利用网络上的概率扩散模型控制传染病传播
Controlling Epidemic Spread using Probabilistic Diffusion Models on Networks
摘要：
流行病的传播通常由社会网络图上的SIR随机过程建模。最佳社交距离的MinINF问题涉及最小化预期感染数量，此时我们最多可以破坏$B$的边;类似地，MinINFNode问题涉及最多删除$B$的顶点。这些都是流行病学和网络科学中的基本问题。虽然已经考虑了一些复杂性，这些问题的复杂性仍然普遍开放。在本文中，我们提出了两个双准则近似算法MinINF，这给了这个问题的第一个非平凡的近似。第一种方法是基于Karger \cite{karger:mathor99}的切割稀疏化结果，并且在传输概率不太小的情况下工作。第二种是基于样本平均近似（SAA）的算法，我们分析了Chung-Lu随机图模型。我们还扩展了我们的一些结果来解决MinINFNode问题。
英文摘要：
The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinINF problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most $B$ edges; similarly the MinINFNode problem involves removing at most $B$ vertices. These are fundamental problems in epidemiology and network science. While a number of heuristics have been considered, the complexity of these problems remains generally open. In this paper, we present two bicriteria approximation algorithms for MinINF, which give the first non-trivial approximations for this problem. The first is based on the cut sparsification result of Karger \cite{karger:mathor99}, and works when the transmission probabilities are not too small. The second is a Sample Average Approximation (SAA) based algorithm, which we analyze for the Chung-Lu random graph model. We also extend some of our results to tackle the MinINFNode problem.
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