幂律树上接触过程的靶向免疫阈值
Targeted Immunisation Thresholds for the Contact Process on Power-Law Trees
AI总结：
针对幂律树/无标度网络中均匀免疫无法阻断低感染率流行病传播的问题，研究靶向免疫最大度顶点的效果，发现最大允许度高于阈值时免疫效果微弱，低于同量级阈值时流行病存活概率骤降甚至清零。
摘要：
无标度配置模型与幂律Galton-Watson树密切相关。已知接触过程流行病可在这些树及对应网络上以任意小的感染率传播，即便均匀免疫一小部分正比例的顶点后，这一特性仍然成立。因此，我们转而对度数最大的顶点进行免疫：我们发现，当最大允许度数高于某一阈值时，免疫后的流行病存活概率与未免疫时相近，这一结论通过对偶性对应于相当的亚稳态密度。而当最大度数低于同量级的阈值时，存活概率会大幅降低甚至为零。
英文摘要：
Scale-free configuration models are intimately connected to power law Galton-Watson trees. It is known that contact process epidemics can propagate on these trees and therefore these networks with arbitrarily small infection rate, and this continues to be true after uniformly immunising a small positive proportion of vertices. So, we instead immunise those with largest degree: above a threshold for the maximum permitted degree, we discover the epidemic with immunisation has survival probability similar to without, by duality corresponding to comparable metastable density. With maximal degree below a threshold on the same order, this survival probability is severely reduced or zero.
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