Abstract
Crime has always been considered the main threat to a peaceful, healthy society since it
breeds mental illness, anxiety, and insecurity in the general population. In this thesis,
we study the interaction between the police and criminals, as well as how the police
remove criminals from society. We make use of a system of non-linear ordinary differential
equations to investigate the impact of the cooperating police on crime deterrence.
We presume that police personnel do not commit crimes and that the only way for susceptible
individuals to become criminals is through contact with criminals. The crime
reproduction number R0 is computed, and it is defined herein in the crime membership
context as the average number of individuals that each single criminal will initiate to
criminality during their membership in a population that is entirely non criminal. The
model exhibits a backward bifurcation phenomenon. This implies that even if R0 is less
than one, crime could still exist in the society. We deploy Descartes’ rule of signs to
determine the possible number of crime-persistent equilibrium points. We use the Routh
Hurwitz stability criterion to determine the stability of the crime-persistent equilibria.
We conduct sensitivity analysis on R0 to evaluate the impact of the model parameters on
crime initiation. To validate the theoretical part of the model, we perform simulations.
Strengthening police cooperation and increasing their ability to remove criminals from
society could be key strategies for crime reduction.