Effects of lattice dilution on the nonequilibrium phase transition in the stochastic susceptible-infectious-recovered model,Physical Review E

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Effects of lattice dilution on the nonequilibrium phase transition in the stochastic susceptible-infectious-recovered model
Physical Review E ( IF 2.2 ) Pub Date : 2022-09-23 , DOI: 10.1103/physreve.106.034132
Ruslan I Mukhamadiarov ₁ , Uwe C Täuber _{2,

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Affiliation

We investigate how site dilution, as would be introduced by immunization, affects the properties of the active-to-absorbing nonequilibrium phase transition in the paradigmatic susceptible-infectious-recovered (SIR) model on regular cubic lattices. According to the Harris criterion, the critical behavior of the SIR model, which is governed by the universal scaling exponents of the dynamic isotropic percolation (DyIP) universality class, should remain unaltered after introducing impurities. However, when the SIR reactions are simulated for immobile agents on two- and three-dimensional lattices subject to quenched disorder, we observe a wide crossover region characterized by varying effective exponents. Only after a sufficient increase of the lattice sizes does it become clear that the SIR system must transition from that crossover regime before the effective critical exponents asymptotically assume the expected DyIP values. We attribute the appearance of this exceedingly long crossover to a time lag in a complete recovery of small disconnected clusters of susceptible sites, which are apt to be generated when the system is prepared with Poisson-distributed quenched disorder. Finally, we demonstrate that this transient region becomes drastically diminished when we significantly increase the value of the recovery rate or enable diffusive agent mobility through short-range hopping.

中文翻译：

晶格稀释对随机易感-感染-恢复模型中非平衡相变的影响

我们研究了通过免疫引入的位点稀释如何影响规则立方晶格上典型的易感-感染-恢复 (SIR) 模型中的主动-吸收非平衡相变的特性。根据 Harris 准则，SIR 模型的临界行为由动态各向同性渗流 (DyIP) 普遍性类的通用标度指数控制，在引入杂质后应保持不变。然而，当模拟二维和三维晶格上受淬火无序的固定剂的 SIR 反应时，我们观察到一个以不同有效指数为特征的宽交叉区域。只有在晶格尺寸充分增加之后，SIR 系统必须在有效临界指数渐近地假定预期的 DyIP 值之前从该交叉机制转变变得清晰。我们将这种超长交叉的出现归因于完全恢复小的不连贯的易感位点集群的时间滞后，当系统准备好泊松分布的淬火无序时，这些集群很容易产生。最后，我们证明当我们显着增加恢复率的值或通过短程跳跃启用扩散剂移动性时，这个瞬态区域会急剧减少。我们将这种超长交叉的出现归因于完全恢复小的不连贯的易感位点集群的时间滞后，当系统准备好泊松分布的淬火无序时，这些集群很容易产生。最后，我们证明当我们显着增加恢复率的值或通过短程跳跃启用扩散剂移动性时，这个瞬态区域会急剧减少。我们将这种超长交叉的出现归因于完全恢复小的不连贯的易感位点集群的时间滞后，当系统准备好泊松分布的淬火无序时，这些集群很容易产生。最后，我们证明当我们显着增加恢复率的值或通过短程跳跃启用扩散剂移动性时，这个瞬态区域会急剧减少。

更新日期：2022-09-24

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