Analysis and Control of a Suicide Dynamics Model

Abstract

Suicide has become a major cause of human death during the last few decades. It is important to understand the dynamics of suicide and identify effective prevention strategies. In this work, bifurcation analysis and multi objective nonlinear model predictive control are performed on a suicide dynamics model. Bifurcation analysis is a powerful mathematical tool used to deal with the nonlinear dynamics of any process. Several factors must be considered, and multiple objectives must be met simultaneously. The MATLAB program MATCONT was used to perform the bifurcation analysis. The MNLMPC calculations were performed using the optimization language PYOMO in conjunction with the state-of-the-art global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the existence of limit and branch points. The MNLMC converged on the Utopia solution (best possible). The limit and branch points (which cause multiple steady-state solutions from a singular point) are very beneficial because they enable the Multi objective nonlinear model predictive control calculations to converge to the Utopia point (the best possible solution) in the model. It is proved (with computational validation) that the branch points were caused because of the existence of two distinct separable functions in one of the equations in the dynamic model. A theorem was developed to demonstrate this fact for any dynamic model.