We consider an agent-based model of emotional contagion coupled with motion in one dimension that has recently been studied in the computer science community. The model involves movement with a speed proportional to a "fear" variable that undergoes a temporal consensus averaging based on distance to other agents. We study the effect of Riemann initial data for this problem, leading to shock dynamics that are studied both within the agent-based model as well as in a continuum limit. We examine the behavior of the model under distinguished limits as the characteristic contagion interaction distance and the interaction timescale both approach zero. The limiting behavior is related to a classical model for pressureless gas dynamics with "sticky" particles. In comparison, we observe a threshold for the interaction distance vs. interaction timescale that produce qualitatively different behavior for the system - in one case particle paths do not cross and there is a natural Eulerian limit involving nonlocal interactions and in the other case particle paths can cross and one may consider only a kinetic model in the continuum limit. © 2014 Springer Science+Business Media New York.

In this paper, we develop two efficient numerical methods for a multiscale kinetic equation in the context of crowd dynamics with emotional contagion [A. Bertozzi, J. Rosado, M. Short and L. Wang, Contagion shocks in one dimension, J. Stat. Phys. 158 (2014) 647–664]. In the continuum limit, the mesoscopic kinetic equation produces a natural Eulerian limit with nonlocal interactions. However, such limit ceases to be valid when the underlying microscopic particle characteristics cross, corresponding to the blow up of the solution in the Eulerian system. One method is to couple these two situations — using Eulerian dynamics for regions without characteristic crossing and kinetic evolution for regions with characteristic crossing. For such a hybrid setting, we provide a regime indicator based on the macroscopic density and fear level, and propose an interface condition via continuity to connect these two regimes. The other method is based on a level set formulation for the continuum system. The level set equation shares similar forms as the kinetic equation, and it successfully captures the multi-valued solution in velocity, which implies that the multi-valued solution other than the viscosity solution should be the physically relevant ones for the continuum system. Numerical examples are presented to show the efficiency of these new methods.

While the evolution of cooperation has been widely studied, little attention has been devoted to adversarial settings wherein one actor can directly harm another. Recent theoretical work addresses this issue, introducing an adversarial game in which the emergence of cooperation is heavily reliant on the presence of "Informants," actors who defect at first-order by harming others, but who cooperate at second-order by punishing other defectors. We experimentally study this adversarial environment in the laboratory with human subjects to test whether Informants are indeed critical for the emergence of cooperation. We find in these experiments that, even more so than predicted by theory, Informants are crucial for the emergence and sustenance of a high cooperation state. A key lesson is that successfully reaching and maintaining a low defection society may require the cultivation of criminals who will also aid in the punishment of others.

The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remains a challenge. Here, we detail three regional-scale models for forecasting and assessing the course of the pandemic. This work demonstrates the utility of parsimonious models for early-time data and provides an accessible framework for generating policy-relevant insights into its course. We show how these models can be connected to each other and to time series data for a particular region. Capable of measuring and forecasting the impacts of social distancing, these models highlight the dangers of relaxing nonpharmaceutical public health interventions in the absence of a vaccine or antiviral therapies.

Governments have implemented social distancing measures to address the ongoing COVID-19 pandemic. The measures include instructions that individuals maintain social distance when in public, school closures, limitations on gatherings and business operations, and instructions to remain at home. Social distancing may have an impact on the volume and distribution of crime. Crimes such as residential burglary may decrease as a byproduct of increased guardianship over personal space and property. Crimes such as domestic violence may increase because of extended periods of contact between potential offenders and victims. Understanding the impact of social distancing on crime is critical for ensuring the safety of police and government capacity to deal with the evolving crisis. Understanding how social distancing policies impact crime may also provide insights into whether people are complying with public health measures. Examination of the most recently available data from both Los Angeles, CA, and Indianapolis, IN, shows that social distancing has had a statistically significant impact on a few specific crime types. However, the overall effect is notably less than might be expected given the scale of the disruption to social and economic life.

Governments have implemented social distancing measures to address the ongoing COVID-19 pandemic. The measures include instructions that individuals maintain social distance when in public, school closures, limitations on gatherings and business operations, and instructions to remain at home. Social distancing may have an impact on the volume and distribution of crime. Crimes such as residential burglary may decrease as a byproduct of increased guardianship over personal space and property. Crimes such as domestic violence may increase because of extended periods of contact between potential offenders and victims. Understanding the impact of social distancing on crime is critical for ensuring the safety of police and government capacity to deal with the evolving crisis. Understanding how social distancing policies impact crime may also provide insights into whether people are complying with public health measures. Examination of the most recently available data from both Los Angeles, CA, and Indianapolis, IN, shows that social distancing has had a statistically significant impact on a few specific crime types. However, the overall effect is notably less than might be expected given the scale of the disruption to social and economic life.