Analysis of Spread of Crime: A Socio-Mathematical Study

Abstract: For the analysis of spreading of the crime, a non-linear model has been suggested as well as stability analysis is performed in this paper. Under normal situations crime is modelled as a contagion spread of infectious disease. Here, the modelling is done by dividing the total population into non-susceptible, susceptible, criminal and jailed populations and the connection between them is given by simultaneous ordinary nonlinear differential equations. The interaction between them plays an important role and hence care has been taken while modelling. The threshold parameter R0 for the elimination of criminal activity is enumerated using the approach of the next generation matrix. Analysis indicates that when R0 1 indicates the endurance of criminal activity in the society. Numerical simulation along with the stability analysis is performed. However, various investigators have already worked in this field, but still there are vital possibilities for further research in this arena in the future.

Keywords: Crime, Equilibria, Mathematical Model, Numerical Simulation, Stability Analysis.