An Integrated Optimal Control Model for Simultaneous Tuberculosis Transmission and Stunting Prevention

This study develops an integrated mathematical model to investigate the interaction between tuberculosis (TB) transmission and childhood stunting, which is aligned with the United Nations Sustainable Development Goals (SDG 3). The population is structured into two age groups (0–5 years and ≥5 years), with stunting explicitly incorporated into the pediatric population to capture its potential influence on TB dynamics. The model is formulated as a system of ordinary differential equations and analyzed using equilibrium and stability analysis, with the basic reproduction number, R 0 . The disease-free equilibrium is locally asymptotically stable when R 0 < 1 , while an endemic equilibrium exists when R 0 > 1 . Sensitivity analysis indicates that the transmission rate ( β ), progression rate from latent to active infection ( σ ), and recovery rate ( γ ) are the most influential parameters affecting R 0 . These parameters are therefore selected as control variables in an optimal control framework to design effective intervention strategies. Numerical simulations show that the combined control strategy significantly reduces TB transmission, resulting in a reduction of more than 80 % in active TB cases within a relatively short intervention period. The results suggest that integrated interventions targeting transmission, disease progression, and recovery are substantially more effective than single-measure strategies. This study provides a quantitative framework to support integrated public health policies addressing TB and childhood stunting simultaneously.