Analysis and Control of an Influenza Transmission Model

Abstract

Influenza is a global health challenge, and effective strategies must be implemented to minimize the damage. The dynamics of influenza transmission must be understood, and control methods that are beneficial and cost-effective must be implemented. In this work, bifurcation analysis and multiobjective nonlinear model predictive control are performed on a dynamic model involving influenza. 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 branchpoints in the influenza model for two different bifurcation parameters. The branch points (which cause multiple steady-state solutions from a singular point) are very beneficial because they enable the Multiobjective nonlinear model predictive control calculations to converge to the Utopia point (the best possible solution) in both models.