An assessment of preferential attachment as a mechanism for human sexual network formation

Forecasting HIV-1 Genetic Cluster Growth in Illinois,United States

BACKGROUND

HIV intervention activities directed toward both those most likely to transmit and their HIV-negative partners have the potential to substantially disrupt HIV transmission. Using HIV sequence data to construct molecular transmission clusters can reveal individuals whose viruses are connected. The utility of various cluster prioritization schemes measuring cluster growth have been demonstrated using surveillance data in New York City and across the United States, by the Centers for Disease Control and Prevention (CDC).

METHODS

We examined clustering and cluster growth prioritization schemes using Illinois HIV sequence data that include cases from Chicago, a large urban center with high HIV prevalence, to compare their ability to predict future cluster growth.

RESULTS

We found that past cluster growth was a far better predictor of future cluster growth than cluster membership alone but found no substantive difference between the schemes used by CDC and the relative cluster growth scheme previously used in New York City (NYC). Focusing on individuals selected simultaneously by both the CDC and the NYC schemes did not provide additional improvements.

CONCLUSION

Growth-based prioritization schemes can easily be automated in HIV surveillance tools and can be used by health departments to identify and respond to clusters where HIV transmission may be actively occurring.

A Semiparametric Bayesian Approach to Epidemics, with Application to the Spread of the Coronavirus MERS in South Korea in 2015

We consider incomplete observations of stochastic processes governing the spread of infectious diseases through finite populations by way of contact. We propose a flexible semiparametric modeling framework with at least three advantages. First, it enables researchers to study the structure of a population contact network and its impact on the spread of infectious diseases. Second, it can accommodate short- and long-tailed degree distributions and detect potential superspreaders, who represent an important public health concern. Third, it addresses the important issue of incomplete data. Starting from first principles, we show when the incomplete-data generating process is ignorable for the purpose of Bayesian inference for the parameters of the population model. We demonstrate the semiparametric modeling framework by simulations and an application to the partially observed MERS epidemic in South Korea in 2015. We conclude with an extended discussion of open questions and directions for future research.

HIV and Sexually Transmitted Infection Epidemic Potential of Networks of Men Who Have Sex With Men in Two Cities

BACKGROUND

The speed with which a pathogen circulates in a sexual network is a function of network connectivity. Cross-sectional connectivity is a function of network features like momentary degree and assortative mixing. Temporal connectivity is driven by partner acquisition rates. The forward-reachable path (FRP) has been proposed as a summary measure of these two aspects of transmission potential. We use empirical data from San Francisco and Atlanta to estimate the generative parameters of the FRP and compare results to the HIV/sexually transmitted infection epidemics in each city.

METHODS

We used temporal exponential random graph models to estimate the generative parameters for each city's dynamic sexual network from survey data. We then simulated stochastic dynamic networks from the fitted models and calculated the FRP for each realization, overall, and stratified by partnership type and demographics.

RESULTS

The overall mean and median paths were higher in San Francisco than in Atlanta. The overall paths for each city were greater than the sum of the paths in each individual partnership network. In the casual partnership network, the mean path was highest in the youngest age group and lowest in the oldest age group, despite the fact that the youngest group had the lowest mean momentary degree and past-year partner counts.

CONCLUSIONS

The FRP by age group revealed the additional utility of the measure beyond the temporal and cross-sectional network connectivity measures. Other nonnetwork factors are still necessary to infer total epidemic potential for any specific pathogen.

Phylogenetic Networks and Parameters Inferred from HIV Nucleotide Sequences of High-Risk and General Population Groups in Uganda: Implications for Epidemic Control

Phylogenetic inference is useful in characterising HIV transmission networks and assessing where prevention is likely to have the greatest impact. However, estimating parameters that influence the network structure is still scarce, but important in evaluating determinants of HIV spread. We analyzed 2017 HIV pol sequences (728 Lake Victoria fisherfolk communities (FFCs), 592 female sex workers (FSWs) and 697 general population (GP)) to identify transmission networks on Maximum Likelihood (ML) phylogenetic trees and refined them using time-resolved phylogenies. Network generative models were fitted to the observed degree distributions and network parameters, and corrected Akaike Information Criteria and Bayesian Information Criteria values were estimated. 347 (17.2%) HIV sequences were linked on ML trees (maximum genetic distance ≤4.5%, ≥95% bootstrap support) and, of these, 303 (86.7%) that consisted of pure A1 (n = 168) and D (n = 135) subtypes were analyzed in BEAST v1.8.4. The majority of networks (at least 40%) were found at a time depth of ≤5 years. The waring and yule models fitted best networks of FFCs and FSWs respectively while the negative binomial model fitted best networks in the GP. The network structure in the HIV-hyperendemic FFCs is likely to be scale-free and shaped by preferential attachment, in contrast to the GP. The findings support the targeting of interventions for FFCs in a timely manner for effective epidemic control. Interventions ought to be tailored according to the dynamics of the HIV epidemic in the target population and understanding the network structure is critical in ensuring the success of HIV prevention programs.

Surveillance of HIV-1 primary infections in France from 2014 to 2016: toward stable resistance, but higher diversity, clustering and virulence?

OBJECTIVES

Patients with primary HIV-1 infection (PHI) are a particular population, giving important insight about ongoing evolution of transmitted drug resistance-associated mutation (TDRAM) prevalence, HIV diversity and clustering patterns. We describe these evolutions of PHI patients diagnosed in France from 2014 to 2016.

METHODS

A total of 1121 PHI patients were included. TDRAMs were characterized using the 2009 Stanford list and the French ANRS algorithm. Viral subtypes and recent transmission clusters (RTCs) were also determined.

RESULTS

Patients were mainly MSM (70%) living in the Paris area (42%). TDRAMs were identified among 10.8% of patients and rose to 18.6% when including etravirine and rilpivirine TDRAMs. Prevalences of PI-, NRTI-, first-generation NNRTI-, second-generation NNRTI- and integrase inhibitor-associated TDRAMs were 2.9%, 5.0%, 4.0%, 9.4% and 5.4%, respectively. In a multivariable analysis, age >40 years and non-R5 tropic viruses were associated with a >2-fold increased risk of TDRAMs. Regarding HIV diversity, subtype B and CRF02_AG (where CRF stands for circulating recombinant form) were the two main lineages (56% and 20%, respectively). CRF02_AG was associated with higher viral load than subtype B (5.83 versus 5.40 log10 copies/mL, P=0.004). We identified 138 RTCs ranging from 2 to 14 patients and including overall 41% from the global population. Patients in RTCs were younger, more frequently born in France and more frequently MSM.

CONCLUSIONS

Since 2007, the proportion of TDRAMs has been stable among French PHI patients. Non-B lineages are increasing and may be associated with more virulent CRF02_AG strains. The presence of large RTCs highlights the need for real-time cluster identification to trigger specific prevention action to achieve better control of the epidemic.

Advances in research of HIV transmission networks

Transmission network analysis is a crucial evaluation tool aiming to explore the characteristics of the human immunodeficiency virus epidemic, develop evidence-based prevention strategies, and contribute to various areas of human immunodeficiency virus/acquired immunodeficiency syndrome prevention and control. Over recent decades, transmission networks have made tremendous strides in terms of modes, methods, applications, and various other aspects. Transmission network methods, including social, sexual, and molecular transmission networks, have played a pivotal role. Each transmission network research method has its advantages, as well as its limitations. In this study, we established a systematic review of these aforementioned transmission networks with respect to their definitions, applications, limitations, recent progress, and synthetic applications.

Bayesian method for inferring the impact of geographical distance on intensity of communication

Spatially-embedded networks represent a large class of real-world networks of great scientific and societal interest. For example, transportation networks (such as railways), communication networks (such as Internet routers), and biological networks (such as fungal foraging networks) are all spatially embedded. Both the density of interactions (presence of edges) and intensity of interactions (edge weights) are typically found to decrease as a function of spatial separation of nodes in these networks. Communication and mobility of groups of individuals have also been shown to decline with their spatial separation, and the so-called gravity model postulates that this decline takes the form of a power-law holding at all distances. There is however some evidence that the rate of decline might change as the distance increases beyond a certain value, called a change point, but there have been few statistically principled methods for determining the existence and location of change points or assessing the change in intensity of interactions associated with them. We introduce such a method within the Bayesian paradigm and apply it to anonymized mobile call detail records (CDRs). Our results are potentially useful in settings where understanding social and spatial mixing of people is important, such as in the design of cluster randomized trials for studying interventions for infectious diseases, but we also anticipate the method to be useful for investigating more generally how distance may affect tie strengths in general in spatially embedded networks.

National and International Dimensions of Human Immunodeficiency Virus-1 Sequence Clusters in a Northern California Clinical Cohort

Background

Recent advances in high-throughput molecular epidemiology are transforming the analysis of viral infections.

Methods

Human immunodeficiency virus (HIV)-1 pol sequences from a Northern Californian cohort (NCC) of 4553 antiretroviral-naive individuals sampled between 1998 and 2016 were analyzed together with 140 000 previously published global pol sequences. The HIV-TRAnsmission Cluster Engine (HIV-TRACE) was used to infer a transmission network comprising links between NCC and previously published sequences having a genetic distance ≤1.5%.

Results

Twenty-five percent of NCC sequences were included in 264 clusters linked to a published sequence, and approximately one third of these (8.0% of the total) were linked to 1 or more non-US sequences. The largest cluster, containing 512 NCC sequences (11.2% of the total), comprised the subtype B lineage that traced its origin to the earliest North American sequences. Approximately 5 percent of NCC sequences belonged to a non-B subtype, and these were more likely to cluster with a non-US sequence. Twenty-two NCC sequences belonged to 1 of 4 large clusters containing sequences from rapidly growing regional epidemics: CRF07_BC (East Asia), subtype A6 (former Soviet Union), a Japanese subtype B lineage, and an East/Southeast Asian CRF01_AE lineage. Bayesian phylogenetics suggested that most non-B sequences resulted from separate introductions but that local spread within the largest CRF01_AE cluster occurred twice.

Conclusions

The NCC contains national and international links to previously published sequences including many to the subtype B strain that originated in North America and several to rapidly growing Asian epidemics. Despite their rapid regional growth, the Asian epidemic strains demonstrated limited NCC spread.

In-depth Sampling of High-risk Populations to Characterize HIV Transmission Epidemics Among Young MSM Using PrEP in France and Quebec

Background

A better understanding of HIV transmission dynamics among populations at high risk is important for development of prevention strategies. We determined HIV transmission networks from infected individuals enrolled in the pre-exposure prophylaxis (PrEP) IPERGAY trial in combination with the ANRS PRIMO and Montreal PHI cohorts to identify and characterize active clusters of transmission in this high-risk population.

Methods

Genotypic resistance tests were performed on plasma samples from 31 IPERGAY participants. Reverse transcriptase sequences were analyzed in combination with unique HIV pol sequences from 1351 individuals enrolled in the PRIMO ANRS cohort (1999–2014) and 511 individuals enrolled in the Montreal PHI cohort (1996–2016). Network analyses were performed to infer putative relationships between all participants.

Results

Overall, 1893 participants were included. Transmission network analyses revealed that 14 individuals (45.2%) from the IPERGAY trial were involved in 13 clusters sampled over a median period (interquartile range) of 2 (0.3–7.8) years, including 7 dyads and 6 larger clusters ranging from 4 to 28 individuals. When comparing characteristics between clustering individuals enrolled in the PRIMO cohort (n = 377) and in IPERGAY (n = 14), we found that IPERGAY participants had a higher viral load (5.93 vs 5.20 log₁₀ copies/mL, P = .032) and reported a higher number of partners in the last 2 months (P < .01).

Conclusions

These results demonstrate high rates of HIV transmission clustering among young high-risk MSM enrolled in the IPERGAY trial. In-depth sampling of high-risk populations may help to uncover unobserved transmission intermediaries and improve prevention efforts that could be targeted to the most active clusters.

Phylogenies from dynamic networks

The relationship between the underlying contact network over which a pathogen spreads and the pathogen phylogenetic trees that are obtained presents an opportunity to use sequence data to learn about contact networks that are difficult to study empirically. However, this relationship is not explicitly known and is usually studied in simulations, often with the simplifying assumption that the contact network is static in time, though human contact networks are dynamic. We simulate pathogen phylogenetic trees on dynamic Erdős-Renyi random networks and on two dynamic networks with skewed degree distribution, of which one is additionally clustered. We use tree shape features to explore how adding dynamics changes the relationships between the overall network structure and phylogenies. Our tree features include the number of small substructures (cherries, pitchforks) in the trees, measures of tree imbalance (Sackin index, Colless index), features derived from network science (diameter, closeness), as well as features using the internal branch lengths from the tip to the root. Using principal component analysis we find that the network dynamics influence the shapes of phylogenies, as does the network type. We also compare dynamic and time-integrated static networks. We find, in particular, that static network models like the widely used Barabasi-Albert model can be poor approximations for dynamic networks. We explore the effects of mis-specifying the network on the performance of classifiers trained identify the transmission rate (using supervised learning methods). We find that both mis-specification of the underlying network and its parameters (mean degree, turnover rate) have a strong adverse effect on the ability to estimate the transmission parameter. We illustrate these results by classifying HIV trees with a classifier that we trained on simulated trees from different networks, infection rates and turnover rates. Our results point to the importance of correctly estimating and modelling contact networks with dynamics when using phylodynamic tools to estimate epidemiological parameters.

Growth of HIV-1 Molecular Transmission Clusters in New York City

Background

HIV-1 genetic sequences can be used to infer viral transmission history and dynamics. Throughout the United States, HIV-1 sequences from drug resistance testing are reported to local public health departments.

Methods

We investigated whether inferred HIV transmission network dynamics can identify individuals and clusters of individuals most likely to give rise to future HIV cases in a surveillance setting. We used HIV-TRACE, a genetic distance-based clustering tool, to infer molecular transmission clusters from HIV-1 pro/RT sequences from 65736 people in the New York City surveillance registry. Logistic and LASSO regression analyses were used to identify correlates of clustering and cluster growth, respectively. We performed retrospective transmission network analyses to evaluate individual- and cluster-level prioritization schemes for identifying parts of the network most likely to give rise to new cases in the subsequent year.

Results

Individual-level prioritization schemes predicted network growth better than random targeting. Across the 3600 inferred molecular transmission clusters, previous growth dynamics were superior predictors of future transmission cluster growth compared to individual-level prediction schemes. Cluster-level prioritization schemes considering previous cluster growth relative to cluster size further improved network growth predictions.

Conclusions

Prevention efforts based on HIV molecular epidemiology may improve public health outcomes in a US surveillance setting.

Inferring HIV-1 Transmission Dynamics in Germany From Recently Transmitted Viruses

BACKGROUND

Although HIV continues to spread globally, novel intervention strategies such as treatment as prevention (TasP) may bring the epidemic to a halt. However, their effective implementation requires a profound understanding of the underlying transmission dynamics.

METHODS

We analyzed parameters of the German HIV epidemic based on phylogenetic clustering of viral sequences from recently infected seroconverters with known infection dates. Viral baseline and follow-up pol sequences (n = 1943) from 1159 drug-naïve individuals were selected from a nationwide long-term observational study initiated in 1997. Putative transmission clusters were computed based on a maximum likelihood phylogeny. Using individual follow-up sequences, we optimized our clustering threshold to maximize the likelihood of co-clustering individuals connected by direct transmission.

RESULTS

The sizes of putative transmission clusters scaled inversely with their abundance and their distribution exhibited a heavy tail. Clusters based on the optimal clustering threshold were significantly more likely to contain members of the same or bordering German federal states. Interinfection times between co-clustered individuals were significantly shorter (26 weeks; interquartile range: 13-83) than in a null model.

CONCLUSIONS

Viral intraindividual evolution may be used to select criteria that maximize co-clustering of transmission pairs in the absence of strong adaptive selection pressure. Interinfection times of co-clustered individuals may then be an indicator of the typical time to onward transmission. Our analysis suggests that onward transmission may have occurred early after infection, when individuals are typically unaware of their serological status. The latter argues that TasP should be combined with HIV testing campaigns to reduce the possibility of transmission before TasP initiation.

Social and Genetic Networks of HIV-1 Transmission in New York City

Background

Sexually transmitted infections spread across contact networks. Partner elicitation and notification are commonly used public health tools to identify, notify, and offer testing to persons linked in these contact networks. For HIV-1, a rapidly evolving pathogen with low per-contact transmission rates, viral genetic sequences are an additional source of data that can be used to infer or refine transmission networks.

Methods and Findings

The New York City Department of Health and Mental Hygiene interviews individuals newly diagnosed with HIV and elicits names of sexual and injection drug using partners. By law, the Department of Health also receives HIV sequences when these individuals enter healthcare and their physicians order resistance testing. Our study used both HIV sequence and partner naming data from 1342 HIV-infected persons in New York City between 2006 and 2012 to infer and compare sexual/drug-use named partner and genetic transmission networks. Using these networks, we determined a range of genetic distance thresholds suitable for identifying potential transmission partners. In 48% of cases, named partners were infected with genetically closely related viruses, compatible with but not necessarily representing or implying, direct transmission. Partner pairs linked through the genetic similarity of their HIV sequences were also linked by naming in 53% of cases. Persons who reported high-risk heterosexual contact were more likely to name at least one partner with a genetically similar virus than those reporting their risk as injection drug use or men who have sex with men.

Conclusions

We analyzed an unprecedentedly large and detailed partner tracing and HIV sequence dataset and determined an empirically justified range of genetic distance thresholds for identifying potential transmission partners. We conclude that genetic linkage provides more reliable evidence for identifying potential transmission partners than partner naming, highlighting the importance and complementarity of both epidemiological and molecular genetic surveillance for characterizing regional HIV-1 epidemics.

Understanding the path over which viruses such as HIV have been transmitted may be crucial for directing public health resources and guiding policy decisions. Contact tracing of named sexual and injection drug-use partners of people recently diagnosed with HIV is an indispensible tool for reconstructing this transmission network. Viral genetic sequence data—routinely collected by public health agencies—can also be used to infer the dynamics of HIV transmission. We analyzed partner naming and viral genetic sequence data in 1342 people living with HIV in New York City reported to the New York City Department of Health and Mental Hygiene between 2006 and 2012. Genetically linked partners were more likely to be named partners than named partners were to be genetically linked. This finding indicates that genetic sequence data are better than partner naming data for reconstructing this viral transmission network. Importantly, the success rate in naming a genetically linked partner varied by transmission risk category (e.g., men who have sex with men, heterosexuals, and injection drug users). This study validates the use viral genetic sequences in reconstructing these viral transmission networks in a public health surveillance setting.

Reconstructing contact network parameters from viral phylogenies

Models of the spread of disease in a population often make the simplifying assumption that the population is homogeneously mixed, or is divided into homogeneously mixed compartments. However, human populations have complex structures formed by social contacts, which can have a significant influence on the rate of epidemic spread. Contact network models capture this structure by explicitly representing each contact which could possibly lead to a transmission. We developed a method based on approximate Bayesian computation (ABC), a likelihood-free inference strategy, for estimating structural parameters of the contact network underlying an observed viral phylogeny. The method combines adaptive sequential Monte Carlo for ABC, Gillespie simulation for propagating epidemics though networks, and a kernel-based tree similarity score. We used the method to fit the Barabási-Albert network model to simulated transmission trees, and also applied it to viral phylogenies estimated from ten published HIV sequence datasets. This model incorporates a feature called preferential attachment (PA), whereby individuals with more existing contacts accumulate new contacts at a higher rate. On simulated data, we found that the strength of PA and the number of infected nodes in the network can often be accurately estimated. On the other hand, the mean degree of the network, as well as the total number of nodes, was not estimable with ABC. We observed sub-linear PA power in all datasets, as well as higher PA power in networks of injection drug users. These results underscore the importance of considering contact structures when performing phylodynamic inference. Our method offers the potential to quantitatively investigate the contact network structure underlying viral epidemics.

A population's higher-risk sexual behaviour is associated with its average sexual behaviour-An ecological analysis of subpopulations in Ethiopia, Kenya, South Africa, Uganda and the United States

BACKGROUND

Given the large variation in the prevalence of sexually transmitted infections between populations it is important to characterize how sexual vary between populations. In this paper we assess how the distribution of lifetime sexual partners varies between populations. We ask: do populations with higher mean lifetime sexual partners merely differ by virtue of the presence of a core-group with increased number of partners or do the population distributions move as more coherent wholes?

METHODS

We defined those in the top decile of lifetime sex partners in each country as constituting the higher-risk behaviour group (HRB). Spearman's correlation was used to evaluate the relationship between mean lifetime partners and prevalence of those in the HRB by ethnic group within Ethiopia, Kenya, South Africa, Uganda and the United States. In each case, data from nationally representative surveys were used. Two-sample Wilcoxon rank-sum were applied to test if there was a difference in the number of lifetime partners between the highest and lowest-risk subpopulations, separately for men and women. To account for autocorrelation, all analyses were conducted using means/medians excluding those in the HRB. A P-value of <0.05 was considered statistically significant.

RESULTS

In each country, a positive correlation existed between subpopulations' mean lifetime partners and the prevalence of the HRB. Spearman's correlation varied from 0.20 to 0.99 for men and 0.74 to 1.0 for women. This association was statistically significant in 6 out of 10 comparisons. There was a statistically significant difference in the number of lifetime partners between the highest and lowest-risk ethnic groups in all countries except South Africa, where the difference was only significant for women.

CONCLUSIONS

Our results suggest that sexual behaviours vary coherently between different populations. As such, sexually transmitted infection control efforts would benefit from including both targeted campaigns focusing on the HRB and population-strategies that seek to address factors responsible for high mean risk behaviour.

SIR epidemics on a scale-free spatial nested modular network

We propose a class of random scale-free spatial networks with nested community structures called SHEM and analyze Reed–Frost epidemics with community related independent transmissions. We show that in a specific example of the SHEM the epidemic threshold may be trivial or not as a function of the relation among community sizes, distribution of the number of communities, and transmission rates.

A theoretical framework to identify invariant thresholds in infectious disease epidemiology

Setting global strategies and targets for disease prevention and control often involves mathematical models. Model structure is typically subject to intense scrutiny, such as confrontation with empirical data and alternative formulations, while a less frequently challenged aspect is the widely adopted reduction of parameters to their average values. Focusing on endemic diseases, we use a general transmission model to explain how mean field approximations decrease the estimated R0 from prevalence data, while threshold phenomena - such as the epidemic and reinfection thresholds - remain invariant. This results in an underestimation of the effort required to control disease, which may be particularly severe when the approximation inappropriately places transmission estimates below important thresholds. These concepts are widely applicable across endemic pathogen systems.

Growth and containment of a hierarchical criminal network

We model the hierarchical evolution of an organized criminal network via antagonistic recruitment and pursuit processes. Within the recruitment phase, a criminal kingpin enlists new members into the network, who in turn seek out other affiliates. New recruits are linked to established criminals according to a probability distribution that depends on the current network structure. At the same time, law enforcement agents attempt to dismantle the growing organization using pursuit strategies that initiate on the lower level nodes and that unfold as self-avoiding random walks. The global details of the organization are unknown to law enforcement, who must explore the hierarchy node by node. We halt the pursuit when certain local criteria of the network are uncovered, encoding if and when an arrest is made; the criminal network is assumed to be eradicated if the kingpin is arrested. We first analyze recruitment and study the large scale properties of the growing network; later we add pursuit and use numerical simulations to study the eradication probability in the case of three pursuit strategies, the time to first eradication, and related costs. Within the context of this model, we find that eradication becomes increasingly costly as the network increases in size and that the optimal way of arresting the kingpin is to intervene at the early stages of network formation. We discuss our results in the context of dark network disruption and their implications on possible law enforcement strategies.

Using social network analysis to inform disease control interventions

Contact patterns between individuals are an important determinant for the spread of infectious diseases in populations. Social network analysis (SNA) describes contact patterns and thus indicates how infectious pathogens may be transmitted. Here we explore network characteristics that may inform the development of disease control programes. This study applies SNA methods to describe a livestock movement network of 180 farms in New Zealand from 2006 to 2010. We found that the number of contacts was overall consistent from year to year, while the choice of trading partners tended to vary. This livestock movement network illustrated how a small number of farms central to the network could play a potentially dominant role for the spread of infection in this population. However, fragmentation of the network could easily be achieved by "removing" a small proportion of farms serving as bridges between otherwise isolated clusters, thus decreasing the probability of large epidemics. This is the first example of a comprehensive analysis of pastoral livestock movements in New Zealand. We conclude that, for our system, recording and exploiting livestock movements can contribute towards risk-based control strategies to prevent and monitor the introduction and the spread of infectious diseases in animal populations.

Inequalities in addressing the HIV epidemic: the story of the Indonesian Ojek community

Purpose

– The purpose of this paper is to identify the potential socio-cultural determinants contributing to inequalities and the susceptibility of the Ojek to Human Immunodeficiency Virus (HIV) infection.

Design/methodology/approach

– In 2010 a qualitative enquiry was employed to collect data concerning the susceptibility of the Ojek to HIV infection. Both one-on-one open-ended in-depth interviews and focus group discussions were employed. Participants included Ojek (hired motorcycle drivers), religious and community leaders, staff from the HIV/Acquired Immune Deficiency Syndrome (AIDS) Commission of Belu and staff from two HIV/AIDS non-governmental organisations. A thematic analysis and a framework approach were used to analyse the data.

Findings

– The findings showed four socio-cultural determinants of susceptibility to HIV infection within the Ojek community. These included: first, mobility and migration; second, patterns of sexual behaviours, sexual networks and sexual incentives; third, cultural norms and social interactions; and fourth, the lack of resources, knowledge and awareness of HIV/AIDS. Underpinned by these factors, the main determinant of HIV susceptibility for the Ojek is an individual’s engagement in sexual intercourse with multiple sex partners, including female commercial sex workers (FCSWs).

Social implications

– There is a need to disseminate HIV/AIDS information and education throughout the Ojek communities, and to engage the general population in the promotion of sexual behavioural change among the Ojek in Belu. Empowerment strategies should also be employed to empower the general community, the Ojek and FCSWs in order to address HIV/AIDS transmission.

Originality/value

– This paper provides evidence of the socio-cultural determinants of HIV inequalities within the Ojek community in Indonesia. An understanding of these determinants would enable the planning, implementation and application of a holistic approach addressing the determinants of HIV in Belu and other similar settings. Additionally, knowledge of such determinants would provide an understanding of the role of inter-sectoral collaboration and community participation in tackling the susceptibility to HIV infection within the Ojek community.

The Effect of Disease-Induced Mortality on Structural Network Properties

As the understanding of the importance of social contact networks in the spread of infectious diseases has increased, so has the interest in understanding the feedback process of the disease altering the social network. While many studies have explored the influence of individual epidemiological parameters and/or underlying network topologies on the resulting disease dynamics, we here provide a systematic overview of the interactions between these two influences on population-level disease outcomes. We show that the sensitivity of the population-level disease outcomes to the combination of epidemiological parameters that describe the disease are critically dependent on the topological structure of the population's contact network. We introduce a new metric for assessing disease-driven structural damage to a network as a population-level outcome. Lastly, we discuss how the expected individual-level disease burden is influenced by the complete suite of epidemiological characteristics for the circulating disease and the ongoing process of network compromise. Our results have broad implications for prediction and mitigation of outbreaks in both natural and human populations.

Dynamics of non-cohabiting sex partnering in sub-Saharan Africa: a modelling study with implications for HIV transmission

Objective

To develop an analytical understanding of non-cohabiting sex partnering in sub-Saharan Africa (SSA) using nationally representative sexual behaviour data.

Method

A non-homogenous Poisson stochastic process model was used to describe the dynamics of non-cohabiting sex. The model was applied to 25 countries in SSA and was fitted to Demographic and Health Survey data. The country-specific mean values and variances of the distributions of number of non-cohabiting partners were estimated.

Results

The model yielded overall robust fits to the empirical distributions stratified by marital status and sex. The median across all country-specific mean values was highest for unmarried men at 0.574 non-cohabiting partners over the last 12 months, followed by that of unmarried women at 0.337, married men at 0.192 and married women at 0.038. The median of variances was highest for unmarried men at 0.127, followed by married men at 0.057, unmarried women at 0.003 and married women at 0.000. The largest variability in mean values across countries was for unmarried men (0.103–1.206), and the largest variability in variances was among unmarried women (0.000–1.994).

Conclusions

Non-cohabiting sex appears to be a random ‘opportunistic’ phenomenon linked to situations that may facilitate it. The mean values and variances of number of partners in SSA show wide variation by country, marital status and sex. Unmarried individuals have larger mean values than their married counterparts, and men have larger mean values than women. Unmarried individuals appear to play a disproportionate role in driving heterogeneity in sexual networks and possibly epidemiology of sexually transmitted infections.

An agent-based epidemic simulation of social behaviors affecting HIV transmission among Taiwanese homosexuals

Computational simulations are currently used to identify epidemic dynamics, to test potential prevention and intervention strategies, and to study the effects of social behaviors on HIV transmission. The author describes an agent-based epidemic simulation model of a network of individuals who participate in high-risk sexual practices, using number of partners, condom usage, and relationship length to distinguish between high- and low-risk populations. Two new concepts—free links and fixed links—are used to indicate tendencies among individuals who either have large numbers of short-term partners or stay in long-term monogamous relationships. An attempt was made to reproduce epidemic curves of reported HIV cases among male homosexuals in Taiwan prior to using the agent-based model to determine the effects of various policies on epidemic dynamics. Results suggest that when suitable adjustments are made based on available social survey statistics, the model accurately simulates real-world behaviors on a large scale.

Epidemic cycles driven by host behaviour

Host immunity and demographics (the recruitment of susceptibles via birthrate) have been demonstrated to be a key determinant of the periodicity of measles, pertussis and dengue epidemics. However, not all epidemic cycles are from pathogens inducing sterilizing immunity or are driven by demographics. Many sexually transmitted infections are driven by sexual behaviour. We present a mathematical model of disease transmission where individuals can disconnect and reconnect depending on the infectious status of their contacts. We fit the model to historic syphilis (Treponema pallidum) and gonorrhea (Neisseria gonorrhoeae) incidence in the USA and explore potential intervention strategies against syphilis. We find that cycles in syphilis incidence can be driven solely by changing sexual behaviour in structured populations. Our model also explains the lack of similar cycles in gonorrhea incidence even if the two infections share the same propagation pathways. Our model similarly illustrates how sudden epidemic outbreaks can occur on time scales smaller than the characteristic demographic time scale of the population and that weaker infections can lead to more violent outbreaks. Behaviour also appears to be critical for control strategies as we found a bigger sensitivity to behavioural interventions than antibiotic treatment. Thus, behavioural interventions may play a larger role than previously thought, especially in the face of antibiotic resistance and low intervention efficacies.

The Matthew effect in empirical data

The Matthew effect describes the phenomenon that in societies, the rich tend to get richer and the potent even more powerful. It is closely related to the concept of preferential attachment in network science, where the more connected nodes are destined to acquire many more links in the future than the auxiliary nodes. Cumulative advantage and success-breads-success also both describe the fact that advantage tends to beget further advantage. The concept is behind the many power laws and scaling behaviour in empirical data, and it is at the heart of self-organization across social and natural sciences. Here, we review the methodology for measuring preferential attachment in empirical data, as well as the observations of the Matthew effect in patterns of scientific collaboration, socio-technical and biological networks, the propagation of citations, the emergence of scientific progress and impact, career longevity, the evolution of common English words and phrases, as well as in education and brain development. We also discuss whether the Matthew effect is due to chance or optimization, for example related to homophily in social systems or efficacy in technological systems, and we outline possible directions for future research.

Sample size considerations in the design of cluster randomized trials of combination HIV prevention

Background Cluster randomized trials have been utilized to evaluate the effectiveness of HIV prevention strategies on reducing incidence. Design of such studies must take into account possible correlation of outcomes within randomized units. Purpose To discuss power and sample size considerations for cluster randomized trials of combination HIV prevention, using an HIV prevention study in Botswana as an illustration. Methods We introduce a new agent-based model to simulate the community-level impact of a combination prevention strategy and investigate how correlation structure within a community affects the coefficient of variation - an essential parameter in designing a cluster randomized trial. Results We construct collections of sexual networks and then propagate HIV on them to simulate the disease epidemic. Increasing level of sexual mixing between intervention and standard-of-care (SOC) communities reduces the difference in cumulative incidence in the two sets of communities. Fifteen clusters per arm and 500 incidence cohort members per community provide 95% power to detect the projected difference in cumulative HIV incidence between SOC and intervention communities (3.93% and 2.34%) at the end of the third study year, using a coefficient of variation 0.25. Although available formulas for calculating sample size for cluster randomized trials can be derived by assuming an exchangeable correlation structure within clusters, we show that deviations from this assumption do not generally affect the validity of such formulas. Limitations We construct sexual networks based on data from Likoma Island, Malawi, and base disease progression on longitudinal estimates from an incidence cohort in Botswana and in Durban as well as a household survey in Mochudi, Botswana. Network data from Botswana and larger sample sizes to estimate rates of disease progression would be useful in assessing the robustness of our model results. Conclusion Epidemic modeling plays a critical role in planning and evaluating interventions for prevention. Simulation studies allow us to take into consideration available information on sexual network characteristics, such as mixing within and between communities as well as coverage levels for different prevention modalities in the combination prevention package.

Networks and plant disease management: concepts and applications

A network is a natural structure with which to describe many aspects of a plant pathosystem. The article seeks to set out in a nonmathematical way some of the network concepts that promise to be useful in managing plant disease. The field has been stimulated by developments designed to help understand and manage animal and human disease, and by technical infrastructures, such as the internet. It overlaps partly with landscape ecology. The study of networks has helped identify likely ways to reduce the flow of disease in traded plants, to find the best sites to monitor as warning sites for annually reinvading diseases, and to understand the fundamentals of how a pathogen spreads in different structures. A tension between the free flow of goods or species down communication channels and free flow of pathogens down the same pathways is highlighted.

Estimating hidden population size using Respondent-Driven Sampling data

Respondent-Driven Sampling (RDS) is n approach to sampling design and inference in hard-to-reach human populations. It is often used in situations where the target population is rare and/or stigmatized in the larger population, so that it is prohibitively expensive to contact them through the available frames. Common examples include injecting drug users, men who have sex with men, and female sex workers. Most analysis of RDS data has focused on estimating aggregate characteristics, such as disease prevalence. However, RDS is often conducted in settings where the population size is unknown and of great independent interest. This paper presents an approach to estimating the size of a target population based on data collected through RDS. The proposed approach uses a successive sampling approximation to RDS to leverage information in the ordered sequence of observed personal network sizes. The inference uses the Bayesian framework, allowing for the incorporation of prior knowledge. A flexible class of priors for the population size is used that aids elicitation. An extensive simulation study provides insight into the performance of the method for estimating population size under a broad range of conditions. A further study shows the approach also improves estimation of aggregate characteristics. Finally, the method demonstrates sensible results when used to estimate the size of known networked populations from the National Longitudinal Study of Adolescent Health, and when used to estimate the size of a hard-to-reach population at high risk for HIV.

The global transmission network of HIV-1

Human immunodeficiency virus type 1 (HIV-1) is pandemic, but its contemporary global transmission network has not been characterized. A better understanding of the properties and dynamics of this network is essential for surveillance, prevention, and eventual eradication of HIV. Here, we apply a simple and computationally efficient network-based approach to all publicly available HIV polymerase sequences in the global database, revealing a contemporary picture of the spread of HIV-1 within and between countries. This approach automatically recovered well-characterized transmission clusters and extended other clusters thought to be contained within a single country across international borders. In addition, previously undescribed transmission clusters were discovered. Together, these clusters represent all known modes of HIV transmission. The extent of international linkage revealed by our comprehensive approach demonstrates the need to consider the global diversity of HIV, even when describing local epidemics. Finally, the speed of this method allows for near-real-time surveillance of the pandemic's progression.

Epidemics scenarios in the "Romantic network"

The networks of sexual contacts together with temporal interactions play key roles in the spread of sexually transmitted infections. Unfortunately, data for this kind of network is scarce. One of the few exceptions, the "Romantic network", is a complete structure of a real sexual network in a high school. Based on many network measurements the authors of the work have concluded that it does not correspond to any other model network. Regarding the temporal structure, several studies indicate that relationship timing can have an effect on the diffusion throughout networks, as relationship order determines transmission routes. The aim is to check if the particular structure, static and dynamic, of the Romantic network is determinant for the propagation of an STI. We performed simulations in two scenarios: the static network where all contacts are available and the dynamic case where contacts evolve over time. In the static case, we compared the epidemic results in the Romantic network with some paradigmatic topologies. In the dynamic scenario, we considered the dynamics of formation of pairs in the Romantic network and we studied the propagation of the diseases. Our results suggest that although this real network cannot be labeled as a Watts-Strogatz network, it is, in regard to the propagation of an STI, very similar to a high disorder network. Additionally, we found that: the effect that any individual contacting an externally infected subject is to make the network closer to a fully connected one, the higher the contact degree of patient zero the faster the spread of the outbreaks, and the epidemic impact is proportional to the numbers of contacts per unit time. Finally, our simulations confirm that relationship timing severely reduced the final outbreak size, and also, show a clear correlation between the average degree and the outbreak size over time.

Social encounter networks: collective properties and disease transmission

A fundamental challenge of modern infectious disease epidemiology is to quantify the networks of social and physical contacts through which transmission can occur. Understanding the collective properties of these interactions is critical for both accurate prediction of the spread of infection and determining optimal control measures. However, even the basic properties of such networks are poorly quantified, forcing predictions to be made based on strong assumptions concerning network structure. Here, we report on the results of a large-scale survey of social encounters mainly conducted in Great Britain. First, we characterize the distribution of contacts, which possesses a lognormal body and a power-law tail with an exponent of −2.45; we provide a plausible mechanistic model that captures this form. Analysis of the high level of local clustering of contacts reveals additional structure within the network, implying that social contacts are degree assortative. Finally, we describe the epidemiological implications of this local network structure: these contradict the usual predictions from networks with heavy-tailed degree distributions and contain public-health messages about control. Our findings help us to determine the types of realistic network structure that should be assumed in future population level studies of infection transmission, leading to better interpretations of epidemiological data and more appropriate policy decisions.

The HIV Epidemic: High-Income Countries

The HIV epidemic in higher-income nations is driven by receptive anal intercourse, injection drug use through needle/syringe sharing, and, less efficiently, vaginal intercourse. Alcohol and noninjecting drug use increase sexual HIV vulnerability. Appropriate diagnostic screening has nearly eliminated blood/blood product-related transmissions and, with antiretroviral therapy, has reduced mother-to-child transmission radically. Affected subgroups have changed over time (e.g., increasing numbers of Black and minority ethnic men who have sex with men). Molecular phylogenetic approaches have established historical links between HIV strains from central Africa to those in the United States and thence to Europe. However, Europe did not just receive virus from the United States, as it was also imported from Africa directly. Initial introductions led to epidemics in different risk groups in Western Europe distinguished by viral clades/sequences, and likewise, more recent explosive epidemics linked to injection drug use in Eastern Europe are associated with specific strains. Recent developments in phylodynamic approaches have made it possible to obtain estimates of sequence evolution rates and network parameters for epidemics.

Transmission network parameters estimated from HIV sequences for a nationwide epidemic

BACKGROUND

Many studies of sexual behavior have shown that individuals vary greatly in their number of sexual partners over time, but it has proved difficult to obtain parameter estimates relating to the dynamics of human immunodeficiency virus (HIV) transmission except in small-scale contact tracing studies. Recent developments in molecular phylodynamics have provided new routes to obtain these parameter estimates, and current clinical practice provides suitable data for entire infected populations.

METHODS

A phylodynamic analysis was performed on partial pol gene sequences obtained for routine clinical care from 14,560 individuals, representing approximately 60% of the HIV-positive men who have sex with men (MSM) under care in the United Kingdom.

RESULTS

Among individuals linked to others in the data set, 29% are linked to only 1 individual, 41% are linked to 2-10 individuals, and 29% are linked to ≥10 individuals. The right-skewed degree distribution can be approximated by a power law, but the data are best fitted by a Waring distribution for all time depths. For time depths of 5-7 years, the distribution parameter ρ lies within the range that indicates infinite variance.

CONCLUSIONS

The transmission network among UK MSM is characterized by preferential association such that a randomly distributed intervention would not be expected to stop the epidemic.

Transmission of Chlamydia trachomatis through sexual partnerships: a comparison between three individual-based models and empirical data

Chlamydia trachomatis is the most common bacterial sexually transmitted infection (STI) in many developed countries. The highest prevalence rates are found among young adults who have frequent partner change rates. Three published individual-based models have incorporated a detailed description of age-specific sexual behaviour in order to quantify the transmission of C. trachomatis in the population and to assess the impact of screening interventions. Owing to varying assumptions about sexual partnership formation and dissolution and the great uncertainty about critical parameters, such models show conflicting results about the impact of preventive interventions. Here, we perform a detailed evaluation of these models by comparing the partnership formation and dissolution dynamics with data from Natsal 2000, a population-based probability sample survey of sexual attitudes and lifestyles in Britain. The data also allow us to describe the dispersion of C. trachomatis infections as a function of sexual behaviour, using the Gini coefficient. We suggest that the Gini coefficient is a useful measure for calibrating infectious disease models that include risk structure and highlight the need to estimate this measure for other STIs.

Statistical analyses support power law distributions found in neuronal avalanches

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.

Frailty effects in networks: comparison and identification of individual heterogeneity versus preferential attachment in evolving networks

Preferential attachment is a proportionate growth process in networks, where nodes receive new links in proportion to their current degree. Preferential attachment is a popular generative mechanism to explain the widespread observation of power-law-distributed networks. An alternative explanation for the phenomenon is a randomly grown network with large individual variation in growth rates among the nodes (frailty). We derive analytically the distribution of individual rates, which will reproduce the connectivity distribution that is obtained from a general preferential attachment process (Yule process), and the structural differences between the two types of graphs are examined by simulations. We present a statistical test to distinguish the two generative mechanisms from each other and we apply the test to both simulated data and two real data sets of scientific citation and sexual partner networks. The findings from the latter analyses argue for frailty effects as an important mechanism underlying the dynamics of complex networks.

Factors associated with numbers of client partners of female sex workers across five districts in South India

BACKGROUND

This study investigated the structural-environmental and individual-level social factors associated with the numbers of commercial sex clients of female sex workers (FSWs) per month (CPM).

METHODS

Data were analyzed from cross-sectional surveys of FSWs in 5 districts in Karnataka state, India (2004-2005). Bivariate and multivariable negative binomial regression models with generalized estimating equations were constructed for each district. Normalized weights were used to account for complex sampling design.

RESULTS

Median (average) CPM varied significantly (P < 0.001) across districts, from 40.0 (56.9) CPM in the district with the highest immunodeficiency virus prevalence (33.9%) to 16.0 (26.1) in the district with the lowest prevalence (9.7%). In multivariable analysis, there was a significant positive association between rates of CPM and sex work as sole income in 4 districts (adjusted incidence rate ratios, AIRR: [95% confidence intervals]: AIRR: 1.3 [1.0-1.7], P < 0.005-1.7 [1.2-2.5], P < 0.01); age, typology (place of solicitation), and marital status were significantly associated with CPM in 3 districts, with an inverse association between age and CPM (P < 0.01). FSWs soliciting clients in brothels had higher rates of CPM than home-based FSWs in 2 districts (AIRR: 1.5 [1.1-2.0]-1.6 [1.0-2.7], P < 0.05), whereas public places-based FSWs had higher rates in 1 district (AIRR: 1.4 [1.1-1.8], P < 0.01); cohabiting FSWs had higher rates than married FSWs in 3 districts, whereas single FSWs had higher rates in one district.

CONCLUSIONS

These results provide support for the continued development of structural core group interventions that address common elements of sex work placing FSWs at higher risk for immunodeficiency virus, as well as geographically focused programs that account for local differences in sexual structure.

HIV transmission by stage of infection and pattern of sexual partnerships

BACKGROUND

Most model analyses examining the role of primary HIV infection in the HIV epidemic ignore the fact that HIV is often transmitted through long-term, concurrent sexual partnerships. We sought to understand how duration and concurrency of sexual partnerships affect the role of transmissions during primary HIV infection.

METHODS

We constructed a stochastic individual-based model of HIV transmission in a homogeneous population where partnerships form and dissolve. Using observed contagiousness by stage of HIV infection, the fraction of transmissions during primary HIV infection at equilibrium was examined across varying partnership durations and concurrencies.

RESULTS

The fraction of transmissions during primary HIV infection has a U-shaped relationship with partnership duration. The fraction drops with increasing partnership duration for partnerships with shorter average duration but rises for partnerships with longer average duration. Partnership concurrency modifies this relationship. The fraction of transmissions during primary HIV infection increases with increasing partnership concurrency for partnerships with shorter average duration, but decreases for partnerships with longer average duration.

CONCLUSIONS

Partnership patterns strongly influence the transmission of HIV and do so differentially by stage of infection. Dynamic partnerships need to be taken into account to make a robust inference on the role of different stages of HIV infection.

Networks and Models with Heterogeneous Population Structure in Epidemiology

Heterogeneous population structure can have a profound effect on infectious disease dynamics, and is particularly important when investigating “tactical” disease control questions. At times, the nature of the network involved in the transmission of the pathogen (bacteria, virus, macro-parasite, etc.) appears to be clear; however, the nature of the network involved is dependent on the scale (e.g. within-host, between-host, or between-population), the nature of the contact, which ranges from the highly specific (e.g. sexual acts or needle sharing at the person-to-person level) to almost completely non-specific (e.g. aerosol transmission, often over long distances as can occur with the highly infectious livestock pathogen foot-and-mouth disease virus—FMDv—at the farm-to-farm level, e.g. Schley et al. in J. R. Soc. Interface 6:455–462, 2008), and the timescale of interest (e.g. at the scale of the individual, the typical infectious period of the host). Theoretical approaches to examining the implications of particular network structures on disease transmission have provided critical insight; however, a greater challenge is the integration of network approaches with data on real population structures. In this chapter, some concepts in disease modelling will be introduced, the relevance of selected network phenomena discussed, and then results from real data and their relationship to network analyses summarised. These include examinations of the patterns of air traffic and its relation to the spread of SARS in 2003 (Colizza et al. in BMC Med., 2007; Hufnagel et al. in Proc. Natl. Acad. Sci. USA 101:15124–15129, 2004), the use of the extensively documented Great Britain livestock movements network (Green et al. in J. Theor. Biol. 239:289–297, 2008; Robinson et al. in J. R. Soc. Interface 4:669–674, 2007; Vernon and Keeling in Proc. R. Soc. Lond. B, Biol. Sci. 276:469–476, 2009) and the growing interest in combining contact structure data with phylogenetics to identify real contact patterns as they directly relate to diseases of interest (Cottam et al. in PLoS Pathogens 4:1000050, 2007; Hughes et al. in PLoS Pathogens 5:1000590, 2009).

A curved exponential family model for complex networks

Networks are being increasingly used to represent relational data. As the patterns of relations tends to be complex, many probabilistic models have been proposed to capture the structural properties of the process that generated the networks. Two features of network phenomena not captured by the simplest models is the variation in the number of relations individual entities have and the clustering of their relations. In this paper we present a statistical model within the curved exponential family class that can represent both arbitrary degree distributions and an average clustering coefficient. We present two tunable parameterizations of the model and give their interpretation. We also present a Markov Chain Monte Carlo (MCMC) algorithm that can be used to generate networks from this model.