Dynamics of Chemoimmunotherapy Models

Chemoimmunotherapy is chemotherapy combined with immunotherapy. Chemotherapy uses different drugs to kill or slow the growth of cancer cells; immunotherapy uses treatments to stimulate or restore the ability of the immune system to fight cancer. Both chemotherapy and immunotherapy are highly nonlinear processes that several factors affect. The two treatments together would be very highly nonlinear. It is necessary to understand and control this combined treatment. 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. Bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) calculations are performed on two chemoimmunotherapy 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 and limit points in the two models. The branch and limit points were beneficial because they enabled the multiobjective nonlinear model predictive control calculations to converge to the Utopia point in both the problems, which is the best solution