Suppressing disease spreading by using information diffusion on multiplex networks

Although there is always an interplay between the dynamics of information diffusion and disease spreading, the empirical research on the systemic coevolution mechanisms connecting these two

spreading dynamics is still lacking. Here we investigate the coevolution mechanisms and dynamics between information and disease spreading by utilizing real data and a proposed spreading

model on multiplex network. Our empirical analysis finds asymmetrical interactions between the information and disease spreading dynamics. Our results obtained from both the theoretical

framework and extensive stochastic numerical simulations suggest that an information outbreak can be triggered in a communication network by its own spreading dynamics or by a disease

outbreak on a contact network, but that the disease threshold is not affected by information spreading. Our key finding is that there is an optimal information transmission rate that

markedly suppresses the disease spreading. We find that the time evolution of the dynamics in the proposed model qualitatively agrees with the real-world spreading processes at the optimal

information transmission rate.

The coevolution dynamics on complex networks has attracted much attention in recent years, since dynamic processes, ubiquitous in the real world, are always interacting with each other1,2.

In biological spreading dynamics, two strains of the same disease spread in the same population and interact through cross immunity3,4,5 or mutual reinforcement6. In social spreading

dynamics, individuals are surrounded by multiple items of information supplied by, e.g., Facebook, Twitter, and YouTube. These sources of information compete with each other for the limited

attention-span of users, and the outcome is that only a few items of information survive and become popular7,8. Recently scholars have become aware of the coevolution or interplay between

biological and social spreadingdynamics9,10,11. When a new disease enters a population, if individuals who are aware of its potential spread take preventive measures to protect

themselves12,13 the disease spreading may be suppressed. Our investigation of the intricate interplay between information and disease spreading is a specific example of disease-behavior

systems14.

Studying the micromechanisms of a disease-behavior system can help us understand coevolution dynamics and enable us to develop ways of predicting and controlling the disease spreading10. In

this effort a number of excellent models15,16,17 have demonstrated the existence of non-trivial phenomena that differ substantially from those when there is independent spreading

dynamics18,19,20,21,22,23,24. Researchers have demonstrated that the outbreak of a disease has a metacritical point16 that is associated with information spreading dynamics and multiplex

network topology and that information propagation is promoted by disease spreading17. Funk et al. found that the disease threshold is altered once the information and disease evolve

simultaneously15. These models make assumptions about the coevolution mechanisms of information and disease spreading and do not demonstrate the interacting mechanisms in real-world systems.

Because we do not understand the microscopic coevolution mechanisms between information and disease spreading dynamics from real-world disease-behavior systems, we do not have a systematic

understanding of coevolution dynamics and do not know how to utilize information diffusion to more effectively suppress the spread of disease.

We present here a systematic investigation of the effects of interacting mechanisms on the coevolution processes of information and disease spreading dynamics. We first demonstrate the

existence of asymmetrical interactions between the two dynamics by using real-world data from information and disease systems to analyze the coevolution. We then propose an asymmetric

spreading dynamic model on multiplex networks to mimic the coupled spreading dynamics, which will allow us to understand the coevolution mechanics. The results, obtained from both the

theoretical analyses and extensive simulations, suggest some interesting phenomena: the information outbreak can be triggered by its own spreading dynamics or the disease outbreak, while the

disease threshold is not affected by the information spreading. Our most important finding is that there is an optimal information transmission rate at which the outbreak size of the

disease reaches its minimum value, and the time evolution of the dynamics in the proposed model qualitatively agrees with the dynamics of real-world spreading.

Information about disease can be obtained in many ways, including face-to-face communication, Facebook, Twitter, and other online tools. Since the growth of the Internet, search engines have

enabled anyone to obtain instantaneous information about disease. Patients seek out and analyze prescriptions using search engines in hopes of obtaining a means of rapid recovery. Healthy

individuals use search engines to identify protective measures against disease to maintain their good health.

Figure 1(a) shows the real-data time series of information nG(t) and disease nD(t) indicating that macroscopically the two systems exhibit similar trends and confirming that the GFT

effectively predicts disease spreading26,27 — although some researchers have expressed skepticism28. To identify the coevolution mechanisms operating between information and disease

spreading, we further investigate the time series from a microscopic point of view. Specifically, we study their relative growth rates vG(t) of nG(t) and vD(t) of nD(t) (see definitions in

Method Section). Figure 1(b) shows the evolution of vG(t) and vD(t). Note that the same and opposite growth trends of vG(t) and vD(t) coexist. For example, at week 53 (week 153), vG(53) > 0

[vG(153) > 0] and vD(53)  0]. Thus the GFT and ILI show the opposite (the same) growth trends.

(a) The relative number of outpatient visits nD(t)/〈nD(t)〉 (blue dashed line) and relative search queries aggregated in GFT nG(t)/〈nG(t)〉 (red solid line) versus t, where and , and tmax is

the number of weeks. (b) The relative growth rate vD(t) (blue dashed line) and vG(t) (red solid line) of nD(t) and nG(t) versus t, respectively. (c) Cross-correlation c(t) between the two

time series of vG(t) and vD(t) for the given window size wl = 3 (blue dashed line) and wl = 20 (red solid line). (d) The fraction of negative correlations fP (blue squares) and positive

correlations fN (red circles) as a function of wl. In (a), nG(t) and nD(t) are divided their average values respectively. In (b), the circles and squares denote the relative growth rate at t

 = 53 and 153, respectively.

To conceptualize the correlations of the growth trends between the two dynamics, we analyze the cross-correlations c(t) between the time series of vG(t) and vD(t) for a given window size

wl29 using the Pearson correlation coefficient c(t) between the two time series and . When c(t) > 0, the growth rates of information and disease share the same trend in the time interval wl.

When c(t)  0 [vD(t) > 0], nG(t) [nD(t)] shows an increasing trend at time t. If not, nG(t) [nD(t)] shows a decreasing trend at time t.

where Rh is the final information size or disease size , and is the ensemble averaging. The value of χ exhibits a peak at the critical point at which the thresholds can be computed.

How to cite this article: Wang, W. et al. Suppressing disease spreading by using information diffusion on multiplex networks. Sci. Rep. 6, 29259; doi: 10.1038/srep29259 (2016).

This work was partially supported by the National Natural Science Foundation of China under Grants Nos 11575041 and 11105025, and China Scholarship Council. L.A.B. thanks ANCyP, Pict 0429/13

and UNMdP for financial support.

Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, 610054, China

Big Data Research Center, University of Electronic Science and Technology of China, Chengdu, 610054, China

Center for Polymer Studies and Department of Physics, Boston University, Boston, 02215, Massachusetts, USA

Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR)-Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata-CONICET, Funes 3350,

Mar del Plata, 7600, Argentina

W.W. and M.T. devised the research project. W.W. and Q.-H.L. performed numerical simulations. W.W., S.-M.C., M.T., L.A.B. and H.E.S. analyzed the results. W.W., Q.-H.L., S.-M.C., M.T.,

L.A.B. and H.E.S. wrote the paper.

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