Stability of a Mathematical Model with Piecewise Constant Arguments for Tumor-Immune Interaction Under Drug Therapy

Author:

Feng Zonghong1,Wu Xinxing12ORCID,Yang Luo1

Affiliation:

1. School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500, P. R. China

2. Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China

Abstract

This paper studies a mathematical model for the interaction between tumor cells and Cytotoxic T lymphocytes (CTLs) under drug therapy. We obtain some sufficient conditions for the local and global asymptotical stabilities of the system by using Schur–Cohn criterion and the theory of Lyapunov function. In addition, it is known that the system without any treatment may undergo Neimark–Sacker bifurcation, and there may exist a chaotic region of values of tumor growth rate where the system exhibits chaotic behavior. So it is important to narrow the chaotic region. This may be done by increasing the intensity of the treatment to some extent. Moreover, for a fixed value of tumor growth rate in the chaotic region, a threshold value [Formula: see text] is predicted of the treatment parameter [Formula: see text]. We can see Neimark–Sacker bifurcation of the system when [Formula: see text], and the chaotic behavior for tumor cells ends and the system becomes locally asymptotically stable when [Formula: see text].

Funder

the National Natural Science Foundation of China

Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and its Applications

Youth Science and Technology Innovation Team of Southwest Petroleum University for Nonlinear Systems

the program of young scholars development fund of SWPU

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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