超图上的传染病：灭绝的谱控制
Epidemics on Hypergraphs: Spectral Thresholds for Extinction
摘要：
当疾病围绕接触图传播时，流行病传播是很好理解的。在一个随机的易感染-易感染的环境中，光谱条件决定了疾病是否消失。然而，使用图对人类交互进行建模是一种简化，只考虑成对关系。这并不完全代表人们在群体中见面的更现实的情况。超边可以用来记录这样的群体交互，产生更忠实和灵活的模型，允许节点的感染率作为感染邻居数量的非线性函数而变化。我们讨论了不同类型的传染病模型在超图设置，并推导出谱条件，表征疾病是否消失。我们研究了精确的个体水平随机模型和确定性平均场常微分方程近似。数值模拟来说明分析。我们还解释了我们的研究结果，并展示了超图模型如何使我们能够区分（a）病原体本质所固有的传染性和（b）行为选择（如社交距离，增加卫生和使用口罩）对传染性的贡献。这就有可能更准确地量化旨在遏制病毒传播的干预措施的效果。
英文摘要：
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human interactions using a graph is a simplification which only considers pairwise relationships. This does not fully represent the more realistic case where people meet in groups. Hyperedges can be used to record such group interactions, yielding more faithful and flexible models, allowing for the rate of infection of a node to vary as a nonlinear function of the number of infectious neighbors. We discuss different types of contagion models in this hypergraph setting, and derive spectral conditions that characterize whether the disease vanishes. We study both the exact individual-level stochastic model and a deterministic mean field ODE approximation. Numerical simulations are provided to illustrate the analysis. We also interpret our results and show how the hypergraph model allows us to distinguish between contributions to infectiousness that (a) are inherent in the nature of the pathogen and (b) arise from behavioural choices (such as social distancing, increased hygiene and use of masks). This raises the possibility of more accurately quantifying the effect of interventions that are designed to contain the spread of a virus.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
