Modeling and dynamical analysis of the impact of alcohol consumption on tuberculosis transmission with optimal control strategies.

Alcohol consumption significantly exacerbates tuberculosis (TB) transmission and severity, creating a critical public health problem by increasing susceptibility and reducing treatment efficacy. To address this, our study develops a novel compartmental model that integrates, for the first time, the dynamics of distinct alcohol use patterns with TB disease progression and key interventions like alcohol protection and TB vaccination. The primary objective was to analyze this co-dynamic system and identify optimal control strategies. Using mathematical modeling, sensitivity analysis, and optimal control theory, we determined that the disease is containable when the reproduction number falls below a threshold. Our analysis identified alcohol and TB transmission rates as the most influential drivers of the epidemic. The key finding, validated through numerical simulations, is that a combined strategy applying alcohol and TB protections for the acutely infected alongside protections and treatment for chronic patients constitutes the most cost-effective intervention, significantly reducing the co-infection burden compared to single or no controls.