TY - JOUR
T1 - Dynamics of the tumor-immune-virus interactions
T2 - Convergence conditions to tumor-only or tumor-free equilibrium points
AU - Starkov, Konstantin E.
AU - Garfias, Giovana Andres
N1 - Publisher Copyright:
© 2019 Laser and Optoelectronics Progress.All rights reserved.
PY - 2019
Y1 - 2019
N2 - In the present paper convergence dynamics of one tumor-immune-virus model is examined with help of the localization method of compact invariant sets and the LaSalle theorem. This model was elaborated by Eftimie et al. in 2016. It is shown that this model possesses the Lagrange stability property of positive half-trajectories and ultimate upper bounds for compact invariant sets are obtained. Conditions of convergence dynamics are found. It is explored the case when any trajectory is attracted to one of tumor-only equilibrium points or tumor-free equilibrium points. Further, it is studied ultimate dynamics of one modification of Eftimie et al. model in which the immune cells injection is included. This modified system possesses the global tumor cells eradication property if the influx rate of immune cells exceeds some value which is estimated. Main results are expressed in terms simple algebraic inequalities imposed on model and treatment parameters.
AB - In the present paper convergence dynamics of one tumor-immune-virus model is examined with help of the localization method of compact invariant sets and the LaSalle theorem. This model was elaborated by Eftimie et al. in 2016. It is shown that this model possesses the Lagrange stability property of positive half-trajectories and ultimate upper bounds for compact invariant sets are obtained. Conditions of convergence dynamics are found. It is explored the case when any trajectory is attracted to one of tumor-only equilibrium points or tumor-free equilibrium points. Further, it is studied ultimate dynamics of one modification of Eftimie et al. model in which the immune cells injection is included. This modified system possesses the global tumor cells eradication property if the influx rate of immune cells exceeds some value which is estimated. Main results are expressed in terms simple algebraic inequalities imposed on model and treatment parameters.
KW - compact invariant set
KW - convergence dynamics
KW - localization
KW - tumor model
KW - tumor-free equilibrium point
KW - tumor-only equilibrium point
UR - http://www.scopus.com/inward/record.url?scp=85058820796&partnerID=8YFLogxK
U2 - 10.3934/mbe.2019020
DO - 10.3934/mbe.2019020
M3 - Artículo
C2 - 30674126
SN - 1547-1063
VL - 16
SP - 421
EP - 437
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
IS - 1
ER -