Prediction of anxiety and depression in university students using a high-precision mathematical model

Abstract

In recent decades, mental health studies have shown a significant increase in anxiety and depression disorders among university students, constituting a multidimensional phenomenon with important academic and clinical implications. These disorders directly affect cognitive and emotional skills such as concentration, planning, self-regulation, and decision-making, generating a negative feedback loop between psychological distress and poor academic performance.

In this context, the present study proposes and validates a mathematical model that quantitatively estimates the emotional burden in university students by integrating psychological, academic, and social variables. This approach facilitates the identification of risk patterns and supports the design of evidence-based preventive interventions.

The results demonstrate that mathematical modeling is an effective tool for analyzing complex emotional states, contributing to the field of computational psychology. At the institutional level, the model provides a solid basis for improving student welfare services, while at the social level, it contributes to the development of public policies aimed at promoting youth mental health. Overall, the proposed model strengthens data-driven decision-making that is objective, reproducible, and scalable across diverse educational contexts.