Mathematical Analysis of Sexual Violence Dynamics with Recidivist Perpetrators

Abstract

Sexual violence remains a serious social issue with far-reaching consequences for both victims and society at large. To capture the dynamics of its spread, this study develops a compartmental mathematical model that divides the population into four subgroups: susceptible individuals ($S$), perpetrators ($V$), punished offenders ($P$), and rehabilitated individuals ($R$). The model incorporates a recidivist parameter, representing the tendency of punished individuals to relapse into offending, that is return from the $P$ to the $V$ class. The analysis includes the determination of equilibrium points, computation of the basic reproduction number using the Next Generation Matrix approach, and assessment of local stability through eigenvalue evaluation of the Jacobian matrix. The results indicate that both equilibrium points are asymptotically stable under certain condition. In addition, the presence of recidivist perpetrators increases the basic reproduction number, thereby amplifying the likelihood of sustained sexual violence within the population. In particular, the relapse rate is shown to play a critical role in destabilizing the violence-free equilibrium, underscoring the importance of addressing recidivism in prevention and intervention strategies. These findings provide new insights into the mathematical modeling of sexual violence and highlight the necessity of targeted policies to mitigate its persistence.