TY - JOUR
T1 - Dynamic Analysis of the Melanoma Model
T2 - From Cancer Persistence to Its Eradication
AU - Starkov, Konstantin E.
AU - Jimenez Beristain, Laura
N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - In this paper, we study the global dynamics of the five-dimensional melanoma model developed by Kronik et al. This model describes interactions of tumor cells with cytotoxic T cells and respective cytokines under cellular immunotherapy. We get the ultimate upper and lower bounds for variables of this model, provide formulas for equilibrium points and present local asymptotic stability/hyperbolic instability conditions. Next, we prove the existence of the attracting set. Based on these results we come to global asymptotic melanoma eradication conditions via global stability analysis. Finally, we provide bounds for a locus of the melanoma persistence equilibrium point, study the case of melanoma persistence and describe conditions under which we observe global attractivity to the unique melanoma persistence equilibrium point.
AB - In this paper, we study the global dynamics of the five-dimensional melanoma model developed by Kronik et al. This model describes interactions of tumor cells with cytotoxic T cells and respective cytokines under cellular immunotherapy. We get the ultimate upper and lower bounds for variables of this model, provide formulas for equilibrium points and present local asymptotic stability/hyperbolic instability conditions. Next, we prove the existence of the attracting set. Based on these results we come to global asymptotic melanoma eradication conditions via global stability analysis. Finally, we provide bounds for a locus of the melanoma persistence equilibrium point, study the case of melanoma persistence and describe conditions under which we observe global attractivity to the unique melanoma persistence equilibrium point.
KW - Melanoma
KW - asymptotically autonomous system
KW - attracting set
KW - cooperative system
KW - cubic polynomial
KW - localization
KW - ordinary differential equations
UR - http://www.scopus.com/inward/record.url?scp=85031305543&partnerID=8YFLogxK
U2 - 10.1142/S0218127417501516
DO - 10.1142/S0218127417501516
M3 - Artículo
SN - 0218-1274
VL - 27
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 10
M1 - 1750151
ER -