Optimal Control Analysis of Smoking Dynamics Model With Cost-Effective Strategies

In this work, we formulate and examine a mathematical model of cigarette smoking dynamics with optimal control theory. Firstly, we demonstrated that the solution of the model is a bounded region and nonnegative, which demonstrated that the model is well posed both mathematically and epidemiologically. Besides, we computed the cigarette smoking–free equilibrium and the endemic equilibrium points of the model. Then, the basic reproduction number was computed using the next-generation matrix, and the stability analysis of the equilibrium points was examined. The analysis shows that the cigarette smoking–free equilibrium point is stable over time if the basic reproduction number is less than one; otherwise, the model will reach the endemic equilibrium point. Also, a sensitivity analysis was conducted to assess the impact of key factors on cigarette smoking dynamics. Moreover, we extended the cigarette smoking dynamics model to an optimal control model via two controls: educating individuals and treating addicted smokers. Then, the existence of optimal controls is proven, and using Pontryagin’s minimum principle, the essential conditions of the optimal control model are examined. Also, if the resource is limited, a cost-effectiveness analysis is considered to identify the least costly strategies. Finally, the numerical simulation of optimality systems concluded that educating individuals to keep them away from the smoking addiction population is the most effective strategy to lessen the addiction of cigarette smoking.