Ph.D. SNI III
Tumor clearance problem for dynamical cancer models with immunotherapy and global stability analysis
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.
Dr. Starkov has published more than 180 research articles in the field of nonlinear dynamics and control theory, 70 of them on index journals such as JCR, ISI, SCOPUS and CONACyT. He is currently developing the CONACyT project “Analysis of systems with complex dynamics in mathematical medicine and physics via the Localization of Compact Invariant Sets method”.
Recently, his investigation has been focused in the analysis of mathematical models of biological systems, particularly those that described tumor evolution with or without treatment such as chemotherapy or immunotherapy.
Dr. Konstantin Starkov has directed several postgraduate theses and is a member of the National System of Researchers at level III (SNI III).