Stability properties of infected networks with low curing rates
Stability properties of infected networks with low curing rates
复制标题
DOI：
10.1109/acc.2014.6859418
复制
发表时间：
2014-06
期刊：
影响因子：
--
通讯作者：
A. Khanafer;T. Başar;B. Gharesifard
中科院分区：
文献类型：
--
作者：
A. Khanafer;T. Başar;B. Gharesifard
在这项工作中，我们分析了最近提出的动力系统，描述了网络中的感染概率的演变的稳定性。我们表明，这个模型可以被看作是一个凹的节点之间的游戏。这个特征使我们能够提供一个简单的条件，可以在分布式的方式检查，稳定的起源。当节点处的治愈率较低时，残余感染留在网络内。利用Hurwitz Mertzel矩阵的性质，我们证明了剩余流行状态是局部指数稳定的。我们还证明了这个状态是全局渐近稳定的。此外，我们调查的问题，稳定的网络时，有限数量的节点的固化率可以控制。特别是，我们刻画了一类无向图所需的控制器的数量。几个模拟证明了我们的结果。
In this work, we analyze the stability properties of a recently proposed dynamical system that describes the evolution of the probability of infection in a network. We show that this model can be viewed as a concave game among the nodes. This characterization allows us to provide a simple condition, that can be checked in a distributed fashion, for stabilizing the origin. When the curing rates at the nodes are low, a residual infection stays within the network. Using properties of Hurwitz Mertzel matrices, we show that the residual epidemic state is locally exponentially stable. We also demonstrate that this state is globally asymptotically stable. Furthermore, we investigate the problem of stabilizing the network when the curing rates of a limited number of nodes can be controlled. In particular, we characterize the number of controllers required for a class of undirected graphs. Several simulations demonstrate our results.