二维拟周期格点上的异步SIR模型
Asynchronous SIR model on Two-Dimensional Quasiperiodic Lattices
摘要：
我们考虑了Penrose和Ammann-Beenker准周期格点上的异步SIR模型，并利用Newman-Ziff算法通过在动态格点上生成簇的树结构来跟踪簇的传播，从而得到了它的临界行为，从而可以在非周期格点上模拟SIR模型并测量与渗流相关的任何可观测量.我们数值计算的序参量，定义在一个地理的方式区分流行病的状态，其特征在于形成的跨越集群的删除节点和地方病的状态，其中没有跨越集群。我们得到了平均的平均集群大小，它起着易感性的作用，和一个累积量比定义的渗流估计的流行阈值。我们的数值结果表明，该系统属于二维动态渗流普适类和准周期的顺序是无关的，根据经典渗流的结果。
英文摘要：
We considered the Asynchronous SIR (susceptible-infected-removed) model on Penrose and Ammann-Beenker quasiperiodic lattices, and obtained its critical behavior by using Newman-Ziff algorithm to track cluster propagation by making a tree structure of clusters grown at the dynamics, allowing to simulate SIR model on non-periodic lattices and measure any observable related to percolation. We numerically calculated the order parameter, defined in a geographical fashion by distinguish between an epidemic state, characterized by a spanning cluster formed by the removed nodes and the endemic state, where there is no spanning cluster. We obtained the averaged mean cluster size which plays the role of a susceptibility, and a cumulant ratio defined for percolation to estimate the epidemic threshold. Our numerical results suggest that the system falls into two-dimensional dynamic percolation universality class and the quasiperiodic order is irrelevant, in according to results for classical percolation.
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