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

对于病例高峰期的数值和时间，新冠肺炎病毒的传播模型产生了相互矛盾的预测。大多数模型倾向于一维指数增长，因此没有考虑空间相关性。其他模型基于神经网络，神经网络能够预测是否有足够的数据可用，而新冠肺炎目前还没有做到这一点。这项研究将使用多重分形图，这是由具有空间相关性的乘法过程产生的。多重分形图由于缺乏特征尺度，可能是分析病毒传播的理想工具，如新冠肺炎；在纽约这样的大城市传播可能类似于在新泽西州纽瓦克这样的小城市发生的传播。多重分形图在很大程度上被各种组织用于地球物理数据，在某些情况下，还被用来了解H1N5等病毒的传播。这项研究将使用纽约市五个区和新泽西州北部(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复原力的项目中从这些社区收集数据。本研究的假设是多重分形图既能反映股票的标度行为，又能反映股票价格随时间的指数增长。多重分形图还解释了研究对象之间的空间相关性，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)的病例地图就会发现斑点，也就是在空间上分布不均匀的热区。研究小组认为，几何体的骨架是分形的(因为缺乏尺度)，因此将分析空间上分布在分形网络上的多重分维。这种方法可能会在包括公共卫生和复原力在内的各个领域开启新的调查模式。这一裁决反映了NSF的法定使命，并通过使用基金会的智力优势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.