CIF: Small: Group Testing for Epidemics Control

该项目开发了在大流行情况下的检测和干预（检疫）方法。COVID-19揭示了流行病学模型和检测在抗击疾病传播中的关键作用。对于任何新的病毒或现有病毒的变种，社会总是需要能够迅速部署战略，以便对人群进行有效的检测，并加强有针对性的干预措施。 群体检测是一种最近引起人们注意的有效检测方法，因为它允许在人群中识别受感染的个体，所需的检测比单独检测每个人所需的检测要少得多。该项目中的一个主要新观察是，像SARS-CoV-2这样的病毒性疾病是由社区传播控制的，并考虑到流行病模型中社区结构的（即使是部分）知识（例如，学生在学校班级中的分布）可以使这种检测更加高效和有效。初步结果表明，使用比传统技术少得多的检测次数来估计感染传播和评估干预措施的影响是可能的。因此，该项目的目标是利用社区结构和流行病动态，使真实的-时间估计的感染和干预具有以下属性：（i）它是鲁棒的模型不确定性;（ii）它提供了可证明的理论性能保证和（iii）它实现了低复杂性的操作。为此，该提案结合了编码理论和控制的工具，并分两步进行。首先，假设完整和完善的知识的真正的基础动态模型，它推导出测试设计和干预策略，以及基本的界限的测试和干预量的数量，为静态和状态估计问题的制定。在第一步的基础上，该建议然后考虑近似的动态模型，因为确切的动态不是完全已知的，或复杂性降低的原因。特别是，该提案发展流行的流行病模型的边缘概率演化的近似，推导和分析离散化模型，探索参数不确定性的影响，并调查可分解的社区模型;在所有情况下，目标是了解这些近似如何可证明地影响相关的基本界限，测试设计，该奖项反映了NSF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。

This project develops testing and intervention (quarantine) methods in the presence of a pandemic. COVID-19 has revealed the key role of epidemiological models and testing in the fight against disease spreading. For any new virus or variant of the existing ones, society will always need to be able to expeditiously deploy strategies that allow efficient testing of populations and empower targeted interventions. Group testing is a method that has recently attracted attention for efficient testing, as it allows to identify the infected individuals in a population with many fewer tests than the ones needed to test everyone individually. A main new observation in this project is that viral diseases like SARS-CoV-2 are governed by community spread, and taking into account (even partial) knowledge of the community structure in an epidemics model (e.g., the distribution of students in classes of a school) can make such testing much more efficient and effective.Preliminary results indicate that it is possible to estimate the infection spread and evaluate the impact of interventions using a much smaller number of tests than traditional techniques.Accordingly, the goal of the project is to leverage community structure and epidemic dynamics to enable real-time estimation of infection and intervention with the following attributes: (i) it is robust to model uncertainties; (ii) it offers provable theoretical performance guarantees and (iii) it achieves low complexity of operation. To do so, the proposal combines tools from coding theory and control, and proceeds in two steps. First, assuming complete and perfect knowledge of the true underlying dynamical model, it derives test designs and intervention strategies, as well as fundamental bounds on the number of tests and amount of intervention, for both a static and state-estimation problem formulation. Building on this first step, the proposal then considers approximations to the dynamic models either because the exact dynamics are not perfectly known, or for complexity-reduction reasons. In particular, the proposal develops approximations on the evolution of marginal probabilities for popular epidemic models, derives and analyzes discretized models, explores the effect of parameter uncertainty and investigate decomposable community models; in all cases, the goal is to understand how these approximations provably affect the associated fundamental bounds, test designs, and intervention strategies to contain the disease.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.