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2017 | Book

Introduction to Temporal Network Epidemiology Read chapter Read first chapter

Temporal Network Epidemiology

Editors: Dr. Naoki Masuda, Prof. Dr. Petter Holme

Publisher: Springer Singapore

Book Series : Theoretical Biology

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This book covers recent developments in epidemic process models and related data on temporally varying networks. It is widely recognized that contact networks are indispensable for describing, understanding, and intervening to stop the spread of infectious diseases in human and animal populations; “network epidemiology” is an umbrella term to describe this research field.

More recently, contact networks have been recognized as being highly dynamic. This observation, also supported by an increasing amount of new data, has led to research on temporal networks, a rapidly growing area. Changes in network structure are often informed by epidemic (or other) dynamics, in which case they are referred to as adaptive networks.

This volume gathers contributions by prominent authors working in temporal and adaptive network epidemiology, a field essential to understanding infectious diseases in real society.

Table of Contents

Frontmatter
Chapter 1. Introduction to Temporal Network Epidemiology
Abstract
In this introductory chapter, we start by briefly summarising temporal and adaptive networks, and epidemic process models frequently used in this volume. Then, we introduce a couple of what we think are key studies in the field, which are fundamental for various chapters in this volume. Finally, we give an overview of each chapter and discuss future work.
Naoki Masuda, Petter Holme
Chapter 2. How Behaviour and the Environment Influence Transmission in Mobile Groups
Abstract
The movement of individuals living in groups leads to the formation of physical interaction networks over which signals such as information or disease can be transmitted. Direct contacts represent the most obvious opportunities for a signal to be transmitted. However, because signals that persist after being deposited into the environment may later be acquired by other group members, indirect environmentally-mediated transmission is also possible. To date, studies of signal transmission within groups have focused on direct physical interactions and ignored the role of indirect pathways. Here, we use an agent-based model to study how the movement of individuals and characteristics of the signal being transmitted modulate transmission. By analysing the dynamic interaction networks generated from these simulations, we show that the addition of indirect pathways speeds up signal transmission, while the addition of physically-realistic collisions between individuals in densely packed environments hampers it. Furthermore, the inclusion of spatial biases that induce the formation of individual territories, reveals the existence of a trade-off such that optimal signal transmission at the group level is only achieved when territories are of intermediate sizes. Our findings provide insight into the selective pressures guiding the evolution of behavioural traits in natural groups, and offer a means by which multi-agent systems can be engineered to achieve desired transmission capabilities.
Thomas E. Gorochowski, Thomas O. Richardson
Chapter 3. Sensitivity to Temporal and Topological Misinformation in Predictions of Epidemic Outbreaks
Abstract
Structures both in the network of who interact with whom, and the timing of these contacts, affect epidemic outbreaks. In practical applications, such information would frequently be inaccurate. In this work, we explore how the accuracy in the prediction of the final outbreak size and the time to extinction of the outbreak depend on the quality of the contact information. We find a fairly general stretched exponential dependence of the deviation from the true outbreak sizes and extinction times on the frequency of errors in both temporal and topological information.
Petter Holme, Luis E. C. Rocha
Chapter 4. Measuring Propagation with Temporal Webs
Abstract
We present a form of temporal network called a “temporal web” that connects nodes across time into a single temporally extended acyclic directed graph as a way to capture contingent behaviors. This representation is especially useful for uncovering and measuring social influence. We first present the general temporal web technique and then use it to analyze three empirical datasets: political relationships in the game EVE Online, interbank loans of the Russian banking system, and Twitter posts regarding the H1N1 vaccine. For each dataset we provide a detailed breakdown of the contingent behaviors using an approach we call temporal influence abduction. We then construct a temporal web for each one and describe the patterns of propagation found. Based on these patterns of propagation we infer more general properties of influence and the impact of certain types of behaviors in each system.
Aaron Bramson, Kevin Hoefman, Milan van den Heuvel, Benjamin Vandermarliere, Koen Schoors
Chapter 5. Mean Field at Distance One
Abstract
To be able to understand how infectious diseases spread on networks, it is important to understand the network structure itself in the absence of infection. In this text we consider dynamic network models that are inspired by the (static) configuration network. The networks are described by population-level averages such as the fraction of the population with k partners, k = 0, 1, 2, … This means that the bookkeeping contains information about individuals and their partners, but no information about partners of partners. Can we average over the population to obtain information about partners of partners? The answer is ‘it depends’, and this is where the mean field at distance one assumption comes into play. In this text we explain that, yes, we may average over the population (in the right way) in the static network. Moreover, we provide evidence in support of a positive answer for the network model that is dynamic due to partnership changes. If, however, we additionally allow for demographic changes, dependencies between partners arise. In earlier work we used the slogan ‘mean field at distance one’ as a justification of simply ignoring the dependencies. Here we discuss the subtleties that come with the mean field at distance one assumption, especially when demography is involved. Particular attention is given to the accuracy of the approximation in the setting with demography. Next, the mean field at distance one assumption is discussed in the context of an infection superimposed on the network. We end with the conjecture that an extension of the bookkeeping leads to an exact description of the network structure.
Ka Yin Leung, Mirjam Kretzschmar, Odo Diekmann
Chapter 6. Towards Identifying and Predicting Spatial Epidemics on Complex Meta-population Networks
Abstract
In the past decade, the network science community has witnessed huge advances in the threshold theory, prediction and control of epidemic dynamics on complex networks. While along with the understanding of spatial epidemics on meta-population networks achieved so far, more challenges have opened the door to identify, retrospect, and predict the epidemic invasion process. This chapter reviews the recent progress towards identifying susceptible-infected compartment parameters and spatial invasion pathways on a meta-population network as well as the minimal case of two-subpopulation version, which may also extend to the prediction of spatial epidemics as well. The artificial and empirical meta-population networks verify the effectiveness of our proposed solutions to the concerned problems. Finally, the whole chapter concludes with the outlook of future research.
Xiang Li, Jian-Bo Wang, Cong Li
Chapter 7. Epidemic Threshold in Temporally-Switching Networks
Abstract
Infectious diseases have been modelled on networks that summarise physical contacts or close proximity of individuals. These networks are known to be complex in both their structure and how they change over time. We present an overview of recent progress in numerically determining the epidemic threshold in temporally-switching networks, and illustrate that slower switching of snapshots relative to epidemic dynamics lowers the epidemic threshold. Therefore, ignoring the temporally-varying nature of networks may underestimate endemicity. We also identify a predictor for the magnitude of this shift which is based on the commutator norm of snapshot adjacency matrices.
Leo Speidel, Konstantin Klemm, Víctor M. Eguíluz, Naoki Masuda
Chapter 8. Control Strategies of Contagion Processes in Time-Varying Networks
Abstract
The vast majority of strategies aimed at controlling contagion processes on networks consider a timescale separation between the evolution of the system and the unfolding of the process. However, in the real world, many networks are highly dynamical and evolve, in time, concurrently to the contagion phenomena. Here, we review the most commonly used immunization strategies on networks. In the first part of the chapter, we focus on controlling strategies in the limit of timescale separation. In the second part instead, we introduce results and methods that relax this approximation. In doing so, we summarize the main findings considering both numerical and analytically approaches in real as well as synthetic time-varying networks.
Márton Karsai, Nicola Perra
Chapter 9. Leveraging Topological and Temporal Structure of Hospital Referral Networks for Epidemic Control
Abstract
Antimicrobial-resistant pathogens constitute a major threat for health care systems worldwide. The hospital-related pathway is a key mechanism of their spread. Contrary to intra-hospital transmission data that requires sophisticated contact tracing technologies, data on inter-hospital transmission is collected on a regular basis. We investigate the dataset of patient referrals between hospitals in a large region of Germany. This dataset contains approximately one million patients over a 3-year period. The dataset is used to build a dynamic network of hospitals where nodes are hospitals and edges represent movements of patients between them. We consider the worst-case scenario of a highly contagious disease corresponding to deterministic infection dynamics. Furthermore, we investigate the impact on epidemic processes of the correction to the temporal network due to home (or community) visits of possibly contagious patients returning to hospitals. Moreover, we implement an extensive stochastic agent-based computational model of epidemics on this network. By leveraging the topological and temporal network structure for epidemic control, we propose intervention schemes able to hinder spread. Our approach can be used to design optimal control strategies for containment of nosocomial diseases in health-care networks.
Vitaly Belik, André Karch, Philipp Hövel, Rafael Mikolajczyk
Chapter 10. Surveillance for Outbreak Detection in Livestock-Trade Networks
Abstract
We analyze an empirical, temporal network of livestock trade and present numerical results of epidemiological dynamics. The considered network is the backbone of the pig trade in Germany, which forms a major route of disease spreading between agricultural premises. The network is comprised of farms that are connected by a link, if animals are traded between them. We propose a concept for epidemic surveillance, which is generally performed on a subset of the system due to limited resources. The goal is to identify agricultural holdings that are more likely to be infected during the early phase of an epidemic outbreak. These farms, which we call sentinels, are excellent candidates to monitor the whole network. To identify potential sentinel nodes, we determine most probable transmission routes by calculating functional clusters. These clusters are formed by nodes that – chosen as seed for an outbreak – have similar invasion paths. We find that it is indeed possible to group the German pig-trade network in such clusters. Furthermore, we select sentinels by choosing nodes out of every cluster. We argue that any epidemic outbreak can be reliably detected at an early stage by monitoring a small number of those sentinels. Considering a susceptible-infected-recovered model, we show that an outbreak can be detected with only 18 sentinels out of almost 100,000 farms with a probability of 65% in approximately 13 days after first infection. This finding can be further improved by including nodes with the largest in-component (highest vulnerability), which increases the detection probability to 86% within 8 days after first occurrence of the disease.
Frederik Schirdewahn, Vittoria Colizza, Hartmut H. K. Lentz, Andreas Koher, Vitaly Belik, Philipp Hövel
Chapter 11. Optimal Containment of Epidemics in Temporal and Adaptive Networks
Abstract
In this chapter, we focus on the problem of containing the spread of diseases taking place on both temporal and adaptive networks (i.e., networks whose structure changes as a result of the epidemic). We specifically focus on the problem of finding the optimal allocation of containment resources (e.g., vaccines, medical personnel, traffic control resources, etc.) to eradicate epidemic outbreaks over the following three models of temporal and adaptive networks: (i) Markovian temporal networks, (ii) aggregated-Markovian temporal networks, and (iii) stochastically adaptive network models. For each model, we present a rigorous and tractable mathematical framework to efficiently find the optimal distribution of control resources to eliminate the disease. In contrast with other existing results, our results are not based on heuristic control strategies, but on a disciplined analysis using tools from dynamical systems and convex optimization.
Masaki Ogura, Victor M. Preciado
Chapter 12. Mapping Out Emerging Network Structures in Dynamic Network Models Coupled with Epidemics
Abstract
We consider the susceptible – infected – susceptible (SIS) epidemic on a dynamic network model with addition and deletion of links depending on node status. We analyse the resulting pairwise model using classical bifurcation theory to map out the spectrum of all possible epidemic behaviours. However, the major focus of the chapter is on the evolution and possible equilibria of the resulting networks. Whereas most studies are driven by determining system-level outcomes, e.g., whether the epidemic dies out or becomes endemic, with little regard for the emerging network structure, here, we want to buck this trend by augmenting the system-level results with mapping out of the structure and properties of the resulting networks. We find that depending on parameter values the network can become disconnected and show bistable-like behaviour whereas the endemic steady state sees the emergence of networks with qualitatively different degree distributions. In particular, we observe de-phased oscillations of both prevalence and network degree during which there is role reversal between the level and nature of the connectivity of susceptible and infected nodes. We conclude with an attempt at describing what a potential bifurcation theory for networks would look like.
István Z. Kiss, Luc Berthouze, Joel C. Miller, Péter L. Simon
Chapter 13. Disease Spreading in Time-Evolving Networked Communities
Abstract
Human communities are organized in complex webs of contacts that may be represented by a graph or network. In this graph, vertices identify individuals and edges establish the existence of some type of relations between them. In real communities, the possible edges may be active or not for variable periods of time. These so-called temporal networks typically result from an endogenous social dynamics, usually coupled to the process under study taking place in the community. For instance, disease spreading may be affected by local information that makes individuals aware of the health status of their social contacts, allowing them to reconsider maintaining or not their social contacts. Here we investigate the impact of such a dynamical network structure on disease dynamics, where infection occurs along the edges of the network. To this end, we define an endogenous network dynamics coupled with disease spreading. We show that the effective infectiousness of a disease taking place along the edges of this temporal network depends on the population size, the number of infected individuals in the population and the capacity of healthy individuals to sever contacts with the infected, ultimately dictated by availability of information regarding each individual’s health status. Importantly, we also show how dynamical networks strongly decrease the average time required to eradicate a disease.
Jorge M. Pacheco, Sven Van Segbroeck, Francisco C. Santos
Chapter 14. Toward a Realistic Modeling of Epidemic Spreading with Activity Driven Networks
Abstract
Models of epidemic spreading are widely used to predict the evolution of an outbreak, test specific intervention scenarios, and steer interventions in the field. Compartmental models are the most common class of models. They are very effective for qualitative analysis, but they rely on simplifying assumptions, such as homogeneous mixing and time scale separation. On the other end of the spectrum, detailed agent-based models, based on realistic mobility pattern models, provide extremely accurate predictions. However, these models require significant computing power and are not suitable for analytical treatment. Our research aims at bridging the gap between these two approaches, toward time-varying network models that are sufficiently accurate to make predictions for real-world applications, while being computationally affordable and amenable to analytical treatment. We leverage the novel paradigm of activity driven networks (ADNs), a particular type of time-varying network that accounts for inherent inhomogeinities within a population. Starting from the basic incarnation of ADNs, we expand on the framework to include behavioral factors triggered by health status and spreading awareness. The enriched paradigm is then utilized to model the 2014–2015 Ebola Virus Disease (EVD) spreading in Liberia, and perform a what-if analysis on the timely application of sanitary interventions in the field. Finally, we propose a new formulation, which is amenable to analytical treatment, beyond the mere computation of the epidemic threshold.
Alessandro Rizzo, Maurizio Porfiri
Metadata
Title
Temporal Network Epidemiology
Editors
Dr. Naoki Masuda
Prof. Dr. Petter Holme
Copyright Year
2017
Publisher
Springer Singapore
Electronic ISBN
978-981-10-5287-3
Print ISBN
978-981-10-5286-6
DOI
https://doi.org/10.1007/978-981-10-5287-3

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