Problems of Ageing and Longevity · Jun 25, 2026
Mathematical modeling of emotional balance: aging trajectories
By Pisaruk A
The quantitative description of subjective well-being trajectories over the life course remains a key challenge in gerontological research. Existing models rarely integrate biological, psychological, and existential dimensions into a unified dynamic system. The objective is to develop and analyze a multicomponent mathematical model of Emotional Balance (EB) dynamics for the age range of 20 to 100 years, incorporating components of biological resource, emotional memory, external stimuli, and future emotional assessment. The model consists of a system of coupled equations that incorporate biological age, emotional memory dynamics via an autoregressive process, as well as sigmoidal functions for expectations and time horizons. External stimuli are represented by a composite function with a Gaussian surge during the period of 60–70 years (retirement). Simulations were performed for three aging profiles: successful, normal, and accelerated. Results and conclusions: A mathematical model of EB dynamics across the adult lifespan has been developed, integrating biological resource (biological age), emotional memory, dynamic external stimuli, hope (expectations), and time resource. Simulation of three aging profiles demonstrates profile-specific trajectory divergence with a significant difference in EB between successful and accelerated aging profiles. The model provides a modular, computationally tractable framework for personalized trajectory modeling in gerontological research and may serve as a basis for simulation-based evaluation of psychosocial interventions. Mathematical modeling confirms that a “successful aging” strategy should aim not only to slow biological deterioration but also to strengthen the psychological weight of emotional memory and maintain the cognitive resource of hope.