Analysis and Control of Measles Dynamic Models

Abstract

Lakshmi N Sridhar

Measles is a communicable and deadly viral disease that can be contracted on contact with an infected individual or via airborne propagules Effective and efficient strategies must be implemented to minimize the damage caused by measles , and to do this, we must understand the dynamics of the measles transmission and implement control methods that are beneficial and cost-effective. In this work, bifurcation analysis and multiobjective nonlinear model predictive control is performed on two dynamic models involving measles transmission. 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 branch and limit points and the MNLMPC calculations converged to the Utopia solution in both the models. The branch and limit 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.

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