MATHEMATICAL MODELING AND ANALYSIS OF CRIME WITH MEDIA IMPACT

Abstract

In this thesis, we proposed and analyzed a nonlinear mathematical model that explains the dynamics of crime that includes media coverage. Some fundamental properties of the model including existence and positivity as well as boundedness of the solutions are investigated. Algebraic expression for the basic reproduction number is computed using the next generation matrix method. The model exhibits two equilibria: the crime-free equilibrium and the persistent equilibrium. The analysis shows that the crime-free equilibrium point is locally asymptotically stable if the basic reproduction number is less than unity (R0 < 1) and the persistent equilibrium point is locally asymptotically stable when the basic reproduction number is greater than one (R0 > 1). It is pointed out that the crime dies out if there is effective media coverage and awareness about crime, otherwise, the crime spreads rapidly in the society and it becomes an epidemic. The Numerical simulation is carried out using Ode45 of Matlab, sensitivity analysis of the basic reproduction number is also constructed. Analytical and numerical result shows that effective use of media coverage is the strategy to reduce the dynamics of crime transmission.