论文标题
具有相变的流行模型的概述，以吸收在复杂网络之上运行的状态
An overview of epidemic models with phase transitions to absorbing states running on top of complex networks
论文作者
论文摘要
数十年来，已经对复杂网络顶部运行的动力系统进行了广泛的研究。但是，由于其适用性范围，该主题仍然是复杂网络理论中最相关的问题之一。经常使用接触过程（CP）和易感感染感染感染的（SIS）模型来描述流行动力学。尽管它们很简单，但这些模型还是可靠的，可以预测真实情况的内核。在这项工作中，我们回顾了这两个过程，这些过程都是众所周知且非常应用的模型示例，这些模型表现出吸收状态相变。在流行病的情况下，个人可以感染或易感。无疾病（吸收）状态与活跃的静置相之间的相变（在感染人群的一部分）之间被流行阈值隔开。对于SIS模型，中心问题是确定在异质网络上的流行阈值。对于CP模型，主要兴趣是将关键指数与网络的统计属性联系起来。
Dynamical systems running on the top of complex networks has 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.
