Mathematical Model Analysis And Optimal Control The Spread Of Smoker By Considering Media Campaign Effect

Source abstract

Smoking remains a critical global health challenge, characterized by the persistent use of traditional tobacco and the rising prevalence of electronic cigarettes. This study introduces a novel mathematical model that captures smoking behavior dynamics by explicitly integrating two distinct smoker populations: traditional tobacco smokers and electronic cigarette users. The model incorporates optimal control strategies focused on prevention through public awareness campaigns and cessation via medical intervention. In the absence of control measures, the model identifies two basic reproduction numbers for tobacco and electronic cigarette smoking, denoted as and , respectively. The smoker-free equilibrium point locally asymptotically stable when . Based on the phase portrait, the characteristic of tobacco-free equilibrium point is unstable, while electronic-free and coexistence equilibrium point asymptotically stable. Numerical simulations demonstrate that the implementation of control strategies significantly reduces smoking prevalence, with the dual-strategy approach achieving the most substantial reduction in the smoking population.