Exploiting temporal network structures of human interaction to effectively immunize populations

Decreasing the number of people who must be vaccinated to immunize a community against an infectious disease could both save resources and decrease outbreak sizes. A key to reaching such a lower threshold of immunization is to find and vaccinate people who, through their behavior, are more likely than average to become infected and to spread the disease further. Fortunately, the very behavior that makes these people important to vaccinate can help us to localize them. Earlier studies have shown that one can use previous contacts to find people that are central in static contact networks. However, real contact patterns are not static. In this paper, we investigate if there is additional information in the temporal contact structure for vaccination protocols to exploit. We answer this affirmative by proposing two immunization methods that exploit temporal correlations and showing that these methods outperform a benchmark static-network protocol in four empirical contact datasets under various epidemic scenarios. Both methods rely only on obtainable, local information, and can be implemented in practice. For the datasets directly related to contact patterns of potential disease spreading (of sexually-transmitted and nosocomial infections respectively), the most efficient protocol is to sample people at random and vaccinate their latest contacts. The network datasets are temporal, which enables us to make more realistic evaluations than earlier studies--we use only information about the past for the purpose of vaccination, and about the future to simulate disease outbreaks. Using analytically tractable models, we identify two temporal structures that explain how the protocols earn their efficiency in the empirical data. This paper is a first step towards real vaccination protocols that exploit temporal-network structure--future work is needed both to characterize the structure of real contact sequences and to devise immunization methods that exploit these.     

The impact of imitation on vaccination behavior in social contact networks

Previous game-theoretic studies of vaccination behavior typically have often assumed that populations are homogeneously mixed and that individuals are fully rational. In reality, there is heterogeneity in the number of contacts per individual, and individuals tend to imitate others who appear to have adopted successful strategies. Here, we use network-based mathematical models to study the effects of both imitation behavior and contact heterogeneity on vaccination coverage and disease dynamics. We integrate contact network epidemiological models with a framework for decision-making, within which individuals make their decisions either based purely on payoff maximization or by imitating the vaccination behavior of a social contact. Simulations suggest that when the cost of vaccination is high imitation behavior may decrease vaccination coverage. However, when the cost of vaccination is small relative to that of infection, imitation behavior increases vaccination coverage, but, surprisingly, also increases the magnitude of epidemics through the clustering of non-vaccinators within the network. Thus, imitation behavior may impede the eradication of infectious diseases. Calculations that ignore behavioral clustering caused by imitation may significantly underestimate the levels of vaccination coverage required to attain herd immunity.     

Impact of Imitation Processes on the Effectiveness of?Ring Vaccination

Ring vaccination can be a highly effective control strategy for an emerging disease or in the final phase of disease eradication, as witnessed in the eradication of smallpox. However, the impact of behavioural dynamics on the effectiveness of ring vaccination has not been explored in mathematical models. Here, we analyze a series of stochastic models of voluntary ring vaccination. Contacts of an index case base vaccinating decisions on their own individual payoffs to vaccinate or not vaccinate, and they can also imitate the behaviour of other contacts of the index case. We find that including imitation changes the probability of containment through ring vaccination considerably. Imitation can cause a strong majority of contacts to choose vaccination in some cases, or to choose non-vaccination in other cases-even when the equivalent solution under perfectly rational (non-imitative) behaviour yields mixed choices. Moreover, imitation processes can result in very different outcomes in different stochastic realizations sampled from the same parameter distributions, by magnifying moderate tendencies toward one behaviour or the other: in some realizations, imitation causes a strong majority of contacts not to vaccinate, while in others, imitation promotes vaccination and reduces the number of secondary infections. Hence, the effectiveness of ring vaccination can depend significantly and unpredictably on imitation processes. Therefore, our results suggest that risk communication efforts should be initiated early in an outbreak when ring vaccination is to be applied, especially among subpopulations that are heavily influenced by peer opinions.     

Social Contact Networks and Disease Eradicability under Voluntary Vaccination

Certain theories suggest that it should be difficult or impossible to eradicate a vaccine-preventable disease under voluntary vaccination: Herd immunity implies that the individual incentive to vaccinate disappears at high coverage levels. Historically, there have been examples of declining coverage for vaccines, such as MMR vaccine and whole-cell pertussis vaccine, that are consistent with this theory. On the other hand, smallpox was globally eradicated by 1980 despite voluntary vaccination policies in many jurisdictions. Previous modeling studies of the interplay between disease dynamics and individual vaccinating behavior have assumed that infection is transmitted in a homogeneously mixing population. By comparison, here we simulate transmission of a vaccine-preventable SEIR infection through a random, static contact network. Individuals choose whether to vaccinate based on infection risks from neighbors, and based on vaccine risks. When neighborhood size is small, rational vaccinating behavior results in rapid containment of the infection through voluntary ring vaccination. As neighborhood size increases (while the average force of infection is held constant), a threshold is reached beyond which the infection can break through partially vaccinated rings, percolating through the whole population and resulting in considerable epidemic final sizes and a large number vaccinated. The former outcome represents convergence between individually and socially optimal outcomes, whereas the latter represents their divergence, as observed in most models of individual vaccinating behavior that assume homogeneous mixing. Similar effects are observed in an extended model using smallpox-specific natural history and transmissibility assumptions. This work illustrates the significant qualitative differences between behavior–infection dynamics in discrete contact-structured populations versus continuous unstructured populations. This work also shows how disease eradicability in populations where voluntary vaccination is the primary control mechanism may depend partly on whether the disease is transmissible only to a few close social contacts or to a larger subset of the population.     

Susceptible-infected-recovered epidemics in dynamic contact networks

Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for the duration of an outbreak. In reality, contact patterns may be quite fluid, with individuals frequently making and breaking social or sexual relationships. Here, we develop a mathematical approach to predicting disease transmission on dynamic networks in which each individual has a characteristic behaviour (typical contact number), but the identities of their contacts change in time. We show that dynamic contact patterns shape epidemiological dynamics in ways that cannot be adequately captured in static network models or mass-action models. Our new model interpolates smoothly between static network models and mass-action models using a mixing parameter, thereby providing a bridge between disparate classes of epidemiological models. Using epidemiological and sexual contact data from an Atlanta high school, we demonstrate the application of this method for forecasting and controlling sexually transmitted disease outbreaks.     

Effects of heterogeneous and clustered contact patterns on infectious disease dynamics

The spread of infectious diseases fundamentally depends on the pattern of contacts between individuals. Although studies of contact networks have shown that heterogeneity in the number of contacts and the duration of contacts can have far-reaching epidemiological consequences, models often assume that contacts are chosen at random and thereby ignore the sociological, temporal and/or spatial clustering of contacts. Here we investigate the simultaneous effects of heterogeneous and clustered contact patterns on epidemic dynamics. To model population structure, we generalize the configuration model which has a tunable degree distribution (number of contacts per node) and level of clustering (number of three cliques). To model epidemic dynamics for this class of random graph, we derive a tractable, low-dimensional system of ordinary differential equations that accounts for the effects of network structure on the course of the epidemic. We find that the interaction between clustering and the degree distribution is complex. Clustering always slows an epidemic, but simultaneously increasing clustering and the variance of the degree distribution can increase final epidemic size. We also show that bond percolation-based approximations can be highly biased if one incorrectly assumes that infectious periods are homogeneous, and the magnitude of this bias increases with the amount of clustering in the network. We apply this approach to model the high clustering of contacts within households, using contact parameters estimated from survey data of social interactions, and we identify conditions under which network models that do not account for household structure will be biased.     

Network frailty and the geometry of herd immunity

The spread of infectious disease through communities depends fundamentally on the underlying patterns of contacts between individuals. Generally, the more contacts one individual has, the more vulnerable they are to infection during an epidemic. Thus, outbreaks disproportionately impact the most highly connected demographics. Epidemics can then lead, through immunization or removal of individuals, to sparser networks that are more resistant to future transmission of a given disease. Using several classes of contact networks-Poisson, scale-free and small-world-we characterize the structural evolution of a network due to an epidemic in terms of frailty (the degree to which highly connected individuals are more vulnerable to infection) and interference (the extent to which the epidemic cuts off connectivity among the susceptible population that remains following an epidemic). The evolution of the susceptible network over the course of an epidemic differs among the classes of networks; frailty, relative to interference, accounts for an increasing component of network evolution on networks with greater variance in contacts. The result is that immunization due to prior epidemics can provide greater community protection than random vaccination on networks with heterogeneous contact patterns, while the reverse is true for highly structured populations.     

Policy Resistance Undermines Superspreader Vaccination Strategies for Influenza

Theoretical models of infection spread on networks predict that targeting vaccination at individuals with a very large number of contacts (superspreaders) can reduce infection incidence by a significant margin. These models generally assume that superspreaders will always agree to be vaccinated. Hence, they cannot capture unintended consequences such as policy resistance, where the behavioral response induced by a new vaccine policy tends to reduce the expected benefits of the policy. Here, we couple a model of influenza transmission on an empirically-based contact network with a psychologically structured model of influenza vaccinating behavior, where individual vaccinating decisions depend on social learning and past experiences of perceived infections, vaccine complications and vaccine failures. We find that policy resistance almost completely undermines the effectiveness of superspreader strategies: the most commonly explored approaches that target a randomly chosen neighbor of an individual, or that preferentially choose neighbors with many contacts, provide at best a relative improvement over their non-targeted counterpart as compared to when behavioral feedbacks are ignored. Increased vaccine coverage in super spreaders is offset by decreased coverage in non-superspreaders, and superspreaders also have a higher rate of perceived vaccine failures on account of being infected more often. Including incentives for vaccination provides modest improvements in outcomes. We conclude that the design of influenza vaccine strategies involving widespread incentive use and/or targeting of superspreaders should account for policy resistance, and mitigate it whenever possible.     

Social encounter networks: characterizing Great Britain

A major goal of infectious disease epidemiology is to understand and predict the spread of infections within human populations, with the intention of better informing decisions regarding control and intervention. However, the development of fully mechanistic models of transmission requires a quantitative understanding of social interactions and collective properties of social networks. We performed a cross-sectional study of the social contacts on given days for more than 5000 respondents in England, Scotland and Wales, through postal and online survey methods. The survey was designed to elicit detailed and previously unreported measures of the immediate social network of participants relevant to infection spread. Here, we describe individual-level contact patterns, focusing on the range of heterogeneity observed and discuss the correlations between contact patterns and other socio-demographic factors. We find that the distribution of the number of contacts approximates a power-law distribution, but postulate that total contact time (which has a shorter-tailed distribution) is more epidemiologically relevant. We observe that children, public-sector and healthcare workers have the highest number of total contact hours and are therefore most likely to catch and transmit infectious disease. Our study also quantifies the transitive connections made between an individual''s contacts (or clustering); this is a key structural characteristic of social networks with important implications for disease transmission and control efficacy. Respondents'' networks exhibit high levels of clustering, which varies across social settings and increases with duration, frequency of contact and distance from home. Finally, we discuss the implications of these findings for the transmission and control of pathogens spread through close contact.     

Revealing mechanisms of infectious disease spread through empirical contact networks

The spread of pathogens fundamentally depends on the underlying contacts between individuals. Modeling the dynamics of infectious disease spread through contact networks, however, can be challenging due to limited knowledge of how an infectious disease spreads and its transmission rate. We developed a novel statistical tool, INoDS (Identifying contact Networks of infectious Disease Spread) that estimates the transmission rate of an infectious disease outbreak, establishes epidemiological relevance of a contact network in explaining the observed pattern of infectious disease spread and enables model comparison between different contact network hypotheses. We show that our tool is robust to incomplete data and can be easily applied to datasets where infection timings of individuals are unknown. We tested the reliability of INoDS using simulation experiments of disease spread on a synthetic contact network and find that it is robust to incomplete data and is reliable under different settings of network dynamics and disease contagiousness compared with previous approaches. We demonstrate the applicability of our method in two host-pathogen systems: Crithidia bombi in bumblebee colonies and Salmonella in wild Australian sleepy lizard populations. INoDS thus provides a novel and reliable statistical tool for identifying transmission pathways of infectious disease spread. In addition, application of INoDS extends to understanding the spread of novel or emerging infectious disease, an alternative approach to laboratory transmission experiments, and overcoming common data-collection constraints.     

Dynamics and Control of Diseases in Networks with Community Structure

The dynamics of infectious diseases spread via direct person-to-person transmission (such as influenza, smallpox, HIV/AIDS, etc.) depends on the underlying host contact network. Human contact networks exhibit strong community structure. Understanding how such community structure affects epidemics may provide insights for preventing the spread of disease between communities by changing the structure of the contact network through pharmaceutical or non-pharmaceutical interventions. We use empirical and simulated networks to investigate the spread of disease in networks with community structure. We find that community structure has a major impact on disease dynamics, and we show that in networks with strong community structure, immunization interventions targeted at individuals bridging communities are more effective than those simply targeting highly connected individuals. Because the structure of relevant contact networks is generally not known, and vaccine supply is often limited, there is great need for efficient vaccination algorithms that do not require full knowledge of the network. We developed an algorithm that acts only on locally available network information and is able to quickly identify targets for successful immunization intervention. The algorithm generally outperforms existing algorithms when vaccine supply is limited, particularly in networks with strong community structure. Understanding the spread of infectious diseases and designing optimal control strategies is a major goal of public health. Social networks show marked patterns of community structure, and our results, based on empirical and simulated data, demonstrate that community structure strongly affects disease dynamics. These results have implications for the design of control strategies.     

Bistability of Evolutionary Stable Vaccination Strategies in the Reinfection SIRI Model

We use the reinfection SIRI epidemiological model to analyze the impact of education programs and vaccine scares on individuals decisions to vaccinate or not. The presence of the reinfection provokes the novelty of the existence of three Nash equilibria for the same level of the morbidity relative risk instead of a single Nash equilibrium as occurs in the SIR model studied by Bauch and Earn (PNAS 101:13391–13394, 2004). The existence of three Nash equilibria, with two of them being evolutionary stable, introduces two scenarios with relevant and opposite features for the same level of the morbidity relative risk: the low-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a low probability; and the high-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a high probability. We introduce the evolutionary vaccination dynamics for the SIRI model and we prove that it is bistable. The bistability of the evolutionary dynamics indicates that the damage provoked by false scares on the vaccination perceived morbidity risks can be much higher and much more persistent than in the SIR model. Furthermore, the vaccination education programs to be efficient they need to implement a mechanism to suddenly increase the vaccination coverage level.     

Inferring a District-Based Hierarchical Structure of Social Contacts from Census Data

Researchers have recently paid attention to social contact patterns among individuals due to their useful applications in such areas as epidemic evaluation and control, public health decisions, chronic disease research and social network research. Although some studies have estimated social contact patterns from social networks and surveys, few have considered how to infer the hierarchical structure of social contacts directly from census data. In this paper, we focus on inferring an individual’s social contact patterns from detailed census data, and generate various types of social contact patterns such as hierarchical-district-structure-based, cross-district and age-district-based patterns. We evaluate newly generated contact patterns derived from detailed 2011 Hong Kong census data by incorporating them into a model and simulation of the 2009 Hong Kong H1N1 epidemic. We then compare the newly generated social contact patterns with the mixing patterns that are often used in the literature, and draw the following conclusions. First, the generation of social contact patterns based on a hierarchical district structure allows for simulations at different district levels. Second, the newly generated social contact patterns reflect individuals social contacts. Third, the newly generated social contact patterns improve the accuracy of the SEIR-based epidemic model.     

Individual risk perception and empirical social structures shape the dynamics of infectious disease outbreaks

The dynamics of a spreading disease and individual behavioral changes are entangled processes that have to be addressed together in order to effectively manage an outbreak. Here, we relate individual risk perception to the adoption of a specific set of control measures, as obtained from an extensive large-scale survey performed via Facebook—involving more than 500,000 respondents from 64 countries—showing that there is a “one-to-one” relationship between perceived epidemic risk and compliance with a set of mitigation rules. We then develop a mathematical model for the spreading of a disease—sharing epidemiological features with COVID-19—that explicitly takes into account non-compliant individual behaviors and evaluates the impact of a population fraction of infectious risk-deniers on the epidemic dynamics. Our modeling study grounds on a wide set of structures, including both synthetic and more than 180 real-world contact patterns, to evaluate, in realistic scenarios, how network features typical of human interaction patterns impact the spread of a disease. In both synthetic and real contact patterns we find that epidemic spreading is hindered for decreasing population fractions of risk-denier individuals. From empirical contact patterns we demonstrate that connectivity heterogeneity and group structure significantly affect the peak of hospitalized population: higher modularity and heterogeneity of social contacts are linked to lower peaks at a fixed fraction of risk-denier individuals while, at the same time, such features increase the relative impact on hospitalizations with respect to the case where everyone correctly perceive the risks.     

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.     

Seasonal Influenza Vaccination amongst Medical Students: A Social Network Analysis Based on a Cross-Sectional Study

Introduction

The Chief Medical Officer for England recommends that healthcare workers have a seasonal influenza vaccination in an attempt to protect both patients and NHS staff. Despite this, many healthcare workers do not have a seasonal influenza vaccination. Social network analysis is a well-established research approach that looks at individuals in the context of their social connections. We examine the effects of social networks on influenza vaccination decision and disease dynamics.

Methods

We used a social network analysis approach to look at vaccination distribution within the network of the Lancaster Medical School students and combined these data with the students’ beliefs about vaccination behaviours. We then developed a model which simulated influenza outbreaks to study the effects of preferentially vaccinating individuals within this network.

Results

Of the 253 eligible students, 217 (86%) provided relational data, and 65% of responders had received a seasonal influenza vaccination. Students who were vaccinated were more likely to think other medical students were vaccinated. However, there was no clustering of vaccinated individuals within the medical student social network. The influenza simulation model demonstrated that vaccination of well-connected individuals may have a disproportional effect on disease dynamics.

Conclusions

This medical student population exhibited vaccination coverage levels similar to those seen in other healthcare groups but below recommendations. However, in this population, a lack of vaccination clustering might provide natural protection from influenza outbreaks. An individual student’s perception of the vaccination coverage amongst their peers appears to correlate with their own decision to vaccinate, but the directionality of this relationship is not clear. When looking at the spread of disease within a population it is important to include social structures alongside vaccination data. Social networks influence disease epidemiology and vaccination campaigns designed with information from social networks could be a future target for policy makers.     

The dynamic nature of contact networks in infectious disease epidemiology

Although contact network models have yielded important insights into infectious disease transmission and control throughout the last decade, researchers have just begun to explore the dynamic nature of contact patterns and their epidemiological significance. Most network models have assumed that contacts are static through time. Developing more realistic models of the social interactions that underlie the spread of infectious diseases thus remains an important challenge for both data gatherers and modelers. In this article, we review some recent data-driven and process-driven approaches that capture the dynamics of human contact, and discuss future challenges for the field.     

Disease Interventions Can Interfere with One Another through Disease-Behaviour Interactions

Theoretical models of disease dynamics on networks can aid our understanding of how infectious diseases spread through a population. Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccination choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. However, these two interventions are usually modelled separately. Here, we construct a simulation model of influenza transmission through a contact network, where individuals can choose whether to become vaccinated and/or practice NPIs. These decisions are based on previous experience with the disease, the current state of infection amongst one''s contacts, and the personal and social impacts of the choices they make. We find that the interventions interfere with one another: because of negative feedback between intervention uptake and infection prevalence, it is difficult to simultaneously increase uptake of all interventions by changing utilities or perceived risks. However, on account of vaccine efficacy being higher than NPI efficacy, measures to expand NPI practice have only a small net impact on influenza incidence due to strongly mitigating feedback from vaccinating behaviour, whereas expanding vaccine uptake causes a significant net reduction in influenza incidence, despite the reduction of NPI practice in response. As a result, measures that support expansion of only vaccination (such as reducing vaccine cost), or measures that simultaneously support vaccination and NPIs (such as emphasizing harms of influenza infection, or satisfaction from preventing infection in others through both interventions) can significantly reduce influenza incidence, whereas measures that only support expansion of NPI practice (such as making hand sanitizers more available) have little net impact on influenza incidence. (However, measures that improve NPI efficacy may fare better.) We conclude that the impact of interference on programs relying on multiple interventions should be more carefully studied, for both influenza and other infectious diseases.     

Contact Patterns in a High School: A Comparison between Data Collected Using Wearable Sensors,Contact Diaries and Friendship Surveys

Given their importance in shaping social networks and determining how information or transmissible diseases propagate in a population, interactions between individuals are the subject of many data collection efforts. To this aim, different methods are commonly used, ranging from diaries and surveys to decentralised infrastructures based on wearable sensors. These methods have each advantages and limitations but are rarely compared in a given setting. Moreover, as surveys targeting friendship relations might suffer less from memory biases than contact diaries, it is interesting to explore how actual contact patterns occurring in day-to-day life compare with friendship relations and with online social links. Here we make progresses in these directions by leveraging data collected in a French high school and concerning (i) face-to-face contacts measured by two concurrent methods, namely wearable sensors and contact diaries, (ii) self-reported friendship surveys, and (iii) online social links. We compare the resulting data sets and find that most short contacts are not reported in diaries while long contacts have a large reporting probability, and that the durations of contacts tend to be overestimated in the diaries. Moreover, measured contacts corresponding to reported friendship can have durations of any length but all long contacts do correspond to a reported friendship. On the contrary, online links that are not also reported in the friendship survey correspond to short face-to-face contacts, highlighting the difference of nature between reported friendships and online links. Diaries and surveys suffer moreover from a low sampling rate, as many students did not fill them, showing that the sensor-based platform had a higher acceptability. We also show that, despite the biases of diaries and surveys, the overall structure of the contact network, as quantified by the mixing patterns between classes, is correctly captured by both networks of self-reported contacts and of friendships, and we investigate the correlations between the number of neighbors of individuals in the three networks. Overall, diaries and surveys tend to yield a correct picture of the global structural organization of the contact network, albeit with much less links, and give access to a sort of backbone of the contact network corresponding to the strongest links, i.e., the contacts of longest cumulative durations.