Epidemics on hypergraphs: spectral thresholds for extinction.
Epidemics on hypergraphs: spectral thresholds for extinction.
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DOI：
10.1098/rspa.2021.0232
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发表时间：
2021-08
期刊：
影响因子：
--
通讯作者：
de Kergorlay HL
中科院分区：
文献类型：
--
作者：
Higham DJ;de Kergorlay HL
当疾病围绕接触图传播时，流行病的传播就很容易理解。在随机易感-感染-易感的环境中，光谱条件表征了疾病是否消失。然而，使用图对人类交互进行建模是一种简化，仅考虑成对关系。这并不能完全代表人们以群体形式见面的更现实的情况。超边可用于记录更高阶的交互，产生更忠实和灵活的模型，并允许节点的感染率取决于组大小，并且还作为感染邻居数量的非线性函数而变化。我们在此超图环境中讨论不同类型的传染模型，并得出表征疾病是否消失的光谱条件。我们研究了精确的个体级随机模型和确定性平均场 ODE 近似。提供数值模拟来说明分析。我们还解释了我们的结果，并展示了超图模型如何使我们能够区分（i）病原体本质所固有的和（ii）行为选择（例如社交距离、加强卫生和使用口罩）对传染性的贡献。这提高了更准确地量化旨在遏制病毒传播的干预措施的效果的可能性。
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible–infected–susceptible setting, spectral conditions characterize 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 higher order interactions, yielding more faithful and flexible models and allowing for the rate of infection of a node to depend on group size and also to vary as a nonlinear function of the number of infectious neighbours. 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 (i) are inherent in the nature of the pathogen and (ii) 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.
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DOI：
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发表时间：
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影响因子：
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作者：
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影响因子：
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作者：
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