Modeling of the Electronic Cigarettes with Awareness Effect

Abstract

One of the prevalent behaviors that are frequently observed within societal structures is the habit of smoking. Concurrently with traditional cigarette consumption, there has been a documented rise in the utilization of electronic cigarettes, commonly known as e-cigarettes or vapes. Electronic cigarettes function by vaporizing an e-liquid, typically composed of nicotine, propylene glycol, glycerin, and flavorings, into an inhalable aerosol, namely, potential new smokers (P₁), potential regular smokers (P₂), active conventional smokers (S), electronic cigarette users (E), and individuals who have quit smoking (Q). The analysis entails the calculation of the smoking-free and smoking-endemic equilibrium points via the Cardano method. Additionally, an analysis of the local stability of each equilibrium point is conducted using the eigenvalues of the Jacobian matrix via the Routh-Hurwitz criterion. The results indicate that when the basic reproduction-number, the system converges to a stable, smoking-free equilibrium, suggesting that smoking behavior will eventually disappear from the population. Conversely, the system tends towards an asymptotically stable smoking-endemic equilibrium. Sensitivity analysis indicates that an increase in the transition rate from conventional smokers to electronic cigarette users (α) has the most significant influence on reducing the value of . The numerical simulations are provided to confirm the results analysis