TY - JOUR
T1 - A Cancer Model for the Angiogenic Switch and Immunotherapy
T2 - Tumor Eradication in Analysis of Ultimate Dynamics
AU - Starkov, Konstantin E.
N1 - Publisher Copyright:
© 2020 World Scientific Publishing Company.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - In this paper, we study ultimate dynamics and derive tumor eradication conditions for the angiogenic switch model developed by Viger et al. This model describes the behavior and interactions between host (x); effector (y); tumor (z); endothelial (w) cell populations. Our approach is based on using the localization method of compact invariant sets and the LaSalle theorem. The ultimate upper bound for each cell population and ultimate lower bound for the effector cell population are found. These bounds describe a location of all bounded dynamics. We construct the domain bounded in x-and z-variables which contains the attracting set of the system. Further, we derive conditions imposed on the model parameters for the location of omega-limit sets in the plane w = 0 (the case of a localized tumor). Next, we present conditions imposed on the model and treatment parameters for the location of omega-limit sets in the plane z = 0 (the case of global tumor eradication). Various types of dynamics including the chaotic attractor and convergence dynamics are described. Numerical simulation illustrating tumor eradication theorems is fulfilled as well.
AB - In this paper, we study ultimate dynamics and derive tumor eradication conditions for the angiogenic switch model developed by Viger et al. This model describes the behavior and interactions between host (x); effector (y); tumor (z); endothelial (w) cell populations. Our approach is based on using the localization method of compact invariant sets and the LaSalle theorem. The ultimate upper bound for each cell population and ultimate lower bound for the effector cell population are found. These bounds describe a location of all bounded dynamics. We construct the domain bounded in x-and z-variables which contains the attracting set of the system. Further, we derive conditions imposed on the model parameters for the location of omega-limit sets in the plane w = 0 (the case of a localized tumor). Next, we present conditions imposed on the model and treatment parameters for the location of omega-limit sets in the plane z = 0 (the case of global tumor eradication). Various types of dynamics including the chaotic attractor and convergence dynamics are described. Numerical simulation illustrating tumor eradication theorems is fulfilled as well.
KW - Nonlinear system
KW - angiogenic switch
KW - chaotic attractor
KW - compact invariant set
KW - convergence dynamics
KW - immunotherapy
KW - localization
KW - tumor
UR - http://www.scopus.com/inward/record.url?scp=85090823751&partnerID=8YFLogxK
U2 - 10.1142/S0218127420501503
DO - 10.1142/S0218127420501503
M3 - Artículo
AN - SCOPUS:85090823751
SN - 0218-1274
VL - 30
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 10
M1 - 2050150
ER -