Biomathematics Unit, Faculty of Life Sciences, Tel Aviv University, Israel.
J Theor Biol. 2011 Nov 7;288:21-8. doi: 10.1016/j.jtbi.2011.07.015. Epub 2011 Aug 7.
Over the last decade considerable research effort has been invested in an attempt to understand the dynamics of viruses as they spread through complex networks, be they the networks in human population, computers or otherwise. The efforts have contributed to an understanding of epidemic behavior in random networks, but were generally unable to accommodate specific nonrandom features of the network's actual topology. Recently, though still in the context of the mean field theory, Chakrabarti et al. (2008) proposed a model that intended to take into account the graph's specific topology and solve a longstanding problem regarding epidemic thresholds in both random and nonrandom networks. Here we review previous theoretical work dealing with this problem (usually based on mean field approximations) and show with several relevant and concrete counter examples that results to date breakdown for nonrandom topologies.
在过去的十年中，人们投入了大量的研究努力，试图理解病毒在复杂网络中传播的动态，无论是在人类群体、计算机还是其他网络中。这些努力有助于理解随机网络中的流行病行为，但通常无法适应网络实际拓扑的特定非随机特征。然而，最近 Chakrabarti 等人（2008 年）在平均场理论的背景下提出了一个模型，旨在考虑图的特定拓扑，并解决随机和非随机网络中流行阈值的一个长期存在的问题。在这里，我们回顾了以前处理这个问题的理论工作（通常基于平均场近似），并通过几个相关和具体的反例表明，迄今为止，对于非随机拓扑，结果是不可靠的。
