Modelling the Interconnected Dynamics of Alcoholism, Tuberculosis and Smoking: A Comprehensive Approach to Public Health Challenges

Alcoholism and smoking are significant health and social challenges that increase susceptibility to tuberculosis (TB) infections. This study develops a mathematical model to analyse the interconnected dynamics of alcoholism, tuberculosis, and smoking (ATS). The model examines the stability of the ATS-free equilibrium and calculates the basic reproduction number. Numerical simulations reveal that alcoholism and smoking independently increase TB infection rates, while co-infections involving combinations of alcoholism, smoking, and tuberculosis amplify disease spread. Sensitivity analysis highlights the impact of contact and progression rates on disease dynamics, suggesting that reducing exposure to alcoholism and smoking could lower TB incidence. Pairwise comparisons of infections and co-infections indicate convergence to equilibrium solutions, offering insights for disease control. The study underscores the importance of protecting vulnerable populations, particularly children, from exposure to alcoholism and smoking to mitigate TB infections. This model provides a comprehensive framework for addressing these interconnected health challenges, with implications for public health strategies and future research.