标题： 社区如何影响流行病传播：基于分层结构的元人口视角 显示英文标题

标题： How communities shape epidemic spreading: A hierarchically structured metapopulation perspective

摘要： 近期新冠疫情、寨卡病毒、埃博拉和流感的爆发重新引起了人们对改进流行病模型以更好地反映疾病传播复杂性的兴趣。 现代方法结合社会规范、移动模式以及异质社区结构，以捕捉社会与生物动态之间的相互作用。 本研究考察了分层结构元种群网络中的流行病传播，在这些网络中，个体在局部社区（如学校、工作场所和剧院）内互动，并在这些社区之间扩散。 通过平均场近似，我们推导出一个比例定律，将传染率与平均连接度联系起来，而稳定性分析则确定了感染激增的阈值。 在具有异质平均度的网络中，谱扰动理论揭示了结构变异性如何加速并放大疾病的传播。 我们发现，度高于平均水平的节点不仅被感染得更早，而且还是关键的疫情驱动因素。 将流行病动力学视为连续相变，我们应用模式形成理论表明，决定系统稳定性的关键特征向量由网络的度分布所塑造。 至关重要的是，通过对Laplacian特征向量的局域化进行分析，我们发现了社区感染密度与关键特征向量的条目之间的一一对应关系——揭示了内部社区结构如何直接塑造全球感染模式。 这项工作为理解并预测结构化人群中流行病动态提供了一个系统的框架，同时强调了社区组织的根本作用。 显示英文摘要

摘要： Recent outbreaks of COVID-19, Zika, Ebola, and influenza have renewed interest in advancing epidemic models to better reflect the complexities of disease spreading. Modern approaches incorporate social norms, mobility patterns, and heterogeneous community structures to capture the interplay between social and biological dynamics. This study examines epidemic propagation in hierarchically structured metapopulation networks, where individuals interact within localized communities -- such as schools, workplaces, and theaters -- and diffuse across them. Using mean-field averaging, we derive a scaling law linking contagion rates to the mean connectivity degree, while stability analysis identifies thresholds for infection surges. In networks with heterogeneous mean degrees, spectral perturbation theory reveals how structural variability accelerates and amplifies disease spreading. We find that nodes with above-average degrees are not only infected earlier but also act as key outbreak drivers. Framing epidemic dynamics as a continuous phase transition, we apply pattern formation theory to show that the critical eigenvectors governing system stability are shaped by the network's degree distribution. Crucially, by analyzing Laplacian eigenvector localization, we uncover a one-to-one correspondence between community infection densities and the entries of the critical eigenvector -- revealing how internal community structure directly shapes global infection patterns. This work provides a systematic framework for understanding and predicting epidemic dynamics in structured populations, while highlighting the fundamental role of community organization.