Mathematical analysis of a smoking model with anti-smoking campaign rate in Thailand

Abstract

Smoking is one of the leading causes of preventable mortality worldwide, affecting multiple organ systems and contributing to numerous chronic diseases. It is well established that smoking increases the risk of lung cancer, cardiovascular diseases such as heart attacks and strokes, and chronic respiratory conditions, including chronic obstructive pulmonary disease (COPD). In Thailand, mathematical modeling has not yet been applied to the study of smoking behavior. To better understand smoking behavior and the effects of anti-smoking interventions, this study develops a nonlinear mathematical model of smoking in Thailand that incorporates the influence of anti-smoking campaigns. The population is categorized into non-smokers, active smokers, permanent quitters, and temporary quitters. This simplification makes the model easier to analyze and more practical to use. The model assumes that non-smokers may become smokers through social interactions and that smokers may quit either temporarily or permanently, with temporary quitters susceptible to relapse. The boundedness of the model is proven, and the basic reproductive number (R₀) is derived using the next-generation matrix method. Stability analyses of both the smoking-free and smoking-present equilibrium points using the Routh–Hurwitz criteria show that the system is locally asymptotically stable when R₀ < 1, indicating effective control of smoking prevalence under these conditions. Numerical simulations further demonstrate that increasing the rate of anti-smoking campaigns significantly reduces the number of active smokers, highlighting the importance of sustained public health interventions. Overall, this combined analytical and numerical framework offers valuable insights into smoking dynamics and provides a practical tool for designing and evaluating strategies to reduce smoking rates and associated health burdens.