论文标题
无尺度网络的流行病暴发
Epidemic Outbreaks on Quenched Scale-Free Networks
论文作者
论文摘要
我们提出了一个有限尺寸的缩放理论，即接触过程具有永久性免疫力的无关尺度网络。我们通过对易感感染感染的模型的类似物对流行病爆发进行了模拟，其中感染的个体攻击仅在一个时间单位中易感性侵蚀，以一种我们可以期望在无标度网络上具有不变的临界阈值。众所周知，可以在键合过程中映射易感感染的被感染的模型，从而使我们能够比较网站上的站点和债券通用类别的关键行为。我们使用了外场有限尺度理论，其中对有限大小的依赖性进入了被定义为受感染个体的初始数量的外部场。我们可以将外部字段的比例强加于$ n^{ - 1} $。该系统提出了流行性流行期的转变，其中临界行为遵守理论上和模拟时表现出的平均场景普遍性类别。
We present a finite-size scaling theory of a contact process with permanent immunity on uncorrelated scale-free networks. We model an epidemic outbreak by an analog of the susceptible-infected-removed model where an infected individual attacks only one susceptible in a time unit in a way we can expect a non-vanishing critical threshold at scale-free networks. As we already know, the susceptible-infected-removed model can be mapped in a bond percolation process, allowing us to compare the critical behavior of site and bond universality classes on networks. We used the external field finite-scale theory, where the dependence on the finite size enters the external field defined as the initial number of infected individuals. We can impose the scale of the external field as $N^{-1}$. The system presents an epidemic-endemic phase transition where the critical behavior obeys the mean-field universality class, as we show theoretically and by simulations.
