Stability and bifurcation analysis of a mathematical model for tumor-immune interaction with piecewise constant arguments of delay

Gurcan F., Kartal S., ÖZTÜRK I., Bozkurt F.

CHAOS SOLITONS & FRACTALS, vol.68, pp.169-179, 2014 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 68
  • Publication Date: 2014
  • Doi Number: 10.1016/j.chaos.2014.08.001
  • Journal Name: CHAOS SOLITONS & FRACTALS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.169-179
  • Erciyes University Affiliated: Yes

Abstract

In this paper, we propose and analyze a Lotka–Volterra competition like model which consists
of system of differential equations with piecewise constant arguments of delay to
study of interaction between tumor cells and Cytotoxic T lymphocytes (CTLs). In order to
get local and global behaviors of the system, we use Schur–Cohn criterion and constructed
a Lyapunov function. Some algebraic conditions which satisfy local and global stability of
the system are obtained. In addition, we investigate the possible bifurcation types for the
system and observe that the system may undergo Neimark–Sacker bifurcation. Moreover,
it is predicted a threshold value above which there is uncontrollable tumor growth, and
below periodic solutions that leading to tumor dormant state occur.