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Enrichment and Characterization of the Tumor Immune and Non-immune Microenvironments in Established Subcutaneous Murine Tumors

Enrichment and Characterization of the Tumor Immune and Non-immune Microenvironments in Established Subcutaneous Murine Tumors

Published on: June 7, 2018

Dynamics of the tumor-immune-virus interactions: Convergence conditions to tumor-only or tumor-free equilibrium

Konstantin E Starkov¹, Giovana Andres Garﬁas

¹Instituto Politecnico Nacional-CITEDI,Avenida IPN N 1310, Nueva Tijuana,Tijuana 22510, B.C., Mexico.

Mathematical Biosciences and Engineering : MBE

|January 25, 2019

Abstract:

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.

Keywords:

tumor-free equilibrium point compact invariant set convergence dynamics localization tumor model tumor-only equilibrium point

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