CIF: Small: Group Testing for Epidemics Control

本项目开发在出现大流行时的检测和干预（隔离）方法。COVID-19揭示了流行病学模型和检测在防治疾病传播中的关键作用。对于任何新病毒或现有病毒的变种，社会将始终需要能够迅速部署战略，以便对人群进行有效检测并授权有针对性的干预。群体检测是一种最近因有效检测而引起关注的方法，因为它允许在人群中识别受感染的个体，而检测所需的检测量要比单独检测每个人所需的检测量少得多。本项目的一个主要新观察结果是，SARS-CoV-2等病毒性疾病受社区传播的影响，在流行病模型中考虑到（甚至是部分）社区结构的知识（例如，学校班级的学生分布）可以使此类测试更加高效和有效。初步结果表明，使用比传统技术少得多的检测就有可能估计感染传播和评估干预措施的影响。因此，该项目的目标是利用社区结构和流行病动态，实现感染和干预的实时估计，并具有以下属性：(i)对不确定性建模具有鲁棒性；(2)提供了可证明的理论性能保证；(3)实现了较低的操作复杂度。为此，该提案结合了编码理论和控制的工具，并分两个步骤进行。首先，假设对真正的潜在动态模型有完整和完善的了解，它推导出测试设计和干预策略，以及静态和状态估计问题公式的测试次数和干预量的基本界限。在第一步的基础上，该建议考虑动态模型的近似值，因为确切的动态不是完全已知的，或者是出于降低复杂性的原因。特别地，提出了流行流行病模型的边际概率演化近似，推导和分析了离散模型，探讨了参数不确定性的影响，研究了可分解的群落模型；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、测试设计和控制疾病的干预策略。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。

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.