Stability of Smoker Population Model

Abstract

— In this article, a model for the smoking habits distribution is studied. The distribution model of smoking habits is divided into three compartments, namely potential smokers (P), active smokers (S), and permanent non-smokers (R). Based on the model analysis, two equilibrium points are obtained, they are the smoke-free equilibrium point and the endemic equilibrium point. Analytical study is carried out by analyzing the stability of the model around the equilibrium point based on the eigen values of the Jacobian matrix. The stability of the model is also associated with the basic reproduction number (Ro) or the parameter that determines the population is free from active smokers or the prevalence of smoking habits occurs. The numerical simulations performed show asymptotically stable smoking population around the smoker-free equilibrium point with  Ro<1 and asymptotically stable endemic equilibrium point with  Ro>1.