Smoking epidemic model with density-dependent death rate and numerical sensitivity analysis

Abstract

Tobacco smoking is one of the biggest health problem in Indonesia. The government has established policies to control the number of smokers in this country. In this paper, an epidemic model of smoking behaviours will be developed. The model divides the population into four classes, namely non-smokers, normal smokers, heavy smokers and ex-smokers. In this model, the death rates of each class are distinguished and density-dependent death rate is also considered. The discussion of equilibrium points and their stability is used to obtain qualitative information about the behavior of each class. The smoking-free equilibrium point and its stability are solved analitically while the endemic equilibrium point and its stability are solved numerically. The final section will discuss the effects of the rate of interaction that causes a non-smoker to become a smoker. The results of this discussion can be used as a consideration in determining the control measures for the number of smokers in this country.