Mathematical analysis of the impact of work, culture and relationships on mental well-being of women

Abstract

Mental well-being of women is a multifaceted outcome shaped by the complex interplay of psychosocial factors. This study develops a compartmental dynamic model using a system of nonlinear ordinary differential equations to quantify the interactions between work-related stress, cultural pressure, relationship satisfaction and mental health. The model is analyzed to establish the positivity and boundedness of solutions, ensuring biological feasibility. Analytical results identify two equilibrium states: a Disease-Free Equilibrium (DFE), representing the absence of mental health strain, and an Endemic Equilibrium (EE), representing a persistent state of mental health challenges. The basic reproduction number, R₀ = η/ξ, is derived, serving as a threshold parameter. When R₀ < 1, the DFE is both locally and globally asymptotically stable, indicating that mental well-being can be naturally restored. Conversely, when R₀ > 1, the EE becomes stable, signifying the sustained prevalence of mental health burdens. Sensitivity analysis identifies the mental health recovery rate (ξ) and the relationship growth rate (η) as the most influential parameters. Numerical simulations corroborate the analytical findings, demonstrating that work stress and cultural pressure exert significant negative impacts on mental health, whereas high-quality relationships provide a substantial protective and restorative effect. The study proposes targeted interventions such as workload management, cultural norm shifting, and strengthening relationship support systems to effectively promote and safeguard women’s mental well-being.