RAPID: Collaborative Research: Quarantined Networks and the Spread of COVID-19

国际社会正在权衡隔离和保持社交距离的必要程度，以应对COVID-19的传播，关键问题是如何通过这些措施减轻疾病传播。最近的预测表明，如果不采取认真的干预措施，世界人口的很大一部分将受到感染，造成数百万人死亡。为了减轻这种最坏的情况，关键的政策决定正在以数学模型为指导。然而，一些著名的模型对人类接触做出了不切实际的假设，即一个人感染亲密家庭成员的可能性与一个完全陌生的人在国家另一端的可能性是一样的。这样的假设对计算有用，但没有考虑到疫情在地理上的全部复杂性。此外，许多模型没有考虑到隔离健康个体的后果。本项目将使用严格的分析和模拟，通过描述更现实的隔离网络结构以及疾病如何在其中传播来解决这些缺点。拟议的研究将使用有关接触网络的真实数据，为控制COVID-19疫情做出预测和建议，从而提高我们对如何最好地控制当前和未来大流行的理解。该项目将涉及对本科生的培训。这项研究将描述隔离对连通性和疾病传播的影响，比以前考虑的更现实的网络。特别重要的是确定临界阈值，一旦超过，就会发生大规模流行病。最近有一项关于这些阈值的研究，但针对的是数字基础设施和社交网络的模型。研究的第一个目标将是确定有偏差的站点渗透对图结构的影响，特别是不同的渗透规则如何影响给定图中最大组件的大小。然后，第二部分将重点讨论SIR模型的临界阈值和流行病规模在渗透后如何变化。这将在组态模型生成的图以及随机空间网络（如吉尔伯特图）上进行严格的探索。此外，这些问题将在现实世界的面对面网络中进行调查，使用当前COVID-19大流行的特定数据。回答这些问题将有助于测试先前模型的稳健性，同时也将探索更强的先发制人距离的有效性。这笔拨款是使用《冠状病毒援助、救济和经济安全（关怀）法案》分配给MPS的补充资金提供的资金。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

As the global community weighs the necessary extent of quarantine and social distancing to fight the spread of COVID-19, the critical question is how disease transmission is mitigated by these measures. Recent predictions suggest that without serious interventions, a large portion of the world population will become infected, resulting in millions of deaths. To mitigate this worst-case scenario, key policy decisions are being guided by mathematical models. However, several prominent models make unrealistic assumptions about human contacts i.e., that an individual is equally likely to infect a close family member as a complete stranger on the other side of the country. Such assumptions are useful for calculations, but fail to take into account the full geographic complexity of the outbreak. Furthermore, many models do not consider the consequences of the quarantine of healthy individuals. This project will use rigorous analysis and simulation to address these shortcomings by describing a more realistic structure of quarantined networks and how disease spreads in them. The proposed research will use real-world data about contact networks to make predictions and recommendations for controlling the COVID-19 outbreak, improving our understanding of how best to contain the current as well as future pandemics. The project will involve the training of undergraduate students.This research will describe the effect of quarantine on connectivity and disease transmission on more realistic networks than have previously been considered. Of particular importance will be locating critical thresholds which, when exceeded, allow large epidemics to occur. There is recent study of these thresholds, but for networks that model digital infrastructure and social networks. The first objective of the research will be to determine the effect of biased site percolation on graph structure, especially how different percolation rules influence the size of the largest component of a given graph. The second part will then focus on how the critical threshold and size of the epidemic for an SIR model change after percolation. This will be explored rigorously on graphs generated from the configuration model as well as random spatial networks such as Gilbert graphs. Additionally, these questions will be investigated on real world face-to-face networks using data specific to the current COVID-19 pandemic. Answering them will help test robustness of previous models, while also exploring the effectiveness of stronger preemptive distancing.This grant is being awarded using funds made available by the Coronavirus Aid, Relief, and Economic Security (CARES) Act supplemental funds allocated to MPS.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.