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超过10亿人的日常生活，各国政府正在努力应对疾病传播的任务。传播率的不确定性以及社会距离、“居家庇护”行政命令和其他干预措施的结果，给美国医疗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力系统、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，以及时最好地减缓这种疾病的传播。该项目将培养一名博士后学者，一名博士生和两名本科生，以解决这些复杂问题所需的研究。流行病建模的标准方法，在社区规模和更大的，是房室模型，其中个人处于少数状态之一（例如，易感，感染，康复，暴露，潜伏），与个人之间的状态移动。COVID-19流行病可以用这种方式建模，抗性是动态的一部分。这种大种群模型的最简单的例子是耦合常微分方程，它描述了每个状态下种群的分数。为了对感染和延迟的随机性进行建模，可以将具有自激点过程的模型拟合到真实世界的数据。该项目比较了与COVID-19传播相关的动力系统和随机模型。这些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法以及传染病本身的传播与人类行为模式之间的耦合，扩展了先前对多层网络上传染病的研究。该项目利用流行病中的高分辨率社会混合模式，因为它们影响（1）已被诊断患有COVID-19的人的观察和人口统计数据，以及（2）疾病传播者，有时未被诊断。（数学科学部），多学科活动办公室（OMA）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进行评估，被认为值得支持审查标准。

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.