Analysis and Control of Oncolytic Virotherapy Dynamic Models

Oncolytic virotherapy is a cancer treatment that uses viruses to selectively infect and destroy cancer cells while leaving healthy cells unharmed. These viruses, known as oncolytic viruses, replicate within tumor cells, causing them to lyse (burst) and release new viral particles that can infect surrounding cancer cells. This process also releases tumor antigens, which can trigger an immune response against the cancer. The dynamics of Oncolytic virotherapy are highly nonlinear. 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 three oncolytic dynamic 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 the existence of a Hopf bifurcation point in one of the models and branch points in all three models. The Hopf bifurcation point was eliminated using an activation factor that involves the tanh function. 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 the models. It is proven (with computational validation) that the branch points were caused because of the existence of two distinct separable functions in one of the equations in each dynamic model. A theorem was developed to demonstrate this fact for any dynamic model.