TY - JOUR
T1 - Ultimate dynamics of the Kirschner–Panetta model
T2 - Tumor eradication and related problems
AU - Starkov, Konstantin E.
AU - Krishchenko, Alexander P.
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/10/17
Y1 - 2017/10/17
N2 - In this paper 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. 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.
AB - In this paper 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. 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.
KW - Compact invariant set
KW - Global stability
KW - Kirschner–Panetta tumor model
KW - Ultimate dynamics
UR - http://www.scopus.com/inward/record.url?scp=85028549161&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2017.08.048
DO - 10.1016/j.physleta.2017.08.048
M3 - Artículo
SN - 0375-9601
VL - 381
SP - 3409
EP - 3416
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 39
ER -