RAPID: Analysis of Multiscale Network Models for the Spread of COVID-19

当前的2019冠状病毒病（COVID-19）大流行已经颠覆了全球10多亿人的日常生活，各国政府正在努力应对这一疾病的传播。传播率的不确定性以及社交距离、“居家隔离”行政命令和其他干预措施的结果，给美国卫生保健系统带来了前所未有的挑战。本项目将直接使用来自动态系统、随机过程和网络的高级数学建模来解决这些问题。这些数学模型是根据COVID-19的具体特征制定的，将为一线人员提供至关重要的见解，他们需要就干预策略和人类行为模式提出建议，以最好地及时减轻这种疾病的传播。该项目将培养一名博士后学者、一名博士生和两名本科生进行解决这些复杂问题所需的研究。在社区规模和更大范围内，流行病建模的标准方法是隔间模型，其中个体处于少数几个状态之一（例如，易感、感染、康复、暴露、潜伏），个体在状态之间移动。COVID-19流行病可以通过这种方式建模，并将耐药性作为动态的一部分。这种大规模人口模型最简单的例子是描述每个州人口比例的耦合常微分方程。为了模拟感染和潜伏期的随机性，具有自激点过程的模型可以拟合现实世界的数据。本项目比较了与COVID-19传播相关的动态系统和随机模型。该模型还纳入了传输路径的网络结构。该项目通过整合多种传播方式以及传染本身的传播与人类行为模式之间的耦合，扩展了先前在多层网络上的传染研究。该项目利用流行病中高分辨率的社会混合模式，因为它们影响(1)已被诊断为COVID-19的人的观察和人口统计数据，以及(2)传播疾病的人，有时没有被诊断出来。该奖项由应用数学项目和计算数学项目（数学科学部）以及多学科活动办公室（OMA）项目共同资助。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。

The current pandemic of coronavirus disease 2019 (COVID-19) has upended the daily lives of more than a billion people worldwide, and governments are struggling with the task of responding to the spread of the disease. Uncertainty in transmission rates and the outcomes of social distancing, "shelter-at-home" executive orders, and other interventions have created unprecedented challenges to the United States health care system. This project will address these issues directly using advanced mathematical modeling from dynamical systems, stochastic processes, and networks. The mathematical models, which are formulated with the specific features of COVID-19 in mind, will provide insights that are critical to people on the front lines who need to make recommendations for intervention strategies and human-behavior patterns to best mitigate the spread of this disease in a timely manner. The project will train a postdoctoral scholar, a PhD student, and two undergraduate students in the research needed to solve these complex problems. The standard approach for epidemic modeling, at the community scale and larger, is compartmental models in which individuals are in one of a small number of states (for example, susceptible, infected, recovered, exposed, latent), with individuals moving between states. The COVID-19 epidemic can be modeled in this way, with resistance as part of the dynamics. The simplest examples of such models for large populations are coupled ordinary differential equations that describe the fraction of a population in each of the states. To model the stochasticity of infection and latency, models with self-exciting point processes can be fit to real-world data. This project compares the dynamical systems and stochastic models of relevance to COVID-19 transmission. The models also incorporate network structure for the transmission pathways. The project extends prior research on contagions on multilayer networks by incorporating multiple transmission methods and coupling between the spread of the contagion itself and human behavior patterns. The project leverages high-resolution societal mixing patterns in epidemics, as they influence both (1) observations and demographics of who has been diagnosed with COVID-19 and (2) who transits the disease, sometimes without being diagnosed.This award is co-funded with the Applied Mathematics program and the Computational Mathematics program (Division of Mathematical Sciences), and the Office of Multidisciplinary Activities (OMA) program.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.