Contagion Spreading on Complex Networks: Fitness-Based Local Dynamics
We propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local dynamics occurring at various nodes. The model exhibits quality-dependent exponential time scales at early times leading to a slo
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Abstract We propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local dynamics occurring at various nodes. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. Our results are consistent with recent empirical observations.
The problem of contagion spreading on complex networks has been intensively studied in the past decade [1–6]. Such study is important in many fields as the contagion could be a biological virus, a computer virus, information or rumor among others. Most commonly studied theoretical models assume a global transmission probability and follow the contagion spreading on various complex structures. While such models capture the general dynamics of contagion spreading, they fall short on some important aspects of spreading phenomena observed in empirical studies. Most notably, such models exhibit an exponentially fast spreading leading to a high prevalence static, final state where a large part of the networks is infected. This runs contradicting to most real-world situations where low prevalence in a quasi-stationary state is observed [7–11]. Here, we introduce and study a realistic model of spreading where contagions are given a measure which allows them to interact with local agents, thus determining their fitness for transmission. We find that our model can reproduce many important characteristics of general spreading phenomena. Accordingly, we introduce a local quantity (called quality) xi for each agent i . We assume that the quality of each agent (node) is directly proportional to the number of its neighbors ki , xi D ki =kmax where kmax D max.ki /, making 0 xi 1 for any given network. We also introduce a parameter ˛ which characterizes
P. Manshour A. Montakhab () Physics Department, Shiraz University, Shiraz 71454, Iran e-mail: [email protected] S.G. Stavrinides et al. (eds.), Chaos and Complex Systems, DOI 10.1007/978-3-642-33914-1 43, © Springer-Verlag Berlin Heidelberg 2013
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Fig. 1 Averaged density of informed nodes versus time in (a) a SF network and (b) an ER network. The networks have the same size of N D 20; 000 and average degree hki D 6. The insets show the exponential growth during the first few steps. Note that the average quality hxi is much smaller on the SF network
the quality of the contagion being spread, where 0 ˛ 1. We consider a local probabilistic rule for acceptance (i.e. transmission) of contagion based on the perceived fitness of the incoming contagion, ˛, which is defined as follows: for each nod
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