TY - JOUR
T1 - Global dynamics of the Kirschner-Panetta model for the tumor immunotherapy
AU - Starkov, Konstantin E.
AU - Coria, Luis N.
PY - 2013/6
Y1 - 2013/6
N2 - In this paper we examine the global dynamics of the Kirschner-Panetta model describing the tumor immunotherapy. We give upper and lower ultimate bounds for densities of cell populations involved in this model. We demonstrate for this dynamics that there is a positively invariant polytope in the positive orthant. We present sufficient conditions on model parameters and treatment parameters under which all trajectories in the positive orthant tend to the tumor-free equilibrium point. We compare our results with Kirschner-Tsygvintsev results and concern biological implications of our assertions.
AB - In this paper we examine the global dynamics of the Kirschner-Panetta model describing the tumor immunotherapy. We give upper and lower ultimate bounds for densities of cell populations involved in this model. We demonstrate for this dynamics that there is a positively invariant polytope in the positive orthant. We present sufficient conditions on model parameters and treatment parameters under which all trajectories in the positive orthant tend to the tumor-free equilibrium point. We compare our results with Kirschner-Tsygvintsev results and concern biological implications of our assertions.
KW - Attraction
KW - Compact invariant set
KW - Immunotherapy
KW - Non-spatial cancer tumor model
KW - Positively invariant domain
KW - Tumor-free equilibrium point
UR - http://www.scopus.com/inward/record.url?scp=84872012121&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2012.10.006
DO - 10.1016/j.nonrwa.2012.10.006
M3 - Artículo
SN - 1468-1218
VL - 14
SP - 1425
EP - 1433
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
IS - 3
ER -