Global Analysis Of Different Compartments In A Giving-Up Smoking Model

Smoking can cause numerous diseases like lung cancer, mouth diseases, bronchitis, stroke, heart diseases, etc. To overcome such and other related diseases, we need to avoid the smoking habit from the population at large scale. The key purpose of this work is to discuss and analyze different kinds of smoking phases which are very common in our society. The model is formulated in the form of a system of ordinary differential equations keeping in view the existing literature. The model is investigated for possible equilibria besides positivity and boundedness of solution. The model exhibits six equilibrium points and the stability analysis of each fixed point is investigated. The local stability analysis of each equilibrium point is carried out with the help of linearization approach and it is shown that these equilibria are locally asymptotically stable under certain conditions. We also checked the fixed points for global analysis with the help of Lyapunov stability theory and stability criteria were obtain therein. We also perform the local sensitivity analysis. To verify the theoretical results, a scheme is developed using non-standard finite difference method. Simulations suggest that the obtained graphical results support our analytical findings with a high degree of accuracy.