Mathematical Modeling for The Effects of Early Life Stress on Brain Development and Mental Health Trajectories

Early life stress, comprising various adverse experiences during childhood and adolescence, has been linked to long lasting impacts on brain development and mental health outcomes.  However, the multifaceted interactions between these factors and their trajectories over time remain incompletely understood.  This study developed a compartmental SEIR (Suscepti-ble–Exposed–Impacted–Resilient) mathematical model to understand the progression and im-pact of Early life stress (ELS) on children and adolescents in urban informal settlements in Kenya.  The model integrates environmental, neurobiological and psychological factors to capture the complex interplay between early life stress, brain maturation processes and mental health outcomes while incorporating demographic dynamics through birth and death rates.  Mathematical and computational techniques were employed on the model differential equations developed and the well-posedness of the model was demonstrated by proving several theorems on the feasibility, boundedness and stabilities.  Mathematical analysis enabled simulations with data from neuroimaging techniques, psychological assessments, biomarkers, longitudinal studies and predictions of mental health outcomes under varying levels.  Key findings show that early childhood (0–5 years) and adolescence (13–17 years) are periods of heightened vulnerability to ELS.  High intensity and prolonged stress exposure signifcantly increase progression to adverse mental health states whereas early, targeted interventions can improve resilience by upto 30% over a decade.  Demographic factors further influence the long term impact of ELS, highlighting the importance of population-level strategies.  In comparison to other mathematical and computational models, the ELS-SEIR model provides a valuable balance between simplicity and detail.  While it does not capture the stochastic randomness of Agent-Based Models or the mechanistic intricacies of bio-physical models, it excels at modeling population-level trends and intervention effects through a clear, analyzable structure.  The SEIR framework provides a valuable tool for identifying critical intervention points, guiding policy, and designing prevention strategies.  These findings have important implications for mental health professionals, policymakers, educators and social service providers aiming to improve wellbeing and resilience across the lifespan in vulnerable communities.