RAPID: Scaling, causality, and modulation of the spread of COVID19

COVID-19病毒传播模型对病例高峰发生的价值和时间产生了相互矛盾的预测。大多数模型倾向于一维指数增长，因此不考虑空间相关性。其他模型基于神经网络，能够预测是否有足够的数据，而目前COVID-19的情况并非如此。本研究将使用多重分形，这是由具有空间相关性的乘法过程产生的。由于缺乏特征尺度，多重分形可能是分析病毒传播的理想工具，例如COVID-19；像纽约这样的大城市的传播可能类似于新泽西州纽瓦克这样的小城市。多重分形已被各种团体广泛用于地球物理数据，在某些情况下，用于了解病毒（如甲型h1n1病毒）的传播。这项研究将使用来自纽约市五个行政区和新泽西州北部（即卑尔根、埃塞克斯和联合县）的数据。该团队已经在一个关于社区恢复力的项目中从这些社区收集数据。本研究假设多重分形既能反映尺度行为，又能反映随时间的指数增长。多重分形也解释了受试者之间的空间相关性，因此可以用来解释连通性，无论是在个人层面还是在城市层面（比如纽约和费城）。此外，看看美国（或世界范围内）的病例地图，就会发现斑点性，即热点地区在空间上的分布并不均匀。研究小组认为，几何的骨架是分形的（因为缺乏尺度），因此将分析在分形网络上空间分布的多重分形。这种方法可能在包括公共卫生和复原力在内的各个领域开辟新的调查模式。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。

Models of the spreading of the COVID-19 virus have yielded conflicting predictions for the value and time of the peak occurrence of cases. Most models tend to be one dimensional exponential growth, and thus do not account for spatial correlation. Other models are based on neural networks, which are capable of predicting if sufficient data are available, which is not at this instant of time the case for COVID-19. This study will use multifractals, which result from multiplicative processes with spatial correlations. Multifractals, due to their lack of a characteristic scale, may be ideal tools to analyze the spread of viruses, such as COVID-19; the spreading in a large city such as NYC could be similar to that occurring in a small city such as Newark, NJ. Multifractals have been used largely for geophysical data by various groups, and in some cases, to understand the spread of viruses, such as H1N5. This study will use data from the five boroughs of New York City and from Northern New Jersey (namely Bergen, Essex, and Union County). The team already has been collecting data from these communities in a project on community resilience. The hypothesis of this research is that multifractals can reflect both the scaling behavior and the exponential increase with time. Multifractals also account for the spatial correlation between subjects, and thus could be used to explain connectivity, be it at the individual level or at the level of cities (say NYC and Philadelphia). In addition, a look at the map of cases at the US (or the world scale) reveals spottiness, that is hot zones that are not uniformly distributed in space. The study team believes that the skeleton of the geometry is fractal (because of the lack of scale), and thus will be analyzing multifractals distributed spatially on a fractal network. This approach may open new modes of investigation in various areas, including public health and resilience.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.