MATHEMATICAL MODELLING OF SMOKING BEHAVIOR: TREATMENT AND PREVENTION OPTIMAL CONTROL

Smoking remains a critical global public health challenge, with both traditional tobacco use and the rising prevalence of e-cigarettes contributing to significant morbidity and mortality. This study introduces a novel mathematical model that captures the dynamics of smoking behavior by explicitly integrating two smoker populations: traditional tobacco users and e-cigarette users. The model incorporates optimal control strategies aimed at prevention, via public health campaigns, and cessation, through smoking cessation treatments. The smoking model without control has two basic reproduction numbers for tobacco smokers and e-cigarette smokers, and . The extinction smoker’s equilibrium is locally asymptotically stable if and . The extinction tobacco smokers equilibrium is locally asymptotically stable if and . The endemic equilibrium tends to be asymptotically stable whenever and . Simulations demonstrate that implementing control strategies significantly reduces smoking prevalence, with the combined two strategies achieving the most substantial reduction.