Tunc Ilker, Shaw Leah B
Department of Applied Science, College of William and Mary, Williamsburg, VA 23187, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):022801. doi: 10.1103/PhysRevE.90.022801. Epub 2014 Aug 4.
When an epidemic spreads in a population, individuals may adaptively change the structure of their social contact network to reduce risk of infection. Here we study the spread of an epidemic on an adaptive network with community structure. We model two communities with different average degrees. The disease model is susceptible-infected-susceptible (SIS), and adaptation is rewiring of links between susceptibles and infectives. Locations of rewired links are selected so that the community structure will be preserved if susceptible-infective links are homogeneously distributed. The bifurcation structure is obtained, and a mean field model is developed that accurately predicts the steady-state behavior of the system. In a static network, weakly connected heterogeneous communities can have significantly different infection levels. In contrast, adaptation promotes similar infection levels and alters the network structure so that communities have more similar average degrees. We estimate the time for network restructuring to allow infection incursion from one community to another and show that it is inversely proportional to the number of cross-links between communities. In extremely heterogeneous systems, periodic oscillations in infection level can occur due to repeated infection incursions.
当一种流行病在人群中传播时，个体可能会适应性地改变其社会接触网络的结构以降低感染风险。在此，我们研究流行病在具有社区结构的自适应网络上的传播。我们对两个平均度不同的社区进行建模。疾病模型为易感 - 感染 - 易感（SIS）模型，适应过程是易感者与感染者之间链接的重新布线。重新布线链接的位置经过选择，以便在易感 - 感染链接均匀分布时能保留社区结构。我们得到了分岔结构，并开发了一个平均场模型，该模型能准确预测系统的稳态行为。在静态网络中，弱连接的异质社区可能具有显著不同的感染水平。相比之下，适应会促进相似的感染水平，并改变网络结构，使社区具有更相似的平均度。我们估计了网络重组以允许感染从一个社区侵入另一个社区所需的时间，并表明该时间与社区之间的交叉链接数量成反比。在极端异质系统中，由于反复的感染侵入，感染水平可能会出现周期性振荡。
