Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Tokyo 153-8505, Japan.
J Theor Biol. 2012 Jul 7;304:121-30. doi: 10.1016/j.jtbi.2012.03.022. Epub 2012 Mar 28.
Since community structures in real networks play a major role for the epidemic spread, we therefore explore two interacting diseases spreading in networks with community structures. As a network model with community structures, we propose a random clique network model composed of different orders of cliques. We further assume that each disease spreads only through one type of cliques; this assumption corresponds to the issue that two diseases spread inside communities and outside them. Considering the relationship between the susceptible-infected-recovered (SIR) model and the bond percolation theory, we apply this theory to clique random networks under the assumption that the occupation probability is clique-type dependent, which is consistent with the observation that infection rates inside a community and outside it are different, and obtain a number of statistical properties for this model. Two interacting diseases that compete the same hosts are also investigated, which leads to a natural generalization of analyzing an arbitrary number of infectious diseases. For two-disease dynamics, the clustering effect is hypersensitive to the cohesiveness and concentration of cliques; this illustrates the impacts of clustering and the composition of subgraphs in networks on epidemic behavior. The analysis of coexistence/bistability regions provides significant insight into the relationship between the network structure and the potential epidemic prevalence.
由于真实网络中的社区结构对传染病的传播起着重要作用，因此我们探索了两种具有社区结构的网络中的相互作用的疾病传播。作为一种具有社区结构的网络模型，我们提出了一个由不同阶的团组成的随机团网络模型。我们进一步假设两种疾病只通过一种类型的团传播；这种假设对应于两种疾病在社区内和社区外传播的问题。考虑到易感-感染-恢复（SIR）模型与键渗流理论之间的关系，我们将该理论应用于团随机网络中，假设占据概率与团类型有关，这与社区内和社区外的感染率不同的观察结果一致，并得到了该模型的一些统计性质。我们还研究了两种相互竞争同一宿主的传染病，这自然地推广了分析任意数量传染病的方法。对于两种疾病的动力学，聚类效应对团的内聚性和浓度非常敏感；这说明了聚类和网络中子图的组成对传染病行为的影响。共存/双稳定性区域的分析为网络结构和潜在传染病流行之间的关系提供了重要的见解。
