A dynamical systems approach to the interplay between tobacco smokers, electronic-cigarette smokers and smoking quitters

Abstract

Abstract In this paper, the effect of e-cigarettes on smoking cessation is studied using the tools of dynamical systems theory. The purpose here is to examine this efficacy by representing and analyzing a non-linear ODE system modeling potential smokers, tobacco smokers, e-cigarette smokers and quitters. The transition from smoking class to e-cigarette smoking class is represented by the “peer pressure”. The model exhibits three possible equilibrium solutions which are the smoking-free equilibrium, e-cigarette smoking-free equilibrium and endemic equilibrium. It is shown that the smoking free equilibrium always exists. Moreover, this equilibrium is stable if the basic reproduction number R 0 is less than unity. When R 0 > 1 , it is shown that the smoking free equilibrium is unstable, and of the other two equilibria is stable. The global stability analysis of the smoking-free equilibrium is also given. Some numerical simulations are plotted using the data obtained from the literature. The theoretical results are also confirmed by numerical results.