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

在国际社会权衡采取必要的隔离措施和社会距离以遏制新冠肺炎传播之际，关键问题是如何通过这些措施减少疾病传播。最近的预测表明，如果不进行认真的干预，世界上很大一部分人口将被感染，导致数百万人死亡。为了缓解这种最糟糕的情况，关键的政策决策正以数学模型为指导。然而，一些著名的模型对人类接触做出了不切实际的假设，即一个人作为一个完全陌生的人，同样有可能将其传染给该国另一端的亲密家庭成员。这些假设对计算很有用，但没有考虑到疫情的全部地理复杂性。此外，许多模型没有考虑对健康个体进行隔离的后果。该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。拟议中的研究将使用有关接触网络的真实数据来预测和建议控制新冠肺炎爆发，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，其网络比以前考虑的更现实。特别重要的是确定临界阈值，一旦超过这个阈值，就会发生大规模流行病。最近有关于这些门槛的研究，但针对的是为数字基础设施和社交网络建模的网络。研究的第一个目标是确定有偏站点渗流对图结构的影响，特别是不同的渗流规则如何影响给定图的最大分量的大小。第二部分将集中讨论SIR模型在渗流后流行病的临界阈值和大小是如何变化的。这将在从配置模型生成的图以及随机空间网络(如Gilbert图)上进行严格的探索。此外，这些问题将使用针对当前新冠肺炎大流行的数据在现实世界的面对面网络上进行调查。回答这些问题将有助于测试以前模型的稳健性，同时还可以探索更强的先发制人距离的有效性。这笔赠款是使用冠状病毒援助、救济和经济安全(CARE)法案提供的资金发放的，补充资金分配给议员。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.