Optimal Control Strategies in a Nonlinear Smoking Cessation Model

Abstract

This study introduces a novel nonlinear smoking cessation model with optimal control strategies and time delays. The model incorporates a convex incidence rate and divides the total population into four classes. We first establish positivity, compute equilibrium points, and determine the basic reproduction number using the next generation method. Global stability is analyzed via the Castillo–Chavez principle for the smoking-free equilibrium and the geometric approach for the endemic equilibrium. Sensitivity analysis is performed to identify influential parameters. The model is extended to include optimal control, where the existence and uniqueness are established, and the impact of time delays is examined. A Hopf bifurcation is shown to occur at a critical delay, indicating oscillatory behavior. Numerical simulations validate the theoretical results and demonstrate improved performance over existing methods in reducing smoking prevalence and associated costs.