RAPID: Collaborative Research: Quarantined Networks and the Spread of COVID-19

Mathematical and Physical Sciences - As the global community weighs the necessary extent of quarantine and social distancing to fight the spread of COVID-19, the critical question is how disease transmission is mitigated by these measures. Recent predictions suggest that without serious interventions, a large portion of the world population will become infected, resulting in millions of deaths. To mitigate this worst-case scenario, key policy decisions are being guided by mathematical models. However, several prominent models make unrealistic assumptions about human contacts i.e., that an individual is equally likely to infect a close family member as a complete stranger on the other side of the country. Such assumptions are useful for calculations, but fail to take into account the full geographic complexity of the outbreak. Furthermore, many models do not consider the consequences of the quarantine of healthy individuals. This project will use rigorous analysis and simulation to address these shortcomings by describing a more realistic structure of quarantined networks and how disease spreads in them. The proposed research will use real-world data about contact networks to make predictions and recommendations for controlling the COVID-19 outbreak, improving our understanding of how best to contain the current as well as future pandemics. The project will involve the training of undergraduate students.

This research will describe the effect of quarantine on connectivity and disease transmission on more realistic networks than have previously been considered. Of particular importance will be locating critical thresholds which, when exceeded, allow large epidemics to occur. There is recent study of these thresholds, but for networks that model digital infrastructure and social networks. The first objective of the research will be to determine the effect of biased site percolation on graph structure, especially how different percolation rules influence the size of the largest component of a given graph. The second part will then focus on how the critical threshold and size of the epidemic for an SIR model change after percolation. This will be explored rigorously on graphs generated from the configuration model as well as random spatial networks such as Gilbert graphs. Additionally, these questions will be investigated on real world face-to-face networks using data specific to the current COVID-19 pandemic. Answering them will help test robustness of previous models, while also exploring the effectiveness of stronger preemptive distancing.

This grant is being awarded using funds made available by the Coronavirus Aid, Relief, and Economic Security (CARES) Act supplemental funds allocated to MPS.

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.