Abstract
This research work is related to a tobacco smoking model having a significance class of users of tobacco in the form of snuffing. For this purpose, the formulation of the model containing snuffing class is presented; then the equilibrium points as regards being smoking free and smoking positive are discussed. The Hurwitz theorem is used for finding the local stability of the model and Lyaponov function theory is used for the search of global stability. We use different controls for control of smoking and the Pontryagin maximum principle for characterization of the optimal level. For the solution of the proposed model, a nonstandard finite difference (NSFD) scheme and the Runge-Kutta fourth order method are used. Finally, some numerical results are presented for control and without control systems with the help of MATLAB.