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

Sooknanan, Joanna; Bhatt, B. S.; Comissiong, Donna M. G.

doi:10.1098/rsos.160083

Cited by 21 publications

(10 citation statements)

References 30 publications

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“…Gang members and criminals are viewed as predators and other individuals as the prey [8]. A modified predator-prey model with transmissible disease in both the predator and prey species is proposed and analysed in [9], with the police as predators and gang members as the prey. An SIR model to analyse recruitment into gangs in a manner reminiscent of spread of infectious disease is given in [10].…”

Section: Introductionmentioning

confidence: 99%

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

2017

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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, scriptRg, 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 scriptRg is less than one. Sensitivity analysis of scriptRg 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.

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Section: Introductionmentioning

confidence: 99%

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

2017

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“…Several mathematical techniques have been employed to study the dynamics of epidemic models from optimal control perspective, see [16][17][18][19]. More recently, mathematical modeling have been used to study the dynamics of criminal gangs, see, [13,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. As it can rarely be found in the literature, our interest is to investigate the impact of optimal control strategy on the dynamics of the age-structured criminal gangs, in a limited-resource setting.…”

Section: Model Formulationmentioning

confidence: 99%

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

Ibrahim

Okuonghae

Ikhile

2022

Int. J. Dynam. Control

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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.

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“…Hence, ω 3 (θ − ω 1 N) is the rest of the red fox's total need fulfilled by alternative prey. Here, we choose a linear functional response for healthy foxes as they can easily search for their food despite a decline in the abundance of rabbits [11,19,23,26,32].…”

Section: The Systematic Development Of the Proposed Modelmentioning

confidence: 99%

Infection dynamics of rabbit and red fox with alternative prey

Gupta¹,

Dhar²,

Sinha³

2022

J. Math. Computer Sci.

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In many countries, the decline in red foxes due to Rabbit hemorrhagic disease (RHD) in primary prey European rabbits is a significant concern. We proposed a four-compartment spatiotemporal rabbits-alternative prey-red fox eco-epidemiological model with mange disease and hunting in red foxes. The essential theoretical properties, such as existence, boundedness, stability, and bifurcation analysis, are executed. We have also conducted Turing instability and Higher-order stability analysis for the spatiotemporal model. Hopf bifurcation is shown at a critical value of hunting rate h = h c using central manifold theory. Numerical simulation reveals that the present dynamic is chaotic for a mange disease transmission rate's threshold value β = β + , the most significant factor in the present dynamics. We can control the red fox population by controlling the mange contact rate despite RHD disease in European rabbits. Also, the model does not have diffusion-driven instability due to alternative prey, and if the system is linearly stable, it remains stable for higher-order.

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

Cited by 21 publications

References 30 publications

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

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

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

Infection dynamics of rabbit and red fox with alternative prey

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