Analysis and Control of Cigarette Smoking and Alcoholism Models

Cigarettes and alcohol are detrimental to human health and are among the leading causes of death today. Both cigarette smoking and alcoholism are addictive and need to be understood and controlled effectively. This paper presents a mathematical framework involving bifurcation analysis and multiobjective nonlinear model predictive control for two models, the first involving cigarette smoking and the second involving alcoholism. Bifurcation analysis is a powerful mathematical tool used to address the nonlinear dynamics of any process. Several factors must be taken into account, and multiple objectives must be achieved simultaneously. The MATLAB program MATCONT was utilized to conduct the bifurcation analysis. The MNLMPC calculations were performed using the optimization language PYOMO in conjunction with the advanced global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the presence of limit and branch points in the two models. These limit and branch points are advantageous as they allow the multiobjective nonlinear model predictive control calculations to converge to the Utopia point, which represents the most beneficial solution. The combination of bifurcation analysis and multiobjective nonlinear model predictive control for models involving cigarette smoking and alcoholism is the main contribution of this paper.