
Each new pregnancy is attributed randomly to a female in the age group concerned who is engaged in a sexual relationship and not already pregnant. All pregnancies result in live births 9 months after their start. The period of pregnancy can be used to simulate the effects of STD on pregnancy outcomes, for example, still-birth due to syphilis, but this option was not used in the current study. The fertility rates used to simulate rural Mwanza in this study were based on the 1996 Demographic Health Survey of rural Tanzania  and are listed in Table 4. We assumed half of all births to be males.
At the birth of a simulated person, the moment of his or her death is sampled from a stepwise linear life table specifying the proportion still alive at certain ages. For the simulation of rural Mwanza, the lifetable was specified according to mortality estimates for HIV-uninfected individuals in the trial cohort (Table 4) . If a simulated person contracts HIV, a moment of HIV-attributable death is sampled from the survival distribution of HIV patients (see Methods, subsection `Biomedical parameters' and Table 1). If the moment of HIV-attributable death is earlier than that of non-HIV-attributable death, the actual moment of death is advanced to the former, and this event is recorded as an HIV-attributable death.
Although STDSIM can simulate migration into and out of the population, this option was not used in this study.
Sexual contacts and relationships between men and women in STDSIM constitute a dynamic network through which STDs can be transmitted. We consider three types of (exclusively hetero-)sexual contact: steady relationships (`marriages'); short relationships; and one-off contacts between a small group of females, who may or may not define themselves as prostitutes, and a larger group of males. In the remainder of this Appendix, we will refer to these individuals as prostitutes and clients, respectively.
Formation of relationships is simulated using the concepts of availability for (supply) and search (demand) of new partners . Figure 6 illustrates this process. New relationships are formed between available men and available women. People become available for relationships for the first time at sexual debut (t1 in Fig. 6). At each subsequent change in the number of current partners, a new duration till availability is determined. This duration (e.g. the interval between t5 to t7) may be shorter than the duration of an ongoing relationship (t5 to the end of the horizon in Fig. 6), thus allowing for concurrent relationships (t8 to t9). Availability temporarily ends when a new relationship is formed. This happens either when someone is selected by a new partner (t5 in Fig. 6), or when a full `period of availability' (t1 to t2) has elapsed and the person selects a partner from the pool of available people of the opposite sex in a preferred age group (e.g. at t2). The mechanisms of availability and partner selection do not reflect actual (psychological, behavioural or social) processes, but allow us to steer the representation of behaviour from both the male and the female population.
Sexual debut is defined as the start of a first `period of availability' for sexual relationships. In the representation of Mwanza, the timepoint of first availability was drawn from a uniform probability distribution with a range of 12–18 years for males, and 12.5–18.5 years for females.
Sexual relationships: availability and partner selection
At each change in an individual's number of current partners, a new duration τ till availability for a new relationship is drawn from an exponential distribution with mean δs,r / rs,a × pi), where: δs,r is the mean duration till availability, which depends on the person's sex (s) and relationship status (r) (currently engaged in a steady, short or no relationship);rs,a is the sex (s) and age (a) group specific promiscuity factor; and pi is the personal promiscuity level.
In this study, the values of δs,r were set at 10 and 25 years for males and females, respectively, at the start of a steady relationship; at 2 and 4 years for unmarried males and females, respectively, at the start of a short relationship; and at 0.5 years for both sexes at the end of a last relationship, i.e. if becoming single again. The values of rs,a are listed in Table 5. Every time an individual passes an age border at which an age-specific parameter that affects a waiting time (e.g. rs,a) changes value, a new duration is drawn according to the parameter value of the new age group. This applies also to the duration of availability (see below).
The personal promiscuity level pi of individual i, which reflects the heterogeneity in promiscuity within age groups, is determined by a gamma distribution with mean 1.0 and shape parameter α:EQUATION Variation in promiscuity within age groups decreases with increasing values of α. In this study, α equalled 1.5.
While being available for new relationships, an individual can be selected by someone of the opposite sex who has just ended his/her period of availability. If a person has not been selected by the end of his/her period of availability, he/she him-/herself then selects a partner from the pool of available people of the opposite sex. This period of availability is drawn from by an exponential probability distribution with a mean of ∊/(rs,a × pi), with ∊ = 0.25 years in this study. See Table 5 for quantification of rs,a and Eq. (1) for pi.
Sexual relationships: partner preferences
Partnership formation is guided by age preference matrices (one for each sex, Table 6) specifying the probability to select a partner from a certain age class. In case no potential partner is available in the preferred age class, a partner is selected in another age class by immediately renewed sampling among the remaining age classes for which the preference is larger than zero (e.g. in Table 6, for males aged 15–19 years: the three female classes < 24 years, but not the older female age classes). If no partner is available in any of the preferred age classes, the person remains available for another period sampled as described above. This cycle repeats until the person has found a new partner.
As the age preference matrices determine age differences at the start of simulated relationships, the realized age differences in partnerships existing at a single point in time, in which long relationships are relatively over-represented, do not necessarily match the user-specified preferences. In the present simulations, the matrices specified males to prefer on average females that were 5 years younger and for females on average to prefer 5-year-older males (Table 6), in line with reported age difference between spouses in Mwanza ; realized age differences in the model population on cross-section averaged only 2 years. Apart from assortativeness by age, no other preferences apply. Thus, promiscuous individuals have no explicit preference for promiscuous partners.
Types and durations of relationships
The probability that a new relationship is steady depends on whether or not at least one of the partners is already engaged in a steady relationship, and on the age of the male partner (Table 5). At the start of a new relationship its duration is drawn, in this study from an exponential distribution with a mean of 25 years for steady relationships, and from a gamma distribution with a mean of 0.5 years and shape parameter 0.5 for short relationships. These distribution functions and parameter values were chosen to obtain fit against the data of Mwanza  for the proportions of males and females married in different age groups (Fig. 1a), simultaneously with the total number of partners during the past year of males in different age groups (Fig. 1b).
In the current version of STDSIM, the frequency of intercourse in relationships varies with the age of the male partner, but does not depend on the number and type of ongoing relationships. For this study, we assumed frequencies of once a week for relationships in which the male was < 15 or between 35 and 54 years of age, 1.5 weekly for males aged 15–34 years, and 0.5 weekly for males aged 55 and over, consistent with data from factory workers in Mwanza town .
The occurrence of one-off contacts between male `clients' and female `prostitutes' is specified by defining a number of frequency classes of prostitute visiting, and subsequently specifying the proportions of married and unmarried males (up to a maximum age, in this study 50 years) in each class. A personal inclination to visiting prostitutes, assigned to each male at birth, determines to which classes a male belongs for the married and unmarried parts of life. As the inclination remains the same throughout life and does not depend on relationship situation, frequency of prostitute visiting is always the same before marriage and after divorce or widowhood. For the distribution of males in this study (Table 7), this means that 5% of males visits prostitutes six times per year irrespective of marital status. Of the 55% visiting prostitutes once yearly while unmarried, 30% quits this practice upon marriage, but would take up prostitute visiting again in case of divorce or widowhood. The other 25% visiting prostitutes once yearly does so irrespective of marital status.
At each prostitute contact as well as at sexual debut, the time interval until the client's next contact is determined according to the exponential distribution with mean ϕ, where 1/ϕ is the personal frequency of prostitute visits.
Prostitutes are recruited according to the male demand from all sexually active females within a user-specified age range, in this study 15–30 years. A prostitute's `career' lasts at least 1 year and ends somewhere before a user-specified maximum age (in this study 35 years), according to a uniform distribution. In this study, the frequency of client contacts per prostitute averaged 1 per week. In the absence of adequate data, we believe this is not unreasonable for rural Mwanza, and it allowed us to achieve adequate fit of numbers of partners of males, which includes each one-off contact as a separate partner, (Fig. 1b) and STD epidemiology (Figs 2 and 3). In this study, client contacts were divided over the pool of prostitutes in time order.
Each year, the model checks, and, if necessary, adapts the number of prostitutes to match the user-specified frequency number of client contacts per prostitute as closely as possible, given the number of visits by clients and the frequency of client contacts of prostitutes. If the number of prostitutes is too small, additional females are recruited. If the number of prostitutes is too large, a randomly selected prostitute terminates her career before the scheduled date. In addition, every time a woman in the starting age range (15–30 years) becomes widowed (i.e. loses her steady partner), a similar check for the number of prostitutes is performed; and if there is a shortage, the widow is recruited as a prostitute.
Start of the simulation
At start of a simulation, an initial population is created; the population used in this study is given in Table 8. All individuals start as singles; formation of sexual relationships and one-off contacts then occurs as described above. STD infections are attributed to the initial population at user-specified prevalences, in this study 3.5% for gonorrhea, 5% for chlamydia, 9% for syphilis and 1.2% for chancroid. Initial STD infections are randomly distributed only among individuals with a high individual promiscuity level (pi > 1) who have had their sexual debut.
Simulations are started in a user-specified year (here 1930) well in advance of the introduction of HIV. This allows the model population to reach dynamic equilibria with respect to demography, partnership formation and STD epidemiology, before the simulated start of HIV spread. Neither the chosen composition of the initial population nor the user-specified STD rates in the initial population are critical to the situation of equilibrium.
HIV is introduced into the model population by randomly infecting one prostitute, in a user-specified year (here 1983). In applications of the model in which one-off contacts are not assumed, HIV introduction occurs by simultaneous infection of 10 sexually active males and 10 sexually active females in the general population. Cited Here...