Modeling the Impact of Sexual Harassment Exposure on Substance Use Dynamics Among Women

Abstract

Substance use among women is a significant public health concern, with traumatic experiences such as sexual harassment increasing the risk of substance use initiation and contributing to long-term physical and mental health consequences despite advancements in prevention and treatment strategies. Inspired by epidemiological models, this project introduces a novel compartmental framework to model substance use transitions among women by modifying a Susceptible-Using-Recovered (SUR) compartmental system. The resulting five-compartment model is governed by a system of coupled ordinary differential equations (ODEs). The model represents transitions between low-risk non-users, harassment-experienced non-users, active substance users, treatment, and remission compartments to simulate substance use dynamics over time. Mathematical analysis establishes the stability of the system and evaluates long-term model behavior. In addition, analytical methods, including integrating factor techniques and Laplace transforms, are applied to examine the solutions of the coupled system of first-order differential equations. Numerical simulations illustrate the progression of substance use, treatment, and remission. In alignment with the United Nations Sustainable Development Goals 3 and 5 on Good Health and Well-Being and Gender Equality, respectively, this research demonstrates the importance of mathematical modeling in understanding substance use dynamics among women and supporting informed substance use prevention and treatment strategies.