Continuum Percolation and Stochastic Epidemic Models on Poisson and Ginibre Point Processes
Continuum Percolation and Stochastic Epidemic Models on Poisson and Ginibre Point Processes
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DOI：
10.1016/j.physa.2021.126191
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Machiko Katori;M. Katori
中科院分区：
文献类型：
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作者：
Machiko Katori;M. Katori
研究最多的二维连续渗流模型是布尔模型，它由具有相同半径的圆盘组成，其中心随机分布在泊松点过程（PPP）上。我们还考虑了Ginibre点过程（GPP）上的布尔渗流模型，GPP是实现超均匀性的一个典型的排斥点过程。我们认为，PPP近似于一种无序的个人配置，而GPP则是一种公民配置，他们采取一种策略，在城市中保持社交距离，以避免传染。我们考虑了在PPP和GPP上形成的超临界渗流团簇上具有传染感染的SIR模型。通过数值模拟，我们研究了渗流现象和感染过程对PPP-和GPP-基础图的依赖性。我们发现，在一个亚临界制度的感染率的PPP为基础的模型显示出现的点，这是由波动的不相关的泊松统计聚集的感染集群。另一方面，在基于GPP的模型中，过程中感染个体的累积数量被抑制。
The most studied continuum percolation model in two dimensions is the Boolean model consisting of disks with the same radius whose centers are randomly distributed on the Poisson point process (PPP). We also consider the Boolean percolation model on the Ginibre point process (GPP) which is a typical repelling point process realizing hyperuniformity. We think that the PPP approximates a disordered configuration of individuals, while the GPP does a configuration of citizens adopting a strategy to keep social distancing in a city in order to avoid contagion. We consider the SIR models with contagious infection on supercritical percolation clusters formed on the PPP and the GPP. By numerical simulations, we studied dependence of the percolation phenomena and the infection processes on the PPP- and the GPP-underlying graphs. We show that in a subcritical regime of infection rate the PPP-based models show emergence of infection clusters on clumping of points which is formed by fluctuation of uncorrelated Poissonian statistics. On the other hand, the cumulative numbers of infected individuals in processes are suppressed in the GPP-based models.