Reaction-diffusion models of crimo–taxis in a street

Abstract

In this paper, two reaction-diffusion models describing the interaction among susceptible people (ordinary citizens), infective people (drug users/dealers), and law enforcement personnel are analyzed. The models here considered are a generalization of the crimo-taxis model originally proposed by Epstein in 1997. The modifications allow us to describe various scenarios. We analyze the equilibrium points, together with their stability, of the homogeneous system. Moreover, according to the Turing approach to reaction–diffusion models, we investigate the instability driven processes and the emergence of patterns in the complete models.