Catching a Gang -- A Mathematical Model of the Spread of Gangs in a Population Treated as an Infectious Disease

Abstract

In this study, criminal gang membership is treated as an infection that spreads through a community by interactions among gang members and the population. A mathematical model consisting of a system of coupled, nonlinear ordinary differential equations is used to describe this spread and to suggest control mechanisms to minimize this infection. The analysis shows the existence of three equilibrium states -two of which contain no gang members. When parameters such as recruitment, conviction and recidivism rates and longer jail sentences are varied, the greatest reduction occurs by changing the parameters in combination. A bifurcation analysis shows transcritical bifurcations and no hopf bifurcations.

Stability Analysis in a Mathematical Model of Corruption in Kenya

“…Proof. In order to obtain the Corrupt persistent equilibrium state, we solve equations (17,18,19) simultaneously; Λ + αC − λS − µS = 0 (17) λS − ω1C = 0 (18) δC − ω2M = 0.…”

“…The use of differential equations to describe social science problems dates back, at least, to the work of Lewis F. Richardson [11] who pioneered the application of mathematical techniques by studying the causes of war, and the relationship between arms race and the eruption of war. Modern applications of compartmental models to the social sciences range from models of political party growth, to models of the spread of crime (see for instance) [12], [13], [14], [15], [16], [17], [18], [19], [20]. In recent years compartmental models have also been used to study terrorism, the spread of fanatic behavior, and radicalization [21], [22], [23], [24] [25], [26], [27].…”

When behaviour turns contagious: the use of deterministic epidemiological models in modeling social contagion phenomena

“…Other forms of violent behavior also lend themselves to these types of models. Since association with delinquent peers is one of the strongest risk factors for gang membership [33], gang membership can be treated as an infection that multiplies due to interaction or peer contagion whereby 'infected' youth convert vulnerable or susceptible youth [34,35] to a life in the gang. Criminal behaviour was also treated as an infection with regards to property crime-spread from criminals to non-criminals in a population divided into classes by employment and criminal status [36].…”

Computational criminology and non-equilibrium evolution mechanisms of social crime dynamic system

“…This reflects the characters of the nonequilibrium process. Since the network crimes appear to be kinetic in nature as the society is developing, crime control system should be a non-equilibrium process [10].…”