A mathematical model for studying rape and its possible mode of control

Abstract

Abstract Estimates of rape against women had been usually taken from two main sources till the early 1980s; The national crime victimization study and the Uniform Crime Report’s official statistics. Scholars argued, however, that the true incidence of rape was greatly underestimated by those data sources. For example, a uniform crime report focuses on recorded incidents, but several violations are not reported to the police. Two methodological causes have contributed to the underestimation of rape by national crime surveys. First, its definition of rape was considered too limited because it covered only carnal information and, thus, omitted many actions, such as offenses other than penile-vaginal penetration, from the scope of contemporary rape laws. Second, critics argued that the national crime survey was inappropriately structured for interviewees who had previously been assaulted to generate allegations of abuse. The crux of this critique was that there was no clear concern about rape in the national crime survey. How to establish evaluation methods that would show the real nature of rape was the crucial question. As a result of this, we are inspired to design a new mathematical model in this paper to study the dynamics of rape in our societies. Several characteristics of the established model, such as model formulation, boundedness, equilibrium solutions, basic reproduction number, global stability analysis are derived. The existence and characterization of the optimal control function are carried out. For sensitivity analysis as well as to show the significance of the control strategies, several simulation results are given. To get a deep insight into the dynamical behavior of the model, numerical simulations are performed and consequently we obtain the graphical results based on parameters taken as variables. The Euler technique is employed to do the job.