Multilayer Network Analysis Research Articles

Insights the dominant contribution of biomass burning to methanol-soluble PM2.5 bounded oxidation potential based on multilayer perceptron neural network analysis in Xi'an, China

Atmospheric fine particulate matter (PM2.5) is associated with cardiorespiratory morbidity and mortality due to its ability to generate reactive oxygen species (ROS). Ambient PM2.5 samples were collected during heating and nonheating seasons in Xi'an, China, and the ROS-generation potential of PM2.5 was quantified using the dithiothreitol (DTT) assay. Additionally, positive matrix factorization combined with multilayer perceptron was employed to apportion sources contributing to the oxidation potential of PM2.5. Both the mass concentration of PM2.5 and the volume-based DTT activity (DTTv) were higher during the heating season than during the nonheating season. The primary contributors to DTTv were combustion (biomass and coal) sources during the heating season (>52 %), whereas secondary formation dominated DTT activity during the nonheating season (35.7 %). In addition, the secondary reaction process promoted the generation of intrinsic oxidation potential (OP) of sources. Among all the sources investigated (traffic source, industrial emission, mineral dust, biomass burning, secondary formation and coal combustion), the inherent oxidation potential of biomass burning was the highest, whereas that of mineral dust was the lowest. Our study indicates that anthropogenic sources, especially biomass burning, should be prioritized in PM2.5 toxicity control strategies.

Practical guidelines and the EMLN R package for handling ecological multilayer networks

Abstract Network analysis provides a powerful framework to study the complexity underlying the structure, dynamics and function of ecological systems. By now, analysing single‐layered networks is a common practice with clear guidelines and well‐established computational tools. Nevertheless, ecological communities are multilayered because they vary over space and time and contain multiple types of interactions. In recent years, the analysis of ecological multilayer networks (EMLNs) has allowed researchers to include such multilayered complexity. However, there is a paucity of practical guidelines and standardised tools to handle EMLN data, even before downstream analysis. In this article, we accomplish three objectives: (1) We provide practical guidelines for handling EMLN data. (2) We developed the EMLN R package to standardise the workflow of creating, storing and working with EMLN objects. The package also enables conversion between multiple formats for downstream analysis with other standard packages. (3) We provide EMLN data sets for research and training purposes. A dedicated website with explanations, detailed examples and code accompanies our paper. This website is a gateway for novice and experienced network ecologists who want to include EMLNs in their research. By simplifying the analysis of multilayer networks and promoting standardised approaches, we facilitate the analysis of EMLNs. This paves the road towards gaining deeper insights into functioning and resilience of natural ecosystems.

Novel multilayer network analysis to assess variation in the spatial co-occurrences of close kin in wild caribou populations

Understanding how individuals within populations are connected genetically and through shared space-use is critical to understanding the demographic patterns of at-risk populations. In recent years, non-invasive genetic sampling methods have allowed us to begin addressing these questions. Using a network analysis framework, we examined the spatial co-occurrence and genetic relatedness of boreal and central mountain caribou (Rangifer tarandus) in populations varying in sizes and trend from across western Canada. Using 15 microsatellites loci and a sex-specific marker, we developed pedigree networks for each population, including first to third order relationships. We constructed networks of individual spatial co-occurrence, and using multilayer network analysis, we determined the degree to which caribou that co-occurred spatially were related. Caribou populations varied in the extent and classes of familial relationships which co-occurred in space. In most populations, spatial co-occurrences were greater than expected only for parent-offspring relationships. A sex-specific analysis of the longest sampled population revealed that this was driven by a significant overlap between mothers and their offspring. Whereas in populations where very few parent-offspring relationship were detected, no significant overlap was found between any relationship categories. The lack of overlap in these populations may be an indication of poor calf survival. On the other hand, the higher degree of overlap with more distant relations (i.e., grandparents) seen in some populations may indicate a population that lacks mobility. Our research presents a new approach to explore both spatial and genetic overlap at the individual level in support of the conservation of threatened populations.

Involvement of the default mode network in patients with transient global amnesia: multilayer network.

We aimed to investigate the alterations in the multilayer network in patients with transient global amnesia (TGA). We enrolled 124 patients with TGA and 80 healthy controls. Both patients with TGA and healthy controls underwent a three-teslar brain magnetic resonance imaging (MRI). A gray matter layer matrix was created using a morphometric similarity network derived from the T1-weighted imaging, and a white matter layer matrix was constructed using structural connectivity based on the diffusion tensor imaging. A multilayer network analysis was performed by applying graph theoretical analysis. There were no significant differences in global network measures between the groups. However, several regions, related to the default mode network, showed significant differences in nodal network measures between the groups. Multi-richness in the left pars opercularis, multi-rich-club degree in the right posterior cingulate gyrus, and weighted multiplex participation in the right posterior cingulate gyrus were higher in patients with TGA compared with healthy controls (15.47 vs. 12.26, p = 0.0005; 41.68 vs. 37.16, p = 0.0005; 0.90 vs. 0.80, p = 0.0005; respectively). The multiplex core-periphery in the left precuneus was higher (0.96 vs. 0.84, p = 0.0005), whereas that in the transverse temporal gyrus was lower in patients with TGA compared with healthy controls (0.00 vs. 0.02, p = 0.0005). We newly find the alterations in the multilayer network in patients with TGA compared with healthy controls, which shows the involvement of the default mode network. These changes may be related to the pathophysiology of TGA.

Exploring the Interdependencies Between Transportation and Stormwater Networks: The Case of Norman, Oklahoma

The significance of critical infrastructure systems in maintaining productivity is undeniable. However, such systems remain susceptible to external disturbances and cascading failures. Instead of operating independently, these physical systems, such as transportation and stormwater systems, form an interdependent system. This interdependence, particularly important during flooding, illustrates that the failure of a stormwater system can disrupt traffic networks. To explore the extent of such interdependency, this study investigates the transportation and stormwater networks in Norman, Oklahoma. Using network science theories and concepts of multilayered networks, this paper analyzes these systems, both individually and in combination. The study identifies closely located components in the road and stormwater networks using Moran's I spatial autocorrelation metric. Next, the connectivity of these networks is represented in a graph format to investigate the topological credentials (i.e., rank of relative importance) of the network components (i.e., water inlets, road intersections as nodes, and stormwater conduits, road segments as links). Moreover, such credentials further change by considering the weights of the network components (i.e., average daily traffic, water flow). The proximity-based connectivity considerations between these networks utilizing Moran's I significance score revealed a good indicator of spatial interdependency. When incorporating directionality, the multilayer network analysis highlights that highly central components tend to cluster spatially, unlike the undirected counterpart. The study also identifies vulnerable locations and network components in a combined network setting that differ from the networks in isolation. In doing so, the research reveals new insights governing the complex reliance of transportation systems on neighboring stormwater systems.

Decoupling in governance: the land governance network in a region of the Colombian Andes

Land governance requires coherence not only in terms of policies but also between its governance functions to achieve the desired goals. In this study, we focus on the functions that direct influence land use (boundary setting and resource appropriation; project formulation and financing; and monitoring, evaluation, and learning), which are expected to form a feedback loop necessary for adaptive co-management. We evaluated the degree of coherence of these three functions (as an approach to efficient management) via geo-located multilayer social network analysis and using an area of the Rio Grande and Chico basin in the Colombian Andes as the case study. According to the results, there is a conflict between production and conservation goals, necessitating collaboration among actors and institutions from various levels. The social network analysis revealed that the three functions are not articulated; instead, there exist two feedback loops (one per goal) in the boundary setting and resource appropriation function, leading to such conflict. The imposition of a governance system on the community by a few actors is recognized as the root of this conflict; hence, the need to move toward a governance with the community by promoting active participation in the various functions and interactions within them. We recommend future studies to assess the impact of governance networks on land-use actions to identify the reasons for land-use change and propose new strategies.

Efficient community detection in multilayer networks using boolean compositions.

Networks (or graphs) are used to model the dyadic relations between entities in complex systems. Analyzing the properties of the networks reveal important characteristics of the underlying system. However, in many disciplines, including social sciences, bioinformatics, and technological systems, multiple relations exist between entities. In such cases, a simple graph is not sufficient to model these multiple relations, and a multilayer network is a more appropriate model. In this paper, we explore community detection in multilayer networks. Specifically, we propose a novel network decoupling strategy for efficiently combining the communities in the different layers using the Boolean primitives AND, OR, and NOT. Our proposed method, network decoupling, is based on analyzing the communities in each network layer individually and then aggregating the analysis results. We (i) describe our network decoupling algorithms for finding communities, (ii) present how network decoupling can be used to express different types of communities in multilayer networks, and (iii) demonstrate the effectiveness of using network decoupling for detecting communities in real-world and synthetic data sets. Compared to other algorithms for detecting communities in multilayer networks, our proposed network decoupling method requires significantly lower computation time while producing results of high accuracy. Based on these results, we anticipate that our proposed network decoupling technique will enable a more detailed analysis of multilayer networks in an efficient manner.

Investigating Material Culture Through Multilayer Network Analysis in Tonto Basin

Network analysis has a strong foundation in Southwest archaeology, yet the analysis of multiple network layers in a single analysis– (multilayer network analysis)– has not been formally applied except within a single artifact type. Many studies consider material culture holistically, yet network analysis has the advantage of focusing specifically on the relationships between entities. This study uses architecture, ceramic, projectile point, and site locations from the Roosevelt Platform Mound Study and combines these data in a multilayer network analysis. This analysis provides a way to test the co-variance of these types of material culture with each other and with spatial variation. Overall, the ceramic and projectile point networks exhibit significant differences. This indicates that the social networks that created these patterns had different social mechanisms. One potential cause of these differences is gendered spheres of interaction with men producing and exchanging projectile points and women producing and exchanging ceramics.

Multilayer network analysis to study complex inter-subsystem interactions in a turbulent thermoacoustic system

Thermoacoustic systems are complex systems where the interactions between the hydrodynamic, acoustic and heat release rate fluctuations lead to diverse dynamics such as chaos, intermittency and ordered dynamics. Such complex interactions cause catastrophically high-amplitude acoustic pressure oscillations and the emergence of order in the spatiotemporal dynamics, referred to as thermoacoustic instability. In this work, we use multilayer networks to study the spatial pattern of inter-subsystem interactions between the vorticity dynamics and thermoacoustic power generated due to acoustically coupled combustion in a bluff-body-stabilised turbulent dump combustor. We construct a two-layered network where the layers represent the thermoacoustic power and vorticity fields. The inter-layer links are determined using cross-variable short-window correlations between vorticity and thermoacoustic power fluctuations at any two locations in the flow field. Analysing the topology of inter-layer networks, using network properties such as degree correlations and link-rank distributions, helps us infer the spatial inhomogeneities in inter-subsystem interactions and unravel the fluid mechanical processes involved during different dynamical states. We show that, during chaotic dynamics, interactions between subsystems are non-localised and spread throughout the flow field of the combustor. During the state of thermoacoustic instability (order), we find that intense interactions occur in between regions of coherent vortex shedding and thermoacoustic power generation and we understand that these processes are strongly and locally coupled. Moreover, we discover that such dense inter-layer connections emerge in spatial pockets in the dump plane of the combustor during the state of intermittency much prior to the onset of order.

Assessing cohesion and diversity in the collaboration network of the SALURBAL project

The SALURBAL (Urban Health in Latin America) Project is an interdisciplinary multinational network aimed at generating and disseminating actionable evidence on the drivers of health in cities of Latin America. We conducted a temporal multilayer network analysis where we measured cohesion over time using network structural properties and assessed diversity within and between different project activities according to participant attributes. Between 2017 and 2020 the SALURBAL network comprised 395 participants across 26 countries, 23 disciplines, and 181 institutions. While the cohesion of the SALURBAL network fluctuated over time, overall, an increase was observed from the first to the last time point of our analysis (clustering coefficient increased [0.83–0.91] and shortest path decreased [1.70–1.68]). SALURBAL also exhibited balanced overall diversity within project activities (0.5–0.6) by designing activities for different purposes such as capacity building, team-building, research, and dissemination. The network’s growth was facilitated by the creation of new diverse collaborations across a range of activities over time, while maintaining the diversity of existing collaborations (0.69–0.75 between activity diversity depending on the attribute). The SALURBAL experience can serve as an example for multinational research projects aiming to build cohesive networks while leveraging heterogeneity in countries, disciplines, career stage, and across sectors.

Cross-Frequency Multilayer Network Analysis with Bispectrum-based Functional Connectivity: A Study of Alzheimer’s Disease

Alzheimer’s disease (AD) is a neurodegenerative disorder known to affect functional connectivity (FC) across many brain regions. Linear FC measures have been applied to study the differences in AD by splitting neurophysiological signals, such as electroencephalography (EEG) recordings, into discrete frequency bands and analysing them in isolation from each other. We address this limitation by quantifying cross-frequency FC in addition to the traditional within-band approach. Cross-bispectrum, a higher-order spectral analysis approach, is used to measure the nonlinear FC and is compared with the cross-spectrum, which only measures the linear FC within bands. This work reports the reconstruction of a cross-frequency FC network where each frequency band is treated as a layer in a multilayer network with both inter- and intra-layer edges. Cross-bispectrum detects cross-frequency differences, mainly increased FC in AD cases in δ-θ coupling. Overall, increased strength of low-frequency coupling and decreased level of high-frequency coupling is observed in AD cases in comparison to healthy controls (HC). We demonstrate that a graph-theoretic analysis of cross-frequency brain networks is crucial to obtain a more detailed insight into their structure and function. Vulnerability analysis reveals that the integration and segregation properties of networks are enabled by different frequency couplings in AD networks compared to HCs. Finally, we use the reconstructed networks for classification. The extra cross-frequency coupling information can improve the classification performance significantly, suggesting an important role of cross-frequency FC. The results highlight the importance of studying nonlinearity and including cross-frequency FC in characterising AD.

Optimal estimation and computational limit of low-rank Gaussian mixtures

Structural matrix-variate observations routinely arise in diverse fields such as multilayer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the fundamental questions like its statistical optimality and computational limit are largely under-explored. In this paper, we propose a low-rank Gaussian mixture model (LrMM) assuming each matrix-valued observation has a planted low-rank structure. Minimax lower bounds for estimating the underlying low-rank matrix are established allowing a whole range of sample sizes and signal strength. Under a minimal condition on signal strength, referred to as the information-theoretical limit or statistical limit, we prove the minimax optimality of a maximum likelihood estimator which, in general, is computationally infeasible. If the signal is stronger than a certain threshold, called the computational limit, we design a computationally fast estimator based on spectral aggregation and demonstrate its minimax optimality. Moreover, when the signal strength is smaller than the computational limit, we provide evidences based on the low-degree likelihood ratio framework to claim that no polynomial-time algorithm can consistently recover the underlying low-rank matrix. Our results reveal multiple phase transitions in the minimax error rates and the statistical-to-computational gap. Numerical experiments confirm our theoretical findings. We further showcase the merit of our spectral aggregation method on the worldwide food trading dataset.

Multilayer network analysis for measuring the inter-connectedness between the oil market and G20 stock markets

We constructed a multilayer information spillover network containing a return spillover layer, a volatility spillover layer, and an extreme risk spillover layer to explore the system risk in the oil and G20 stock markets during 2006–2022. This paper explores the topology of the static and dynamic multilayer networks from both system-level and market-level perspectives. We find that: (i) At the system-level, the structure of layers is significantly different from each other, and risk is transmitted mainly in the volatility spillover layer. In times of crisis, the spillover effect between layers increases. In addition, multilayer networks are more sensitive to risk identification and can identify risks earlier. (ii) At the market-level, developed markets tend to have high connectivity and act as risk-emitter in spillover networks. Developing markets tend to be risk-receivers. Markets with a homogeneous economic structure are more likely to receive shocks and change from risk-receiving to risk-emitting markets. Multilayer information spillover networks provide comprehensive information on financial linkages between national stock markets, which helps regulators and investors to prevent system risks better and allocate assets appropriately.

Characterizing the importance of nodes with information feedback in multilayer networks

Characterizing the importance of agents or events with possible related information is an important topic in information science. Due to the related agents and events usually can be described by the interconnected multilayer networks, so it is also one of the core themes in network-science. Previous researchers have proposed various tensor-based methods to discuss the centrality of interconnected multilayer networks, but the research on heterogeneous multilayer networks is insufficient. In this paper, based on PageRank algorithm in single-layer network, information feedback is introduced to describe the interaction among different layers. Then the coupled information feedback algorithm is developed to measure the centrality of the nodes in multilayer networks. First, the importance of nodes is measured according to PageRank in single network. Second, the links between the different layers are considered as the transmission and feedback paths for the information about the centrality of the nodes with interlayer links. This feedback mechanism could show us the global importance introduced by the interdependence of different layers. The feedback strength is parameterized and can be adjusted. With the feedback of information among different layers, an iterative update method for evaluating the importance of nodes in multilayer networks is constructed. Finally, several interesting cases are presented to illustrate how the feedback strength affects the rank of the nodes in the networks. The effectiveness of the proposed method is verified by an experimental analysis of the Author-Paper multilayer networks from the APS database and two other actual multilayer networks.

Modelling past and future land‐use changes from mining, agriculture, industry and biodiversity in a rapidly developing Southeast Asian region

AbstractRapidly developing regions in Southeast Asia, such as Kuantan, Malaysia, require robust spatial analysis to understand changing landscape patterns and their socioenvironmental impacts to guide sustainable development and conservation planning. This study aims to characterise and evaluate the historic and future projections of land‐use and land‐cover (LULC) change patterns to understand the dynamics of the regional development process and identify potential future land‐use conflicts. We first map coarse‐scale land‐cover classes using Landsat 5 TM and Landsat 8 OLI data and a Random Forest classifier in the Google Earth Engine platform, and then use auxiliary reference data to manually construct fine‐scale LULC for 3 years: 2010, 2015 and 2020. Subsequently, we modelled future LULC change patterns in 2030 using Land Change Modeller, which applies a multilayer perceptron neural network and Markov chain analysis. The study showed that the region's land cover in the last 10 years has been largely altered by human intervention, driven by an increase in oil palm plantations, followed by mining, residential and industrial site expansion, with a consequent decline in forest and vegetation cover. The 2030 land‐use projections revealed a continuation of these land‐use development patterns. The modelling showed that industry, mining and residential LULC are clustered and growing closer in proximity while expanding extensively, likely causing future land‐use conflict and lead to further environmental degradation. Furthermore, our analysis showed extensive decline in forest cover within reserves. Our modelling demonstrated that natural resource management needs to take an integrated approach as the drivers of land‐use changes are complex, competing and dynamic.

A Complex Insight for Quality of Service Based on Spreading Dynamics and Multilayer Networks in a 6G Scenario

Within the 6G vision, the future of mobile communication networks is expected to become more complex, heterogeneous, and characterized by denser deployments with a myriad of users in an ever-more dynamic environment. There is an increasing intent to provide services following the microservice architecture, thus gaining from higher scalability and significant reliability. Microservices introduce novel challenges and the level of granularity impacts performances, due to complex composition patterns. This openness in design demands service requirements be heterogeneous and dynamic. To this end, we propose a framework and a mathematical approach to investigate the complex quality of services. We exploit the temporal multilayer network representation and analysis jointly, with the spreading dynamics of user experience. We study the joint impact of structural heterogeneity and the evolutionary dynamics of the temporal multilayer quality network, composed of networked parameters, and a temporal multilayer social network, populated by a social layered structure of users. We conducted simulations to display our findings on how this modeling approach enables evaluation of otherwise-overlooked information on quality arising from a profound investigation of the structural-complexity and social-dynamics measurements.

Structural-functional connectivity bandwidth predicts processing speed in mild traumatic brain Injury: A multiplex network analysis

An emerging body of work has revealed alterations in structural (SC) and functional (FC) brain connectivity following mild TBI (mTBI), with mixed findings. However, these studies seldom integrate complimentary neuroimaging modalities within a unified framework. Multilayer network analysis is an emerging technique to uncover how white matter organization enables functional communication. Using our novel graph metric (SC-FC Bandwidth), we quantified the information capacity of synchronous brain regions in 53 mild TBI patients (46 females; age mean = 40.2 years (y), σ = 16.7 (y), range: 18–79 (y). Diffusion MRI and resting state fMRI were administered at the acute and chronic post-injury intervals. Moreover, participants completed a cognitive task to measure processing speed (30 Seconds and Counting Task; 30-SACT). Processing speed was significantly increased at the chronic, relative to the acute post-injury intervals (p = <0.001). Nonlinear principal components of direct (t = -1.84, p = 0.06) and indirect SC-FC Bandwidth (t = 3.86, p = <0.001) predicted processing speed with a moderate effect size (R2 = 0.43, p < 0.001), while controlling for age. A subnetwork of interhemispheric edges with increased SC-FC Bandwidth was identified at the chronic, relative to the acute mTBI post-injury interval (pFDR = 0.05). Increased interhemispheric SC-FC Bandwidth of this network corresponded with improved processing speed at the chronic post-injury interval (partial r = 0.32, p = 0.02). Our findings revealed that mild TBI results in complex reorganization of brain connectivity optimized for maximum information flow, supporting improved cognitive performance as a compensatory mechanism. Moving forward, this measurement may complement clinical assessment as an objective marker of mTBI recovery.

Economic and virtual water multilayer networks in China

Supply chains are complex systems that can be conceptualized as networks. Several studies have examined the structural properties of economic networks (i.e., given in units of financial value) and virtual water supply chain networks (i.e., where economic connections are reported in terms of their embodied water). In both cases, connections both within and between economic sectors are important to fully represent structural network properties, highlighting the importance of multilayer network analyses. The similarities and differences between economic and virtual water multilayer networks are yet to be well understood. The goal of this study is to consistently compare the economic and virtual water multilayer networks within China. Environmentally extended multi-regional input–output (EE-MRIO) data is used to build multilayer networks between 31 provinces and 41 economic sectors (nodes are province-sectors) for commodities and services in the year 2017, using both economic [¥] and virtual water [m3] weights. This study shows that virtual water multilayer networks are relevant to address questions of water sustainability, scarcity, and hazards in supply chains, but that examining virtual water networks in isolation may not identify the economically important core nodes. Consideration of both economic and embedded resource networks could enhance our understanding of complex supply chains.

Multi-modal and multi-subject modular organization of human brain networks

The human brain is a complex network of anatomically interconnected brain areas. Spontaneous neural activity is constrained by this architecture, giving rise to patterns of statistical dependencies between the activity of remote neural elements. The non-trivial relationship between structural and functional connectivity poses many unsolved challenges about cognition, disease, development, learning and aging. While numerous studies have focused on statistical relationships between edge weights in anatomical and functional networks, less is known about dependencies between their modules and communities. In this work, we investigate and characterize the relationship between anatomical and functional modular organization of the human brain, developing a novel multi-layer framework that expands the classical concept of multi-layer modularity. By simultaneously mapping anatomical and functional networks estimated from different subjects into communities, this approach allows us to carry out a multi-subject and multi-modal analysis of the brain’s modular organization. Here, we investigate the relationship between anatomical and functional modules during resting state, finding unique and shared structures. The proposed framework constitutes a methodological advance in the context of multi-layer network analysis and paves the way to further investigate the relationship between structural and functional network organization in clinical cohorts, during cognitively demanding tasks, and in developmental or lifespan studies.

Multilayer network analysis of FMD transmission and containment among beef cattle farms

As a highly contagious livestock viral disease, foot-and-mouth disease poses a great threat to the beef-cattle industry. Direct animal movement is always considered as a major route for between-farm transmission of FMD virus. Sharing contaminated equipment and vehicles have also attracted increasing interests as an indirect but considerable route for FMD virus transmission. With the rapid development of communication technologies, information-sharing techniques have been used to control epidemics. In this paper, we built farm-level time-series three-layer networks to simulate the between-farm FMD virus transmission in southwest Kansas by cattle movements (direct-contact layer) and truck visits (indirect-contact layer) and evaluate the impact of information-sharing techniques (information-sharing layer) on mitigating the epidemic. Here, the information-sharing network is defined as the structure that enables the quarantine of farms that are connected with infected farms. When a farm is infected, its infection status is shared with the neighboring farms in the information-sharing network, which in turn become quarantined. The results show that truck visits can enlarge the epidemic size and prolong the epidemic duration of the FMD outbreak by cattle movements, and that the information-sharing technique is able to mitigate the epidemic. The mitigation effect of the information-sharing network varies with the information-sharing network topology and different participation levels. In general, an increased participation leads to a decreased epidemic size and an increased quarantine size. We compared the mitigation performance of three different information-sharing networks (random network, contact-based network, and distance-based network) and found the outbreak on the network with contact-based information-sharing layer has the smallest epidemic size under almost any participation level and smallest quarantine size with high participation. Furthermore, we explored the potential economic loss from the infection and the quarantine. By varying the ratio of the average loss of quarantine to the loss of infection, we found high participation results in reduced economic losses under the realistic assumption that culling costs are much greater than quarantine costs.