We present a kinetic theory for swarming systems of interacting, self-propelled discrete particles. Starting from the Liouville equation for the many-body problem we derive a kinetic equation for the single particle probability distribution function and the related macroscopic hydrodynamic equations. General solutions include flocks of constant density and fixed velocity and other non-trivial morphologies such as compactly supported rotating mills. The kinetic theory approach leads us to the identification of macroscopic structures otherwise not recognized as solutions of the hydrodynamic equations, such as double mills of two superimposed flows. We find the conditions allowing for the existence of such solutions and compare to the case of single mills.

We examine trends in drug overdose deaths by race, gender, and geography in the United States during the period 2013–2020. Race and gender specific crude rates were extracted from the final National Vital Statistics System multiple cause-of-death mortality files for several jurisdictions and used to calculate the male-to-female ratios of crude rates between 2013 and 2020. We established 2013–2019 temporal trends for four major drug types: psychostimulants with addiction potential (T43.6, such as methamphetamines); heroin (T40.1); natural and semi-synthetic opioids (T40.2, such as those contained in prescription pain-killers); synthetic opioids (T40.4, such as fentanyl and its derivatives) through a quadratic regression and determined whether changes in the pandemic year 2020 were statistically significant. We also identified which race, gender and states were most impacted by drug overdose deaths. Nationwide, the year 2020 saw statistically significant increases in overdose deaths from all drug categories except heroin, surpassing predictions based on 2013–2019 trends. Crude rates for Black individuals of both genders surpassed those for White individuals for fentanyl and psychostimulants in 2018, creating a gap that widened through 2020. In some regions, mortality among White persons decreased while overdose deaths for Black persons kept rising. The largest 2020 mortality statistic is for Black males in the District of Columbia, with a record 134 overdose deaths per 100,000 due to fentanyl, 9.4 times more than the fatality rate among White males. Male overdose crude rates in 2020 remain larger than those of females for all drug categories except in Idaho, Utah and Arkansas where crude rates of overdose deaths by natural and semisynthetic opioids for females exceeded those of males. Drug prevention, mitigation and no-harm strategies should include racial, geographical and gender-specific efforts, to better identify and serve at-risk groups.

The evolution of human cooperation has been the subject of much research, especially within the framework of evolutionary public goods games, where several mechanisms have been proposed to account for persistent cooperation. Yet, in addressing this issue, little attention has been given to games of a more adversarial nature, in which defecting players, rather than simply free riding, actively seek to harm others. Here, we develop an adversarial evolutionary game using the specific example of criminal activity, recasting the familiar public goods strategies of punishers, cooperators, and defectors in this light. We then introduce a strategy\char22{}the informant\char22{}with no clear analog in public goods games and show that individuals employing this strategy are a key to the emergence of systems where cooperation dominates. We also find that a defection-dominated regime may be transitioned to one that is cooperation-dominated by converting an optimal number of players into informants. We discuss these findings, the role of informants, and possible intervention strategies in extreme adversarial societies, such as those marred by wars and insurgencies.

Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of “carrot and stick” intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications.

Factors such as varied definitions of mortality, uncertainty in disease prevalence, and biased sampling complicate the quantification of fatality during an epidemic. Regardless of the employed fatality measure, the infected population and the number of infection-caused deaths need to be consistently estimated for comparing mortality across regions. We combine historical and current mortality data, a statistical testing model, and an SIR epidemic model, to improve estimation of mortality. We find that the average excess death across the entire US from January 2020 until February 2021 is 9 $$\%$$% higher than the number of reported COVID-19 deaths. In some areas, such as New York City, the number of weekly deaths is about eight times higher than in previous years. Other countries such as Peru, Ecuador, Mexico, and Spain exhibit excess deaths significantly higher than their reported COVID-19 deaths. Conversely, we find statistically insignificant or even negative excess deaths for at least most of 2020 in places such as Germany, Denmark, and Norway.