TY - JOUR
T1 - On some dynamical properties of a seven-dimensional cancer model with immunotherapy
AU - Starkov, Konstantin E.
AU - Villegas, Antonio
PY - 2014/2
Y1 - 2014/2
N2 - In this paper we study some features of global behavior of a seven-dimensional tumor growth model under immunotherapy described by Joshi et al. [2009]. We find the upper bounds for ultimate dynamics of all types of cell populations involved in this model. A few lower bounds are found as well. Further, we prove the existence of the bounded positively invariant polytope. Finally, we show that if the parameter modeling the flow of antigen presenting cells is very large then the tumor-free equilibrium point attracts all points in the positive orthant.
AB - In this paper we study some features of global behavior of a seven-dimensional tumor growth model under immunotherapy described by Joshi et al. [2009]. We find the upper bounds for ultimate dynamics of all types of cell populations involved in this model. A few lower bounds are found as well. Further, we prove the existence of the bounded positively invariant polytope. Finally, we show that if the parameter modeling the flow of antigen presenting cells is very large then the tumor-free equilibrium point attracts all points in the positive orthant.
KW - Tumor growth model
KW - compact invariant set
KW - global dynamics
KW - omega-limit set
UR - http://www.scopus.com/inward/record.url?scp=84896304428&partnerID=8YFLogxK
U2 - 10.1142/S0218127414500205
DO - 10.1142/S0218127414500205
M3 - Artículo
SN - 0218-1274
VL - 24
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 2
M1 - 1450020
ER -