TY - JOUR
T1 - Global stability and tumor clearance conditions for a cancer chemotherapy system
AU - Valle, Paul A.
AU - Starkov, Konstantin E.
AU - Coria, Luis N.
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/11/1
Y1 - 2016/11/1
N2 - In this paper we study the global dynamics of a cancer chemotherapy system presented by de Pillis et al. (2007). This mathematical model describes the interaction between tumor cells, effector-immune cells, circulating lymphocytes and chemotherapy treatment. By applying the localization method of compact invariant sets, we find lower and upper bounds for these three cells populations. Further, we define a bounded domain in R+,04 where all compact invariant sets of the system are located and provide conditions under which this domain is positively invariant. We apply LaSalle's invariance principle and one result concerning two-dimensional competitive systems in order to derive sufficient conditions for tumor clearance and global asymptotic stability of the tumor-free equilibrium point. These conditions are computed by using bounds of the localization domain and they are given in terms of the chemotherapy treatment. Finally, we perform numerical simulations in order to illustrate our results.
AB - In this paper we study the global dynamics of a cancer chemotherapy system presented by de Pillis et al. (2007). This mathematical model describes the interaction between tumor cells, effector-immune cells, circulating lymphocytes and chemotherapy treatment. By applying the localization method of compact invariant sets, we find lower and upper bounds for these three cells populations. Further, we define a bounded domain in R+,04 where all compact invariant sets of the system are located and provide conditions under which this domain is positively invariant. We apply LaSalle's invariance principle and one result concerning two-dimensional competitive systems in order to derive sufficient conditions for tumor clearance and global asymptotic stability of the tumor-free equilibrium point. These conditions are computed by using bounds of the localization domain and they are given in terms of the chemotherapy treatment. Finally, we perform numerical simulations in order to illustrate our results.
KW - Chemotherapy
KW - Compact invariant set
KW - Global stability
KW - Tumor clearance
UR - http://www.scopus.com/inward/record.url?scp=84966440358&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2016.04.025
DO - 10.1016/j.cnsns.2016.04.025
M3 - Artículo
SN - 1007-5704
VL - 40
SP - 206
EP - 215
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
ER -