On the fractional-order smoking epidemic model

Abstract

In this study, we introduce a fractional dynamic model to explain how the smoking habit spreads across people when active smokers are given nicotine gum parameters to consume. It was demonstrated that the basic reproduction number affects the stability of both the smoking-endemic equilibrium and the smokingfree equilibrium. These results are in accordance with the epidemic theory. A numerical example is given to demonstrate the validity of the results. The results show that the giving the consumption of the nicotine gum parameter to the active smoker able to reduce the number of people who are actively smoking, increase the number of people who have a risk of smoking ones, and increase the permanent smoker quitter, thus the model gives adequate information about the spread of the smoking habit.