Analysis of a Smoking Dynamics Model with Age-Dependent Incidence Function

Abstract

Smoking remains a major public health concern, influenced significantly by age structure and household environments. In this study, we develop and analyze an age-structured mathematical model that incorporates age-dependent incidence and household effects to better understand smoking dynamics. We establish the model’s well-posedness by proving the existence and uniqueness of solutions. The global stability of both smoking-free and endemic equilibria is analyzed using a suitably constructed Lyapunov function. For numerical simulations, we apply the nonstandard finite difference (NSFD) method and compare the results with those obtained via the classical fourth-order Runge–Kutta (RK4) scheme. The findings underscore the importance of age-specific interventions and offer a framework for future studies incorporating relapse, control strategies, or stochastic effects.