Exploring the Impact of Nonlinearities in Police Recruitment and Criminal Capture Rates: A Population Dynamics Approach

The interplay between criminal activity and crime control/prevention measures is inherently dynamic. This paper presents a simple nonlinear dynamical system in which criminal activity levels are coupled to policing effort. Through the process of non-dimensionalisation and sensitivity analysis, policing efficiency and the responsiveness of policing effort are identified as key parameter groupings. An analysis of the system shows that bi-stability is a feature of the dynamics. When there is no feedback between criminal activity and police recruitment, a saddle-node bifurcation occurs and threshold levels of criminal activity are required for the activity to be maintained. When feedback is permitted, we also find a backward bifurcation and criminal activity can be contained for policing efficiency below its threshold level. We demonstrate proof of concept for how the model might be used as a predictive tool with real data.