Abstract
There has been growing interest in exploring the interplay between epidemic spreading with human response, since it is natural for people to take various measures when they become aware of epidemics. As a proper way to describe the multiple connections among people in reality, multiplex network, a set of nodes interacting through multiple sets of edges, has attracted much attention. In this paper, to explore the coupled dynamical processes, a multiplex network with two layers is built. Specifically, the information spreading layer is a time varying network generated by the activity driven model, while the contagion layer is a static network. We extend the microscopic Markov chain approach to derive the epidemic threshold of the model. Compared with extensive Monte Carlo simulations, the method shows high accuracy for the prediction of the epidemic threshold. Besides, taking different spreading models of awareness into consideration, we explored the interplay between epidemic spreading with awareness spreading. The results show that the awareness spreading can not only enhance the epidemic threshold but also reduce the prevalence of epidemics. When the spreading of awareness is defined as susceptible-infected-susceptible model, there exists a critical value where the dynamical process on the awareness layer can control the onset of epidemics; while if it is a threshold model, the epidemic threshold emerges an abrupt transition with the local awareness ratio α approximating 0.5. Moreover, we also find that temporal changes in the topology hinder the spread of awareness which directly affect the epidemic threshold, especially when the awareness layer is threshold model. Given that the threshold model is a widely used model for social contagion, this is an important and meaningful result. Our results could also lead to interesting future research about the different time-scales of structural changes in multiplex networks.
Highlights
The problem of modeling how epidemics spread among individuals has been extensively studied by people from various fields for many years.1–5 In the field of physics, most approaches to these problems are related to the theory of phase transition, statistical physics, and critical phenomenon.6–10 Especially in last decades, the study of complex1054-1500/2016/26(4)/043110/10/$30.00Published by AIP Publishing.043110-2 Guo et al.Chaos 26, 043110 (2016)networks has provided new grounds to the understanding of epidemic dynamics for physicists.11,12 They proposed various models, such as the classical susceptible-infectedsusceptible model (SIS),13 susceptible-infected-recovery model (SIR),14 and so on,15,16 to shed light on modeling the epidemic dynamics
In this paper, through considering the interactions among individuals as a time varying network where the awareness diffusion process occurs, we have explored the effects that the spread of awareness has on epidemic spreading
With the help of the multiplex network, we are able to model the interplay between these two kinds of dynamical processes
Summary
The problem of modeling how epidemics spread among individuals has been extensively studied by people from various fields for many years. In the field of physics, most approaches to these problems are related to the theory of phase transition, statistical physics, and critical phenomenon. Especially in last decades, the study of complex. Since a time-aggregated representation of network’s interactions neglects the time-varying nature of real systems, it is meaningful for us to model the information layer as a time varying network and to study the effects that information spreading process has on epidemic spreading. This scenario is common in reality if we consider the spreading of epidemic information originating from social media, for example, the spreading of Severe Acute Respiratory Syndromes. We find that the temporal changes in the topology hinder the spread of awareness which directly affect the epidemic threshold, especially when the awareness layer is the threshold model
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