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.
|Effective start/end date||4/15/20 → 3/31/23|
- National Science Foundation: $200,000.00