A modified predator-prey model for the interaction of police and gangs

Modeling the role of police corruption in the reduction of organized crime: Mexico as a case study

Among all types of corruption, police corruption is probably the one that most directly hurts society, as those trusted with protecting the people either side with the criminals that victimize the citizens, or are themselves, criminals. However, both corruption and its effects are very difficult to measure quantitatively other than by perception surveys, but the perception that citizens have of this phenomenon may be different from reality. Using a simple agent-based model, we analyze the effect on crime rates as a result of both corruption and the perception of corruption within law-enforcement corporations. Our results show a phase transition in which crime can propagate across the population even when the majority of police officers are honest. We find that one of the parameters that strongly controls crime incidence is the probability that regular citizens become criminals. In contrast, other actions, such as arresting crime lords, or the amount of crime-associated money that is confiscated, have little impact on the long-term crime incidence. Our results suggest that in addition to combating corruption within law-enforcement institutions, to further reduce the incidence of crime, policymakers should strive to restore confidence in these institutions and the justice system.

Optimal control model for criminal gang population in a limited-resource setting

In this present paper, the principles of optimal control theory is applied to a non-linear mathematical model for the population dynamics of criminal gangs with variability in the sub-population. To decrease (minimize) the progression rate of susceptible populations with no access to crime prevention programs from joining criminal gangs and increase (maximize) the rate of arrested and prosecution of criminals, we incorporate time-dependent control functions. These two functions represent the crime prevention strategy for the susceptible population and case finding control for the criminal gang population, in a limited-resource setting. Furthermore, we present a cost-effectiveness analysis for crime control intervention-related benefits to ascertain the most cost-effective and efficient optimal control strategy. The optimal control functions presented herein are solved by employing the Runge-Kutta Method of order four. Numerical results are demonstrated for different scenarios to exemplify the impact of the controls on the criminal gangs’ population.

Biofilm matrix cloaks bacterial quorum sensing chemoattractants from predator detection

Microbes often secrete high levels of quorum sensing (QS) autoinducers into the environment to coordinate gene expression and biofilm formation, but risk detection and subsequent predation by bacterivorous predators. With such prominent signaling molecules acting as chemoattractants that diffuse into the environment at alarmingly high concentrations, it is unclear if bacterial cells can mask their chemical trails from predator detection. Here, we describe a microbial-based anti-detection adaptation, termed as "biofilm cloak", where the biofilm prey produced biofilm matrix exopolysaccharides that "locked" and reduced the leaching of autoinducers into the milieu, thereby concealing their trails to the detection by the bacterivorous Caenorhabditis elegans nematode. The exopolysaccharides act as common good for the non-producers to hide their autoinducers from predator detection. Deficiency in chemosensory gene odr-10 in mutant animals abrogated their ability to detect autoinducers and migrate toward their prey in a directed manner, which led to lower population growth rate of animals. Hence, restriction of bacterial communication activities to the confinements of biofilms is a novel approach for predator evasion, which plays a fundamental role in shaping ecological dynamics of microbial communities and predator-prey interactions.

Modelling the role of correctional services on gangs: insights through a mathematical model

Research has shown that gang membership increases the chances of offending, antisocial behaviour and drug use. Gang membership should be acknowledged as part of crime prevention and policy designs, and when developing interventions and preventative programmes. Correctional services are designed to rehabilitate convicted offenders. We formulate a deterministic mathematical model using nonlinear ordinary differential equations to investigate the role of correctional services on the dynamics of gangs. The recruitment into gang membership is assumed to happen through an imitation process. An epidemic threshold value, [Formula: see text], termed the gang reproduction number, is proposed and defined herein in the gangs' context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that gangs may persist in the population even if [Formula: see text] is less than one. Sensitivity analysis of [Formula: see text] was performed to determine the relative importance of different parameters in gang initiation. The critical efficacy ε* is evaluated and the implications of having functional correctional services are discussed.