International Journal of Differential Equations and Applications Volume 14 No. 4 2015, 343-356 ISSN: 1311-2872 url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijdea.v14i4.2577 P A acadpubl.eu THE EFFECT OF HEAVY SMOKERS ON THE DYNAMICS OF A SMOKING MODEL Zainab Alkhudhari 1 , Sarah Al-Sheikh 2 § , Salma Al-Tuwairqi 3 1,2,3 Department of Mathematics King Abdulaziz University Jeddah, 21551, SAUDI ARABIA Abstract: In this paper we present a non-linear mathematical model which analyzes the spread of smoking in a population. The population is divided into five classes: potential smokers, occasional smokers, heavy smokers, temporary quitters and permanent quitters. We study the effect of considering the class of occasional smokers and the impact of adding this class to the smoking model in [1] on the stability of its equilibria. This model is similar to the model in [2] where we studied the effect of occasional smokers on potential smokers, but here we’re going to consider the effect of heavy smokers on potential smokers and it’s impact on the stability of the model. Numerical results are also given to support our results and to compair the two models. Key Words: smoking model, smoking generation number, linearization, next generation matrix, Routh-Herwitz, Liapunov function, local stability, global stability 1. Introduction There is a lot of studies that has been done on the epidemics of smoking and it’s hazards. The World Health Organization estimates that tobacco causes approximately 5 million deaths annually worldwide, and this number is expected Received: November 10, 2014 c  2015 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author