It is well established that contact network structure influences infectious disease dynamics.1–9 For example, for the same disease parameters and average behaviors, an outbreak is more likely to spread in a random network than a clustered network with community structure.7,9 Similarly, networks that have scale-free properties can maintain an infectious disease even with very low transmissibility due to the presence of highly connected individuals that serve as hubs in the population.4–6 Despite the rich literature describing the relationship between network structure and infectious disease dynamics, only a small number of studies have compared the effectiveness and efficiency of infectious disease interventions over different types of network structures.2,10–16 None have investigated how network structures interact with the relative efficiency among multiple disease interventions.
In infectious disease outbreaks, interventions targeting the contacts of infected cases can potentially identify clusters of connected infections.16,17 These types of interventions may have a particularly strong dependence on the population's contact network structure. For example, contact tracing involves tracing through chains of contacts to find undiagnosed cases; thus, both the effectiveness and the resources required to conduct contact tracing depend directly on the underlying contact network structure. Past studies have shown that contact tracing is more effective in controlling a disease outbreak in clustered networks than in random networks.2,11,12 It has also been demonstrated that to detect the same proportion of infections, contact tracing requires more resources in scale-free networks than in random networks.10
Partner management strategies are routinely used in response to detected cases of sexually transmitted infections (STIs). In the case of STIs, contact tracing is reserved only for the most serious STIs (e.g., HIV and syphilis) because it is resource-intensive.18 Contact tracing must be undertaken centrally by public health staff to maintain continuity and confidentiality, as individuals within chains are identified and contacted. For less severe STIs, like cases of chlamydia and gonorrhea, less resource-intensive approaches (e.g., partner notification [PN] and expedited partner therapy [EPT]) are typically used. Partner notification relies on the index patient voluntarily notifying sex partners of potential STI exposure and encouraging partners to seek testing. Although less costly, PN also tends to be less effective than contact tracing; individuals may not feel comfortable notifying partners directly, and any notification that does occur might not be as impactful as official communication from a health department.19 Thus, empirical studies find that few partners ultimately seek testing under PN, resulting in, among other things, a high risk of reinfection of the index case.20–22 To increase partner treatment rates, EPT was developed to allow the index patients to deliver antibiotic regimens directly to their partners without requiring medical evaluation.18 Studies of EPT find that it both increases the timeliness of treatment and increases the proportion of partners notified, as the index case is empowered to deliver a solution (namely, antibiotic treatment) alongside the difficult news of a potential STI exposure.23 However, treated partners are unlikely to seek testing to confirm whether they were in fact infected, precluding opportunities to identify infections among an infected partners' partners or any further down the transmission chain.
Prior studies comparing the effectiveness and efficiency of PN and EPT did not consider the impact of network structure.24,25 However, the structure of a sexual contact network may have a particular influence on the relative efficiency and effectiveness of these partner management strategies because these strategies intervene upon transmission pathways that are wholly determined by the network. In this article, we examine how the cost, effectiveness, and efficiency of partner management strategies for a treatable STI changes with different assumptions about the network structure, keeping the population's average sexual behavior the same. We consider 4 representative network structures (random, community-structured, scale-free, and empirical) that are commonly used in infectious disease modeling and have real-world implication in the context of sexual contact networks. The random network assumes random mixing, meaning that an individual has the same probability of forming a connection with anyone in the population and is most similar to the dynamics seen in compartmental models of infectious disease.3,26 Community-structured networks are a somewhat more realistic version of the random network, where individuals form connections preferentially with individuals who have similar attributes (e.g., race, age, and socioeconomic status), represented as being within the same “community.”27–30 Community structure generally hinders disease spread.7,9 Scale-free networks are used to reflect populations where most individuals have few partners, but a small number individuals having many partners, acting as hubs in the population.31s,32s These highly connected individuals are easily infected and can also quickly infect their many partners. Finally, we consider an empirically informed network, constructed based on the reported number of sex partners in the past 12 months in men who have sex with men (MSM) in Seattle/King county.33s We use partner management strategies for STIs as a case study in evaluating the impact that network structure may have on the effectiveness and efficiency of interventions for the control and treatment of infectious disease.
We simulated outbreaks of a hypothetical, treatable chlamydia/gonorrhea-like STI in a closed, same-sex population, parameterized to reflect the sexual behaviors of MSM. Sexually transmitted infection introduction was modeled using a constant external force of infection (EFOI). Sexually transmitted infection spread within the population was modeled as occurring through a dynamic sexual contact network after a Susceptible-Infected-Susceptible disease model, simulated in biweekly time steps. We evaluated the costs and disease impacts of 4 different partner management strategies (none, PN, EPT, and contact tracing) over a 2-year time horizon in 4 different types of sexual network structures (random, community-structured, scale-free, empirical). We conducted a cost-effectiveness analysis (CEA) to determine if and how the efficiency of partner management strategies varies across different network structures. Model parameters were estimated from the literature (Table 1). The detail description of network generation and network dynamics is provided in Supplemental Digital Content 1 (SDC1), http://links.lww.com/OLQ/A436. The simulation model was implemented in Python 126.96.36.199s
We simulated the spread of the hypothetical STI through each of the random, community-structured, scale-free, and empirical networks following the Susceptible-Infected-Susceptible framework. A susceptible individual (S) could be infected through sex with an infected sex partner in an active relationship, or through external sexual contacts. The population was assumed to have a 0% prevalence of infection at the start of the simulation, with infection being introduced externally at a constant EFOI. We considered 2 EFOI scenarios: 0.5 (low level) and 5 (high level) persons infected per cycle. The probability of disease transmission per sex act was assumed to be 13.5% based on chlamydia transmission probability estimated in model-based studies.35s,36s Transmission could be reduced by 60% with condom use,37s which was assumed in 44% of sex acts.38s An infected individual (I) could spontaneously recover back to the susceptible state at a rate of 1/6 months.39s,40s
An infected individual could be identified and treated through routine annual screening or via partner management (e.g., PN, EPT, and contact tracing). As a simplification, we assumed that all infections were asymptomatic, consistent with the high proportion of asymptomatic chlamydial infections in men.41s,42s Thus, in the simulation, individuals did not seek treatment in response to symptoms. We allowed routine screening to be correlated with the number of sex partner of individuals in the past 12 months. We described the routine screening and the restriction of testing behavior more in detail in SDC1 (http://links.lww.com/OLQ/A436). We did not model treatment failure.
Partner Management Strategies
We considered 4 partner management strategies: routine screening alone (no partner management), PN, EPT, and contact tracing. All partner management strategies were implemented on top of routine screening. Each partner management strategy was associated with 2 compliance parameters. Patient compliance reflects how likely a patient might contact or deliver medicine to each sex partner. Partner compliance indicates how likely a partner seeks testing or takes the medicine. Patient and partner compliance under each partner management strategy was taken from a randomized control trial that evaluated the effectiveness of EPT and PN among men who had urethritis due to infection with chlamydia or gonorrhea.22 Under PN, 49% of partners were notified and 71% of notified partners sought testing. Under EPT, 70% of partners were delivered treatment and 79% of them completed the treatment course. We assumed that the trial results applied to current partners, but that for past partners, patient compliance would decay with the time since partnership termination following an exponential function , where t denotes the current cycle and reflects the end cycle of a relationship between individual i and j. This probability drops to 0.3% for PN and 0.4% for EPT, respectively, for a relationship that ended 5 months prior. We assumed that index patients would only reach out to partners from the past 6 months.
In the absence of quantitative assessments, we assumed that contact tracing has the same patient and partner compliance levels equal to the maximum of that of EPT or PN, consistent with a general consensus that contact tracing has the highest compliance of any partner management approach.18,43s In the base case, index patients reported 70% of their partners to public health staff and 79% of partners contacted by public health staff seeking testing under contact tracing. This is consistent with a general consensus that contact tracing is more effective than PN.18,43s However, these assumptions were varied in sensitivity analysis. Contact tracing was simulated by maintaining a roster of partner names; each cycle, names of partners of new index cases were added, whereas names of contacted partners were removed. We assumed that in any given cycle, a maximum of 14 partners could be contacted, reflecting agency capacity constraints. Partners were prioritized for tracing by the number of times they had been named by index cases.16,18
Costs and Health Outcomes
Costs were incurred for STI testing, treatment, and contact tracing (Table 1).16,44s Primary health outcomes included incidence, prevalence, average number of infections per person, average duration of infection, and total infected person-months, in the population over the 2-year time horizon.
Model Simulation and CEAs
We performed 10,000 simulations for each partner management scenario for each type of network structure to obtain stable estimates of costs and health outcomes. At the beginning of each simulation, we initiated a disease-free population and simulated relationship dynamics for 3 years to allow the sexual contact network to stabilize (see SDC1, http://links.lww.com/OLQ/A436, for details). After the 3-year burn-in period, we introduced infection into the disease-free population through the EFOI and simulated spread for 2 years. Partner management strategies were also implemented and evaluated over the 2-year time horizon.
We conducted a CEA of partner management strategies using the base case partner compliance parameter in each of 4 network structures (base case analysis). For a given network structure, we first calculated the costs and total infected person-months (effectiveness) accrued over the 2-year time horizon, averaged over the 10,000 simulations, for each partner strategy. For the purposes of the CEA, costs and effectiveness were discounted annually at 3%.45s Strongly and weakly dominated strategies (strategies that avert fewer infected person-months at a higher cost) were identified and eliminated. Among nondominated strategies, we calculated the incremental cost-effectiveness ratio (ICER), as the incremental cost per additional infected person-months averted of switching to a strategy from its next least costly counterpart strategy.
We varied patient compliance parameters in sensitivity analysis to evaluate how CEA results changed across the different network structures and EFOI scenarios. We considered all combinations of partner compliance of PN and EPT ranging from 10% to 100%. Simulations were conducted for all combinations in 10% increments. A generalized additive meta-model was used to extrapolate cost and effectiveness outcomes on a finer scale.46s,47s For all simulations, partner compliance under contact tracing was assumed to be the maximum compliance of the PN or EPT strategy. For each combination of PN and EPT partner compliance values, the optimal partner management strategy was defined as the strategy averting the greatest number of infected person-months with an ICER less than a willingness-to-pay (WTP) threshold. In this context, the WTP represents the monetary value of health gains from averting a month of infection with the hypothetical STI. A greater WTP would reflect an STI with greater sequalae. Given the hypothetical nature of our analysis, we present 2-way sensitivity analysis results with different WTP thresholds as an illustration of how the optimal decision might change.
Base Case Analysis
The projected prevalence (last cycle), incidence, average duration of infection, and total infected person-months for a given partner management strategy varied with network structures in both EFOI scenarios (Table 2, Supplemental Table S1, http://links.lww.com/OLQ/A436). Under routine screening alone, community-structured networks had the lowest burden of disease (prevalence, incidence, and infected person-months), whereas scale-free networks had the highest. However, scale-free networks yielded the shortest average duration of infection. The correlation between the average number of infections and the number of sex partners was the highest in scale-free networks (~0.5) than the correlation in the other network structures (0.1–0.3). In routine screening alone, although the number of screening tests was the same in different network structures, the number of sex partners (in the past 6 months) of the index cases varied widely, being smallest in community-structured networks and highest in scale-free networks. This has implications for the resource requirements of partner management strategies. The prevalence in the partners of index cases was higher than the population prevalence in all network structures and was the highest in community-structured networks.
Partner management strategies reduced disease burden and improved health outcomes because these strategies increased the number of individuals screened/tested/treated (Table 2, Supplemental Table S1, http://links.lww.com/OLQ/A436). Generally, the strategy that was most effective at reducing disease burden was the one that treated the most infected partners of index cases. In random and community-structured networks, contact tracing was the most effective strategy, resulting in the greatest reduction in prevalence, incidence, average duration of infection, and total infected person-months. In empirical networks, contact tracing was the most effective strategy at a low EFOI (Supplemental Table S1, http://links.lww.com/OLQ/A436), but EPT was most effective at a high EFOI, although it resulted in slightly fewer infected partners being treated than contact tracing (Table 2). However, in empirical networks, the percent of infected partners being treated in contact tracing reduced from 55% (higher than that of EPT) at a low EFOI to 37% (lower than that of EPT). In scale-free networks, PN was the most effective strategy. In contrast to the other network structures, contact tracing treated the fewest sex partners in scale-free networks because it reached its capacity constraint.
Compared with the other network structures, scale-free networks had the highest costs and greatest number of infected person-months under any partner management strategy because of the higher burden of infection (Table 3, Supplemental Table S2, http://links.lww.com/OLQ/A436). Regardless of the EFOI scenarios or WTP threshold, EPT was never dominated and its efficiency relative to screening alone (in terms of ICER) was very similar between EFOI scenarios in any given network structure. For the other strategies, PN was strongly dominated in all network structures except for scale-free networks; contact tracing was strongly dominated in scale-free networks under both EFOI scenarios and in empirical networks under the low EFOI scenario. In scale-free networks, the efficiency of PN relative to EPT increased from a low EFOI to a high EFOI. In random and community-structures networks, similarly the relative efficiency of contact tracing to EPT increased from a low EFOI to a high EFOI. In empirical networks, contact tracing was the next efficient strategy relative to EPT at a low EFOI but became strongly dominated at a high EFOI.
The optimal strategy at different combinations of PN and EPT partner compliance levels under a high EFOI is shown for a low WTP of $200 (Fig. 1) and high WTP of $500 (Fig. 2) per infected person-months averted. At a low WTP, the optimal strategy followed a similar pattern across partner compliance levels across the different network structures (Fig. 1). The optimal strategy was one of either EPT or PN; EPT was optimal even if its partner compliance was slightly lower than PN. Contact tracing was not optimal in any of the 4 network structures at a low WTP. A high WTP did not substantially change the pattern of the optimal strategy in empirical networks (Fig. 2). However, in scale-free networks, at a high WTP, PN was the optimal strategy for a larger share of partner compliance values (Fig. 2). Contact tracing was never optimal in both empirical and scale-free networks. In random and community-structured networks, at a high WTP, contact tracing was optimal for moderate-to-high levels of partner compliance, with partner compliance values for which PN was optimal being largely diminished (Fig. 2).
Regarding the optimal strategies at a low EFOI, similar patterns were observed in community-structured and scale-free networks (Supplemental Figs. S3 and S4, http://links.lww.com/OLQ/A436). In random networks, contact tracing was optimal even at a low WTP when PN partner compliance was very high (Supplemental Fig. S3, http://links.lww.com/OLQ/A436). At a high WTP, contact tracing was optimal for a larger share of partner compliance values in random and community-structured than under a high EFOI (Supplemental Fig. S4, http://links.lww.com/OLQ/A436). In empirical networks, although the pattern of optimal strategies at a low WTP was similar to the pattern observed in the high EFOI scenario, at a high WTP, contact tracing was optimal for a large portion of partner compliance values in contrast to never being optimal under a high EFOI (Supplemental Figs. S3 and S4, http://links.lww.com/OLQ/A436).
Mathematical models evaluating disease control strategies for infectious diseases rarely investigate how the optimal strategy varies with the structure of the underlying contact network. We demonstrated that network structure can result in substantially different epidemiological and economic outcomes, which in turn affects the efficiency and optimal strategy choice for controlling epidemics. This has implications for model-based approaches that aim to evaluate infectious disease interventions.
The findings based on our model and parameter setting were consistent with the literature.10–12,16,17 Without any partner management, we saw that community-structured networks had the least severe epidemiological outcomes. In contrast, scale-free networks tended to accelerate STI spread due to the highly connected individuals, as evidenced by the high correlation between the number of infections and the number of partners. Partner management strategies reduced disease burden across the different types of network structures, but to varying degrees.
The performance of partner management strategies (the number of infected partners tested and/or treated) differed by network structure, impacting the overall efficiency of these strategies. In the base case, PN yielded the least number of sex partner tested and treated in random, community-structured, and empirical networks owing to having the lowest patient and partner compliance. However, in scale-free networks, PN yielded the greatest number of treated infected partners owing to the much larger number of partners that could be reached compared with contact tracing, which was limited by a maximum operating capacity. In scale-free networks, PN also outperformed EPT, highlighting the importance of tracing through scale-free networks to efficiently identify new infections, something that EPT does not do.
The efficiency of each partner management strategy also differed by network structure under our model and parameter setting. Expedited partner therapy was less efficient (higher ICER) in scale-free networks than in the other network structures. The pattern of the optimal strategy at different levels of PN and EPT partner compliance also varied with network structure, WTP, and the rate of EFOI. As WTP increased, contact tracing was more likely to be optimal in random and community-structured networks, and in empirical networks at a low EFOI. However, contact tracing was never optimal in scale-free networks regardless of EFOI and in empirical networks under high EFOI.
Our findings showed that the network structure of a population might matter in determining the efficiency and effectiveness of interventions in certain contexts. It is critical to collect the information of network structure to inform infectious disease policies that operate over that structure. Although we used stylized network structures, the property of each network structure could inform the process of collecting network information. Key information would include the number of sex partners, the presence of highly connected individuals, and the level of sexual mixing assortativity across different attributes. Properties from other types of network could be considered (e.g., small-world networks).48s,49s
The focus of our study was to investigate if and how the network structure of a population influences the performance and efficiency of infectious disease interventions. The purpose of our analysis was not to directly guide real-world STI policy in MSM. Although we included EPT in our study, in practice, EPT is not recommended for MSM because of the high risk of infection with other diseases (e.g., HIV and syphilis) that would go undiagnosed under EPT but could be detected if partners were tested via PN or contact tracing.18 Considering these different objectives (reducing the burden of bacterial STIs vs. diagnosing more serious co-occurring conditions) would be critical in developing a model to inform real-world STI policies. Such considerations would increase the value of PN and contact tracing, changing the results of our CEA.
Our study is subject to several limitations. We considered PN and EPT as being mutually exclusive strategies. In practice, PN and EPT could be used in combination. The index patient might use PN for partners who are more likely to seek testing, but request EPT for partners who are unwilling to visit clinics.23 We did not investigate how relationship dynamics might affect the effectiveness and cost-effectiveness of partner management strategies. If a population has a higher partner turnover rate, PN and contact tracing may be preferred over EPT. Moreover, we did not consider the impact of different sexual positioning that is relevant to chlamydial and gonococcal infections and instead assumed a probability of disease transmission that reflects an average of different sexual positioning.50s,51s Furthermore, we did not consider antibiotic resistance that might occur to repeated and frequent treatment or other sources of treatment failure. Treatment failure is most difficult to address under EPT, where the treatment for partners is not overseen by a health care provider. Although we did not explicitly incorporate treatment failure into our analysis, we do consider lower levels of partner compliance in sensitivity analysis, which approximates the effect of treatment failure under the EPT strategy. Lastly, we only conducted sensitivity analysis on partner compliance parameters; other model parameters, including disease dynamics, sexual behaviors, and diagnostic testing behaviors, were kept fixed. Therefore, the impact of network structures on the effectiveness and efficiency of partner management strategies can only be interpreted for our specific parameter setting.
Our findings suggested that the structure of the underlying contact network might matter in evaluating interventions in infectious diseases in certain contexts. Future CEA studies that aim to make infectious disease intervention recommendations could be improved by considering the specific network structure, sexual behavior, and screening and compliance behaviors of their relevant population.
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For further references, please see “Supplemental References,” http://links.lww.com/OLQ/A436.