Stability Analysis of Conventional and E-Cigarette Smokers Behavior Model with Saturation Effects

Smoking behavior is a harmful habit that poses serious health risks and has been regarded as a lifestyle by certain segments of society, regardless of age, gender, or social status. This study develops and analyzes a mathematical model of smoking behavior that classifies between conventional smokers and e-cigarette smokers, incorporates interaction with lung cancer patients, and considers the saturation effect on potential smokers as the number of smokers in the population increases. The method is determining assumptions to create a compartment diagram and construct the model. This model has four equilibrium points. The results show that when R01 1, R02 1, the smoker-free equilibrium point is asymptotically stable. When R01 1, R02 1, the endemic equilibrium point of e-cigarette smokers becomes stable. When R01 1 and R02 1, the endemic equilibrium point of conventional smokers becomes stable. Meanwhile, when R01 1 and R02 1, the endemic equilibrium point of coexistence of conventional and e-cigarette smokers becomes stable. Numerical simulations show that the intensity of smoking transmission affects the dynamics of the system. The lower the transmission rate by conventional and e-cigarette smokers, the faster the transition to a smoker-free population. The saturation effect plays a role in limiting excessive contact between potential smokers and smokers.