Analyzing High School Student Mental Health using SEITR Compartmental Model of Epidemiology

Abstract

With the influx of big-data and social media in our fast-paced and dynamic world, stress and anxiety have become pervasive concerns, affecting individuals through in-person interactions and online experiences According to a 2022 CDC survey, a concerning 37% of US high school students reported "poor mental health," highlighting the urgency to better comprehend the spread and dynamics of stress and anxiety within this population. This project aims to achieve this by employing an SIR-based mathematical model, originally devised for infectious diseases, to analyze the influences and dissemination of high-school stress and anxiety. In this project, an SEITR model was considered, where "S" denotes the susceptible group representing high-school students vulnerable to stress and anxiety, "E" represents the exposed group indirectly impacted by stress and anxiety through factors like academic pressure and online interactions, "I" symbolizes the infected group actively experiencing stress and anxiety symptoms, "T" accounts for treatment options to alleviate these conditions, and "R" indicates the recovered group that successfully manages and overcomes stress and anxiety. This governing system of differential equations was solved numerically and the influence of various parameters were studied. We also employed parameter identification techniques and physics informed neural networks (PINN’s) to validate the model. The basic reproduction number for the SEITR model was also derived. Overall, the numerical results provided detailed insights into the importance of the role of social media and in-person interactions on the spread and management of stress and anxiety. It also suggested that social media's influence can amplify stress and anxiety, with curated lives, cyberbullying, and unrealistic expectations exacerbating psychological distress, while in-person interactions in high-school settings contribute significantly to stress and anxiety levels. Integrating the effects of social media and in-person interaction within the SEITR model provides a comprehensive understanding of factors influencing the spread and management of stress and anxiety in high-school populations. By shedding light on these dynamics, this study sought to improve the overall stress and anxiety outcomes of high-school students and guide future research and policy initiatives into mental health studies.