Polya传染网络的传播与治愈策略
Initialization and Curing Policies for Polya Contagion Networks
摘要：
本文研究了网络流行病的资源分配的优化策略，使用一个模型，来自经典的波利亚过程。这个模型的基本机制，称为波利亚网络传染过程，是基于一个修改后的瓮抽样方案，占时间和空间的网络中相邻节点之间的传染。我们提出了各种感染指标，并使用它们来开发两个问题：一个发生在初始化和不断发生的波利亚网络过程的发展。我们将这些问题视为固定预算的资源分配问题，并分析了一套潜在的政策。由于这些问题的复杂性，我们引入有效的代理措施，在每种情况下的平均感染率。我们还证明了所谓的预期网络曝光的双边感染治疗游戏承认一个纳什均衡。在固化和初始化的情况下，我们引入启发式的政策，主要功能的基础上，限制特定的网络设置中的目标节点的数量。模拟运行中到大规模的网络，以比较我们的算法的性能，证明收敛的梯度下降算法上运行的简化代理措施。
英文摘要：
This paper investigates optimization policies for resource distribution in network epidemics using a model that derives from the classical Polya process. The basic mechanics of this model, called the Polya network contagion process, are based on a modified urn sampling scheme that accounts for both temporal and spatial contagion between neighbouring nodes in a network. We present various infection metrics and use them to develop two problems: one which takes place upon initialization and one which occurs continually as the Polya network process develops. We frame these problems as resource allocation problems with fixed budgets, and analyze a suite of potential policies. Due to the complexity of these problems, we introduce effective proxy measures for the average infection rate in each case. We also prove that the two-sided infection-curing game on the so-called expected network exposure admits a Nash equilibrium. In both the curing and initialization scenarios, we introduce heuristic policies that primarily function on the basis of limiting the number of targeted nodes within a particular network setup. Simulations are run for mid-to-large scale networks to compare performance of our heuristics to provably convergent gradient descent algorithms run on the simplified proxy measures.
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