Stability Of A Smoking Model With Stage Structure And Its Optimal Control

Health hazards of smoking have becoming a consensus. Every year over2.5million people die from smoking. Smoking has become the most fatal factor lead to death of human beings in21century. Even so, the number of smokers still continues to grow everyday. Especially the situation of adolescents smoking is getting much more serious. So quit smoking has become the superior of society’s concern. Smoking can be considered as a chronic infectious disease. Smoking behavior of one person may infect others around him. In recent years more and more scholars do research on quit smoking models using biomathematics. Mainly about stability analysis and optimal control and some other issues.The first chapter introduces the health hazards of smoking and the benefits of quitting smoking, while researching the background and innovative point of the model. In addition, there are some preliminary knowledge needed.In Chapter two, a smoking model with stage structure is studied, the smoking-free equilibrium and smoking-present equilibrium is obtained. We obtain the basic reproductive number by using the next generation method and proved that smoking-free equilibrium is asymptotically stable according to the comparison theorem. Finally, some numerical simulations are given to illustrate our results.In Chapter three, optimal control strategy of a smoking model with stage structure is studied. First we construct the model and calculate the basic reproductive number. Then Pontryagin maximum principle enables us to solve the relative problems of optimal control.Finally, we summarize some conclusions and make some improvements of the model for future research.