Modelling sexually transmitted infections: the effect of partnership activity and number of partners on R0

We model a sexually transmitted infection in a network population where individuals have different numbers of partners, separated into steady and casual partnerships, where the risk of transmission is higher in steady partnerships. An individual's number of partners of the two types defines its degree, and the degrees in the community specify the degree distribution. For this structured network population a simple model for disease transmission is defined and the basic reproduction number R0 is derived, R0 being a size-biased (i.e. biasing individuals with many partners) average number of new infections caused by individuals during the early stages of the epidemic. First a homosexual population is considered and then a heterosexual population. The heterosexual model is fitted to data from a census survey on sexual activity from the Swedish island of Gotland. The main empirical finding is that, for relevant transmission rates, the effect that so-called superspreaders have on R0 is over-estimated when not admitting for different types of partnerships.     

Monogamous networks and the spread of sexually transmitted diseases

Patterns of sexual mixing and heterogeneity in the number of sexual partners can have a huge effect on the spread of a sexually transmitted disease (STD). The sexual mixing network identifies all partnerships within a population over a given period and is a powerful tool in the study of such infections. Previous models assumed all links within the network to be concurrent active partnerships. We present a novel modelling approach in which we adapt the notion of a sexual contact network to a monogamous population by allowing the nature of the links to change. We use the underlying network to represent potential sexual partnerships, only some of which are active at any one time. Thus serial monogamy can be modelled while maintaining the patterns of mixing displayed by the population.     

Likelihood-based inference for stochastic models of sexual network formation

Sexually-transmitted diseases (STDs) constitute a major public health concern. Mathematical models for the transmission dynamics of STDs indicate that heterogeneity in sexual activity level allow them to persist even when the typical behavior of the population would not support endemicity. This insight focuses attention on the distribution of sexual activity level in a population. In this paper, we develop several stochastic process models for the formation of sexual partnership networks. Using likelihood-based model selection procedures, we assess the fit of the different models to three large distributions of sexual partner counts: (1) Rakai, Uganda, (2) Sweden, and (3) the USA. Five of the six single-sex networks were fit best by the negative binomial model. The American women's network was best fit by a power-law model, the Yule. For most networks, several competing models fit approximately equally well. These results suggest three conclusions: (1) no single unitary process clearly underlies the formation of these sexual networks, (2) behavioral heterogeneity plays an essential role in network structure, (3) substantial model uncertainty exists for sexual network degree distributions. Behavioral research focused on the mechanisms of partnership formation will play an essential role in specifying the best model for empirical degree distributions. We discuss the limitations of inferences from such data, and the utility of degree-based epidemiological models more generally.     

The dynamics of sexual contact networks: effects on disease spread and control

Sexually transmitted pathogens persist in populations despite the availability of biomedical interventions and knowledge of behavioural changes that would reduce individual-level risk. While behavioural risk factors are shared between many sexually transmitted infections, the prevalence of these diseases across different risk groups varies. Understanding this heterogeneity and identifying better control strategies depends on an improved understanding of the complex social contact networks over which pathogens spread. To date, most efforts to study the impact of sexual network structure on disease dynamics have focused on static networks. However, the interaction between the dynamics of partnership formation and dissolution and the dynamics of transmission plays a role, both in restricting the effective network accessible to the pathogen, and in modulating the transmission dynamics. We present a simple method to simulate dynamical networks of sexual partnerships. We inform the model using survey data on sexual attitudes and lifestyles, and investigate how the duration of infectiousness changes the effective contact network over which disease may spread. We then simulate several control strategies: screening, vaccination and behavioural interventions. Previous theory and research has advanced the importance of core groups for spread and control of STD. Our work is consistent with the importance of core groups, but extends this idea to consider how the duration of infectiousness associated with a particular pathogen interacts with host behaviours to define these high risk subpopulations. Characteristics of the parts of the network accessible to the pathogen, which represent the network structure of sexual contacts from the “point of view” of the pathogen, are substantially different from those of the network as a whole. The pathogen itself plays an important role in determining this effective network structure; specifically, we find that if the pathogen’s duration of infectiousness is short, infection is more concentrated in high-activity, high-concurrency individuals even when all other factors are held constant. Widespread screening programmes would be enhanced by follow-up interventions targeting higher-risk individuals, because screening shortens the expected duration of infectiousness and causes a greater relative decrease in prevalence among lower-activity than in higher-activity individuals. Even for pathogens with longer durations of infectiousness, our findings suggest that targeting vaccination and behavioural interventions towards high-activity individuals provides comparable benefits to population-wide interventions.     

A versatile ODE approximation to a network model for the spread of sexually transmitted diseases

 We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been attempted. Our goals are 1) to investigate issues relating to the application of moment closure approximations to dynamic and irregular networks, and 2) to understand the impact of concurrent casual partnerships on STD transmission through a population of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations. We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic. Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure approximation is very flexible in the kinds of network models it can approximate. Received: 26 August 2001 / Revised version: 15 March 2002 / Published online: 23 August 2002 C.T.B. was supported by the NSF. Key words or phrases: Moment closure approximation – Network model – Pair approximation – Sexually transmitted diseases – Steady/casual partnership network     

The influence of concurrent partnerships on the dynamics of HIV/AIDS.

Most models of the spread of HIV/AIDS assume that the probability of transmission from an infected individual to a susceptible partner has some constant value per sexual act, compounding independently randomly (so that ten acts with one person chosen from a particular group has, on average, the same risk as one act with each of ten different people from that group). Guided by available data, other models treat the transmission process as being some characteristic (but highly variable) value per partnership, independent of the number of acts. This latter approach does not allow for the possible effects of concurrent partnerships, and therefore does not take account of the possibility that an initially uninfected partner of a given susceptible individual may become infected over the duration of their partnership. We present a new model, based on transmission per partnership, that takes account of partnership duration. If the number of overlapping partnerships is high enough (so that R0 greater than 1 among "standing crops" of partners), any initial infection will spread very fast--on the time scale of a few times the latent interval (a few months)--among existing networks of partners. After this initial "fast phase," the subsequent epidemic proceeds more slowly along conventional lines as new partnerships are formed. These properties of the model are illustrated numerically and by analytic studies (using singular perturbation theory). The possibility of such "two time-scale" phenomena could have implications for data analysis based on statistical back-projection.     

High Prevalence of HIV Infection and Bisexual Networks among a Sample of Men Who Have Sex with Men in Eastern China

Objective

To examine homosexual and heterosexual behaviors, behavioral networks and HIV infection among men who have sex with men (MSM) in Eastern China.

Methods

A cross-sectional survey was conducted among MSM in 2013 in a rural prefecture of Zhejiang province. Participants were interviewed for their sexual behaviors and sexual networks and were tested for HIV infection.

Results

A total of 620 MSM from gay bath houses and bars participated in the survey. Of them, 58.2% aged 18 to 39 years and 49.5% were currently married with a female. The age of first homosexual contact was 26.7 years on average, ranging from 12 to 66 years. 91.0% had multiple male sex partners and 86.1% also had female sex partners in lifetime. 70 (11.3%) of the participants were tested HIV-positive. A total of 620 independent egocentric sexual networks involving 620 study participants and 1,971 reported sexual partners in the past 12 months were constructed, including 70 networks for the 70 HIV-positive participants with their 221 sexual partners and 550 networks for the 550 HIV-negative participants with their 1,750 sexual partners. The median network degree was 3 (IQR 2-4) overall and was not different between HIV-positive participants (Median: 3; IQR: 2-4) and HIV-negative participants (Median: 3; IQR: 2-4) (Mann-Whitney test, Z=-0.015, P=0.998). The proportion of networks with a multiple male sexual partnership was 63.7% overall, 62.8% for HIV-positive participants and 63.8% for HIV-negative participants (χ²=0.025, P=0.875). The proportion of networks with both male and female sexual partners was 44.8% overall, 47.1% for HIV-positive participants and 44.5% for HIV-negative participants (χ²=0.169, P=0.681). Consistent condom use and knowledge of HIV infection status were rare within the network partners.

Conclusions

The currently high HIV prevalence and complicated bisexual networks among MSM in the study area provides enhanced evidence for developing tailored prevention strategies for HIV transmission among and beyond the MSM population.     

Analysis and simulation of a stochastic, discrete-individual model of STD transmission with partnership concurrency

Deterministic differential equation models indicate that partnership concurrency and non-homogeneous mixing patterns play an important role in the spread of sexually transmitted infections. Stochastic discrete-individual simulation studies arrive at similar conclusions, but from a very different modeling perspective. This paper presents a stochastic discrete-individual infection model that helps to unify these two approaches to infection modeling. The model allows for both partnership concurrency, as well as the infection, recovery, and reinfection of an individual from repeated contact with a partner, as occurs with many mucosal infections. The simplest form of the model is a network-valued Markov chain, where the network's nodes are individuals and arcs represent partnerships. Connections between the differential equation and discrete-individual approaches are constructed with large-population limits that approximate endemic levels and equilibrium probability distributions that describe partnership concurrency. A more general form of the discrete-individual model that allows for semi-Markovian dynamics and heterogeneous contact patterns is implemented in simulation software. Analytical and simulation results indicate that the basic reproduction number R(0) increases when reinfection is possible, and the epidemic rate of rise and endemic levels are not related by 1-1/R(0), when partnerships are not point-time processes.     

What Drives the US and Peruvian HIV Epidemics in Men Who Have Sex with Men (MSM)?

In this work, we estimate the proportions of transmissions occurring in main vs. casual partnerships, and by the sexual role, infection stage, and testing and treatment history of the infected partner, for men who have sex with men (MSM) in the US and Peru. We use dynamic, stochastic models based in exponential random graph models (ERGMs), obtaining inputs from multiple large-scale MSM surveys. Parallel main partnership and casual sexual networks are simulated. Each man is characterized by age, race, circumcision status, sexual role behavior, and propensity for unprotected anal intercourse (UAI); his history is modeled from entry into the adult population, with potential transitions including HIV infection, detection, treatment, AIDS diagnosis, and death. We implemented two model variants differing in assumptions about acute infectiousness, and assessed sensitivity to other key inputs. Our two models suggested that only 4–5% (Model 1) or 22–29% (Model 2) of HIV transmission results from contacts with acute-stage partners; the plurality (80–81% and 49%, respectively) stem from chronic-stage partners and the remainder (14–16% and 27–35%, respectively) from AIDS-stage partners. Similar proportions of infections stem from partners whose infection is undiagnosed (24–31%), diagnosed but untreated (36–46%), and currently being treated (30–36%). Roughly one-third of infections (32–39%) occur within main partnerships. Results by country were qualitatively similar, despite key behavioral differences; one exception was that transmission from the receptive to insertive partner appears more important in Peru (34%) than the US (21%). The broad balance in transmission contexts suggests that education about risk, careful assessment, pre-exposure prophylaxis, more frequent testing, earlier treatment, and risk-reduction, disclosure, and adherence counseling may all contribute substantially to reducing the HIV incidence among MSM in the US and Peru.     

A stochastic model for the development of an AIDS epidemic in a heterosexual population.

A non-age-dependent model, describing the evolution of a bisexual population, is developed in this paper and applied to projecting an AIDS epidemic in a heterosexual population. Included in the formulation are frequency- and non-frequency-dependent rules of partnership formation as well as five states of HIV disease, affecting the probability of infection per sexual contact. Results from computer experiments, designed to study the development of an AIDS epidemic in a heterosexual population fed by single males with a 50% prevalence of HIV infection prior to becoming active in heterosexual partnerships, are reported. In these experiments, the only source of HIV infection for females was sexual contacts with infected males within partnerships. Data on the probability of infection per sexual contact with an infected partner and the number of sexual contacts per month were incorporated into the model. However, the numbers used for the initial population of singles, couples, and those becoming sexually active per month were hypothetical. Even though the prevalence of HIV infection among males entering heterosexual partnerships was high, after 30 years the projected prevalence of HIV infection among females ranged from about 10 to 15% depending in part on the expected duration of partnerships and on whether the frequency- or non-frequency-dependent model was used. In these experiments, solutions of the embedded, nonlinear, deterministic equations for the incidence of HIV infection and the cumulative number of deaths due to AIDS proved to be good measures of central tendency for the sample functions of the stochastic population process.     

Modelling the impact of correlations between condom use and sexual contact pattern on the dynamics of sexually transmitted infections

Background

It is believed that sexually active people, i.e. people having multiple or concurrent sexual partners, are at a high risk of sexually transmitted infections (STI), but they are likely to be more aware of the risk and may exhibit greater fraction of the use of condom. The purpose of the present study is to examine the correlation between condom use and sexual contact pattern and clarify its impact on the transmission dynamics of STIs using a mathematical model.

Methods

The definition of sexual contact pattern can be broad, but we focus on two specific aspects: (i) type of partnership (i.e. steady or casual partnership) and (ii) existence of concurrency (i.e. with single or multiple partners). Systematic review and meta-analysis of published studies are performed, analysing literature that epidemiologically examined the relationship between condom use and sexual contact pattern. Subsequently, we employ an epidemiological model and compute the reproduction number that accounts for with and without concurrency so that the corresponding coverage of condom use and its correlation with existence of concurrency can be explicitly investigated using the mathematical model. Combining the model with parameters estimated from the meta-analysis along with other assumed parameters, the impact of varying the proportion of population with multiple partners on the reproduction number is examined.

Results

Based on systematic review, we show that a greater number of people used condoms during sexual contact with casual partners than with steady partners. Furthermore, people with multiple partners use condoms more frequently than people with a single partner alone. Our mathematical model revealed a positive relationship between the effective reproduction number and the proportion of people with multiple partners. Nevertheless, the association was reversed to be negative by employing a slightly greater value of the relative risk of condom use for people with multiple partners than that empirically estimated.

Conclusions

Depending on the correlation between condom use and the existence of concurrency, association between the proportion of people with multiple partners and the reproduction number can be reversed, suggesting the sexually active population is not necessary a primary target population to encourage condom use (i.e., sexually less active individuals could equivalently be a target in some cases).

     

Short-term Mobility and Increased Partnership Concurrency among Men in Zimbabwe

Background

Migration has long been understood as an underlying factor for HIV transmission, and sexual partner concurrency has been increasingly studied as an important component of HIV transmission dynamics. However, less work has examined the role of short-term mobility in sexual partner concurrency using a network approach. Short-term mobility may be a risk for HIV for the migrant’s partner as well either through the partner’s risk behaviors while the migrant is away, such as the partner having additional partners, or via exposure to the return migrant.

Methods

Using data from the 2010–11 Zimbabwe Demographic and Health Survey, weighted generalized linear regression models were used to investigate the associations between short-term mobility and partnership concurrency at the individual and partnership levels.

Results

At the individual level, we find strong evidence of an association between short-term mobility and concurrency. Men who traveled were more likely to have concurrent partnerships compared to men who did not travel and the relationship was non-linear: each trip was associated with a 2% higher probability of concurrency, with a diminishing risk at 60 trips (p<0.001). At the partnership level, short-term mobility by the male only or both partners was associated with male concurrency. Couples in which the female only traveled exhibited less male concurrency.

Conclusions

Short-term mobility has the ability to impact population-level transmission dynamics by facilitating partnership concurrency and thus onward HIV transmission. Short-term migrants may be an important population to target for HIV testing, treatment, or social and behavioral interventions to prevent the spread of HIV.     

Susceptible-infected-removed epidemic models with dynamic partnerships

The author extends the classical, stochastic, Susceptible-Infected-Removed (SIR) epidemic model to allow for disease transmission through a dynamic network of partnerships. A new method of analysis allows for a fairly complete understanding of the dynamics of the system for small and large time. The key insight is to analyze the model by tracking the configurations of all possible dyads, rather than individuals. For large populations, the initial dynamics are approximated by a branching process whose threshold for growth determines the epidemic threshold, R ₀, and whose growth rate, , determines the rate at which the number of cases increases. The fraction of the population that is ever infected, , is shown to bear the same relationship to R ₀ as in models without partnerships. Explicit formulas for these three fundamental quantities are obtained for the simplest version of the model, in which the population is treated as homogeneous, and all transitions are Markov. The formulas allow a modeler to determine the error introduced by the usual assumption of instantaneous contacts for any particular set of biological and sociological parameters. The model and the formulas are then generalized to allow for non-Markov partnership dynamics, non-uniform contact rates within partnerships, and variable infectivity. The model and the method of analysis could also be further generalized to allow for demographic effects, recurrent susceptibility and heterogeneous populations, using the same strategies that have been developed for models without partnerships.     

The Risk of Stable Partnerships: Associations between Partnership Characteristics and Unprotected Anal Intercourse among Men Who Have Sex with Men and Transgender Women Recently Diagnosed with HIV and/or STI in Lima,Peru

Background

Partnership type is an important factor associated with unprotected anal intercourse (UAI) and subsequent risk for HIV and sexually transmitted infections (STI). We examined the association of partnership type with UAI among men who have sex with men (MSM) and male-to-female transgender women (TGW) in Lima, Peru, recently diagnosed with HIV and/or STI.

Methods

We report data from a cross-sectional analysis of MSM and TGW recently diagnosed with HIV and/or STI in Lima, Peru between 2011 and 2012. We surveyed participants regarding UAI with up to their three most recent sexual partners according to partner type. Multivariable Generalized Estimate Equating (GEE) models with Poisson distribution were used to estimate prevalence ratios (PR) for UAI according to partner type.

Results

Among 339 MSM and TGW recently diagnosed with HIV and/or STI (mean age: 30.6 years, SD 9.0), 65.5% self-identified as homosexual/gay, 16.0% as bisexual, 15.2% as male-to-female transgender, and 3.3% as heterosexual. Participants provided information on 893 recent male or TGW partners with whom they had engaged in insertive or receptive anal intercourse: 28.9% stable partners, 56.4% non-stable/non-transactional partners (i.e. casual or anonymous), and 14.7% transactional partners (i.e. transactional sex client or sex worker). Unprotected anal intercourse was reported with 41.3% of all partners. In multivariable analysis, factors associated with UAI included partnership type (non-stable/non-transactional partner APR 0.73, [95% CI 0.59–0.91], transactional partner APR 0.53 [0.36–0.78], p<0.05) and the number of previous sexual encounters with the partner (>10 encounters APR 1.43 [1.06–1.92], p<0.05).

Conclusion

UAI was more commonly reported for stable partners and in partnerships with >10 sexual encounters, suggesting UAI is more prevalent in partnerships with a greater degree of interpersonal commitment. Further research assessing partner-level factors and behavior is critical for improving HIV and/or STI prevention efforts among Peruvian MSM and TGW.     

General practice partnerships: till death us do part?

OBJECTIVES--To investigate applications for general practice partnership vacancies by established general practitioner principals, the reasons for changing partnerships, and the disincentives to these moves. DESIGN--Confidential postal questionnaire. SUBJECTS--Applicants to 367 general practices in the United Kingdom advertising for a new full time partner. MAIN OUTCOME MEASURES--The proportion of job applications containing at least one application from established principals, proportion of principals appointed as new partners, incentives and disincentives to changing partnership. RESULTS--Of 325 replies (89% response rate) received, 292 were suitable for further analysis. 210/241 (87%) of all applications contained some applications from at least one established principal. 12% of all applications were made by principals. 41/296 (14%) of the newly appointed partners had previously been an established principal. The main reasons for leaving the previous partnership were a desire to move locality or not getting on with previous partners. The disincentives to changing partnerships were largely financial, including the cost of the move and loss of income. CONCLUSIONS--It is possible for established principals in general practice to overcome the disincentives and to change partnerships. There did not seem to be any overall prejudice against appointing principals, in contrast to previously published views.     

Intimate Injection Partnerships Are at Elevated Risk of High-Risk Injecting: A Multi-Level Longitudinal Study of HCV-Serodiscordant Injection Partnerships in San Francisco,CA

Background

It is increasingly recognized that the risk for HIV and hepatitis C (HCV) transmission among people who inject drugs (PWID), such as syringe sharing, occurs in the context of relationships between (at least) two people. Evidence suggests that the risk associated with injection behavior varies with injection partner types.

Methods

We utilized longitudinal dyad-level data from a study of young PWID from San Francisco (2006 to 2013) to investigate the relationship-level factors influencing high-risk injecting within HCV-serodiscordant injection partners (i.e., individuals who injected together ≥5 times in the prior month). Utilizing data from 70 HCV-serodiscordant injection partnerships, we used generalized linear models to examine relationship-level predictors (i.e., partnership composition, partnership closeness, and partnership dynamics) of: (1) receptive syringe sharing (RSS); and (2) receptive cooker use (RCU), as reported by the HCV-negative injection partner.

Results

As reported by the “at-risk” HCV-negative injection partner, receptive syringe sharing (RSS) and receptive cooker use (RCU) were 19% and 33% at enrollment, and 11% and 12% over all visits (total follow-up time 55 person-years) resulting in 13 new HCV-infections (incidence rate: 23.8/100 person-years). Person-level factors, injection partnership composition, and partnership dynamics were not significantly associated with either RSS or RCU. Instead, intimate injection partnerships (those who lived together and were also in a sexual relationship) were independently associated with a 5-times greater risk of both RSS and a 7-times greater risk of RCU when compared to injecting only partnerships.

Conclusion

Our findings suggest a positive, and amplified effect of relationship factors on injecting drug risk behaviors among young PWID injection partnerships. The majority of interventions to reduce injection drug use related harms focus on individual-based education to increase drug use knowledge. Our findings support the need to expand harm reduction strategies to relationship-based messaging and interventions.     

Epidemic Spread on Weighted Networks

The contact structure between hosts shapes disease spread. Most network-based models used in epidemiology tend to ignore heterogeneity in the weighting of contacts between two individuals. However, this assumption is known to be at odds with the data for many networks (e.g. sexual contact networks) and to have a critical influence on epidemics'' behavior. One of the reasons why models usually ignore heterogeneity in transmission is that we currently lack tools to analyze weighted networks, such that most studies rely on numerical simulations. Here, we present a novel framework to estimate key epidemiological variables, such as the rate of early epidemic expansion () and the basic reproductive ratio (), from joint probability distributions of number of partners (contacts) and number of interaction events through which contacts are weighted. These distributions are much easier to infer than the exact shape of the network, which makes the approach widely applicable. The framework also allows for a derivation of the full time course of epidemic prevalence and contact behaviour, which we validate with numerical simulations on networks. Overall, incorporating more realistic contact networks into epidemiological models can improve our understanding of the emergence and spread of infectious diseases.     

Statistical analysis of HIV infectivity based on partner studies

Partner studies produce data on the infection status of partners of individuals known or assumed to be infected with the human immunodeficiency virus (HIV) after a known or estimated number of contacts. Previous studies have assumed a constant probability of transmission (infectivity) of the virus at each contact. Recently, interest has focused on the possibility of heterogeneity of infectivity across partnerships. This paper develops parametric and nonparametric procedures based on partner data in order to examine the risk of infection after a given number of contacts. Graphical methods and inference techniques are presented that allow the investigator to evaluate the constant infectivity model and consider the impact of heterogeneity of infectivity, error in measurement of the number of contacts, and regression effects of other covariates. The majority of the methods can be computationally implemented easily with use of software to fit generalized linear models. The concepts and techniques are closely related to ideas from discrete survival analysis. A data set on heterosexual transmission is used to illustrate the methods.     

Interval estimates for epidemic thresholds in two-sex network models

Epidemic thresholds in network models of heterogeneous populations characterized by highly right-skewed contact distributions can be very small. When the population is above the threshold, an epidemic is inevitable and conventional control measures to reduce the transmissibility of a pathogen will fail to eradicate it. We consider a two-sex network model for a sexually transmitted disease which assumes random mixing conditional on the degree distribution. We derive expressions for the basic reproductive number (R(0)) for one and heterogeneous two-population in terms of characteristics of the degree distributions and transmissibility. We calculate interval estimates for the epidemic thresholds for stochastic process models in three human populations based on representative surveys of sexual behavior (Uganda, Sweden, USA). For Uganda and Sweden, the epidemic threshold is greater than zero with high confidence. For the USA, the interval includes zero. We discuss the implications of these findings along with the limitations of epidemic models which assume random mixing.