Asymptotic analysis of a giving up smoking model with relapse and harmonic mean type incidence rate

Abstract

In this article, we develop a smoking model while considering some important features related to smoking habit like relapse and harmonic mean type incidence rate. The model is developed by using the existing literature and some key and updated research in the field. Besides proving of basic properties related to the model, we prove that the model has a smoking-free equilibrium which is locally and globally asymptotically stable whenever R0<1. It is also proved that the model has a smoking-present equilibrium which is both locally and globally asymptotically stable under certain conditions besides R0>1. To control the smoking behavior in the population, a control problem is formulated considering three control measures, namely; education campaign, anti-nicotine gum and anti-nicotine drugs. The study suggest that proper use of such controls can effectively decrease smoking use from the population.