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Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks
Physical Review X ( IF 12.5 ) Pub Date : 2020-03-24 , DOI: 10.1103/physrevx.10.011070
Claudio Castellano , Romualdo Pastor-Satorras

We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which represents a generalization of degree-ordered percolation, we derive a scaling solution on uncorrelated complex networks, unveiling the existence of diverse mechanisms leading to the formation of a percolating cluster. The scaling solution accurately reproduces universal properties of the transition. This finding is used to infer the critical properties of the susceptible-infected-susceptible model for epidemics in infinite and finite power-law distributed networks. Here, discrepancies between analytical approaches and numerical results regarding the finite-size scaling of the epidemic threshold are a crucial open issue in the literature. We find that the scaling exponent assumes a nontrivial value during a long preasymptotic regime. We calculate this value, finding good agreement with numerical evidence. We also show that the crossover to the true asymptotic regime occurs for sizes much beyond currently feasible simulations. Our findings allow us to rationalize and reconcile all previously published results (both analytical and numerical), thus ending a long-standing debate.

中文翻译:

网络中的累积合并渗流和敏感感染敏感模型的流行病过渡

我们考虑累积合并渗透(CMP),这是一个远程渗透过程,描述了网络中簇的迭代合并,具体取决于簇的质量和相互距离。对于特定类型的CMP过程(表示度排序渗流的泛化),我们导出了不相关复杂网络的缩放解决方案,揭示了导致渗流簇形成的各种机制的存在。缩放解决方案可以准确地再现过渡的通用属性。该发现可用于推断无限和有限幂律分布网络中流行病的易感性感染易感模型的关键特性。这里,关于流行病阈值的有限规模缩放的分析方法与数值结果之间的差异是文献中一个至关重要的未决问题。我们发现,在长渐近渐进状态期间,缩放指数假设为一个非平凡的值。我们计算出该值,并与数值证据找到了很好的一致性。我们还表明,到真正的渐近体制的交叉发生的大小远远超出了当前可行的模拟范围。我们的发现使我们能够合理化和调和以前发布的所有结果(包括分析和数值结果),从而结束了长期的辩论。我们还表明,到真正的渐近体制的交叉发生的大小远远超出了当前可行的模拟范围。我们的发现使我们能够合理化和调和以前发布的所有结果(包括分析和数值结果),从而结束了长期的辩论。我们还表明,到真正的渐近体制的交叉发生的大小远远超出了当前可行的模拟范围。我们的发现使我们能够合理化和调和所有先前发表的结果(包括分析和数值结果),从而结束了长期的辩论。
更新日期:2020-03-24
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