Mathematical modeling of tumor-immune competitive system, considering the role of time delay

Subhas Khajanchi and Juan J. Nieto

Applied Mathematics and Computation, 2019, vol. 340, issue C, 180-205

Abstract: In this paper, we consider a three-dimensional nonlinear delay differential system (tumor cells, cytotoxic-T lymphocytes, T-helper cells) with single interaction delay. We perform linear stability of the equilibria and the existence of Hopf bifurcation in which the discrete time delay is used as a bifurcation parameter. We estimate the length of delay to preserve the stability of period-1 limit cycle. We also investigate the direction, period, and the stability of bifurcated periodic solutions by applying normal form method and center manifold theory. We observe that the discrete time delay plays an important role in stability switching. Numerical simulations are presented to illustrate the rich dynamical behavior of the model with different values for the time delay τ including the existence of periodic oscillations, which demonstrate the phenomena of long-term tumor relapse.

Keywords: Tumor cells; Immune system; Time delay; Hopf bifurcation; Stability analysis (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:340:y:2019:i:c:p:180-205

DOI: 10.1016/j.amc.2018.08.018

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