SEIR Model for Stunting Risk Dynamics in Children Based on Nutritional Data in North Sumatra

Abstract

Stunting remains a major chronic nutritional challenge in Indonesia, particularly in North Sumatra Province, where prevalence reaches 21.1% among children aged 2-4 years. This study develops a modified SEIR (Susceptible-Exposed-Infected-Recovered) mathematical model to analyse stunting risk dynamics based on nutritional intake patterns, using secondary data from the BPS, SSGI 2023, and the North Sumatra Health Profile 2023. Model compartments represent susceptible children (S), low-birth-weight infants indicating exposure risk (E), severely malnourished children (I), and recovered children after nutritional intervention (R). Parameter estimation employed least-squares fitting, with numerical simulations conducted over 12 months using a fourth-order Runge-Kutta method implemented in Python. Results reveal declining susceptible population trends alongside increases in the exposed (E: 1,362→1,525) and infected (I: 449→723) compartments, despite rising recovery rates (R: 414→2,900), indicating that current nutritional interventions are insufficient to suppress new stunting risk cases. The basic reproduction number proxy (R₀≈1.20) suggests self-sustaining risk propagation. The model demonstrates good fit to empirical SSGI data (MSE=0.012) and provides a quantitative basis for evidence-based nutritional policy formulation in North Sumatra, particularly targeting high-risk districts (Nias, Mandailing Natal, Langkat) identified through spatial analysis.