Abstract
Complex crime patterns create a global crime pandemic for which there is no absolute solution.
Crime creates social inequalities and its fear affects the society’s quality of life.
Current social dynamics are wedged in capitalism, technology, politics and community interdependence
guaranteeing every society a physical or an online criminal or victim. This
gives rise to a policing population. We study the police-criminal interaction dynamics to
determine the impact that they have on police recruitment, fear of the police and crime
control strategies, given a baseline police population. We investigate how the position of
a criminal in a social network influences the dynamics of cybercrime. We use non-linear
ordinary differential equations of the Lotkka-Volterra type to formulate various model systems
and perform numerical simulations in Matlab. The steady-states and their stability
are determined and analyzed. Analysis reveals bifurcations due to various thresholds. The
baseline police is necessary but insufficient to maintain a sustainable co-existence of both
populations. Cybercrime occurs in a more heterogeneous network structure, independent
of where the criminal is located relative to the network. These results are fundamental in
the designing and implementation of containment strategies in the fight against crime.
Key words: Interaction; Criminal activity; Police effort; Cybercrime; Predator-prey model;
Bifurcation; Population dynamics; Sensitivity analysis.