Mathematical model analysis of crime dynamics incorporating media coverage and police force

Abstract

In this paper, a mathematical model is proposed to recognize the dynamics of crime. Unlike some of other previous model, we have taken into account the impact of media coverage, police force and moral/religious activity on crime. Some fundamental properties of the model including existence and positivity as well as boundedness of the solutions of the model are investigated. The model exhibits two equilibria: the crime-free and the persistent equilibrium points. We sufficiently analyze asymptotic behavior of the solutions which depends on the basic reproduction number. Numerical simulation is carried out using Ode45 of Matlab, sensitivity analysis of the basic reproduction number is also constructed.