Tumor clearance problem for dynamical cancer models with immunotherapy and global stability analysis
Sala de Juntas E.T.S.I.Industriales
Lunes 23 de Octubre del 2017
Grupo de Oncología Matemática

Konstantin Starkov, profesor del Instituto Politécnico Nacional de Tijuana, Mexico

Lunes, 23 de octubre, 11:30h. Sala Juntas E.T.S.I.Industriales

In this talk we examine the tumor clearance problem in dynamical cancer models with immunotherapy with help of global stability analysis. As an example, we consider the ultimate dynamics of the Kirschner-Panetta model which was created for studying the immune response to tumors under special types of immunotherapy. Our approach  is based on using localization method of compact invariant sets and some results concerning positively invariant domains. New ultimate upper bounds for compact invariant sets of this model are given, as well as sufficient conditions for the existence of a positively invariant polytope. We establish three types of conditions for the nonexistence of compact invariant sets in the domain of the tumor-cell population. Our main results are two types of conditions for global tumor elimination depending on the ratio between the  proliferation rate of the immune cells and their mortality rate. These conditions are described in terms of simple algebraic inequalities imposed on model parameters and treatment parameters. Our theoretical studies of ultimate dynamics are complemented by numerical simulation results.