Threshold dynamics and optimal control of an age-structured giving up smoking model

In this paper, a new giving up smoking model is proposed by incorporating the continuous age-structure in the chain smokers class, which is known as a class of age-structured giving up smoking model. Smoking generation number is defined and proved to be a classic threshold parameter. Two steady states of the model are found. The corresponding characteristic equations are analyzed, and the proper Lyapunov functionals are constructed to show the local and global stability of both steady states. Optimal control strategy is presented and numerical simulations are made to support the main results.