Collaborative Research: A comprehensive approach to modeling, learning, analysis and control of epidemic processes over time-varying and multi-layer networks

许多自然和工程系统由底层的网络组件组成，动态过程在其上演化。例如，传染病在人际接触和国际旅行网络中的传播过程，高峰交通现象在交通基础设施中的传播，病毒或蠕虫在计算机网络中的传播，以及在社交媒体平台上发布的文章、推文或谣言的分享和再分享。工程系统越来越多地在本地和大规模网络的各个层次上相互连接。在基础和分析层面上对病毒过程如何在不同网络结构中演变、传播速度、多种病毒类型和多网络层的发生如何影响传播过程动态、以及如何通过采用深思熟虑的控制政策来抑制和/或减轻这些过程有更强的理解，将极大地影响全球各种系统的健康、安全和保障。COVID-19的传播显然对所有六大洲有人居住的人们的健康以及世界经济产生了广泛影响。本文提出的研究将大大提高我们对COVID-19等流行病的理解，并产生有助于限制人类生命损失并减少病毒经济影响的一般政策指导方针。本项目开发的方法将有利于应对随后的流行病暴发、第二波COVID-19以及更广泛的一般病毒过程。在整个项目中，pi将根据他们过去的经验，尽一切努力从代表性不足的群体中招募和指导学生，并将通过包括本科生和当地高中生研究人员来建立外展工作。虽然在过去的10-15年里对网络上的流行病过程的动态进行了广泛的研究，但过去的工作主要集中在静态网络上传播的SIS和SIR过程上。在拟议的项目中，我们的重点将是在多个尺度上由多层组成的大型且可能时变的网络上对动态流行病过程进行建模、分析和控制。我们将特别考虑时变网络中SAIRS（易感-无症状-感染-恢复-易感）过程的数据建模和分析；这项工作将包括网络流行病过程模型的非线性动力学的稳定性和均衡分析，网络结构识别，从不完善和非随机数据中估计参数和结构，以及从代理层面到社会层面开发可实现的控制策略。本研究计划将在传染病的数学建模与分析、时变非线性与线性分析方法、优化与控制理论政策制定、网络推理与分析、随机样本约束下的序贯抽样策略、网络上的平均场博弈等领域取得广泛的基础成果。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。

Numerous natural and engineered systems consist of underlying networked components over which dynamical processes evolve. Examples include the spread of infectious disease processes over human contact and international travel networks, the propagation of peak traffic phenomenon over the transportation infrastructure, the spread of viruses or worms over computer networks, and sharing and re-sharing of posted articles, tweets, or rumors over social media platforms. Engineered systems are increasingly interconnected over various levels of both local and large-scale networks. Developing a stronger understanding at fundamental and analytical levels of how viral processes evolve across different network structures, the rates at which they spread, how the occurrence of multiple viral types and multiple network layers affect the spread process dynamics, and how these processes can be suppressed and/or mitigated by employing deliberate control policies will greatly impact the health, safety and security of a vast variety of systems around the globe. The spread of COVID-19 has clearly had broad implications for the health of people on all six inhabited continents as well as the world's economy. The research proposed herein will substantially enhance our understanding of epidemics such as COVID-19 and lead to general policy guidelines that will help limit the loss of human life and reduce the economic impacts of the virus. The methods to be developed in this project will be beneficial for battling subsequent epidemic outbreaks, a second wave of COVID-19, and on a broader scale general viral process. Throughout this project the PIs will build on their past experiences to make every effort towards recruiting and mentoring students from under-represented groups, and will establish outreach efforts by including undergraduate and local high school student researchers.Although the dynamics of epidemic processes over networks have been extensively studied for the past 10-15 years, past work has been focused largely on SIS and SIR processes spreading over static networks. In the proposed project, our focus will be on modeling, analysis and control of dynamic epidemic processes over large and possibly time-varying networks, comprised of multiple layers at multiple scales. We will specifically consider data-informed modeling and analysis of SAIRS (susceptible-asymptomatic-infected-recovered-susceptible) processes over time-varying networks; this work will include stability and equilibria analysis of the nonlinear dynamics of networked epidemic process models, network structure identification, estimation of parameters and structure from imperfect and non-random data, and development of realizable control strategies from the agent level to societal levels. The research proposed will draw on and contribute to wide-ranging foundational results in mathematical modeling and analysis of infectious diseases, time-varying nonlinear and linear analysis methods, optimization and control-theoretic policy formulation, network inference and analysis, sequential sampling strategies with stochastic sample constraints, and mean-field games over networks.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.