Finding the optimal mix of smoking initiation and cessation interventions to reduce smoking prevalence.

There are more than one billion smokers globally according to the World Health Organization (WHO) report in 2017. Every year tobacco use causes nearly 6 million deaths worldwide. To deal with the smoking epidemic, society needs to invest resources efficiently. In this paper we introduce an optimal control model to determine the optimal mix of smoking initiation and cessation interventions to reduce smoking. We construct the model to reach a smoking prevalence target within a specific time horizon while minimizing cost. Our performance measure captures the cost of policy implementation over time, adjusting for inflation and social discounting. The analytical solutions to the model are presented in forms of ordinary differential equations (ODE). We then conduct several numerical simulations using data from the National Health Interview Survey (NHIS) and empirical studies. We first present analytical solutions for our model to solve for the optimal mix of smoking interventions. Then we simulate a public health policy to achieve 5% smoking prevalence in the US by 2030 using different combinations of real-life interventions. We examine the optimal trajectories, allocative efficiency and annual total cost of smoking cessation and initiation interventions. We find consistent results across all simulations. Our specific example reveals that the most efficient way to reach stated goal is by targeting cessation interventions first, and then gradually shifting resources to initiation interventions over time. While our numerical results are specific to the intervention we selected, our framework can be easily expanded to consider other potential interventions. We discuss the implications of our approach for the formulation of dynamic public health policies.