Mathematical modeling, analysis and simulation of the spread of smoking in the United States using Optimal Control

Abstract

In this work, we consider a mathematical study for assessing the dynamics of smoking and its public health impact in a community. Specifically, a compartmental model for smoking as an infectious disease is considered using a coupled system of ordinary differential equations. The model describes the spread of smoking in the population through six compartments corresponding to different subpopulations. We introduce into this system of coupled equations, the use of public education campaigns aimed at elucidating the health impacts of smoking. Specifically, we introduce a variable corresponding to education as a control which causes a change in behavior resulting in two susceptible classes. We perform stability analysis, derive the basic reproduction number and use optimal control theory to characterize education as a control  in order to achieve the goal of minimizing the exposed and infected populations, while maximizing the susceptible populations and minimizing the cost of education. Our numerical results show that education can be used as a regulatory mechanism to mitigate the spread of smoking. We hope that the model created can help provide insights to achieve maximum reduction in smoking prevalence while optimizing cost-effectiveness that will then allow policymakers to determine the optimal allocation of financial resources for such campaigns.