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The impact of distributed time delay in a tumor-immune interaction system

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  • Sardar, Mrinmoy
  • Biswas, Santosh
  • Khajanchi, Subhas

Abstract

The impact of continuously distributed delay has been investigated in this paper to describe the interaction among tumor cells, tumor-specific CD8+T cells, helper T cells and immuno-stimulatory cytokine interleukin-2 (IL-2) through a system of coupled nonlinear ordinary differential equations. We analyze the qualitative properties of the model such as positivity of the solutions and the existence of biologically feasible equilibrium points. Next, we discuss the local asymptotic stability for the delayed and non-delayed system. Our model system experiences Hopf bifurcation with respect to the activation rate λ1 of tumor-specific CD8+T cells. The effect of continuously distributed delay involved in immune-activation on the system dynamics of the tumor is demonstrated. Our study reveals that the activation rate of CD8+T cells can prevent the oscillation of tumor-presence equilibria as well as tumor-free equilibria of the system. Then we performed some numerical results and interpret their biological implications to validate our analytical findings.

Suggested Citation

  • Sardar, Mrinmoy & Biswas, Santosh & Khajanchi, Subhas, 2021. "The impact of distributed time delay in a tumor-immune interaction system," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308754
    DOI: 10.1016/j.chaos.2020.110483
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    References listed on IDEAS

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    1. Catherine M. Koebel & William Vermi & Jeremy B. Swann & Nadeen Zerafa & Scott J. Rodig & Lloyd J. Old & Mark J. Smyth & Robert D. Schreiber, 2007. "Adaptive immunity maintains occult cancer in an equilibrium state," Nature, Nature, vol. 450(7171), pages 903-907, December.
    2. Khajanchi, Subhas & Nieto, Juan J., 2019. "Mathematical modeling of tumor-immune competitive system, considering the role of time delay," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 180-205.
    3. Khajanchi, Subhas, 2015. "Bifurcation analysis of a delayed mathematical model for tumor growth," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 264-276.
    4. Khajanchi, Subhas, 2018. "Modeling the dynamics of glioma-immune surveillance," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 108-118.
    5. Khajanchi, Subhas & Ghosh, Dibakar, 2015. "The combined effects of optimal control in cancer remission," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 375-388.
    6. Khajanchi, Subhas, 2017. "Modeling the dynamics of stage-structure predator-prey system with Monod–Haldane type response function," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 122-143.
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    Cited by:

    1. Han, Haoming & Zhang, Jing & Liu, Yan, 2023. "Stability analysis of hybrid high-order nonlinear multiple time-delayed coupled systems via aperiodically intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Khajanchi, Subhas, 2021. "The impact of immunotherapy on a glioma immune interaction model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Sardar, Mrinmoy & Khajanchi, Subhas & Biswas, Santosh & Ghosh, Sumana, 2024. "A mathematical model for tumor-immune competitive system with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    4. Tang, Xiaosong, 2022. "Periodic solutions and spatial patterns induced by mixed delays in a diffusive spruce budworm model with Holling II predation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 420-429.

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