ANALYSIS FOR THE DYNAMICS OF CONTROL OF CRIME AGAINST WOMEN IN INDIA: AN OPTIMIZATION CONTROL STRATEGY

Abstract

In this study, a non-linear mathematical model for the dynamics of crime against women in India has been considered based on the principles of optimal control theory. Four time-dependent control mechanisms are incorporated in the present study to curb (minimize) the growing rate of susceptible and hence victim population and enhance (maximize) the crime quitting rate of criminals. These functions reflect the susceptible population’s restriction-reduction plan and crime prevention approach to the criminal population. The Pontryagin’s maximum principle is used to solve the described optimum control functions. Consequently, the optimal strategies for the control variables have been determined. Numerical findings for several situations are presented to illustrate the effect of controls on the number of victims and criminals. The numerical simulation shows that when the control measures are implemented, there is a noticeable decrease in the number of victims and criminals in comparison to the scenario of no control. Thus, we conclude that to reduce the number of victims and criminals, the government should fund awareness campaigns, enact laws that work, install security cameras, provide emergency devices to susceptible, teach them self-defense techniques, and encourage criminals to change their ways.