A mathematical model for the treatment of delinquent behaviour

A public health approach to reducing violence within the CARICOM region

“…The public health approach can help reduce crime by treating crime and violence like a disease and looking for innovative ways to prevent this “disease” from spreading. In fact, several mathematical models of crime as a disease already exist and they allow for the examination of preventive approaches in different scenarios ( 11 ). Such analytic modelling based on data collected should assist in the design of public health approaches to violence reduction.…”

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

“…Furthermore, it is well established that optimal control results are tied to the optimal control model, how the controls are used in the model and how the associated objective functional is defined [ 42 ] As a result, this will genuinely guide us on how the controls presented herein are being placed in the constraints to be formulated. The constraint equations subjected to the objective function is given by In system ( 2.4 ), , represents the rate of change in susceptible individuals within the age bracket 0–7 years (they are resistant to crime) with respect to time t ; , means the rate of change in susceptible individuals within the age bracket 8–17 years (they are exposed to delinquent behaviors from their peers) with respect to time t ; , represents the rate of change in susceptible individuals within the age bracket 18–above years (they are expose to delinquent behaviors from their peers) with respect to time t ; , implies the rate of change in criminal gang population (within the age bracket 8–17 years) with status offenses (eg., tobacco consumption, alcohol consumption, assault, breaking and entering, etc [ 43 , 44 ]), with respect to time t ; , represents the rate of change in criminal gang population (within the age bracket 8–17 years) that exhibit capital offenses (murder), with respect to time t ; , represents the rate of change in criminal gang population (within the age bracket 18–above years) with non-status offenses (eg., murder, robbery, fraud, illegal sale of drugs, human trafficking, money laundering, kidnapping, illegal smuggling of goods, weapon and drug trafficking, domestic violence, rape, etc) [ 45 ], with respect to time t ; , means the rate of change in the individuals under rehabilitation (individual within the age bracket 8–17 years) with respect to time t ; , implies the rate of change in the individuals in government remand homes (individual within the age bracket 8–17 years) with respect to time t ; , represents the rate of change in the prosecuted and law-enforced gang members (individual within the age bracket 18 - above years) serving jail terms with respect to time t ; N is the total population at any given time t . The parameters are as well defined in the Table 1 .…”

Stability Analysis in a Mathematical Model of Corruption in Kenya

“…It therefore follows, that the condition necessary for λ * > 0 is whenever R0 > 1. The expression for corrupt persistent equilibrium point is evaluated by substituting equation (23) into equations (20), (21) and (22) to yield;…”

“…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].…”