Law Enforcement: The key to a Crime-free Society

This paper intends to simulate a simple artificial society divided into two populations: criminal and non-criminal. The time evolution of the system is modeled using a set of differential equations, borrowing relevant features from the prey-predator, epidemic spread, and harvesting models. Each population can switch type upon interaction. The stability and equilibrium points of this system are examined, concluding that harvesting and interaction rates play an important role in the evolution of the system toward different stable equilibria between populations, which eventually coalesce into one. The results indicate that as long as the harvesting and conversion rates remain sufficiently small, the criminal population thrives. However, when either of the two crosses a certain value, the criminal population becomes extinct.