Project Overview

In this project we study the impact of spatial relationships on the spread of diseases such as COVID-19. We study the correlation between infection rates in different counties in order to determine how localized or widespread these correlations are. By examining the correlations we can study how and when the pandemic transitioned from being a local incident to being a regional and national incident. We can also look at what areas were critical for spreading the virus across distances and when this spreading occurred. This approach has the potential to help us determine what events were impactful in the spread of the virus and what policy decisions were and were not able to contain the spread of the virus.

We analyze COVID-related data for USA at the county level using the Johns Hopkins dataset. We evaluate this data over 7 day windows, over which we compute the average number of cases for each county and the difference in these averages over subsequent weeks. We then compute the two-point correlation in this difference between each pair of counties. We categorize each pair based on its distance and study how the correlation varies over distance. If the correlation drops off quickly over distance and there is only local transmission this is an indication that infection rates are only being influenced by nearby counties. Conversely, if the correlation remains high over long distances then infection rates are being influenced by more distant regions, which indicates longer-distance transmission.

This project is supported by a NSF-BSF grant. The Rutgers group is supported by NSF through the Ecology and Evolution of Infectious Diseases Program in the Division of Environmental Biology, using funds from the Coronavirus Aid, Relief, and Economic Security (CARES) Act, grant DEB-2035297. This project is also part of an international collaboration with Bar-Ilan University, funded through BSF grant 2020645. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or BSF.

Findings

During the early stages of the pandemic (February through October of 2020) we primarily observed localized, short-distance correlations but did not observe persistent long-range correlations. This indicates that the virus was being spread locally but not being transmitted over longer distances, which likely slowed the spread of the virus considerably. Overall, this indicates that the policies such as travel restrictions and social distancing were successful in delaying the spread of the virus. This delay was significant because it gave medical facilities the time they needed to prepare for the pandemic and it gave the research community time to develop vaccines and other countermeasures.

Looking more closely at the one year of spreading from February 2020 to February 2021 (when vaccinations started becoming widely available), we observed three main phases in terms of spatial spreading. In spring 2020, spreading was contained within small clusters and there were only a few local outbreaks mainly located in the Northeast. From May 2020 to October 2020, correlations in new active cases were weaker across the country but at the same time the underlying clusters started growing in size while still remaining mostly localized in space. November 2020 marks the beginning of the third stage, when correlations spanned the largest part of the country as these clusters merged. This spanning cluster coincided with the first peak of the epidemic (November of 2020) and lasted for less than a month. Even though this spanning cluster was dissolved in less than a month, correlations remained strong for the rest of this time interval indicating that virus transmission could still increase in a fast pace.

Another trend we observed was that spreading during the first two phases of the pamdimic was confined primarily to urban regions while spread between rural regions only started occurring in the third phase (after November 2020). In particular, we observed strong correlations among neighboring urban centers throughout this year. In contrast, there were only weak or no correlations between rural areas prior to November 2020, even for counties which are geographically close to each other. After November 2020, these correlations increased in strength and became comparable to those between urban counties. This behavior helps to explain the cluster which formed during November of 2020.

Select a week using the slider or press Play to see an animation of COVID-19 evolution in USA.

- The map at the left shows the fraction of the population in a county which tested positive for COVID-19 during that week. The map at the right shows the relative change of new cases between the current and previous week.
- The plots at the bottom show: a) the total number of cases in the country since the beginning of the epidemic, b) the spatial correlation function averaged over all counties, and c) the 'trajectory' of the epidemic in the phase space of (short distance correlation) vs (correlation length).

Our full results including interactive maps are contained in a google datastudio project that can be accessed using the following link:

https://datastudio.google.com/reporting/4b581375-ee89-4fdb-a4a5-daef4f7a4618/page/A24DC

Plots and maps for urban regions (counties with populations greater than 250,000) can be accessed using the following link.

https://datastudio.google.com/reporting/4b581375-ee89-4fdb-a4a5-daef4f7a4618/page/HiuFC

Plots and maps for rural regions (counties with populations less than 250,000) can be found at.

https://datastudio.google.com/reporting/4b581375-ee89-4fdb-a4a5-daef4f7a4618/page/D24DC

Project PIs:
Lazaros Gallos Email: lgallos@dimacs.rutgers.edu Lazaros Gallos is an Associate Director and Research Professor at DIMACS at Rutgers University, where he also directs the long-running DIMACS REU summer program. DIMACS fosters research and educational programs on topics that lie at the interface of discrete mathematics and theoretical computer science. He is a member of the Editorial Boards at Scientific Reports, at PLOS ONE, and at Entropy. He has also been an Associate Editor for the highly selective APS journal Physical Review X. His research interests are broad and cover a lot of inter-disciplinary ground. For the last few years he has been working on complex networks science. Currently, he works on (a) understanding fundamental mechanisms behind online social interactions, (b) epidemics spreading, (c) modules organization in the brain, and (d) applications of Machine Learning in Network Science.
Shlomo Havlin Email: havlins@gmail.com Shlomo Havlin is a Professor in the Physics Department at Bar-Ilan University in Israel. Dr. Havlin has won many awards including the Israel Prize for his accomplishments in Physics, which he won in 2018. In the past he served as President of the Israel Physical Society (1996-1999), Dean of Faculty of Exact Sciences at Bar-Ilan University (1999-2001) and as Chairman of the Department of Physics at Bar-Ilan University (1984-1988). Dr. Havlin's research interest include research itno the applications of statistical physics to areas such as complex networks, infrastructure resilience, geophysics, climate, medicine, biology, and others. Most recently, he has focused on developing a percolation framework to study interacting networks such as the interdependence between infrastructure networks; developing a novel framework to study climate networks, and novel methods for understanding traffic congestion in urban settings.
Postdoctoral Researchers:
Adrian Chan Email: adrian.kaho.chan@gmail.com Adrian Chan is a postdoctoral researcher at the Physics Department at Bar-Ilan University in Israel.
Troy McMahon Email: troymcmahon1@gmail.com Troy McMahon is a postdoctoral researcher at Rutgers University where he does research involving spatio-temporal trends in the spread of infectious diseases such as COVID. Troy is also involved in the PRACSIS robotics laboratory where he researches applications of learning to kinodynamic planning. Troy received his PhD. in Computer Science in 2016 from Texas A&M University under the supervision of professor Nancy Amato, where his doctoral research emphasized motion planning for constrained systems and high degree of freedom problems. After completing his PhD., Troy worked as a postdoctoral researcher at the University of Michigan with professor Chad Jenkins on manipulation planning. As part of this work he developed the concept of wayfields to encode common actions (such as opening a drawer or picking up an object) as cost-maps overlayed onto an environment and used in combination with motion-planning algorithms to perform the action.
Students:
Yun-Huen (Nikki) Cheng Email: cheng26y@mtholyoke.edu Nikki Cheng is a student at Mount Holyoke College, majoring in Math. She is working in this project through her participation at the 2021 DIMACS REU program.

A spatio-temporal analysis of the spreading patterns of COVID-19

Project Overview

Findings

Select a week using the slider or press Play to see an animation of COVID-19 evolution in USA.

Project PIs:

Lazaros Gallos

Shlomo Havlin

Postdoctoral Researchers:

Adrian Chan

Troy McMahon

Students:

Yun-Huen (Nikki) Cheng