Departamento de Física, Universidade Federal de Lavras, Caixa postal 3037, CEP:37200-900, Lavras, Minas Gerais, Brazil.
Chaos. 2021 Jan;31(1):012101. doi: 10.1063/5.0033130.
Dynamical systems running on the top of complex networks have been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact process (CP) and the susceptible-infected-susceptible (SIS) model are used quite often to describe epidemic dynamics. Despite their simplicity, these models are robust to predict the kernel of real situations. In this work, we review concisely both processes that are well-known and very applied examples of models that exhibit absorbing-state phase transitions. In the epidemic scenario, individuals can be infected or susceptible. A phase transition between a disease-free (absorbing) state and an active stationary phase (where a fraction of the population is infected) are separated by an epidemic threshold. For the SIS model, the central issue is to determine this epidemic threshold on heterogeneous networks. For the CP model, the main interest is to relate critical exponents with statistical properties of the network.
几十年来，在复杂网络上运行的动力系统一直受到广泛研究。但由于其广泛的适用性，这个主题仍然是复杂网络理论中最相关的问题之一。接触过程 (CP) 和易感染-感染-易感染 (SIS) 模型经常被用来描述传染病动力学。尽管它们很简单，但这些模型对于预测真实情况的核心非常稳健。在这项工作中，我们简要回顾了这两个过程，它们是展示吸收态相变的著名且非常适用的模型的示例。在传染病场景中，个体可能会被感染或易感染。无病（吸收）状态和活跃的固定阶段（部分人群被感染）之间的相变由流行病阈值隔开。对于 SIS 模型，核心问题是确定异质网络上的这个流行病阈值。对于 CP 模型，主要兴趣在于将临界指数与网络的统计特性联系起来。
