An Analytical Study of Optimal Control within a Mathematical Model of Smoking Behavior

In this work a dynamical model of smoking is presented. There are so many harmful effects of smoking on our health. Smoking is a source of the air pollution and it puts the life of others at risk that lives in the nature. The model is categorized into five classes. These include non-smoking individuals, non-regular smokers, active smoking individuals, those people who have given up smoking temporarily and the people who quit the smoking on permanent basis. This mathematical smoking model depends on four optimal controls, i.e., education effort against smoking, against smoking gum, against an alkaloid poison that occur in tobacco and smoking banned by government in public areas, all are defined in the model. The solution to the optimal control problem is derived using the Pontryagin Maximum Principle (PMP) and an analytical approach has been adopted for this purpose.