The Role of Node Heterogeneity in the Coupled Spreading of Epidemics and Awareness
Zheng
Z (2016) The Role of Node Heterogeneity in the
Coupled Spreading of Epidemics and Awareness.
PLoS ONE 11(8): e0161037. doi:10.1371/journal.
pone.0161037
The Role of Node Heterogeneity in the Coupled Spreading of Epidemics and Awareness
Quantong Guo 0 1
Yanjun Lei 0 1
Chengyi Xia 1
Lu Guo 1
Xin Jiang 0 1
Zhiming Zheng 0 1
0 School of Mathematics and Systems Science, Beihang University & Key Laboratory of Mathematics Informatics Behavioral Semantics(LMIB) , Beijing 100191, China , 2 School of Mathematical Sciences, Peking University , Beijing 100191, China , 3 Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology , Tianjin 300384, China , 4 Key Laboratory of Computer Vision and System (Ministry of Education),Tianjin University of Technology , Tianjin 300384, China, 5 Luoyang Branch of China Construction Bank, Luoyang 471000 , China
1 Editor: Luo-Luo Jiang, Wenzhou University , CHINA
Exploring the interplay between information spreading and epidemic spreading is a topic that has been receiving increasing attention. As an efficient means of depicting the spreading of information, which manifests as a cascade phenomenon, awareness cascading is utilized to investigate this coupled transmission. Because in reality, different individuals facing the same epidemic will exhibit distinct behaviors according to their own experiences and attributes, it is important for us to consider the heterogeneity of individuals. Consequently, we propose a heterogeneous spreading model. To describe the heterogeneity, two of the most important but radically different methods for this purpose, the degree and k-core measures, are studied in this paper through three models based on different assumptions. Adopting a Markov chain approach, we succeed in predicting the epidemic threshold trend. Furthermore, we find that when the k-core measure is used to classify individuals, the spreading process is robust to these models, meaning that regardless of the model used, the spreading process is nearly identical at the macroscopic level. In addition, the k-core measure leads to a much larger final epidemic size than the degree measure. These results are cross-checked through numerous simulations, not only of a synthetic network but also of a real multiplex network. The presented findings provide a better understanding of k-core individuals and reveal the importance of considering network structure when investigating various dynamic processes.
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OPEN ACCESS
Introduction
As one of the most important dynamic processes in complex networks, the diffusion process
[
1, 2
], especially the spreading of epidemics [
3–9
], has been receiving increasing interest for
decades. Various models have been developed to describe the diffusion of epidemics [10],
Luoyang Branch of China Construction Bank
provided support in the form of salaries for author Lu
Guo, but did not have any additional role in the study
design, data collection and analysis, decision to
publish, or preparation of the manuscript. The specific
roles of this author are articulated in the “author
contributions” section.
rumors [
11
], innovation [
12
] and so on. Different factors [
13–15
], such as the frequency of
contact between individuals, the disease duration, and the immunity of particular individuals, have
been considered in these models to provide a realistic and comprehensive understanding of the
spreading process. In particular, as an important representation of the spread of information
about epidemics, awareness spreading [
16–20
] has attracted increasing interest. A pioneering
step in this direction was taken by Funk et al. [
16
], who studied the spreading of epidemics
while accounting for the spread of awareness. Their results show that the final epidemic size can
be markedly reduced, whereas the epidemic threshold can be reduced only when the awareness
is sufficiently strong. At the same time, due to the different spreading paths of awareness and
epidemics, considering the spreading of the coupled dynamic process only on the same
singlelayer network makes it difficult to obtain a comprehensive understanding of the process as a
whole. As a result, as a natural means of describing mixed complex systems, methods based on
multiplex networks [
21–30
] have recently found success in revealing abundant features of
various dynamic processes, including epidemic spreading. Within the framework of multiplex
networks, Clara et al. [
31, 32
] developed a UAU-SIS model and found that a metacritical point
exists from which an epidemic can be delayed and contained. Guo et al. [
33
] proposed a local
awareness-controlled contagion spreading model in which the awareness layer is a threshold
model and also used the same framework as a UAU-SIS model to analyze the problem. The
analytical results showed high accuracy compared with Monte Carlo simulations.
However, in these studies, there exists a hidden as (...truncated)