非齐性总体社区网络上传染病传播的最优治愈策略
Optimal curing policy for epidemic spreading over a community network with heterogeneous population
摘要：
设计一个有效的治疗政策，能够阻止一个流行病的过程在一个负担得起的成本，必须考虑到人口接触网络的结构，支持传染过程。因此，我们解决了在人群中分配恢复资源的问题，以尽可能低的成本防止流行病在网络中无限期地持续下去。具体地说，我们分析了一个易感染的易感流行病过程的加权图上传播，通过一阶平均场近似。首先，我们描述了接触网络的动态的流行病之间的一个非齐性总体，这可能是分为社区的影响。对于社区网络的情况下，我们的调查依赖于公平分区的图论概念，我们表明，流行病的阈值，对流行病传播的网络鲁棒性的一个关键措施，可以确定使用一个低维的动力系统。利用计算的流行病阈值，我们确定了成本最优的治疗策略，通过解决一个凸极小化问题，它具有一个减少的社区网络的情况下的维数。最后，我们考虑了一个两层的最优固化问题，对于这个问题，我们设计了一个在网络规模下具有多项式时间复杂度的算法。
英文摘要：
The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a first-order mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.
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