Networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. The foundations of epidemiology and early epidemiological models were based on population wide random-mixing, but in practice each individual has a finite set of contacts to whom they can pass infection; the ensemble of all such contacts forms a ‘mixing network’. Knowledge of the structure of the network allows models to compute the epidemic dynamics at the population scale from the individual-level behaviour of infections. Therefore, characteristics of mixing networks—and how these deviate from the random-mixing norm—have become important applied concerns that may enhance the understanding and prediction of epidemic patterns and intervention measures. Here, we review the basis of epidemiological theory (based on random-mixing models) and network theory (based on work from the social sciences and graph theory). We then describe a variety of methods that allow the mixing network, or an approximation to the network, to be ascertained. It is often the case that time and resources limit our ability to accurately find all connections within a network, and hence a generic understanding of the relationship between network structure and disease dynamics is needed. Therefore, we review some of the variety of idealized network types and approximation techniques that have been utilized to elucidate this link. Finally, we look to the future to suggest how the two fields of network theory and epidemiological modelling can deliver an improved understanding of disease dynamics and better public health through effective disease control.

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Networks and epidemic models.

A wide range of communicable human diseases can be considered as spreading through a network of possible transmission routes. The implied network structure is vital in determining disease dynamics, especially when the average number of connections per individual is small as is the case for many sexually transmitted diseases (STDs). Here we develop an intuitive mathematical framework to deal with the heterogeneities implicit within contact networks and those that arise because of the infection process. These models are compared with full stochastic simulations and show excellent agreement across a wide range of parameters. We show how such models can be used to estimate parameters of epidemiological importance, and how they can be extended to examine the effectiveness of various control strategies, in particular screening programs and contact tracing.

https://www.pnas.org/content/pnas/99/20/13330.full.pdf

Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases.

Respondent-driven sampling (RDS) is a network-based technique for estimating traits in hard-to-reach populations, for example, the prevalence of HIV among drug injectors. In recent years RDS has been used in more than 120 studies in more than 20 countries and by leading public health organizations, including the Centers for Disease Control and Prevention in the United States. Despite the widespread use and growing popularity of RDS, there has been little empirical validation of the methodology. Here we investigate the performance of RDS by simulating sampling from 85 known, network populations. Across a variety of traits we find that RDS is substantially less accurate than generally acknowledged and that reported RDS confidence intervals are misleadingly narrow. Moreover, because we model a best-case scenario in which the theoretical RDS sampling assumptions hold exactly, it is unlikely that RDS performs any better in practice than in our simulations. Notably, the poor performance of RDS is driven not by the bias but by the high variance of estimates, a possibility that had been largely overlooked in the RDS literature. Given the consistency of our results across networks and our generous sampling conditions, we conclude that RDS as currently practiced may not be suitable for key aspects of public health surveillance where it is now extensively applied.

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Assessing respondent-driven sampling

OBJECTIVES: This study examined whether networks of drug-injecting and sexual relationships among drug injectors are associated with individual human immunodeficiency virus (HIV) serostatus and with behavioral likelihood of future infection. METHODS: A cross-sectional survey of 767 drug injectors in New York City was performed with chain-referral and linking procedures to measure large-scale (sociometric) risk networks. Graph-theoretic algebraic techniques were used to detect 92 connected components (drug injectors linked to each other directly or through others) and a 105-member 2-core within a large connected component of 230 members. RESULTS: Drug injectors in the 2-core of the large component were more likely than others to be infected with HIV. Seronegative 2-core members engaged in a wide range of high-risk behaviors, including engaging in risk behaviors with infected drug injectors. CONCLUSIONS: Sociometric risk networks seem to be pathways along which HIV travels in drug-injecting peer groups. The...

https://ajph.aphapublications.org/doi/pdfplus/10.2105/AJPH.87.8.1289

Sociometric risk networks and risk for HIV infection.

Although mixing patterns are thought to be important determinants of the spread of airborne infectious diseases, to our knowledge, there have been no attempts to directly quantify them for humans. We report on a preliminary study to identify such mixing patterns. A sample of 92 adults were asked to detail the individuals with whom they had conversed over the period of one, randomly assigned, day. Sixty-five (71%) completed the questionnaire, providing their age, the age of their contacts and the social context in which the contacts took place. The data were analysed using multilevel modelling. The study identified, and allowed the quantification of, contact patterns within this sample that may be of epidemiological significance. For example, the degree of assortativeness of mixing with respect to age was dependent not only on the age of participants but the number of contacts made. Estimates of the relative magnitude of contact rates between different social settings were made, with implications for outbreak potential. Simple questionnaire modifications are suggested which would yield information on the structure and dynamics of social networks and the intensity of contacts. Surveys of this nature may enable the quantification of who acquires infection from whom and from where.

/pdf/who-mixes-with-whom-a-method-to-determine-the-contact-a9sorpxqg0.pdf

Who mixes with whom? A method to determine the contact patterns of adults that may lead to the spread of airborne infections

OBJECTIVE To determine how heterosexuals at risk for HIV infection interconnect in social networks and how such relationships affect HIV transmission. DESIGN Cross-sectional study with face-to-face interviews to ascertain sociosexual connections; serologic testing. PARTICIPANTS Prostitute women (n = 133), their paying (n = 129) and non-paying (n = 47) male partners; injecting drug users (n = 200) and their sex partners (n = 41). Participants were recruited in sexually transmitted disease and methadone clinics, an HIV-testing site, and through street outreach in Colorado Springs, Colorado, USA. MAIN OUTCOME MEASURES Reported behaviors, risk perceptions, sociosexual linkages, and HIV prevalence. RESULTS Respondents were well informed, but reported engaging in high-risk behaviors frequently. Nevertheless, over 70% of respondents perceived themselves to be at low risk for HIV infection. The 595 respondents identified a social network of 5162 people to which they belonged. Network analytic methods indicated 147 separate connected components of this network; eight of the 19 HIV-positive individuals in the network were located in smaller components remote from the largest connected component. CONCLUSION The isolated position of HIV-positive individuals may serve as a barrier to HIV transmission and may account for the lack of diffusion of HIV in heterosexual populations in this region. Network analysis appears useful for understanding the dynamics of disease transmission and warrants further development as a tool for intervention and control.

Tammy S. Maldonado

Papers

Mapping a social network of heterosexuals at high risk for HIV infection.