Modeling and Analysis of the Interaction of Police and Criminal Populations:
A Competing Species Model
The rise of the criminal population in the United States has brought concern, debate, and contention to the modern world. The strategies of criminals are national and are no longer concentrated in a particular location. In this paper, we present a dynamical model of the interaction between criminal and police populations. The formulation is based on models of interactions between competing species type dynamics. An exploration of the long-term dynamics and stability of homogeneous equilibrium solutions and their stability is given. The paper is given in multiple parts. Part two presents the mathematical model and analyzes the situation for current population levels. Part three analyzes the situation when an additional number of members are introduced into the criminal population. Part four analyzes the scenario where the criminal population is reduced. Part five presents conclusions.
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