标题： 社区如何影响流行病传播：一种分层结构的元种群视角 显示英文标题

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

摘要： 最近的新冠疫情、寨卡病毒、埃博拉病毒和流感爆发重新引起了人们对推进流行病模型的兴趣，以更好地反映疾病传播的复杂性。 现代方法结合了社会规范、移动模式和异质性社区结构，以捕捉社会和生物动态之间的相互作用。 本研究考察了分层结构的元种群网络中的流行病传播，其中个体在局部社区（如学校、工作场所和剧院）内互动，并在这些社区之间扩散。 使用平均场平均法，我们推导出一种将传染率与平均连通度联系起来的标度定律，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如何加速和放大疾病传播。 我们发现，平均度以上的节点不仅被更早感染，还作为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，决定系统稳定性的临界特征向量是由网络的度分布塑造的。 至关重要的是，通过分析拉普拉斯特征向量的局域化，我们发现社区感染密度与临界特征向量的条目之间存在一一对应关系——揭示了内部社区结构如何直接塑造全局感染模式。 这项工作为理解并预测结构化种群中的流行病动力学提供了一个系统的框架，同时突出了社区组织的基本作用。 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.