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Contagion spreading on complex networks with local deterministic dynamics

机译:具有局部确定性动力学的复杂网络上的传染蔓延

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Typically, contagion strength is modeled by a transmission rate (/), whereby all nodes in a network are treated uniformly in a mean-field approximation. However, local agents react differently to the same contagion based on their local characteristics. Following our recent work (Montakhab and Manshour, 2012), we investigate contagion spreading models with local dynamics on complex networks. We therefore quantify contagions by their quality, 0 ≤ α ≤ 1, and follow their spreading as their transmission condition (fitness) is evaluated by local agents. Instead of considering stochastic dynamics, here we consider various deterministic local rules. We find that initial spreading with exponential quality-dependent time scales is followed by a stationary state with a prevalence depending on the quality of the contagion. We also observe various interesting phenomena, for example, high prevalence without the participation of the hubs. This special feature of our "threshold rule" provides a mechanism for high prevalence spreading without the participation of "super-spreaders", in sharp contrast with many standard mechanism of spreading where hubs are believed to play the central role. On the other hand, if local nodes act as agents who stop the transmission once a threshold is reached, we find that spreading is severely hindered in a heterogeneous population while in a homogeneous one significant spreading may occur. We further decouple local characteristics from underlying topology in order to study the role of network topology in various models and find that as long as small-world effect exists, the underlying topology does not contribute to the final stationary state but only affects the initial spreading velocity.
机译:通常,传染强度由传输速率(/)建模,从而网络中的所有节点均以均值场近似方式统一处理。但是,本地代理基于其本地特征对相同的传染有不同的反应。在我们最近的工作(Montakhab和Manshour,2012)之后,我们研究了在复杂网络上具有局部动力学的传染扩散模型。因此,我们通过传染病的质量0≤α≤1来量化传染病,并通过当地代理商评估其传播条件(适应性)来追踪其传播。在这里,我们考虑各种确定性的局部规则,而不是考虑随机动力学。我们发现,初始扩散具有与指数质量有关的时标,其后是稳态,其流行程度取决于感染的质量。我们还观察到各种有趣的现象,例如,没有中心参与的高流行率。我们的“阈值规则”的这一特殊功能提供了一种高流行度传播的机制,而无需“超级传播者”的参与,这与许多标准传播机制形成鲜明的对比,在这些传播机制中,集线器起着核心作用。另一方面,如果本地节点充当一旦达到阈值就停止传输的代理,我们会发现异质种群中的传播受到严重阻碍,而同质种群中可能会发生明显的传播。为了进一步研究网络拓扑在各种模型中的作用,我们进一步将局部特征与基础拓扑解耦,发现只要存在小世界效应,基础拓扑就不会影响最终的稳态,而只会影响初始扩散速度。

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