Global stability of an age-structured model of smoking and its treatment

Abstract

Smoking is a serious global public health problem. The ability to quit smoking is closely related to age; in addition, personal determination and education usually play an important role in quitting smoking. In order to capture such characteristics, we developed a novel age-structured smoking dynamical model. By defining the smoking generation number [Formula: see text], the local stability, global stability of the boundary equilibrium and endemic equilibrium are obtained using Lyapunov functions. The uniform persistence and the well-posedness and asymptotic smoothness of the solutions are also studied. Sensitivity analyzes show that the lower the age of onset of smoking and the higher the determination to stop, the greater the likelihood of quitting smoking and numerical studies support the theoretical results.