Smoking is one of the main health concerns in Indonesia. According to Riset Kesehatan Dasar in 2013, there are approximately a total of 29.3% of the Indonesia’s population are smoking, an increase of 0.1% from 2007. As in 31 December 2016, according to World Health Organization report on the global tobacco epidemic, the prevalence of daily smoking for male is 62%, whereas for female is 1.7%, a total of 31.9% from Indonesia’s population.

 

This work presents a mathematical model that investigates the impact of smokers on the transmission dynamics of the smoking behavior in Indonesia’s population. The population is classified into three classes: potential smokers, smokers, and ex-smokers. A potential smoker could be influenced to be a smoker, but couldn’t directly be an ex-smoker. Whereas a smoker or an ex-smoker can’t be a potential smoker anymore.

In this model two equilibrium points are found. One of them is the smoking-free equilibrium and the other relates to the presence of smoking. Then, the local and global stability of both equilibrium points are examined. Lastly, numerical simulations are carried to illustrate the analytic conclusions.

 

This model is described by non-linear differential equations using fractional quantities instead of actual populations by scaling the population of each class by the total population. There is also the density-dependent and density-independent death rate in the model to accommodate the difference between death rate of potential smokers, smokers, and ex-smokers.