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Identifying Influential Spreaders of Epidemics on Community Networks
Shi-Long Luo, Kai Gong, Li Kang
TL;DR
Identifying spreaders that can suppress outbreaks remains an open issue, especially in networks with community structure. The paper proposes a k-shell strategy that processes weak and strong ties separately; it reports better performance than degree, betweenness, and k-shell strategies in most cases, with stability under missing network information.
Problem
Identifying influential spreaders that can hinder disease spread remains an open issue, and complex community structure makes the task challenging.
Source: §1 · pp. 1–2Method
The proposed strategy separates weak- and strong-tie processing in k-shell decomposition to identify influential spreaders.
Source: §5 · p. 10Results
In most cases, the strategy was more effective than degree, betweenness, and k-shell decomposition, with effectiveness attributed to neighbors’ connectivity patterns.
Source: §5 · p. 10Takeaways & Limitations
The method remained stable throughout processes involving missing network information.
Source: §5 · p. 10Finding optimal values of the strategy’s variable remains unresolved.
Source: §5 · p. 10
Abstract
from arXiv · showhide
An efficient strategy for the identification of influential spreaders that could be used to control epidemics within populations would be of considerable importance. Generally, populations are characterized by its community structures and by the heterogeneous distributions of weak ties among nodes bridging over communities. A strategy for community networks capable of identifying influential spreaders that accelerate the spread of disease is here proposed. In this strategy, influential spreaders serve as target nodes. This is based on the idea that, in k-shell decomposition, weak ties and strong ties are processed separately. The strategy was used on empirical networks constructed from online social networks, and results indicated that this strategy is more accurate than other strategies. Its effectiveness stems from the patterns of connectivity among neighbors, and it successfully identified the important nodes. In addition, the performance of the strategy remained robust even when there were errors in the structure of the network.
1. INTRODUCTION
Identifying spreaders that can suppress outbreaks remains an open problem in community networks, whose complex mesoscopic structure makes the task challenging. The paper proposes separating weak- and strong-tie processing in k-shell decomposition; it reports better empirical-network performance than degree, betweenness, and k-shell strategies, with robustness to noise.
1. INTRODUCTION
- Identifying spreaders that can effectively hinder disease spread remains an open issue, and complex community structure makes the task challenging.Source: §1 · pp. 2–3
- The proposed k-shell with community strategy identifies spreaders by processing weak and strong ties separately.Source: §1 · p. 3
- The strategy performed better on empirical networks than degree, betweenness, and k-shell decomposition strategies, and simulations indicated robustness to noise.The reported effectiveness is attributed to connectivity patterns among neighbors.Source: §1 · p. 3
2. DATAS AND MODEL
The study compares spreader-identification strategies on empirical Facebook networks and uses an SIR model to quantify epidemic spread. Its network construction links students through dormitory friendship or shared major and year across dormitories.
2.1 Network Construction
- The empirical networks were built from anonymous student data at four U.S. universities, linking online friends in the same dormitory and students in different dormitories who shared a major and year.Source: §2.1 · p. 3
- The networks exhibited small-world characteristics, high clustering, short average path length, and high modularity.Source: §2.1 · p. 4
2.2 Dynamic Model
- An SIR model with identical active-contact capability compared different identification strategies (Zhou et al. 2006), recording average infected size M and the fraction of the population ever infected at epidemic end.Each individual had infectivity A = 2, and the probability that a susceptible node would be infected was β = 0.5.Source: §2.2 · p. 4
3. METHODS
The methods section outlines degree, betweenness, and k-shell strategies, then introduces a k-shell with community strategy that treats weak and strong ties separately. Its k-score combines the resulting core indices using a parameter that shifts emphasis between local hubs and bridge hubs.
3.1 Identification Strategies
- Degree, betweenness, and k-shell decomposition are compared as identification strategies, while the k-shell process does not account for heterogeneous weak ties.Source: §3.1 · p. 5
3.2 K-Shell with Community Strategy
- The proposed strategy separately prunes weak ties between communities and strong ties within communities, assigning each node corresponding core indices before calculating its k-score.Source: §3.2 · pp. 5–6
- The k-score combines strong- and weak-tie core indices using α, a coefficient between 0 and 1; α = 1 was preferred for hub nodes in local structure.Source: §3.2 · pp. 5–6
4. RESULTS
The empirical results characterize community roles and neighbor connectivity, compare k-score with other spreading-efficiency strategies, and test its robustness to missing connections.
4.1 Heterogeneity and Roles in Empirical Networks
- Figure 4 indicates that local hubs (Z ≥ 2.5) have nearly all connections either local (P < 0.2) or across a few communities (P < 0.6).Source: §4.1 · p. 7
4.2 Comparison of Spreading Efficiency
- In most strategy comparisons, Δε was positive; for Caltech, k-score was 7.66% (40.43%, 55.06%) higher than k-core (degree, betweenness).For Princeton, Georgetown, and the University network, the corresponding differences were 5.28% (12.91%, 42.19%), 5.66% (17.88%, 41.65%), and 4.93% (15.48%, 40.34%), respectively.Source: §4.2 · p. 8
4.3 Comparison of Average Number of Connections among Neighbors
- In almost all cases, k-score-selected nodes had neighbors with more extensive connections than nodes selected by other strategies, improving efficient-spreader identification.Source: §4.3 · p. 9
4.4 Robustness of the Strategy
- Under random removal of connections, the strategy remained stable (τ > 0.8) even when more than 20% of connections were removed.Source: §4.4 · p. 9
5. CONCLUSIONS AND DISCUSSION
Influential disease spreaders are difficult to identify in community networks. The proposed k-shell-with-community strategy separates weak and strong ties and, in most cases, identifies spreaders more accurately than comparison methods.
5. CONCLUSIONS AND DISCUSSION
- The k-shell-with-community strategy is based on processing weak and strong ties separately in k-shell decomposition.The study considers the importance of heterogeneous weak ties under real-world conditions.Source: §5 · pp. 9–10
- In most cases, the strategy identified influential spreaders more effectively than degree, betweenness, and k-shell decomposition, with more accurate results.The evaluation used empirical online social networks among students at U.S. universities.Source: §5 · p. 10
- The reported advantage is attributed to more striking connectivity patterns among neighbors, which accompany faster, more effective spread through the network.The paper links these neighbor patterns to the strategy's ability to identify influential spreaders.Source: §5 · p. 10
- The method is described as stable under missing processes, while strategy performance is generally influenced by network structure.The conclusion also characterizes the method as robust.Source: §5 · p. 10
- α near 1 favors identifying hubs in one area, while α near 0 favors bridge-hubs over communities; both conditions are unacceptable, and the optimum remains unresolved.The paper identifies choosing an optimal value of the variable as an open issue.Source: §5 · p. 10
FIGURE LEGENDS
The figure legends illustrate how the strategy distinguishes nodes within a network and describe empirical comparisons and robustness tests across university networks.
FIGURE LEGENDS
- In the schematic, nodes sharing a k-core index receive different weak-tie core indices; node B has the highest k-score at 3.5, versus 3 for A, 2.5 for C, and 2 for D.The example uses α = 0.5.Source: FIGURE LEGENDS · p. 11
- The empirical comparison plots weak- and strong-tie neighbor-set differences across strategies and varying f, with symbols identifying four university networks.Caltech, Princeton, Georgetown, and Oklahoma are represented by squares, circles, upward-facing triangles, and downward-facing triangles, respectively.Source: FIGURE LEGENDS · pp. 11–12
- Figure 7 plots τ against the number f of randomly removed connections to assess robustness, averaging 2,000 realizations for each removal level.The listed α values are 0.95 for Caltech and Princeton, 0.88 for Georgetown, and 0.96 for Oklahoma.Source: FIGURE LEGENDS · p. 12
TABLES
Table 1 lists structural properties for empirical university networks, while Figures 1–7 depict tie patterns, node roles, spreading-efficiency comparisons, and robustness under network noise.
TABLES
- Table 1 lists network size, edges, degree, path length, clustering, assortativity, heterogeneity, community count, and modularity for the named university networks.The caption names Caltech, Princeton, and Georgetown, plus a truncated reference to another university.Source: Table 1 · p. 15
- Figures 1–4 depict weak and strong ties, a strategy schematic, their empirical distributions, and node roles in Z-P space.Source: Figure 1 · p. 16, Figure 2 · p. 17, Figure 3 · p. 18
- Figures 5–7 address spreading-efficiency comparisons, neighboring-node weak and strong ties, and strategy robustness under random connection removal.Source: Figure 5 · p. 20, Figure 6 · p. 21, Figure 7 · p. 22