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

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 R0 is less than unity. When R0>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.