Dynamics of Chemotherapy Models

Chemotherapy is a drug treatment that uses powerful chemicals to kill fast-growing cancer cells. Cancer cells grow and multiply much more quickly than most cells in the body, and it is necessary to destroy the cancerous cells to prevent the loss of life. Many different chemotherapy drugs are available. Since cancer cells multiply rapidly, the interaction dynamics between the drugs and the cancer cells need to be understood and controlled. Bifurcation analysis is a powerful mathematical tool used to describe the dynamics of any process. Several factors must be considered, and multiple objectives need to be met simultaneously. Bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) calculations were performed on two chemotherapy models. 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 branch points in both models. The branch points were beneficial because they enabled the multiobjective nonlinear model predictive control calculations to converge to the Utopia point, which is the best solution.