Biomathematics Unit, Department of Zoology, Faculty of Life Sciences, Tel Aviv University, Israel.
J Theor Biol. 2012 Dec 21;315:110-8. doi: 10.1016/j.jtbi.2012.08.036. Epub 2012 Sep 7.
It is now well appreciated that population structure can have a major impact on disease dynamics, outbreak sizes and epidemic thresholds. Indeed, on some networks, epidemics occur only for sufficiently high transmissibility, whereas in others (e.g. scale-free networks), no such threshold effect exists. While the effects of variability in connectivity are relatively well known, the effects of clustering in the population on disease dynamics are still debated. We develop a simple and intuitive model for calculating the reproductive number R(0) on clustered networks with arbitrary degree distribution. The model clearly shows that in general, clustering impedes epidemic spread; however, its effects are usually small and/or coupled with other topological properties of the network. The model is generalized to take into account degree-dependent transmissibility (e.g., relevant for disease vectors). The model is also used to easily rederive a known result concerning the formation of the giant component.
现在人们已经充分认识到，人口结构会对疾病动态、疫情规模和传染病阈值产生重大影响。事实上，在某些网络中，传染病只有在足够高的传染性下才会发生，而在其他网络中（例如无标度网络），则不存在这种阈值效应。虽然连通性变化的影响相对较为明确，但人口聚类对疾病动态的影响仍存在争议。我们开发了一个简单直观的模型，用于计算具有任意度分布的聚类网络上的基本再生数 R(0)。该模型清楚地表明，在一般情况下，聚类会阻碍传染病的传播；然而，其影响通常较小，并且/或者与网络的其他拓扑特性相关联。该模型被推广以考虑与度相关的传染性（例如，与疾病载体相关）。该模型还用于轻松重新推导关于巨型组件形成的一个已知结果。
