How disease models in static networks can fail to approximate disease in dynamic networks

Bifurcation analysis in an epidemic model on adaptive networks

In this paper, we study a delayed adaptive network epidemic model in which the local spatial connections of susceptible and susceptible individuals have time-delay effects on the rate of demographic change of local spatial connections of susceptible and susceptible individuals. We prove that the Hopf bifurcation occurs at the critical value τ₀ with delay τ as the bifurcation parameter. Then, by using the normal form method and the central manifold theory, the criteria for the bifurcation direction and stability are derived. Finally, numerical simulations are presented to show the feasibility of our results.

A model for leveraging animal movement to understand spatio-temporal disease dynamics

The ongoing explosion of fine-resolution movement data in animal systems provides a unique opportunity to empirically quantify spatial, temporal and individual variation in transmission risk and improve our ability to forecast disease outbreaks. However, we lack a generalizable model that can leverage movement data to quantify transmission risk and how it affects pathogen invasion and persistence on heterogeneous landscapes. We developed a flexible model 'Movement-driven modelling of spatio-temporal infection risk' (MoveSTIR) that leverages diverse data on animal movement to derive metrics of direct and indirect contact by decomposing transmission into constituent processes of contact formation and duration and pathogen deposition and acquisition. We use MoveSTIR to demonstrate that ignoring fine-scale animal movements on actual landscapes can mis-characterize transmission risk and epidemiological dynamics. MoveSTIR unifies previous work on epidemiological contact networks and can address applied and theoretical questions at the nexus of movement and disease ecology.

How territoriality reduces disease transmission among social insect colonies

Abstract

Social behavior can have a major impact on the dynamics of infectious disease outbreaks. For animals that live in dense social groups, such as the eusocial insects, pathogens pose an especially large risk because frequent contacts among individuals can allow rapid spread within colonies. While there has been a large body of work examining adaptations to mitigate the spread of infectious disease within social insect colonies, there has been less work on strategies to prevent the introduction of pathogens into colonies in the first place. We develop an agent-based model to examine the effect of territorial behavior on the transmission of infectious diseases between social insect colonies. We find that by preventing the introduction of infected foreign workers into a colony, territoriality can flatten the curve of an epidemic, delaying the introduction of an infectious disease and reducing its maximum prevalence, but only for diseases with moderate to low transmissibility. Our results have implications for understanding how pathogen risk influences the evolution of territorial behavior in social insects and other highly social animals.

Significance statement

Infectious disease outbreaks can impose a large fitness cost to animals that live in social groups. The frequency and pattern of contacts both within and among groups can have a large impact on the speed and extent of an epidemic. Using an individual-based model, we examined how the exclusion of foreign workers from a territory around the nest influences disease transmission between social insect colonies. We find that territoriality can protect colonies from outbreaks of low to moderately contagious pathogens by delaying the spillover from other colonies and reducing the maximum number of workers who are infected. These results suggest that the relative threat posed by infectious diseases may have played an important role in shaping the diversity of territorial behaviors seen in different social insect species.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00265-021-03095-0.

COVID-19 related interdisciplinary methods: Preventing errors and detecting research opportunities

More than 130,000 peer-reviewed studies have been published within one year after COVID-19 emerged in many countries. This large and rapidly growing field may overwhelm the synthesizing abilities of both researchers and policy-makers. To provide a sinopsis, prevent errors, and detect cognitive gaps that may require interdisciplinary research methods, the literature on COVID-19 is summarized, twice. The overall purpose of this study is to generate a dialogue meant to explain the genesis of and/or find remedies for omissions and contradictions. The first review starts in Biology and ends in Policy. Policy is chosen as a destination because it is the setting where cognitive integration must occur. The second review follows the opposite path: it begins with stated policies on COVID-19 and then their assumptions and disciplinary relationships are identified. The purpose of this interdisciplinary method on methods is to yield a relational and explanatory view of the field -one strategy likely to be incomplete but usable when large bodies of literature need to be rapidly summarized. These reviews identify nine inter-related problems, research needs, or omissions, namely: (1) nation-wide, geo-referenced, epidemiological data collection systems (open to and monitored by the public); (2) metrics meant to detect non-symptomatic cases -e.g., test positivity-; (3) cost-benefit oriented methods, which should demonstrate they detect silent viral spreaders even with limited testing; (4) new personalized tests that inform on biological functions and disease correlates, such as cell-mediated immunity, co-morbidities, and immuno-suppression; (5) factors that influence vaccine effectiveness; (6) economic predictions that consider the long-term consequences likely to follow epidemics that growth exponentially; (7) the errors induced by self-limiting and/or implausible paradigms, such as binary and reductionist approaches; (8) new governance models that emphasize problem-solving skills, social participation, and the use of scientific knowledge; and (9) new educational programs that utilize visual aids and audience-specific communication strategies. The analysis indicates that, to optimally address these problems, disciplinary and social integration is needed. By asking what is/are the potential cause(s) and consequence(s) of each issue, this methodology generates visualizations that reveal possible relationships as well as omissions and contradictions. While inherently limited in scope and likely to become obsolete, these shortcomings are avoided when this 'method on methods' is frequently practiced. Open-ended, inter-/trans-disciplinary perspectives and broad social participation may help researchers and citizens to construct, de-construct, and re-construct COVID-19 related research.

Concurrency measures in the era of temporal network epidemiology: a review

Diseases spread over temporal networks of interaction events between individuals. Structures of these temporal networks hold the keys to understanding epidemic propagation. One early concept of the literature to aid in discussing these structures is concurrency-quantifying individuals' tendency to form time-overlapping 'partnerships'. Although conflicting evaluations and an overabundance of operational definitions have marred the history of concurrency, it remains important, especially in the area of sexually transmitted infections. Today, much of theoretical epidemiology uses more direct models of contact patterns, and there is an emerging body of literature trying to connect methods to the concurrency literature. In this review, we will cover the development of the concept of concurrency and these new approaches.

The role of social structure and dynamics in the maintenance of endemic disease

Social interactions are required for the direct transmission of infectious diseases. Consequently, the social network structure of populations plays a key role in shaping infectious disease dynamics. A huge research effort has examined how specific social network structures make populations more (or less) vulnerable to damaging epidemics. However, it can be just as important to understand how social networks can contribute to endemic disease dynamics, in which pathogens are maintained at stable levels for prolonged periods of time. Hosts that can maintain endemic disease may serve as keystone hosts for multi-host pathogens within an ecological community, and also have greater potential to act as key wildlife reservoirs of agricultural and zoonotic diseases. Here, we examine combinations of social and demographic processes that can foster endemic disease in hosts. We synthesise theoretical and empirical work to demonstrate the importance of both social structure and social dynamics in maintaining endemic disease. We also highlight the importance of distinguishing between the local and global persistence of infection and reveal how different social processes drive variation in the scale at which infectious diseases appear endemic. Our synthesis provides a framework by which to understand how sociality contributes to the long-term maintenance of infectious disease in wildlife hosts and provides a set of tools to unpick the social and demographic mechanisms involved in any given host-pathogen system.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00265-021-03055-8.

How disease constrains the evolution of social systems

Animal populations are occasionally shocked by epidemics of contagious diseases. The ability of social systems to withstand epidemic shocks and mitigate disruptions could shape the evolution of complex animal societies. We present a mathematical model to explore the potential impact of disease on the evolutionary fitness of different organizational strategies for populations of social species whose survival depends on collaborative efficiency. We show that infectious diseases select for a specific feature in the organization of collaborative roles-cohort stability-and that this feature is costly, and therefore unlikely to be maintained in environments where infection risks are absent. Our study provides evidence for an often-stated (but rarely supported) claim that pathogens have been the dominant force shaping the complexity of division of labour in eusocial societies of honeybees and termites and establishes a general theoretical approach for assessing evolutionary constraints on social organization from disease risk in other collaborative taxa.

Individual Specialization and Multihost Epidemics: Disease Spread in Plant-Pollinator Networks

Many parasites infect multiple species and persist through a combination of within- and between-species transmission. Multispecies transmission networks are typically constructed at the species level, linking two species if any individuals of those species interact. However, generalist species often consist of specialized individuals that prefer different subsets of available resources, so individual- and species-level contact networks can differ systematically. To explore the epidemiological impacts of host specialization, we build and study a model for pollinator pathogens on plant-pollinator networks, in which individual pollinators have dynamic preferences for different flower species. We find that modeling and analysis that ignore individual host specialization can predict die-off of a disease that is actually strongly persistent and can badly over- or underpredict steady-state disease prevalence. Effects of individual preferences remain substantial whenever mean preference duration exceeds half of the mean time from infection to recovery or death. Similar results hold in a model where hosts foraging in different habitats have different frequencies of contact with an environmental reservoir for the pathogen. Thus, even if all hosts have the same long-run average behavior, dynamic individual differences can profoundly affect disease persistence and prevalence.

Description of social contacts among student cases of pandemic influenza during the containment phase, Melbourne, Australia, 2009

Introduction

Students comprised the majority of early cases of influenza A(H1N1)pdm09 in Melbourne, Australia. Students and school settings were targeted for public health interventions following the emergence of pH1N1. This study was conducted to describe changes in social contacts among the earliest confirmed student cases of pH1N1 in Melbourne, Australia, to inform future pandemic control policy and explore transmission model assumptions.

Methods

A retrospective cross-sectional behavioural study of student cases with laboratory-confirmed pH1N1 between 28 April and 3 June 2009 was conducted in 2009. Demographics, symptom onset dates and detailed information on regular and additional extracurricular activities were collected. Summary measures for activities were calculated, including median group size and median number of close contacts and attendance during the students’ exposure and infectious periods or during school closures. A multivariable model was used to assess associations between rates of participation in extracurricular activities and both school closures and students’ infectious periods.

Results

Among 162 eligible cases, 99 students participated. Students reported social contact in both curricular and extra-curricular activities. Group size and total number of close contacts varied. While participation in activities decreased during the students’ infectious periods and during school closures, social contact was common during periods when isolation was advised and during school closures.

Discussion

This study demonstrates the potential central role of young people in pandemic disease transmission given the level of non-adherence to prevention and control measures. These finding have public health implications for both informing modelling estimates of future pandemics and targeting prevention and control strategies to young people.

Epidemic Threshold in Continuous-Time Evolving Networks

Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the weak commutation condition allowing the interpretation of annealed networks, activity-driven networks, and time scale separation into one formalism. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.

Advances from the nexus of animal behaviour and pathogen transmission: new directions and opportunities using contact networks

Contact network models have enabled significant advances in understanding the influence of behaviour on parasite and pathogen transmission. They are an important tool that links variation in individual behaviour, to epidemiological consequences at the population level. Here, in our introduction to this special issue, we highlight the importance of applying network approaches to disease ecological and epidemiological questions, and how this has provided a much deeper understanding of these research areas. Recent advances in tracking host behaviour (bio-logging: e.g., GPS tracking, barcoding) and tracking pathogens (high-resolution sequencing), as well as methodological advances (multi-layer networks, computational techniques) started producing exciting new insights into disease transmission through contact networks. We discuss some of the exciting directions that the field is taking, some of the challenges, and importantly the opportunities that lie ahead. For instance, we suggest to integrate multiple transmission pathways, multiple pathogens, and in some systems, multiple host species, into the next generation of network models. Corresponding opportunities exist in utilising molecular techniques, such as high-resolution sequencing, to establish causality in network connectivity and disease outcomes. Such novel developments and the continued integration of network tools offers a more complete understanding of pathogen transmission processes, their underlying mechanisms and their evolutionary consequences.

Sampling of temporal networks: Methods and biases

Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example, human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is that they are sampled within temporal and spatial frames. Furthermore, one might wish to subsample networks to reduce their size for better visualization or to perform computationally intensive simulations. The sampling method may affect the network structure and thus caution is necessary to generalize results based on samples. In this paper, we study four sampling strategies applied to a variety of real-life temporal networks. We quantify the biases generated by each sampling strategy on a number of relevant statistics such as link activity, temporal paths and epidemic spread. We find that some biases are common in a variety of networks and statistics, but one strategy, uniform sampling of nodes, shows improved performance in most scenarios. Given the particularities of temporal network data and the variety of network structures, we recommend that the choice of sampling methods be problem oriented to minimize the potential biases for the specific research questions on hand. Our results help researchers to better design network data collection protocols and to understand the limitations of sampled temporal network data.

Control of epidemics via social partnership adjustment

Epidemic control is of great importance for human society. Adjusting interacting partners is an effective individualized control strategy. Intuitively, it is done either by shortening the interaction time between susceptible and infected individuals or by increasing the opportunities for contact between susceptible individuals. Here, we provide a comparative study on these two control strategies by establishing an epidemic model with nonuniform stochastic interactions. It seems that the two strategies should be similar, since shortening the interaction time between susceptible and infected individuals somehow increases the chances for contact between susceptible individuals. However, analytical results indicate that the effectiveness of the former strategy sensitively depends on the infectious intensity and the combinations of different interaction rates, whereas the latter one is quite robust and efficient. Simulations are shown to verify our analytical predictions. Our work may shed light on the strategic choice of disease control.

Data-driven network modelling of disease transmission using complete population movement data: spread of VTEC O157 in Swedish cattle

European Union legislation requires member states to keep national databases of all bovine animals. This allows for disease spread models that includes the time-varying contact network and population demographic. However, performing data-driven simulations with a high degree of detail are computationally challenging. We have developed an efficient and flexible discrete-event simulator SimInf for stochastic disease spread modelling that divides work among multiple processors to accelerate the computations. The model integrates disease dynamics as continuous-time Markov chains and livestock data as events. In this study, all Swedish livestock data (births, movements and slaughter) from July 1st 2005 to December 31st 2013 were included in the simulations. Verotoxigenic Escherichia coli O157:H7 (VTEC O157) are capable of causing serious illness in humans. Cattle are considered to be the main reservoir of the bacteria. A better understanding of the epidemiology in the cattle population is necessary to be able to design and deploy targeted measures to reduce the VTEC O157 prevalence and, subsequently, human exposure. To explore the spread of VTEC O157 in the entire Swedish cattle population during the period under study, a within- and between-herd disease spread model was used. Real livestock data was incorporated to model demographics of the population. Cattle were moved between herds according to real movement data. The results showed that the spatial pattern in prevalence may be due to regional differences in livestock movements. However, the movements, births and slaughter of cattle could not explain the temporal pattern of VTEC O157 prevalence in cattle, despite their inherently distinct seasonality.

The Effect of Keystone Individuals on Collective Outcomes Can Be Mediated through Interactions or Behavioral Persistence

Collective behavior emerges from interactions among group members who often vary in their behavior. The presence of just one or a few keystone individuals, such as leaders or tutors, may have a large effect on collective outcomes. These individuals can catalyze behavioral changes in other group members, thus altering group composition and collective behavior. The influence of keystone individuals on group function may lead to trade-offs between ecological situations, because the behavioral composition they facilitate may be suitable in one situation but not another. We use computer simulations to examine various mechanisms that allow keystone individuals to exert their influence on group members. We further discuss a trade-off between two potentially conflicting collective outcomes, cooperative prey attack and disease dynamics. Our simulations match empirical data from a social spider system and produce testable predictions for the causes and consequences of the influence of keystone individuals on group composition and collective outcomes. We find that a group's behavioral composition can be impacted by the keystone individual through changes to interaction patterns or behavioral persistence over time. Group behavioral composition and the mechanisms that drive the distribution of phenotypes influence collective outcomes and lead to trade-offs between disease dynamics and cooperative prey attack.

Individual differences in boldness influence patterns of social interactions and the transmission of cuticular bacteria among group-mates

Despite the importance of host attributes for the likelihood of associated microbial transmission, individual variation is seldom considered in studies of wildlife disease. Here, we test the influence of host phenotypes on social network structure and the likelihood of cuticular bacterial transmission from exposed individuals to susceptible group-mates using female social spiders (Stegodyphus dumicola). Based on the interactions of resting individuals of known behavioural types, we assessed whether individuals assorted according to their behavioural traits. We found that individuals preferentially interacted with individuals of unlike behavioural phenotypes. We next applied a green fluorescent protein-transformed cuticular bacterium,Pantoeasp., to individuals and allowed them to interact with an unexposed colony-mate for 24 h. We found evidence for transmission of bacteria in 55% of cases. The likelihood of transmission was influenced jointly by the behavioural phenotypes of both the exposed and susceptible individuals: transmission was more likely when exposed spiders exhibited higher 'boldness' relative to their colony-mate, and when unexposed individuals were in better body condition. Indirect transmission via shared silk took place in only 15% of cases. Thus, bodily contact appears key to transmission in this system. These data represent a fundamental step towards understanding how individual traits influence larger-scale social and epidemiological dynamics.

Using national movement databases to help inform responses to swine disease outbreaks in Scotland: the impact of uncertainty around incursion time

Modelling is an important component of contingency planning and control of disease outbreaks. Dynamic network models are considered more useful than static models because they capture important dynamic patterns of farm behaviour as evidenced through animal movements. This study evaluates the usefulness of a dynamic network model of swine fever to predict pre-detection spread via movements of pigs, when there may be considerable uncertainty surrounding the time of incursion of infection. It explores the utility and limitations of animal movement data to inform such models and as such, provides some insight into the impact of improving traceability through real-time animal movement reporting and the use of electronic animal movement databases. The study concludes that the type of premises and uncertainty of the time of disease incursion will affect model accuracy and highlights the need for improvements in these areas.

Experimental resource pulses influence social-network dynamics and the potential for information flow in tool-using crows

Social-network dynamics have profound consequences for biological processes such as information flow, but are notoriously difficult to measure in the wild. We used novel transceiver technology to chart association patterns across 19 days in a wild population of the New Caledonian crow--a tool-using species that may socially learn, and culturally accumulate, tool-related information. To examine the causes and consequences of changing network topology, we manipulated the environmental availability of the crows' preferred tool-extracted prey, and simulated, in silico, the diffusion of information across field-recorded time-ordered networks. Here we show that network structure responds quickly to environmental change and that novel information can potentially spread rapidly within multi-family communities, especially when tool-use opportunities are plentiful. At the same time, we report surprisingly limited social contact between neighbouring crow communities. Such scale dependence in information-flow dynamics is likely to influence the evolution and maintenance of material cultures.

Understanding Social Contagion in Adoption Processes Using Dynamic Social Networks

There are many studies in the marketing and diffusion literature of the conditions in which social contagion affects adoption processes. Yet most of these studies assume that social interactions do not change over time, even though actors in social networks exhibit different likelihoods of being influenced across the diffusion period. Rooted in physics and epidemiology theories, this study proposes a Susceptible Infectious Susceptible (SIS) model to assess the role of social contagion in adoption processes, which takes changes in social dynamics over time into account. To study the adoption over a span of ten years, the authors used detailed data sets from a community of consumers and determined the importance of social contagion, as well as how the interplay of social and non-social influences from outside the community drives adoption processes. Although social contagion matters for diffusion, it is less relevant in shaping adoption when the study also includes social dynamics among members of the community. This finding is relevant for managers and entrepreneurs who trust in word-of-mouth marketing campaigns whose effect may be overestimated if marketers fail to acknowledge variations in social interactions.

Information content of contact-pattern representations and predictability of epidemic outbreaks

To understand the contact patterns of a population--who is in contact with whom, and when the contacts happen--is crucial for modeling outbreaks of infectious disease. Traditional theoretical epidemiology assumes that any individual can meet any with equal probability. A more modern approach, network epidemiology, assumes people are connected into a static network over which the disease spreads. Newer yet, temporal network epidemiology, includes the time in the contact representations. In this paper, we investigate the effect of these successive inclusions of more information. Using empirical proximity data, we study both outbreak sizes from unknown sources, and from known states of ongoing outbreaks. In the first case, there are large differences going from a fully mixed simulation to a network, and from a network to a temporal network. In the second case, differences are smaller. We interpret these observations in terms of the temporal network structure of the data sets. For example, a fast overturn of nodes and links seem to make the temporal information more important.

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.

Spatial-Temporal Dynamics of High-Resolution Animal Networks: What Can We Learn from Domestic Animals?

Animal social network is the key to understand many ecological and epidemiological processes. We used real-time location system (RTLS) to accurately track cattle position, analyze their proximity networks, and tested the hypothesis of temporal stationarity and spatial homogeneity in these networks during different daily time periods and in different areas of the pen. The network structure was analyzed using global network characteristics (network density), subgroup clustering (modularity), triadic property (transitivity), and dyadic interactions (correlation coefficient from a quadratic assignment procedure) at hourly level. We demonstrated substantial spatial-temporal heterogeneity in these networks and potential link between indirect animal-environment contact and direct animal-animal contact. But such heterogeneity diminished if data were collected at lower spatial (aggregated at entire pen level) or temporal (aggregated at daily level) resolution. The network structure (described by the characteristics such as density, modularity, transitivity, etc.) also changed substantially at different time and locations. There were certain time (feeding) and location (hay) that the proximity network structures were more consistent based on the dyadic interaction analysis. These results reveal new insights for animal network structure and spatial-temporal dynamics, provide more accurate descriptions of animal social networks, and allow more accurate modeling of multiple (both direct and indirect) disease transmission pathways.

Link removal for the control of stochastically evolving epidemics over networks: a comparison of approaches

For many communicable diseases, knowledge of the underlying contact network through which the disease spreads is essential to determining appropriate control measures. When behavior change is the primary intervention for disease prevention, it is important to understand how to best modify network connectivity using the limited resources available to control disease spread. We describe and compare four algorithms for selecting a limited number of links to remove from a network: two "preventive" approaches (edge centrality, R0 minimization), where the decision of which links to remove is made prior to any disease outbreak and depends only on the network structure; and two "reactive" approaches (S-I edge centrality, optimal quarantining), where information about the initial disease states of the nodes is incorporated into the decision of which links to remove. We evaluate the performance of these algorithms in minimizing the total number of infections that occur over the course of an acute outbreak of disease. We consider different network structures, including both static and dynamic Erdös-Rényi random networks with varying levels of connectivity, a real-world network of residential hotels connected through injection drug use, and a network exhibiting community structure. We show that reactive approaches outperform preventive approaches in averting infections. Among reactive approaches, removing links in order of S-I edge centrality is favored when the link removal budget is small, while optimal quarantining performs best when the link removal budget is sufficiently large. The budget threshold above which optimal quarantining outperforms the S-I edge centrality algorithm is a function of both network structure (higher for unstructured Erdös-Rényi random networks compared to networks with community structure or the real-world network) and disease infectiousness (lower for highly infectious diseases). We conduct a value-of-information analysis of knowing which nodes are initially infected by comparing the performance improvement achieved by reactive over preventive strategies. We find that such information is most valuable for moderate budget levels, with increasing value as disease spread becomes more likely (due to either increased connectedness of the network or increased infectiousness of the disease).

Birth and death of links control disease spreading in empirical contact networks

We investigate what structural aspects of a collection of twelve empirical temporal networks of human contacts are important to disease spreading. We scan the entire parameter spaces of the two canonical models of infectious disease epidemiology—the Susceptible-Infectious-Susceptible (SIS) and Susceptible-Infectious-Removed (SIR) models. The results from these simulations are compared to reference data where we eliminate structures in the interevent intervals, the time to the first contact in the data, or the time from the last contact to the end of the sampling. The picture we find is that the birth and death of links, and the total number of contacts over a link, are essential to predict outbreaks. On the other hand, the exact times of contacts between the beginning and end, or the interevent interval distribution, do not matter much. In other words, a simplified picture of these empirical data sets that suffices for epidemiological purposes is that links are born, is active with some intensity, and die.

Network epidemiology and plant trade networks

Models of epidemics in complex networks are improving our predictive understanding of infectious disease outbreaks. Nonetheless, applying network theory to plant pathology is still a challenge. This overview summarizes some key developments in network epidemiology that are likely to facilitate its application in the study and management of plant diseases. Recent surveys have provided much-needed datasets on contact patterns and human mobility in social networks, but plant trade networks are still understudied. Human (and plant) mobility levels across the planet are unprecedented-there is thus much potential in the use of network theory by plant health authorities and researchers. Given the directed and hierarchical nature of plant trade networks, there is a need for plant epidemiologists to further develop models based on undirected and homogeneous networks. More realistic plant health scenarios would also be obtained by developing epidemic models in dynamic, rather than static, networks. For plant diseases spread by the horticultural and ornamental trade, there is the challenge of developing spatio-temporal epidemic simulations integrating network data. The use of network theory in plant epidemiology is a promising avenue and could contribute to anticipating and preventing plant health emergencies such as European ash dieback.

Modeling the effect of transient populations on epidemics in Washington DC

Large numbers of transients visit big cities, where they come into contact with many people at crowded areas. However, epidemiological studies have not paid much attention to the role of this subpopulation in disease spread. We evaluate the effect of transients on epidemics by extending a synthetic population model for the Washington DC metro area to include leisure and business travelers. A synthetic population is obtained by combining multiple data sources to build a detailed minute-by-minute simulation of population interaction resulting in a contact network. We simulate an influenza-like illness over the contact network to evaluate the effects of transients on the number of infected residents. We find that there are significantly more infections when transients are considered. Since much population mixing happens at major tourism locations, we evaluate two targeted interventions: closing museums and promoting healthy behavior (such as the use of hand sanitizers, covering coughs, etc.) at museums. Surprisingly, closing museums has no beneficial effect. However, promoting healthy behavior at the museums can both reduce and delay the epidemic peak. We analytically derive the reproductive number and perform stability analysis using an ODE-based model.

Epidemiologically optimal static networks from temporal network data

One of network epidemiology's central assumptions is that the contact structure over which infectious diseases propagate can be represented as a static network. However, contacts are highly dynamic, changing at many time scales. In this paper, we investigate conceptually simple methods to construct static graphs for network epidemiology from temporal contact data. We evaluate these methods on empirical and synthetic model data. For almost all our cases, the network representation that captures most relevant information is a so-called exponential-threshold network. In these, each contact contributes with a weight decreasing exponentially with time, and there is an edge between a pair of vertices if the weight between them exceeds a threshold. Networks of aggregated contacts over an optimally chosen time window perform almost as good as the exponential-threshold networks. On the other hand, networks of accumulated contacts over the entire sampling time, and networks of concurrent partnerships, perform worse. We discuss these observations in the context of the temporal and topological structure of the data sets.

To understand how diseases spread in a population, it is important to study the network of people in contact. Many methods to model epidemic outbreaks make the assumption that one can treat this network as static. In reality, we know that contact patterns between people change in time, and old contacts are soon irrelevant—it does not matter that we know Marie Antoinette's lovers to understand the HIV epidemic. This paper investigates methods for constructing networks of people that are as relevant as possible for disease spreading. The most promising method we call exponential-threshold network works by letting contacts contribute less, the further from the beginning of an outbreak they take place. We investigate the methods both on artificial models of the contact patterns and empirical data. Except searching for the optimal network representation, we also investigate how the structure of the original data set affects the performance of the representations.

Predicting and controlling infectious disease epidemics using temporal networks

Infectious diseases can be considered to spread over social networks of people or animals. Mainly owing to the development of data recording and analysis techniques, an increasing amount of social contact data with time stamps has been collected in the last decade. Such temporal data capture the dynamics of social networks on a timescale relevant to epidemic spreading and can potentially lead to better ways to analyze, forecast, and prevent epidemics. However, they also call for extended analysis tools for network epidemiology, which has, to date, mostly viewed networks as static entities. We review recent results of network epidemiology for such temporal network data and discuss future developments.

Epidemic spreading induced by diversity of agents' mobility

In this paper, we study the impact of the preference of an individual for public transport on the spread of infectious disease, through a quantity known as the public mobility. Our theoretical and numerical results based on a constructed model reveal that if the average public mobility of the agents is fixed, an increase in the diversity of the agents' public mobility reduces the epidemic threshold, beyond which an enhancement in the rate of infection is observed. Our findings provide an approach to improve the resistance of a society against infectious disease, while preserving the utilization rate of the public transportation system.

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.

Dengue epidemics and human mobility

In this work we explore the effects of human mobility on the dispersion of a vector borne disease. We combine an already presented stochastic model for dengue with a simple representation of the daily motion of humans on a schematic city of 20 × 20 blocks with 100 inhabitants in each block. The pattern of motion of the individuals is described in terms of complex networks in which links connect different blocks and the link length distribution is in accordance with recent findings on human mobility. It is shown that human mobility can turn out to be the main driving force of the disease dispersal.

Snowbirds and infection--new phenomena in pneumonia and influenza hospitalizations from winter migration of older adults: a spatiotemporal analysis

BACKGROUND

Despite advances in surveillance and prevention, pneumonia and influenza (P&I) remain among the leading causes of mortality in the United States. Elderly adults experience the most severe morbidity from influenza-associated diseases, and have the highest rates of seasonal migration within the U.S. compared to other subpopulations. The objective of this study is to assess spatiotemporal patterns in influenza-associated hospitalizations in the elderly, by time, geography, and intensity of P&I. Given the high seasonal migration of individuals to Florida, this state was examined more closely using harmonic regression to assess spatial and temporal patterns of P&I hospitalizations by state of residence.

METHODS

Data containing all Medicare-eligible hospitalizations in the United States for 1991-2006 with P&I (ICD-9-CM codes 480-487) were abstracted for the 65+ population. Hospitalizations were classified by state of residence, provider state, and date of admissions, specifically comparing those admitted between October and March to those admitted between April and September. We then compared the hospitalization profile data of Florida residents with that of out-of-state residents by state of primary residence and time of year (in-season or out-of-season).

RESULTS

We observed distinct seasonal patterns of nonresident P&I hospitalizations, especially comparing typical winter destination states, such as California, Arizona, Texas, and Florida, to other states. Although most other states generally experienced a higher proportion of non-resident P&I during the summer months (April-September), these states had higher nonresident P&I during the traditional peak influenza season (October-March).

CONCLUSIONS

This study is among the first to quantify spatiotemporal P&I hospitalization patterns in the elderly, focusing on the change of patterns that are possibly due to seasonal population migration. Understanding migration and influenza-associated disease patterns in this vulnerable population is critical to prepare for and potentially prevent influenza outbreaks in this vulnerable population.

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.

Epidemic spreading in evolving networks

A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to suppress epidemic spreading. In particular it is found, that as in static networks under a mean-field approximation, rewiring networks with degree distribution exponent γ>3 exhibit a threshold in the infection rate below which epidemics die out in the steady state. However the threshold is higher in the rewiring case. For 2<γ≤3 no such threshold exists, but for small infection rate the steady state density of infected nodes (prevalence) is smaller for rewiring networks.

Adaptive networks: Coevolution of disease and topology

Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have been analyzed using low complexity analytical formalisms, revealing nevertheless some novel dynamical features. However, current methods have failed to reproduce with accuracy the simultaneous time evolution of the disease and the underlying network topology. In the framework of the adaptive susceptible-infectious-susceptible (SIS) model of Gross [Phys. Rev. Lett. 96, 208701 (2006)]10.1103/PhysRevLett.96.208701, we introduce an improved compartmental formalism able to handle this coevolutionary task successfully. With this approach, we analyze the interplay and outcomes of both dynamical elements, process and structure, on adaptive networks featuring different degree distributions at the initial stage.

Rewiring for adaptation

The idea behind adaptive behavioral epidemiology is that groups and individuals respond to the knowledge of a disease threat by changing their habits to avoid interactions with those who are contagious. Network-based models take this adaptive behavior into account by allowing the network to "rewire" its connections.

Epidemic prediction and control in weighted networks

Contact networks are often used in epidemiological studies to describe the patterns of interactions within a population. Often, such networks merely indicate which individuals interact, without giving any indication of the strength or intensity of interactions. Here, we use weighted networks, in which every connection has an associated weight, to explore the influence of heterogeneous contact strengths on the effectiveness of control measures. We show that, by using contact weights to evaluate an individual's influence on an epidemic, individual infection risk can be estimated and targeted interventions such as preventative vaccination can be applied effectively. We use a diary study of social mixing behaviour to indicate the patterns of contact weights displayed by a real population in a range of different contexts, including physical interactions; we use these data to show that considerations of link weight can in some cases lead to improved interventions in the case of infections that spread through close contact interactions. However, we also see that simpler measures, such as an individual's total number of social contacts or even just their number of contacts during a single day, can lead to great improvements on random vaccination. We therefore conclude that, for many infections, enhanced social contact data can be simply used to improve disease control but that it is not necessary to have full social mixing information in order to enhance interventions.

Fluctuating epidemics on adaptive networks

A model for epidemics on an adaptive network is considered. Nodes follow a susceptible-infective-recovered-susceptible pattern. Connections are rewired to break links from noninfected nodes to infected nodes and are reformed to connect to other noninfected nodes, as the nodes that are not infected try to avoid the infection. Monte Carlo simulation and numerical solution of a mean field model are employed. The introduction of rewiring affects both the network structure and the epidemic dynamics. Degree distributions are altered, and the average distance from a node to the nearest infective increases. The rewiring leads to regions of bistability where either an endemic or a disease-free steady state can exist. Fluctuations around the endemic state and the lifetime of the endemic state are considered. The fluctuations are found to exhibit power law behavior.