Global stability and optimal control of an age-structured quit-smoking model with quit-smoking duration

In this paper, we introduce an age-structured quit-smoking model that incorporates the duration of smoking cessation, a crucial parameter related to smoking cessation counseling and disease treatment. We identify the threshold value R0, which determines the existence and stability of the smoking-free steady state. Our findings show that the smoking-free steady state is locally and globally stable if R-0<1, whereas it becomes unstable, and the unique steady state with present smokers emerges and is locally and globally stable if R-0>1. We propose an optimal control strategy, and our results show its ability to effectively decrease the number of smokers and promote smoking cessation. To validate our findings and to study the influence of varying parameters on the model's dynamics, numerical simulations are carried out. A concise conclusion is then shared at the end of the paper.