Modeling the dynamics of some common reported offenses by the Ghana police service

Abstract

Crime is a universal phenomenon and it affects national development and stability of a country. Crime rate has always been an issue to policy makers and the security agencies globally. Crime which occurs in societies may be described by their impact and nature as minor or serious. In this study, a non-linear mathematical model is formulated to analyze the dynamics of some reported offenses by the Ghana Police Service. The model was developed using system of differential equations by categorizing the population into susceptibles, serious crime offenders, minor crime offenders, imprisoned criminals and reformed individuals. The model crime reproduction number was obtained by considering a constant death and recruitment type demography. The equilibrium of the crime model was determined and its stability analyzed. Sensitivity analysis of the proposed model is conducted to investigate and identify specific parameters that have high impact in decreasing the spread of crime. To support the theoretical aspect of the model, numerical simulations are carried out. From the simulation it is observed that high rate of government intervention will reduce to the barest minimum the number of crime in a population. Some commonly reported offenses data from the Ghana Police Service, the Criminal Investigation Department (C.I.D) was used to estimate some parameter values for numerical simulations to demonstrate the model’s predictions.