Modeling the effect of police deterrence on the prevalence of crime in the society

•The effect of police force on crime is studied using nonlinear mathematical model.•The immigration of criminals is restricted by police force.•By ceasing the immigration of criminals, police force can eliminate crime from society.•An explicit expression for critical number of baseline police force is derived.•Numerical simulation and sensitivity analysis is performed on key parameters.

In this paper, a nonlinear mathematical model has been proposed and analyzed to study the effect of police force in controlling crime in a society with variable population size. In the modeling process, it is considered that immigration rate of susceptibles as well as criminals, is altered by police force. It is considered that the police force not only captures the criminals but also lessen their inflow in the region under consideration. A particular case of the proposed model has also been analyzed by assuming that there is no immigration of criminals into the society. The model analysis reveals that by ceasing immigration of criminals and maintaining a sufficient number of baseline police force, the crime in the society can be controlled completely. An explicit expression for critical number of baseline police force has been derived analytically. Numerical simulation and sensitivity analysis is also carried out to investigate the influence of certain key parameters on the dynamics of crime in the society.