The challenges of modeling and forecasting the spread of COVID-19.

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.

Impact of social distancing during COVID-19 pandemic on crime in Los Angeles and Indianapolis.

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.

Modelling radicalization: how small violent fringe sects develop into large indoctrinated societies.

We model radicalization in a society consisting of two competing religious, ethnic or political groups. Each of the 'sects' is divided into moderate and radical factions, with intra-group transitions occurring either spontaneously or through indoctrination. We also include the possibility of one group violently attacking the other. The intra-group transition rates of one group are modelled to explicitly depend on the actions and characteristics of the other, including violent episodes, effectively coupling the dynamics of the two sects. We use a game theoretic framework and assume that radical factions may tune 'strategic' parameters to optimize given utility functions aimed at maximizing their ranks while minimizing the damage inflicted by their rivals. Constraints include limited overall resources that must be optimally allocated between indoctrination and external attacks on the other group. Various scenarios are considered, from symmetric sects whose behaviours mirror each other, to totally asymmetric ones where one sect may have a larger population or a superior resource availability. We discuss under what conditions sects preferentially employ indoctrination or violence, and how allowing sects to readjust their strategies allows for small, violent sects to grow into large, indoctrinated communities.

Criminal defectors lead to the emergence of cooperation in an experimental, adversarial game.

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.

Dissipation and displacement of hotspots in reaction-diffusion models of crime.

The mechanisms driving the nucleation, spread, and dissipation of crime hotspots are poorly understood. As a consequence, the ability of law enforcement agencies to use mapped crime patterns to design crime prevention strategies is severely hampered. We also lack robust expectations about how different policing interventions should impact crime. Here we present a mathematical framework based on reaction-diffusion partial differential equations for studying the dynamics of crime hotspots. The system of equations is based on empirical evidence for how offenders move and mix with potential victims or targets. Analysis shows that crime hotspots form when the enhanced risk of repeat crimes diffuses locally, but not so far as to bind distant crime together. Crime hotspots may form as either supercritical or subcritical bifurcations, the latter the result of large spikes in crime that override linearly stable, uniform crime distributions. Our mathematical methods show that subcritical crime hotspots may be permanently eradicated with police suppression, whereas supercritical hotspots are displaced following a characteristic spatial pattern. Our results thus provide a mechanistic explanation for recent failures to observe crime displacement in experimental field tests of hotspot policing.

Flows driven by flagella of multicellular organisms enhance long-range molecular transport.

Evolution from unicellular organisms to larger multicellular ones requires matching their needs to the rate of exchange of molecular nutrients with the environment. This logistic problem poses a severe constraint on development. For organisms whose body plan is a spherical shell, such as the volvocine green algae, the current (molecules per second) of needed nutrients grows quadratically with radius, whereas the rate at which diffusion alone exchanges molecules grows linearly, leading to a bottleneck radius beyond which the diffusive current cannot meet metabolic demands. By using Volvox carteri, we examine the role that advection of fluid by the coordinated beating of surface-mounted flagella plays in enhancing nutrient uptake and show that it generates a boundary layer of concentration of the diffusing solute. That concentration gradient produces an exchange rate that is quadratic in the radius, as required, thus circumventing the bottleneck and facilitating evolutionary transitions to multicellularity and germ-soma differentiation in the volvocalean green algae.

Stalactite growth as a free-boundary problem: a geometric law and its platonic ideal.

The chemical mechanisms underlying the growth of cave formations such as stalactites are well known, yet no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. Here we consider the interplay of thin-film fluid dynamics, calcium carbonate chemistry, and CO2 transport in the cave to show that stalactites evolve according to a novel local geometric growth law which exhibits extreme amplification at the tip as a consequence of the locally-varying fluid layer thickness. Studies of this model show that a broad class of initial conditions is attracted to an ideal shape which is strikingly close to a statistical average of natural stalactites.