The Role of Community Mixing Styles in Shaping Epidemic Behaviors in Weighted Networks

Vittoria Colizza,Yong Min,Jie Chang,Ying Ge,Xiaogang Jin

doi:10.1371/journal.pone.0057100

Vittoria Colizza, Yong Min + Show 3 more

Open Access

https://doi.org/10.1371/journal.pone.0057100

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Journal: PLoS ONE	Publication Date: Feb 20, 2013
Citations: 55	License type: CC BY 4.0

Affiliation: Zhejiang University of Technology, Zhejiang University

Abstract

The dynamics of infectious diseases that are spread through direct contact have been proven to depend on the strength of community structure or modularity within the underlying network. It has been recently shown that weighted networks with similar modularity values may exhibit different mixing styles regarding the number of connections among communities and their respective weights. However, the effect of mixing style on epidemic behavior was still unclear. In this paper, we simulate the spread of disease within networks with different mixing styles: a dense-weak style (i.e., many edges among the communities with small weights) and a sparse-strong style (i.e., a few edges among the communities with large weights). Simulation results show that, with the same modularity: 1) the mixing style significantly influences the epidemic size, speed, pattern and immunization strategy; 2) the increase of the number of communities amplifies the effect of the mixing style; 3) when the mixing style changes from sparse-strong to dense-weak, there is a ‘saturation point’, after which the epidemic size and pattern become stable. We also provide a mean-field solution of the epidemic threshold and size on weighted community networks with arbitrary external and internal degree distribution. The solution explains the effect of the second moment of the degree distribution, and a symmetric effect of internal and external connections (incl. degree distribution and weight). Our study has both potential significance for designing more accurate metrics for the community structure and exploring diffusion dynamics on metapopulation networks.

Highlights

Structural features are critical in explaining epidemic dynamics on complex networks [1,2,3,4,5,6,7,8]
These networks have the same number of communities and modularity value, the dense-weak style networks result in a larger epidemic size and a faster epidemic speed than the sparse-strong style networks
When considering additional features of the network structure within real populations, one of the most important findings was the demonstration that the modularity value can strongly affect epidemic dynamics [14]. Our results extend this finding and show that even in weighted networks with the same modularity, fundamentally different epidemic dynamics are observed due to different mixing styles among communities

Summary

Introduction

Structural features (e.g. heterogeneous degree distribution, small-world property, clustering effect, etc.) are critical in explaining epidemic dynamics on complex networks [1,2,3,4,5,6,7,8]. Community structure (i.e. the groups of nodes with strong connectivity among their members and weak connectivity to outside nodes) is one of the most important structural features, and broadly exists in social networks, food webs, worldwide trade networks, etc. Studies demonstrated that a weighted network shows different mixing styles, i.e. the pair of connection density and weight distributions among communities [16,17]. We try to isolate the effect of the mixing style from other structural features and describe how mixing style affects epidemic dynamics and the immunization strategies in weighted community networks

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