A multi-age mathematical model of psychological stress, HbA1c dynamics, and metabolic disorders with control strategies

Abstract

This article investigates how psychological stress-social, economic, and intellectual-affects HbA1c dynamics and related health outcomes across different age groups. The population is divided into six compartments: healthy, stressed, elevated HbA1c, prediabetic, diabetic, and individuals with cardiovascular complications. Age-specific analysis includes young adults (18–25), middle-aged adults (45–66), and older adults (\(>70\)), emphasizing differences in stress response and metabolic regulation. Two intervention strategies are proposed: \(u(t)\), targeting stress reduction through family support and yoga practice, and \(v(t)\), promoting healthy diet and lifestyle habits. Numerical simulations demonstrate that combining both strategies effectively lowers HbA1c levels, slows diabetes progression, and reduces cardiovascular risks across all age groups. The optimal control problem is formulated to minimize the number of stressed and metabolically dysregulated individuals as well as the associated intervention costs, and Pontryagin’s Maximum Principle is applied to determine the optimal strategies.