Exploring the Effectiveness of an Optimal Control Model for Marijuana Consumption

Abstract

The primary aims of this research is to reduce marijuana use within the general population, addressing its harmful effects and its status as an illegal substance that poses ongoing risks to public health in developing countries. To tackle this issue, we have developed a mathematical model that translates real-world marijuana consumption into mathematical terms using first-order nonlinear ordinary differential equations. A key objective of this study is to modify the NERAPH "Non-smokers, Experimental-smokers, Recreational-smokers, Addicts, Hospitalized individuals, and Prisoners" model by incorporating optimal control measures. This modified model is designed to estimate the initial rate of marijuana transmission within these groups. To implement effective control strategies, we conduct sensitivity analyses to identify the most impactful parameters. These findings enable us to recommend targeted control variables for the most sensitive parameters, leading to the development of an optimal control model aimed at reducing marijuana consumption as efficiently as possible. Finally, we compare the outcomes of the basic and optimal control models through numerical results to evaluate the effectiveness of each approach. This comparison provides a clear measure of how optimal control techniques enhance the model's ability to reduce marijuana use more effectively than the existing basic model.