Analysis and Control of Pneumonia Transmission Dynamic Models

Abstract

Pneumonia is an acute respiratory disease that poses a major threat to human health and causes millions of deaths every year. It is a global health challenge, and effective strategies must be implemented to minimize the damage. Therefore, the dynamics of pneumonia transmission must be understood, and control methods that are beneficial and cost-effective must be implemented. 

In this work, bifurcation analysis and Mult objective nonlinear model predictive control is performed on two dynamic models involving pneumonia 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 in the first model and a branch point in the second model. The branch and limit points (which cause multiple steady-state solutions from a singular point) are very beneficial because they enable the Mult objective nonlinear model predictive control calculations to converge to the Utopia point (the best possible solution) in both models.