Mathematical modeling and simulation of stress phenomena for medical students with optimal control

Abstract

Stress is a pervasive issue among medical students, arising from demanding academic workloads, psychological pressures, and limited recovery opportunities. The consequences of unmanaged stress include adverse mental health outcomes, impaired academic performance, and increased burnout rates. This paper presents a novel mathematical model that encapsulates stress dynamics, workload impact, secondary symptoms, and resilience. The model introduces two control variables: u(t), modulating the influence of workload, and v(t), enhancing resilience. A system of nonlinear differential equations describes the interaction among these factors. The framework leverages optimal control strategies to minimize stress levels and improve resilience sustainably. Numerical simulations demonstrate the effectiveness of these strategies, highlighting the potential for precise interventions to mitigate stress. This work provides a foundation for evidence-based decision making in academic and psychological support systems, offering insights into the effective management of stress in demanding educational environment.