Targeted immunization of centralized nodes in large-scale networks has attracted significant attention. However, in real-world scenarios, knowledge and observations of the network may be limited, thereby precluding a full assessment of the optimal nodes to immunize (or quarantine) in order to avoid epidemic spreading such as that of the current coronavirus disease (COVID-19) epidemic. Here, we study a novel immunization strategy where only n nodes are observed at a time and the most central among these n nodes is immunized. This process can globally immunize a network. We find that even for small n (≈10) there is significant improvement in the immunization (quarantine), which is very close to the levels of immunization with full knowledge. We develop an analytical framework for our method and determine the critical percolation threshold p_c and the size of the giant component P_∞ for networks with arbitrary degree distributions P(k). In the limit of n → ∞ we recover prior work on targeted immunization, whereas for n = 1 we recover the known case of random immunization. Between these two extremes, we observe that, as n increases, p_c increases quickly towards its optimal value under targeted immunization with complete information. In particular, we find a new general scaling relationship between |p_c(∞) − p_c(n)| and n as |p_c(∞) − p_c(n)| ∼ n⁻¹exp(−αn). For scale-free (SF) networks, where P(k) ∼ k^−γ, 2 < γ < 3, we find that p_c has a transition from zero to nonzero when n increases from n = 1 to O(log N) (where N is the size of the network). Thus, for SF networks, having knowledge of ≈log N nodes and immunizing the most optimal among them can dramatically reduce epidemic spreading. We also demonstrate our limited knowledge immunization strategy on several real-world networks and confirm that in these real networks, p_c increases significantly even for small n.

中文翻译：

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有限知识下的高效网络免疫


大规模网络中中心化节点的定向免疫引起了人们的广泛关注。然而，在现实场景中，对网络的了解和观察可能是有限的，从而无法对免疫（或隔离）的最佳节点进行全面评估，以避免流行病传播，例如当前的冠状病毒病（COVID-19）。 19）流行病。在这里，我们研究了一种新颖的免疫策略，其中一次仅观察n 个节点，并且对这n 个节点中最中心的节点进行免疫。此过程可以对网络进行全局免疫。我们发现，即使对于很小的n （≈10），免疫（检疫）也有显着改善，这非常接近完全知识的免疫水平。我们为我们的方法开发了一个分析框架，并确定了具有任意度分布P ( k ) 的网络的临界渗流阈值p _c和巨型组件P _∞的大小。在n → ∞ 的限制下，我们恢复先前关于靶向免疫的工作，而对于n = 1，我们恢复已知的随机免疫情况。在这两个极端之间，我们观察到，随着n 的增加，在具有完整信息的定向免疫下_， pc迅速增加到其最佳值。 特别是，我们发现 | 之间存在新的一般缩放关系。 p _c (∞) − p _c ( n )|和n作为 | p _c (∞) − p _c ( n )| ∼ n ⁻¹ exp(−α n )。对于无标度（SF）网络，其中P ( k ) ∼ k ^−γ , 2 < γ < 3 ，我们发现_当n从n = 1 增加到O (log N )（其中N是网络的大小）。因此，对于 SF 网络来说，了解 ≈log N个节点并免疫其中最优的节点可以显着减少流行病传播。我们还在几个真实网络上展示了我们有限的知识免疫策略，并确认在这些真实网络中，即使对于较小的n ， p _c也会显着增加。