Acquisition of a sexually transmitted infection (STI) depends on the probability of engaging in a sexual partnership with an STI-infected individual, being susceptible to the infection, and the efficiency of transmission in a sex act [1,2]. Even though STIs share the same mode of transmission, the nature of sexual behavior may favor transmission of specific STIs over others [1–6]. Moreover, risk of STI acquisition does not depend only on an individual's behavior, but on the ‘ecology’ of the individual within the sexual network, that is the partner and partner's partners behavior [7–11].
The combination of an individual's partners and their partners’ partners forms a small part of a bigger sexual network that connects individuals (directly or indirectly) through their present or past partnerships [1,8]. Networks play an essential role in STI patterns; individuals who engage in serial monogamous partnerships are probably less likely to spread STIs than those who engage in concurrent partnerships [11,12]. STIs’ natural history and infectiousness profile also contribute to the observed variability in STI epidemiology .
STI epidemiology is, in principle best studied by collecting and analyzing data from biobehavioral surveys and case–control and longitudinal studies. Although these remain a standard practice, their implementation and cost is challenging. They involve investigation of sensitive behaviors, are logistically difficult, and require costly biological assays and sophisticated technologies to ascertain current infection or previous exposure . In addition to selection bias in study participation, social desirability bias can result in distorted and uninterpretable findings . As individuals are not likely to know the partners of their partners, there are also inherent informational limitations in individual egocentric data [14,15].
With these challenges to empirical data, we used in-silico simulations of HIV and herpes simplex virus type 2 (HSV-2) transmission in a population to explore ‘microscopically’ the link between sexual networks and HIV/HSV-2 patterns. We explored infection transmission in diverse network structures informed by observed behavior patterns and tuned by ranges of different network statistics. This approach enabled us to explore associations and risks of exposure beyond what can be implemented in an actual observational study.
We aimed specifically to determine the mean effects of key network statistics on infection transmission, and to what extent they are independent of each other. We further aimed to assess whether HSV-2 prevalence, despite differences in natural history and infectiousness profile, is associated with HIV prevalence and can (as a proxy) forecast HIV epidemic potential in a population yet to experience a full-blown epidemic. An overarching goal of our study is to inform the investigation of the network factors that have led to such large HIV epidemics in Sub-Saharan Africa (SSA), but nowhere else.
We constructed an individual-based Monte Carlo simulation model describing sex partnering, birth and death, and HIV/HSV-2 transmission in a given population. Each individual is born, dies, forms/dissolves marital/nonmarital partnerships, or acquires HIV/HSV-2 at event-specific probabilities at each time step in each simulation run. Transmission was assumed to occur only through sex. An initial population of 2000 individuals was assumed (for computational reasons), but this population can vary with time by random birth/death events. The model was structured as a one-sex model to avoid complexities in the definitions and analytics of network statistics. As our present interest is on the natural dynamics as the HIV epidemics emerged in SSA, we did not incorporate more recent intervention scale-up such as HIV antiretroviral therapy. Final analyses were conducted at endemic equilibrium for both infections.
Infection natural history and transmission
HIV/HSV-2 natural history and transmission parameters, and infection stage structures, were based on earlier work and recent data updates (Table 1) [16,17]. HIV progression was divided into the stages of acute, chronic, and advanced with durations of 49 days, 9 years, and 2 years, respectively – based on compilation of data and analyses of cohort studies [18–22]. AIDS mortality was included as a hazard rate. HIV transmission probability per coital act per stage was based on analyses of the Rakai study [18–20,23,24].
HSV-2 natural history was described by the stages of primary infection, latent infection, and reactivation . Viral shedding was assumed to occur only during primary infection and reactivations at a frequency of 14% of the time [16,25]. HSV-2 transmission probability per coital act during shedding was determined through several analyses . Based on evidence of the pattern, sites, and frequency of subclinical reactivations , all seropositive persons were assumed equally infectious regardless of clinical symptoms.
With the conflicting evidence on the biological interaction of HIV and HSV-2, and on the potential effects of any interaction on HIV acquisition and transmission [16,27–32], no HIV/HSV-2 biological interaction was assumed.
Sexual behavior and networks
Marital partnerships were assumed to form/dissolve at a specific rate with no polygamy. Marital rate (probability per unit time for a person to marry) was estimated using a mathematical model for partnership formation/dissolution and maximum likelihood applied to the current marriage age-specific prevalence in accordance with Demographic and Health Survey (DHS) data from Kenya . Average marriage duration was set at 20 years, also according to DHS data from Kenya and other countries in SSA .
Nonmarital partnerships were assumed to form/dissolve among both unmarried (premarital sex) and married (extramarital sex) individuals, but at different rates. Rates of premarital/extramarital partnership formation followed a gamma distribution with parameters estimated using DHS data from 20 SSA countries  per Omori et al.  methodology. An average duration of 6 months was assumed for nonmarital partnerships, as a representative value informed by previous work [20,35].
In a weighted random network, such as our baseline network, degree correlation, and clustering coefficient (both defined below and in Text S1, http://links.lww.com/QAD/B106) are determined by the degree (number of partners) distribution . A weighted random network is a network where each individual randomly selects partners from among all individuals in the population, but each individual may have different propensity to form a partnership – a situation known as proportionate mixing .
We aimed to investigate STI dynamics in diverse networks where degree correlation and clustering coefficient can vary independently. To control these factors while maintaining the degree distribution, ‘rewiring’ of newly formed partnerships is required . We used a rewiring prescription introduced by Yuasa and Shirayama  utilizing a tuning factor with two parameters, k corr and k clu, controlling degree correlation and clustering coefficient, respectively. If
, the network is a random weighted network, otherwise, degree correlation and clustering coefficient can be varied.
The age-specific population distribution was estimated using Kenya's 2008–2009 DHS data . The age-specific natural death rate was set using Kenya's demographic indicators .
Based on relevance to STI epidemiology, we investigated five types of network statistics: population mean and variance of the number of partners over the last year for married/unmarried individuals, degree correlation for nonmarital/all partnerships, clustering coefficient for nonmarital/all partnerships, and concurrency prevalence for nonmarital/all partnerships. The 1-year timeframe for the number of partners was chosen based on DHS data availability [33,34]. Degree correlation measures the correlation between the number of partners of each partner in a partnership (Text S1, http://links.lww.com/QAD/B106) . Clustering coefficient measures the degree to which individuals in the network tend to cluster together (Text S1, http://links.lww.com/QAD/B106) . Concurrency prevalence measures the proportion of individuals who have at least two partners at a specific time point (Text S1, http://links.lww.com/QAD/B106) .
Plan of analysis
We generated 500 sexual networks by varying the mean and variance of number of partners for married/unmarried individuals, and κ corr and κ clu. The choice of 500 is a balance between computing time versus the need to have diverse networks and to estimate measures with sufficiently narrow confidence intervals to make valid inferences. Parameters were sampled from plausible ranges. For each dynamical network, HIV/HSV-2 transmission was also simulated. Each simulation was seeded with 10 infected individuals for each of HIV/HSV-2, and was run with a ‘burn-in’ time of 200 years to reach equilibrium. Accordingly, we generated 500 HIV/HSV-2 epidemics in 500 different networks.
Network statistics and HIV/HSV-2 prevalences were calculated in each simulation. Spearman's rank correlation coefficient (SRCC) was calculated to estimate the associations between HIV/HSV-2 prevalences and each of the network statistics. Associations were considered strong if SRCC was at least 0.6, of intermediate strength if SRCC was between 0.2 and 0.6, and weak if SRCC was less than 0.2. Subsequently, to examine potential collinearities between network statistics and to control for confounding, multiple linear regression analyses were conducted and adjusted associations assessed. These analyses were conducted on the population-based summary measures of the simulated networks/epidemics. The dependent variable was HIV (or HSV-2) prevalence, as a continuous variable, and the independent variables were the network statistics.
The regression statistical model was selected using the variance inflation factor (VIF)  and Akaike's information criterion  as criteria. To account for the collinearities while building the models, the VIF was calculated and model selection was based on VIF less than 10. Among models satisfying the VIF criterion, the final model was selected by minimizing Akaike's information criterion. The final model was then used to calculate associations and estimate effect sizes, that is, the standardized partial regression coefficients (estimated parameters of the independent variables in the regression equation) . Effect sizes were considered strong if effect size was at least 0.6, of intermediate strength if effect size was between 0.2 and 0.6 and weak if effect size was less than 0.2. A strong effect size would imply that the independent variable (a network statistic) has a strong influence on the dependent variable (infection prevalence). Statistical analyses were implemented in R version 3.2.3. (R Foundation, Vienna, Austria).
One aim of the study was to assess whether HSV-2 prevalence, given its ecological association with HIV prevalence with the shared mode of transmission, can inform us about HIV epidemic potential, that is the endemic level of HIV prevalence, by acting as a proxy ‘summary collective measure’ of sexual risk behavior. To address this question, we conducted multiple regression analyses for HIV prevalence where HSV-2 prevalence was included as an independent variable, whether as the only variable or with other network statistics.
Figure 1a–f shows the association between HIV/HSV-2 prevalences across the 500 simulations at different scales of network statistics. HSV-2 prevalence was consistently higher than HIV prevalence, and apart from settings with HSV-2 prevalence greater than 60%, HIV prevalence was one-third or less of HSV-2 prevalence. HIV/HSV-2 prevalences were associated with an SRCC of 0.64 (95% confidence interval: 0.58–0.69).
In examining the univariable (unadjusted) associations between each network statistic and HIV/HSV-2 prevalences, it was evident that network statistics sometimes affected HIV/HSV-2 prevalences differentially. Higher concurrency, for example, drove higher prevalence for both infections (Fig. 1c and f). In contrast, degree correlation among nonmarital partnerships affected each prevalence differently (Fig. 1a).
Table 2 shows the associations between network statistics and HIV prevalence as measured by SRCC. HIV prevalence was strongly and positively correlated with unmarried mean/variance of number of partners and concurrency prevalence among nonmarital/all partnerships. Meanwhile, it had intermediate-strength positive associations with married mean/variance of number of partners and clustering coefficient among all partnerships, but intermediate-strength negative association with degree correlation among all partnerships. Lastly, HIV prevalence had weak associations with degree correlation and clustering coefficient, both among nonmarital partnerships.
Table 2 also shows the associations between network statistics and HSV-2 prevalence as measured by SRCC. HSV-2 prevalence was strongly and positively correlated with unmarried mean number of partners and concurrency prevalence of nonmarital/all partnerships. Meanwhile, it had intermediate-strength positive associations with unmarried variance of number of partners, married mean/variance of number of partners, and degree correlation among nonmarital partnerships, but intermediate-strength negative associations with degree correlation among all partnerships and clustering coefficient among nonmarital/all partnerships. HSV-2 prevalence was not weakly associated with any of the network statistics.
Several collinearities were detected in the regression analyses (Fig. 2a). These included: concurrency prevalence among nonmarital/all partnerships versus unmarried/married mean/variance of number of partners, concurrency prevalence among nonmarital versus all partnerships, degree correlation among nonmarital versus all partnerships, and clustering coefficient among nonmarital versus all partnerships. We used, therefore, two classes (i.e., two types) of models in the final regression analyses to control for collinearities: Concurrency Class, which included one of the two concurrency measures, but no measure of number of partners; and Number of Partners Class including unmarried/married mean/variance of number of partners, but no concurrency measure.
Table 2 shows the best-fit models in the Concurrency Class. For each infection, the final model included degree correlation and clustering coefficient, both for nonmarital partnerships, and concurrency prevalence for all partnerships. The HIV model explained 88% of the variation. In this model, concurrency prevalence was a strong predictor of HIV prevalence, with weak effects for degree correlation and clustering coefficient. The HSV-2 model explained 79% of the variation. In this model, concurrency prevalence was also a strong predictor of HSV-2 prevalence, with intermediate strength but negative effect for clustering coefficient, and weak effect for degree correlation.
Table 2 also shows the best-fit models in the Number of Partners Class. For each infection, the final model included unmarried/married mean/variance of number of partners, and degree correlation and clustering coefficient, both for nonmarital partnerships. The HIV model explained 90% of the variation. In this model, unmarried mean number of partners was a strong predictor of HIV prevalence, with intermediate-strength effect for unmarried variance of number of partners and weak effects for the other variables. The HSV-2 model explained 88% of the variation. In this model, unmarried/married mean/variance of number of partners and clustering coefficient had intermediate-strength effects (that was negative for clustering coefficient), and degree correlation had a weak effect. Figure 2b and c summarize these effects and their scales.
Table 3 shows the results of HIV models where HSV-2 prevalence was included as an independent variable. HSV-2 prevalence was a strong predictor of HIV prevalence whether alone, or with the addition of degree correlation and clustering coefficient. However, with the addition of concurrency prevalence, HSV-2 prevalence was a weak predictor as concurrency prevalence alone explained most of HIV prevalence variation. With inclusion of concurrency prevalence, clustering coefficient, and degree correlation in the model, HSV-2 prevalence was not predictive of HIV prevalence and had a vanishing effect size – inclusion of network statistics explicitly as independent variables in the model prevented HSV-2 prevalence from ‘acting’ as a collective measure of sexual risk behavior.
We explored the sexual network determinants of HIV/HSV-2 prevalences and the epidemiological overlap between these two infections. Not surprisingly, we found that each infection prevalence is predicted by key network summary statistics. However, the network effects on each infection showed similarity and variation in nature and scale. Unmarried mean/variance of number of partners and concurrency prevalence were overall strong predictors for both infections. The other network statistics had smaller effects that varied by infection. The network statistics considered here explained most of the variation in HIV/HSV-2 prevalences across these simulations.
Importantly, we found that network statistics effects on prevalence were not independent of each other. Concurrency prevalence captured the same effect as that of mean/variance of number of partners. Our results demonstrated also that HSV-2 prevalence is a proxy of HIV prevalence, and therefore, of HIV epidemic potential among populations where HIV has not yet been introduced, or has not yet reached its endemic equilibrium (stable endemic level). With both infections being transmitted sexually and propagating in the same sexual network, HSV-2 prevalence acts as a ‘summary collective measure’ of the network statistics that drive HIV transmission.
HIV prevalence was also found to be one-third or less of HSV-2 prevalence. If HSV-2 prevalence was less than 20% in a given population, such as among many female sex worker populations in the Middle East and North Africa [3,44], our results indicate that HIV is unlikely to reach a concentrated epidemic level among these sex workers (>5% prevalence). Meanwhile, if HSV-2 prevalence was at 50%, there is sufficient sexual risk behavior in the network to sustain a large HIV epidemic, as found in the general population HIV epidemics in SSA . It would be of interest to assess whether these modeling predictions are consistent with the HIV/HSV-2 association in empirical data. The latter could be assessed through a global systematic review and meta-analyses of existing studies with primary data for both infections.
HSV-2 prevalence was found to be a proxy of HIV prevalence, acting as a ‘biomarker’ or a ‘temperature scale’ of the sexual risk behavior that drives HIV transmission in a population. This is akin to hepatitis C virus, which was shown to be a ‘temperature scale’ of the injecting risk behavior that drives HIV transmission among people who inject drugs [46–48]. HSV-2 prevalence, together with other factors such as costs and health benefits, can be used as a criterion in the prioritization, optimization, and resource allocation of HIV prevention interventions, as has been suggested previously . HSV-2 prevalence can help in identifying which populations and/or sexual networks to target while designing cost-effective HIV/STI-specific prevention interventions.
Though HIV and HSV-2 propagate in the same network, there are distinctions in how network statistics affect each infection transmission. Clustering had an opposite effect on each infection, driving higher HIV transmission but lower HSV-2 transmission. HIV is possibly more difficult to propagate in networks, with its lower infectiousness and shorter infection duration, and much of its transmission could be occurring in clusters, reminiscent of core group STI dynamics . Meanwhile, HSV-2 spreads more easily in networks, with its higher infectiousness and longer infection duration, and therefore, can reach a larger population segment. High clustering in a network may limit HSV-2's ability to reach remote areas of the network, just as observed in an analysis of generic epidemic transmission .
Higher degree correlation among nonmarital partnerships was associated with higher HSV-2, but lower HIV transmission. Degree correlation may facilitate the formation of larger connected sections within a network (larger components), thereby probably allowing HSV-2 to reach a larger population segment and remote areas of the network. Meanwhile, higher degree correlation among all partnerships, that is, with inclusion of marital partnerships, was negatively associated with HIV/HSV-2 transmission, as it indicated tendency for monogamy.
Our findings indicate hidden complexity, if not danger, in concluding that specific network aspects are core drivers of STI epidemics without cautious analysis that control for other network factors and their interdependency. Our results, for example, showed that concurrency was strongly predictive of HIV prevalence, apparently supporting the literature implicating concurrency as the key factor to explain SSA fulminant HIV transmission . However, such a conclusion seems unwarranted as our results indicate that concurrency's effect is not independent of the number of partners effect. Concurrency appeared largely as a proxy for the high mean/variance of number of partners – not a surprising outcome considering the analytical association between concurrency and mean/variance of number of partners [41,50]. HIV prevalence in our analysis reflected primarily mean/variance of number of partners, with smaller effects for clustering and degree correlation. These factors alone explained 90% of HIV prevalence variation (Table 2).
Our study has limitations. We focused on specific network statistics based on presumptive relevance to HIV/HSV-2. Other network measures or behavioral attributes may shed further light on STI dynamics. For example, we did not explicitly explore role of commercial sex, but this may have a sizable independent effect. Our analyses were conducted on population-based summary data, and technically could be subject to ecological fallacy. For analytical tractability, we used a one-sex model, but this limitation is not perceived to be critical as the core transmission dynamics is already captured allowing the model to effectively simulate same sex or heterosexual transmission in a population. We assumed no HIV/HSV-2 biological interaction, despite earlier observational evidence [16,27,28], as subsequent clinical trials have questioned such biological interaction [30–32].
We included broad ranges for the network statistics in context of absence of empirical measures for some network statistics, such as degree correlation and clustering. We focused on studying the ‘mean’ overall association between each network statistic and HIV/HSV-2 prevalences over broad ranges for these variables. Each of these associations, nevertheless, is nonlinear and complex, and may change in strength or nature at different scales of network statistics or prevalence levels. Moreover, different interventions, whether they affect both infections directly (such as condom use), or whether they affect one of them differentially (such as antiretroviral therapy) can further influence these nonlinear associations and their interactions. These intricacies warrant detailed examination in further work.
In conclusion, HIV transmission and HSV-2 transmission in sexual networks share similarities that allow us to use HSV-2 prevalence as a proxy of HIV epidemic potential, and accordingly inform HIV prevention interventions. There are also distinctions in the network factors that drive each infection transmission. HIV prevalence reflected primarily mean/variance of number of partners (or alternatively concurrency), whereas HSV-2 prevalence was affected by a range of network statistics. Key infection effects of network statistics were found not to be independent – concurrency captured similar effects as those of mean/variance of number of partners. This genre of epidemic analyses, particularly when extended to more infections, can elucidate the behavioral factors that drive STI transmission, how STIs can inform us about the structure of sexual networks, and how to best design interventions to control transmission.
The authors gratefully acknowledge the fine support of Ms Adona Canlas in the preparation of this manuscript, and the manuscript language review of Dr Ross MacDonald, both from Weill Cornel Medicine. The authors are also grateful for infrastructure support provided by the Biostatistics, Epidemiology, and Biomathematics Research Core at Weill Cornell Medicine-Qatar.
Funding: The publication was made possible by NPRP grant number 5–752–3–177 from the Qatar National Research Fund (a member of Qatar Foundation). Ryosuke Omori acknowledges also the support of Japan Science and Technology Agency (JST), PRESTO, and Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Young Scientists (B) 15K19217. The statements made herein are solely the responsibility of the authors and the funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
R.O. designed the study, developed the mathematical model, and performed the analyses. L.J.A-R. led the conception and conduct of the study.
Conflicts of interest
There are no conflicts of interest.
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