Controlling crime with its associated cost during festive periods using mathematical techniques

In this paper, we seek to control crime at its minimal level during festive periods such as Christmas, Valentine’s day and entertainment events such as music awards. We used epidemiological-borrowed concepts to understand and model the dynamics of crime during these periods. We analyze the fundamental properties of the model, compute the crime basic reproduction number, R0, using the next generation matrix approach and use the output to establish the steady states of the model. The crime-free steady state is found to be locally stable whenever R0<1. The center manifold theorem is used to show the existence of bifurcation at R0=1. The model is then transformed into an optimal control problem with three control interventions (education, detention and sacking) to obtain the best strategy to control crime at its minimum level. The control reproduction number was determined to show scenarios when the implementation of the controls give an R0<1 or R0>1. Moreover, numerical simulations are carried out to affirm the theoretical properties of the model. From the simulations, education is observed to be the best single strategy to apply but, alternatively, incorporating two or more control interventions equally give a better result. Finally, cost effectiveness analysis was employed on the control strategies and it shows that education and sacking are the most cost-effective strategies to minimise crime during events.