By Brandon Behring, Alessandro Rizzo, and Maurizio Porfiri
Recent strides in the fight against COVID-19 have shown that non-pharmaceutical interventions (NPIs) are critical tools that help combat disease spread. Even during the current vaccination campaign, maintaining social distance and continuing to wear masks fundamentally supports ongoing immunization efforts.
While the importance and effectiveness of NPIs is generally understood, their differential effect remains elusive and is the subject of our research. We attempt to unravel the individual contributions of social distancing and mask-wearing on the diffusion of COVID-19, and quantify the portion of the population that must implement one or both NPIs to guarantee that the spread will stop. We have thus designed and implemented a model that is based on the theory of time-varying networks to mimic the behavior of a population that partially adopts NPIs. Our model allows us to evaluate the effect of such a scenario.
Figure 1. Illustration of a network of contacts for the spread of COVID-19 in a population where only a fraction of the individuals (cones) wear a mask and practice social distancing (cones with white stripes). Figure courtesy of Anna Sawulska and Maurizio Porfiri.
Our network model encompasses nodes (data points) and edges (links between nodes). Researchers use network models in applications that range from marketing to the tracking of bird migration patterns. In our model, individuals are associated with the network nodes and their health status can progress across the following states: susceptible, exposed, infected, and removed (recovered or dead). The edges represent potential contacts between pairs of individuals (see Figure 1). The model accounts for heterogeneity in human activities, whereby a few highly active nodes are responsible for much of the network’s contacts. This arrangement mirrors typical empirical observations in populations, where most people have few interactions and only a couple of individuals interact with many others.
We tune the model to the U.S. using public data sources, such as mobility data and Facebook surveys from the Institute for Health Metrics and Evaluation at the University of Washington. These data sources indicate that people who wear masks also tend to reduce their mobility. Based on this premise, our model splits nodes into two groups: (i) individuals who regularly wear masks and socially distance, and (ii) those whose behavior remains largely unchanged by an epidemic or pandemic. An analytical study of the epidemic threshold—the combination of parameters that lead to an exponential growth of cases—demonstrated a substitute and concurrent effect of mask-wearing and social distancing, whereby masks with an ideal (100 percent) efficacy proved to be as effective as vaccines. Focusing on more realistic cases of non-ideal efficacy of NPIs, we can quantify that 60 percent is the fraction of the population that must adopt both NPIs to move towards complete eradication of the pandemic.
To gauge our model’s effectiveness, we also executed a statistically validated study to corroborate our results with data from The New York Times. We analyzed the cumulative cases per capita in all 50 states and Washington, D.C. between July 14, 2020—when the Centers for Disease Control and Prevention officially recommended mask-wearing—and December 10, 2020. Analysis showed that U.S. states that suffered from the largest number of infections last fall were also those where people complied less with public health guidelines, thereby falling well above the epidemic threshold that our model predicts.
Ultimately, our main finding reveals that neither social distancing nor mask-wearing alone are likely sufficient to halt the spread of COVID-19, unless almost the entire population adheres to the single measure in question. However, if a significant fraction of the population adheres to both measures, these tactics can prevent viral spreading even without mass vaccination [1].
Alessandro Rizzo presented this research during a minisymposium at the 2021 SIAM Conference on Applications of Dynamical Systems, which took place virtually in May 2021.
Acknowledgments: This research is partially founded by the U.S. National Science Foundation (Grant CMMI-2027990) and the Compagnia di San Paolo in Torino, Italy.
References
[1] Behring, B.M., Rizzo, A., & Porfiri, M. (2021). How adherence to public health measures shapes epidemic spreading: A temporal network model. Chaos, 31(4), 043115.
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Brandon Behring is a postdoctoral researcher in the Dynamical Systems Laboratory (directed by Maurizio Porfiri) at New York University’s (NYU) Tandon School of Engineering. |
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Alessandro Rizzo is an associate professor at Politecnico di Torino in Italy and a visiting professor at NYU’s Tandon School of Engineering. He is the founder and director of Politecnico di Torino’s Complex Systems Laboratory, where he conducts and supervises research on complex systems and networks, networked and social robotics, and nonlinear dynamical systems. He also received a 2019 Amazon Research Award in robotics. |
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Maurizio Porfiri is an institute professor at NYU’s Tandon School of Engineering, with appointments in the Center for Urban Science and Progress, the Department of Mechanical and Aerospace Engineering, and the Department of Biomedical Engineering. He is founder and director of the Dynamical Systems Laboratory at NYU, where he conducts and supervises research on theory and interdisciplinary applications of dynamical systems.
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