Ultimate Dynamics of a Cancer Modelwith Angiogenic Switch and Combined Therapy

The properties of the ultimate dynamics of one 5D model of cancer tumor growth in the angiogenesis phase with additional modeling of chemotherapy and immunotherapy are considered. The ultimate upper bounds for all cell populations, as well as the lower bound for the immune cell population, are found. The conditions for global asymptotic eradication of the tumor are obtained in two situations: when only chemotherapy is used and when a combination of chemotherapy and immunotherapy is used. The study is based on the method of localization of compact invariant sets. The article also describes the boundary and internal equilibrium points and presents the results of numerical simulation illustrating the results obtained analytically.