Stability Analysis and Optimal Control Strategy of Smoking Behavior Cessation Mathematical Model

Cigarettes are one of the tobacco products that contain many chemicals that cause various types of diseases. In addition, cigarettes can also cause addiction and dependence for smokers. The purpose of this work is to analyze the equilibrium point of the mathematical model of the cessation of smoking behavior and the application of optimal control in the form of education (u₁) and candy treatment (u₂). Based on the analysis of the uncontrolled model, two equilibrium points were obtained, namely the non-endemic equilibrium point and the endemic equilibrium point. The local stability of the equilibrium point and the existence of the endemic equilibrium point depend on the basic reproduction number (R₀). The non-endemic equilibrium point is asymptotically stable if fulfills two conditions, there are _u(^-nM_2u++d+^0u₎ < 1 and R₀ < 1, while the endemic equilibrium point is asymptotically stable if R₀ > 1. In this paper, parameter sensitivity analysis will also be carried out to determine the most influential parameters on the model. From the results of sensitivity analysis, the most influential parameters are parameters and . Furthermore, the control variable problem in the model is determined using the Pontryagin Maximum Principle. The results of numerical simulations show that giving control in the form of education and candy treatment simultaneously provides effective results to minimize the individual population of smoking with minimal costs.