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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

5 Scopus Citations
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  • Zonghong Feng
  • Xinxing Wu
  • Luo Yang

Related Research Unit(s)


Original languageEnglish
Article number1950009
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number1
Publication statusPublished - Jan 2019


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 γ 0 is predicted of the treatment parameter γ. We can see Neimark-Sacker bifurcation of the system when γ = γ0 , and the chaotic behavior for tumor cells ends and the system becomes locally asymptotically stable when γ > γ0 .

Research Area(s)

  • chaos, local and global asymptotical stability, Lotka-Volterra equation, Neimark-Sacker bifurcation, Tumor-immune system